%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : COM187^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:41:53 AM UTC 2026
% Result : Theorem 2.93s 1.63s
% Output : Refutation 2.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COM187^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n023.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 04:17:19 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.43 ---- Original DTF file ---
% 0.16/0.43 thf(spec,logic,$$dhol).
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 % File : COM187^1 : TPTP v9.2.1. Released v7.0.0.
% 0.16/0.43 % Domain : Computing Theory
% 0.16/0.43 % Problem : Grammars and languages 549
% 0.16/0.43 % Version : [Bla16] axioms : Especial.
% 0.16/0.43 % English :
% 0.16/0.43
% 0.16/0.43 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.16/0.43 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.16/0.43 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.16/0.43 % Source : [Bla16]
% 0.16/0.43 % Names : gram_lang__549.p [Bla16]
% 0.16/0.43
% 0.16/0.43 % Status : Theorem
% 0.16/0.43 % Rating : 0.33 v9.1.0, 0.00 v8.1.0, 0.25 v7.5.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.16/0.43 % Syntax : Number of formulae : 310 ( 109 unt; 45 typ; 0 def)
% 0.16/0.43 % Number of atoms : 723 ( 325 equ; 0 cnn)
% 0.16/0.43 % Maximal formula atoms : 7 ( 2 avg)
% 0.16/0.43 % Number of connectives : 4872 ( 79 ~; 12 |; 82 &;4348 @)
% 0.16/0.43 % ( 0 <=>; 351 =>; 0 <=; 0 <~>)
% 0.16/0.43 % Maximal formula depth : 21 ( 8 avg)
% 0.16/0.43 % Number of types : 4 ( 3 usr)
% 0.16/0.43 % Number of type conns : 286 ( 286 >; 0 *; 0 +; 0 <<)
% 0.16/0.43 % Number of symbols : 45 ( 42 usr; 5 con; 0-7 aty)
% 0.16/0.43 % Number of variables : 1157 ( 36 ^;1032 !; 57 ?;1157 :)
% 0.16/0.43 % ( 32 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.43 % SPC : TH1_THM_EQU_NAR
% 0.16/0.43
% 0.16/0.43 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.16/0.43 % 2016-07-13 14:43:13.600
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 %----Could-be-implicit typings (7)
% 0.16/0.43 thf(ty_t_Product__Type_Oprod,type,
% 0.16/0.43 product_prod: $tType > $tType > $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_Sum__Type_Osum,type,
% 0.16/0.43 sum_sum: $tType > $tType > $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_DTree_Odtree,type,
% 0.16/0.43 dtree: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_Set_Oset,type,
% 0.16/0.43 set: $tType > $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_DTree_OT,type,
% 0.16/0.43 t: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_DTree_ON,type,
% 0.16/0.43 n: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_itself,type,
% 0.16/0.43 itself: $tType > $tType ).
% 0.16/0.43
% 0.16/0.43 %----Explicit typings (38)
% 0.16/0.43 thf(sy_cl_Finite__Set_Ofinite,type,
% 0.16/0.43 finite_finite:
% 0.16/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_DTree_ONode,type,
% 0.16/0.43 node: n > ( set @ ( sum_sum @ t @ dtree ) ) > dtree ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_DTree_Ocont,type,
% 0.16/0.43 cont: dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_DTree_Odtree_Oroot,type,
% 0.16/0.43 root: dtree > n ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_DTree_Ounfold,type,
% 0.16/0.43 unfold:
% 0.16/0.43 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ A ) ) ) > A > dtree ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Finite__Set_Ofinite,type,
% 0.16/0.43 finite_finite2:
% 0.16/0.43 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Fun_Ocomp,type,
% 0.16/0.43 comp:
% 0.16/0.43 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Fun_Oid,type,
% 0.16/0.43 id:
% 0.16/0.43 !>[A: $tType] : ( A > A ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Fun_Oinj__on,type,
% 0.16/0.43 inj_on:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OP,type,
% 0.16/0.43 gram_L1451583632elle_P: set @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OS,type,
% 0.16/0.43 gram_L1451583635elle_S: n > ( set @ ( sum_sum @ t @ n ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr,type,
% 0.16/0.43 gram_L1231612515_deftr: n > dtree ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst,type,
% 0.16/0.43 gram_L1004374585hsubst: dtree > dtree > dtree ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c,type,
% 0.16/0.43 gram_L1905609002ubst_c: dtree > dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r,type,
% 0.16/0.43 gram_L1905609017ubst_r: dtree > n ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr,type,
% 0.16/0.43 gram_L1333338417e_inFr: ( set @ n ) > dtree > t > $o ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2,type,
% 0.16/0.43 gram_L805317441_inFr2: ( set @ n ) > dtree > t > $o ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFrr,type,
% 0.16/0.43 gram_L805317505_inFrr: ( set @ n ) > dtree > t > $o ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr,type,
% 0.16/0.43 gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr,type,
% 0.16/0.43 gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr2,type,
% 0.16/0.43 gram_L1283001940subtr2: ( set @ n ) > dtree > dtree > $o ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OsubtrOf,type,
% 0.16/0.43 gram_L1614515765ubtrOf: dtree > n > dtree ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf,type,
% 0.16/0.43 gram_L864798063lle_wf: dtree > $o ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_If,type,
% 0.16/0.43 if:
% 0.16/0.43 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.16/0.43 bot_bot:
% 0.16/0.43 !>[A: $tType] : A ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Product__Type_OPair,type,
% 0.16/0.43 product_Pair:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Pure_Otype,type,
% 0.16/0.43 type:
% 0.16/0.43 !>[A: $tType] : ( itself @ A ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Set_OCollect,type,
% 0.16/0.43 collect:
% 0.16/0.43 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Set_Oimage,type,
% 0.16/0.43 image:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Set_Oinsert,type,
% 0.16/0.43 insert:
% 0.16/0.43 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Set_Ovimage,type,
% 0.16/0.43 vimage:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Sum__Type_OInl,type,
% 0.16/0.43 sum_Inl:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Sum__Type_OInr,type,
% 0.16/0.43 sum_Inr:
% 0.16/0.43 !>[B: $tType,A: $tType] : ( B > ( sum_sum @ A @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Sum__Type_Omap__sum,type,
% 0.16/0.43 sum_map_sum:
% 0.16/0.43 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C ) > ( B > D ) > ( sum_sum @ A @ B ) > ( sum_sum @ C @ D ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum,type,
% 0.16/0.43 sum_rec_sum:
% 0.16/0.43 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_member,type,
% 0.16/0.43 member:
% 0.16/0.43 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_tr,type,
% 0.16/0.43 tr: dtree ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_tr0,type,
% 0.16/0.43 tr0: dtree ).
% 0.16/0.43
% 0.16/0.43 %----Relevant facts (256)
% 0.16/0.43 thf(fact_0__092_060open_062cont_A_Ilocal_Ohsubst_Atr_J_A_061_A_Iid_A_092_060oplus_062_Alocal_Ohsubst_J_A_096_Acont_Atr_092_060close_062,axiom,
% 0.16/0.43 ( ( cont @ ( gram_L1004374585hsubst @ tr0 @ tr ) )
% 0.16/0.43 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ tr0 ) ) @ ( cont @ tr ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % \<open>cont (local.hsubst tr) = (id \<oplus> local.hsubst) ` cont tr\<close>
% 0.16/0.43 thf(fact_1_assms,axiom,
% 0.16/0.43 ( ( root @ tr )
% 0.16/0.43 != ( root @ tr0 ) ) ).
% 0.16/0.43
% 0.16/0.43 % assms
% 0.16/0.43 thf(fact_2_Inl__m__oplus,axiom,
% 0.16/0.43 ! [B: $tType,C: $tType,A: $tType,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.16/0.43 ( ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ ( image @ ( sum_sum @ A @ C ) @ ( sum_sum @ A @ B ) @ ( sum_map_sum @ A @ A @ C @ B @ ( id @ A ) @ F ) @ Tns ) )
% 0.16/0.43 = ( vimage @ A @ ( sum_sum @ A @ C ) @ ( sum_Inl @ A @ C ) @ Tns ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inl_m_oplus
% 0.16/0.43 thf(fact_3_Inl__oplus__iff,axiom,
% 0.16/0.43 ! [B: $tType,C: $tType,A: $tType,Tr: A,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.16/0.43 ( ( member @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B @ Tr ) @ ( image @ ( sum_sum @ A @ C ) @ ( sum_sum @ A @ B ) @ ( sum_map_sum @ A @ A @ C @ B @ ( id @ A ) @ F ) @ Tns ) )
% 0.16/0.43 = ( member @ ( sum_sum @ A @ C ) @ ( sum_Inl @ A @ C @ Tr ) @ Tns ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inl_oplus_iff
% 0.16/0.43 thf(fact_4_vimage__id,axiom,
% 0.16/0.43 ! [A: $tType] :
% 0.16/0.43 ( ( vimage @ A @ A @ ( id @ A ) )
% 0.16/0.43 = ( id @ ( set @ A ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % vimage_id
% 0.16/0.43 thf(fact_5_image__id,axiom,
% 0.16/0.43 ! [A: $tType] :
% 0.16/0.43 ( ( image @ A @ A @ ( id @ A ) )
% 0.16/0.43 = ( id @ ( set @ A ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % image_id
% 0.16/0.43 thf(fact_6_Inl__oplus__elim,axiom,
% 0.16/0.43 ! [B: $tType,C: $tType,A: $tType,Tr: A,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.16/0.43 ( ( member @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B @ Tr ) @ ( image @ ( sum_sum @ A @ C ) @ ( sum_sum @ A @ B ) @ ( sum_map_sum @ A @ A @ C @ B @ ( id @ A ) @ F ) @ Tns ) )
% 0.16/0.43 => ( member @ ( sum_sum @ A @ C ) @ ( sum_Inl @ A @ C @ Tr ) @ Tns ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inl_oplus_elim
% 0.16/0.43 thf(fact_7_cont__hsubst__eq,axiom,
% 0.16/0.43 ! [Tr: dtree] :
% 0.16/0.43 ( ( ( root @ Tr )
% 0.16/0.43 = ( root @ tr0 ) )
% 0.16/0.43 => ( ( cont @ ( gram_L1004374585hsubst @ tr0 @ Tr ) )
% 0.16/0.43 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ tr0 ) ) @ ( cont @ tr0 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % cont_hsubst_eq
% 0.16/0.43 thf(fact_8_cont__hsubst__neq,axiom,
% 0.16/0.43 ! [Tr: dtree] :
% 0.16/0.43 ( ( ( root @ Tr )
% 0.16/0.43 != ( root @ tr0 ) )
% 0.16/0.43 => ( ( cont @ ( gram_L1004374585hsubst @ tr0 @ Tr ) )
% 0.16/0.43 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ tr0 ) ) @ ( cont @ Tr ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % cont_hsubst_neq
% 0.16/0.43 thf(fact_9_sum_Oinject_I1_J,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,X1: A,Y1: A] :
% 0.16/0.43 ( ( ( sum_Inl @ A @ B @ X1 )
% 0.16/0.43 = ( sum_Inl @ A @ B @ Y1 ) )
% 0.16/0.43 = ( X1 = Y1 ) ) ).
% 0.16/0.43
% 0.16/0.43 % sum.inject(1)
% 0.16/0.43 thf(fact_10_old_Osum_Oinject_I1_J,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,A2: A,A3: A] :
% 0.16/0.43 ( ( ( sum_Inl @ A @ B @ A2 )
% 0.16/0.43 = ( sum_Inl @ A @ B @ A3 ) )
% 0.16/0.43 = ( A2 = A3 ) ) ).
% 0.16/0.43
% 0.16/0.43 % old.sum.inject(1)
% 0.16/0.43 thf(fact_11_vimageI,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F: B > A,A2: B,B2: A,B3: set @ A] :
% 0.16/0.43 ( ( ( F @ A2 )
% 0.16/0.43 = B2 )
% 0.16/0.43 => ( ( member @ A @ B2 @ B3 )
% 0.16/0.43 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ B3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % vimageI
% 0.16/0.43 thf(fact_12_vimage__eq,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 0.16/0.43 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 0.16/0.43 = ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 0.16/0.43
% 0.16/0.43 % vimage_eq
% 0.16/0.43 thf(fact_13_id__apply,axiom,
% 0.16/0.43 ! [A: $tType] :
% 0.16/0.43 ( ( id @ A )
% 0.16/0.43 = ( ^ [X: A] : X ) ) ).
% 0.16/0.43
% 0.16/0.43 % id_apply
% 0.16/0.43 thf(fact_14_hsubst__eq,axiom,
% 0.16/0.43 ! [Tr: dtree] :
% 0.16/0.43 ( ( ( root @ Tr )
% 0.16/0.43 = ( root @ tr0 ) )
% 0.16/0.43 => ( ( gram_L1004374585hsubst @ tr0 @ Tr )
% 0.16/0.43 = ( gram_L1004374585hsubst @ tr0 @ tr0 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % hsubst_eq
% 0.16/0.43 thf(fact_15_image__eqI,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,B2: A,F: B > A,X2: B,A4: set @ B] :
% 0.16/0.43 ( ( B2
% 0.16/0.43 = ( F @ X2 ) )
% 0.16/0.43 => ( ( member @ B @ X2 @ A4 )
% 0.16/0.43 => ( member @ A @ B2 @ ( image @ B @ A @ F @ A4 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % image_eqI
% 0.16/0.43 thf(fact_16_root__hsubst,axiom,
% 0.16/0.43 ! [Tr: dtree] :
% 0.16/0.43 ( ( root @ ( gram_L1004374585hsubst @ tr0 @ Tr ) )
% 0.16/0.43 = ( root @ Tr ) ) ).
% 0.16/0.43
% 0.16/0.43 % root_hsubst
% 0.16/0.43 thf(fact_17_hsubst__c__def,axiom,
% 0.16/0.43 ! [Tr: dtree] :
% 0.16/0.43 ( ( ( ( root @ Tr )
% 0.16/0.43 = ( root @ tr0 ) )
% 0.16/0.43 => ( ( gram_L1905609002ubst_c @ tr0 @ Tr )
% 0.16/0.43 = ( cont @ tr0 ) ) )
% 0.16/0.43 & ( ( ( root @ Tr )
% 0.16/0.43 != ( root @ tr0 ) )
% 0.16/0.43 => ( ( gram_L1905609002ubst_c @ tr0 @ Tr )
% 0.16/0.43 = ( cont @ Tr ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % hsubst_c_def
% 0.16/0.43 thf(fact_18_Inl__cont__hsubst__eq,axiom,
% 0.16/0.43 ! [Tr: dtree] :
% 0.16/0.43 ( ( ( root @ Tr )
% 0.16/0.43 = ( root @ tr0 ) )
% 0.16/0.43 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ tr0 @ Tr ) ) )
% 0.16/0.43 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ tr0 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inl_cont_hsubst_eq
% 0.16/0.43 thf(fact_19_Inl__prodOf,axiom,
% 0.16/0.43 ! [Tr: dtree] :
% 0.16/0.43 ( ( vimage @ t @ ( sum_sum @ t @ n ) @ ( sum_Inl @ t @ n ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.16/0.43 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inl_prodOf
% 0.16/0.43 thf(fact_20_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__hsubst,axiom,
% 0.16/0.43 ! [Tr0: dtree,Tr: dtree] :
% 0.16/0.43 ( ( root @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.16/0.43 = ( root @ Tr ) ) ).
% 0.16/0.43
% 0.16/0.43 % Gram_Lang_Mirabelle_ojxrtuoybn.root_hsubst
% 0.16/0.43 thf(fact_21_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__eq,axiom,
% 0.16/0.43 ! [Tr: dtree,Tr0: dtree] :
% 0.16/0.43 ( ( ( root @ Tr )
% 0.16/0.43 = ( root @ Tr0 ) )
% 0.16/0.43 => ( ( gram_L1004374585hsubst @ Tr0 @ Tr )
% 0.16/0.43 = ( gram_L1004374585hsubst @ Tr0 @ Tr0 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Gram_Lang_Mirabelle_ojxrtuoybn.hsubst_eq
% 0.16/0.43 thf(fact_22_rev__image__eqI,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,X2: A,A4: set @ A,B2: B,F: A > B] :
% 0.16/0.43 ( ( member @ A @ X2 @ A4 )
% 0.16/0.43 => ( ( B2
% 0.16/0.43 = ( F @ X2 ) )
% 0.16/0.43 => ( member @ B @ B2 @ ( image @ A @ B @ F @ A4 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % rev_image_eqI
% 0.16/0.43 thf(fact_23_ball__imageD,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,F: B > A,A4: set @ B,P: A > $o] :
% 0.16/0.43 ( ! [X3: A] :
% 0.16/0.43 ( ( member @ A @ X3 @ ( image @ B @ A @ F @ A4 ) )
% 0.16/0.43 => ( P @ X3 ) )
% 0.16/0.43 => ! [X4: B] :
% 0.16/0.43 ( ( member @ B @ X4 @ A4 )
% 0.16/0.43 => ( P @ ( F @ X4 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ball_imageD
% 0.16/0.43 thf(fact_24_image__cong,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,M: set @ A,N: set @ A,F: A > B,G: A > B] :
% 0.16/0.43 ( ( M = N )
% 0.16/0.43 => ( ! [X3: A] :
% 0.16/0.43 ( ( member @ A @ X3 @ N )
% 0.16/0.43 => ( ( F @ X3 )
% 0.16/0.43 = ( G @ X3 ) ) )
% 0.16/0.43 => ( ( image @ A @ B @ F @ M )
% 0.16/0.43 = ( image @ A @ B @ G @ N ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % image_cong
% 0.16/0.43 thf(fact_25_bex__imageD,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,F: B > A,A4: set @ B,P: A > $o] :
% 0.16/0.43 ( ? [X4: A] :
% 0.16/0.43 ( ( member @ A @ X4 @ ( image @ B @ A @ F @ A4 ) )
% 0.16/0.43 & ( P @ X4 ) )
% 0.16/0.43 => ? [X3: B] :
% 0.16/0.43 ( ( member @ B @ X3 @ A4 )
% 0.16/0.43 & ( P @ ( F @ X3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % bex_imageD
% 0.16/0.43 thf(fact_26_image__iff,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,Z: A,F: B > A,A4: set @ B] :
% 0.16/0.43 ( ( member @ A @ Z @ ( image @ B @ A @ F @ A4 ) )
% 0.16/0.43 = ( ? [X: B] :
% 0.16/0.43 ( ( member @ B @ X @ A4 )
% 0.16/0.43 & ( Z
% 0.16/0.43 = ( F @ X ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % image_iff
% 0.16/0.43 thf(fact_27_imageI,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,X2: A,A4: set @ A,F: A > B] :
% 0.16/0.43 ( ( member @ A @ X2 @ A4 )
% 0.16/0.43 => ( member @ B @ ( F @ X2 ) @ ( image @ A @ B @ F @ A4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % imageI
% 0.16/0.43 thf(fact_28_eq__id__iff,axiom,
% 0.16/0.43 ! [A: $tType,F: A > A] :
% 0.16/0.43 ( ( ! [X: A] :
% 0.16/0.43 ( ( F @ X )
% 0.16/0.43 = X ) )
% 0.16/0.43 = ( F
% 0.16/0.43 = ( id @ A ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % eq_id_iff
% 0.16/0.43 thf(fact_29_id__def,axiom,
% 0.16/0.43 ! [A: $tType] :
% 0.16/0.43 ( ( id @ A )
% 0.16/0.43 = ( ^ [X: A] : X ) ) ).
% 0.16/0.43
% 0.16/0.43 % id_def
% 0.16/0.43 thf(fact_30_vimage__Collect,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,P: B > $o,F: A > B,Q: A > $o] :
% 0.16/0.43 ( ! [X3: A] :
% 0.16/0.43 ( ( P @ ( F @ X3 ) )
% 0.16/0.43 = ( Q @ X3 ) )
% 0.16/0.43 => ( ( vimage @ A @ B @ F @ ( collect @ B @ P ) )
% 0.16/0.43 = ( collect @ A @ Q ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % vimage_Collect
% 0.16/0.43 thf(fact_31_vimageI2,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F: B > A,A2: B,A4: set @ A] :
% 0.16/0.43 ( ( member @ A @ ( F @ A2 ) @ A4 )
% 0.16/0.43 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ A4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % vimageI2
% 0.16/0.43 thf(fact_32_vimageE,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 0.16/0.43 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 0.16/0.43 => ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 0.16/0.43
% 0.16/0.43 % vimageE
% 0.16/0.43 thf(fact_33_vimageD,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,A2: A,F: A > B,A4: set @ B] :
% 0.16/0.43 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ A4 ) )
% 0.16/0.43 => ( member @ B @ ( F @ A2 ) @ A4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % vimageD
% 0.16/0.43 thf(fact_34_Inl__inject,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,X2: A,Y: A] :
% 0.16/0.43 ( ( ( sum_Inl @ A @ B @ X2 )
% 0.16/0.43 = ( sum_Inl @ A @ B @ Y ) )
% 0.16/0.43 => ( X2 = Y ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inl_inject
% 0.16/0.43 thf(fact_35_Gram__Lang__Mirabelle__ojxrtuoybn_OInl__cont__hsubst__eq,axiom,
% 0.16/0.43 ! [Tr: dtree,Tr0: dtree] :
% 0.16/0.43 ( ( ( root @ Tr )
% 0.16/0.43 = ( root @ Tr0 ) )
% 0.16/0.43 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.16/0.43 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Gram_Lang_Mirabelle_ojxrtuoybn.Inl_cont_hsubst_eq
% 0.16/0.43 thf(fact_36_Gram__Lang__Mirabelle__ojxrtuoybn_Ocont__hsubst__neq,axiom,
% 0.16/0.43 ! [Tr: dtree,Tr0: dtree] :
% 0.16/0.43 ( ( ( root @ Tr )
% 0.16/0.43 != ( root @ Tr0 ) )
% 0.16/0.43 => ( ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.16/0.43 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ Tr0 ) ) @ ( cont @ Tr ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Gram_Lang_Mirabelle_ojxrtuoybn.cont_hsubst_neq
% 0.16/0.43 thf(fact_37_Gram__Lang__Mirabelle__ojxrtuoybn_Ocont__hsubst__eq,axiom,
% 0.16/0.43 ! [Tr: dtree,Tr0: dtree] :
% 0.16/0.43 ( ( ( root @ Tr )
% 0.16/0.43 = ( root @ Tr0 ) )
% 0.16/0.43 => ( ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.16/0.43 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ Tr0 ) ) @ ( cont @ Tr0 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Gram_Lang_Mirabelle_ojxrtuoybn.cont_hsubst_eq
% 0.16/0.43 thf(fact_38_map__sum__InlD,axiom,
% 0.16/0.43 ! [D: $tType,B: $tType,C: $tType,A: $tType,F: C > A,G: D > B,Z: sum_sum @ C @ D,X2: A] :
% 0.16/0.43 ( ( ( sum_map_sum @ C @ A @ D @ B @ F @ G @ Z )
% 0.16/0.43 = ( sum_Inl @ A @ B @ X2 ) )
% 0.16/0.43 => ? [Y2: C] :
% 0.16/0.43 ( ( Z
% 0.16/0.43 = ( sum_Inl @ C @ D @ Y2 ) )
% 0.16/0.43 & ( ( F @ Y2 )
% 0.16/0.43 = X2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % map_sum_InlD
% 0.16/0.43 thf(fact_39_map__sum_Osimps_I1_J,axiom,
% 0.16/0.43 ! [B: $tType,D: $tType,C: $tType,A: $tType,F1: A > C,F2: B > D,A2: A] :
% 0.16/0.43 ( ( sum_map_sum @ A @ C @ B @ D @ F1 @ F2 @ ( sum_Inl @ A @ B @ A2 ) )
% 0.16/0.43 = ( sum_Inl @ C @ D @ ( F1 @ A2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % map_sum.simps(1)
% 0.16/0.43 thf(fact_40_old_Osum_Osimps_I7_J,axiom,
% 0.16/0.43 ! [B: $tType,T: $tType,A: $tType,F1: A > T,F2: B > T,A2: A] :
% 0.16/0.43 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F2 @ ( sum_Inl @ A @ B @ A2 ) )
% 0.16/0.43 = ( F1 @ A2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % old.sum.simps(7)
% 0.16/0.43 thf(fact_41_map__sum__if__distrib__then_I1_J,axiom,
% 0.16/0.43 ! [D: $tType,B: $tType,C: $tType,A: $tType,E: $o,F: A > B,G: C > D,X2: A,Y: sum_sum @ A @ C] :
% 0.16/0.43 ( ( E
% 0.16/0.43 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E @ ( sum_Inl @ A @ C @ X2 ) @ Y ) )
% 0.16/0.43 = ( sum_Inl @ B @ D @ ( F @ X2 ) ) ) )
% 0.16/0.43 & ( ~ E
% 0.16/0.43 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E @ ( sum_Inl @ A @ C @ X2 ) @ Y ) )
% 0.16/0.43 = ( sum_map_sum @ A @ B @ C @ D @ F @ G @ Y ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % map_sum_if_distrib_then(1)
% 0.16/0.43 thf(fact_42_map__sum__if__distrib__else_I1_J,axiom,
% 0.16/0.43 ! [C: $tType,D: $tType,B: $tType,A: $tType,E: $o,F: A > B,G: C > D,X2: sum_sum @ A @ C,Y: A] :
% 0.16/0.43 ( ( E
% 0.16/0.43 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E @ X2 @ ( sum_Inl @ A @ C @ Y ) ) )
% 0.16/0.43 = ( sum_map_sum @ A @ B @ C @ D @ F @ G @ X2 ) ) )
% 0.16/0.43 & ( ~ E
% 0.16/0.43 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E @ X2 @ ( sum_Inl @ A @ C @ Y ) ) )
% 0.16/0.43 = ( sum_Inl @ B @ D @ ( F @ Y ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % map_sum_if_distrib_else(1)
% 0.16/0.43 thf(fact_43_dtree__cong,axiom,
% 0.16/0.43 ! [Tr: dtree,Tr2: dtree] :
% 0.16/0.43 ( ( ( root @ Tr )
% 0.16/0.43 = ( root @ Tr2 ) )
% 0.16/0.43 => ( ( ( cont @ Tr )
% 0.16/0.43 = ( cont @ Tr2 ) )
% 0.16/0.43 => ( Tr = Tr2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % dtree_cong
% 0.16/0.43 thf(fact_44_sum_Omap__id0,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType] :
% 0.16/0.43 ( ( sum_map_sum @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) )
% 0.16/0.43 = ( id @ ( sum_sum @ A @ B ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % sum.map_id0
% 0.16/0.43 thf(fact_45_mem__Collect__eq,axiom,
% 0.16/0.43 ! [A: $tType,A2: A,P: A > $o] :
% 0.16/0.43 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.16/0.43 = ( P @ A2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % mem_Collect_eq
% 0.16/0.43 thf(fact_46_Collect__mem__eq,axiom,
% 0.16/0.43 ! [A: $tType,A4: set @ A] :
% 0.16/0.43 ( ( collect @ A
% 0.16/0.43 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 0.16/0.43 = A4 ) ).
% 0.16/0.43
% 0.16/0.43 % Collect_mem_eq
% 0.16/0.43 thf(fact_47_Collect__cong,axiom,
% 0.16/0.43 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.16/0.43 ( ! [X3: A] :
% 0.16/0.43 ( ( P @ X3 )
% 0.16/0.43 = ( Q @ X3 ) )
% 0.16/0.43 => ( ( collect @ A @ P )
% 0.16/0.43 = ( collect @ A @ Q ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Collect_cong
% 0.16/0.43 thf(fact_48_ext,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.16/0.43 ( ! [X3: A] :
% 0.16/0.43 ( ( F @ X3 )
% 0.16/0.43 = ( G @ X3 ) )
% 0.16/0.43 => ( F = G ) ) ).
% 0.16/0.43
% 0.16/0.43 % ext
% 0.16/0.43 thf(fact_49_sum_Omap__id,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,T2: sum_sum @ A @ B] :
% 0.16/0.43 ( ( sum_map_sum @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) @ T2 )
% 0.16/0.43 = T2 ) ).
% 0.16/0.43
% 0.16/0.43 % sum.map_id
% 0.16/0.43 thf(fact_50_Sup_OSUP__id__eq,axiom,
% 0.16/0.43 ! [A: $tType,Sup: ( set @ A ) > A,A4: set @ A] :
% 0.16/0.43 ( ( Sup @ ( image @ A @ A @ ( id @ A ) @ A4 ) )
% 0.16/0.43 = ( Sup @ A4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % Sup.SUP_id_eq
% 0.16/0.43 thf(fact_51_Inf_OINF__id__eq,axiom,
% 0.16/0.43 ! [A: $tType,Inf: ( set @ A ) > A,A4: set @ A] :
% 0.16/0.43 ( ( Inf @ ( image @ A @ A @ ( id @ A ) @ A4 ) )
% 0.16/0.43 = ( Inf @ A4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inf.INF_id_eq
% 0.16/0.43 thf(fact_52_Inr__m__oplus,axiom,
% 0.16/0.43 ! [A: $tType,C: $tType,B: $tType,F: C > A,Tns: set @ ( sum_sum @ B @ C )] :
% 0.16/0.43 ( ( vimage @ A @ ( sum_sum @ B @ A ) @ ( sum_Inr @ A @ B ) @ ( image @ ( sum_sum @ B @ C ) @ ( sum_sum @ B @ A ) @ ( sum_map_sum @ B @ B @ C @ A @ ( id @ B ) @ F ) @ Tns ) )
% 0.16/0.43 = ( image @ C @ A @ F @ ( vimage @ C @ ( sum_sum @ B @ C ) @ ( sum_Inr @ C @ B ) @ Tns ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inr_m_oplus
% 0.16/0.43 thf(fact_53_Inr__cont__hsubst__eq,axiom,
% 0.16/0.43 ! [Tr: dtree] :
% 0.16/0.43 ( ( ( root @ Tr )
% 0.16/0.43 = ( root @ tr0 ) )
% 0.16/0.43 => ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1004374585hsubst @ tr0 @ Tr ) ) )
% 0.16/0.43 = ( image @ dtree @ dtree @ ( gram_L1004374585hsubst @ tr0 ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ tr0 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inr_cont_hsubst_eq
% 0.16/0.43 thf(fact_54_inFr2_OBase,axiom,
% 0.16/0.43 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 0.16/0.43 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr2.Base
% 0.16/0.43 thf(fact_55_sum_Oinject_I2_J,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,X22: B,Y22: B] :
% 0.16/0.43 ( ( ( sum_Inr @ B @ A @ X22 )
% 0.16/0.43 = ( sum_Inr @ B @ A @ Y22 ) )
% 0.16/0.43 = ( X22 = Y22 ) ) ).
% 0.16/0.43
% 0.16/0.43 % sum.inject(2)
% 0.16/0.43 thf(fact_56_old_Osum_Oinject_I2_J,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,B2: B,B4: B] :
% 0.16/0.43 ( ( ( sum_Inr @ B @ A @ B2 )
% 0.16/0.43 = ( sum_Inr @ B @ A @ B4 ) )
% 0.16/0.43 = ( B2 = B4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % old.sum.inject(2)
% 0.16/0.43 thf(fact_57_Inl__Inr__False,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,X2: A,Y: B] :
% 0.16/0.43 ( ( sum_Inl @ A @ B @ X2 )
% 0.16/0.43 != ( sum_Inr @ B @ A @ Y ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inl_Inr_False
% 0.16/0.43 thf(fact_58_Inr__Inl__False,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,X2: B,Y: A] :
% 0.16/0.43 ( ( sum_Inr @ B @ A @ X2 )
% 0.16/0.43 != ( sum_Inl @ A @ B @ Y ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inr_Inl_False
% 0.16/0.43 thf(fact_59_old_Osum_Osimps_I8_J,axiom,
% 0.16/0.43 ! [A: $tType,T: $tType,B: $tType,F1: A > T,F2: B > T,B2: B] :
% 0.16/0.43 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F2 @ ( sum_Inr @ B @ A @ B2 ) )
% 0.16/0.43 = ( F2 @ B2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % old.sum.simps(8)
% 0.16/0.43 thf(fact_60_Inr__oplus__iff,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,C: $tType,Tr: B,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.16/0.43 ( ( member @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A @ Tr ) @ ( image @ ( sum_sum @ A @ C ) @ ( sum_sum @ A @ B ) @ ( sum_map_sum @ A @ A @ C @ B @ ( id @ A ) @ F ) @ Tns ) )
% 0.16/0.43 = ( ? [N2: C] :
% 0.16/0.43 ( ( member @ ( sum_sum @ A @ C ) @ ( sum_Inr @ C @ A @ N2 ) @ Tns )
% 0.16/0.43 & ( ( F @ N2 )
% 0.16/0.43 = Tr ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inr_oplus_iff
% 0.16/0.43 thf(fact_61_Inr__inject,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,X2: B,Y: B] :
% 0.16/0.43 ( ( ( sum_Inr @ B @ A @ X2 )
% 0.16/0.43 = ( sum_Inr @ B @ A @ Y ) )
% 0.16/0.43 => ( X2 = Y ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inr_inject
% 0.16/0.43 thf(fact_62_obj__sumE__f,axiom,
% 0.16/0.43 ! [A: $tType,C: $tType,B: $tType,S: B,F: ( sum_sum @ A @ C ) > B,P: $o] :
% 0.16/0.43 ( ! [X3: A] :
% 0.16/0.43 ( ( S
% 0.16/0.43 = ( F @ ( sum_Inl @ A @ C @ X3 ) ) )
% 0.16/0.43 => P )
% 0.16/0.43 => ( ! [X3: C] :
% 0.16/0.43 ( ( S
% 0.16/0.43 = ( F @ ( sum_Inr @ C @ A @ X3 ) ) )
% 0.16/0.43 => P )
% 0.16/0.43 => ! [X4: sum_sum @ A @ C] :
% 0.16/0.43 ( ( S
% 0.16/0.43 = ( F @ X4 ) )
% 0.16/0.43 => P ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % obj_sumE_f
% 0.16/0.43 thf(fact_63_map__sum__if__distrib__else_I2_J,axiom,
% 0.16/0.43 ! [E2: $tType,F3: $tType,H: $tType,G2: $tType,E: $o,F: E2 > F3,G: G2 > H,X2: sum_sum @ E2 @ G2,Y: G2] :
% 0.16/0.43 ( ( E
% 0.16/0.43 => ( ( sum_map_sum @ E2 @ F3 @ G2 @ H @ F @ G @ ( if @ ( sum_sum @ E2 @ G2 ) @ E @ X2 @ ( sum_Inr @ G2 @ E2 @ Y ) ) )
% 0.16/0.43 = ( sum_map_sum @ E2 @ F3 @ G2 @ H @ F @ G @ X2 ) ) )
% 0.16/0.43 & ( ~ E
% 0.16/0.43 => ( ( sum_map_sum @ E2 @ F3 @ G2 @ H @ F @ G @ ( if @ ( sum_sum @ E2 @ G2 ) @ E @ X2 @ ( sum_Inr @ G2 @ E2 @ Y ) ) )
% 0.16/0.43 = ( sum_Inr @ H @ F3 @ ( G @ Y ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % map_sum_if_distrib_else(2)
% 0.16/0.43 thf(fact_64_map__sum__if__distrib__then_I2_J,axiom,
% 0.16/0.43 ! [H: $tType,F3: $tType,G2: $tType,E2: $tType,E: $o,F: E2 > F3,G: G2 > H,X2: G2,Y: sum_sum @ E2 @ G2] :
% 0.16/0.43 ( ( E
% 0.16/0.43 => ( ( sum_map_sum @ E2 @ F3 @ G2 @ H @ F @ G @ ( if @ ( sum_sum @ E2 @ G2 ) @ E @ ( sum_Inr @ G2 @ E2 @ X2 ) @ Y ) )
% 0.16/0.43 = ( sum_Inr @ H @ F3 @ ( G @ X2 ) ) ) )
% 0.16/0.43 & ( ~ E
% 0.16/0.43 => ( ( sum_map_sum @ E2 @ F3 @ G2 @ H @ F @ G @ ( if @ ( sum_sum @ E2 @ G2 ) @ E @ ( sum_Inr @ G2 @ E2 @ X2 ) @ Y ) )
% 0.16/0.43 = ( sum_map_sum @ E2 @ F3 @ G2 @ H @ F @ G @ Y ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % map_sum_if_distrib_then(2)
% 0.16/0.43 thf(fact_65_sum_Odistinct_I1_J,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,X1: A,X22: B] :
% 0.16/0.43 ( ( sum_Inl @ A @ B @ X1 )
% 0.16/0.43 != ( sum_Inr @ B @ A @ X22 ) ) ).
% 0.16/0.43
% 0.16/0.43 % sum.distinct(1)
% 0.16/0.43 thf(fact_66_old_Osum_Odistinct_I2_J,axiom,
% 0.16/0.43 ! [B5: $tType,A5: $tType,B6: B5,A6: A5] :
% 0.16/0.43 ( ( sum_Inr @ B5 @ A5 @ B6 )
% 0.16/0.43 != ( sum_Inl @ A5 @ B5 @ A6 ) ) ).
% 0.16/0.43
% 0.16/0.43 % old.sum.distinct(2)
% 0.16/0.43 thf(fact_67_old_Osum_Odistinct_I1_J,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,A2: A,B4: B] :
% 0.16/0.43 ( ( sum_Inl @ A @ B @ A2 )
% 0.16/0.43 != ( sum_Inr @ B @ A @ B4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % old.sum.distinct(1)
% 0.16/0.43 thf(fact_68_sumE,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 0.16/0.43 ( ! [X3: A] :
% 0.16/0.43 ( S
% 0.16/0.43 != ( sum_Inl @ A @ B @ X3 ) )
% 0.16/0.43 => ~ ! [Y2: B] :
% 0.16/0.43 ( S
% 0.16/0.43 != ( sum_Inr @ B @ A @ Y2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % sumE
% 0.16/0.43 thf(fact_69_Inr__not__Inl,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,B2: B,A2: A] :
% 0.16/0.43 ( ( sum_Inr @ B @ A @ B2 )
% 0.16/0.43 != ( sum_Inl @ A @ B @ A2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inr_not_Inl
% 0.16/0.43 thf(fact_70_split__sum__ex,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType] :
% 0.16/0.43 ( ( ^ [P2: ( sum_sum @ A @ B ) > $o] :
% 0.16/0.43 ? [X5: sum_sum @ A @ B] : ( P2 @ X5 ) )
% 0.16/0.43 = ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 0.16/0.43 ( ? [X: A] : ( P3 @ ( sum_Inl @ A @ B @ X ) )
% 0.16/0.43 | ? [X: B] : ( P3 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % split_sum_ex
% 0.16/0.43 thf(fact_71_split__sum__all,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType] :
% 0.16/0.43 ( ( ^ [P2: ( sum_sum @ A @ B ) > $o] :
% 0.16/0.43 ! [X5: sum_sum @ A @ B] : ( P2 @ X5 ) )
% 0.16/0.43 = ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 0.16/0.43 ( ! [X: A] : ( P3 @ ( sum_Inl @ A @ B @ X ) )
% 0.16/0.43 & ! [X: B] : ( P3 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % split_sum_all
% 0.16/0.43 thf(fact_72_old_Osum_Oexhaust,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,Y: sum_sum @ A @ B] :
% 0.16/0.43 ( ! [A7: A] :
% 0.16/0.43 ( Y
% 0.16/0.43 != ( sum_Inl @ A @ B @ A7 ) )
% 0.16/0.43 => ~ ! [B7: B] :
% 0.16/0.43 ( Y
% 0.16/0.43 != ( sum_Inr @ B @ A @ B7 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % old.sum.exhaust
% 0.16/0.43 thf(fact_73_old_Osum_Oinducts,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,P: ( sum_sum @ A @ B ) > $o,Sum: sum_sum @ A @ B] :
% 0.16/0.43 ( ! [A7: A] : ( P @ ( sum_Inl @ A @ B @ A7 ) )
% 0.16/0.43 => ( ! [B7: B] : ( P @ ( sum_Inr @ B @ A @ B7 ) )
% 0.16/0.43 => ( P @ Sum ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % old.sum.inducts
% 0.16/0.43 thf(fact_74_map__sum_Osimps_I2_J,axiom,
% 0.16/0.43 ! [A: $tType,C: $tType,D: $tType,B: $tType,F1: A > C,F2: B > D,A2: B] :
% 0.16/0.43 ( ( sum_map_sum @ A @ C @ B @ D @ F1 @ F2 @ ( sum_Inr @ B @ A @ A2 ) )
% 0.16/0.43 = ( sum_Inr @ D @ C @ ( F2 @ A2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % map_sum.simps(2)
% 0.16/0.43 thf(fact_75_map__sum__InrD,axiom,
% 0.16/0.43 ! [C: $tType,A: $tType,D: $tType,B: $tType,F: C > A,G: D > B,Z: sum_sum @ C @ D,X2: B] :
% 0.16/0.43 ( ( ( sum_map_sum @ C @ A @ D @ B @ F @ G @ Z )
% 0.16/0.43 = ( sum_Inr @ B @ A @ X2 ) )
% 0.16/0.43 => ? [Y2: D] :
% 0.16/0.43 ( ( Z
% 0.16/0.43 = ( sum_Inr @ D @ C @ Y2 ) )
% 0.16/0.43 & ( ( G @ Y2 )
% 0.16/0.43 = X2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % map_sum_InrD
% 0.16/0.43 thf(fact_76_inFr2__Ind,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 0.16/0.43 ( ( gram_L805317441_inFr2 @ Ns @ Tr1 @ T2 )
% 0.16/0.43 => ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.16/0.43 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr2_Ind
% 0.16/0.43 thf(fact_77_root__prodOf,axiom,
% 0.16/0.43 ! [Tr2: dtree,Tr: dtree] :
% 0.16/0.43 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 0.16/0.43 => ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ ( root @ Tr2 ) ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % root_prodOf
% 0.16/0.43 thf(fact_78_inFr2__root__in,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.16/0.43 ( ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 )
% 0.16/0.43 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr2_root_in
% 0.16/0.43 thf(fact_79_Inl__Inr__image__cong,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,A4: set @ ( sum_sum @ A @ B ),B3: set @ ( sum_sum @ A @ B )] :
% 0.16/0.43 ( ( ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ A4 )
% 0.16/0.43 = ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ B3 ) )
% 0.16/0.43 => ( ( ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ A4 )
% 0.16/0.43 = ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ B3 ) )
% 0.16/0.43 => ( A4 = B3 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inl_Inr_image_cong
% 0.16/0.43 thf(fact_80_Inr__oplus__elim,axiom,
% 0.16/0.43 ! [A: $tType,C: $tType,B: $tType,Tr: B,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.16/0.43 ( ( member @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A @ Tr ) @ ( image @ ( sum_sum @ A @ C ) @ ( sum_sum @ A @ B ) @ ( sum_map_sum @ A @ A @ C @ B @ ( id @ A ) @ F ) @ Tns ) )
% 0.16/0.43 => ? [N3: C] :
% 0.16/0.43 ( ( member @ ( sum_sum @ A @ C ) @ ( sum_Inr @ C @ A @ N3 ) @ Tns )
% 0.16/0.43 & ( ( F @ N3 )
% 0.16/0.43 = Tr ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inr_oplus_elim
% 0.16/0.43 thf(fact_81_Gram__Lang__Mirabelle__ojxrtuoybn_OInr__cont__hsubst__eq,axiom,
% 0.16/0.43 ! [Tr: dtree,Tr0: dtree] :
% 0.16/0.43 ( ( ( root @ Tr )
% 0.16/0.43 = ( root @ Tr0 ) )
% 0.16/0.43 => ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.16/0.43 = ( image @ dtree @ dtree @ ( gram_L1004374585hsubst @ Tr0 ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr0 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Gram_Lang_Mirabelle_ojxrtuoybn.Inr_cont_hsubst_eq
% 0.16/0.43 thf(fact_82_Inf_OINF__cong,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,A4: set @ B,B3: set @ B,C2: B > A,D2: B > A,Inf: ( set @ A ) > A] :
% 0.16/0.43 ( ( A4 = B3 )
% 0.16/0.43 => ( ! [X3: B] :
% 0.16/0.43 ( ( member @ B @ X3 @ B3 )
% 0.16/0.43 => ( ( C2 @ X3 )
% 0.16/0.43 = ( D2 @ X3 ) ) )
% 0.16/0.43 => ( ( Inf @ ( image @ B @ A @ C2 @ A4 ) )
% 0.16/0.43 = ( Inf @ ( image @ B @ A @ D2 @ B3 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inf.INF_cong
% 0.16/0.43 thf(fact_83_Sup_OSUP__cong,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,A4: set @ B,B3: set @ B,C2: B > A,D2: B > A,Sup: ( set @ A ) > A] :
% 0.16/0.43 ( ( A4 = B3 )
% 0.16/0.43 => ( ! [X3: B] :
% 0.16/0.43 ( ( member @ B @ X3 @ B3 )
% 0.16/0.43 => ( ( C2 @ X3 )
% 0.16/0.43 = ( D2 @ X3 ) ) )
% 0.16/0.43 => ( ( Sup @ ( image @ B @ A @ C2 @ A4 ) )
% 0.16/0.43 = ( Sup @ ( image @ B @ A @ D2 @ B3 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Sup.SUP_cong
% 0.16/0.43 thf(fact_84_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c__def,axiom,
% 0.16/0.43 ( gram_L1905609002ubst_c
% 0.16/0.43 = ( ^ [Tr02: dtree,Tr3: dtree] :
% 0.16/0.43 ( if @ ( set @ ( sum_sum @ t @ dtree ) )
% 0.16/0.43 @ ( ( root @ Tr3 )
% 0.16/0.43 = ( root @ Tr02 ) )
% 0.16/0.43 @ ( cont @ Tr02 )
% 0.16/0.43 @ ( cont @ Tr3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Gram_Lang_Mirabelle_ojxrtuoybn.hsubst_c_def
% 0.16/0.43 thf(fact_85_hsubst__def,axiom,
% 0.16/0.43 ( ( gram_L1004374585hsubst @ tr0 )
% 0.16/0.43 = ( unfold @ dtree @ gram_L1905609017ubst_r @ ( gram_L1905609002ubst_c @ tr0 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % hsubst_def
% 0.16/0.43 thf(fact_86_root__subtrOf,axiom,
% 0.16/0.43 ! [N4: n,Tr: dtree] :
% 0.16/0.43 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N4 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.16/0.43 => ( ( root @ ( gram_L1614515765ubtrOf @ Tr @ N4 ) )
% 0.16/0.43 = N4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % root_subtrOf
% 0.16/0.43 thf(fact_87_Inr__subtrOf,axiom,
% 0.16/0.43 ! [N4: n,Tr: dtree] :
% 0.16/0.43 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N4 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.16/0.43 => ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( gram_L1614515765ubtrOf @ Tr @ N4 ) ) @ ( cont @ Tr ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Inr_subtrOf
% 0.16/0.43 thf(fact_88_subtrOf,axiom,
% 0.16/0.43 ! [N4: n,Tr: dtree] :
% 0.16/0.43 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N4 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( gram_L1614515765ubtrOf @ Tr @ N4 ) ) @ ( cont @ Tr ) )
% 0.16/0.43 & ( ( root @ ( gram_L1614515765ubtrOf @ Tr @ N4 ) )
% 0.16/0.43 = N4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtrOf
% 0.16/0.43 thf(fact_89_finite__hsubst__c,axiom,
% 0.16/0.43 ! [N4: dtree] : ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ ( gram_L1905609002ubst_c @ tr0 @ N4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % finite_hsubst_c
% 0.16/0.43 thf(fact_90_obj__sumE,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 0.16/0.43 ( ! [X3: A] :
% 0.16/0.43 ( S
% 0.16/0.43 != ( sum_Inl @ A @ B @ X3 ) )
% 0.16/0.43 => ~ ! [X3: B] :
% 0.16/0.43 ( S
% 0.16/0.43 != ( sum_Inr @ B @ A @ X3 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % obj_sumE
% 0.16/0.43 thf(fact_91_Node__root__cont,axiom,
% 0.16/0.43 ! [Tr: dtree] :
% 0.16/0.43 ( ( node @ ( root @ Tr ) @ ( cont @ Tr ) )
% 0.16/0.43 = Tr ) ).
% 0.16/0.43
% 0.16/0.43 % Node_root_cont
% 0.16/0.43 thf(fact_92_inFr_Ocases,axiom,
% 0.16/0.43 ! [A1: set @ n,A22: dtree,A32: t] :
% 0.16/0.43 ( ( gram_L1333338417e_inFr @ A1 @ A22 @ A32 )
% 0.16/0.43 => ( ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.16/0.43 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A32 ) @ ( cont @ A22 ) ) )
% 0.16/0.43 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.16/0.43 => ! [Tr12: dtree] :
% 0.16/0.43 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A22 ) )
% 0.16/0.43 => ~ ( gram_L1333338417e_inFr @ A1 @ Tr12 @ A32 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr.cases
% 0.16/0.43 thf(fact_93_root__Node,axiom,
% 0.16/0.43 ! [N4: n,As: set @ ( sum_sum @ t @ dtree )] :
% 0.16/0.43 ( ( root @ ( node @ N4 @ As ) )
% 0.16/0.43 = N4 ) ).
% 0.16/0.43
% 0.16/0.43 % root_Node
% 0.16/0.43 thf(fact_94_dtree__simps,axiom,
% 0.16/0.43 ! [As: set @ ( sum_sum @ t @ dtree ),As2: set @ ( sum_sum @ t @ dtree ),N4: n,N5: n] :
% 0.16/0.43 ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As )
% 0.16/0.43 => ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As2 )
% 0.16/0.43 => ( ( ( node @ N4 @ As )
% 0.16/0.43 = ( node @ N5 @ As2 ) )
% 0.16/0.43 = ( ( N4 = N5 )
% 0.16/0.43 & ( As = As2 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % dtree_simps
% 0.16/0.43 thf(fact_95_cont__Node,axiom,
% 0.16/0.43 ! [As: set @ ( sum_sum @ t @ dtree ),N4: n] :
% 0.16/0.43 ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As )
% 0.16/0.43 => ( ( cont @ ( node @ N4 @ As ) )
% 0.16/0.43 = As ) ) ).
% 0.16/0.43
% 0.16/0.43 % cont_Node
% 0.16/0.43 thf(fact_96_dtree__cases,axiom,
% 0.16/0.43 ! [Tr: dtree] :
% 0.16/0.43 ~ ! [N3: n,As3: set @ ( sum_sum @ t @ dtree )] :
% 0.16/0.43 ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As3 )
% 0.16/0.43 => ( Tr
% 0.16/0.43 != ( node @ N3 @ As3 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % dtree_cases
% 0.16/0.43 thf(fact_97_finite__cont,axiom,
% 0.16/0.43 ! [Tr: dtree] : ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ ( cont @ Tr ) ) ).
% 0.16/0.43
% 0.16/0.43 % finite_cont
% 0.16/0.43 thf(fact_98_Gram__Lang__Mirabelle__ojxrtuoybn_Ofinite__hsubst__c,axiom,
% 0.16/0.43 ! [Tr0: dtree,N4: dtree] : ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ ( gram_L1905609002ubst_c @ Tr0 @ N4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % Gram_Lang_Mirabelle_ojxrtuoybn.finite_hsubst_c
% 0.16/0.43 thf(fact_99_inFr__root__in,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.16/0.43 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.16/0.43 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr_root_in
% 0.16/0.43 thf(fact_100_not__root__inFr,axiom,
% 0.16/0.43 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.16/0.43 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.43 => ~ ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % not_root_inFr
% 0.16/0.43 thf(fact_101_inFr__inFr2,axiom,
% 0.16/0.43 gram_L1333338417e_inFr = gram_L805317441_inFr2 ).
% 0.16/0.43
% 0.16/0.43 % inFr_inFr2
% 0.16/0.43 thf(fact_102_unfold_I1_J,axiom,
% 0.16/0.43 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ A ) ),B2: A] :
% 0.16/0.43 ( ( root @ ( unfold @ A @ Rt @ Ct @ B2 ) )
% 0.16/0.43 = ( Rt @ B2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % unfold(1)
% 0.16/0.43 thf(fact_103_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__def,axiom,
% 0.16/0.43 ( gram_L1004374585hsubst
% 0.16/0.43 = ( ^ [Tr02: dtree] : ( unfold @ dtree @ gram_L1905609017ubst_r @ ( gram_L1905609002ubst_c @ Tr02 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Gram_Lang_Mirabelle_ojxrtuoybn.hsubst_def
% 0.16/0.43 thf(fact_104_not__arg__cong__Inr,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,X2: A,Y: A] :
% 0.16/0.43 ( ( X2 != Y )
% 0.16/0.43 => ( ( sum_Inr @ A @ B @ X2 )
% 0.16/0.43 != ( sum_Inr @ A @ B @ Y ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % not_arg_cong_Inr
% 0.16/0.43 thf(fact_105_unfold_I2_J,axiom,
% 0.16/0.43 ! [A: $tType,Ct: A > ( set @ ( sum_sum @ t @ A ) ),B2: A,Rt: A > n] :
% 0.16/0.43 ( ( finite_finite2 @ ( sum_sum @ t @ A ) @ ( Ct @ B2 ) )
% 0.16/0.43 => ( ( cont @ ( unfold @ A @ Rt @ Ct @ B2 ) )
% 0.16/0.43 = ( image @ ( sum_sum @ t @ A ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ A @ dtree @ ( id @ t ) @ ( unfold @ A @ Rt @ Ct ) ) @ ( Ct @ B2 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % unfold(2)
% 0.16/0.43 thf(fact_106_hsubst__r__def,axiom,
% 0.16/0.43 gram_L1905609017ubst_r = root ).
% 0.16/0.43
% 0.16/0.43 % hsubst_r_def
% 0.16/0.43 thf(fact_107_inFr_OInd,axiom,
% 0.16/0.43 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,T2: t] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.16/0.43 => ( ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 )
% 0.16/0.43 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr.Ind
% 0.16/0.43 thf(fact_108_inFr_OBase,axiom,
% 0.16/0.43 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 0.16/0.43 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr.Base
% 0.16/0.43 thf(fact_109_inFr_Oinducts,axiom,
% 0.16/0.43 ! [X1: set @ n,X22: dtree,X32: t,P: ( set @ n ) > dtree > t > $o] :
% 0.16/0.43 ( ( gram_L1333338417e_inFr @ X1 @ X22 @ X32 )
% 0.16/0.43 => ( ! [Tr4: dtree,Ns2: set @ n,T3: t] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr4 ) )
% 0.16/0.43 => ( P @ Ns2 @ Tr4 @ T3 ) ) )
% 0.16/0.43 => ( ! [Tr4: dtree,Ns2: set @ n,Tr12: dtree,T3: t] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr4 ) )
% 0.16/0.43 => ( ( gram_L1333338417e_inFr @ Ns2 @ Tr12 @ T3 )
% 0.16/0.43 => ( ( P @ Ns2 @ Tr12 @ T3 )
% 0.16/0.43 => ( P @ Ns2 @ Tr4 @ T3 ) ) ) ) )
% 0.16/0.43 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr.inducts
% 0.16/0.43 thf(fact_110_inFr_Osimps,axiom,
% 0.16/0.43 ( gram_L1333338417e_inFr
% 0.16/0.43 = ( ^ [A12: set @ n,A23: dtree,A33: t] :
% 0.16/0.43 ( ? [Tr3: dtree,Ns3: set @ n,T4: t] :
% 0.16/0.43 ( ( A12 = Ns3 )
% 0.16/0.43 & ( A23 = Tr3 )
% 0.16/0.43 & ( A33 = T4 )
% 0.16/0.43 & ( member @ n @ ( root @ Tr3 ) @ Ns3 )
% 0.16/0.43 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr3 ) ) )
% 0.16/0.43 | ? [Tr3: dtree,Ns3: set @ n,Tr13: dtree,T4: t] :
% 0.16/0.43 ( ( A12 = Ns3 )
% 0.16/0.43 & ( A23 = Tr3 )
% 0.16/0.43 & ( A33 = T4 )
% 0.16/0.43 & ( member @ n @ ( root @ Tr3 ) @ Ns3 )
% 0.16/0.43 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr3 ) )
% 0.16/0.43 & ( gram_L1333338417e_inFr @ Ns3 @ Tr13 @ T4 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr.simps
% 0.16/0.43 thf(fact_111_inFrr__def,axiom,
% 0.16/0.43 ( gram_L805317505_inFrr
% 0.16/0.43 = ( ^ [Ns3: set @ n,Tr3: dtree,T4: t] :
% 0.16/0.43 ? [Tr5: dtree] :
% 0.16/0.43 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr5 ) @ ( cont @ Tr3 ) )
% 0.16/0.43 & ( gram_L1333338417e_inFr @ Ns3 @ Tr5 @ T4 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFrr_def
% 0.16/0.43 thf(fact_112_finite__imageI,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F4: set @ A,H2: A > B] :
% 0.16/0.43 ( ( finite_finite2 @ A @ F4 )
% 0.16/0.43 => ( finite_finite2 @ B @ ( image @ A @ B @ H2 @ F4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % finite_imageI
% 0.16/0.43 thf(fact_113_surj__subtrOf,axiom,
% 0.16/0.43 ! [Tr: dtree,Tr2: dtree] :
% 0.16/0.43 ( ( gram_L864798063lle_wf @ Tr )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 0.16/0.43 => ? [N3: n] :
% 0.16/0.43 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N3 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.16/0.43 & ( ( gram_L1614515765ubtrOf @ Tr @ N3 )
% 0.16/0.43 = Tr2 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % surj_subtrOf
% 0.16/0.43 thf(fact_114_finite__code,axiom,
% 0.16/0.43 ! [A: $tType] :
% 0.16/0.43 ( ( finite_finite @ A @ ( type @ A ) )
% 0.16/0.43 => ( ( finite_finite2 @ A )
% 0.16/0.43 = ( ^ [A8: set @ A] : $true ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % finite_code
% 0.16/0.43 thf(fact_115_subtrOf__root,axiom,
% 0.16/0.43 ! [Tr: dtree,Tr2: dtree] :
% 0.16/0.43 ( ( gram_L864798063lle_wf @ Tr )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 0.16/0.43 => ( ( gram_L1614515765ubtrOf @ Tr @ ( root @ Tr2 ) )
% 0.16/0.43 = Tr2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtrOf_root
% 0.16/0.43 thf(fact_116_wf__inj,axiom,
% 0.16/0.43 ! [Tr: dtree,Tr1: dtree,Tr22: dtree] :
% 0.16/0.43 ( ( gram_L864798063lle_wf @ Tr )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr ) )
% 0.16/0.43 => ( ( ( root @ Tr1 )
% 0.16/0.43 = ( root @ Tr22 ) )
% 0.16/0.43 = ( Tr1 = Tr22 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % wf_inj
% 0.16/0.43 thf(fact_117_wf__cont,axiom,
% 0.16/0.43 ! [Tr: dtree,Tr2: dtree] :
% 0.16/0.43 ( ( gram_L864798063lle_wf @ Tr )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 0.16/0.43 => ( gram_L864798063lle_wf @ Tr2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % wf_cont
% 0.16/0.43 thf(fact_118_finite,axiom,
% 0.16/0.43 ! [A: $tType] :
% 0.16/0.43 ( ( finite_finite @ A @ ( type @ A ) )
% 0.16/0.43 => ! [A4: set @ A] : ( finite_finite2 @ A @ A4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % finite
% 0.16/0.43 thf(fact_119_finite__set__choice,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,A4: set @ A,P: A > B > $o] :
% 0.16/0.43 ( ( finite_finite2 @ A @ A4 )
% 0.16/0.43 => ( ! [X3: A] :
% 0.16/0.43 ( ( member @ A @ X3 @ A4 )
% 0.16/0.43 => ? [X12: B] : ( P @ X3 @ X12 ) )
% 0.16/0.43 => ? [F5: A > B] :
% 0.16/0.43 ! [X4: A] :
% 0.16/0.43 ( ( member @ A @ X4 @ A4 )
% 0.16/0.43 => ( P @ X4 @ ( F5 @ X4 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % finite_set_choice
% 0.16/0.43 thf(fact_120_inFr2_Ocases,axiom,
% 0.16/0.43 ! [A1: set @ n,A22: dtree,A32: t] :
% 0.16/0.43 ( ( gram_L805317441_inFr2 @ A1 @ A22 @ A32 )
% 0.16/0.43 => ( ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.16/0.43 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A32 ) @ ( cont @ A22 ) ) )
% 0.16/0.43 => ~ ! [Tr12: dtree,Tr4: dtree,Ns1: set @ n] :
% 0.16/0.43 ( ( A1
% 0.16/0.43 = ( insert @ n @ ( root @ Tr4 ) @ Ns1 ) )
% 0.16/0.43 => ( ( A22 = Tr4 )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr4 ) )
% 0.16/0.43 => ~ ( gram_L805317441_inFr2 @ Ns1 @ Tr12 @ A32 ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr2.cases
% 0.16/0.43 thf(fact_121_inFr2_Osimps,axiom,
% 0.16/0.43 ( gram_L805317441_inFr2
% 0.16/0.43 = ( ^ [A12: set @ n,A23: dtree,A33: t] :
% 0.16/0.43 ( ? [Tr3: dtree,Ns3: set @ n,T4: t] :
% 0.16/0.43 ( ( A12 = Ns3 )
% 0.16/0.43 & ( A23 = Tr3 )
% 0.16/0.43 & ( A33 = T4 )
% 0.16/0.43 & ( member @ n @ ( root @ Tr3 ) @ Ns3 )
% 0.16/0.43 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr3 ) ) )
% 0.16/0.43 | ? [Tr13: dtree,Tr3: dtree,Ns12: set @ n,T4: t] :
% 0.16/0.43 ( ( A12
% 0.16/0.43 = ( insert @ n @ ( root @ Tr3 ) @ Ns12 ) )
% 0.16/0.43 & ( A23 = Tr3 )
% 0.16/0.43 & ( A33 = T4 )
% 0.16/0.43 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr3 ) )
% 0.16/0.43 & ( gram_L805317441_inFr2 @ Ns12 @ Tr13 @ T4 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr2.simps
% 0.16/0.43 thf(fact_122_inFr2_Oinducts,axiom,
% 0.16/0.43 ! [X1: set @ n,X22: dtree,X32: t,P: ( set @ n ) > dtree > t > $o] :
% 0.16/0.43 ( ( gram_L805317441_inFr2 @ X1 @ X22 @ X32 )
% 0.16/0.43 => ( ! [Tr4: dtree,Ns2: set @ n,T3: t] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr4 ) )
% 0.16/0.43 => ( P @ Ns2 @ Tr4 @ T3 ) ) )
% 0.16/0.43 => ( ! [Tr12: dtree,Tr4: dtree,Ns1: set @ n,T3: t] :
% 0.16/0.43 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr4 ) )
% 0.16/0.43 => ( ( gram_L805317441_inFr2 @ Ns1 @ Tr12 @ T3 )
% 0.16/0.43 => ( ( P @ Ns1 @ Tr12 @ T3 )
% 0.16/0.43 => ( P @ ( insert @ n @ ( root @ Tr4 ) @ Ns1 ) @ Tr4 @ T3 ) ) ) )
% 0.16/0.43 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr2.inducts
% 0.16/0.43 thf(fact_123_wf__inj__on,axiom,
% 0.16/0.43 ! [Tr: dtree] :
% 0.16/0.43 ( ( gram_L864798063lle_wf @ Tr )
% 0.16/0.43 => ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % wf_inj_on
% 0.16/0.43 thf(fact_124_insert__absorb2,axiom,
% 0.16/0.43 ! [A: $tType,X2: A,A4: set @ A] :
% 0.16/0.43 ( ( insert @ A @ X2 @ ( insert @ A @ X2 @ A4 ) )
% 0.16/0.43 = ( insert @ A @ X2 @ A4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % insert_absorb2
% 0.16/0.43 thf(fact_125_insert__iff,axiom,
% 0.16/0.43 ! [A: $tType,A2: A,B2: A,A4: set @ A] :
% 0.16/0.43 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A4 ) )
% 0.16/0.43 = ( ( A2 = B2 )
% 0.16/0.43 | ( member @ A @ A2 @ A4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % insert_iff
% 0.16/0.43 thf(fact_126_insertCI,axiom,
% 0.16/0.43 ! [A: $tType,A2: A,B3: set @ A,B2: A] :
% 0.16/0.43 ( ( ~ ( member @ A @ A2 @ B3 )
% 0.16/0.43 => ( A2 = B2 ) )
% 0.16/0.43 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % insertCI
% 0.16/0.43 thf(fact_127_insert__image,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,X2: A,A4: set @ A,F: A > B] :
% 0.16/0.43 ( ( member @ A @ X2 @ A4 )
% 0.16/0.43 => ( ( insert @ B @ ( F @ X2 ) @ ( image @ A @ B @ F @ A4 ) )
% 0.16/0.43 = ( image @ A @ B @ F @ A4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % insert_image
% 0.16/0.43 thf(fact_128_image__insert,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,F: B > A,A2: B,B3: set @ B] :
% 0.16/0.43 ( ( image @ B @ A @ F @ ( insert @ B @ A2 @ B3 ) )
% 0.16/0.43 = ( insert @ A @ ( F @ A2 ) @ ( image @ B @ A @ F @ B3 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % image_insert
% 0.16/0.43 thf(fact_129_finite__insert,axiom,
% 0.16/0.43 ! [A: $tType,A2: A,A4: set @ A] :
% 0.16/0.43 ( ( finite_finite2 @ A @ ( insert @ A @ A2 @ A4 ) )
% 0.16/0.43 = ( finite_finite2 @ A @ A4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % finite_insert
% 0.16/0.43 thf(fact_130_finite_OinsertI,axiom,
% 0.16/0.43 ! [A: $tType,A4: set @ A,A2: A] :
% 0.16/0.43 ( ( finite_finite2 @ A @ A4 )
% 0.16/0.43 => ( finite_finite2 @ A @ ( insert @ A @ A2 @ A4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % finite.insertI
% 0.16/0.43 thf(fact_131_inj__on__image__iff,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,A4: set @ A,G: A > B,F: A > A] :
% 0.16/0.43 ( ! [X3: A] :
% 0.16/0.43 ( ( member @ A @ X3 @ A4 )
% 0.16/0.43 => ! [Xa: A] :
% 0.16/0.43 ( ( member @ A @ Xa @ A4 )
% 0.16/0.43 => ( ( ( G @ ( F @ X3 ) )
% 0.16/0.43 = ( G @ ( F @ Xa ) ) )
% 0.16/0.43 = ( ( G @ X3 )
% 0.16/0.43 = ( G @ Xa ) ) ) ) )
% 0.16/0.43 => ( ( inj_on @ A @ A @ F @ A4 )
% 0.16/0.43 => ( ( inj_on @ A @ B @ G @ ( image @ A @ A @ F @ A4 ) )
% 0.16/0.43 = ( inj_on @ A @ B @ G @ A4 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inj_on_image_iff
% 0.16/0.43 thf(fact_132_inj__img__insertE,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F: A > B,A4: set @ A,X2: B,B3: set @ B] :
% 0.16/0.43 ( ( inj_on @ A @ B @ F @ A4 )
% 0.16/0.43 => ( ~ ( member @ B @ X2 @ B3 )
% 0.16/0.43 => ( ( ( insert @ B @ X2 @ B3 )
% 0.16/0.43 = ( image @ A @ B @ F @ A4 ) )
% 0.16/0.43 => ~ ! [X6: A,A9: set @ A] :
% 0.16/0.43 ( ~ ( member @ A @ X6 @ A9 )
% 0.16/0.43 => ( ( A4
% 0.16/0.43 = ( insert @ A @ X6 @ A9 ) )
% 0.16/0.43 => ( ( X2
% 0.16/0.43 = ( F @ X6 ) )
% 0.16/0.43 => ( B3
% 0.16/0.43 != ( image @ A @ B @ F @ A9 ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inj_img_insertE
% 0.16/0.43 thf(fact_133_inj__on__id,axiom,
% 0.16/0.43 ! [A: $tType,A4: set @ A] : ( inj_on @ A @ A @ ( id @ A ) @ A4 ) ).
% 0.16/0.43
% 0.16/0.43 % inj_on_id
% 0.16/0.43 thf(fact_134_mk__disjoint__insert,axiom,
% 0.16/0.43 ! [A: $tType,A2: A,A4: set @ A] :
% 0.16/0.43 ( ( member @ A @ A2 @ A4 )
% 0.16/0.43 => ? [B8: set @ A] :
% 0.16/0.43 ( ( A4
% 0.16/0.43 = ( insert @ A @ A2 @ B8 ) )
% 0.16/0.43 & ~ ( member @ A @ A2 @ B8 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % mk_disjoint_insert
% 0.16/0.43 thf(fact_135_inj__on__inverseI,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,A4: set @ A,G: B > A,F: A > B] :
% 0.16/0.43 ( ! [X3: A] :
% 0.16/0.43 ( ( member @ A @ X3 @ A4 )
% 0.16/0.43 => ( ( G @ ( F @ X3 ) )
% 0.16/0.43 = X3 ) )
% 0.16/0.43 => ( inj_on @ A @ B @ F @ A4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % inj_on_inverseI
% 0.16/0.43 thf(fact_136_insert__commute,axiom,
% 0.16/0.43 ! [A: $tType,X2: A,Y: A,A4: set @ A] :
% 0.16/0.43 ( ( insert @ A @ X2 @ ( insert @ A @ Y @ A4 ) )
% 0.16/0.43 = ( insert @ A @ Y @ ( insert @ A @ X2 @ A4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % insert_commute
% 0.16/0.43 thf(fact_137_inj__on__contraD,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F: A > B,A4: set @ A,X2: A,Y: A] :
% 0.16/0.43 ( ( inj_on @ A @ B @ F @ A4 )
% 0.16/0.43 => ( ( X2 != Y )
% 0.16/0.43 => ( ( member @ A @ X2 @ A4 )
% 0.16/0.43 => ( ( member @ A @ Y @ A4 )
% 0.16/0.43 => ( ( F @ X2 )
% 0.16/0.43 != ( F @ Y ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inj_on_contraD
% 0.16/0.43 thf(fact_138_insert__eq__iff,axiom,
% 0.16/0.43 ! [A: $tType,A2: A,A4: set @ A,B2: A,B3: set @ A] :
% 0.16/0.43 ( ~ ( member @ A @ A2 @ A4 )
% 0.16/0.43 => ( ~ ( member @ A @ B2 @ B3 )
% 0.16/0.43 => ( ( ( insert @ A @ A2 @ A4 )
% 0.16/0.43 = ( insert @ A @ B2 @ B3 ) )
% 0.16/0.43 = ( ( ( A2 = B2 )
% 0.16/0.43 => ( A4 = B3 ) )
% 0.16/0.43 & ( ( A2 != B2 )
% 0.16/0.43 => ? [C3: set @ A] :
% 0.16/0.43 ( ( A4
% 0.16/0.43 = ( insert @ A @ B2 @ C3 ) )
% 0.16/0.43 & ~ ( member @ A @ B2 @ C3 )
% 0.16/0.43 & ( B3
% 0.16/0.43 = ( insert @ A @ A2 @ C3 ) )
% 0.16/0.43 & ~ ( member @ A @ A2 @ C3 ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % insert_eq_iff
% 0.16/0.43 thf(fact_139_insert__absorb,axiom,
% 0.16/0.43 ! [A: $tType,A2: A,A4: set @ A] :
% 0.16/0.43 ( ( member @ A @ A2 @ A4 )
% 0.16/0.43 => ( ( insert @ A @ A2 @ A4 )
% 0.16/0.43 = A4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % insert_absorb
% 0.16/0.43 thf(fact_140_inj__on__eq__iff,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F: A > B,A4: set @ A,X2: A,Y: A] :
% 0.16/0.43 ( ( inj_on @ A @ B @ F @ A4 )
% 0.16/0.43 => ( ( member @ A @ X2 @ A4 )
% 0.16/0.43 => ( ( member @ A @ Y @ A4 )
% 0.16/0.43 => ( ( ( F @ X2 )
% 0.16/0.43 = ( F @ Y ) )
% 0.16/0.43 = ( X2 = Y ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inj_on_eq_iff
% 0.16/0.43 thf(fact_141_insert__ident,axiom,
% 0.16/0.43 ! [A: $tType,X2: A,A4: set @ A,B3: set @ A] :
% 0.16/0.43 ( ~ ( member @ A @ X2 @ A4 )
% 0.16/0.43 => ( ~ ( member @ A @ X2 @ B3 )
% 0.16/0.43 => ( ( ( insert @ A @ X2 @ A4 )
% 0.16/0.43 = ( insert @ A @ X2 @ B3 ) )
% 0.16/0.43 = ( A4 = B3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % insert_ident
% 0.16/0.43 thf(fact_142_inj__on__cong,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,A4: set @ A,F: A > B,G: A > B] :
% 0.16/0.43 ( ! [A7: A] :
% 0.16/0.43 ( ( member @ A @ A7 @ A4 )
% 0.16/0.43 => ( ( F @ A7 )
% 0.16/0.43 = ( G @ A7 ) ) )
% 0.16/0.43 => ( ( inj_on @ A @ B @ F @ A4 )
% 0.16/0.43 = ( inj_on @ A @ B @ G @ A4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inj_on_cong
% 0.16/0.43 thf(fact_143_Set_Oset__insert,axiom,
% 0.16/0.43 ! [A: $tType,X2: A,A4: set @ A] :
% 0.16/0.43 ( ( member @ A @ X2 @ A4 )
% 0.16/0.43 => ~ ! [B8: set @ A] :
% 0.16/0.43 ( ( A4
% 0.16/0.43 = ( insert @ A @ X2 @ B8 ) )
% 0.16/0.43 => ( member @ A @ X2 @ B8 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Set.set_insert
% 0.16/0.43 thf(fact_144_inj__on__def,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType] :
% 0.16/0.43 ( ( inj_on @ A @ B )
% 0.16/0.43 = ( ^ [F6: A > B,A8: set @ A] :
% 0.16/0.43 ! [X: A] :
% 0.16/0.43 ( ( member @ A @ X @ A8 )
% 0.16/0.43 => ! [Y3: A] :
% 0.16/0.43 ( ( member @ A @ Y3 @ A8 )
% 0.16/0.43 => ( ( ( F6 @ X )
% 0.16/0.43 = ( F6 @ Y3 ) )
% 0.16/0.43 => ( X = Y3 ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inj_on_def
% 0.16/0.43 thf(fact_145_insertI2,axiom,
% 0.16/0.43 ! [A: $tType,A2: A,B3: set @ A,B2: A] :
% 0.16/0.43 ( ( member @ A @ A2 @ B3 )
% 0.16/0.43 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % insertI2
% 0.16/0.43 thf(fact_146_insertI1,axiom,
% 0.16/0.43 ! [A: $tType,A2: A,B3: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B3 ) ) ).
% 0.16/0.43
% 0.16/0.43 % insertI1
% 0.16/0.43 thf(fact_147_insertE,axiom,
% 0.16/0.43 ! [A: $tType,A2: A,B2: A,A4: set @ A] :
% 0.16/0.43 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A4 ) )
% 0.16/0.43 => ( ( A2 != B2 )
% 0.16/0.43 => ( member @ A @ A2 @ A4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % insertE
% 0.16/0.43 thf(fact_148_inj__onI,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,A4: set @ A,F: A > B] :
% 0.16/0.43 ( ! [X3: A,Y2: A] :
% 0.16/0.43 ( ( member @ A @ X3 @ A4 )
% 0.16/0.43 => ( ( member @ A @ Y2 @ A4 )
% 0.16/0.43 => ( ( ( F @ X3 )
% 0.16/0.43 = ( F @ Y2 ) )
% 0.16/0.43 => ( X3 = Y2 ) ) ) )
% 0.16/0.43 => ( inj_on @ A @ B @ F @ A4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % inj_onI
% 0.16/0.43 thf(fact_149_inj__onD,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F: A > B,A4: set @ A,X2: A,Y: A] :
% 0.16/0.43 ( ( inj_on @ A @ B @ F @ A4 )
% 0.16/0.43 => ( ( ( F @ X2 )
% 0.16/0.43 = ( F @ Y ) )
% 0.16/0.43 => ( ( member @ A @ X2 @ A4 )
% 0.16/0.43 => ( ( member @ A @ Y @ A4 )
% 0.16/0.43 => ( X2 = Y ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inj_onD
% 0.16/0.43 thf(fact_150_finite__imageD,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,F: B > A,A4: set @ B] :
% 0.16/0.43 ( ( finite_finite2 @ A @ ( image @ B @ A @ F @ A4 ) )
% 0.16/0.43 => ( ( inj_on @ B @ A @ F @ A4 )
% 0.16/0.43 => ( finite_finite2 @ B @ A4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % finite_imageD
% 0.16/0.43 thf(fact_151_finite__image__iff,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F: A > B,A4: set @ A] :
% 0.16/0.43 ( ( inj_on @ A @ B @ F @ A4 )
% 0.16/0.43 => ( ( finite_finite2 @ B @ ( image @ A @ B @ F @ A4 ) )
% 0.16/0.43 = ( finite_finite2 @ A @ A4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % finite_image_iff
% 0.16/0.43 thf(fact_152_inFr__Ind__minus,axiom,
% 0.16/0.43 ! [Ns13: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 0.16/0.43 ( ( gram_L1333338417e_inFr @ Ns13 @ Tr1 @ T2 )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.16/0.43 => ( gram_L1333338417e_inFr @ ( insert @ n @ ( root @ Tr ) @ Ns13 ) @ Tr @ T2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr_Ind_minus
% 0.16/0.43 thf(fact_153_inFr2_OInd,axiom,
% 0.16/0.43 ! [Tr1: dtree,Tr: dtree,Ns13: set @ n,T2: t] :
% 0.16/0.43 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.16/0.43 => ( ( gram_L805317441_inFr2 @ Ns13 @ Tr1 @ T2 )
% 0.16/0.43 => ( gram_L805317441_inFr2 @ ( insert @ n @ ( root @ Tr ) @ Ns13 ) @ Tr @ T2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr2.Ind
% 0.16/0.43 thf(fact_154_wf__subtr__inj__on,axiom,
% 0.16/0.43 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 0.16/0.43 ( ( gram_L864798063lle_wf @ Tr1 )
% 0.16/0.43 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.16/0.43 => ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % wf_subtr_inj_on
% 0.16/0.43 thf(fact_155_wf_Ocases,axiom,
% 0.16/0.43 ! [A2: dtree] :
% 0.16/0.43 ( ( gram_L864798063lle_wf @ A2 )
% 0.16/0.43 => ~ ( ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ A2 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ A2 ) ) ) @ gram_L1451583632elle_P )
% 0.16/0.43 => ( ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ A2 ) ) )
% 0.16/0.43 => ~ ! [Tr6: dtree] :
% 0.16/0.43 ( ( member @ dtree @ Tr6 @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ A2 ) ) )
% 0.16/0.43 => ( gram_L864798063lle_wf @ Tr6 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % wf.cases
% 0.16/0.43 thf(fact_156_wf_Osimps,axiom,
% 0.16/0.43 ( gram_L864798063lle_wf
% 0.16/0.43 = ( ^ [A10: dtree] :
% 0.16/0.43 ? [Tr3: dtree] :
% 0.16/0.43 ( ( A10 = Tr3 )
% 0.16/0.43 & ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ Tr3 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr3 ) ) ) @ gram_L1451583632elle_P )
% 0.16/0.43 & ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr3 ) ) )
% 0.16/0.43 & ! [X: dtree] :
% 0.16/0.43 ( ( member @ dtree @ X @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr3 ) ) )
% 0.16/0.43 => ( gram_L864798063lle_wf @ X ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % wf.simps
% 0.16/0.43 thf(fact_157_wf__coind,axiom,
% 0.16/0.43 ! [Phi: dtree > $o,Tr: dtree] :
% 0.16/0.43 ( ( Phi @ Tr )
% 0.16/0.43 => ( ! [Tr4: dtree] :
% 0.16/0.43 ( ( Phi @ Tr4 )
% 0.16/0.43 => ( ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ Tr4 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr4 ) ) ) @ gram_L1451583632elle_P )
% 0.16/0.43 & ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr4 ) ) )
% 0.16/0.43 & ! [X3: dtree] :
% 0.16/0.43 ( ( member @ dtree @ X3 @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr4 ) ) )
% 0.16/0.43 => ( ( Phi @ X3 )
% 0.16/0.43 | ( gram_L864798063lle_wf @ X3 ) ) ) ) )
% 0.16/0.43 => ( gram_L864798063lle_wf @ Tr ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % wf_coind
% 0.16/0.43 thf(fact_158_inj__Inr,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,A4: set @ A] : ( inj_on @ A @ ( sum_sum @ B @ A ) @ ( sum_Inr @ A @ B ) @ A4 ) ).
% 0.16/0.43
% 0.16/0.43 % inj_Inr
% 0.16/0.43 thf(fact_159_inj__Inl,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,A4: set @ A] : ( inj_on @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ A4 ) ).
% 0.16/0.43
% 0.16/0.43 % inj_Inl
% 0.16/0.43 thf(fact_160_subtr__trans,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr32: dtree] :
% 0.16/0.43 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.16/0.43 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr32 )
% 0.16/0.43 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr32 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr_trans
% 0.16/0.43 thf(fact_161_used,axiom,
% 0.16/0.43 ! [N4: n] :
% 0.16/0.43 ? [Tns2: set @ ( sum_sum @ t @ n )] : ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ N4 @ Tns2 ) @ gram_L1451583632elle_P ) ).
% 0.16/0.43
% 0.16/0.43 % used
% 0.16/0.43 thf(fact_162_finite__in__P,axiom,
% 0.16/0.43 ! [N4: n,Tns: set @ ( sum_sum @ t @ n )] :
% 0.16/0.43 ( ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ N4 @ Tns ) @ gram_L1451583632elle_P )
% 0.16/0.43 => ( finite_finite2 @ ( sum_sum @ t @ n ) @ Tns ) ) ).
% 0.16/0.43
% 0.16/0.43 % finite_in_P
% 0.16/0.43 thf(fact_163_subtr__rootR__in,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.16/0.43 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.16/0.43 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr_rootR_in
% 0.16/0.43 thf(fact_164_subtr__rootL__in,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.16/0.43 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.16/0.43 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr_rootL_in
% 0.16/0.43 thf(fact_165_subtr_ORefl,axiom,
% 0.16/0.43 ! [Tr: dtree,Ns: set @ n] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.43 => ( gram_L716654942_subtr @ Ns @ Tr @ Tr ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr.Refl
% 0.16/0.43 thf(fact_166_wf__subtr,axiom,
% 0.16/0.43 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 0.16/0.43 ( ( gram_L864798063lle_wf @ Tr1 )
% 0.16/0.43 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.16/0.43 => ( gram_L864798063lle_wf @ Tr ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % wf_subtr
% 0.16/0.43 thf(fact_167_subtr__inFr,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr: dtree,T2: t,Tr1: dtree] :
% 0.16/0.43 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.16/0.43 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.16/0.43 => ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr_inFr
% 0.16/0.43 thf(fact_168_wf__subtr__P,axiom,
% 0.16/0.43 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 0.16/0.43 ( ( gram_L864798063lle_wf @ Tr1 )
% 0.16/0.43 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.16/0.43 => ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ Tr ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) ) @ gram_L1451583632elle_P ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % wf_subtr_P
% 0.16/0.43 thf(fact_169_subtr__inductL,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Phi: ( set @ n ) > dtree > dtree > $o] :
% 0.16/0.43 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.16/0.43 => ( ! [Ns2: set @ n,Tr4: dtree] : ( Phi @ Ns2 @ Tr4 @ Tr4 )
% 0.16/0.43 => ( ! [Ns2: set @ n,Tr12: dtree,Tr23: dtree,Tr33: dtree] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr12 ) @ Ns2 )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 0.16/0.43 => ( ( gram_L716654942_subtr @ Ns2 @ Tr23 @ Tr33 )
% 0.16/0.43 => ( ( Phi @ Ns2 @ Tr23 @ Tr33 )
% 0.16/0.43 => ( Phi @ Ns2 @ Tr12 @ Tr33 ) ) ) ) )
% 0.16/0.43 => ( Phi @ Ns @ Tr1 @ Tr22 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr_inductL
% 0.16/0.43 thf(fact_170_subtr_Oinducts,axiom,
% 0.16/0.43 ! [X1: set @ n,X22: dtree,X32: dtree,P: ( set @ n ) > dtree > dtree > $o] :
% 0.16/0.43 ( ( gram_L716654942_subtr @ X1 @ X22 @ X32 )
% 0.16/0.43 => ( ! [Tr4: dtree,Ns2: set @ n] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.16/0.43 => ( P @ Ns2 @ Tr4 @ Tr4 ) )
% 0.16/0.43 => ( ! [Tr33: dtree,Ns2: set @ n,Tr12: dtree,Tr23: dtree] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr33 ) @ Ns2 )
% 0.16/0.43 => ( ( gram_L716654942_subtr @ Ns2 @ Tr12 @ Tr23 )
% 0.16/0.43 => ( ( P @ Ns2 @ Tr12 @ Tr23 )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ Tr33 ) )
% 0.16/0.43 => ( P @ Ns2 @ Tr12 @ Tr33 ) ) ) ) )
% 0.16/0.43 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr.inducts
% 0.16/0.43 thf(fact_171_subtr__StepL,axiom,
% 0.16/0.43 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr32: dtree] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 0.16/0.43 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr32 )
% 0.16/0.43 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr32 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr_StepL
% 0.16/0.43 thf(fact_172_subtr_Osimps,axiom,
% 0.16/0.43 ( gram_L716654942_subtr
% 0.16/0.43 = ( ^ [A12: set @ n,A23: dtree,A33: dtree] :
% 0.16/0.43 ( ? [Tr3: dtree,Ns3: set @ n] :
% 0.16/0.43 ( ( A12 = Ns3 )
% 0.16/0.43 & ( A23 = Tr3 )
% 0.16/0.43 & ( A33 = Tr3 )
% 0.16/0.43 & ( member @ n @ ( root @ Tr3 ) @ Ns3 ) )
% 0.16/0.43 | ? [Tr34: dtree,Ns3: set @ n,Tr13: dtree,Tr24: dtree] :
% 0.16/0.43 ( ( A12 = Ns3 )
% 0.16/0.43 & ( A23 = Tr13 )
% 0.16/0.43 & ( A33 = Tr34 )
% 0.16/0.43 & ( member @ n @ ( root @ Tr34 ) @ Ns3 )
% 0.16/0.43 & ( gram_L716654942_subtr @ Ns3 @ Tr13 @ Tr24 )
% 0.16/0.43 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr24 ) @ ( cont @ Tr34 ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr.simps
% 0.16/0.43 thf(fact_173_subtr_Ocases,axiom,
% 0.16/0.43 ! [A1: set @ n,A22: dtree,A32: dtree] :
% 0.16/0.43 ( ( gram_L716654942_subtr @ A1 @ A22 @ A32 )
% 0.16/0.43 => ( ( ( A32 = A22 )
% 0.16/0.43 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.16/0.43 => ~ ( ( member @ n @ ( root @ A32 ) @ A1 )
% 0.16/0.43 => ! [Tr23: dtree] :
% 0.16/0.43 ( ( gram_L716654942_subtr @ A1 @ A22 @ Tr23 )
% 0.16/0.43 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ A32 ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr.cases
% 0.16/0.43 thf(fact_174_subtr_OStep,axiom,
% 0.16/0.43 ! [Tr32: dtree,Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr32 ) @ Ns )
% 0.16/0.43 => ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr32 ) )
% 0.16/0.43 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr32 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr.Step
% 0.16/0.43 thf(fact_175_inFr__subtr,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.16/0.43 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.16/0.43 => ? [Tr7: dtree] :
% 0.16/0.43 ( ( gram_L716654942_subtr @ Ns @ Tr7 @ Tr )
% 0.16/0.43 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr7 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inFr_subtr
% 0.16/0.43 thf(fact_176_wf__P,axiom,
% 0.16/0.43 ! [Tr: dtree] :
% 0.16/0.43 ( ( gram_L864798063lle_wf @ Tr )
% 0.16/0.43 => ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ Tr ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) ) @ gram_L1451583632elle_P ) ) ).
% 0.16/0.43
% 0.16/0.43 % wf_P
% 0.16/0.43 thf(fact_177_wf__raw__coind,axiom,
% 0.16/0.43 ! [Phi: dtree > $o,Tr: dtree] :
% 0.16/0.43 ( ( Phi @ Tr )
% 0.16/0.43 => ( ! [Tr4: dtree] :
% 0.16/0.43 ( ( Phi @ Tr4 )
% 0.16/0.43 => ( ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ Tr4 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr4 ) ) ) @ gram_L1451583632elle_P )
% 0.16/0.43 & ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr4 ) ) )
% 0.16/0.43 & ! [X3: dtree] :
% 0.16/0.43 ( ( member @ dtree @ X3 @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr4 ) ) )
% 0.16/0.43 => ( Phi @ X3 ) ) ) )
% 0.16/0.43 => ( gram_L864798063lle_wf @ Tr ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % wf_raw_coind
% 0.16/0.43 thf(fact_178_wf_Ocoinduct,axiom,
% 0.16/0.43 ! [X7: dtree > $o,X2: dtree] :
% 0.16/0.43 ( ( X7 @ X2 )
% 0.16/0.43 => ( ! [X3: dtree] :
% 0.16/0.43 ( ( X7 @ X3 )
% 0.16/0.43 => ? [Tr8: dtree] :
% 0.16/0.43 ( ( X3 = Tr8 )
% 0.16/0.43 & ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ Tr8 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr8 ) ) ) @ gram_L1451583632elle_P )
% 0.16/0.43 & ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr8 ) ) )
% 0.16/0.43 & ! [Xa: dtree] :
% 0.16/0.43 ( ( member @ dtree @ Xa @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr8 ) ) )
% 0.16/0.43 => ( ( X7 @ Xa )
% 0.16/0.43 | ( gram_L864798063lle_wf @ Xa ) ) ) ) )
% 0.16/0.43 => ( gram_L864798063lle_wf @ X2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % wf.coinduct
% 0.16/0.43 thf(fact_179_wf_Ointros,axiom,
% 0.16/0.43 ! [Tr: dtree] :
% 0.16/0.43 ( ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ Tr ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) ) @ gram_L1451583632elle_P )
% 0.16/0.43 => ( ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr ) ) )
% 0.16/0.43 => ( ! [Tr7: dtree] :
% 0.16/0.43 ( ( member @ dtree @ Tr7 @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr ) ) )
% 0.16/0.43 => ( gram_L864798063lle_wf @ Tr7 ) )
% 0.16/0.43 => ( gram_L864798063lle_wf @ Tr ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % wf.intros
% 0.16/0.43 thf(fact_180_S__P,axiom,
% 0.16/0.43 ! [N4: n] : ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ N4 @ ( gram_L1451583635elle_S @ N4 ) ) @ gram_L1451583632elle_P ) ).
% 0.16/0.43
% 0.16/0.43 % S_P
% 0.16/0.43 thf(fact_181_inItr_Oinducts,axiom,
% 0.16/0.43 ! [X1: set @ n,X22: dtree,X32: n,P: ( set @ n ) > dtree > n > $o] :
% 0.16/0.43 ( ( gram_L830233218_inItr @ X1 @ X22 @ X32 )
% 0.16/0.43 => ( ! [Tr4: dtree,Ns2: set @ n] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.16/0.43 => ( P @ Ns2 @ Tr4 @ ( root @ Tr4 ) ) )
% 0.16/0.43 => ( ! [Tr4: dtree,Ns2: set @ n,Tr12: dtree,N3: n] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr4 ) )
% 0.16/0.43 => ( ( gram_L830233218_inItr @ Ns2 @ Tr12 @ N3 )
% 0.16/0.43 => ( ( P @ Ns2 @ Tr12 @ N3 )
% 0.16/0.43 => ( P @ Ns2 @ Tr4 @ N3 ) ) ) ) )
% 0.16/0.43 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inItr.inducts
% 0.16/0.43 thf(fact_182_inItr_Osimps,axiom,
% 0.16/0.43 ( gram_L830233218_inItr
% 0.16/0.43 = ( ^ [A12: set @ n,A23: dtree,A33: n] :
% 0.16/0.43 ( ? [Tr3: dtree,Ns3: set @ n] :
% 0.16/0.43 ( ( A12 = Ns3 )
% 0.16/0.43 & ( A23 = Tr3 )
% 0.16/0.43 & ( A33
% 0.16/0.43 = ( root @ Tr3 ) )
% 0.16/0.43 & ( member @ n @ ( root @ Tr3 ) @ Ns3 ) )
% 0.16/0.43 | ? [Tr3: dtree,Ns3: set @ n,Tr13: dtree,N2: n] :
% 0.16/0.43 ( ( A12 = Ns3 )
% 0.16/0.43 & ( A23 = Tr3 )
% 0.16/0.43 & ( A33 = N2 )
% 0.16/0.43 & ( member @ n @ ( root @ Tr3 ) @ Ns3 )
% 0.16/0.43 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr3 ) )
% 0.16/0.43 & ( gram_L830233218_inItr @ Ns3 @ Tr13 @ N2 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inItr.simps
% 0.16/0.43 thf(fact_183_finite__S,axiom,
% 0.16/0.43 ! [N4: n] : ( finite_finite2 @ ( sum_sum @ t @ n ) @ ( gram_L1451583635elle_S @ N4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % finite_S
% 0.16/0.43 thf(fact_184_inItr_OBase,axiom,
% 0.16/0.43 ! [Tr: dtree,Ns: set @ n] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.43 => ( gram_L830233218_inItr @ Ns @ Tr @ ( root @ Tr ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inItr.Base
% 0.16/0.43 thf(fact_185_inItr__root__in,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr: dtree,N4: n] :
% 0.16/0.43 ( ( gram_L830233218_inItr @ Ns @ Tr @ N4 )
% 0.16/0.43 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.16/0.43
% 0.16/0.43 % inItr_root_in
% 0.16/0.43 thf(fact_186_subtr__inItr,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr: dtree,N4: n,Tr1: dtree] :
% 0.16/0.43 ( ( gram_L830233218_inItr @ Ns @ Tr @ N4 )
% 0.16/0.43 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.16/0.43 => ( gram_L830233218_inItr @ Ns @ Tr1 @ N4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr_inItr
% 0.16/0.43 thf(fact_187_inItr__subtr,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr: dtree,N4: n] :
% 0.16/0.43 ( ( gram_L830233218_inItr @ Ns @ Tr @ N4 )
% 0.16/0.43 => ? [Tr7: dtree] :
% 0.16/0.43 ( ( gram_L716654942_subtr @ Ns @ Tr7 @ Tr )
% 0.16/0.43 & ( ( root @ Tr7 )
% 0.16/0.43 = N4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inItr_subtr
% 0.16/0.43 thf(fact_188_inItr_OInd,axiom,
% 0.16/0.43 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,N4: n] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.16/0.43 => ( ( gram_L830233218_inItr @ Ns @ Tr1 @ N4 )
% 0.16/0.43 => ( gram_L830233218_inItr @ Ns @ Tr @ N4 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inItr.Ind
% 0.16/0.43 thf(fact_189_inItr_Ocases,axiom,
% 0.16/0.43 ! [A1: set @ n,A22: dtree,A32: n] :
% 0.16/0.43 ( ( gram_L830233218_inItr @ A1 @ A22 @ A32 )
% 0.16/0.43 => ( ( ( A32
% 0.16/0.43 = ( root @ A22 ) )
% 0.16/0.43 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.16/0.43 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.16/0.43 => ! [Tr12: dtree] :
% 0.16/0.43 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A22 ) )
% 0.16/0.43 => ~ ( gram_L830233218_inItr @ A1 @ Tr12 @ A32 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inItr.cases
% 0.16/0.43 thf(fact_190_cont__deftr,axiom,
% 0.16/0.43 ! [N4: n] :
% 0.16/0.43 ( ( cont @ ( gram_L1231612515_deftr @ N4 ) )
% 0.16/0.43 = ( image @ ( sum_sum @ t @ n ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ n @ dtree @ ( id @ t ) @ gram_L1231612515_deftr ) @ ( gram_L1451583635elle_S @ N4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % cont_deftr
% 0.16/0.43 thf(fact_191_subtr2_OStep,axiom,
% 0.16/0.43 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr32: dtree] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 0.16/0.43 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr32 )
% 0.16/0.43 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr32 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr2.Step
% 0.16/0.43 thf(fact_192_subtr2_Ocases,axiom,
% 0.16/0.43 ! [A1: set @ n,A22: dtree,A32: dtree] :
% 0.16/0.43 ( ( gram_L1283001940subtr2 @ A1 @ A22 @ A32 )
% 0.16/0.43 => ( ( ( A32 = A22 )
% 0.16/0.43 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.16/0.43 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.16/0.43 => ! [Tr23: dtree] :
% 0.16/0.43 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A22 ) @ ( cont @ Tr23 ) )
% 0.16/0.43 => ~ ( gram_L1283001940subtr2 @ A1 @ Tr23 @ A32 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr2.cases
% 0.16/0.43 thf(fact_193_root__deftr,axiom,
% 0.16/0.43 ! [N4: n] :
% 0.16/0.43 ( ( root @ ( gram_L1231612515_deftr @ N4 ) )
% 0.16/0.43 = N4 ) ).
% 0.16/0.43
% 0.16/0.43 % root_deftr
% 0.16/0.43 thf(fact_194_subtr__subtr2,axiom,
% 0.16/0.43 gram_L716654942_subtr = gram_L1283001940subtr2 ).
% 0.16/0.43
% 0.16/0.43 % subtr_subtr2
% 0.16/0.43 thf(fact_195_subtr2__trans,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr32: dtree] :
% 0.16/0.43 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.16/0.43 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr32 )
% 0.16/0.43 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr32 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr2_trans
% 0.16/0.43 thf(fact_196_subtr2_ORefl,axiom,
% 0.16/0.43 ! [Tr: dtree,Ns: set @ n] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.16/0.43 => ( gram_L1283001940subtr2 @ Ns @ Tr @ Tr ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr2.Refl
% 0.16/0.43 thf(fact_197_subtr2__rootL__in,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.16/0.43 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.16/0.43 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr2_rootL_in
% 0.16/0.43 thf(fact_198_subtr2__rootR__in,axiom,
% 0.16/0.43 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.16/0.43 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.16/0.43 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr2_rootR_in
% 0.16/0.43 thf(fact_199_wf__deftr,axiom,
% 0.16/0.43 ! [N4: n] : ( gram_L864798063lle_wf @ ( gram_L1231612515_deftr @ N4 ) ) ).
% 0.16/0.43
% 0.16/0.43 % wf_deftr
% 0.16/0.43 thf(fact_200_deftr__def,axiom,
% 0.16/0.43 ( gram_L1231612515_deftr
% 0.16/0.43 = ( unfold @ n @ ( id @ n ) @ gram_L1451583635elle_S ) ) ).
% 0.16/0.43
% 0.16/0.43 % deftr_def
% 0.16/0.43 thf(fact_201_subtr2_Oinducts,axiom,
% 0.16/0.43 ! [X1: set @ n,X22: dtree,X32: dtree,P: ( set @ n ) > dtree > dtree > $o] :
% 0.16/0.43 ( ( gram_L1283001940subtr2 @ X1 @ X22 @ X32 )
% 0.16/0.43 => ( ! [Tr4: dtree,Ns2: set @ n] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.16/0.43 => ( P @ Ns2 @ Tr4 @ Tr4 ) )
% 0.16/0.43 => ( ! [Tr12: dtree,Ns2: set @ n,Tr23: dtree,Tr33: dtree] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr12 ) @ Ns2 )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 0.16/0.43 => ( ( gram_L1283001940subtr2 @ Ns2 @ Tr23 @ Tr33 )
% 0.16/0.43 => ( ( P @ Ns2 @ Tr23 @ Tr33 )
% 0.16/0.43 => ( P @ Ns2 @ Tr12 @ Tr33 ) ) ) ) )
% 0.16/0.43 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr2.inducts
% 0.16/0.43 thf(fact_202_subtr2__StepR,axiom,
% 0.16/0.43 ! [Tr32: dtree,Ns: set @ n,Tr22: dtree,Tr1: dtree] :
% 0.16/0.43 ( ( member @ n @ ( root @ Tr32 ) @ Ns )
% 0.16/0.43 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr32 ) )
% 0.16/0.43 => ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.16/0.43 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr32 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr2_StepR
% 0.16/0.43 thf(fact_203_subtr2_Osimps,axiom,
% 0.16/0.43 ( gram_L1283001940subtr2
% 0.16/0.43 = ( ^ [A12: set @ n,A23: dtree,A33: dtree] :
% 0.16/0.43 ( ? [Tr3: dtree,Ns3: set @ n] :
% 0.16/0.43 ( ( A12 = Ns3 )
% 0.16/0.43 & ( A23 = Tr3 )
% 0.16/0.43 & ( A33 = Tr3 )
% 0.16/0.43 & ( member @ n @ ( root @ Tr3 ) @ Ns3 ) )
% 0.16/0.43 | ? [Tr13: dtree,Ns3: set @ n,Tr24: dtree,Tr34: dtree] :
% 0.16/0.43 ( ( A12 = Ns3 )
% 0.16/0.43 & ( A23 = Tr13 )
% 0.16/0.43 & ( A33 = Tr34 )
% 0.16/0.43 & ( member @ n @ ( root @ Tr13 ) @ Ns3 )
% 0.16/0.43 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr24 ) )
% 0.16/0.43 & ( gram_L1283001940subtr2 @ Ns3 @ Tr24 @ Tr34 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % subtr2.simps
% 0.16/0.43 thf(fact_204_root__o__subst,axiom,
% 0.16/0.43 ( ( comp @ dtree @ n @ dtree @ root @ ( gram_L1004374585hsubst @ tr0 ) )
% 0.16/0.43 = root ) ).
% 0.16/0.43
% 0.16/0.43 % root_o_subst
% 0.16/0.43 thf(fact_205_inf__img__fin__dom,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F: B > A,A4: set @ B] :
% 0.16/0.43 ( ( finite_finite2 @ A @ ( image @ B @ A @ F @ A4 ) )
% 0.16/0.43 => ( ~ ( finite_finite2 @ B @ A4 )
% 0.16/0.43 => ? [X3: A] :
% 0.16/0.43 ( ( member @ A @ X3 @ ( image @ B @ A @ F @ A4 ) )
% 0.16/0.43 & ~ ( finite_finite2 @ B @ ( vimage @ B @ A @ F @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inf_img_fin_dom
% 0.16/0.43 thf(fact_206_empty__Collect__eq,axiom,
% 0.16/0.43 ! [A: $tType,P: A > $o] :
% 0.16/0.43 ( ( ( bot_bot @ ( set @ A ) )
% 0.16/0.43 = ( collect @ A @ P ) )
% 0.16/0.43 = ( ! [X: A] :
% 0.16/0.43 ~ ( P @ X ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % empty_Collect_eq
% 0.16/0.43 thf(fact_207_Collect__empty__eq,axiom,
% 0.16/0.43 ! [A: $tType,P: A > $o] :
% 0.16/0.43 ( ( ( collect @ A @ P )
% 0.16/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.16/0.43 = ( ! [X: A] :
% 0.16/0.43 ~ ( P @ X ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Collect_empty_eq
% 0.16/0.43 thf(fact_208_all__not__in__conv,axiom,
% 0.16/0.43 ! [A: $tType,A4: set @ A] :
% 0.16/0.43 ( ( ! [X: A] :
% 0.16/0.43 ~ ( member @ A @ X @ A4 ) )
% 0.16/0.43 = ( A4
% 0.16/0.43 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % all_not_in_conv
% 0.16/0.43 thf(fact_209_empty__iff,axiom,
% 0.16/0.43 ! [A: $tType,C4: A] :
% 0.16/0.43 ~ ( member @ A @ C4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % empty_iff
% 0.16/0.43 thf(fact_210_comp__apply,axiom,
% 0.16/0.43 ! [C: $tType,A: $tType,B: $tType] :
% 0.16/0.43 ( ( comp @ B @ A @ C )
% 0.16/0.43 = ( ^ [F6: B > A,G3: C > B,X: C] : ( F6 @ ( G3 @ X ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % comp_apply
% 0.16/0.43 thf(fact_211_image__is__empty,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,F: B > A,A4: set @ B] :
% 0.16/0.43 ( ( ( image @ B @ A @ F @ A4 )
% 0.16/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.16/0.43 = ( A4
% 0.16/0.43 = ( bot_bot @ ( set @ B ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % image_is_empty
% 0.16/0.43 thf(fact_212_empty__is__image,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,F: B > A,A4: set @ B] :
% 0.16/0.43 ( ( ( bot_bot @ ( set @ A ) )
% 0.16/0.43 = ( image @ B @ A @ F @ A4 ) )
% 0.16/0.43 = ( A4
% 0.16/0.43 = ( bot_bot @ ( set @ B ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % empty_is_image
% 0.16/0.43 thf(fact_213_image__empty,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F: B > A] :
% 0.16/0.43 ( ( image @ B @ A @ F @ ( bot_bot @ ( set @ B ) ) )
% 0.16/0.43 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % image_empty
% 0.16/0.43 thf(fact_214_singletonI,axiom,
% 0.16/0.43 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % singletonI
% 0.16/0.43 thf(fact_215_inj__on__empty,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F: A > B] : ( inj_on @ A @ B @ F @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % inj_on_empty
% 0.16/0.43 thf(fact_216_fun_Omap__id,axiom,
% 0.16/0.43 ! [A: $tType,D: $tType,T2: D > A] :
% 0.16/0.43 ( ( comp @ A @ A @ D @ ( id @ A ) @ T2 )
% 0.16/0.43 = T2 ) ).
% 0.16/0.43
% 0.16/0.43 % fun.map_id
% 0.16/0.43 thf(fact_217_comp__id,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F: A > B] :
% 0.16/0.43 ( ( comp @ A @ B @ A @ F @ ( id @ A ) )
% 0.16/0.43 = F ) ).
% 0.16/0.43
% 0.16/0.43 % comp_id
% 0.16/0.43 thf(fact_218_id__comp,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,G: A > B] :
% 0.16/0.43 ( ( comp @ B @ B @ A @ ( id @ B ) @ G )
% 0.16/0.43 = G ) ).
% 0.16/0.43
% 0.16/0.43 % id_comp
% 0.16/0.43 thf(fact_219_vimage__empty,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F: A > B] :
% 0.16/0.43 ( ( vimage @ A @ B @ F @ ( bot_bot @ ( set @ B ) ) )
% 0.16/0.43 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % vimage_empty
% 0.16/0.43 thf(fact_220_comp__inj__on__iff,axiom,
% 0.16/0.43 ! [B: $tType,C: $tType,A: $tType,F: A > B,A4: set @ A,F7: B > C] :
% 0.16/0.43 ( ( inj_on @ A @ B @ F @ A4 )
% 0.16/0.43 => ( ( inj_on @ B @ C @ F7 @ ( image @ A @ B @ F @ A4 ) )
% 0.16/0.43 = ( inj_on @ A @ C @ ( comp @ B @ C @ A @ F7 @ F ) @ A4 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % comp_inj_on_iff
% 0.16/0.43 thf(fact_221_inj__on__imageI,axiom,
% 0.16/0.43 ! [B: $tType,C: $tType,A: $tType,G: C > B,F: A > C,A4: set @ A] :
% 0.16/0.43 ( ( inj_on @ A @ B @ ( comp @ C @ B @ A @ G @ F ) @ A4 )
% 0.16/0.44 => ( inj_on @ C @ B @ G @ ( image @ A @ C @ F @ A4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inj_on_imageI
% 0.16/0.44 thf(fact_222_comp__inj__on,axiom,
% 0.16/0.44 ! [B: $tType,C: $tType,A: $tType,F: A > B,A4: set @ A,G: B > C] :
% 0.16/0.44 ( ( inj_on @ A @ B @ F @ A4 )
% 0.16/0.44 => ( ( inj_on @ B @ C @ G @ ( image @ A @ B @ F @ A4 ) )
% 0.16/0.44 => ( inj_on @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ A4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % comp_inj_on
% 0.16/0.44 thf(fact_223_map__sum_Ocompositionality,axiom,
% 0.16/0.44 ! [D: $tType,F3: $tType,E2: $tType,C: $tType,B: $tType,A: $tType,F: C > E2,G: D > F3,H2: A > C,I: B > D,Sum: sum_sum @ A @ B] :
% 0.16/0.44 ( ( sum_map_sum @ C @ E2 @ D @ F3 @ F @ G @ ( sum_map_sum @ A @ C @ B @ D @ H2 @ I @ Sum ) )
% 0.16/0.44 = ( sum_map_sum @ A @ E2 @ B @ F3 @ ( comp @ C @ E2 @ A @ F @ H2 ) @ ( comp @ D @ F3 @ B @ G @ I ) @ Sum ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_sum.compositionality
% 0.16/0.44 thf(fact_224_sum_Omap__comp,axiom,
% 0.16/0.44 ! [D: $tType,F3: $tType,E2: $tType,C: $tType,B: $tType,A: $tType,G1: C > E2,G22: D > F3,F1: A > C,F2: B > D,V: sum_sum @ A @ B] :
% 0.16/0.44 ( ( sum_map_sum @ C @ E2 @ D @ F3 @ G1 @ G22 @ ( sum_map_sum @ A @ C @ B @ D @ F1 @ F2 @ V ) )
% 0.16/0.44 = ( sum_map_sum @ A @ E2 @ B @ F3 @ ( comp @ C @ E2 @ A @ G1 @ F1 ) @ ( comp @ D @ F3 @ B @ G22 @ F2 ) @ V ) ) ).
% 0.16/0.44
% 0.16/0.44 % sum.map_comp
% 0.16/0.44 thf(fact_225_map__sum_Ocomp,axiom,
% 0.16/0.44 ! [A: $tType,C: $tType,E2: $tType,F3: $tType,D: $tType,B: $tType,F: C > E2,G: D > F3,H2: A > C,I: B > D] :
% 0.16/0.44 ( ( comp @ ( sum_sum @ C @ D ) @ ( sum_sum @ E2 @ F3 ) @ ( sum_sum @ A @ B ) @ ( sum_map_sum @ C @ E2 @ D @ F3 @ F @ G ) @ ( sum_map_sum @ A @ C @ B @ D @ H2 @ I ) )
% 0.16/0.44 = ( sum_map_sum @ A @ E2 @ B @ F3 @ ( comp @ C @ E2 @ A @ F @ H2 ) @ ( comp @ D @ F3 @ B @ G @ I ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_sum.comp
% 0.16/0.44 thf(fact_226_Inf_OINF__image,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,C: $tType,Inf: ( set @ A ) > A,G: B > A,F: C > B,A4: set @ C] :
% 0.16/0.44 ( ( Inf @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A4 ) ) )
% 0.16/0.44 = ( Inf @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Inf.INF_image
% 0.16/0.44 thf(fact_227_Sup_OSUP__image,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,C: $tType,Sup: ( set @ A ) > A,G: B > A,F: C > B,A4: set @ C] :
% 0.16/0.44 ( ( Sup @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A4 ) ) )
% 0.16/0.44 = ( Sup @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Sup.SUP_image
% 0.16/0.44 thf(fact_228_image__comp,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,C: $tType,F: B > A,G: C > B,R: set @ C] :
% 0.16/0.44 ( ( image @ B @ A @ F @ ( image @ C @ B @ G @ R ) )
% 0.16/0.44 = ( image @ C @ A @ ( comp @ B @ A @ C @ F @ G ) @ R ) ) ).
% 0.16/0.44
% 0.16/0.44 % image_comp
% 0.16/0.44 thf(fact_229_image__eq__imp__comp,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,D: $tType,C: $tType,F: B > A,A4: set @ B,G: C > A,B3: set @ C,H2: A > D] :
% 0.16/0.44 ( ( ( image @ B @ A @ F @ A4 )
% 0.16/0.44 = ( image @ C @ A @ G @ B3 ) )
% 0.16/0.44 => ( ( image @ B @ D @ ( comp @ A @ D @ B @ H2 @ F ) @ A4 )
% 0.16/0.44 = ( image @ C @ D @ ( comp @ A @ D @ C @ H2 @ G ) @ B3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % image_eq_imp_comp
% 0.16/0.44 thf(fact_230_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__o__subst,axiom,
% 0.16/0.44 ! [Tr0: dtree] :
% 0.16/0.44 ( ( comp @ dtree @ n @ dtree @ root @ ( gram_L1004374585hsubst @ Tr0 ) )
% 0.16/0.44 = root ) ).
% 0.16/0.44
% 0.16/0.44 % Gram_Lang_Mirabelle_ojxrtuoybn.root_o_subst
% 0.16/0.44 thf(fact_231_infinite__finite__induct,axiom,
% 0.16/0.44 ! [A: $tType,P: ( set @ A ) > $o,A4: set @ A] :
% 0.16/0.44 ( ! [A11: set @ A] :
% 0.16/0.44 ( ~ ( finite_finite2 @ A @ A11 )
% 0.16/0.44 => ( P @ A11 ) )
% 0.16/0.44 => ( ( P @ ( bot_bot @ ( set @ A ) ) )
% 0.16/0.44 => ( ! [X3: A,F8: set @ A] :
% 0.16/0.44 ( ( finite_finite2 @ A @ F8 )
% 0.16/0.44 => ( ~ ( member @ A @ X3 @ F8 )
% 0.16/0.44 => ( ( P @ F8 )
% 0.16/0.44 => ( P @ ( insert @ A @ X3 @ F8 ) ) ) ) )
% 0.16/0.44 => ( P @ A4 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % infinite_finite_induct
% 0.16/0.44 thf(fact_232_finite__ne__induct,axiom,
% 0.16/0.44 ! [A: $tType,F4: set @ A,P: ( set @ A ) > $o] :
% 0.16/0.44 ( ( finite_finite2 @ A @ F4 )
% 0.16/0.44 => ( ( F4
% 0.16/0.44 != ( bot_bot @ ( set @ A ) ) )
% 0.16/0.44 => ( ! [X3: A] : ( P @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.44 => ( ! [X3: A,F8: set @ A] :
% 0.16/0.44 ( ( finite_finite2 @ A @ F8 )
% 0.16/0.44 => ( ( F8
% 0.16/0.44 != ( bot_bot @ ( set @ A ) ) )
% 0.16/0.44 => ( ~ ( member @ A @ X3 @ F8 )
% 0.16/0.44 => ( ( P @ F8 )
% 0.16/0.44 => ( P @ ( insert @ A @ X3 @ F8 ) ) ) ) ) )
% 0.16/0.44 => ( P @ F4 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % finite_ne_induct
% 0.16/0.44 thf(fact_233_finite_Oinducts,axiom,
% 0.16/0.44 ! [A: $tType,X2: set @ A,P: ( set @ A ) > $o] :
% 0.16/0.44 ( ( finite_finite2 @ A @ X2 )
% 0.16/0.44 => ( ( P @ ( bot_bot @ ( set @ A ) ) )
% 0.16/0.44 => ( ! [A11: set @ A,A7: A] :
% 0.16/0.44 ( ( finite_finite2 @ A @ A11 )
% 0.16/0.44 => ( ( P @ A11 )
% 0.16/0.44 => ( P @ ( insert @ A @ A7 @ A11 ) ) ) )
% 0.16/0.44 => ( P @ X2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % finite.inducts
% 0.16/0.44 thf(fact_234_finite__induct,axiom,
% 0.16/0.44 ! [A: $tType,F4: set @ A,P: ( set @ A ) > $o] :
% 0.16/0.44 ( ( finite_finite2 @ A @ F4 )
% 0.16/0.44 => ( ( P @ ( bot_bot @ ( set @ A ) ) )
% 0.16/0.44 => ( ! [X3: A,F8: set @ A] :
% 0.16/0.44 ( ( finite_finite2 @ A @ F8 )
% 0.16/0.44 => ( ~ ( member @ A @ X3 @ F8 )
% 0.16/0.44 => ( ( P @ F8 )
% 0.16/0.44 => ( P @ ( insert @ A @ X3 @ F8 ) ) ) ) )
% 0.16/0.44 => ( P @ F4 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % finite_induct
% 0.16/0.44 thf(fact_235_finite_Osimps,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( finite_finite2 @ A )
% 0.16/0.44 = ( ^ [A10: set @ A] :
% 0.16/0.44 ( ( A10
% 0.16/0.44 = ( bot_bot @ ( set @ A ) ) )
% 0.16/0.44 | ? [A8: set @ A,B9: A] :
% 0.16/0.44 ( ( A10
% 0.16/0.44 = ( insert @ A @ B9 @ A8 ) )
% 0.16/0.44 & ( finite_finite2 @ A @ A8 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % finite.simps
% 0.16/0.44 thf(fact_236_finite_Ocases,axiom,
% 0.16/0.44 ! [A: $tType,A2: set @ A] :
% 0.16/0.44 ( ( finite_finite2 @ A @ A2 )
% 0.16/0.44 => ( ( A2
% 0.16/0.44 != ( bot_bot @ ( set @ A ) ) )
% 0.16/0.44 => ~ ! [A11: set @ A] :
% 0.16/0.44 ( ? [A7: A] :
% 0.16/0.44 ( A2
% 0.16/0.44 = ( insert @ A @ A7 @ A11 ) )
% 0.16/0.44 => ~ ( finite_finite2 @ A @ A11 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % finite.cases
% 0.16/0.44 thf(fact_237_singleton__inject,axiom,
% 0.16/0.44 ! [A: $tType,A2: A,B2: A] :
% 0.16/0.44 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.16/0.44 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.44 => ( A2 = B2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % singleton_inject
% 0.16/0.44 thf(fact_238_insert__not__empty,axiom,
% 0.16/0.44 ! [A: $tType,A2: A,A4: set @ A] :
% 0.16/0.44 ( ( insert @ A @ A2 @ A4 )
% 0.16/0.44 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % insert_not_empty
% 0.16/0.44 thf(fact_239_doubleton__eq__iff,axiom,
% 0.16/0.44 ! [A: $tType,A2: A,B2: A,C4: A,D3: A] :
% 0.16/0.44 ( ( ( insert @ A @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.44 = ( insert @ A @ C4 @ ( insert @ A @ D3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.16/0.44 = ( ( ( A2 = C4 )
% 0.16/0.44 & ( B2 = D3 ) )
% 0.16/0.44 | ( ( A2 = D3 )
% 0.16/0.44 & ( B2 = C4 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % doubleton_eq_iff
% 0.16/0.44 thf(fact_240_singleton__iff,axiom,
% 0.16/0.44 ! [A: $tType,B2: A,A2: A] :
% 0.16/0.44 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.44 = ( B2 = A2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % singleton_iff
% 0.16/0.44 thf(fact_241_singletonD,axiom,
% 0.16/0.44 ! [A: $tType,B2: A,A2: A] :
% 0.16/0.44 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.16/0.44 => ( B2 = A2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % singletonD
% 0.16/0.44 thf(fact_242_fun_Omap__id0,axiom,
% 0.16/0.44 ! [A: $tType,D: $tType] :
% 0.16/0.44 ( ( comp @ A @ A @ D @ ( id @ A ) )
% 0.16/0.44 = ( id @ ( D > A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fun.map_id0
% 0.16/0.44 thf(fact_243_pointfree__idE,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: B > A,G: A > B,X2: A] :
% 0.16/0.44 ( ( ( comp @ B @ A @ A @ F @ G )
% 0.16/0.44 = ( id @ A ) )
% 0.16/0.44 => ( ( F @ ( G @ X2 ) )
% 0.16/0.44 = X2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % pointfree_idE
% 0.16/0.44 thf(fact_244_comp__eq__id__dest,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B2: A > C,C4: A > B,V: A] :
% 0.16/0.44 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.16/0.44 = ( comp @ B @ B @ A @ ( id @ B ) @ C4 ) )
% 0.16/0.44 => ( ( A2 @ ( B2 @ V ) )
% 0.16/0.44 = ( C4 @ V ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % comp_eq_id_dest
% 0.16/0.44 thf(fact_245_vimage__comp,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,F: A > B,G: B > C,X2: set @ C] :
% 0.16/0.44 ( ( vimage @ A @ B @ F @ ( vimage @ B @ C @ G @ X2 ) )
% 0.16/0.44 = ( vimage @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ X2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % vimage_comp
% 0.16/0.44 thf(fact_246_set_Ocompositionality,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,F: C > B,G: B > A,Set: set @ A] :
% 0.16/0.44 ( ( vimage @ C @ B @ F @ ( vimage @ B @ A @ G @ Set ) )
% 0.16/0.44 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ Set ) ) ).
% 0.16/0.44
% 0.16/0.44 % set.compositionality
% 0.16/0.44 thf(fact_247_rewriteR__comp__comp2,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,E2: $tType,D: $tType,A: $tType,G: C > B,H2: A > C,R1: D > B,R2: A > D,F: B > E2,L: D > E2] :
% 0.16/0.44 ( ( ( comp @ C @ B @ A @ G @ H2 )
% 0.16/0.44 = ( comp @ D @ B @ A @ R1 @ R2 ) )
% 0.16/0.44 => ( ( ( comp @ B @ E2 @ D @ F @ R1 )
% 0.16/0.44 = L )
% 0.16/0.44 => ( ( comp @ C @ E2 @ A @ ( comp @ B @ E2 @ C @ F @ G ) @ H2 )
% 0.16/0.44 = ( comp @ D @ E2 @ A @ L @ R2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % rewriteR_comp_comp2
% 0.16/0.44 thf(fact_248_rewriteL__comp__comp2,axiom,
% 0.16/0.44 ! [A: $tType,C: $tType,B: $tType,D: $tType,E2: $tType,F: C > B,G: A > C,L1: D > B,L2: A > D,H2: E2 > A,R: E2 > D] :
% 0.16/0.44 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.16/0.44 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 0.16/0.44 => ( ( ( comp @ A @ D @ E2 @ L2 @ H2 )
% 0.16/0.44 = R )
% 0.16/0.44 => ( ( comp @ C @ B @ E2 @ F @ ( comp @ A @ C @ E2 @ G @ H2 ) )
% 0.16/0.44 = ( comp @ D @ B @ E2 @ L1 @ R ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % rewriteL_comp_comp2
% 0.16/0.44 thf(fact_249_rewriteR__comp__comp,axiom,
% 0.16/0.44 ! [C: $tType,D: $tType,B: $tType,A: $tType,G: C > B,H2: A > C,R: A > B,F: B > D] :
% 0.16/0.44 ( ( ( comp @ C @ B @ A @ G @ H2 )
% 0.16/0.44 = R )
% 0.16/0.44 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F @ G ) @ H2 )
% 0.16/0.44 = ( comp @ B @ D @ A @ F @ R ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % rewriteR_comp_comp
% 0.16/0.44 thf(fact_250_rewriteL__comp__comp,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,D: $tType,F: C > B,G: A > C,L: A > B,H2: D > A] :
% 0.16/0.44 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.16/0.44 = L )
% 0.16/0.44 => ( ( comp @ C @ B @ D @ F @ ( comp @ A @ C @ D @ G @ H2 ) )
% 0.16/0.44 = ( comp @ A @ B @ D @ L @ H2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % rewriteL_comp_comp
% 0.16/0.44 thf(fact_251_fun_Omap__comp,axiom,
% 0.16/0.44 ! [B: $tType,C: $tType,A: $tType,D: $tType,G: B > C,F: A > B,V: D > A] :
% 0.16/0.44 ( ( comp @ B @ C @ D @ G @ ( comp @ A @ B @ D @ F @ V ) )
% 0.16/0.44 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G @ F ) @ V ) ) ).
% 0.16/0.44
% 0.16/0.44 % fun.map_comp
% 0.16/0.44 thf(fact_252_set_Ocomp,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,F: C > B,G: B > A] :
% 0.16/0.44 ( ( comp @ ( set @ B ) @ ( set @ C ) @ ( set @ A ) @ ( vimage @ C @ B @ F ) @ ( vimage @ B @ A @ G ) )
% 0.16/0.44 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % set.comp
% 0.16/0.44 thf(fact_253_comp__eq__dest__lhs,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B2: A > C,C4: A > B,V: A] :
% 0.16/0.44 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.16/0.44 = C4 )
% 0.16/0.44 => ( ( A2 @ ( B2 @ V ) )
% 0.16/0.44 = ( C4 @ V ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % comp_eq_dest_lhs
% 0.16/0.44 thf(fact_254_comp__eq__elim,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C4: D > B,D3: A > D] :
% 0.16/0.44 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.16/0.44 = ( comp @ D @ B @ A @ C4 @ D3 ) )
% 0.16/0.44 => ! [V2: A] :
% 0.16/0.44 ( ( A2 @ ( B2 @ V2 ) )
% 0.16/0.44 = ( C4 @ ( D3 @ V2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % comp_eq_elim
% 0.16/0.44 thf(fact_255_comp__eq__dest,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C4: D > B,D3: A > D,V: A] :
% 0.16/0.44 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.16/0.44 = ( comp @ D @ B @ A @ C4 @ D3 ) )
% 0.16/0.44 => ( ( A2 @ ( B2 @ V ) )
% 0.16/0.44 = ( C4 @ ( D3 @ V ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % comp_eq_dest
% 0.16/0.44
% 0.16/0.44 %----Type constructors (5)
% 0.16/0.44 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 0.16/0.44 ! [A5: $tType,A13: $tType] :
% 0.16/0.44 ( ( ( finite_finite @ A5 @ ( type @ A5 ) )
% 0.16/0.44 & ( finite_finite @ A13 @ ( type @ A13 ) ) )
% 0.16/0.44 => ( finite_finite @ ( A5 > A13 ) @ ( type @ ( A5 > A13 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_Set_Oset___Finite__Set_Ofinite_1,axiom,
% 0.16/0.44 ! [A5: $tType] :
% 0.16/0.44 ( ( finite_finite @ A5 @ ( type @ A5 ) )
% 0.16/0.44 => ( finite_finite @ ( set @ A5 ) @ ( type @ ( set @ A5 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_HOL_Obool___Finite__Set_Ofinite_2,axiom,
% 0.16/0.44 finite_finite @ $o @ ( type @ $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_3,axiom,
% 0.16/0.44 ! [A5: $tType,A13: $tType] :
% 0.16/0.44 ( ( ( finite_finite @ A5 @ ( type @ A5 ) )
% 0.16/0.44 & ( finite_finite @ A13 @ ( type @ A13 ) ) )
% 0.16/0.44 => ( finite_finite @ ( sum_sum @ A5 @ A13 ) @ ( type @ ( sum_sum @ A5 @ A13 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_4,axiom,
% 0.16/0.44 ! [A5: $tType,A13: $tType] :
% 0.16/0.44 ( ( ( finite_finite @ A5 @ ( type @ A5 ) )
% 0.16/0.44 & ( finite_finite @ A13 @ ( type @ A13 ) ) )
% 0.16/0.44 => ( finite_finite @ ( product_prod @ A5 @ A13 ) @ ( type @ ( product_prod @ A5 @ A13 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 %----Helper facts (3)
% 0.16/0.44 thf(help_If_3_1_T,axiom,
% 0.16/0.44 ! [P: $o] :
% 0.16/0.44 ( ( P = $true )
% 0.16/0.44 | ( P = $false ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(help_If_2_1_T,axiom,
% 0.16/0.44 ! [A: $tType,X2: A,Y: A] :
% 0.16/0.44 ( ( if @ A @ $false @ X2 @ Y )
% 0.16/0.44 = Y ) ).
% 0.16/0.44
% 0.16/0.44 thf(help_If_1_1_T,axiom,
% 0.16/0.44 ! [A: $tType,X2: A,Y: A] :
% 0.16/0.44 ( ( if @ A @ $true @ X2 @ Y )
% 0.16/0.44 = X2 ) ).
% 0.16/0.44
% 0.16/0.44 %----Conjectures (1)
% 0.16/0.44 thf(conj_0,conjecture,
% 0.16/0.44 ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ tr0 ) ) @ ( cont @ tr ) ) )
% 0.16/0.44 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ tr ) ) ) ).
% 0.16/0.44
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 ------------------------
% 0.24/1.50 ---- Embedded in THF ---
% 0.24/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.24/1.50 %%% Generated on Tue Feb 24 04:17:20 EST 2026
% 0.24/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.24/1.50 %%% Logic specification used:
% 0.24/1.50 %%% thf(spec, logic, $$dhol).
% 0.24/1.50
% 0.24/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.wlnNTaEhLw/DTF2DTF23752.p
% 0.24/1.50 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 0.24/1.50 thf(ty_t_Sum__Type_Osum, type, sum_sum: ($tType > ($tType > $tType))).
% 0.24/1.50 thf(ty_t_DTree_Odtree, type, dtree: $tType).
% 0.24/1.50 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.24/1.50 thf(ty_t_DTree_OT, type, t: $tType).
% 0.24/1.50 thf(ty_t_DTree_ON, type, n: $tType).
% 0.24/1.50 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 0.24/1.50 thf(sy_cl_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.24/1.50 thf(sy_c_DTree_ONode, type, node: (n > ((set @ ((sum_sum @ t) @ dtree)) > dtree))).
% 0.24/1.50 thf(sy_c_DTree_Ocont, type, cont: (dtree > (set @ ((sum_sum @ t) @ dtree)))).
% 0.24/1.50 thf(sy_c_DTree_Odtree_Oroot, type, root: (dtree > n)).
% 0.24/1.50 thf(sy_c_DTree_Ounfold, type, unfold: (!> [A:$tType]: (((A > n) > ((A > (set @ ((sum_sum @ t) @ A))) > (A > dtree)))))).
% 0.24/1.51 thf(sy_c_Finite__Set_Ofinite, type, finite_finite2: (!> [A:$tType]: (((set @ A) > $o)))).
% 0.24/1.51 thf(sy_c_Fun_Ocomp, type, comp: (!> [B:$tType,C:$tType,A:$tType]: (((B > C) > ((A > B) > (A > C)))))).
% 0.24/1.51 thf(sy_c_Fun_Oid, type, id: (!> [A:$tType]: ((A > A)))).
% 0.24/1.51 thf(sy_c_Fun_Oinj__on, type, inj_on: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > $o))))).
% 0.24/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OP, type, gram_L1451583632elle_P: (set @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n))))).
% 0.24/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OS, type, gram_L1451583635elle_S: (n > (set @ ((sum_sum @ t) @ n)))).
% 0.24/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr, type, gram_L1231612515_deftr: (n > dtree)).
% 0.24/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst, type, gram_L1004374585hsubst: (dtree > (dtree > dtree))).
% 0.24/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c, type, gram_L1905609002ubst_c: (dtree > (dtree > (set @ ((sum_sum @ t) @ dtree))))).
% 0.24/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r, type, gram_L1905609017ubst_r: (dtree > n)).
% 0.24/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr, type, gram_L1333338417e_inFr: ((set @ n) > (dtree > (t > $o)))).
% 0.24/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2, type, gram_L805317441_inFr2: ((set @ n) > (dtree > (t > $o)))).
% 0.24/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFrr, type, gram_L805317505_inFrr: ((set @ n) > (dtree > (t > $o)))).
% 0.24/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr, type, gram_L830233218_inItr: ((set @ n) > (dtree > (n > $o)))).
% 0.24/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr, type, gram_L716654942_subtr: ((set @ n) > (dtree > (dtree > $o)))).
% 0.24/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr2, type, gram_L1283001940subtr2: ((set @ n) > (dtree > (dtree > $o)))).
% 0.24/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OsubtrOf, type, gram_L1614515765ubtrOf: (dtree > (n > dtree))).
% 0.24/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf, type, gram_L864798063lle_wf: (dtree > $o)).
% 0.24/1.51 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 0.24/1.51 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 0.24/1.51 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 0.24/1.51 thf(sy_c_Pure_Otype, type, type: (!> [A:$tType]: ((itself @ A)))).
% 0.24/1.51 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.24/1.51 thf(sy_c_Set_Oimage, type, image: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > (set @ B)))))).
% 0.24/1.51 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 0.24/1.51 thf(sy_c_Set_Ovimage, type, vimage: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ B) > (set @ A)))))).
% 0.24/1.51 thf(sy_c_Sum__Type_OInl, type, sum_Inl: (!> [A:$tType,B:$tType]: ((A > ((sum_sum @ A) @ B))))).
% 0.24/1.51 thf(sy_c_Sum__Type_OInr, type, sum_Inr: (!> [B:$tType,A:$tType]: ((B > ((sum_sum @ A) @ B))))).
% 0.24/1.51 thf(sy_c_Sum__Type_Omap__sum, type, sum_map_sum: (!> [A:$tType,C:$tType,B:$tType,D:$tType]: (((A > C) > ((B > D) > (((sum_sum @ A) @ B) > ((sum_sum @ C) @ D))))))).
% 0.24/1.51 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum, type, sum_rec_sum: (!> [A:$tType,T:$tType,B:$tType]: (((A > T) > ((B > T) > (((sum_sum @ A) @ B) > T)))))).
% 0.24/1.51 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.24/1.51 thf(sy_v_tr, type, tr: dtree).
% 0.24/1.51 thf(sy_v_tr0, type, tr0: dtree).
% 0.24/1.51 thf(fact_0__092_060open_062cont_A_Ilocal_Ohsubst_Atr_J_A_061_A_Iid_A_092_060oplus_062_Alocal_Ohsubst_J_A_096_Acont_Atr_092_060close_062, axiom, ((cont @ ((gram_L1004374585hsubst @ tr0) @ tr)) = ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ dtree)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ dtree) @ (id @ t)) @ (gram_L1004374585hsubst @ tr0))) @ (cont @ tr)))).
% 0.24/1.51 thf(fact_1_assms, axiom, ((root @ tr) != (root @ tr0))).
% 0.24/1.51 thf(fact_2_Inl__m__oplus, axiom, (! [B:$tType,C:$tType,A:$tType,F:(C > B),Tns:(set @ ((sum_sum @ A) @ C))]: ((((((vimage @ A) @ ((sum_sum @ A) @ B)) @ ((sum_Inl @ A) @ B)) @ ((((image @ ((sum_sum @ A) @ C)) @ ((sum_sum @ A) @ B)) @ ((((((sum_map_sum @ A) @ A) @ C) @ B) @ (id @ A)) @ F)) @ Tns)) = ((((vimage @ A) @ ((sum_sum @ A) @ C)) @ ((sum_Inl @ A) @ C)) @ Tns))))).
% 0.24/1.51 thf(fact_3_Inl__oplus__iff, axiom, (! [B:$tType,C:$tType,A:$tType,Tr:A,F:(C > B),Tns:(set @ ((sum_sum @ A) @ C))]: (((((member @ ((sum_sum @ A) @ B)) @ (((sum_Inl @ A) @ B) @ Tr)) @ ((((image @ ((sum_sum @ A) @ C)) @ ((sum_sum @ A) @ B)) @ ((((((sum_map_sum @ A) @ A) @ C) @ B) @ (id @ A)) @ F)) @ Tns)) = (((member @ ((sum_sum @ A) @ C)) @ (((sum_Inl @ A) @ C) @ Tr)) @ Tns))))).
% 0.24/1.51 thf(fact_4_vimage__id, axiom, (! [A:$tType]: (((((vimage @ A) @ A) @ (id @ A)) = (id @ (set @ A)))))).
% 0.24/1.51 thf(fact_5_image__id, axiom, (! [A:$tType]: (((((image @ A) @ A) @ (id @ A)) = (id @ (set @ A)))))).
% 0.24/1.51 thf(fact_6_Inl__oplus__elim, axiom, (! [B:$tType,C:$tType,A:$tType,Tr:A,F:(C > B),Tns:(set @ ((sum_sum @ A) @ C))]: (((((member @ ((sum_sum @ A) @ B)) @ (((sum_Inl @ A) @ B) @ Tr)) @ ((((image @ ((sum_sum @ A) @ C)) @ ((sum_sum @ A) @ B)) @ ((((((sum_map_sum @ A) @ A) @ C) @ B) @ (id @ A)) @ F)) @ Tns)) => (((member @ ((sum_sum @ A) @ C)) @ (((sum_Inl @ A) @ C) @ Tr)) @ Tns))))).
% 0.24/1.51 thf(fact_7_cont__hsubst__eq, axiom, (! [Tr:dtree]: ((((root @ Tr) = (root @ tr0)) => ((cont @ ((gram_L1004374585hsubst @ tr0) @ Tr)) = ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ dtree)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ dtree) @ (id @ t)) @ (gram_L1004374585hsubst @ tr0))) @ (cont @ tr0))))))).
% 0.24/1.51 thf(fact_8_cont__hsubst__neq, axiom, (! [Tr:dtree]: ((((root @ Tr) != (root @ tr0)) => ((cont @ ((gram_L1004374585hsubst @ tr0) @ Tr)) = ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ dtree)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ dtree) @ (id @ t)) @ (gram_L1004374585hsubst @ tr0))) @ (cont @ Tr))))))).
% 0.24/1.51 thf(fact_9_sum_Oinject_I1_J, axiom, (! [B:$tType,A:$tType,X1:A,Y1:A]: ((((((sum_Inl @ A) @ B) @ X1) = (((sum_Inl @ A) @ B) @ Y1)) = (X1 = Y1))))).
% 0.24/1.51 thf(fact_10_old_Osum_Oinject_I1_J, axiom, (! [B:$tType,A:$tType,A2:A,A3:A]: ((((((sum_Inl @ A) @ B) @ A2) = (((sum_Inl @ A) @ B) @ A3)) = (A2 = A3))))).
% 0.24/1.51 thf(fact_11_vimageI, axiom, (! [B:$tType,A:$tType,F:(B > A),A2:B,B2:A,B3:(set @ A)]: ((((F @ A2) = B2) => ((((member @ A) @ B2) @ B3) => (((member @ B) @ A2) @ ((((vimage @ B) @ A) @ F) @ B3))))))).
% 0.24/1.51 thf(fact_12_vimage__eq, axiom, (! [A:$tType,B:$tType,A2:A,F:(A > B),B3:(set @ B)]: (((((member @ A) @ A2) @ ((((vimage @ A) @ B) @ F) @ B3)) = (((member @ B) @ (F @ A2)) @ B3))))).
% 0.24/1.51 thf(fact_13_id__apply, axiom, (! [A:$tType]: (((id @ A) = (^ [X:A]: (X)))))).
% 0.24/1.51 thf(fact_14_hsubst__eq, axiom, (! [Tr:dtree]: ((((root @ Tr) = (root @ tr0)) => (((gram_L1004374585hsubst @ tr0) @ Tr) = ((gram_L1004374585hsubst @ tr0) @ tr0)))))).
% 0.24/1.51 thf(fact_15_image__eqI, axiom, (! [A:$tType,B:$tType,B2:A,F:(B > A),X2:B,A4:(set @ B)]: (((B2 = (F @ X2)) => ((((member @ B) @ X2) @ A4) => (((member @ A) @ B2) @ ((((image @ B) @ A) @ F) @ A4))))))).
% 0.24/1.51 thf(fact_16_root__hsubst, axiom, (! [Tr:dtree]: (((root @ ((gram_L1004374585hsubst @ tr0) @ Tr)) = (root @ Tr))))).
% 0.24/1.51 thf(fact_17_hsubst__c__def, axiom, (! [Tr:dtree]: (((((root @ Tr) = (root @ tr0)) => (((gram_L1905609002ubst_c @ tr0) @ Tr) = (cont @ tr0))) & (((root @ Tr) != (root @ tr0)) => (((gram_L1905609002ubst_c @ tr0) @ Tr) = (cont @ Tr))))))).
% 0.24/1.51 thf(fact_18_Inl__cont__hsubst__eq, axiom, (! [Tr:dtree]: ((((root @ Tr) = (root @ tr0)) => (((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ ((gram_L1004374585hsubst @ tr0) @ Tr))) = ((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ tr0))))))).
% 0.24/1.51 thf(fact_19_Inl__prodOf, axiom, (! [Tr:dtree]: ((((((vimage @ t) @ ((sum_sum @ t) @ n)) @ ((sum_Inl @ t) @ n)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr))) = ((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ Tr)))))).
% 0.24/1.51 thf(fact_20_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__hsubst, axiom, (! [Tr0:dtree,Tr:dtree]: (((root @ ((gram_L1004374585hsubst @ Tr0) @ Tr)) = (root @ Tr))))).
% 0.24/1.51 thf(fact_21_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__eq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) = (root @ Tr0)) => (((gram_L1004374585hsubst @ Tr0) @ Tr) = ((gram_L1004374585hsubst @ Tr0) @ Tr0)))))).
% 0.24/1.51 thf(fact_22_rev__image__eqI, axiom, (! [B:$tType,A:$tType,X2:A,A4:(set @ A),B2:B,F:(A > B)]: (((((member @ A) @ X2) @ A4) => ((B2 = (F @ X2)) => (((member @ B) @ B2) @ ((((image @ A) @ B) @ F) @ A4))))))).
% 0.24/1.51 thf(fact_23_ball__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A4:(set @ B),P:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ ((((image @ B) @ A) @ F) @ A4)) => (P @ X3)))) => (! [X4:B]: (((((member @ B) @ X4) @ A4) => (P @ (F @ X4))))))))).
% 0.24/1.51 thf(fact_24_image__cong, axiom, (! [B:$tType,A:$tType,M:(set @ A),N:(set @ A),F:(A > B),G:(A > B)]: (((M = N) => ((! [X3:A]: (((((member @ A) @ X3) @ N) => ((F @ X3) = (G @ X3))))) => (((((image @ A) @ B) @ F) @ M) = ((((image @ A) @ B) @ G) @ N))))))).
% 0.24/1.51 thf(fact_25_bex__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A4:(set @ B),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((((image @ B) @ A) @ F) @ A4)) & (P @ X4)))) => (? [X3:B]: (((((member @ B) @ X3) @ A4) & (P @ (F @ X3))))))))).
% 0.24/1.51 thf(fact_26_image__iff, axiom, (! [A:$tType,B:$tType,Z:A,F:(B > A),A4:(set @ B)]: (((((member @ A) @ Z) @ ((((image @ B) @ A) @ F) @ A4)) = (? [X:B]: (((((member @ B) @ X) @ A4) & (Z = (F @ X))))))))).
% 0.24/1.51 thf(fact_27_imageI, axiom, (! [B:$tType,A:$tType,X2:A,A4:(set @ A),F:(A > B)]: (((((member @ A) @ X2) @ A4) => (((member @ B) @ (F @ X2)) @ ((((image @ A) @ B) @ F) @ A4)))))).
% 0.24/1.51 thf(fact_28_eq__id__iff, axiom, (! [A:$tType,F:(A > A)]: (((! [X:A]: (((F @ X) = X))) = (F = (id @ A)))))).
% 0.24/1.51 thf(fact_29_id__def, axiom, (! [A:$tType]: (((id @ A) = (^ [X:A]: (X)))))).
% 0.24/1.51 thf(fact_30_vimage__Collect, axiom, (! [B:$tType,A:$tType,P:(B > $o),F:(A > B),Q:(A > $o)]: (((! [X3:A]: (((P @ (F @ X3)) = (Q @ X3)))) => (((((vimage @ A) @ B) @ F) @ ((collect @ B) @ P)) = ((collect @ A) @ Q)))))).
% 0.24/1.51 thf(fact_31_vimageI2, axiom, (! [B:$tType,A:$tType,F:(B > A),A2:B,A4:(set @ A)]: (((((member @ A) @ (F @ A2)) @ A4) => (((member @ B) @ A2) @ ((((vimage @ B) @ A) @ F) @ A4)))))).
% 0.24/1.51 thf(fact_32_vimageE, axiom, (! [A:$tType,B:$tType,A2:A,F:(A > B),B3:(set @ B)]: (((((member @ A) @ A2) @ ((((vimage @ A) @ B) @ F) @ B3)) => (((member @ B) @ (F @ A2)) @ B3))))).
% 0.24/1.51 thf(fact_33_vimageD, axiom, (! [A:$tType,B:$tType,A2:A,F:(A > B),A4:(set @ B)]: (((((member @ A) @ A2) @ ((((vimage @ A) @ B) @ F) @ A4)) => (((member @ B) @ (F @ A2)) @ A4))))).
% 0.24/1.51 thf(fact_34_Inl__inject, axiom, (! [B:$tType,A:$tType,X2:A,Y:A]: ((((((sum_Inl @ A) @ B) @ X2) = (((sum_Inl @ A) @ B) @ Y)) => (X2 = Y))))).
% 0.24/1.51 thf(fact_35_Gram__Lang__Mirabelle__ojxrtuoybn_OInl__cont__hsubst__eq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) = (root @ Tr0)) => (((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ ((gram_L1004374585hsubst @ Tr0) @ Tr))) = ((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ Tr0))))))).
% 0.24/1.51 thf(fact_36_Gram__Lang__Mirabelle__ojxrtuoybn_Ocont__hsubst__neq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) != (root @ Tr0)) => ((cont @ ((gram_L1004374585hsubst @ Tr0) @ Tr)) = ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ dtree)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ dtree) @ (id @ t)) @ (gram_L1004374585hsubst @ Tr0))) @ (cont @ Tr))))))).
% 0.24/1.51 thf(fact_37_Gram__Lang__Mirabelle__ojxrtuoybn_Ocont__hsubst__eq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) = (root @ Tr0)) => ((cont @ ((gram_L1004374585hsubst @ Tr0) @ Tr)) = ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ dtree)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ dtree) @ (id @ t)) @ (gram_L1004374585hsubst @ Tr0))) @ (cont @ Tr0))))))).
% 0.24/1.51 thf(fact_38_map__sum__InlD, axiom, (! [D:$tType,B:$tType,C:$tType,A:$tType,F:(C > A),G:(D > B),Z:((sum_sum @ C) @ D),X2:A]: ((((((((((sum_map_sum @ C) @ A) @ D) @ B) @ F) @ G) @ Z) = (((sum_Inl @ A) @ B) @ X2)) => (? [Y2:C]: (((Z = (((sum_Inl @ C) @ D) @ Y2)) & ((F @ Y2) = X2)))))))).
% 0.24/1.51 thf(fact_39_map__sum_Osimps_I1_J, axiom, (! [B:$tType,D:$tType,C:$tType,A:$tType,F1:(A > C),F2:(B > D),A2:A]: (((((((((sum_map_sum @ A) @ C) @ B) @ D) @ F1) @ F2) @ (((sum_Inl @ A) @ B) @ A2)) = (((sum_Inl @ C) @ D) @ (F1 @ A2)))))).
% 0.24/1.51 thf(fact_40_old_Osum_Osimps_I7_J, axiom, (! [B:$tType,T:$tType,A:$tType,F1:(A > T),F2:(B > T),A2:A]: ((((((((sum_rec_sum @ A) @ T) @ B) @ F1) @ F2) @ (((sum_Inl @ A) @ B) @ A2)) = (F1 @ A2))))).
% 0.24/1.51 thf(fact_41_map__sum__if__distrib__then_I1_J, axiom, (! [D:$tType,B:$tType,C:$tType,A:$tType,E:$o,F:(A > B),G:(C > D),X2:A,Y:((sum_sum @ A) @ C)]: (((E => ((((((((sum_map_sum @ A) @ B) @ C) @ D) @ F) @ G) @ ((((if @ ((sum_sum @ A) @ C)) @ E) @ (((sum_Inl @ A) @ C) @ X2)) @ Y)) = (((sum_Inl @ B) @ D) @ (F @ X2)))) & ((~ (E)) => ((((((((sum_map_sum @ A) @ B) @ C) @ D) @ F) @ G) @ ((((if @ ((sum_sum @ A) @ C)) @ E) @ (((sum_Inl @ A) @ C) @ X2)) @ Y)) = (((((((sum_map_sum @ A) @ B) @ C) @ D) @ F) @ G) @ Y))))))).
% 0.24/1.51 thf(fact_42_map__sum__if__distrib__else_I1_J, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,E:$o,F:(A > B),G:(C > D),X2:((sum_sum @ A) @ C),Y:A]: (((E => ((((((((sum_map_sum @ A) @ B) @ C) @ D) @ F) @ G) @ ((((if @ ((sum_sum @ A) @ C)) @ E) @ X2) @ (((sum_Inl @ A) @ C) @ Y))) = (((((((sum_map_sum @ A) @ B) @ C) @ D) @ F) @ G) @ X2))) & ((~ (E)) => ((((((((sum_map_sum @ A) @ B) @ C) @ D) @ F) @ G) @ ((((if @ ((sum_sum @ A) @ C)) @ E) @ X2) @ (((sum_Inl @ A) @ C) @ Y))) = (((sum_Inl @ B) @ D) @ (F @ Y)))))))).
% 0.24/1.51 thf(fact_43_dtree__cong, axiom, (! [Tr:dtree,Tr2:dtree]: ((((root @ Tr) = (root @ Tr2)) => (((cont @ Tr) = (cont @ Tr2)) => (Tr = Tr2)))))).
% 0.24/1.51 thf(fact_44_sum_Omap__id0, axiom, (! [B:$tType,A:$tType]: ((((((((sum_map_sum @ A) @ A) @ B) @ B) @ (id @ A)) @ (id @ B)) = (id @ ((sum_sum @ A) @ B)))))).
% 0.24/1.51 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 0.24/1.51 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A4)))) = A4)))).
% 0.24/1.51 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.24/1.51 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 0.24/1.51 thf(fact_49_sum_Omap__id, axiom, (! [B:$tType,A:$tType,T2:((sum_sum @ A) @ B)]: (((((((((sum_map_sum @ A) @ A) @ B) @ B) @ (id @ A)) @ (id @ B)) @ T2) = T2)))).
% 0.24/1.51 thf(fact_50_Sup_OSUP__id__eq, axiom, (! [A:$tType,Sup:((set @ A) > A),A4:(set @ A)]: (((Sup @ ((((image @ A) @ A) @ (id @ A)) @ A4)) = (Sup @ A4))))).
% 0.24/1.51 thf(fact_51_Inf_OINF__id__eq, axiom, (! [A:$tType,Inf:((set @ A) > A),A4:(set @ A)]: (((Inf @ ((((image @ A) @ A) @ (id @ A)) @ A4)) = (Inf @ A4))))).
% 0.24/1.51 thf(fact_52_Inr__m__oplus, axiom, (! [A:$tType,C:$tType,B:$tType,F:(C > A),Tns:(set @ ((sum_sum @ B) @ C))]: ((((((vimage @ A) @ ((sum_sum @ B) @ A)) @ ((sum_Inr @ A) @ B)) @ ((((image @ ((sum_sum @ B) @ C)) @ ((sum_sum @ B) @ A)) @ ((((((sum_map_sum @ B) @ B) @ C) @ A) @ (id @ B)) @ F)) @ Tns)) = ((((image @ C) @ A) @ F) @ ((((vimage @ C) @ ((sum_sum @ B) @ C)) @ ((sum_Inr @ C) @ B)) @ Tns)))))).
% 0.24/1.51 thf(fact_53_Inr__cont__hsubst__eq, axiom, (! [Tr:dtree]: ((((root @ Tr) = (root @ tr0)) => (((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ ((gram_L1004374585hsubst @ tr0) @ Tr))) = ((((image @ dtree) @ dtree) @ (gram_L1004374585hsubst @ tr0)) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ tr0)))))))).
% 0.24/1.51 thf(fact_54_inFr2_OBase, axiom, (! [Tr:dtree,Ns:(set @ n),T2:t]: (((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T2)) @ (cont @ Tr)) => (((gram_L805317441_inFr2 @ Ns) @ Tr) @ T2)))))).
% 0.24/1.51 thf(fact_55_sum_Oinject_I2_J, axiom, (! [A:$tType,B:$tType,X22:B,Y22:B]: ((((((sum_Inr @ B) @ A) @ X22) = (((sum_Inr @ B) @ A) @ Y22)) = (X22 = Y22))))).
% 0.24/1.51 thf(fact_56_old_Osum_Oinject_I2_J, axiom, (! [A:$tType,B:$tType,B2:B,B4:B]: ((((((sum_Inr @ B) @ A) @ B2) = (((sum_Inr @ B) @ A) @ B4)) = (B2 = B4))))).
% 0.24/1.51 thf(fact_57_Inl__Inr__False, axiom, (! [A:$tType,B:$tType,X2:A,Y:B]: (((((sum_Inl @ A) @ B) @ X2) != (((sum_Inr @ B) @ A) @ Y))))).
% 0.24/1.51 thf(fact_58_Inr__Inl__False, axiom, (! [B:$tType,A:$tType,X2:B,Y:A]: (((((sum_Inr @ B) @ A) @ X2) != (((sum_Inl @ A) @ B) @ Y))))).
% 0.24/1.51 thf(fact_59_old_Osum_Osimps_I8_J, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > T),F2:(B > T),B2:B]: ((((((((sum_rec_sum @ A) @ T) @ B) @ F1) @ F2) @ (((sum_Inr @ B) @ A) @ B2)) = (F2 @ B2))))).
% 0.24/1.51 thf(fact_60_Inr__oplus__iff, axiom, (! [B:$tType,A:$tType,C:$tType,Tr:B,F:(C > B),Tns:(set @ ((sum_sum @ A) @ C))]: (((((member @ ((sum_sum @ A) @ B)) @ (((sum_Inr @ B) @ A) @ Tr)) @ ((((image @ ((sum_sum @ A) @ C)) @ ((sum_sum @ A) @ B)) @ ((((((sum_map_sum @ A) @ A) @ C) @ B) @ (id @ A)) @ F)) @ Tns)) = (? [N2:C]: (((((member @ ((sum_sum @ A) @ C)) @ (((sum_Inr @ C) @ A) @ N2)) @ Tns) & ((F @ N2) = Tr)))))))).
% 0.24/1.51 thf(fact_61_Inr__inject, axiom, (! [A:$tType,B:$tType,X2:B,Y:B]: ((((((sum_Inr @ B) @ A) @ X2) = (((sum_Inr @ B) @ A) @ Y)) => (X2 = Y))))).
% 0.24/1.51 thf(fact_62_obj__sumE__f, axiom, (! [A:$tType,C:$tType,B:$tType,S:B,F:(((sum_sum @ A) @ C) > B),P:$o]: (((! [X3:A]: (((S = (F @ (((sum_Inl @ A) @ C) @ X3))) => P))) => ((! [X3:C]: (((S = (F @ (((sum_Inr @ C) @ A) @ X3))) => P))) => (! [X4:((sum_sum @ A) @ C)]: (((S = (F @ X4)) => P)))))))).
% 0.24/1.51 thf(fact_63_map__sum__if__distrib__else_I2_J, axiom, (! [E2:$tType,F3:$tType,H:$tType,G2:$tType,E:$o,F:(E2 > F3),G:(G2 > H),X2:((sum_sum @ E2) @ G2),Y:G2]: (((E => ((((((((sum_map_sum @ E2) @ F3) @ G2) @ H) @ F) @ G) @ ((((if @ ((sum_sum @ E2) @ G2)) @ E) @ X2) @ (((sum_Inr @ G2) @ E2) @ Y))) = (((((((sum_map_sum @ E2) @ F3) @ G2) @ H) @ F) @ G) @ X2))) & ((~ (E)) => ((((((((sum_map_sum @ E2) @ F3) @ G2) @ H) @ F) @ G) @ ((((if @ ((sum_sum @ E2) @ G2)) @ E) @ X2) @ (((sum_Inr @ G2) @ E2) @ Y))) = (((sum_Inr @ H) @ F3) @ (G @ Y)))))))).
% 0.24/1.51 thf(fact_64_map__sum__if__distrib__then_I2_J, axiom, (! [H:$tType,F3:$tType,G2:$tType,E2:$tType,E:$o,F:(E2 > F3),G:(G2 > H),X2:G2,Y:((sum_sum @ E2) @ G2)]: (((E => ((((((((sum_map_sum @ E2) @ F3) @ G2) @ H) @ F) @ G) @ ((((if @ ((sum_sum @ E2) @ G2)) @ E) @ (((sum_Inr @ G2) @ E2) @ X2)) @ Y)) = (((sum_Inr @ H) @ F3) @ (G @ X2)))) & ((~ (E)) => ((((((((sum_map_sum @ E2) @ F3) @ G2) @ H) @ F) @ G) @ ((((if @ ((sum_sum @ E2) @ G2)) @ E) @ (((sum_Inr @ G2) @ E2) @ X2)) @ Y)) = (((((((sum_map_sum @ E2) @ F3) @ G2) @ H) @ F) @ G) @ Y))))))).
% 0.24/1.51 thf(fact_65_sum_Odistinct_I1_J, axiom, (! [A:$tType,B:$tType,X1:A,X22:B]: (((((sum_Inl @ A) @ B) @ X1) != (((sum_Inr @ B) @ A) @ X22))))).
% 0.24/1.51 thf(fact_66_old_Osum_Odistinct_I2_J, axiom, (! [B5:$tType,A5:$tType,B6:B5,A6:A5]: (((((sum_Inr @ B5) @ A5) @ B6) != (((sum_Inl @ A5) @ B5) @ A6))))).
% 0.24/1.51 thf(fact_67_old_Osum_Odistinct_I1_J, axiom, (! [A:$tType,B:$tType,A2:A,B4:B]: (((((sum_Inl @ A) @ B) @ A2) != (((sum_Inr @ B) @ A) @ B4))))).
% 0.24/1.51 thf(fact_68_sumE, axiom, (! [A:$tType,B:$tType,S:((sum_sum @ A) @ B)]: (((! [X3:A]: ((S != (((sum_Inl @ A) @ B) @ X3)))) => (~ ((! [Y2:B]: ((S != (((sum_Inr @ B) @ A) @ Y2)))))))))).
% 0.24/1.51 thf(fact_69_Inr__not__Inl, axiom, (! [B:$tType,A:$tType,B2:B,A2:A]: (((((sum_Inr @ B) @ A) @ B2) != (((sum_Inl @ A) @ B) @ A2))))).
% 0.24/1.51 thf(fact_70_split__sum__ex, axiom, (! [B:$tType,A:$tType]: (((^ [P2:(((sum_sum @ A) @ B) > $o)]: ((? [X5:((sum_sum @ A) @ B)]: ((P2 @ X5))))) = (^ [P3:(((sum_sum @ A) @ B) > $o)]: (((? [X:A]: ((P3 @ (((sum_Inl @ A) @ B) @ X)))) | (? [X:B]: ((P3 @ (((sum_Inr @ B) @ A) @ X))))))))))).
% 0.24/1.51 thf(fact_71_split__sum__all, axiom, (! [B:$tType,A:$tType]: (((^ [P2:(((sum_sum @ A) @ B) > $o)]: ((! [X5:((sum_sum @ A) @ B)]: ((P2 @ X5))))) = (^ [P3:(((sum_sum @ A) @ B) > $o)]: (((! [X:A]: ((P3 @ (((sum_Inl @ A) @ B) @ X)))) & (! [X:B]: ((P3 @ (((sum_Inr @ B) @ A) @ X))))))))))).
% 0.24/1.51 thf(fact_72_old_Osum_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((sum_sum @ A) @ B)]: (((! [A7:A]: ((Y != (((sum_Inl @ A) @ B) @ A7)))) => (~ ((! [B7:B]: ((Y != (((sum_Inr @ B) @ A) @ B7)))))))))).
% 0.24/1.51 thf(fact_73_old_Osum_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((sum_sum @ A) @ B) > $o),Sum:((sum_sum @ A) @ B)]: (((! [A7:A]: ((P @ (((sum_Inl @ A) @ B) @ A7)))) => ((! [B7:B]: ((P @ (((sum_Inr @ B) @ A) @ B7)))) => (P @ Sum)))))).
% 0.24/1.51 thf(fact_74_map__sum_Osimps_I2_J, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,F1:(A > C),F2:(B > D),A2:B]: (((((((((sum_map_sum @ A) @ C) @ B) @ D) @ F1) @ F2) @ (((sum_Inr @ B) @ A) @ A2)) = (((sum_Inr @ D) @ C) @ (F2 @ A2)))))).
% 0.24/1.51 thf(fact_75_map__sum__InrD, axiom, (! [C:$tType,A:$tType,D:$tType,B:$tType,F:(C > A),G:(D > B),Z:((sum_sum @ C) @ D),X2:B]: ((((((((((sum_map_sum @ C) @ A) @ D) @ B) @ F) @ G) @ Z) = (((sum_Inr @ B) @ A) @ X2)) => (? [Y2:D]: (((Z = (((sum_Inr @ D) @ C) @ Y2)) & ((G @ Y2) = X2)))))))).
% 0.24/1.51 thf(fact_76_inFr2__Ind, axiom, (! [Ns:(set @ n),Tr1:dtree,T2:t,Tr:dtree]: (((((gram_L805317441_inFr2 @ Ns) @ Tr1) @ T2) => ((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => (((gram_L805317441_inFr2 @ Ns) @ Tr) @ T2))))))).
% 0.24/1.51 thf(fact_77_root__prodOf, axiom, (! [Tr2:dtree,Tr:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr2)) @ (cont @ Tr)) => (((member @ ((sum_sum @ t) @ n)) @ (((sum_Inr @ n) @ t) @ (root @ Tr2))) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr))))))).
% 0.24/1.51 thf(fact_78_inFr2__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t]: (((((gram_L805317441_inFr2 @ Ns) @ Tr) @ T2) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 0.24/1.51 thf(fact_79_Inl__Inr__image__cong, axiom, (! [B:$tType,A:$tType,A4:(set @ ((sum_sum @ A) @ B)),B3:(set @ ((sum_sum @ A) @ B))]: (((((((vimage @ A) @ ((sum_sum @ A) @ B)) @ ((sum_Inl @ A) @ B)) @ A4) = ((((vimage @ A) @ ((sum_sum @ A) @ B)) @ ((sum_Inl @ A) @ B)) @ B3)) => ((((((vimage @ B) @ ((sum_sum @ A) @ B)) @ ((sum_Inr @ B) @ A)) @ A4) = ((((vimage @ B) @ ((sum_sum @ A) @ B)) @ ((sum_Inr @ B) @ A)) @ B3)) => (A4 = B3)))))).
% 0.24/1.51 thf(fact_80_Inr__oplus__elim, axiom, (! [A:$tType,C:$tType,B:$tType,Tr:B,F:(C > B),Tns:(set @ ((sum_sum @ A) @ C))]: (((((member @ ((sum_sum @ A) @ B)) @ (((sum_Inr @ B) @ A) @ Tr)) @ ((((image @ ((sum_sum @ A) @ C)) @ ((sum_sum @ A) @ B)) @ ((((((sum_map_sum @ A) @ A) @ C) @ B) @ (id @ A)) @ F)) @ Tns)) => (? [N3:C]: (((((member @ ((sum_sum @ A) @ C)) @ (((sum_Inr @ C) @ A) @ N3)) @ Tns) & ((F @ N3) = Tr)))))))).
% 0.24/1.51 thf(fact_81_Gram__Lang__Mirabelle__ojxrtuoybn_OInr__cont__hsubst__eq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) = (root @ Tr0)) => (((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ ((gram_L1004374585hsubst @ Tr0) @ Tr))) = ((((image @ dtree) @ dtree) @ (gram_L1004374585hsubst @ Tr0)) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr0)))))))).
% 0.24/1.51 thf(fact_82_Inf_OINF__cong, axiom, (! [A:$tType,B:$tType,A4:(set @ B),B3:(set @ B),C2:(B > A),D2:(B > A),Inf:((set @ A) > A)]: (((A4 = B3) => ((! [X3:B]: (((((member @ B) @ X3) @ B3) => ((C2 @ X3) = (D2 @ X3))))) => ((Inf @ ((((image @ B) @ A) @ C2) @ A4)) = (Inf @ ((((image @ B) @ A) @ D2) @ B3)))))))).
% 0.24/1.51 thf(fact_83_Sup_OSUP__cong, axiom, (! [A:$tType,B:$tType,A4:(set @ B),B3:(set @ B),C2:(B > A),D2:(B > A),Sup:((set @ A) > A)]: (((A4 = B3) => ((! [X3:B]: (((((member @ B) @ X3) @ B3) => ((C2 @ X3) = (D2 @ X3))))) => ((Sup @ ((((image @ B) @ A) @ C2) @ A4)) = (Sup @ ((((image @ B) @ A) @ D2) @ B3)))))))).
% 0.24/1.51 thf(fact_84_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c__def, axiom, (gram_L1905609002ubst_c = (^ [Tr02:dtree,Tr3:dtree]: (((((if @ (set @ ((sum_sum @ t) @ dtree))) @ ((root @ Tr3) = (root @ Tr02))) @ (cont @ Tr02)) @ (cont @ Tr3)))))).
% 0.24/1.51 thf(fact_85_hsubst__def, axiom, ((gram_L1004374585hsubst @ tr0) = (((unfold @ dtree) @ gram_L1905609017ubst_r) @ (gram_L1905609002ubst_c @ tr0)))).
% 0.24/1.51 thf(fact_86_root__subtrOf, axiom, (! [N4:n,Tr:dtree]: (((((member @ ((sum_sum @ t) @ n)) @ (((sum_Inr @ n) @ t) @ N4)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr))) => ((root @ ((gram_L1614515765ubtrOf @ Tr) @ N4)) = N4))))).
% 0.24/1.51 thf(fact_87_Inr__subtrOf, axiom, (! [N4:n,Tr:dtree]: (((((member @ ((sum_sum @ t) @ n)) @ (((sum_Inr @ n) @ t) @ N4)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr))) => (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ ((gram_L1614515765ubtrOf @ Tr) @ N4))) @ (cont @ Tr)))))).
% 0.24/1.51 thf(fact_88_subtrOf, axiom, (! [N4:n,Tr:dtree]: (((((member @ ((sum_sum @ t) @ n)) @ (((sum_Inr @ n) @ t) @ N4)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr))) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ ((gram_L1614515765ubtrOf @ Tr) @ N4))) @ (cont @ Tr)) & ((root @ ((gram_L1614515765ubtrOf @ Tr) @ N4)) = N4)))))).
% 0.24/1.51 thf(fact_89_finite__hsubst__c, axiom, (! [N4:dtree]: (((finite_finite2 @ ((sum_sum @ t) @ dtree)) @ ((gram_L1905609002ubst_c @ tr0) @ N4))))).
% 0.24/1.51 thf(fact_90_obj__sumE, axiom, (! [A:$tType,B:$tType,S:((sum_sum @ A) @ B)]: (((! [X3:A]: ((S != (((sum_Inl @ A) @ B) @ X3)))) => (~ ((! [X3:B]: ((S != (((sum_Inr @ B) @ A) @ X3)))))))))).
% 0.24/1.51 thf(fact_91_Node__root__cont, axiom, (! [Tr:dtree]: ((((node @ (root @ Tr)) @ (cont @ Tr)) = Tr)))).
% 0.24/1.51 thf(fact_92_inFr_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:t]: (((((gram_L1333338417e_inFr @ A1) @ A22) @ A32) => (((((member @ n) @ (root @ A22)) @ A1) => (~ ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ A32)) @ (cont @ A22))))) => (~ (((((member @ n) @ (root @ A22)) @ A1) => (! [Tr12:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ A22)) => (~ ((((gram_L1333338417e_inFr @ A1) @ Tr12) @ A32)))))))))))))).
% 0.24/1.51 thf(fact_93_root__Node, axiom, (! [N4:n,As:(set @ ((sum_sum @ t) @ dtree))]: (((root @ ((node @ N4) @ As)) = N4)))).
% 0.24/1.51 thf(fact_94_dtree__simps, axiom, (! [As:(set @ ((sum_sum @ t) @ dtree)),As2:(set @ ((sum_sum @ t) @ dtree)),N4:n,N5:n]: ((((finite_finite2 @ ((sum_sum @ t) @ dtree)) @ As) => (((finite_finite2 @ ((sum_sum @ t) @ dtree)) @ As2) => ((((node @ N4) @ As) = ((node @ N5) @ As2)) = ((N4 = N5) & (As = As2)))))))).
% 0.24/1.51 thf(fact_95_cont__Node, axiom, (! [As:(set @ ((sum_sum @ t) @ dtree)),N4:n]: ((((finite_finite2 @ ((sum_sum @ t) @ dtree)) @ As) => ((cont @ ((node @ N4) @ As)) = As))))).
% 0.24/1.51 thf(fact_96_dtree__cases, axiom, (! [Tr:dtree]: ((~ ((! [N3:n,As3:(set @ ((sum_sum @ t) @ dtree))]: ((((finite_finite2 @ ((sum_sum @ t) @ dtree)) @ As3) => (Tr != ((node @ N3) @ As3)))))))))).
% 0.24/1.51 thf(fact_97_finite__cont, axiom, (! [Tr:dtree]: (((finite_finite2 @ ((sum_sum @ t) @ dtree)) @ (cont @ Tr))))).
% 0.24/1.51 thf(fact_98_Gram__Lang__Mirabelle__ojxrtuoybn_Ofinite__hsubst__c, axiom, (! [Tr0:dtree,N4:dtree]: (((finite_finite2 @ ((sum_sum @ t) @ dtree)) @ ((gram_L1905609002ubst_c @ Tr0) @ N4))))).
% 0.24/1.51 thf(fact_99_inFr__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 0.24/1.51 thf(fact_100_not__root__inFr, axiom, (! [Tr:dtree,Ns:(set @ n),T2:t]: (((~ ((((member @ n) @ (root @ Tr)) @ Ns))) => (~ ((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2))))))).
% 0.24/1.51 thf(fact_101_inFr__inFr2, axiom, (gram_L1333338417e_inFr = gram_L805317441_inFr2)).
% 0.24/1.51 thf(fact_102_unfold_I1_J, axiom, (! [A:$tType,Rt:(A > n),Ct:(A > (set @ ((sum_sum @ t) @ A))),B2:A]: (((root @ ((((unfold @ A) @ Rt) @ Ct) @ B2)) = (Rt @ B2))))).
% 0.24/1.51 thf(fact_103_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__def, axiom, (gram_L1004374585hsubst = (^ [Tr02:dtree]: ((((unfold @ dtree) @ gram_L1905609017ubst_r) @ (gram_L1905609002ubst_c @ Tr02)))))).
% 0.24/1.51 thf(fact_104_not__arg__cong__Inr, axiom, (! [B:$tType,A:$tType,X2:A,Y:A]: (((X2 != Y) => ((((sum_Inr @ A) @ B) @ X2) != (((sum_Inr @ A) @ B) @ Y)))))).
% 0.24/1.51 thf(fact_105_unfold_I2_J, axiom, (! [A:$tType,Ct:(A > (set @ ((sum_sum @ t) @ A))),B2:A,Rt:(A > n)]: ((((finite_finite2 @ ((sum_sum @ t) @ A)) @ (Ct @ B2)) => ((cont @ ((((unfold @ A) @ Rt) @ Ct) @ B2)) = ((((image @ ((sum_sum @ t) @ A)) @ ((sum_sum @ t) @ dtree)) @ ((((((sum_map_sum @ t) @ t) @ A) @ dtree) @ (id @ t)) @ (((unfold @ A) @ Rt) @ Ct))) @ (Ct @ B2))))))).
% 0.24/1.51 thf(fact_106_hsubst__r__def, axiom, (gram_L1905609017ubst_r = root)).
% 0.24/1.51 thf(fact_107_inFr_OInd, axiom, (! [Tr:dtree,Ns:(set @ n),Tr1:dtree,T2:t]: (((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => ((((gram_L1333338417e_inFr @ Ns) @ Tr1) @ T2) => (((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2))))))).
% 0.24/1.51 thf(fact_108_inFr_OBase, axiom, (! [Tr:dtree,Ns:(set @ n),T2:t]: (((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T2)) @ (cont @ Tr)) => (((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2)))))).
% 0.24/1.51 thf(fact_109_inFr_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:t,P:((set @ n) > (dtree > (t > $o)))]: (((((gram_L1333338417e_inFr @ X1) @ X22) @ X32) => ((! [Tr4:dtree,Ns2:(set @ n),T3:t]: (((((member @ n) @ (root @ Tr4)) @ Ns2) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T3)) @ (cont @ Tr4)) => (((P @ Ns2) @ Tr4) @ T3))))) => ((! [Tr4:dtree,Ns2:(set @ n),Tr12:dtree,T3:t]: (((((member @ n) @ (root @ Tr4)) @ Ns2) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr4)) => ((((gram_L1333338417e_inFr @ Ns2) @ Tr12) @ T3) => ((((P @ Ns2) @ Tr12) @ T3) => (((P @ Ns2) @ Tr4) @ T3))))))) => (((P @ X1) @ X22) @ X32))))))).
% 0.24/1.51 thf(fact_110_inFr_Osimps, axiom, (gram_L1333338417e_inFr = (^ [A12:(set @ n),A23:dtree,A33:t]: (((? [Tr3:dtree,Ns3:(set @ n),T4:t]: (((A12 = Ns3) & ((A23 = Tr3) & ((A33 = T4) & ((((member @ n) @ (root @ Tr3)) @ Ns3) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T4)) @ (cont @ Tr3)))))))) | (? [Tr3:dtree,Ns3:(set @ n),Tr13:dtree,T4:t]: (((A12 = Ns3) & ((A23 = Tr3) & ((A33 = T4) & ((((member @ n) @ (root @ Tr3)) @ Ns3) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr3)) & (((gram_L1333338417e_inFr @ Ns3) @ Tr13) @ T4))))))))))))).
% 0.24/1.51 thf(fact_111_inFrr__def, axiom, (gram_L805317505_inFrr = (^ [Ns3:(set @ n),Tr3:dtree,T4:t]: ((? [Tr5:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr5)) @ (cont @ Tr3)) & (((gram_L1333338417e_inFr @ Ns3) @ Tr5) @ T4)))))))).
% 0.24/1.51 thf(fact_112_finite__imageI, axiom, (! [B:$tType,A:$tType,F4:(set @ A),H2:(A > B)]: ((((finite_finite2 @ A) @ F4) => ((finite_finite2 @ B) @ ((((image @ A) @ B) @ H2) @ F4)))))).
% 0.24/1.51 thf(fact_113_surj__subtrOf, axiom, (! [Tr:dtree,Tr2:dtree]: (((gram_L864798063lle_wf @ Tr) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr2)) @ (cont @ Tr)) => (? [N3:n]: (((((member @ ((sum_sum @ t) @ n)) @ (((sum_Inr @ n) @ t) @ N3)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr))) & (((gram_L1614515765ubtrOf @ Tr) @ N3) = Tr2))))))))).
% 0.24/1.51 thf(fact_114_finite__code, axiom, (! [A:$tType]: ((((finite_finite @ A) @ (type @ A)) => ((finite_finite2 @ A) = (^ [A8:(set @ A)]: ($true))))))).
% 0.24/1.51 thf(fact_115_subtrOf__root, axiom, (! [Tr:dtree,Tr2:dtree]: (((gram_L864798063lle_wf @ Tr) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr2)) @ (cont @ Tr)) => (((gram_L1614515765ubtrOf @ Tr) @ (root @ Tr2)) = Tr2)))))).
% 0.24/1.51 thf(fact_116_wf__inj, axiom, (! [Tr:dtree,Tr1:dtree,Tr22:dtree]: (((gram_L864798063lle_wf @ Tr) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr22)) @ (cont @ Tr)) => (((root @ Tr1) = (root @ Tr22)) = (Tr1 = Tr22)))))))).
% 0.24/1.51 thf(fact_117_wf__cont, axiom, (! [Tr:dtree,Tr2:dtree]: (((gram_L864798063lle_wf @ Tr) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr2)) @ (cont @ Tr)) => (gram_L864798063lle_wf @ Tr2)))))).
% 0.24/1.51 thf(fact_118_finite, axiom, (! [A:$tType]: ((((finite_finite @ A) @ (type @ A)) => (! [A4:(set @ A)]: (((finite_finite2 @ A) @ A4))))))).
% 0.24/1.51 thf(fact_119_finite__set__choice, axiom, (! [B:$tType,A:$tType,A4:(set @ A),P:(A > (B > $o))]: ((((finite_finite2 @ A) @ A4) => ((! [X3:A]: (((((member @ A) @ X3) @ A4) => (? [X12:B]: (((P @ X3) @ X12)))))) => (? [F5:(A > B)]: ((! [X4:A]: (((((member @ A) @ X4) @ A4) => ((P @ X4) @ (F5 @ X4)))))))))))).
% 0.24/1.51 thf(fact_120_inFr2_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:t]: (((((gram_L805317441_inFr2 @ A1) @ A22) @ A32) => (((((member @ n) @ (root @ A22)) @ A1) => (~ ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ A32)) @ (cont @ A22))))) => (~ ((! [Tr12:dtree,Tr4:dtree,Ns1:(set @ n)]: (((A1 = (((insert @ n) @ (root @ Tr4)) @ Ns1)) => ((A22 = Tr4) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr4)) => (~ ((((gram_L805317441_inFr2 @ Ns1) @ Tr12) @ A32))))))))))))))).
% 0.24/1.51 thf(fact_121_inFr2_Osimps, axiom, (gram_L805317441_inFr2 = (^ [A12:(set @ n),A23:dtree,A33:t]: (((? [Tr3:dtree,Ns3:(set @ n),T4:t]: (((A12 = Ns3) & ((A23 = Tr3) & ((A33 = T4) & ((((member @ n) @ (root @ Tr3)) @ Ns3) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T4)) @ (cont @ Tr3)))))))) | (? [Tr13:dtree,Tr3:dtree,Ns12:(set @ n),T4:t]: (((A12 = (((insert @ n) @ (root @ Tr3)) @ Ns12)) & ((A23 = Tr3) & ((A33 = T4) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr3)) & (((gram_L805317441_inFr2 @ Ns12) @ Tr13) @ T4)))))))))))).
% 0.24/1.51 thf(fact_122_inFr2_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:t,P:((set @ n) > (dtree > (t > $o)))]: (((((gram_L805317441_inFr2 @ X1) @ X22) @ X32) => ((! [Tr4:dtree,Ns2:(set @ n),T3:t]: (((((member @ n) @ (root @ Tr4)) @ Ns2) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T3)) @ (cont @ Tr4)) => (((P @ Ns2) @ Tr4) @ T3))))) => ((! [Tr12:dtree,Tr4:dtree,Ns1:(set @ n),T3:t]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr4)) => ((((gram_L805317441_inFr2 @ Ns1) @ Tr12) @ T3) => ((((P @ Ns1) @ Tr12) @ T3) => (((P @ (((insert @ n) @ (root @ Tr4)) @ Ns1)) @ Tr4) @ T3)))))) => (((P @ X1) @ X22) @ X32))))))).
% 0.24/1.51 thf(fact_123_wf__inj__on, axiom, (! [Tr:dtree]: (((gram_L864798063lle_wf @ Tr) => ((((inj_on @ dtree) @ n) @ root) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr))))))).
% 0.24/1.51 thf(fact_124_insert__absorb2, axiom, (! [A:$tType,X2:A,A4:(set @ A)]: (((((insert @ A) @ X2) @ (((insert @ A) @ X2) @ A4)) = (((insert @ A) @ X2) @ A4))))).
% 0.24/1.51 thf(fact_125_insert__iff, axiom, (! [A:$tType,A2:A,B2:A,A4:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B2) @ A4)) = ((A2 = B2) | (((member @ A) @ A2) @ A4)))))).
% 0.24/1.51 thf(fact_126_insertCI, axiom, (! [A:$tType,A2:A,B3:(set @ A),B2:A]: ((((~ ((((member @ A) @ A2) @ B3))) => (A2 = B2)) => (((member @ A) @ A2) @ (((insert @ A) @ B2) @ B3)))))).
% 0.24/1.51 thf(fact_127_insert__image, axiom, (! [B:$tType,A:$tType,X2:A,A4:(set @ A),F:(A > B)]: (((((member @ A) @ X2) @ A4) => ((((insert @ B) @ (F @ X2)) @ ((((image @ A) @ B) @ F) @ A4)) = ((((image @ A) @ B) @ F) @ A4)))))).
% 0.24/1.51 thf(fact_128_image__insert, axiom, (! [A:$tType,B:$tType,F:(B > A),A2:B,B3:(set @ B)]: ((((((image @ B) @ A) @ F) @ (((insert @ B) @ A2) @ B3)) = (((insert @ A) @ (F @ A2)) @ ((((image @ B) @ A) @ F) @ B3)))))).
% 0.24/1.51 thf(fact_129_finite__insert, axiom, (! [A:$tType,A2:A,A4:(set @ A)]: ((((finite_finite2 @ A) @ (((insert @ A) @ A2) @ A4)) = ((finite_finite2 @ A) @ A4))))).
% 0.24/1.51 thf(fact_130_finite_OinsertI, axiom, (! [A:$tType,A4:(set @ A),A2:A]: ((((finite_finite2 @ A) @ A4) => ((finite_finite2 @ A) @ (((insert @ A) @ A2) @ A4)))))).
% 0.24/1.51 thf(fact_131_inj__on__image__iff, axiom, (! [B:$tType,A:$tType,A4:(set @ A),G:(A > B),F:(A > A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A4) => (! [Xa:A]: (((((member @ A) @ Xa) @ A4) => (((G @ (F @ X3)) = (G @ (F @ Xa))) = ((G @ X3) = (G @ Xa))))))))) => (((((inj_on @ A) @ A) @ F) @ A4) => (((((inj_on @ A) @ B) @ G) @ ((((image @ A) @ A) @ F) @ A4)) = ((((inj_on @ A) @ B) @ G) @ A4))))))).
% 0.24/1.51 thf(fact_132_inj__img__insertE, axiom, (! [B:$tType,A:$tType,F:(A > B),A4:(set @ A),X2:B,B3:(set @ B)]: ((((((inj_on @ A) @ B) @ F) @ A4) => ((~ ((((member @ B) @ X2) @ B3))) => (((((insert @ B) @ X2) @ B3) = ((((image @ A) @ B) @ F) @ A4)) => (~ ((! [X6:A,A9:(set @ A)]: (((~ ((((member @ A) @ X6) @ A9))) => ((A4 = (((insert @ A) @ X6) @ A9)) => ((X2 = (F @ X6)) => (B3 != ((((image @ A) @ B) @ F) @ A9))))))))))))))).
% 0.24/1.51 thf(fact_133_inj__on__id, axiom, (! [A:$tType,A4:(set @ A)]: (((((inj_on @ A) @ A) @ (id @ A)) @ A4)))).
% 0.24/1.51 thf(fact_134_mk__disjoint__insert, axiom, (! [A:$tType,A2:A,A4:(set @ A)]: (((((member @ A) @ A2) @ A4) => (? [B8:(set @ A)]: (((A4 = (((insert @ A) @ A2) @ B8)) & (~ ((((member @ A) @ A2) @ B8)))))))))).
% 0.24/1.51 thf(fact_135_inj__on__inverseI, axiom, (! [B:$tType,A:$tType,A4:(set @ A),G:(B > A),F:(A > B)]: (((! [X3:A]: (((((member @ A) @ X3) @ A4) => ((G @ (F @ X3)) = X3)))) => ((((inj_on @ A) @ B) @ F) @ A4))))).
% 0.24/1.51 thf(fact_136_insert__commute, axiom, (! [A:$tType,X2:A,Y:A,A4:(set @ A)]: (((((insert @ A) @ X2) @ (((insert @ A) @ Y) @ A4)) = (((insert @ A) @ Y) @ (((insert @ A) @ X2) @ A4)))))).
% 0.24/1.51 thf(fact_137_inj__on__contraD, axiom, (! [B:$tType,A:$tType,F:(A > B),A4:(set @ A),X2:A,Y:A]: ((((((inj_on @ A) @ B) @ F) @ A4) => ((X2 != Y) => ((((member @ A) @ X2) @ A4) => ((((member @ A) @ Y) @ A4) => ((F @ X2) != (F @ Y))))))))).
% 0.24/1.51 thf(fact_138_insert__eq__iff, axiom, (! [A:$tType,A2:A,A4:(set @ A),B2:A,B3:(set @ A)]: (((~ ((((member @ A) @ A2) @ A4))) => ((~ ((((member @ A) @ B2) @ B3))) => (((((insert @ A) @ A2) @ A4) = (((insert @ A) @ B2) @ B3)) = (((A2 = B2) => (A4 = B3)) & ((A2 != B2) => (? [C3:(set @ A)]: (((A4 = (((insert @ A) @ B2) @ C3)) & ((~ ((((member @ A) @ B2) @ C3))) & ((B3 = (((insert @ A) @ A2) @ C3)) & (~ ((((member @ A) @ A2) @ C3)))))))))))))))).
% 0.24/1.51 thf(fact_139_insert__absorb, axiom, (! [A:$tType,A2:A,A4:(set @ A)]: (((((member @ A) @ A2) @ A4) => ((((insert @ A) @ A2) @ A4) = A4))))).
% 0.24/1.51 thf(fact_140_inj__on__eq__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),A4:(set @ A),X2:A,Y:A]: ((((((inj_on @ A) @ B) @ F) @ A4) => ((((member @ A) @ X2) @ A4) => ((((member @ A) @ Y) @ A4) => (((F @ X2) = (F @ Y)) = (X2 = Y)))))))).
% 0.24/1.51 thf(fact_141_insert__ident, axiom, (! [A:$tType,X2:A,A4:(set @ A),B3:(set @ A)]: (((~ ((((member @ A) @ X2) @ A4))) => ((~ ((((member @ A) @ X2) @ B3))) => (((((insert @ A) @ X2) @ A4) = (((insert @ A) @ X2) @ B3)) = (A4 = B3))))))).
% 0.24/1.51 thf(fact_142_inj__on__cong, axiom, (! [B:$tType,A:$tType,A4:(set @ A),F:(A > B),G:(A > B)]: (((! [A7:A]: (((((member @ A) @ A7) @ A4) => ((F @ A7) = (G @ A7))))) => (((((inj_on @ A) @ B) @ F) @ A4) = ((((inj_on @ A) @ B) @ G) @ A4)))))).
% 0.24/1.51 thf(fact_143_Set_Oset__insert, axiom, (! [A:$tType,X2:A,A4:(set @ A)]: (((((member @ A) @ X2) @ A4) => (~ ((! [B8:(set @ A)]: (((A4 = (((insert @ A) @ X2) @ B8)) => (((member @ A) @ X2) @ B8)))))))))).
% 0.24/1.51 thf(fact_144_inj__on__def, axiom, (! [B:$tType,A:$tType]: ((((inj_on @ A) @ B) = (^ [F6:(A > B),A8:(set @ A)]: ((! [X:A]: (((((member @ A) @ X) @ A8) => (! [Y3:A]: (((((member @ A) @ Y3) @ A8) => (((F6 @ X) = (F6 @ Y3)) => (X = Y3)))))))))))))).
% 0.24/1.51 thf(fact_145_insertI2, axiom, (! [A:$tType,A2:A,B3:(set @ A),B2:A]: (((((member @ A) @ A2) @ B3) => (((member @ A) @ A2) @ (((insert @ A) @ B2) @ B3)))))).
% 0.24/1.51 thf(fact_146_insertI1, axiom, (! [A:$tType,A2:A,B3:(set @ A)]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ B3))))).
% 0.24/1.51 thf(fact_147_insertE, axiom, (! [A:$tType,A2:A,B2:A,A4:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B2) @ A4)) => ((A2 != B2) => (((member @ A) @ A2) @ A4)))))).
% 0.24/1.51 thf(fact_148_inj__onI, axiom, (! [B:$tType,A:$tType,A4:(set @ A),F:(A > B)]: (((! [X3:A,Y2:A]: (((((member @ A) @ X3) @ A4) => ((((member @ A) @ Y2) @ A4) => (((F @ X3) = (F @ Y2)) => (X3 = Y2)))))) => ((((inj_on @ A) @ B) @ F) @ A4))))).
% 0.24/1.51 thf(fact_149_inj__onD, axiom, (! [B:$tType,A:$tType,F:(A > B),A4:(set @ A),X2:A,Y:A]: ((((((inj_on @ A) @ B) @ F) @ A4) => (((F @ X2) = (F @ Y)) => ((((member @ A) @ X2) @ A4) => ((((member @ A) @ Y) @ A4) => (X2 = Y)))))))).
% 0.24/1.51 thf(fact_150_finite__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A4:(set @ B)]: ((((finite_finite2 @ A) @ ((((image @ B) @ A) @ F) @ A4)) => (((((inj_on @ B) @ A) @ F) @ A4) => ((finite_finite2 @ B) @ A4)))))).
% 0.24/1.51 thf(fact_151_finite__image__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),A4:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ A4) => (((finite_finite2 @ B) @ ((((image @ A) @ B) @ F) @ A4)) = ((finite_finite2 @ A) @ A4)))))).
% 0.24/1.51 thf(fact_152_inFr__Ind__minus, axiom, (! [Ns13:(set @ n),Tr1:dtree,T2:t,Tr:dtree]: (((((gram_L1333338417e_inFr @ Ns13) @ Tr1) @ T2) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => (((gram_L1333338417e_inFr @ (((insert @ n) @ (root @ Tr)) @ Ns13)) @ Tr) @ T2)))))).
% 0.24/1.51 thf(fact_153_inFr2_OInd, axiom, (! [Tr1:dtree,Tr:dtree,Ns13:(set @ n),T2:t]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => ((((gram_L805317441_inFr2 @ Ns13) @ Tr1) @ T2) => (((gram_L805317441_inFr2 @ (((insert @ n) @ (root @ Tr)) @ Ns13)) @ Tr) @ T2)))))).
% 0.24/1.51 thf(fact_154_wf__subtr__inj__on, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr:dtree]: (((gram_L864798063lle_wf @ Tr1) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => ((((inj_on @ dtree) @ n) @ root) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr)))))))).
% 0.24/1.51 thf(fact_155_wf_Ocases, axiom, (! [A2:dtree]: (((gram_L864798063lle_wf @ A2) => (~ (((((member @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n)))) @ ((((product_Pair @ n) @ (set @ ((sum_sum @ t) @ n))) @ (root @ A2)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ A2)))) @ gram_L1451583632elle_P) => (((((inj_on @ dtree) @ n) @ root) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ A2))) => (~ ((! [Tr6:dtree]: (((((member @ dtree) @ Tr6) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ A2))) => (gram_L864798063lle_wf @ Tr6)))))))))))))).
% 0.24/1.51 thf(fact_156_wf_Osimps, axiom, (gram_L864798063lle_wf = (^ [A10:dtree]: ((? [Tr3:dtree]: (((A10 = Tr3) & ((((member @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n)))) @ ((((product_Pair @ n) @ (set @ ((sum_sum @ t) @ n))) @ (root @ Tr3)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr3)))) @ gram_L1451583632elle_P) & (((((inj_on @ dtree) @ n) @ root) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr3))) & (! [X:dtree]: (((((member @ dtree) @ X) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr3))) => (gram_L864798063lle_wf @ X))))))))))))).
% 0.24/1.51 thf(fact_157_wf__coind, axiom, (! [Phi:(dtree > $o),Tr:dtree]: (((Phi @ Tr) => ((! [Tr4:dtree]: (((Phi @ Tr4) => ((((member @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n)))) @ ((((product_Pair @ n) @ (set @ ((sum_sum @ t) @ n))) @ (root @ Tr4)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr4)))) @ gram_L1451583632elle_P) & (((((inj_on @ dtree) @ n) @ root) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr4))) & (! [X3:dtree]: (((((member @ dtree) @ X3) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr4))) => ((Phi @ X3) | (gram_L864798063lle_wf @ X3)))))))))) => (gram_L864798063lle_wf @ Tr)))))).
% 0.24/1.51 thf(fact_158_inj__Inr, axiom, (! [B:$tType,A:$tType,A4:(set @ A)]: (((((inj_on @ A) @ ((sum_sum @ B) @ A)) @ ((sum_Inr @ A) @ B)) @ A4)))).
% 0.24/1.51 thf(fact_159_inj__Inl, axiom, (! [B:$tType,A:$tType,A4:(set @ A)]: (((((inj_on @ A) @ ((sum_sum @ A) @ B)) @ ((sum_Inl @ A) @ B)) @ A4)))).
% 0.24/1.51 thf(fact_160_subtr__trans, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree,Tr32:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => ((((gram_L716654942_subtr @ Ns) @ Tr22) @ Tr32) => (((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr32)))))).
% 0.24/1.51 thf(fact_161_used, axiom, (! [N4:n]: ((? [Tns2:(set @ ((sum_sum @ t) @ n))]: ((((member @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n)))) @ ((((product_Pair @ n) @ (set @ ((sum_sum @ t) @ n))) @ N4) @ Tns2)) @ gram_L1451583632elle_P)))))).
% 0.24/1.51 thf(fact_162_finite__in__P, axiom, (! [N4:n,Tns:(set @ ((sum_sum @ t) @ n))]: (((((member @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n)))) @ ((((product_Pair @ n) @ (set @ ((sum_sum @ t) @ n))) @ N4) @ Tns)) @ gram_L1451583632elle_P) => ((finite_finite2 @ ((sum_sum @ t) @ n)) @ Tns))))).
% 0.24/1.51 thf(fact_163_subtr__rootR__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr22)) @ Ns))))).
% 0.24/1.51 thf(fact_164_subtr__rootL__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr1)) @ Ns))))).
% 0.24/1.51 thf(fact_165_subtr_ORefl, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L716654942_subtr @ Ns) @ Tr) @ Tr))))).
% 0.24/1.51 thf(fact_166_wf__subtr, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr:dtree]: (((gram_L864798063lle_wf @ Tr1) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => (gram_L864798063lle_wf @ Tr)))))).
% 0.24/1.51 thf(fact_167_subtr__inFr, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t,Tr1:dtree]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => (((gram_L1333338417e_inFr @ Ns) @ Tr1) @ T2)))))).
% 0.24/1.51 thf(fact_168_wf__subtr__P, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr:dtree]: (((gram_L864798063lle_wf @ Tr1) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => (((member @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n)))) @ ((((product_Pair @ n) @ (set @ ((sum_sum @ t) @ n))) @ (root @ Tr)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr)))) @ gram_L1451583632elle_P)))))).
% 0.24/1.51 thf(fact_169_subtr__inductL, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree,Phi:((set @ n) > (dtree > (dtree > $o)))]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => ((! [Ns2:(set @ n),Tr4:dtree]: ((((Phi @ Ns2) @ Tr4) @ Tr4))) => ((! [Ns2:(set @ n),Tr12:dtree,Tr23:dtree,Tr33:dtree]: (((((member @ n) @ (root @ Tr12)) @ Ns2) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr23)) => ((((gram_L716654942_subtr @ Ns2) @ Tr23) @ Tr33) => ((((Phi @ Ns2) @ Tr23) @ Tr33) => (((Phi @ Ns2) @ Tr12) @ Tr33))))))) => (((Phi @ Ns) @ Tr1) @ Tr22))))))).
% 0.24/1.51 thf(fact_170_subtr_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:dtree,P:((set @ n) > (dtree > (dtree > $o)))]: (((((gram_L716654942_subtr @ X1) @ X22) @ X32) => ((! [Tr4:dtree,Ns2:(set @ n)]: (((((member @ n) @ (root @ Tr4)) @ Ns2) => (((P @ Ns2) @ Tr4) @ Tr4)))) => ((! [Tr33:dtree,Ns2:(set @ n),Tr12:dtree,Tr23:dtree]: (((((member @ n) @ (root @ Tr33)) @ Ns2) => ((((gram_L716654942_subtr @ Ns2) @ Tr12) @ Tr23) => ((((P @ Ns2) @ Tr12) @ Tr23) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr23)) @ (cont @ Tr33)) => (((P @ Ns2) @ Tr12) @ Tr33))))))) => (((P @ X1) @ X22) @ X32))))))).
% 0.24/1.51 thf(fact_171_subtr__StepL, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr22:dtree,Tr32:dtree]: (((((member @ n) @ (root @ Tr1)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr22)) => ((((gram_L716654942_subtr @ Ns) @ Tr22) @ Tr32) => (((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr32))))))).
% 0.24/1.51 thf(fact_172_subtr_Osimps, axiom, (gram_L716654942_subtr = (^ [A12:(set @ n),A23:dtree,A33:dtree]: (((? [Tr3:dtree,Ns3:(set @ n)]: (((A12 = Ns3) & ((A23 = Tr3) & ((A33 = Tr3) & (((member @ n) @ (root @ Tr3)) @ Ns3)))))) | (? [Tr34:dtree,Ns3:(set @ n),Tr13:dtree,Tr24:dtree]: (((A12 = Ns3) & ((A23 = Tr13) & ((A33 = Tr34) & ((((member @ n) @ (root @ Tr34)) @ Ns3) & ((((gram_L716654942_subtr @ Ns3) @ Tr13) @ Tr24) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr24)) @ (cont @ Tr34)))))))))))))).
% 0.24/1.51 thf(fact_173_subtr_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:dtree]: (((((gram_L716654942_subtr @ A1) @ A22) @ A32) => (((A32 = A22) => (~ ((((member @ n) @ (root @ A22)) @ A1)))) => (~ (((((member @ n) @ (root @ A32)) @ A1) => (! [Tr23:dtree]: (((((gram_L716654942_subtr @ A1) @ A22) @ Tr23) => (~ ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr23)) @ (cont @ A32))))))))))))))).
% 0.24/1.51 thf(fact_174_subtr_OStep, axiom, (! [Tr32:dtree,Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((member @ n) @ (root @ Tr32)) @ Ns) => ((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr22)) @ (cont @ Tr32)) => (((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr32))))))).
% 0.24/1.51 thf(fact_175_inFr__subtr, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2) => (? [Tr7:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr7) @ Tr) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T2)) @ (cont @ Tr7))))))))).
% 0.24/1.51 thf(fact_176_wf__P, axiom, (! [Tr:dtree]: (((gram_L864798063lle_wf @ Tr) => (((member @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n)))) @ ((((product_Pair @ n) @ (set @ ((sum_sum @ t) @ n))) @ (root @ Tr)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr)))) @ gram_L1451583632elle_P))))).
% 0.24/1.51 thf(fact_177_wf__raw__coind, axiom, (! [Phi:(dtree > $o),Tr:dtree]: (((Phi @ Tr) => ((! [Tr4:dtree]: (((Phi @ Tr4) => ((((member @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n)))) @ ((((product_Pair @ n) @ (set @ ((sum_sum @ t) @ n))) @ (root @ Tr4)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr4)))) @ gram_L1451583632elle_P) & (((((inj_on @ dtree) @ n) @ root) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr4))) & (! [X3:dtree]: (((((member @ dtree) @ X3) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr4))) => (Phi @ X3))))))))) => (gram_L864798063lle_wf @ Tr)))))).
% 0.24/1.51 thf(fact_178_wf_Ocoinduct, axiom, (! [X7:(dtree > $o),X2:dtree]: (((X7 @ X2) => ((! [X3:dtree]: (((X7 @ X3) => (? [Tr8:dtree]: (((X3 = Tr8) & ((((member @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n)))) @ ((((product_Pair @ n) @ (set @ ((sum_sum @ t) @ n))) @ (root @ Tr8)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr8)))) @ gram_L1451583632elle_P) & (((((inj_on @ dtree) @ n) @ root) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr8))) & (! [Xa:dtree]: (((((member @ dtree) @ Xa) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr8))) => ((X7 @ Xa) | (gram_L864798063lle_wf @ Xa))))))))))))) => (gram_L864798063lle_wf @ X2)))))).
% 0.24/1.51 thf(fact_179_wf_Ointros, axiom, (! [Tr:dtree]: (((((member @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n)))) @ ((((product_Pair @ n) @ (set @ ((sum_sum @ t) @ n))) @ (root @ Tr)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr)))) @ gram_L1451583632elle_P) => (((((inj_on @ dtree) @ n) @ root) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr))) => ((! [Tr7:dtree]: (((((member @ dtree) @ Tr7) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr))) => (gram_L864798063lle_wf @ Tr7)))) => (gram_L864798063lle_wf @ Tr))))))).
% 0.24/1.51 thf(fact_180_S__P, axiom, (! [N4:n]: ((((member @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n)))) @ ((((product_Pair @ n) @ (set @ ((sum_sum @ t) @ n))) @ N4) @ (gram_L1451583635elle_S @ N4))) @ gram_L1451583632elle_P)))).
% 0.24/1.51 thf(fact_181_inItr_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:n,P:((set @ n) > (dtree > (n > $o)))]: (((((gram_L830233218_inItr @ X1) @ X22) @ X32) => ((! [Tr4:dtree,Ns2:(set @ n)]: (((((member @ n) @ (root @ Tr4)) @ Ns2) => (((P @ Ns2) @ Tr4) @ (root @ Tr4))))) => ((! [Tr4:dtree,Ns2:(set @ n),Tr12:dtree,N3:n]: (((((member @ n) @ (root @ Tr4)) @ Ns2) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr4)) => ((((gram_L830233218_inItr @ Ns2) @ Tr12) @ N3) => ((((P @ Ns2) @ Tr12) @ N3) => (((P @ Ns2) @ Tr4) @ N3))))))) => (((P @ X1) @ X22) @ X32))))))).
% 0.24/1.51 thf(fact_182_inItr_Osimps, axiom, (gram_L830233218_inItr = (^ [A12:(set @ n),A23:dtree,A33:n]: (((? [Tr3:dtree,Ns3:(set @ n)]: (((A12 = Ns3) & ((A23 = Tr3) & ((A33 = (root @ Tr3)) & (((member @ n) @ (root @ Tr3)) @ Ns3)))))) | (? [Tr3:dtree,Ns3:(set @ n),Tr13:dtree,N2:n]: (((A12 = Ns3) & ((A23 = Tr3) & ((A33 = N2) & ((((member @ n) @ (root @ Tr3)) @ Ns3) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr3)) & (((gram_L830233218_inItr @ Ns3) @ Tr13) @ N2))))))))))))).
% 0.24/1.51 thf(fact_183_finite__S, axiom, (! [N4:n]: (((finite_finite2 @ ((sum_sum @ t) @ n)) @ (gram_L1451583635elle_S @ N4))))).
% 0.24/1.51 thf(fact_184_inItr_OBase, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L830233218_inItr @ Ns) @ Tr) @ (root @ Tr)))))).
% 0.24/1.51 thf(fact_185_inItr__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,N4:n]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N4) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 0.24/1.51 thf(fact_186_subtr__inItr, axiom, (! [Ns:(set @ n),Tr:dtree,N4:n,Tr1:dtree]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N4) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => (((gram_L830233218_inItr @ Ns) @ Tr1) @ N4)))))).
% 0.24/1.51 thf(fact_187_inItr__subtr, axiom, (! [Ns:(set @ n),Tr:dtree,N4:n]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N4) => (? [Tr7:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr7) @ Tr) & ((root @ Tr7) = N4)))))))).
% 0.24/1.51 thf(fact_188_inItr_OInd, axiom, (! [Tr:dtree,Ns:(set @ n),Tr1:dtree,N4:n]: (((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => ((((gram_L830233218_inItr @ Ns) @ Tr1) @ N4) => (((gram_L830233218_inItr @ Ns) @ Tr) @ N4))))))).
% 0.24/1.51 thf(fact_189_inItr_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:n]: (((((gram_L830233218_inItr @ A1) @ A22) @ A32) => (((A32 = (root @ A22)) => (~ ((((member @ n) @ (root @ A22)) @ A1)))) => (~ (((((member @ n) @ (root @ A22)) @ A1) => (! [Tr12:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ A22)) => (~ ((((gram_L830233218_inItr @ A1) @ Tr12) @ A32)))))))))))))).
% 0.24/1.51 thf(fact_190_cont__deftr, axiom, (! [N4:n]: (((cont @ (gram_L1231612515_deftr @ N4)) = ((((image @ ((sum_sum @ t) @ n)) @ ((sum_sum @ t) @ dtree)) @ ((((((sum_map_sum @ t) @ t) @ n) @ dtree) @ (id @ t)) @ gram_L1231612515_deftr)) @ (gram_L1451583635elle_S @ N4)))))).
% 0.24/1.51 thf(fact_191_subtr2_OStep, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr22:dtree,Tr32:dtree]: (((((member @ n) @ (root @ Tr1)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr22)) => ((((gram_L1283001940subtr2 @ Ns) @ Tr22) @ Tr32) => (((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr32))))))).
% 0.24/1.51 thf(fact_192_subtr2_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:dtree]: (((((gram_L1283001940subtr2 @ A1) @ A22) @ A32) => (((A32 = A22) => (~ ((((member @ n) @ (root @ A22)) @ A1)))) => (~ (((((member @ n) @ (root @ A22)) @ A1) => (! [Tr23:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ A22)) @ (cont @ Tr23)) => (~ ((((gram_L1283001940subtr2 @ A1) @ Tr23) @ A32)))))))))))))).
% 0.24/1.51 thf(fact_193_root__deftr, axiom, (! [N4:n]: (((root @ (gram_L1231612515_deftr @ N4)) = N4)))).
% 0.24/1.51 thf(fact_194_subtr__subtr2, axiom, (gram_L716654942_subtr = gram_L1283001940subtr2)).
% 0.24/1.51 thf(fact_195_subtr2__trans, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree,Tr32:dtree]: (((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => ((((gram_L1283001940subtr2 @ Ns) @ Tr22) @ Tr32) => (((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr32)))))).
% 0.24/1.51 thf(fact_196_subtr2_ORefl, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L1283001940subtr2 @ Ns) @ Tr) @ Tr))))).
% 0.24/1.51 thf(fact_197_subtr2__rootL__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr1)) @ Ns))))).
% 0.24/1.51 thf(fact_198_subtr2__rootR__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr22)) @ Ns))))).
% 0.24/1.51 thf(fact_199_wf__deftr, axiom, (! [N4:n]: ((gram_L864798063lle_wf @ (gram_L1231612515_deftr @ N4))))).
% 0.24/1.51 thf(fact_200_deftr__def, axiom, (gram_L1231612515_deftr = (((unfold @ n) @ (id @ n)) @ gram_L1451583635elle_S))).
% 0.24/1.51 thf(fact_201_subtr2_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:dtree,P:((set @ n) > (dtree > (dtree > $o)))]: (((((gram_L1283001940subtr2 @ X1) @ X22) @ X32) => ((! [Tr4:dtree,Ns2:(set @ n)]: (((((member @ n) @ (root @ Tr4)) @ Ns2) => (((P @ Ns2) @ Tr4) @ Tr4)))) => ((! [Tr12:dtree,Ns2:(set @ n),Tr23:dtree,Tr33:dtree]: (((((member @ n) @ (root @ Tr12)) @ Ns2) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr23)) => ((((gram_L1283001940subtr2 @ Ns2) @ Tr23) @ Tr33) => ((((P @ Ns2) @ Tr23) @ Tr33) => (((P @ Ns2) @ Tr12) @ Tr33))))))) => (((P @ X1) @ X22) @ X32))))))).
% 0.24/1.51 thf(fact_202_subtr2__StepR, axiom, (! [Tr32:dtree,Ns:(set @ n),Tr22:dtree,Tr1:dtree]: (((((member @ n) @ (root @ Tr32)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr22)) @ (cont @ Tr32)) => ((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => (((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr32))))))).
% 0.24/1.51 thf(fact_203_subtr2_Osimps, axiom, (gram_L1283001940subtr2 = (^ [A12:(set @ n),A23:dtree,A33:dtree]: (((? [Tr3:dtree,Ns3:(set @ n)]: (((A12 = Ns3) & ((A23 = Tr3) & ((A33 = Tr3) & (((member @ n) @ (root @ Tr3)) @ Ns3)))))) | (? [Tr13:dtree,Ns3:(set @ n),Tr24:dtree,Tr34:dtree]: (((A12 = Ns3) & ((A23 = Tr13) & ((A33 = Tr34) & ((((member @ n) @ (root @ Tr13)) @ Ns3) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr24)) & (((gram_L1283001940subtr2 @ Ns3) @ Tr24) @ Tr34))))))))))))).
% 0.24/1.51 thf(fact_204_root__o__subst, axiom, ((((((comp @ dtree) @ n) @ dtree) @ root) @ (gram_L1004374585hsubst @ tr0)) = root)).
% 0.24/1.51 thf(fact_205_inf__img__fin__dom, axiom, (! [B:$tType,A:$tType,F:(B > A),A4:(set @ B)]: ((((finite_finite2 @ A) @ ((((image @ B) @ A) @ F) @ A4)) => ((~ (((finite_finite2 @ B) @ A4))) => (? [X3:A]: (((((member @ A) @ X3) @ ((((image @ B) @ A) @ F) @ A4)) & (~ (((finite_finite2 @ B) @ ((((vimage @ B) @ A) @ F) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))))))))))))).
% 0.24/1.51 thf(fact_206_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X:A]: ((~ ((P @ X))))))))).
% 0.24/1.51 thf(fact_207_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X:A]: ((~ ((P @ X))))))))).
% 0.24/1.51 thf(fact_208_all__not__in__conv, axiom, (! [A:$tType,A4:(set @ A)]: (((! [X:A]: ((~ ((((member @ A) @ X) @ A4))))) = (A4 = (bot_bot @ (set @ A))))))).
% 0.24/1.51 thf(fact_209_empty__iff, axiom, (! [A:$tType,C4:A]: ((~ ((((member @ A) @ C4) @ (bot_bot @ (set @ A)))))))).
% 0.24/1.51 thf(fact_210_comp__apply, axiom, (! [C:$tType,A:$tType,B:$tType]: (((((comp @ B) @ A) @ C) = (^ [F6:(B > A),G3:(C > B),X:C]: ((F6 @ (G3 @ X)))))))).
% 0.24/1.51 thf(fact_211_image__is__empty, axiom, (! [A:$tType,B:$tType,F:(B > A),A4:(set @ B)]: (((((((image @ B) @ A) @ F) @ A4) = (bot_bot @ (set @ A))) = (A4 = (bot_bot @ (set @ B))))))).
% 0.24/1.51 thf(fact_212_empty__is__image, axiom, (! [A:$tType,B:$tType,F:(B > A),A4:(set @ B)]: ((((bot_bot @ (set @ A)) = ((((image @ B) @ A) @ F) @ A4)) = (A4 = (bot_bot @ (set @ B))))))).
% 0.24/1.51 thf(fact_213_image__empty, axiom, (! [B:$tType,A:$tType,F:(B > A)]: ((((((image @ B) @ A) @ F) @ (bot_bot @ (set @ B))) = (bot_bot @ (set @ A)))))).
% 0.24/1.51 thf(fact_214_singletonI, axiom, (! [A:$tType,A2:A]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 0.24/1.51 thf(fact_215_inj__on__empty, axiom, (! [B:$tType,A:$tType,F:(A > B)]: (((((inj_on @ A) @ B) @ F) @ (bot_bot @ (set @ A)))))).
% 0.24/1.51 thf(fact_216_fun_Omap__id, axiom, (! [A:$tType,D:$tType,T2:(D > A)]: (((((((comp @ A) @ A) @ D) @ (id @ A)) @ T2) = T2)))).
% 0.24/1.51 thf(fact_217_comp__id, axiom, (! [B:$tType,A:$tType,F:(A > B)]: (((((((comp @ A) @ B) @ A) @ F) @ (id @ A)) = F)))).
% 0.24/1.51 thf(fact_218_id__comp, axiom, (! [B:$tType,A:$tType,G:(A > B)]: (((((((comp @ B) @ B) @ A) @ (id @ B)) @ G) = G)))).
% 0.24/1.51 thf(fact_219_vimage__empty, axiom, (! [B:$tType,A:$tType,F:(A > B)]: ((((((vimage @ A) @ B) @ F) @ (bot_bot @ (set @ B))) = (bot_bot @ (set @ A)))))).
% 0.24/1.51 thf(fact_220_comp__inj__on__iff, axiom, (! [B:$tType,C:$tType,A:$tType,F:(A > B),A4:(set @ A),F7:(B > C)]: ((((((inj_on @ A) @ B) @ F) @ A4) => (((((inj_on @ B) @ C) @ F7) @ ((((image @ A) @ B) @ F) @ A4)) = ((((inj_on @ A) @ C) @ (((((comp @ B) @ C) @ A) @ F7) @ F)) @ A4)))))).
% 0.24/1.51 thf(fact_221_inj__on__imageI, axiom, (! [B:$tType,C:$tType,A:$tType,G:(C > B),F:(A > C),A4:(set @ A)]: ((((((inj_on @ A) @ B) @ (((((comp @ C) @ B) @ A) @ G) @ F)) @ A4) => ((((inj_on @ C) @ B) @ G) @ ((((image @ A) @ C) @ F) @ A4)))))).
% 0.24/1.51 thf(fact_222_comp__inj__on, axiom, (! [B:$tType,C:$tType,A:$tType,F:(A > B),A4:(set @ A),G:(B > C)]: ((((((inj_on @ A) @ B) @ F) @ A4) => (((((inj_on @ B) @ C) @ G) @ ((((image @ A) @ B) @ F) @ A4)) => ((((inj_on @ A) @ C) @ (((((comp @ B) @ C) @ A) @ G) @ F)) @ A4)))))).
% 0.24/1.51 thf(fact_223_map__sum_Ocompositionality, axiom, (! [D:$tType,F3:$tType,E2:$tType,C:$tType,B:$tType,A:$tType,F:(C > E2),G:(D > F3),H2:(A > C),I:(B > D),Sum:((sum_sum @ A) @ B)]: (((((((((sum_map_sum @ C) @ E2) @ D) @ F3) @ F) @ G) @ (((((((sum_map_sum @ A) @ C) @ B) @ D) @ H2) @ I) @ Sum)) = (((((((sum_map_sum @ A) @ E2) @ B) @ F3) @ (((((comp @ C) @ E2) @ A) @ F) @ H2)) @ (((((comp @ D) @ F3) @ B) @ G) @ I)) @ Sum))))).
% 0.24/1.51 thf(fact_224_sum_Omap__comp, axiom, (! [D:$tType,F3:$tType,E2:$tType,C:$tType,B:$tType,A:$tType,G1:(C > E2),G22:(D > F3),F1:(A > C),F2:(B > D),V:((sum_sum @ A) @ B)]: (((((((((sum_map_sum @ C) @ E2) @ D) @ F3) @ G1) @ G22) @ (((((((sum_map_sum @ A) @ C) @ B) @ D) @ F1) @ F2) @ V)) = (((((((sum_map_sum @ A) @ E2) @ B) @ F3) @ (((((comp @ C) @ E2) @ A) @ G1) @ F1)) @ (((((comp @ D) @ F3) @ B) @ G22) @ F2)) @ V))))).
% 0.24/1.51 thf(fact_225_map__sum_Ocomp, axiom, (! [A:$tType,C:$tType,E2:$tType,F3:$tType,D:$tType,B:$tType,F:(C > E2),G:(D > F3),H2:(A > C),I:(B > D)]: (((((((comp @ ((sum_sum @ C) @ D)) @ ((sum_sum @ E2) @ F3)) @ ((sum_sum @ A) @ B)) @ ((((((sum_map_sum @ C) @ E2) @ D) @ F3) @ F) @ G)) @ ((((((sum_map_sum @ A) @ C) @ B) @ D) @ H2) @ I)) = ((((((sum_map_sum @ A) @ E2) @ B) @ F3) @ (((((comp @ C) @ E2) @ A) @ F) @ H2)) @ (((((comp @ D) @ F3) @ B) @ G) @ I)))))).
% 0.24/1.51 thf(fact_226_Inf_OINF__image, axiom, (! [B:$tType,A:$tType,C:$tType,Inf:((set @ A) > A),G:(B > A),F:(C > B),A4:(set @ C)]: (((Inf @ ((((image @ B) @ A) @ G) @ ((((image @ C) @ B) @ F) @ A4))) = (Inf @ ((((image @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)) @ A4)))))).
% 0.24/1.51 thf(fact_227_Sup_OSUP__image, axiom, (! [B:$tType,A:$tType,C:$tType,Sup:((set @ A) > A),G:(B > A),F:(C > B),A4:(set @ C)]: (((Sup @ ((((image @ B) @ A) @ G) @ ((((image @ C) @ B) @ F) @ A4))) = (Sup @ ((((image @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)) @ A4)))))).
% 0.24/1.51 thf(fact_228_image__comp, axiom, (! [B:$tType,A:$tType,C:$tType,F:(B > A),G:(C > B),R:(set @ C)]: ((((((image @ B) @ A) @ F) @ ((((image @ C) @ B) @ G) @ R)) = ((((image @ C) @ A) @ (((((comp @ B) @ A) @ C) @ F) @ G)) @ R))))).
% 0.24/1.51 thf(fact_229_image__eq__imp__comp, axiom, (! [B:$tType,A:$tType,D:$tType,C:$tType,F:(B > A),A4:(set @ B),G:(C > A),B3:(set @ C),H2:(A > D)]: (((((((image @ B) @ A) @ F) @ A4) = ((((image @ C) @ A) @ G) @ B3)) => (((((image @ B) @ D) @ (((((comp @ A) @ D) @ B) @ H2) @ F)) @ A4) = ((((image @ C) @ D) @ (((((comp @ A) @ D) @ C) @ H2) @ G)) @ B3)))))).
% 0.24/1.51 thf(fact_230_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__o__subst, axiom, (! [Tr0:dtree]: (((((((comp @ dtree) @ n) @ dtree) @ root) @ (gram_L1004374585hsubst @ Tr0)) = root)))).
% 0.24/1.51 thf(fact_231_infinite__finite__induct, axiom, (! [A:$tType,P:((set @ A) > $o),A4:(set @ A)]: (((! [A11:(set @ A)]: (((~ (((finite_finite2 @ A) @ A11))) => (P @ A11)))) => ((P @ (bot_bot @ (set @ A))) => ((! [X3:A,F8:(set @ A)]: ((((finite_finite2 @ A) @ F8) => ((~ ((((member @ A) @ X3) @ F8))) => ((P @ F8) => (P @ (((insert @ A) @ X3) @ F8))))))) => (P @ A4))))))).
% 0.24/1.51 thf(fact_232_finite__ne__induct, axiom, (! [A:$tType,F4:(set @ A),P:((set @ A) > $o)]: ((((finite_finite2 @ A) @ F4) => ((F4 != (bot_bot @ (set @ A))) => ((! [X3:A]: ((P @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))))) => ((! [X3:A,F8:(set @ A)]: ((((finite_finite2 @ A) @ F8) => ((F8 != (bot_bot @ (set @ A))) => ((~ ((((member @ A) @ X3) @ F8))) => ((P @ F8) => (P @ (((insert @ A) @ X3) @ F8)))))))) => (P @ F4)))))))).
% 0.24/1.51 thf(fact_233_finite_Oinducts, axiom, (! [A:$tType,X2:(set @ A),P:((set @ A) > $o)]: ((((finite_finite2 @ A) @ X2) => ((P @ (bot_bot @ (set @ A))) => ((! [A11:(set @ A),A7:A]: ((((finite_finite2 @ A) @ A11) => ((P @ A11) => (P @ (((insert @ A) @ A7) @ A11)))))) => (P @ X2))))))).
% 0.24/1.51 thf(fact_234_finite__induct, axiom, (! [A:$tType,F4:(set @ A),P:((set @ A) > $o)]: ((((finite_finite2 @ A) @ F4) => ((P @ (bot_bot @ (set @ A))) => ((! [X3:A,F8:(set @ A)]: ((((finite_finite2 @ A) @ F8) => ((~ ((((member @ A) @ X3) @ F8))) => ((P @ F8) => (P @ (((insert @ A) @ X3) @ F8))))))) => (P @ F4))))))).
% 0.24/1.51 thf(fact_235_finite_Osimps, axiom, (! [A:$tType]: (((finite_finite2 @ A) = (^ [A10:(set @ A)]: (((A10 = (bot_bot @ (set @ A))) | (? [A8:(set @ A),B9:A]: (((A10 = (((insert @ A) @ B9) @ A8)) & ((finite_finite2 @ A) @ A8))))))))))).
% 0.24/1.51 thf(fact_236_finite_Ocases, axiom, (! [A:$tType,A2:(set @ A)]: ((((finite_finite2 @ A) @ A2) => ((A2 != (bot_bot @ (set @ A))) => (~ ((! [A11:(set @ A)]: (((? [A7:A]: ((A2 = (((insert @ A) @ A7) @ A11)))) => (~ (((finite_finite2 @ A) @ A11))))))))))))).
% 0.24/1.51 thf(fact_237_singleton__inject, axiom, (! [A:$tType,A2:A,B2:A]: ((((((insert @ A) @ A2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) => (A2 = B2))))).
% 0.24/1.51 thf(fact_238_insert__not__empty, axiom, (! [A:$tType,A2:A,A4:(set @ A)]: (((((insert @ A) @ A2) @ A4) != (bot_bot @ (set @ A)))))).
% 0.24/1.51 thf(fact_239_doubleton__eq__iff, axiom, (! [A:$tType,A2:A,B2:A,C4:A,D3:A]: ((((((insert @ A) @ A2) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C4) @ (((insert @ A) @ D3) @ (bot_bot @ (set @ A))))) = (((A2 = C4) & (B2 = D3)) | ((A2 = D3) & (B2 = C4))))))).
% 0.24/1.51 thf(fact_240_singleton__iff, axiom, (! [A:$tType,B2:A,A2:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = (B2 = A2))))).
% 0.24/1.51 thf(fact_241_singletonD, axiom, (! [A:$tType,B2:A,A2:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) => (B2 = A2))))).
% 0.24/1.51 thf(fact_242_fun_Omap__id0, axiom, (! [A:$tType,D:$tType]: ((((((comp @ A) @ A) @ D) @ (id @ A)) = (id @ (D > A)))))).
% 0.24/1.51 thf(fact_243_pointfree__idE, axiom, (! [B:$tType,A:$tType,F:(B > A),G:(A > B),X2:A]: ((((((((comp @ B) @ A) @ A) @ F) @ G) = (id @ A)) => ((F @ (G @ X2)) = X2))))).
% 0.24/1.51 thf(fact_244_comp__eq__id__dest, axiom, (! [C:$tType,B:$tType,A:$tType,A2:(C > B),B2:(A > C),C4:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = (((((comp @ B) @ B) @ A) @ (id @ B)) @ C4)) => ((A2 @ (B2 @ V)) = (C4 @ V)))))).
% 0.24/1.51 thf(fact_245_vimage__comp, axiom, (! [A:$tType,B:$tType,C:$tType,F:(A > B),G:(B > C),X2:(set @ C)]: ((((((vimage @ A) @ B) @ F) @ ((((vimage @ B) @ C) @ G) @ X2)) = ((((vimage @ A) @ C) @ (((((comp @ B) @ C) @ A) @ G) @ F)) @ X2))))).
% 0.24/1.51 thf(fact_246_set_Ocompositionality, axiom, (! [C:$tType,B:$tType,A:$tType,F:(C > B),G:(B > A),Set:(set @ A)]: ((((((vimage @ C) @ B) @ F) @ ((((vimage @ B) @ A) @ G) @ Set)) = ((((vimage @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)) @ Set))))).
% 0.24/1.51 thf(fact_247_rewriteR__comp__comp2, axiom, (! [C:$tType,B:$tType,E2:$tType,D:$tType,A:$tType,G:(C > B),H2:(A > C),R1:(D > B),R2:(A > D),F:(B > E2),L:(D > E2)]: ((((((((comp @ C) @ B) @ A) @ G) @ H2) = (((((comp @ D) @ B) @ A) @ R1) @ R2)) => (((((((comp @ B) @ E2) @ D) @ F) @ R1) = L) => ((((((comp @ C) @ E2) @ A) @ (((((comp @ B) @ E2) @ C) @ F) @ G)) @ H2) = (((((comp @ D) @ E2) @ A) @ L) @ R2))))))).
% 0.24/1.51 thf(fact_248_rewriteL__comp__comp2, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,E2:$tType,F:(C > B),G:(A > C),L1:(D > B),L2:(A > D),H2:(E2 > A),R:(E2 > D)]: ((((((((comp @ C) @ B) @ A) @ F) @ G) = (((((comp @ D) @ B) @ A) @ L1) @ L2)) => (((((((comp @ A) @ D) @ E2) @ L2) @ H2) = R) => ((((((comp @ C) @ B) @ E2) @ F) @ (((((comp @ A) @ C) @ E2) @ G) @ H2)) = (((((comp @ D) @ B) @ E2) @ L1) @ R))))))).
% 0.24/1.51 thf(fact_249_rewriteR__comp__comp, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,G:(C > B),H2:(A > C),R:(A > B),F:(B > D)]: ((((((((comp @ C) @ B) @ A) @ G) @ H2) = R) => ((((((comp @ C) @ D) @ A) @ (((((comp @ B) @ D) @ C) @ F) @ G)) @ H2) = (((((comp @ B) @ D) @ A) @ F) @ R)))))).
% 0.24/1.51 thf(fact_250_rewriteL__comp__comp, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,F:(C > B),G:(A > C),L:(A > B),H2:(D > A)]: ((((((((comp @ C) @ B) @ A) @ F) @ G) = L) => ((((((comp @ C) @ B) @ D) @ F) @ (((((comp @ A) @ C) @ D) @ G) @ H2)) = (((((comp @ A) @ B) @ D) @ L) @ H2)))))).
% 0.24/1.51 thf(fact_251_fun_Omap__comp, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,G:(B > C),F:(A > B),V:(D > A)]: (((((((comp @ B) @ C) @ D) @ G) @ (((((comp @ A) @ B) @ D) @ F) @ V)) = (((((comp @ A) @ C) @ D) @ (((((comp @ B) @ C) @ A) @ G) @ F)) @ V))))).
% 0.24/1.51 thf(fact_252_set_Ocomp, axiom, (! [A:$tType,B:$tType,C:$tType,F:(C > B),G:(B > A)]: (((((((comp @ (set @ B)) @ (set @ C)) @ (set @ A)) @ (((vimage @ C) @ B) @ F)) @ (((vimage @ B) @ A) @ G)) = (((vimage @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)))))).
% 0.24/1.51 thf(fact_253_comp__eq__dest__lhs, axiom, (! [C:$tType,B:$tType,A:$tType,A2:(C > B),B2:(A > C),C4:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = C4) => ((A2 @ (B2 @ V)) = (C4 @ V)))))).
% 0.24/1.51 thf(fact_254_comp__eq__elim, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A2:(C > B),B2:(A > C),C4:(D > B),D3:(A > D)]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = (((((comp @ D) @ B) @ A) @ C4) @ D3)) => (! [V2:A]: (((A2 @ (B2 @ V2)) = (C4 @ (D3 @ V2))))))))).
% 0.24/1.51 thf(fact_255_comp__eq__dest, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A2:(C > B),B2:(A > C),C4:(D > B),D3:(A > D),V:A]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = (((((comp @ D) @ B) @ A) @ C4) @ D3)) => ((A2 @ (B2 @ V)) = (C4 @ (D3 @ V))))))).
% 0.24/1.51 thf(tcon_fun___Finite__Set_Ofinite, axiom, (! [A5:$tType,A13:$tType]: (((((finite_finite @ A5) @ (type @ A5)) & ((finite_finite @ A13) @ (type @ A13))) => ((finite_finite @ (A5 > A13)) @ (type @ (A5 > A13))))))).
% 0.24/1.51 thf(tcon_Set_Oset___Finite__Set_Ofinite_1, axiom, (! [A5:$tType]: ((((finite_finite @ A5) @ (type @ A5)) => ((finite_finite @ (set @ A5)) @ (type @ (set @ A5))))))).
% 0.24/1.51 thf(tcon_HOL_Obool___Finite__Set_Ofinite_2, axiom, ((finite_finite @ $o) @ (type @ $o))).
% 0.24/1.51 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_3, axiom, (! [A5:$tType,A13:$tType]: (((((finite_finite @ A5) @ (type @ A5)) & ((finite_finite @ A13) @ (type @ A13))) => ((finite_finite @ ((sum_sum @ A5) @ A13)) @ (type @ ((sum_sum @ A5) @ A13))))))).
% 0.24/1.51 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_4, axiom, (! [A5:$tType,A13:$tType]: (((((finite_finite @ A5) @ (type @ A5)) & ((finite_finite @ A13) @ (type @ A13))) => ((finite_finite @ ((product_prod @ A5) @ A13)) @ (type @ ((product_prod @ A5) @ A13))))))).
% 0.24/1.51 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 0.24/1.51 thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $false) @ X2) @ Y) = Y)))).
% 0.24/1.51 thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $true) @ X2) @ Y) = X2)))).
% 0.24/1.51 thf(conj_0, conjecture, (((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ dtree)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ dtree) @ (id @ t)) @ (gram_L1004374585hsubst @ tr0))) @ (cont @ tr))) = ((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ tr)))).
% 0.24/1.51 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.wlnNTaEhLw/DTF2DTF23752.p
% 0.24/1.51 ------------------------
% 0.24/1.56 ---- Cleaned THF ---
% 0.24/1.56 thf(ty_t_Product__Type_Oprod,type,
% 0.24/1.56 product_prod: $tType > $tType > $tType ).
% 0.24/1.56
% 0.24/1.56 thf(ty_t_Sum__Type_Osum,type,
% 0.24/1.56 sum_sum: $tType > $tType > $tType ).
% 0.24/1.56
% 0.24/1.56 thf(ty_t_DTree_Odtree,type,
% 0.24/1.56 dtree: $tType ).
% 0.24/1.56
% 0.24/1.56 thf(ty_t_Set_Oset,type,
% 0.24/1.56 set: $tType > $tType ).
% 0.24/1.56
% 0.24/1.56 thf(ty_t_DTree_OT,type,
% 0.24/1.56 t: $tType ).
% 0.24/1.56
% 0.24/1.56 thf(ty_t_DTree_ON,type,
% 0.24/1.56 n: $tType ).
% 0.24/1.56
% 0.24/1.56 thf(ty_t_itself,type,
% 0.24/1.56 itself: $tType > $tType ).
% 0.24/1.56
% 0.24/1.56 thf(sy_cl_Finite__Set_Ofinite,type,
% 0.24/1.56 finite_finite:
% 0.24/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_DTree_ONode,type,
% 0.24/1.56 node: n > ( set @ ( sum_sum @ t @ dtree ) ) > dtree ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_DTree_Ocont,type,
% 0.24/1.56 cont: dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_DTree_Odtree_Oroot,type,
% 0.24/1.56 root: dtree > n ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_DTree_Ounfold,type,
% 0.24/1.56 unfold:
% 0.24/1.56 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ A ) ) ) > A > dtree ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Finite__Set_Ofinite,type,
% 0.24/1.56 finite_finite2:
% 0.24/1.56 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Fun_Ocomp,type,
% 0.24/1.56 comp:
% 0.24/1.56 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Fun_Oid,type,
% 0.24/1.56 id:
% 0.24/1.56 !>[A: $tType] : ( A > A ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Fun_Oinj__on,type,
% 0.24/1.56 inj_on:
% 0.24/1.56 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > $o ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OP,type,
% 0.24/1.56 gram_L1451583632elle_P: set @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OS,type,
% 0.24/1.56 gram_L1451583635elle_S: n > ( set @ ( sum_sum @ t @ n ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr,type,
% 0.24/1.56 gram_L1231612515_deftr: n > dtree ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst,type,
% 0.24/1.56 gram_L1004374585hsubst: dtree > dtree > dtree ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c,type,
% 0.24/1.56 gram_L1905609002ubst_c: dtree > dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r,type,
% 0.24/1.56 gram_L1905609017ubst_r: dtree > n ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr,type,
% 0.24/1.56 gram_L1333338417e_inFr: ( set @ n ) > dtree > t > $o ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2,type,
% 0.24/1.56 gram_L805317441_inFr2: ( set @ n ) > dtree > t > $o ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFrr,type,
% 0.24/1.56 gram_L805317505_inFrr: ( set @ n ) > dtree > t > $o ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr,type,
% 0.24/1.56 gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr,type,
% 0.24/1.56 gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr2,type,
% 0.24/1.56 gram_L1283001940subtr2: ( set @ n ) > dtree > dtree > $o ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OsubtrOf,type,
% 0.24/1.56 gram_L1614515765ubtrOf: dtree > n > dtree ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf,type,
% 0.24/1.56 gram_L864798063lle_wf: dtree > $o ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_If,type,
% 0.24/1.56 if:
% 0.24/1.56 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.24/1.56 bot_bot:
% 0.24/1.56 !>[A: $tType] : A ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Product__Type_OPair,type,
% 0.24/1.56 product_Pair:
% 0.24/1.56 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Pure_Otype,type,
% 0.24/1.56 type:
% 0.24/1.56 !>[A: $tType] : ( itself @ A ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Set_OCollect,type,
% 0.24/1.56 collect:
% 0.24/1.56 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Set_Oimage,type,
% 0.24/1.56 image:
% 0.24/1.56 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Set_Oinsert,type,
% 0.24/1.56 insert:
% 0.24/1.56 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Set_Ovimage,type,
% 0.24/1.56 vimage:
% 0.24/1.56 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Sum__Type_OInl,type,
% 0.24/1.56 sum_Inl:
% 0.24/1.56 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Sum__Type_OInr,type,
% 0.24/1.56 sum_Inr:
% 0.24/1.56 !>[B: $tType,A: $tType] : ( B > ( sum_sum @ A @ B ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Sum__Type_Omap__sum,type,
% 0.24/1.56 sum_map_sum:
% 0.24/1.56 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C ) > ( B > D ) > ( sum_sum @ A @ B ) > ( sum_sum @ C @ D ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum,type,
% 0.24/1.56 sum_rec_sum:
% 0.24/1.56 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_c_member,type,
% 0.24/1.56 member:
% 0.24/1.56 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.24/1.56
% 0.24/1.56 thf(sy_v_tr,type,
% 0.24/1.56 tr: dtree ).
% 0.24/1.56
% 0.24/1.56 thf(sy_v_tr0,type,
% 0.24/1.56 tr0: dtree ).
% 0.24/1.56
% 0.24/1.56 thf(fact_0__092_060open_062cont_A_Ilocal_Ohsubst_Atr_J_A_061_A_Iid_A_092_060oplus_062_Alocal_Ohsubst_J_A_096_Acont_Atr_092_060close_062,axiom,
% 0.24/1.56 ( ( cont @ ( gram_L1004374585hsubst @ tr0 @ tr ) )
% 0.24/1.56 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ tr0 ) ) @ ( cont @ tr ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_1_assms,axiom,
% 0.24/1.56 ( ( root @ tr )
% 0.24/1.56 != ( root @ tr0 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_2_Inl__m__oplus,axiom,
% 0.24/1.56 ! [B: $tType,C: $tType,A: $tType,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.24/1.56 ( ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ ( image @ ( sum_sum @ A @ C ) @ ( sum_sum @ A @ B ) @ ( sum_map_sum @ A @ A @ C @ B @ ( id @ A ) @ F ) @ Tns ) )
% 0.24/1.56 = ( vimage @ A @ ( sum_sum @ A @ C ) @ ( sum_Inl @ A @ C ) @ Tns ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_3_Inl__oplus__iff,axiom,
% 0.24/1.56 ! [B: $tType,C: $tType,A: $tType,Tr: A,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.24/1.56 ( ( member @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B @ Tr ) @ ( image @ ( sum_sum @ A @ C ) @ ( sum_sum @ A @ B ) @ ( sum_map_sum @ A @ A @ C @ B @ ( id @ A ) @ F ) @ Tns ) )
% 0.24/1.56 = ( member @ ( sum_sum @ A @ C ) @ ( sum_Inl @ A @ C @ Tr ) @ Tns ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_4_vimage__id,axiom,
% 0.24/1.56 ! [A: $tType] :
% 0.24/1.56 ( ( vimage @ A @ A @ ( id @ A ) )
% 0.24/1.56 = ( id @ ( set @ A ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_5_image__id,axiom,
% 0.24/1.56 ! [A: $tType] :
% 0.24/1.56 ( ( image @ A @ A @ ( id @ A ) )
% 0.24/1.56 = ( id @ ( set @ A ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_6_Inl__oplus__elim,axiom,
% 0.24/1.56 ! [B: $tType,C: $tType,A: $tType,Tr: A,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.24/1.56 ( ( member @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B @ Tr ) @ ( image @ ( sum_sum @ A @ C ) @ ( sum_sum @ A @ B ) @ ( sum_map_sum @ A @ A @ C @ B @ ( id @ A ) @ F ) @ Tns ) )
% 0.24/1.56 => ( member @ ( sum_sum @ A @ C ) @ ( sum_Inl @ A @ C @ Tr ) @ Tns ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_7_cont__hsubst__eq,axiom,
% 0.24/1.56 ! [Tr: dtree] :
% 0.24/1.56 ( ( ( root @ Tr )
% 0.24/1.56 = ( root @ tr0 ) )
% 0.24/1.56 => ( ( cont @ ( gram_L1004374585hsubst @ tr0 @ Tr ) )
% 0.24/1.56 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ tr0 ) ) @ ( cont @ tr0 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_8_cont__hsubst__neq,axiom,
% 0.24/1.56 ! [Tr: dtree] :
% 0.24/1.56 ( ( ( root @ Tr )
% 0.24/1.56 != ( root @ tr0 ) )
% 0.24/1.56 => ( ( cont @ ( gram_L1004374585hsubst @ tr0 @ Tr ) )
% 0.24/1.56 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ tr0 ) ) @ ( cont @ Tr ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_9_sum_Oinject_I1_J,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,X1: A,Y1: A] :
% 0.24/1.56 ( ( ( sum_Inl @ A @ B @ X1 )
% 0.24/1.56 = ( sum_Inl @ A @ B @ Y1 ) )
% 0.24/1.56 = ( X1 = Y1 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_10_old_Osum_Oinject_I1_J,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,A2: A,A3: A] :
% 0.24/1.56 ( ( ( sum_Inl @ A @ B @ A2 )
% 0.24/1.56 = ( sum_Inl @ A @ B @ A3 ) )
% 0.24/1.56 = ( A2 = A3 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_11_vimageI,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F: B > A,A2: B,B2: A,B3: set @ A] :
% 0.24/1.56 ( ( ( F @ A2 )
% 0.24/1.56 = B2 )
% 0.24/1.56 => ( ( member @ A @ B2 @ B3 )
% 0.24/1.56 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ B3 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_12_vimage__eq,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 0.24/1.56 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 0.24/1.56 = ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_13_id__apply,axiom,
% 0.24/1.56 ! [A: $tType] :
% 0.24/1.56 ( ( id @ A )
% 0.24/1.56 = ( ^ [X: A] : X ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_14_hsubst__eq,axiom,
% 0.24/1.56 ! [Tr: dtree] :
% 0.24/1.56 ( ( ( root @ Tr )
% 0.24/1.56 = ( root @ tr0 ) )
% 0.24/1.56 => ( ( gram_L1004374585hsubst @ tr0 @ Tr )
% 0.24/1.56 = ( gram_L1004374585hsubst @ tr0 @ tr0 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_15_image__eqI,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,B2: A,F: B > A,X2: B,A4: set @ B] :
% 0.24/1.56 ( ( B2
% 0.24/1.56 = ( F @ X2 ) )
% 0.24/1.56 => ( ( member @ B @ X2 @ A4 )
% 0.24/1.56 => ( member @ A @ B2 @ ( image @ B @ A @ F @ A4 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_16_root__hsubst,axiom,
% 0.24/1.56 ! [Tr: dtree] :
% 0.24/1.56 ( ( root @ ( gram_L1004374585hsubst @ tr0 @ Tr ) )
% 0.24/1.56 = ( root @ Tr ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_17_hsubst__c__def,axiom,
% 0.24/1.56 ! [Tr: dtree] :
% 0.24/1.56 ( ( ( ( root @ Tr )
% 0.24/1.56 = ( root @ tr0 ) )
% 0.24/1.56 => ( ( gram_L1905609002ubst_c @ tr0 @ Tr )
% 0.24/1.56 = ( cont @ tr0 ) ) )
% 0.24/1.56 & ( ( ( root @ Tr )
% 0.24/1.56 != ( root @ tr0 ) )
% 0.24/1.56 => ( ( gram_L1905609002ubst_c @ tr0 @ Tr )
% 0.24/1.56 = ( cont @ Tr ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_18_Inl__cont__hsubst__eq,axiom,
% 0.24/1.56 ! [Tr: dtree] :
% 0.24/1.56 ( ( ( root @ Tr )
% 0.24/1.56 = ( root @ tr0 ) )
% 0.24/1.56 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ tr0 @ Tr ) ) )
% 0.24/1.56 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ tr0 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_19_Inl__prodOf,axiom,
% 0.24/1.56 ! [Tr: dtree] :
% 0.24/1.56 ( ( vimage @ t @ ( sum_sum @ t @ n ) @ ( sum_Inl @ t @ n ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.24/1.56 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_20_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__hsubst,axiom,
% 0.24/1.56 ! [Tr0: dtree,Tr: dtree] :
% 0.24/1.56 ( ( root @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.24/1.56 = ( root @ Tr ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_21_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__eq,axiom,
% 0.24/1.56 ! [Tr: dtree,Tr0: dtree] :
% 0.24/1.56 ( ( ( root @ Tr )
% 0.24/1.56 = ( root @ Tr0 ) )
% 0.24/1.56 => ( ( gram_L1004374585hsubst @ Tr0 @ Tr )
% 0.24/1.56 = ( gram_L1004374585hsubst @ Tr0 @ Tr0 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_22_rev__image__eqI,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,X2: A,A4: set @ A,B2: B,F: A > B] :
% 0.24/1.56 ( ( member @ A @ X2 @ A4 )
% 0.24/1.56 => ( ( B2
% 0.24/1.56 = ( F @ X2 ) )
% 0.24/1.56 => ( member @ B @ B2 @ ( image @ A @ B @ F @ A4 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_23_ball__imageD,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,F: B > A,A4: set @ B,P: A > $o] :
% 0.24/1.56 ( ! [X3: A] :
% 0.24/1.56 ( ( member @ A @ X3 @ ( image @ B @ A @ F @ A4 ) )
% 0.24/1.56 => ( P @ X3 ) )
% 0.24/1.56 => ! [X4: B] :
% 0.24/1.56 ( ( member @ B @ X4 @ A4 )
% 0.24/1.56 => ( P @ ( F @ X4 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_24_image__cong,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,M: set @ A,N: set @ A,F: A > B,G: A > B] :
% 0.24/1.56 ( ( M = N )
% 0.24/1.56 => ( ! [X3: A] :
% 0.24/1.56 ( ( member @ A @ X3 @ N )
% 0.24/1.56 => ( ( F @ X3 )
% 0.24/1.56 = ( G @ X3 ) ) )
% 0.24/1.56 => ( ( image @ A @ B @ F @ M )
% 0.24/1.56 = ( image @ A @ B @ G @ N ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_25_bex__imageD,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,F: B > A,A4: set @ B,P: A > $o] :
% 0.24/1.56 ( ? [X4: A] :
% 0.24/1.56 ( ( member @ A @ X4 @ ( image @ B @ A @ F @ A4 ) )
% 0.24/1.56 & ( P @ X4 ) )
% 0.24/1.56 => ? [X3: B] :
% 0.24/1.56 ( ( member @ B @ X3 @ A4 )
% 0.24/1.56 & ( P @ ( F @ X3 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_26_image__iff,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,Z: A,F: B > A,A4: set @ B] :
% 0.24/1.56 ( ( member @ A @ Z @ ( image @ B @ A @ F @ A4 ) )
% 0.24/1.56 = ( ? [X: B] :
% 0.24/1.56 ( ( member @ B @ X @ A4 )
% 0.24/1.56 & ( Z
% 0.24/1.56 = ( F @ X ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_27_imageI,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,X2: A,A4: set @ A,F: A > B] :
% 0.24/1.56 ( ( member @ A @ X2 @ A4 )
% 0.24/1.56 => ( member @ B @ ( F @ X2 ) @ ( image @ A @ B @ F @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_28_eq__id__iff,axiom,
% 0.24/1.56 ! [A: $tType,F: A > A] :
% 0.24/1.56 ( ( ! [X: A] :
% 0.24/1.56 ( ( F @ X )
% 0.24/1.56 = X ) )
% 0.24/1.56 = ( F
% 0.24/1.56 = ( id @ A ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_29_id__def,axiom,
% 0.24/1.56 ! [A: $tType] :
% 0.24/1.56 ( ( id @ A )
% 0.24/1.56 = ( ^ [X: A] : X ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_30_vimage__Collect,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,P: B > $o,F: A > B,Q: A > $o] :
% 0.24/1.56 ( ! [X3: A] :
% 0.24/1.56 ( ( P @ ( F @ X3 ) )
% 0.24/1.56 = ( Q @ X3 ) )
% 0.24/1.56 => ( ( vimage @ A @ B @ F @ ( collect @ B @ P ) )
% 0.24/1.56 = ( collect @ A @ Q ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_31_vimageI2,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F: B > A,A2: B,A4: set @ A] :
% 0.24/1.56 ( ( member @ A @ ( F @ A2 ) @ A4 )
% 0.24/1.56 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_32_vimageE,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 0.24/1.56 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 0.24/1.56 => ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_33_vimageD,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,A2: A,F: A > B,A4: set @ B] :
% 0.24/1.56 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ A4 ) )
% 0.24/1.56 => ( member @ B @ ( F @ A2 ) @ A4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_34_Inl__inject,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,X2: A,Y: A] :
% 0.24/1.56 ( ( ( sum_Inl @ A @ B @ X2 )
% 0.24/1.56 = ( sum_Inl @ A @ B @ Y ) )
% 0.24/1.56 => ( X2 = Y ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_35_Gram__Lang__Mirabelle__ojxrtuoybn_OInl__cont__hsubst__eq,axiom,
% 0.24/1.56 ! [Tr: dtree,Tr0: dtree] :
% 0.24/1.56 ( ( ( root @ Tr )
% 0.24/1.56 = ( root @ Tr0 ) )
% 0.24/1.56 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.24/1.56 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_36_Gram__Lang__Mirabelle__ojxrtuoybn_Ocont__hsubst__neq,axiom,
% 0.24/1.56 ! [Tr: dtree,Tr0: dtree] :
% 0.24/1.56 ( ( ( root @ Tr )
% 0.24/1.56 != ( root @ Tr0 ) )
% 0.24/1.56 => ( ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.24/1.56 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ Tr0 ) ) @ ( cont @ Tr ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_37_Gram__Lang__Mirabelle__ojxrtuoybn_Ocont__hsubst__eq,axiom,
% 0.24/1.56 ! [Tr: dtree,Tr0: dtree] :
% 0.24/1.56 ( ( ( root @ Tr )
% 0.24/1.56 = ( root @ Tr0 ) )
% 0.24/1.56 => ( ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.24/1.56 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ Tr0 ) ) @ ( cont @ Tr0 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_38_map__sum__InlD,axiom,
% 0.24/1.56 ! [D: $tType,B: $tType,C: $tType,A: $tType,F: C > A,G: D > B,Z: sum_sum @ C @ D,X2: A] :
% 0.24/1.56 ( ( ( sum_map_sum @ C @ A @ D @ B @ F @ G @ Z )
% 0.24/1.56 = ( sum_Inl @ A @ B @ X2 ) )
% 0.24/1.56 => ? [Y2: C] :
% 0.24/1.56 ( ( Z
% 0.24/1.56 = ( sum_Inl @ C @ D @ Y2 ) )
% 0.24/1.56 & ( ( F @ Y2 )
% 0.24/1.56 = X2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_39_map__sum_Osimps_I1_J,axiom,
% 0.24/1.56 ! [B: $tType,D: $tType,C: $tType,A: $tType,F1: A > C,F2: B > D,A2: A] :
% 0.24/1.56 ( ( sum_map_sum @ A @ C @ B @ D @ F1 @ F2 @ ( sum_Inl @ A @ B @ A2 ) )
% 0.24/1.56 = ( sum_Inl @ C @ D @ ( F1 @ A2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_40_old_Osum_Osimps_I7_J,axiom,
% 0.24/1.56 ! [B: $tType,T: $tType,A: $tType,F1: A > T,F2: B > T,A2: A] :
% 0.24/1.56 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F2 @ ( sum_Inl @ A @ B @ A2 ) )
% 0.24/1.56 = ( F1 @ A2 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_41_map__sum__if__distrib__then_I1_J,axiom,
% 0.24/1.56 ! [D: $tType,B: $tType,C: $tType,A: $tType,E: $o,F: A > B,G: C > D,X2: A,Y: sum_sum @ A @ C] :
% 0.24/1.56 ( ( E
% 0.24/1.56 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E @ ( sum_Inl @ A @ C @ X2 ) @ Y ) )
% 0.24/1.56 = ( sum_Inl @ B @ D @ ( F @ X2 ) ) ) )
% 0.24/1.56 & ( ~ E
% 0.24/1.56 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E @ ( sum_Inl @ A @ C @ X2 ) @ Y ) )
% 0.24/1.56 = ( sum_map_sum @ A @ B @ C @ D @ F @ G @ Y ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_42_map__sum__if__distrib__else_I1_J,axiom,
% 0.24/1.56 ! [C: $tType,D: $tType,B: $tType,A: $tType,E: $o,F: A > B,G: C > D,X2: sum_sum @ A @ C,Y: A] :
% 0.24/1.56 ( ( E
% 0.24/1.56 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E @ X2 @ ( sum_Inl @ A @ C @ Y ) ) )
% 0.24/1.56 = ( sum_map_sum @ A @ B @ C @ D @ F @ G @ X2 ) ) )
% 0.24/1.56 & ( ~ E
% 0.24/1.56 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E @ X2 @ ( sum_Inl @ A @ C @ Y ) ) )
% 0.24/1.56 = ( sum_Inl @ B @ D @ ( F @ Y ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_43_dtree__cong,axiom,
% 0.24/1.56 ! [Tr: dtree,Tr2: dtree] :
% 0.24/1.56 ( ( ( root @ Tr )
% 0.24/1.56 = ( root @ Tr2 ) )
% 0.24/1.56 => ( ( ( cont @ Tr )
% 0.24/1.56 = ( cont @ Tr2 ) )
% 0.24/1.56 => ( Tr = Tr2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_44_sum_Omap__id0,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType] :
% 0.24/1.56 ( ( sum_map_sum @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) )
% 0.24/1.56 = ( id @ ( sum_sum @ A @ B ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_45_mem__Collect__eq,axiom,
% 0.24/1.56 ! [A: $tType,A2: A,P: A > $o] :
% 0.24/1.56 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.24/1.56 = ( P @ A2 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_46_Collect__mem__eq,axiom,
% 0.24/1.56 ! [A: $tType,A4: set @ A] :
% 0.24/1.56 ( ( collect @ A
% 0.24/1.56 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 0.24/1.56 = A4 ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_47_Collect__cong,axiom,
% 0.24/1.56 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.24/1.56 ( ! [X3: A] :
% 0.24/1.56 ( ( P @ X3 )
% 0.24/1.56 = ( Q @ X3 ) )
% 0.24/1.56 => ( ( collect @ A @ P )
% 0.24/1.56 = ( collect @ A @ Q ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_48_ext,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.24/1.56 ( ! [X3: A] :
% 0.24/1.56 ( ( F @ X3 )
% 0.24/1.56 = ( G @ X3 ) )
% 0.24/1.56 => ( F = G ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_49_sum_Omap__id,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,T2: sum_sum @ A @ B] :
% 0.24/1.56 ( ( sum_map_sum @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) @ T2 )
% 0.24/1.56 = T2 ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_50_Sup_OSUP__id__eq,axiom,
% 0.24/1.56 ! [A: $tType,Sup: ( set @ A ) > A,A4: set @ A] :
% 0.24/1.56 ( ( Sup @ ( image @ A @ A @ ( id @ A ) @ A4 ) )
% 0.24/1.56 = ( Sup @ A4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_51_Inf_OINF__id__eq,axiom,
% 0.24/1.56 ! [A: $tType,Inf: ( set @ A ) > A,A4: set @ A] :
% 0.24/1.56 ( ( Inf @ ( image @ A @ A @ ( id @ A ) @ A4 ) )
% 0.24/1.56 = ( Inf @ A4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_52_Inr__m__oplus,axiom,
% 0.24/1.56 ! [A: $tType,C: $tType,B: $tType,F: C > A,Tns: set @ ( sum_sum @ B @ C )] :
% 0.24/1.56 ( ( vimage @ A @ ( sum_sum @ B @ A ) @ ( sum_Inr @ A @ B ) @ ( image @ ( sum_sum @ B @ C ) @ ( sum_sum @ B @ A ) @ ( sum_map_sum @ B @ B @ C @ A @ ( id @ B ) @ F ) @ Tns ) )
% 0.24/1.56 = ( image @ C @ A @ F @ ( vimage @ C @ ( sum_sum @ B @ C ) @ ( sum_Inr @ C @ B ) @ Tns ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_53_Inr__cont__hsubst__eq,axiom,
% 0.24/1.56 ! [Tr: dtree] :
% 0.24/1.56 ( ( ( root @ Tr )
% 0.24/1.56 = ( root @ tr0 ) )
% 0.24/1.56 => ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1004374585hsubst @ tr0 @ Tr ) ) )
% 0.24/1.56 = ( image @ dtree @ dtree @ ( gram_L1004374585hsubst @ tr0 ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ tr0 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_54_inFr2_OBase,axiom,
% 0.24/1.56 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 0.24/1.56 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_55_sum_Oinject_I2_J,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,X22: B,Y22: B] :
% 0.24/1.56 ( ( ( sum_Inr @ B @ A @ X22 )
% 0.24/1.56 = ( sum_Inr @ B @ A @ Y22 ) )
% 0.24/1.56 = ( X22 = Y22 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_56_old_Osum_Oinject_I2_J,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,B2: B,B4: B] :
% 0.24/1.56 ( ( ( sum_Inr @ B @ A @ B2 )
% 0.24/1.56 = ( sum_Inr @ B @ A @ B4 ) )
% 0.24/1.56 = ( B2 = B4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_57_Inl__Inr__False,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,X2: A,Y: B] :
% 0.24/1.56 ( ( sum_Inl @ A @ B @ X2 )
% 0.24/1.56 != ( sum_Inr @ B @ A @ Y ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_58_Inr__Inl__False,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,X2: B,Y: A] :
% 0.24/1.56 ( ( sum_Inr @ B @ A @ X2 )
% 0.24/1.56 != ( sum_Inl @ A @ B @ Y ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_59_old_Osum_Osimps_I8_J,axiom,
% 0.24/1.56 ! [A: $tType,T: $tType,B: $tType,F1: A > T,F2: B > T,B2: B] :
% 0.24/1.56 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F2 @ ( sum_Inr @ B @ A @ B2 ) )
% 0.24/1.56 = ( F2 @ B2 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_60_Inr__oplus__iff,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,C: $tType,Tr: B,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.24/1.56 ( ( member @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A @ Tr ) @ ( image @ ( sum_sum @ A @ C ) @ ( sum_sum @ A @ B ) @ ( sum_map_sum @ A @ A @ C @ B @ ( id @ A ) @ F ) @ Tns ) )
% 0.24/1.56 = ( ? [N2: C] :
% 0.24/1.56 ( ( member @ ( sum_sum @ A @ C ) @ ( sum_Inr @ C @ A @ N2 ) @ Tns )
% 0.24/1.56 & ( ( F @ N2 )
% 0.24/1.56 = Tr ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_61_Inr__inject,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,X2: B,Y: B] :
% 0.24/1.56 ( ( ( sum_Inr @ B @ A @ X2 )
% 0.24/1.56 = ( sum_Inr @ B @ A @ Y ) )
% 0.24/1.56 => ( X2 = Y ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_62_obj__sumE__f,axiom,
% 0.24/1.56 ! [A: $tType,C: $tType,B: $tType,S: B,F: ( sum_sum @ A @ C ) > B,P: $o] :
% 0.24/1.56 ( ! [X3: A] :
% 0.24/1.56 ( ( S
% 0.24/1.56 = ( F @ ( sum_Inl @ A @ C @ X3 ) ) )
% 0.24/1.56 => P )
% 0.24/1.56 => ( ! [X3: C] :
% 0.24/1.56 ( ( S
% 0.24/1.56 = ( F @ ( sum_Inr @ C @ A @ X3 ) ) )
% 0.24/1.56 => P )
% 0.24/1.56 => ! [X4: sum_sum @ A @ C] :
% 0.24/1.56 ( ( S
% 0.24/1.56 = ( F @ X4 ) )
% 0.24/1.56 => P ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_63_map__sum__if__distrib__else_I2_J,axiom,
% 0.24/1.56 ! [E2: $tType,F3: $tType,H: $tType,G2: $tType,E: $o,F: E2 > F3,G: G2 > H,X2: sum_sum @ E2 @ G2,Y: G2] :
% 0.24/1.56 ( ( E
% 0.24/1.56 => ( ( sum_map_sum @ E2 @ F3 @ G2 @ H @ F @ G @ ( if @ ( sum_sum @ E2 @ G2 ) @ E @ X2 @ ( sum_Inr @ G2 @ E2 @ Y ) ) )
% 0.24/1.56 = ( sum_map_sum @ E2 @ F3 @ G2 @ H @ F @ G @ X2 ) ) )
% 0.24/1.56 & ( ~ E
% 0.24/1.56 => ( ( sum_map_sum @ E2 @ F3 @ G2 @ H @ F @ G @ ( if @ ( sum_sum @ E2 @ G2 ) @ E @ X2 @ ( sum_Inr @ G2 @ E2 @ Y ) ) )
% 0.24/1.56 = ( sum_Inr @ H @ F3 @ ( G @ Y ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_64_map__sum__if__distrib__then_I2_J,axiom,
% 0.24/1.56 ! [H: $tType,F3: $tType,G2: $tType,E2: $tType,E: $o,F: E2 > F3,G: G2 > H,X2: G2,Y: sum_sum @ E2 @ G2] :
% 0.24/1.56 ( ( E
% 0.24/1.56 => ( ( sum_map_sum @ E2 @ F3 @ G2 @ H @ F @ G @ ( if @ ( sum_sum @ E2 @ G2 ) @ E @ ( sum_Inr @ G2 @ E2 @ X2 ) @ Y ) )
% 0.24/1.56 = ( sum_Inr @ H @ F3 @ ( G @ X2 ) ) ) )
% 0.24/1.56 & ( ~ E
% 0.24/1.56 => ( ( sum_map_sum @ E2 @ F3 @ G2 @ H @ F @ G @ ( if @ ( sum_sum @ E2 @ G2 ) @ E @ ( sum_Inr @ G2 @ E2 @ X2 ) @ Y ) )
% 0.24/1.56 = ( sum_map_sum @ E2 @ F3 @ G2 @ H @ F @ G @ Y ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_65_sum_Odistinct_I1_J,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,X1: A,X22: B] :
% 0.24/1.56 ( ( sum_Inl @ A @ B @ X1 )
% 0.24/1.56 != ( sum_Inr @ B @ A @ X22 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_66_old_Osum_Odistinct_I2_J,axiom,
% 0.24/1.56 ! [B5: $tType,A5: $tType,B6: B5,A6: A5] :
% 0.24/1.56 ( ( sum_Inr @ B5 @ A5 @ B6 )
% 0.24/1.56 != ( sum_Inl @ A5 @ B5 @ A6 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_67_old_Osum_Odistinct_I1_J,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,A2: A,B4: B] :
% 0.24/1.56 ( ( sum_Inl @ A @ B @ A2 )
% 0.24/1.56 != ( sum_Inr @ B @ A @ B4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_68_sumE,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 0.24/1.56 ( ! [X3: A] :
% 0.24/1.56 ( S
% 0.24/1.56 != ( sum_Inl @ A @ B @ X3 ) )
% 0.24/1.56 => ~ ! [Y2: B] :
% 0.24/1.56 ( S
% 0.24/1.56 != ( sum_Inr @ B @ A @ Y2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_69_Inr__not__Inl,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,B2: B,A2: A] :
% 0.24/1.56 ( ( sum_Inr @ B @ A @ B2 )
% 0.24/1.56 != ( sum_Inl @ A @ B @ A2 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_70_split__sum__ex,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType] :
% 0.24/1.56 ( ( ^ [P2: ( sum_sum @ A @ B ) > $o] :
% 0.24/1.56 ? [X5: sum_sum @ A @ B] : ( P2 @ X5 ) )
% 0.24/1.56 = ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 0.24/1.56 ( ? [X: A] : ( P3 @ ( sum_Inl @ A @ B @ X ) )
% 0.24/1.56 | ? [X: B] : ( P3 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_71_split__sum__all,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType] :
% 0.24/1.56 ( ( ^ [P2: ( sum_sum @ A @ B ) > $o] :
% 0.24/1.56 ! [X5: sum_sum @ A @ B] : ( P2 @ X5 ) )
% 0.24/1.56 = ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 0.24/1.56 ( ! [X: A] : ( P3 @ ( sum_Inl @ A @ B @ X ) )
% 0.24/1.56 & ! [X: B] : ( P3 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_72_old_Osum_Oexhaust,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,Y: sum_sum @ A @ B] :
% 0.24/1.56 ( ! [A7: A] :
% 0.24/1.56 ( Y
% 0.24/1.56 != ( sum_Inl @ A @ B @ A7 ) )
% 0.24/1.56 => ~ ! [B7: B] :
% 0.24/1.56 ( Y
% 0.24/1.56 != ( sum_Inr @ B @ A @ B7 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_73_old_Osum_Oinducts,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,P: ( sum_sum @ A @ B ) > $o,Sum: sum_sum @ A @ B] :
% 0.24/1.56 ( ! [A7: A] : ( P @ ( sum_Inl @ A @ B @ A7 ) )
% 0.24/1.56 => ( ! [B7: B] : ( P @ ( sum_Inr @ B @ A @ B7 ) )
% 0.24/1.56 => ( P @ Sum ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_74_map__sum_Osimps_I2_J,axiom,
% 0.24/1.56 ! [A: $tType,C: $tType,D: $tType,B: $tType,F1: A > C,F2: B > D,A2: B] :
% 0.24/1.56 ( ( sum_map_sum @ A @ C @ B @ D @ F1 @ F2 @ ( sum_Inr @ B @ A @ A2 ) )
% 0.24/1.56 = ( sum_Inr @ D @ C @ ( F2 @ A2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_75_map__sum__InrD,axiom,
% 0.24/1.56 ! [C: $tType,A: $tType,D: $tType,B: $tType,F: C > A,G: D > B,Z: sum_sum @ C @ D,X2: B] :
% 0.24/1.56 ( ( ( sum_map_sum @ C @ A @ D @ B @ F @ G @ Z )
% 0.24/1.56 = ( sum_Inr @ B @ A @ X2 ) )
% 0.24/1.56 => ? [Y2: D] :
% 0.24/1.56 ( ( Z
% 0.24/1.56 = ( sum_Inr @ D @ C @ Y2 ) )
% 0.24/1.56 & ( ( G @ Y2 )
% 0.24/1.56 = X2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_76_inFr2__Ind,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 0.24/1.56 ( ( gram_L805317441_inFr2 @ Ns @ Tr1 @ T2 )
% 0.24/1.56 => ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.24/1.56 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_77_root__prodOf,axiom,
% 0.24/1.56 ! [Tr2: dtree,Tr: dtree] :
% 0.24/1.56 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 0.24/1.56 => ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ ( root @ Tr2 ) ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_78_inFr2__root__in,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.24/1.56 ( ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 )
% 0.24/1.56 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_79_Inl__Inr__image__cong,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,A4: set @ ( sum_sum @ A @ B ),B3: set @ ( sum_sum @ A @ B )] :
% 0.24/1.56 ( ( ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ A4 )
% 0.24/1.56 = ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ B3 ) )
% 0.24/1.56 => ( ( ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ A4 )
% 0.24/1.56 = ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ B3 ) )
% 0.24/1.56 => ( A4 = B3 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_80_Inr__oplus__elim,axiom,
% 0.24/1.56 ! [A: $tType,C: $tType,B: $tType,Tr: B,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.24/1.56 ( ( member @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A @ Tr ) @ ( image @ ( sum_sum @ A @ C ) @ ( sum_sum @ A @ B ) @ ( sum_map_sum @ A @ A @ C @ B @ ( id @ A ) @ F ) @ Tns ) )
% 0.24/1.56 => ? [N3: C] :
% 0.24/1.56 ( ( member @ ( sum_sum @ A @ C ) @ ( sum_Inr @ C @ A @ N3 ) @ Tns )
% 0.24/1.56 & ( ( F @ N3 )
% 0.24/1.56 = Tr ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_81_Gram__Lang__Mirabelle__ojxrtuoybn_OInr__cont__hsubst__eq,axiom,
% 0.24/1.56 ! [Tr: dtree,Tr0: dtree] :
% 0.24/1.56 ( ( ( root @ Tr )
% 0.24/1.56 = ( root @ Tr0 ) )
% 0.24/1.56 => ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.24/1.56 = ( image @ dtree @ dtree @ ( gram_L1004374585hsubst @ Tr0 ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr0 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_82_Inf_OINF__cong,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,A4: set @ B,B3: set @ B,C2: B > A,D2: B > A,Inf: ( set @ A ) > A] :
% 0.24/1.56 ( ( A4 = B3 )
% 0.24/1.56 => ( ! [X3: B] :
% 0.24/1.56 ( ( member @ B @ X3 @ B3 )
% 0.24/1.56 => ( ( C2 @ X3 )
% 0.24/1.56 = ( D2 @ X3 ) ) )
% 0.24/1.56 => ( ( Inf @ ( image @ B @ A @ C2 @ A4 ) )
% 0.24/1.56 = ( Inf @ ( image @ B @ A @ D2 @ B3 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_83_Sup_OSUP__cong,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,A4: set @ B,B3: set @ B,C2: B > A,D2: B > A,Sup: ( set @ A ) > A] :
% 0.24/1.56 ( ( A4 = B3 )
% 0.24/1.56 => ( ! [X3: B] :
% 0.24/1.56 ( ( member @ B @ X3 @ B3 )
% 0.24/1.56 => ( ( C2 @ X3 )
% 0.24/1.56 = ( D2 @ X3 ) ) )
% 0.24/1.56 => ( ( Sup @ ( image @ B @ A @ C2 @ A4 ) )
% 0.24/1.56 = ( Sup @ ( image @ B @ A @ D2 @ B3 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_84_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c__def,axiom,
% 0.24/1.56 ( gram_L1905609002ubst_c
% 0.24/1.56 = ( ^ [Tr02: dtree,Tr3: dtree] :
% 0.24/1.56 ( if @ ( set @ ( sum_sum @ t @ dtree ) )
% 0.24/1.56 @ ( ( root @ Tr3 )
% 0.24/1.56 = ( root @ Tr02 ) )
% 0.24/1.56 @ ( cont @ Tr02 )
% 0.24/1.56 @ ( cont @ Tr3 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_85_hsubst__def,axiom,
% 0.24/1.56 ( ( gram_L1004374585hsubst @ tr0 )
% 0.24/1.56 = ( unfold @ dtree @ gram_L1905609017ubst_r @ ( gram_L1905609002ubst_c @ tr0 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_86_root__subtrOf,axiom,
% 0.24/1.56 ! [N4: n,Tr: dtree] :
% 0.24/1.56 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N4 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.24/1.56 => ( ( root @ ( gram_L1614515765ubtrOf @ Tr @ N4 ) )
% 0.24/1.56 = N4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_87_Inr__subtrOf,axiom,
% 0.24/1.56 ! [N4: n,Tr: dtree] :
% 0.24/1.56 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N4 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.24/1.56 => ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( gram_L1614515765ubtrOf @ Tr @ N4 ) ) @ ( cont @ Tr ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_88_subtrOf,axiom,
% 0.24/1.56 ! [N4: n,Tr: dtree] :
% 0.24/1.56 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N4 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( gram_L1614515765ubtrOf @ Tr @ N4 ) ) @ ( cont @ Tr ) )
% 0.24/1.56 & ( ( root @ ( gram_L1614515765ubtrOf @ Tr @ N4 ) )
% 0.24/1.56 = N4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_89_finite__hsubst__c,axiom,
% 0.24/1.56 ! [N4: dtree] : ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ ( gram_L1905609002ubst_c @ tr0 @ N4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_90_obj__sumE,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 0.24/1.56 ( ! [X3: A] :
% 0.24/1.56 ( S
% 0.24/1.56 != ( sum_Inl @ A @ B @ X3 ) )
% 0.24/1.56 => ~ ! [X3: B] :
% 0.24/1.56 ( S
% 0.24/1.56 != ( sum_Inr @ B @ A @ X3 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_91_Node__root__cont,axiom,
% 0.24/1.56 ! [Tr: dtree] :
% 0.24/1.56 ( ( node @ ( root @ Tr ) @ ( cont @ Tr ) )
% 0.24/1.56 = Tr ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_92_inFr_Ocases,axiom,
% 0.24/1.56 ! [A1: set @ n,A22: dtree,A32: t] :
% 0.24/1.56 ( ( gram_L1333338417e_inFr @ A1 @ A22 @ A32 )
% 0.24/1.56 => ( ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.24/1.56 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A32 ) @ ( cont @ A22 ) ) )
% 0.24/1.56 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.24/1.56 => ! [Tr12: dtree] :
% 0.24/1.56 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A22 ) )
% 0.24/1.56 => ~ ( gram_L1333338417e_inFr @ A1 @ Tr12 @ A32 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_93_root__Node,axiom,
% 0.24/1.56 ! [N4: n,As: set @ ( sum_sum @ t @ dtree )] :
% 0.24/1.56 ( ( root @ ( node @ N4 @ As ) )
% 0.24/1.56 = N4 ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_94_dtree__simps,axiom,
% 0.24/1.56 ! [As: set @ ( sum_sum @ t @ dtree ),As2: set @ ( sum_sum @ t @ dtree ),N4: n,N5: n] :
% 0.24/1.56 ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As )
% 0.24/1.56 => ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As2 )
% 0.24/1.56 => ( ( ( node @ N4 @ As )
% 0.24/1.56 = ( node @ N5 @ As2 ) )
% 0.24/1.56 = ( ( N4 = N5 )
% 0.24/1.56 & ( As = As2 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_95_cont__Node,axiom,
% 0.24/1.56 ! [As: set @ ( sum_sum @ t @ dtree ),N4: n] :
% 0.24/1.56 ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As )
% 0.24/1.56 => ( ( cont @ ( node @ N4 @ As ) )
% 0.24/1.56 = As ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_96_dtree__cases,axiom,
% 0.24/1.56 ! [Tr: dtree] :
% 0.24/1.56 ~ ! [N3: n,As3: set @ ( sum_sum @ t @ dtree )] :
% 0.24/1.56 ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As3 )
% 0.24/1.56 => ( Tr
% 0.24/1.56 != ( node @ N3 @ As3 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_97_finite__cont,axiom,
% 0.24/1.56 ! [Tr: dtree] : ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ ( cont @ Tr ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_98_Gram__Lang__Mirabelle__ojxrtuoybn_Ofinite__hsubst__c,axiom,
% 0.24/1.56 ! [Tr0: dtree,N4: dtree] : ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ ( gram_L1905609002ubst_c @ Tr0 @ N4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_99_inFr__root__in,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.24/1.56 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.24/1.56 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_100_not__root__inFr,axiom,
% 0.24/1.56 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.24/1.56 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 0.24/1.56 => ~ ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_101_inFr__inFr2,axiom,
% 0.24/1.56 gram_L1333338417e_inFr = gram_L805317441_inFr2 ).
% 0.24/1.56
% 0.24/1.56 thf(fact_102_unfold_I1_J,axiom,
% 0.24/1.56 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ A ) ),B2: A] :
% 0.24/1.56 ( ( root @ ( unfold @ A @ Rt @ Ct @ B2 ) )
% 0.24/1.56 = ( Rt @ B2 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_103_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__def,axiom,
% 0.24/1.56 ( gram_L1004374585hsubst
% 0.24/1.56 = ( ^ [Tr02: dtree] : ( unfold @ dtree @ gram_L1905609017ubst_r @ ( gram_L1905609002ubst_c @ Tr02 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_104_not__arg__cong__Inr,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,X2: A,Y: A] :
% 0.24/1.56 ( ( X2 != Y )
% 0.24/1.56 => ( ( sum_Inr @ A @ B @ X2 )
% 0.24/1.56 != ( sum_Inr @ A @ B @ Y ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_105_unfold_I2_J,axiom,
% 0.24/1.56 ! [A: $tType,Ct: A > ( set @ ( sum_sum @ t @ A ) ),B2: A,Rt: A > n] :
% 0.24/1.56 ( ( finite_finite2 @ ( sum_sum @ t @ A ) @ ( Ct @ B2 ) )
% 0.24/1.56 => ( ( cont @ ( unfold @ A @ Rt @ Ct @ B2 ) )
% 0.24/1.56 = ( image @ ( sum_sum @ t @ A ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ A @ dtree @ ( id @ t ) @ ( unfold @ A @ Rt @ Ct ) ) @ ( Ct @ B2 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_106_hsubst__r__def,axiom,
% 0.24/1.56 gram_L1905609017ubst_r = root ).
% 0.24/1.56
% 0.24/1.56 thf(fact_107_inFr_OInd,axiom,
% 0.24/1.56 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,T2: t] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.24/1.56 => ( ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 )
% 0.24/1.56 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_108_inFr_OBase,axiom,
% 0.24/1.56 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 0.24/1.56 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_109_inFr_Oinducts,axiom,
% 0.24/1.56 ! [X1: set @ n,X22: dtree,X32: t,P: ( set @ n ) > dtree > t > $o] :
% 0.24/1.56 ( ( gram_L1333338417e_inFr @ X1 @ X22 @ X32 )
% 0.24/1.56 => ( ! [Tr4: dtree,Ns2: set @ n,T3: t] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr4 ) )
% 0.24/1.56 => ( P @ Ns2 @ Tr4 @ T3 ) ) )
% 0.24/1.56 => ( ! [Tr4: dtree,Ns2: set @ n,Tr12: dtree,T3: t] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr4 ) )
% 0.24/1.56 => ( ( gram_L1333338417e_inFr @ Ns2 @ Tr12 @ T3 )
% 0.24/1.56 => ( ( P @ Ns2 @ Tr12 @ T3 )
% 0.24/1.56 => ( P @ Ns2 @ Tr4 @ T3 ) ) ) ) )
% 0.24/1.56 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_110_inFr_Osimps,axiom,
% 0.24/1.56 ( gram_L1333338417e_inFr
% 0.24/1.56 = ( ^ [A12: set @ n,A23: dtree,A33: t] :
% 0.24/1.56 ( ? [Tr3: dtree,Ns3: set @ n,T4: t] :
% 0.24/1.56 ( ( A12 = Ns3 )
% 0.24/1.56 & ( A23 = Tr3 )
% 0.24/1.56 & ( A33 = T4 )
% 0.24/1.56 & ( member @ n @ ( root @ Tr3 ) @ Ns3 )
% 0.24/1.56 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr3 ) ) )
% 0.24/1.56 | ? [Tr3: dtree,Ns3: set @ n,Tr13: dtree,T4: t] :
% 0.24/1.56 ( ( A12 = Ns3 )
% 0.24/1.56 & ( A23 = Tr3 )
% 0.24/1.56 & ( A33 = T4 )
% 0.24/1.56 & ( member @ n @ ( root @ Tr3 ) @ Ns3 )
% 0.24/1.56 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr3 ) )
% 0.24/1.56 & ( gram_L1333338417e_inFr @ Ns3 @ Tr13 @ T4 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_111_inFrr__def,axiom,
% 0.24/1.56 ( gram_L805317505_inFrr
% 0.24/1.56 = ( ^ [Ns3: set @ n,Tr3: dtree,T4: t] :
% 0.24/1.56 ? [Tr5: dtree] :
% 0.24/1.56 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr5 ) @ ( cont @ Tr3 ) )
% 0.24/1.56 & ( gram_L1333338417e_inFr @ Ns3 @ Tr5 @ T4 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_112_finite__imageI,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F4: set @ A,H2: A > B] :
% 0.24/1.56 ( ( finite_finite2 @ A @ F4 )
% 0.24/1.56 => ( finite_finite2 @ B @ ( image @ A @ B @ H2 @ F4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_113_surj__subtrOf,axiom,
% 0.24/1.56 ! [Tr: dtree,Tr2: dtree] :
% 0.24/1.56 ( ( gram_L864798063lle_wf @ Tr )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 0.24/1.56 => ? [N3: n] :
% 0.24/1.56 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N3 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.24/1.56 & ( ( gram_L1614515765ubtrOf @ Tr @ N3 )
% 0.24/1.56 = Tr2 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_114_finite__code,axiom,
% 0.24/1.56 ! [A: $tType] :
% 0.24/1.56 ( ( finite_finite @ A @ ( type @ A ) )
% 0.24/1.56 => ( ( finite_finite2 @ A )
% 0.24/1.56 = ( ^ [A8: set @ A] : $true ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_115_subtrOf__root,axiom,
% 0.24/1.56 ! [Tr: dtree,Tr2: dtree] :
% 0.24/1.56 ( ( gram_L864798063lle_wf @ Tr )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 0.24/1.56 => ( ( gram_L1614515765ubtrOf @ Tr @ ( root @ Tr2 ) )
% 0.24/1.56 = Tr2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_116_wf__inj,axiom,
% 0.24/1.56 ! [Tr: dtree,Tr1: dtree,Tr22: dtree] :
% 0.24/1.56 ( ( gram_L864798063lle_wf @ Tr )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr ) )
% 0.24/1.56 => ( ( ( root @ Tr1 )
% 0.24/1.56 = ( root @ Tr22 ) )
% 0.24/1.56 = ( Tr1 = Tr22 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_117_wf__cont,axiom,
% 0.24/1.56 ! [Tr: dtree,Tr2: dtree] :
% 0.24/1.56 ( ( gram_L864798063lle_wf @ Tr )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 0.24/1.56 => ( gram_L864798063lle_wf @ Tr2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_118_finite,axiom,
% 0.24/1.56 ! [A: $tType] :
% 0.24/1.56 ( ( finite_finite @ A @ ( type @ A ) )
% 0.24/1.56 => ! [A4: set @ A] : ( finite_finite2 @ A @ A4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_119_finite__set__choice,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,A4: set @ A,P: A > B > $o] :
% 0.24/1.56 ( ( finite_finite2 @ A @ A4 )
% 0.24/1.56 => ( ! [X3: A] :
% 0.24/1.56 ( ( member @ A @ X3 @ A4 )
% 0.24/1.56 => ? [X12: B] : ( P @ X3 @ X12 ) )
% 0.24/1.56 => ? [F5: A > B] :
% 0.24/1.56 ! [X4: A] :
% 0.24/1.56 ( ( member @ A @ X4 @ A4 )
% 0.24/1.56 => ( P @ X4 @ ( F5 @ X4 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_120_inFr2_Ocases,axiom,
% 0.24/1.56 ! [A1: set @ n,A22: dtree,A32: t] :
% 0.24/1.56 ( ( gram_L805317441_inFr2 @ A1 @ A22 @ A32 )
% 0.24/1.56 => ( ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.24/1.56 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A32 ) @ ( cont @ A22 ) ) )
% 0.24/1.56 => ~ ! [Tr12: dtree,Tr4: dtree,Ns1: set @ n] :
% 0.24/1.56 ( ( A1
% 0.24/1.56 = ( insert @ n @ ( root @ Tr4 ) @ Ns1 ) )
% 0.24/1.56 => ( ( A22 = Tr4 )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr4 ) )
% 0.24/1.56 => ~ ( gram_L805317441_inFr2 @ Ns1 @ Tr12 @ A32 ) ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_121_inFr2_Osimps,axiom,
% 0.24/1.56 ( gram_L805317441_inFr2
% 0.24/1.56 = ( ^ [A12: set @ n,A23: dtree,A33: t] :
% 0.24/1.56 ( ? [Tr3: dtree,Ns3: set @ n,T4: t] :
% 0.24/1.56 ( ( A12 = Ns3 )
% 0.24/1.56 & ( A23 = Tr3 )
% 0.24/1.56 & ( A33 = T4 )
% 0.24/1.56 & ( member @ n @ ( root @ Tr3 ) @ Ns3 )
% 0.24/1.56 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr3 ) ) )
% 0.24/1.56 | ? [Tr13: dtree,Tr3: dtree,Ns12: set @ n,T4: t] :
% 0.24/1.56 ( ( A12
% 0.24/1.56 = ( insert @ n @ ( root @ Tr3 ) @ Ns12 ) )
% 0.24/1.56 & ( A23 = Tr3 )
% 0.24/1.56 & ( A33 = T4 )
% 0.24/1.56 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr3 ) )
% 0.24/1.56 & ( gram_L805317441_inFr2 @ Ns12 @ Tr13 @ T4 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_122_inFr2_Oinducts,axiom,
% 0.24/1.56 ! [X1: set @ n,X22: dtree,X32: t,P: ( set @ n ) > dtree > t > $o] :
% 0.24/1.56 ( ( gram_L805317441_inFr2 @ X1 @ X22 @ X32 )
% 0.24/1.56 => ( ! [Tr4: dtree,Ns2: set @ n,T3: t] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr4 ) )
% 0.24/1.56 => ( P @ Ns2 @ Tr4 @ T3 ) ) )
% 0.24/1.56 => ( ! [Tr12: dtree,Tr4: dtree,Ns1: set @ n,T3: t] :
% 0.24/1.56 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr4 ) )
% 0.24/1.56 => ( ( gram_L805317441_inFr2 @ Ns1 @ Tr12 @ T3 )
% 0.24/1.56 => ( ( P @ Ns1 @ Tr12 @ T3 )
% 0.24/1.56 => ( P @ ( insert @ n @ ( root @ Tr4 ) @ Ns1 ) @ Tr4 @ T3 ) ) ) )
% 0.24/1.56 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_123_wf__inj__on,axiom,
% 0.24/1.56 ! [Tr: dtree] :
% 0.24/1.56 ( ( gram_L864798063lle_wf @ Tr )
% 0.24/1.56 => ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_124_insert__absorb2,axiom,
% 0.24/1.56 ! [A: $tType,X2: A,A4: set @ A] :
% 0.24/1.56 ( ( insert @ A @ X2 @ ( insert @ A @ X2 @ A4 ) )
% 0.24/1.56 = ( insert @ A @ X2 @ A4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_125_insert__iff,axiom,
% 0.24/1.56 ! [A: $tType,A2: A,B2: A,A4: set @ A] :
% 0.24/1.56 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A4 ) )
% 0.24/1.56 = ( ( A2 = B2 )
% 0.24/1.56 | ( member @ A @ A2 @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_126_insertCI,axiom,
% 0.24/1.56 ! [A: $tType,A2: A,B3: set @ A,B2: A] :
% 0.24/1.56 ( ( ~ ( member @ A @ A2 @ B3 )
% 0.24/1.56 => ( A2 = B2 ) )
% 0.24/1.56 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_127_insert__image,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,X2: A,A4: set @ A,F: A > B] :
% 0.24/1.56 ( ( member @ A @ X2 @ A4 )
% 0.24/1.56 => ( ( insert @ B @ ( F @ X2 ) @ ( image @ A @ B @ F @ A4 ) )
% 0.24/1.56 = ( image @ A @ B @ F @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_128_image__insert,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,F: B > A,A2: B,B3: set @ B] :
% 0.24/1.56 ( ( image @ B @ A @ F @ ( insert @ B @ A2 @ B3 ) )
% 0.24/1.56 = ( insert @ A @ ( F @ A2 ) @ ( image @ B @ A @ F @ B3 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_129_finite__insert,axiom,
% 0.24/1.56 ! [A: $tType,A2: A,A4: set @ A] :
% 0.24/1.56 ( ( finite_finite2 @ A @ ( insert @ A @ A2 @ A4 ) )
% 0.24/1.56 = ( finite_finite2 @ A @ A4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_130_finite_OinsertI,axiom,
% 0.24/1.56 ! [A: $tType,A4: set @ A,A2: A] :
% 0.24/1.56 ( ( finite_finite2 @ A @ A4 )
% 0.24/1.56 => ( finite_finite2 @ A @ ( insert @ A @ A2 @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_131_inj__on__image__iff,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,A4: set @ A,G: A > B,F: A > A] :
% 0.24/1.56 ( ! [X3: A] :
% 0.24/1.56 ( ( member @ A @ X3 @ A4 )
% 0.24/1.56 => ! [Xa: A] :
% 0.24/1.56 ( ( member @ A @ Xa @ A4 )
% 0.24/1.56 => ( ( ( G @ ( F @ X3 ) )
% 0.24/1.56 = ( G @ ( F @ Xa ) ) )
% 0.24/1.56 = ( ( G @ X3 )
% 0.24/1.56 = ( G @ Xa ) ) ) ) )
% 0.24/1.56 => ( ( inj_on @ A @ A @ F @ A4 )
% 0.24/1.56 => ( ( inj_on @ A @ B @ G @ ( image @ A @ A @ F @ A4 ) )
% 0.24/1.56 = ( inj_on @ A @ B @ G @ A4 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_132_inj__img__insertE,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F: A > B,A4: set @ A,X2: B,B3: set @ B] :
% 0.24/1.56 ( ( inj_on @ A @ B @ F @ A4 )
% 0.24/1.56 => ( ~ ( member @ B @ X2 @ B3 )
% 0.24/1.56 => ( ( ( insert @ B @ X2 @ B3 )
% 0.24/1.56 = ( image @ A @ B @ F @ A4 ) )
% 0.24/1.56 => ~ ! [X6: A,A9: set @ A] :
% 0.24/1.56 ( ~ ( member @ A @ X6 @ A9 )
% 0.24/1.56 => ( ( A4
% 0.24/1.56 = ( insert @ A @ X6 @ A9 ) )
% 0.24/1.56 => ( ( X2
% 0.24/1.56 = ( F @ X6 ) )
% 0.24/1.56 => ( B3
% 0.24/1.56 != ( image @ A @ B @ F @ A9 ) ) ) ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_133_inj__on__id,axiom,
% 0.24/1.56 ! [A: $tType,A4: set @ A] : ( inj_on @ A @ A @ ( id @ A ) @ A4 ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_134_mk__disjoint__insert,axiom,
% 0.24/1.56 ! [A: $tType,A2: A,A4: set @ A] :
% 0.24/1.56 ( ( member @ A @ A2 @ A4 )
% 0.24/1.56 => ? [B8: set @ A] :
% 0.24/1.56 ( ( A4
% 0.24/1.56 = ( insert @ A @ A2 @ B8 ) )
% 0.24/1.56 & ~ ( member @ A @ A2 @ B8 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_135_inj__on__inverseI,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,A4: set @ A,G: B > A,F: A > B] :
% 0.24/1.56 ( ! [X3: A] :
% 0.24/1.56 ( ( member @ A @ X3 @ A4 )
% 0.24/1.56 => ( ( G @ ( F @ X3 ) )
% 0.24/1.56 = X3 ) )
% 0.24/1.56 => ( inj_on @ A @ B @ F @ A4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_136_insert__commute,axiom,
% 0.24/1.56 ! [A: $tType,X2: A,Y: A,A4: set @ A] :
% 0.24/1.56 ( ( insert @ A @ X2 @ ( insert @ A @ Y @ A4 ) )
% 0.24/1.56 = ( insert @ A @ Y @ ( insert @ A @ X2 @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_137_inj__on__contraD,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F: A > B,A4: set @ A,X2: A,Y: A] :
% 0.24/1.56 ( ( inj_on @ A @ B @ F @ A4 )
% 0.24/1.56 => ( ( X2 != Y )
% 0.24/1.56 => ( ( member @ A @ X2 @ A4 )
% 0.24/1.56 => ( ( member @ A @ Y @ A4 )
% 0.24/1.56 => ( ( F @ X2 )
% 0.24/1.56 != ( F @ Y ) ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_138_insert__eq__iff,axiom,
% 0.24/1.56 ! [A: $tType,A2: A,A4: set @ A,B2: A,B3: set @ A] :
% 0.24/1.56 ( ~ ( member @ A @ A2 @ A4 )
% 0.24/1.56 => ( ~ ( member @ A @ B2 @ B3 )
% 0.24/1.56 => ( ( ( insert @ A @ A2 @ A4 )
% 0.24/1.56 = ( insert @ A @ B2 @ B3 ) )
% 0.24/1.56 = ( ( ( A2 = B2 )
% 0.24/1.56 => ( A4 = B3 ) )
% 0.24/1.56 & ( ( A2 != B2 )
% 0.24/1.56 => ? [C3: set @ A] :
% 0.24/1.56 ( ( A4
% 0.24/1.56 = ( insert @ A @ B2 @ C3 ) )
% 0.24/1.56 & ~ ( member @ A @ B2 @ C3 )
% 0.24/1.56 & ( B3
% 0.24/1.56 = ( insert @ A @ A2 @ C3 ) )
% 0.24/1.56 & ~ ( member @ A @ A2 @ C3 ) ) ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_139_insert__absorb,axiom,
% 0.24/1.56 ! [A: $tType,A2: A,A4: set @ A] :
% 0.24/1.56 ( ( member @ A @ A2 @ A4 )
% 0.24/1.56 => ( ( insert @ A @ A2 @ A4 )
% 0.24/1.56 = A4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_140_inj__on__eq__iff,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F: A > B,A4: set @ A,X2: A,Y: A] :
% 0.24/1.56 ( ( inj_on @ A @ B @ F @ A4 )
% 0.24/1.56 => ( ( member @ A @ X2 @ A4 )
% 0.24/1.56 => ( ( member @ A @ Y @ A4 )
% 0.24/1.56 => ( ( ( F @ X2 )
% 0.24/1.56 = ( F @ Y ) )
% 0.24/1.56 = ( X2 = Y ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_141_insert__ident,axiom,
% 0.24/1.56 ! [A: $tType,X2: A,A4: set @ A,B3: set @ A] :
% 0.24/1.56 ( ~ ( member @ A @ X2 @ A4 )
% 0.24/1.56 => ( ~ ( member @ A @ X2 @ B3 )
% 0.24/1.56 => ( ( ( insert @ A @ X2 @ A4 )
% 0.24/1.56 = ( insert @ A @ X2 @ B3 ) )
% 0.24/1.56 = ( A4 = B3 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_142_inj__on__cong,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,A4: set @ A,F: A > B,G: A > B] :
% 0.24/1.56 ( ! [A7: A] :
% 0.24/1.56 ( ( member @ A @ A7 @ A4 )
% 0.24/1.56 => ( ( F @ A7 )
% 0.24/1.56 = ( G @ A7 ) ) )
% 0.24/1.56 => ( ( inj_on @ A @ B @ F @ A4 )
% 0.24/1.56 = ( inj_on @ A @ B @ G @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_143_Set_Oset__insert,axiom,
% 0.24/1.56 ! [A: $tType,X2: A,A4: set @ A] :
% 0.24/1.56 ( ( member @ A @ X2 @ A4 )
% 0.24/1.56 => ~ ! [B8: set @ A] :
% 0.24/1.56 ( ( A4
% 0.24/1.56 = ( insert @ A @ X2 @ B8 ) )
% 0.24/1.56 => ( member @ A @ X2 @ B8 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_144_inj__on__def,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType] :
% 0.24/1.56 ( ( inj_on @ A @ B )
% 0.24/1.56 = ( ^ [F6: A > B,A8: set @ A] :
% 0.24/1.56 ! [X: A] :
% 0.24/1.56 ( ( member @ A @ X @ A8 )
% 0.24/1.56 => ! [Y3: A] :
% 0.24/1.56 ( ( member @ A @ Y3 @ A8 )
% 0.24/1.56 => ( ( ( F6 @ X )
% 0.24/1.56 = ( F6 @ Y3 ) )
% 0.24/1.56 => ( X = Y3 ) ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_145_insertI2,axiom,
% 0.24/1.56 ! [A: $tType,A2: A,B3: set @ A,B2: A] :
% 0.24/1.56 ( ( member @ A @ A2 @ B3 )
% 0.24/1.56 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_146_insertI1,axiom,
% 0.24/1.56 ! [A: $tType,A2: A,B3: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B3 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_147_insertE,axiom,
% 0.24/1.56 ! [A: $tType,A2: A,B2: A,A4: set @ A] :
% 0.24/1.56 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A4 ) )
% 0.24/1.56 => ( ( A2 != B2 )
% 0.24/1.56 => ( member @ A @ A2 @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_148_inj__onI,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,A4: set @ A,F: A > B] :
% 0.24/1.56 ( ! [X3: A,Y2: A] :
% 0.24/1.56 ( ( member @ A @ X3 @ A4 )
% 0.24/1.56 => ( ( member @ A @ Y2 @ A4 )
% 0.24/1.56 => ( ( ( F @ X3 )
% 0.24/1.56 = ( F @ Y2 ) )
% 0.24/1.56 => ( X3 = Y2 ) ) ) )
% 0.24/1.56 => ( inj_on @ A @ B @ F @ A4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_149_inj__onD,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F: A > B,A4: set @ A,X2: A,Y: A] :
% 0.24/1.56 ( ( inj_on @ A @ B @ F @ A4 )
% 0.24/1.56 => ( ( ( F @ X2 )
% 0.24/1.56 = ( F @ Y ) )
% 0.24/1.56 => ( ( member @ A @ X2 @ A4 )
% 0.24/1.56 => ( ( member @ A @ Y @ A4 )
% 0.24/1.56 => ( X2 = Y ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_150_finite__imageD,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,F: B > A,A4: set @ B] :
% 0.24/1.56 ( ( finite_finite2 @ A @ ( image @ B @ A @ F @ A4 ) )
% 0.24/1.56 => ( ( inj_on @ B @ A @ F @ A4 )
% 0.24/1.56 => ( finite_finite2 @ B @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_151_finite__image__iff,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F: A > B,A4: set @ A] :
% 0.24/1.56 ( ( inj_on @ A @ B @ F @ A4 )
% 0.24/1.56 => ( ( finite_finite2 @ B @ ( image @ A @ B @ F @ A4 ) )
% 0.24/1.56 = ( finite_finite2 @ A @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_152_inFr__Ind__minus,axiom,
% 0.24/1.56 ! [Ns13: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 0.24/1.56 ( ( gram_L1333338417e_inFr @ Ns13 @ Tr1 @ T2 )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.24/1.56 => ( gram_L1333338417e_inFr @ ( insert @ n @ ( root @ Tr ) @ Ns13 ) @ Tr @ T2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_153_inFr2_OInd,axiom,
% 0.24/1.56 ! [Tr1: dtree,Tr: dtree,Ns13: set @ n,T2: t] :
% 0.24/1.56 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.24/1.56 => ( ( gram_L805317441_inFr2 @ Ns13 @ Tr1 @ T2 )
% 0.24/1.56 => ( gram_L805317441_inFr2 @ ( insert @ n @ ( root @ Tr ) @ Ns13 ) @ Tr @ T2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_154_wf__subtr__inj__on,axiom,
% 0.24/1.56 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 0.24/1.56 ( ( gram_L864798063lle_wf @ Tr1 )
% 0.24/1.56 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.24/1.56 => ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_155_wf_Ocases,axiom,
% 0.24/1.56 ! [A2: dtree] :
% 0.24/1.56 ( ( gram_L864798063lle_wf @ A2 )
% 0.24/1.56 => ~ ( ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ A2 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ A2 ) ) ) @ gram_L1451583632elle_P )
% 0.24/1.56 => ( ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ A2 ) ) )
% 0.24/1.56 => ~ ! [Tr6: dtree] :
% 0.24/1.56 ( ( member @ dtree @ Tr6 @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ A2 ) ) )
% 0.24/1.56 => ( gram_L864798063lle_wf @ Tr6 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_156_wf_Osimps,axiom,
% 0.24/1.56 ( gram_L864798063lle_wf
% 0.24/1.56 = ( ^ [A10: dtree] :
% 0.24/1.56 ? [Tr3: dtree] :
% 0.24/1.56 ( ( A10 = Tr3 )
% 0.24/1.56 & ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ Tr3 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr3 ) ) ) @ gram_L1451583632elle_P )
% 0.24/1.56 & ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr3 ) ) )
% 0.24/1.56 & ! [X: dtree] :
% 0.24/1.56 ( ( member @ dtree @ X @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr3 ) ) )
% 0.24/1.56 => ( gram_L864798063lle_wf @ X ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_157_wf__coind,axiom,
% 0.24/1.56 ! [Phi: dtree > $o,Tr: dtree] :
% 0.24/1.56 ( ( Phi @ Tr )
% 0.24/1.56 => ( ! [Tr4: dtree] :
% 0.24/1.56 ( ( Phi @ Tr4 )
% 0.24/1.56 => ( ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ Tr4 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr4 ) ) ) @ gram_L1451583632elle_P )
% 0.24/1.56 & ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr4 ) ) )
% 0.24/1.56 & ! [X3: dtree] :
% 0.24/1.56 ( ( member @ dtree @ X3 @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr4 ) ) )
% 0.24/1.56 => ( ( Phi @ X3 )
% 0.24/1.56 | ( gram_L864798063lle_wf @ X3 ) ) ) ) )
% 0.24/1.56 => ( gram_L864798063lle_wf @ Tr ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_158_inj__Inr,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,A4: set @ A] : ( inj_on @ A @ ( sum_sum @ B @ A ) @ ( sum_Inr @ A @ B ) @ A4 ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_159_inj__Inl,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,A4: set @ A] : ( inj_on @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ A4 ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_160_subtr__trans,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr32: dtree] :
% 0.24/1.56 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.24/1.56 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr32 )
% 0.24/1.56 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr32 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_161_used,axiom,
% 0.24/1.56 ! [N4: n] :
% 0.24/1.56 ? [Tns2: set @ ( sum_sum @ t @ n )] : ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ N4 @ Tns2 ) @ gram_L1451583632elle_P ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_162_finite__in__P,axiom,
% 0.24/1.56 ! [N4: n,Tns: set @ ( sum_sum @ t @ n )] :
% 0.24/1.56 ( ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ N4 @ Tns ) @ gram_L1451583632elle_P )
% 0.24/1.56 => ( finite_finite2 @ ( sum_sum @ t @ n ) @ Tns ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_163_subtr__rootR__in,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.24/1.56 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.24/1.56 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_164_subtr__rootL__in,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.24/1.56 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.24/1.56 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_165_subtr_ORefl,axiom,
% 0.24/1.56 ! [Tr: dtree,Ns: set @ n] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.24/1.56 => ( gram_L716654942_subtr @ Ns @ Tr @ Tr ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_166_wf__subtr,axiom,
% 0.24/1.56 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 0.24/1.56 ( ( gram_L864798063lle_wf @ Tr1 )
% 0.24/1.56 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.24/1.56 => ( gram_L864798063lle_wf @ Tr ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_167_subtr__inFr,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr: dtree,T2: t,Tr1: dtree] :
% 0.24/1.56 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.24/1.56 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.24/1.56 => ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_168_wf__subtr__P,axiom,
% 0.24/1.56 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 0.24/1.56 ( ( gram_L864798063lle_wf @ Tr1 )
% 0.24/1.56 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.24/1.56 => ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ Tr ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) ) @ gram_L1451583632elle_P ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_169_subtr__inductL,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Phi: ( set @ n ) > dtree > dtree > $o] :
% 0.24/1.56 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.24/1.56 => ( ! [Ns2: set @ n,Tr4: dtree] : ( Phi @ Ns2 @ Tr4 @ Tr4 )
% 0.24/1.56 => ( ! [Ns2: set @ n,Tr12: dtree,Tr23: dtree,Tr33: dtree] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr12 ) @ Ns2 )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 0.24/1.56 => ( ( gram_L716654942_subtr @ Ns2 @ Tr23 @ Tr33 )
% 0.24/1.56 => ( ( Phi @ Ns2 @ Tr23 @ Tr33 )
% 0.24/1.56 => ( Phi @ Ns2 @ Tr12 @ Tr33 ) ) ) ) )
% 0.24/1.56 => ( Phi @ Ns @ Tr1 @ Tr22 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_170_subtr_Oinducts,axiom,
% 0.24/1.56 ! [X1: set @ n,X22: dtree,X32: dtree,P: ( set @ n ) > dtree > dtree > $o] :
% 0.24/1.56 ( ( gram_L716654942_subtr @ X1 @ X22 @ X32 )
% 0.24/1.56 => ( ! [Tr4: dtree,Ns2: set @ n] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.24/1.56 => ( P @ Ns2 @ Tr4 @ Tr4 ) )
% 0.24/1.56 => ( ! [Tr33: dtree,Ns2: set @ n,Tr12: dtree,Tr23: dtree] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr33 ) @ Ns2 )
% 0.24/1.56 => ( ( gram_L716654942_subtr @ Ns2 @ Tr12 @ Tr23 )
% 0.24/1.56 => ( ( P @ Ns2 @ Tr12 @ Tr23 )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ Tr33 ) )
% 0.24/1.56 => ( P @ Ns2 @ Tr12 @ Tr33 ) ) ) ) )
% 0.24/1.56 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_171_subtr__StepL,axiom,
% 0.24/1.56 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr32: dtree] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 0.24/1.56 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr32 )
% 0.24/1.56 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr32 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_172_subtr_Osimps,axiom,
% 0.24/1.56 ( gram_L716654942_subtr
% 0.24/1.56 = ( ^ [A12: set @ n,A23: dtree,A33: dtree] :
% 0.24/1.56 ( ? [Tr3: dtree,Ns3: set @ n] :
% 0.24/1.56 ( ( A12 = Ns3 )
% 0.24/1.56 & ( A23 = Tr3 )
% 0.24/1.56 & ( A33 = Tr3 )
% 0.24/1.56 & ( member @ n @ ( root @ Tr3 ) @ Ns3 ) )
% 0.24/1.56 | ? [Tr34: dtree,Ns3: set @ n,Tr13: dtree,Tr24: dtree] :
% 0.24/1.56 ( ( A12 = Ns3 )
% 0.24/1.56 & ( A23 = Tr13 )
% 0.24/1.56 & ( A33 = Tr34 )
% 0.24/1.56 & ( member @ n @ ( root @ Tr34 ) @ Ns3 )
% 0.24/1.56 & ( gram_L716654942_subtr @ Ns3 @ Tr13 @ Tr24 )
% 0.24/1.56 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr24 ) @ ( cont @ Tr34 ) ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_173_subtr_Ocases,axiom,
% 0.24/1.56 ! [A1: set @ n,A22: dtree,A32: dtree] :
% 0.24/1.56 ( ( gram_L716654942_subtr @ A1 @ A22 @ A32 )
% 0.24/1.56 => ( ( ( A32 = A22 )
% 0.24/1.56 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.24/1.56 => ~ ( ( member @ n @ ( root @ A32 ) @ A1 )
% 0.24/1.56 => ! [Tr23: dtree] :
% 0.24/1.56 ( ( gram_L716654942_subtr @ A1 @ A22 @ Tr23 )
% 0.24/1.56 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ A32 ) ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_174_subtr_OStep,axiom,
% 0.24/1.56 ! [Tr32: dtree,Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr32 ) @ Ns )
% 0.24/1.56 => ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr32 ) )
% 0.24/1.56 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr32 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_175_inFr__subtr,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.24/1.56 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.24/1.56 => ? [Tr7: dtree] :
% 0.24/1.56 ( ( gram_L716654942_subtr @ Ns @ Tr7 @ Tr )
% 0.24/1.56 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr7 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_176_wf__P,axiom,
% 0.24/1.56 ! [Tr: dtree] :
% 0.24/1.56 ( ( gram_L864798063lle_wf @ Tr )
% 0.24/1.56 => ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ Tr ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) ) @ gram_L1451583632elle_P ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_177_wf__raw__coind,axiom,
% 0.24/1.56 ! [Phi: dtree > $o,Tr: dtree] :
% 0.24/1.56 ( ( Phi @ Tr )
% 0.24/1.56 => ( ! [Tr4: dtree] :
% 0.24/1.56 ( ( Phi @ Tr4 )
% 0.24/1.56 => ( ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ Tr4 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr4 ) ) ) @ gram_L1451583632elle_P )
% 0.24/1.56 & ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr4 ) ) )
% 0.24/1.56 & ! [X3: dtree] :
% 0.24/1.56 ( ( member @ dtree @ X3 @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr4 ) ) )
% 0.24/1.56 => ( Phi @ X3 ) ) ) )
% 0.24/1.56 => ( gram_L864798063lle_wf @ Tr ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_178_wf_Ocoinduct,axiom,
% 0.24/1.56 ! [X7: dtree > $o,X2: dtree] :
% 0.24/1.56 ( ( X7 @ X2 )
% 0.24/1.56 => ( ! [X3: dtree] :
% 0.24/1.56 ( ( X7 @ X3 )
% 0.24/1.56 => ? [Tr8: dtree] :
% 0.24/1.56 ( ( X3 = Tr8 )
% 0.24/1.56 & ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ Tr8 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr8 ) ) ) @ gram_L1451583632elle_P )
% 0.24/1.56 & ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr8 ) ) )
% 0.24/1.56 & ! [Xa: dtree] :
% 0.24/1.56 ( ( member @ dtree @ Xa @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr8 ) ) )
% 0.24/1.56 => ( ( X7 @ Xa )
% 0.24/1.56 | ( gram_L864798063lle_wf @ Xa ) ) ) ) )
% 0.24/1.56 => ( gram_L864798063lle_wf @ X2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_179_wf_Ointros,axiom,
% 0.24/1.56 ! [Tr: dtree] :
% 0.24/1.56 ( ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ ( root @ Tr ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) ) @ gram_L1451583632elle_P )
% 0.24/1.56 => ( ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr ) ) )
% 0.24/1.56 => ( ! [Tr7: dtree] :
% 0.24/1.56 ( ( member @ dtree @ Tr7 @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr ) ) )
% 0.24/1.56 => ( gram_L864798063lle_wf @ Tr7 ) )
% 0.24/1.56 => ( gram_L864798063lle_wf @ Tr ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_180_S__P,axiom,
% 0.24/1.56 ! [N4: n] : ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ N4 @ ( gram_L1451583635elle_S @ N4 ) ) @ gram_L1451583632elle_P ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_181_inItr_Oinducts,axiom,
% 0.24/1.56 ! [X1: set @ n,X22: dtree,X32: n,P: ( set @ n ) > dtree > n > $o] :
% 0.24/1.56 ( ( gram_L830233218_inItr @ X1 @ X22 @ X32 )
% 0.24/1.56 => ( ! [Tr4: dtree,Ns2: set @ n] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.24/1.56 => ( P @ Ns2 @ Tr4 @ ( root @ Tr4 ) ) )
% 0.24/1.56 => ( ! [Tr4: dtree,Ns2: set @ n,Tr12: dtree,N3: n] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr4 ) )
% 0.24/1.56 => ( ( gram_L830233218_inItr @ Ns2 @ Tr12 @ N3 )
% 0.24/1.56 => ( ( P @ Ns2 @ Tr12 @ N3 )
% 0.24/1.56 => ( P @ Ns2 @ Tr4 @ N3 ) ) ) ) )
% 0.24/1.56 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_182_inItr_Osimps,axiom,
% 0.24/1.56 ( gram_L830233218_inItr
% 0.24/1.56 = ( ^ [A12: set @ n,A23: dtree,A33: n] :
% 0.24/1.56 ( ? [Tr3: dtree,Ns3: set @ n] :
% 0.24/1.56 ( ( A12 = Ns3 )
% 0.24/1.56 & ( A23 = Tr3 )
% 0.24/1.56 & ( A33
% 0.24/1.56 = ( root @ Tr3 ) )
% 0.24/1.56 & ( member @ n @ ( root @ Tr3 ) @ Ns3 ) )
% 0.24/1.56 | ? [Tr3: dtree,Ns3: set @ n,Tr13: dtree,N2: n] :
% 0.24/1.56 ( ( A12 = Ns3 )
% 0.24/1.56 & ( A23 = Tr3 )
% 0.24/1.56 & ( A33 = N2 )
% 0.24/1.56 & ( member @ n @ ( root @ Tr3 ) @ Ns3 )
% 0.24/1.56 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr3 ) )
% 0.24/1.56 & ( gram_L830233218_inItr @ Ns3 @ Tr13 @ N2 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_183_finite__S,axiom,
% 0.24/1.56 ! [N4: n] : ( finite_finite2 @ ( sum_sum @ t @ n ) @ ( gram_L1451583635elle_S @ N4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_184_inItr_OBase,axiom,
% 0.24/1.56 ! [Tr: dtree,Ns: set @ n] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.24/1.56 => ( gram_L830233218_inItr @ Ns @ Tr @ ( root @ Tr ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_185_inItr__root__in,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr: dtree,N4: n] :
% 0.24/1.56 ( ( gram_L830233218_inItr @ Ns @ Tr @ N4 )
% 0.24/1.56 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_186_subtr__inItr,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr: dtree,N4: n,Tr1: dtree] :
% 0.24/1.56 ( ( gram_L830233218_inItr @ Ns @ Tr @ N4 )
% 0.24/1.56 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.24/1.56 => ( gram_L830233218_inItr @ Ns @ Tr1 @ N4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_187_inItr__subtr,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr: dtree,N4: n] :
% 0.24/1.56 ( ( gram_L830233218_inItr @ Ns @ Tr @ N4 )
% 0.24/1.56 => ? [Tr7: dtree] :
% 0.24/1.56 ( ( gram_L716654942_subtr @ Ns @ Tr7 @ Tr )
% 0.24/1.56 & ( ( root @ Tr7 )
% 0.24/1.56 = N4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_188_inItr_OInd,axiom,
% 0.24/1.56 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,N4: n] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.24/1.56 => ( ( gram_L830233218_inItr @ Ns @ Tr1 @ N4 )
% 0.24/1.56 => ( gram_L830233218_inItr @ Ns @ Tr @ N4 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_189_inItr_Ocases,axiom,
% 0.24/1.56 ! [A1: set @ n,A22: dtree,A32: n] :
% 0.24/1.56 ( ( gram_L830233218_inItr @ A1 @ A22 @ A32 )
% 0.24/1.56 => ( ( ( A32
% 0.24/1.56 = ( root @ A22 ) )
% 0.24/1.56 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.24/1.56 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.24/1.56 => ! [Tr12: dtree] :
% 0.24/1.56 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A22 ) )
% 0.24/1.56 => ~ ( gram_L830233218_inItr @ A1 @ Tr12 @ A32 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_190_cont__deftr,axiom,
% 0.24/1.56 ! [N4: n] :
% 0.24/1.56 ( ( cont @ ( gram_L1231612515_deftr @ N4 ) )
% 0.24/1.56 = ( image @ ( sum_sum @ t @ n ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ n @ dtree @ ( id @ t ) @ gram_L1231612515_deftr ) @ ( gram_L1451583635elle_S @ N4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_191_subtr2_OStep,axiom,
% 0.24/1.56 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr32: dtree] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 0.24/1.56 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr32 )
% 0.24/1.56 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr32 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_192_subtr2_Ocases,axiom,
% 0.24/1.56 ! [A1: set @ n,A22: dtree,A32: dtree] :
% 0.24/1.56 ( ( gram_L1283001940subtr2 @ A1 @ A22 @ A32 )
% 0.24/1.56 => ( ( ( A32 = A22 )
% 0.24/1.56 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.24/1.56 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.24/1.56 => ! [Tr23: dtree] :
% 0.24/1.56 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A22 ) @ ( cont @ Tr23 ) )
% 0.24/1.56 => ~ ( gram_L1283001940subtr2 @ A1 @ Tr23 @ A32 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_193_root__deftr,axiom,
% 0.24/1.56 ! [N4: n] :
% 0.24/1.56 ( ( root @ ( gram_L1231612515_deftr @ N4 ) )
% 0.24/1.56 = N4 ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_194_subtr__subtr2,axiom,
% 0.24/1.56 gram_L716654942_subtr = gram_L1283001940subtr2 ).
% 0.24/1.56
% 0.24/1.56 thf(fact_195_subtr2__trans,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr32: dtree] :
% 0.24/1.56 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.24/1.56 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr32 )
% 0.24/1.56 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr32 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_196_subtr2_ORefl,axiom,
% 0.24/1.56 ! [Tr: dtree,Ns: set @ n] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.24/1.56 => ( gram_L1283001940subtr2 @ Ns @ Tr @ Tr ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_197_subtr2__rootL__in,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.24/1.56 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.24/1.56 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_198_subtr2__rootR__in,axiom,
% 0.24/1.56 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.24/1.56 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.24/1.56 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_199_wf__deftr,axiom,
% 0.24/1.56 ! [N4: n] : ( gram_L864798063lle_wf @ ( gram_L1231612515_deftr @ N4 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_200_deftr__def,axiom,
% 0.24/1.56 ( gram_L1231612515_deftr
% 0.24/1.56 = ( unfold @ n @ ( id @ n ) @ gram_L1451583635elle_S ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_201_subtr2_Oinducts,axiom,
% 0.24/1.56 ! [X1: set @ n,X22: dtree,X32: dtree,P: ( set @ n ) > dtree > dtree > $o] :
% 0.24/1.56 ( ( gram_L1283001940subtr2 @ X1 @ X22 @ X32 )
% 0.24/1.56 => ( ! [Tr4: dtree,Ns2: set @ n] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.24/1.56 => ( P @ Ns2 @ Tr4 @ Tr4 ) )
% 0.24/1.56 => ( ! [Tr12: dtree,Ns2: set @ n,Tr23: dtree,Tr33: dtree] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr12 ) @ Ns2 )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 0.24/1.56 => ( ( gram_L1283001940subtr2 @ Ns2 @ Tr23 @ Tr33 )
% 0.24/1.56 => ( ( P @ Ns2 @ Tr23 @ Tr33 )
% 0.24/1.56 => ( P @ Ns2 @ Tr12 @ Tr33 ) ) ) ) )
% 0.24/1.56 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_202_subtr2__StepR,axiom,
% 0.24/1.56 ! [Tr32: dtree,Ns: set @ n,Tr22: dtree,Tr1: dtree] :
% 0.24/1.56 ( ( member @ n @ ( root @ Tr32 ) @ Ns )
% 0.24/1.56 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr32 ) )
% 0.24/1.56 => ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.24/1.56 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr32 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_203_subtr2_Osimps,axiom,
% 0.24/1.56 ( gram_L1283001940subtr2
% 0.24/1.56 = ( ^ [A12: set @ n,A23: dtree,A33: dtree] :
% 0.24/1.56 ( ? [Tr3: dtree,Ns3: set @ n] :
% 0.24/1.56 ( ( A12 = Ns3 )
% 0.24/1.56 & ( A23 = Tr3 )
% 0.24/1.56 & ( A33 = Tr3 )
% 0.24/1.56 & ( member @ n @ ( root @ Tr3 ) @ Ns3 ) )
% 0.24/1.56 | ? [Tr13: dtree,Ns3: set @ n,Tr24: dtree,Tr34: dtree] :
% 0.24/1.56 ( ( A12 = Ns3 )
% 0.24/1.56 & ( A23 = Tr13 )
% 0.24/1.56 & ( A33 = Tr34 )
% 0.24/1.56 & ( member @ n @ ( root @ Tr13 ) @ Ns3 )
% 0.24/1.56 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr24 ) )
% 0.24/1.56 & ( gram_L1283001940subtr2 @ Ns3 @ Tr24 @ Tr34 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_204_root__o__subst,axiom,
% 0.24/1.56 ( ( comp @ dtree @ n @ dtree @ root @ ( gram_L1004374585hsubst @ tr0 ) )
% 0.24/1.56 = root ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_205_inf__img__fin__dom,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F: B > A,A4: set @ B] :
% 0.24/1.56 ( ( finite_finite2 @ A @ ( image @ B @ A @ F @ A4 ) )
% 0.24/1.56 => ( ~ ( finite_finite2 @ B @ A4 )
% 0.24/1.56 => ? [X3: A] :
% 0.24/1.56 ( ( member @ A @ X3 @ ( image @ B @ A @ F @ A4 ) )
% 0.24/1.56 & ~ ( finite_finite2 @ B @ ( vimage @ B @ A @ F @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_206_empty__Collect__eq,axiom,
% 0.24/1.56 ! [A: $tType,P: A > $o] :
% 0.24/1.56 ( ( ( bot_bot @ ( set @ A ) )
% 0.24/1.56 = ( collect @ A @ P ) )
% 0.24/1.56 = ( ! [X: A] :
% 0.24/1.56 ~ ( P @ X ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_207_Collect__empty__eq,axiom,
% 0.24/1.56 ! [A: $tType,P: A > $o] :
% 0.24/1.56 ( ( ( collect @ A @ P )
% 0.24/1.56 = ( bot_bot @ ( set @ A ) ) )
% 0.24/1.56 = ( ! [X: A] :
% 0.24/1.56 ~ ( P @ X ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_208_all__not__in__conv,axiom,
% 0.24/1.56 ! [A: $tType,A4: set @ A] :
% 0.24/1.56 ( ( ! [X: A] :
% 0.24/1.56 ~ ( member @ A @ X @ A4 ) )
% 0.24/1.56 = ( A4
% 0.24/1.56 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_209_empty__iff,axiom,
% 0.24/1.56 ! [A: $tType,C4: A] :
% 0.24/1.56 ~ ( member @ A @ C4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_210_comp__apply,axiom,
% 0.24/1.56 ! [C: $tType,A: $tType,B: $tType] :
% 0.24/1.56 ( ( comp @ B @ A @ C )
% 0.24/1.56 = ( ^ [F6: B > A,G3: C > B,X: C] : ( F6 @ ( G3 @ X ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_211_image__is__empty,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,F: B > A,A4: set @ B] :
% 0.24/1.56 ( ( ( image @ B @ A @ F @ A4 )
% 0.24/1.56 = ( bot_bot @ ( set @ A ) ) )
% 0.24/1.56 = ( A4
% 0.24/1.56 = ( bot_bot @ ( set @ B ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_212_empty__is__image,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,F: B > A,A4: set @ B] :
% 0.24/1.56 ( ( ( bot_bot @ ( set @ A ) )
% 0.24/1.56 = ( image @ B @ A @ F @ A4 ) )
% 0.24/1.56 = ( A4
% 0.24/1.56 = ( bot_bot @ ( set @ B ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_213_image__empty,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F: B > A] :
% 0.24/1.56 ( ( image @ B @ A @ F @ ( bot_bot @ ( set @ B ) ) )
% 0.24/1.56 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_214_singletonI,axiom,
% 0.24/1.56 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_215_inj__on__empty,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F: A > B] : ( inj_on @ A @ B @ F @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_216_fun_Omap__id,axiom,
% 0.24/1.56 ! [A: $tType,D: $tType,T2: D > A] :
% 0.24/1.56 ( ( comp @ A @ A @ D @ ( id @ A ) @ T2 )
% 0.24/1.56 = T2 ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_217_comp__id,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F: A > B] :
% 0.24/1.56 ( ( comp @ A @ B @ A @ F @ ( id @ A ) )
% 0.24/1.56 = F ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_218_id__comp,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,G: A > B] :
% 0.24/1.56 ( ( comp @ B @ B @ A @ ( id @ B ) @ G )
% 0.24/1.56 = G ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_219_vimage__empty,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F: A > B] :
% 0.24/1.56 ( ( vimage @ A @ B @ F @ ( bot_bot @ ( set @ B ) ) )
% 0.24/1.56 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_220_comp__inj__on__iff,axiom,
% 0.24/1.56 ! [B: $tType,C: $tType,A: $tType,F: A > B,A4: set @ A,F7: B > C] :
% 0.24/1.56 ( ( inj_on @ A @ B @ F @ A4 )
% 0.24/1.56 => ( ( inj_on @ B @ C @ F7 @ ( image @ A @ B @ F @ A4 ) )
% 0.24/1.56 = ( inj_on @ A @ C @ ( comp @ B @ C @ A @ F7 @ F ) @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_221_inj__on__imageI,axiom,
% 0.24/1.56 ! [B: $tType,C: $tType,A: $tType,G: C > B,F: A > C,A4: set @ A] :
% 0.24/1.56 ( ( inj_on @ A @ B @ ( comp @ C @ B @ A @ G @ F ) @ A4 )
% 0.24/1.56 => ( inj_on @ C @ B @ G @ ( image @ A @ C @ F @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_222_comp__inj__on,axiom,
% 0.24/1.56 ! [B: $tType,C: $tType,A: $tType,F: A > B,A4: set @ A,G: B > C] :
% 0.24/1.56 ( ( inj_on @ A @ B @ F @ A4 )
% 0.24/1.56 => ( ( inj_on @ B @ C @ G @ ( image @ A @ B @ F @ A4 ) )
% 0.24/1.56 => ( inj_on @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_223_map__sum_Ocompositionality,axiom,
% 0.24/1.56 ! [D: $tType,F3: $tType,E2: $tType,C: $tType,B: $tType,A: $tType,F: C > E2,G: D > F3,H2: A > C,I: B > D,Sum: sum_sum @ A @ B] :
% 0.24/1.56 ( ( sum_map_sum @ C @ E2 @ D @ F3 @ F @ G @ ( sum_map_sum @ A @ C @ B @ D @ H2 @ I @ Sum ) )
% 0.24/1.56 = ( sum_map_sum @ A @ E2 @ B @ F3 @ ( comp @ C @ E2 @ A @ F @ H2 ) @ ( comp @ D @ F3 @ B @ G @ I ) @ Sum ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_224_sum_Omap__comp,axiom,
% 0.24/1.56 ! [D: $tType,F3: $tType,E2: $tType,C: $tType,B: $tType,A: $tType,G1: C > E2,G22: D > F3,F1: A > C,F2: B > D,V: sum_sum @ A @ B] :
% 0.24/1.56 ( ( sum_map_sum @ C @ E2 @ D @ F3 @ G1 @ G22 @ ( sum_map_sum @ A @ C @ B @ D @ F1 @ F2 @ V ) )
% 0.24/1.56 = ( sum_map_sum @ A @ E2 @ B @ F3 @ ( comp @ C @ E2 @ A @ G1 @ F1 ) @ ( comp @ D @ F3 @ B @ G22 @ F2 ) @ V ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_225_map__sum_Ocomp,axiom,
% 0.24/1.56 ! [A: $tType,C: $tType,E2: $tType,F3: $tType,D: $tType,B: $tType,F: C > E2,G: D > F3,H2: A > C,I: B > D] :
% 0.24/1.56 ( ( comp @ ( sum_sum @ C @ D ) @ ( sum_sum @ E2 @ F3 ) @ ( sum_sum @ A @ B ) @ ( sum_map_sum @ C @ E2 @ D @ F3 @ F @ G ) @ ( sum_map_sum @ A @ C @ B @ D @ H2 @ I ) )
% 0.24/1.56 = ( sum_map_sum @ A @ E2 @ B @ F3 @ ( comp @ C @ E2 @ A @ F @ H2 ) @ ( comp @ D @ F3 @ B @ G @ I ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_226_Inf_OINF__image,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,C: $tType,Inf: ( set @ A ) > A,G: B > A,F: C > B,A4: set @ C] :
% 0.24/1.56 ( ( Inf @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A4 ) ) )
% 0.24/1.56 = ( Inf @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_227_Sup_OSUP__image,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,C: $tType,Sup: ( set @ A ) > A,G: B > A,F: C > B,A4: set @ C] :
% 0.24/1.56 ( ( Sup @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A4 ) ) )
% 0.24/1.56 = ( Sup @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A4 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_228_image__comp,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,C: $tType,F: B > A,G: C > B,R: set @ C] :
% 0.24/1.56 ( ( image @ B @ A @ F @ ( image @ C @ B @ G @ R ) )
% 0.24/1.56 = ( image @ C @ A @ ( comp @ B @ A @ C @ F @ G ) @ R ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_229_image__eq__imp__comp,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,D: $tType,C: $tType,F: B > A,A4: set @ B,G: C > A,B3: set @ C,H2: A > D] :
% 0.24/1.56 ( ( ( image @ B @ A @ F @ A4 )
% 0.24/1.56 = ( image @ C @ A @ G @ B3 ) )
% 0.24/1.56 => ( ( image @ B @ D @ ( comp @ A @ D @ B @ H2 @ F ) @ A4 )
% 0.24/1.56 = ( image @ C @ D @ ( comp @ A @ D @ C @ H2 @ G ) @ B3 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_230_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__o__subst,axiom,
% 0.24/1.56 ! [Tr0: dtree] :
% 0.24/1.56 ( ( comp @ dtree @ n @ dtree @ root @ ( gram_L1004374585hsubst @ Tr0 ) )
% 0.24/1.56 = root ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_231_infinite__finite__induct,axiom,
% 0.24/1.56 ! [A: $tType,P: ( set @ A ) > $o,A4: set @ A] :
% 0.24/1.56 ( ! [A11: set @ A] :
% 0.24/1.56 ( ~ ( finite_finite2 @ A @ A11 )
% 0.24/1.56 => ( P @ A11 ) )
% 0.24/1.56 => ( ( P @ ( bot_bot @ ( set @ A ) ) )
% 0.24/1.56 => ( ! [X3: A,F8: set @ A] :
% 0.24/1.56 ( ( finite_finite2 @ A @ F8 )
% 0.24/1.56 => ( ~ ( member @ A @ X3 @ F8 )
% 0.24/1.56 => ( ( P @ F8 )
% 0.24/1.56 => ( P @ ( insert @ A @ X3 @ F8 ) ) ) ) )
% 0.24/1.56 => ( P @ A4 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_232_finite__ne__induct,axiom,
% 0.24/1.56 ! [A: $tType,F4: set @ A,P: ( set @ A ) > $o] :
% 0.24/1.56 ( ( finite_finite2 @ A @ F4 )
% 0.24/1.56 => ( ( F4
% 0.24/1.56 != ( bot_bot @ ( set @ A ) ) )
% 0.24/1.56 => ( ! [X3: A] : ( P @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.24/1.56 => ( ! [X3: A,F8: set @ A] :
% 0.24/1.56 ( ( finite_finite2 @ A @ F8 )
% 0.24/1.56 => ( ( F8
% 0.24/1.56 != ( bot_bot @ ( set @ A ) ) )
% 0.24/1.56 => ( ~ ( member @ A @ X3 @ F8 )
% 0.24/1.56 => ( ( P @ F8 )
% 0.24/1.56 => ( P @ ( insert @ A @ X3 @ F8 ) ) ) ) ) )
% 0.24/1.56 => ( P @ F4 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_233_finite_Oinducts,axiom,
% 0.24/1.56 ! [A: $tType,X2: set @ A,P: ( set @ A ) > $o] :
% 0.24/1.56 ( ( finite_finite2 @ A @ X2 )
% 0.24/1.56 => ( ( P @ ( bot_bot @ ( set @ A ) ) )
% 0.24/1.56 => ( ! [A11: set @ A,A7: A] :
% 0.24/1.56 ( ( finite_finite2 @ A @ A11 )
% 0.24/1.56 => ( ( P @ A11 )
% 0.24/1.56 => ( P @ ( insert @ A @ A7 @ A11 ) ) ) )
% 0.24/1.56 => ( P @ X2 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_234_finite__induct,axiom,
% 0.24/1.56 ! [A: $tType,F4: set @ A,P: ( set @ A ) > $o] :
% 0.24/1.56 ( ( finite_finite2 @ A @ F4 )
% 0.24/1.56 => ( ( P @ ( bot_bot @ ( set @ A ) ) )
% 0.24/1.56 => ( ! [X3: A,F8: set @ A] :
% 0.24/1.56 ( ( finite_finite2 @ A @ F8 )
% 0.24/1.56 => ( ~ ( member @ A @ X3 @ F8 )
% 0.24/1.56 => ( ( P @ F8 )
% 0.24/1.56 => ( P @ ( insert @ A @ X3 @ F8 ) ) ) ) )
% 0.24/1.56 => ( P @ F4 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_235_finite_Osimps,axiom,
% 0.24/1.56 ! [A: $tType] :
% 0.24/1.56 ( ( finite_finite2 @ A )
% 0.24/1.56 = ( ^ [A10: set @ A] :
% 0.24/1.56 ( ( A10
% 0.24/1.56 = ( bot_bot @ ( set @ A ) ) )
% 0.24/1.56 | ? [A8: set @ A,B9: A] :
% 0.24/1.56 ( ( A10
% 0.24/1.56 = ( insert @ A @ B9 @ A8 ) )
% 0.24/1.56 & ( finite_finite2 @ A @ A8 ) ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_236_finite_Ocases,axiom,
% 0.24/1.56 ! [A: $tType,A2: set @ A] :
% 0.24/1.56 ( ( finite_finite2 @ A @ A2 )
% 0.24/1.56 => ( ( A2
% 0.24/1.56 != ( bot_bot @ ( set @ A ) ) )
% 0.24/1.56 => ~ ! [A11: set @ A] :
% 0.24/1.56 ( ? [A7: A] :
% 0.24/1.56 ( A2
% 0.24/1.56 = ( insert @ A @ A7 @ A11 ) )
% 0.24/1.56 => ~ ( finite_finite2 @ A @ A11 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_237_singleton__inject,axiom,
% 0.24/1.56 ! [A: $tType,A2: A,B2: A] :
% 0.24/1.56 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.24/1.56 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.24/1.56 => ( A2 = B2 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_238_insert__not__empty,axiom,
% 0.24/1.56 ! [A: $tType,A2: A,A4: set @ A] :
% 0.24/1.56 ( ( insert @ A @ A2 @ A4 )
% 0.24/1.56 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_239_doubleton__eq__iff,axiom,
% 0.24/1.56 ! [A: $tType,A2: A,B2: A,C4: A,D3: A] :
% 0.24/1.56 ( ( ( insert @ A @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.24/1.56 = ( insert @ A @ C4 @ ( insert @ A @ D3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.24/1.56 = ( ( ( A2 = C4 )
% 0.24/1.56 & ( B2 = D3 ) )
% 0.24/1.56 | ( ( A2 = D3 )
% 0.24/1.56 & ( B2 = C4 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_240_singleton__iff,axiom,
% 0.24/1.56 ! [A: $tType,B2: A,A2: A] :
% 0.24/1.56 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.24/1.56 = ( B2 = A2 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_241_singletonD,axiom,
% 0.24/1.56 ! [A: $tType,B2: A,A2: A] :
% 0.24/1.56 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.24/1.56 => ( B2 = A2 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_242_fun_Omap__id0,axiom,
% 0.24/1.56 ! [A: $tType,D: $tType] :
% 0.24/1.56 ( ( comp @ A @ A @ D @ ( id @ A ) )
% 0.24/1.56 = ( id @ ( D > A ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_243_pointfree__idE,axiom,
% 0.24/1.56 ! [B: $tType,A: $tType,F: B > A,G: A > B,X2: A] :
% 0.24/1.56 ( ( ( comp @ B @ A @ A @ F @ G )
% 0.24/1.56 = ( id @ A ) )
% 0.24/1.56 => ( ( F @ ( G @ X2 ) )
% 0.24/1.56 = X2 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_244_comp__eq__id__dest,axiom,
% 0.24/1.56 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B2: A > C,C4: A > B,V: A] :
% 0.24/1.56 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.24/1.56 = ( comp @ B @ B @ A @ ( id @ B ) @ C4 ) )
% 0.24/1.56 => ( ( A2 @ ( B2 @ V ) )
% 0.24/1.56 = ( C4 @ V ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_245_vimage__comp,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,C: $tType,F: A > B,G: B > C,X2: set @ C] :
% 0.24/1.56 ( ( vimage @ A @ B @ F @ ( vimage @ B @ C @ G @ X2 ) )
% 0.24/1.56 = ( vimage @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ X2 ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_246_set_Ocompositionality,axiom,
% 0.24/1.56 ! [C: $tType,B: $tType,A: $tType,F: C > B,G: B > A,Set: set @ A] :
% 0.24/1.56 ( ( vimage @ C @ B @ F @ ( vimage @ B @ A @ G @ Set ) )
% 0.24/1.56 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ Set ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_247_rewriteR__comp__comp2,axiom,
% 0.24/1.56 ! [C: $tType,B: $tType,E2: $tType,D: $tType,A: $tType,G: C > B,H2: A > C,R1: D > B,R2: A > D,F: B > E2,L: D > E2] :
% 0.24/1.56 ( ( ( comp @ C @ B @ A @ G @ H2 )
% 0.24/1.56 = ( comp @ D @ B @ A @ R1 @ R2 ) )
% 0.24/1.56 => ( ( ( comp @ B @ E2 @ D @ F @ R1 )
% 0.24/1.56 = L )
% 0.24/1.56 => ( ( comp @ C @ E2 @ A @ ( comp @ B @ E2 @ C @ F @ G ) @ H2 )
% 0.24/1.56 = ( comp @ D @ E2 @ A @ L @ R2 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_248_rewriteL__comp__comp2,axiom,
% 0.24/1.56 ! [A: $tType,C: $tType,B: $tType,D: $tType,E2: $tType,F: C > B,G: A > C,L1: D > B,L2: A > D,H2: E2 > A,R: E2 > D] :
% 0.24/1.56 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.24/1.56 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 0.24/1.56 => ( ( ( comp @ A @ D @ E2 @ L2 @ H2 )
% 0.24/1.56 = R )
% 0.24/1.56 => ( ( comp @ C @ B @ E2 @ F @ ( comp @ A @ C @ E2 @ G @ H2 ) )
% 0.24/1.56 = ( comp @ D @ B @ E2 @ L1 @ R ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_249_rewriteR__comp__comp,axiom,
% 0.24/1.56 ! [C: $tType,D: $tType,B: $tType,A: $tType,G: C > B,H2: A > C,R: A > B,F: B > D] :
% 0.24/1.56 ( ( ( comp @ C @ B @ A @ G @ H2 )
% 0.24/1.56 = R )
% 0.24/1.56 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F @ G ) @ H2 )
% 0.24/1.56 = ( comp @ B @ D @ A @ F @ R ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_250_rewriteL__comp__comp,axiom,
% 0.24/1.56 ! [C: $tType,B: $tType,A: $tType,D: $tType,F: C > B,G: A > C,L: A > B,H2: D > A] :
% 0.24/1.56 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.24/1.56 = L )
% 0.24/1.56 => ( ( comp @ C @ B @ D @ F @ ( comp @ A @ C @ D @ G @ H2 ) )
% 0.24/1.56 = ( comp @ A @ B @ D @ L @ H2 ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_251_fun_Omap__comp,axiom,
% 0.24/1.56 ! [B: $tType,C: $tType,A: $tType,D: $tType,G: B > C,F: A > B,V: D > A] :
% 0.24/1.56 ( ( comp @ B @ C @ D @ G @ ( comp @ A @ B @ D @ F @ V ) )
% 0.24/1.56 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G @ F ) @ V ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_252_set_Ocomp,axiom,
% 0.24/1.56 ! [A: $tType,B: $tType,C: $tType,F: C > B,G: B > A] :
% 0.24/1.56 ( ( comp @ ( set @ B ) @ ( set @ C ) @ ( set @ A ) @ ( vimage @ C @ B @ F ) @ ( vimage @ B @ A @ G ) )
% 0.24/1.56 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_253_comp__eq__dest__lhs,axiom,
% 0.24/1.56 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B2: A > C,C4: A > B,V: A] :
% 0.24/1.56 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.24/1.56 = C4 )
% 0.24/1.56 => ( ( A2 @ ( B2 @ V ) )
% 0.24/1.56 = ( C4 @ V ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_254_comp__eq__elim,axiom,
% 0.24/1.56 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C4: D > B,D3: A > D] :
% 0.24/1.56 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.24/1.56 = ( comp @ D @ B @ A @ C4 @ D3 ) )
% 0.24/1.56 => ! [V2: A] :
% 0.24/1.56 ( ( A2 @ ( B2 @ V2 ) )
% 0.24/1.56 = ( C4 @ ( D3 @ V2 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(fact_255_comp__eq__dest,axiom,
% 0.24/1.56 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C4: D > B,D3: A > D,V: A] :
% 0.24/1.56 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.24/1.56 = ( comp @ D @ B @ A @ C4 @ D3 ) )
% 0.24/1.56 => ( ( A2 @ ( B2 @ V ) )
% 0.24/1.56 = ( C4 @ ( D3 @ V ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 0.24/1.56 ! [A5: $tType,A13: $tType] :
% 0.24/1.56 ( ( ( finite_finite @ A5 @ ( type @ A5 ) )
% 0.24/1.56 & ( finite_finite @ A13 @ ( type @ A13 ) ) )
% 0.24/1.56 => ( finite_finite @ ( A5 > A13 ) @ ( type @ ( A5 > A13 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(tcon_Set_Oset___Finite__Set_Ofinite_1,axiom,
% 0.24/1.56 ! [A5: $tType] :
% 0.24/1.56 ( ( finite_finite @ A5 @ ( type @ A5 ) )
% 0.24/1.56 => ( finite_finite @ ( set @ A5 ) @ ( type @ ( set @ A5 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(tcon_HOL_Obool___Finite__Set_Ofinite_2,axiom,
% 0.24/1.56 finite_finite @ $o @ ( type @ $o ) ).
% 0.24/1.56
% 0.24/1.56 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_3,axiom,
% 0.24/1.56 ! [A5: $tType,A13: $tType] :
% 0.24/1.56 ( ( ( finite_finite @ A5 @ ( type @ A5 ) )
% 0.24/1.56 & ( finite_finite @ A13 @ ( type @ A13 ) ) )
% 0.24/1.56 => ( finite_finite @ ( sum_sum @ A5 @ A13 ) @ ( type @ ( sum_sum @ A5 @ A13 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_4,axiom,
% 0.24/1.56 ! [A5: $tType,A13: $tType] :
% 0.24/1.56 ( ( ( finite_finite @ A5 @ ( type @ A5 ) )
% 0.24/1.56 & ( finite_finite @ A13 @ ( type @ A13 ) ) )
% 0.24/1.56 => ( finite_finite @ ( product_prod @ A5 @ A13 ) @ ( type @ ( product_prod @ A5 @ A13 ) ) ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(help_If_3_1_T,axiom,
% 0.24/1.56 ! [P: $o] :
% 0.24/1.56 ( ( P = $true )
% 0.24/1.56 | ( P = $false ) ) ).
% 0.24/1.56
% 0.24/1.56 thf(help_If_2_1_T,axiom,
% 0.24/1.56 ! [A: $tType,X2: A,Y: A] :
% 0.24/1.56 ( ( if @ A @ $false @ X2 @ Y )
% 0.24/1.56 = Y ) ).
% 0.24/1.56
% 0.24/1.56 thf(help_If_1_1_T,axiom,
% 0.24/1.56 ! [A: $tType,X2: A,Y: A] :
% 0.24/1.56 ( ( if @ A @ $true @ X2 @ Y )
% 0.24/1.56 = X2 ) ).
% 0.24/1.56
% 0.24/1.56 thf(conj_0,conjecture,
% 0.24/1.56 ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ tr0 ) ) @ ( cont @ tr ) ) )
% 0.24/1.56 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ tr ) ) ) ).
% 0.24/1.56 ------------------------
% 0.24/1.58 % (23858)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23752 for (2999ds/183Mi)
% 0.24/1.59 % (23861)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23752 for (2999ds/2Mi)
% 0.24/1.59 % (23859)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_23752 for (2999ds/4Mi)
% 0.24/1.59 % (23864)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23752 for (2999ds/18Mi)
% 0.24/1.59 % (23862)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_23752 for (2999ds/2Mi)
% 0.24/1.59 % (23863)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_23752 for (2999ds/275Mi)
% 0.24/1.59 % (23861)Instruction limit reached!
% 0.24/1.59 % (23861)------------------------------
% 0.24/1.59 % (23861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.24/1.59 % (23861)Termination reason: Unknown
% 0.24/1.59 % (23860)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_23752 for (2999ds/27Mi)
% 0.24/1.59 % (23862)Instruction limit reached!
% 0.24/1.59 % (23862)------------------------------
% 0.24/1.59 % (23862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.24/1.59 % (23861)Termination phase: shuffling
% 0.24/1.59
% 0.24/1.59 % (23862)Termination reason: Unknown
% 0.24/1.59 % (23861)Memory used [KB]: 1407
% 0.24/1.59 % (23862)Termination phase: shuffling
% 0.24/1.59 % (23861)Time elapsed: 0.003 s
% 0.24/1.59
% 0.24/1.59 % (23861)Instructions burned: 3 (million)
% 0.24/1.59 % (23862)Memory used [KB]: 1407
% 0.24/1.59 % (23861)------------------------------
% 0.24/1.59 % (23861)------------------------------
% 0.24/1.59 % (23862)Time elapsed: 0.003 s
% 0.24/1.59 % (23862)Instructions burned: 3 (million)
% 0.24/1.59 % (23862)------------------------------
% 0.24/1.59 % (23862)------------------------------
% 0.24/1.59 % (23859)Instruction limit reached!
% 0.24/1.59 % (23859)------------------------------
% 0.24/1.59 % (23859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.24/1.59 % (23859)Termination reason: Unknown
% 0.24/1.59 % (23859)Termination phase: shuffling
% 0.24/1.59
% 0.24/1.59 % (23859)Memory used [KB]: 1535
% 0.24/1.59 % (23859)Time elapsed: 0.004 s
% 0.24/1.59 % (23859)Instructions burned: 5 (million)
% 0.24/1.59 % (23859)------------------------------
% 0.24/1.59 % (23859)------------------------------
% 2.93/1.60 % (23864)Instruction limit reached!
% 2.93/1.60 % (23864)------------------------------
% 2.93/1.60 % (23864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.60 % (23864)Termination reason: Unknown
% 2.93/1.60 % (23864)Termination phase: shuffling
% 2.93/1.60
% 2.93/1.60 % (23864)Memory used [KB]: 1791
% 2.93/1.60 % (23864)Time elapsed: 0.011 s
% 2.93/1.60 % (23864)Instructions burned: 19 (million)
% 2.93/1.60 % (23864)------------------------------
% 2.93/1.60 % (23864)------------------------------
% 2.93/1.61 % (23860)Instruction limit reached!
% 2.93/1.61 % (23860)------------------------------
% 2.93/1.61 % (23860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.61 % (23860)Termination reason: Unknown
% 2.93/1.61 % (23860)Termination phase: Property scanning
% 2.93/1.61
% 2.93/1.61 % (23860)Memory used [KB]: 1918
% 2.93/1.61 % (23860)Time elapsed: 0.018 s
% 2.93/1.61 % (23860)Instructions burned: 28 (million)
% 2.93/1.61 % (23860)------------------------------
% 2.93/1.61 % (23860)------------------------------
% 2.93/1.61 % (23865)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23752 for (2999ds/3Mi)
% 2.93/1.61 % (23866)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_23752 for (2999ds/37Mi)
% 2.93/1.61 % (23867)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_23752 for (2999ds/15Mi)
% 2.93/1.61 % (23865)Instruction limit reached!
% 2.93/1.61 % (23865)------------------------------
% 2.93/1.61 % (23865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.61 % (23865)Termination reason: Unknown
% 2.93/1.61 % (23865)Termination phase: shuffling
% 2.93/1.61
% 2.93/1.61 % (23865)Memory used [KB]: 1407
% 2.93/1.61 % (23865)Time elapsed: 0.003 s
% 2.93/1.61 % (23865)Instructions burned: 3 (million)
% 2.93/1.61 % (23865)------------------------------
% 2.93/1.61 % (23865)------------------------------
% 2.93/1.62 % (23867)Instruction limit reached!
% 2.93/1.62 % (23867)------------------------------
% 2.93/1.62 % (23867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.62 % (23867)Termination reason: Unknown
% 2.93/1.62 % (23867)Termination phase: shuffling
% 2.93/1.62
% 2.93/1.62 % (23867)Memory used [KB]: 1663
% 2.93/1.62 % (23867)Time elapsed: 0.009 s
% 2.93/1.62 % (23867)Instructions burned: 15 (million)
% 2.93/1.62 % (23867)------------------------------
% 2.93/1.62 % (23867)------------------------------
% 2.93/1.62 % (23868)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23752 for (2999ds/3Mi)
% 2.93/1.62 % (23868)Instruction limit reached!
% 2.93/1.62 % (23868)------------------------------
% 2.93/1.62 % (23868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.62 % (23868)Termination reason: Unknown
% 2.93/1.62 % (23868)Termination phase: shuffling
% 2.93/1.62
% 2.93/1.62 % (23868)Memory used [KB]: 1407
% 2.93/1.62 % (23868)Time elapsed: 0.003 s
% 2.93/1.62 % (23868)Instructions burned: 4 (million)
% 2.93/1.62 % (23868)------------------------------
% 2.93/1.62 % (23868)------------------------------
% 2.93/1.63 % (23870)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23752 for (2999ds/7Mi)
% 2.93/1.63 % (23866)Instruction limit reached!
% 2.93/1.63 % (23866)------------------------------
% 2.93/1.63 % (23866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (23866)Termination reason: Unknown
% 2.93/1.63 % (23866)Termination phase: shuffling
% 2.93/1.63
% 2.93/1.63 % (23866)Memory used [KB]: 2174
% 2.93/1.63 % (23866)Time elapsed: 0.019 s
% 2.93/1.63 % (23866)Instructions burned: 38 (million)
% 2.93/1.63 % (23866)------------------------------
% 2.93/1.63 % (23866)------------------------------
% 2.93/1.63 % (23869)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_23752 for (2999ds/1041Mi)
% 2.93/1.63 % (23870)Instruction limit reached!
% 2.93/1.63 % (23870)------------------------------
% 2.93/1.63 % (23870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (23870)Termination reason: Unknown
% 2.93/1.63 % (23870)Termination phase: shuffling
% 2.93/1.63
% 2.93/1.63 % (23870)Memory used [KB]: 1535
% 2.93/1.63 % (23870)Time elapsed: 0.005 s
% 2.93/1.63 % (23870)Instructions burned: 7 (million)
% 2.93/1.63 % (23870)------------------------------
% 2.93/1.63 % (23870)------------------------------
% 2.93/1.63 % (23863)First to succeed.
% 2.93/1.63 % (23863)Refutation found. Thanks to Tanya!
% 2.93/1.63 % SZS status Theorem for DTF2THF_23752
% 2.93/1.63 % SZS output start Proof for DTF2THF_23752
% 2.93/1.63 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.93/1.63 thf(type_def_7, type, n: $tType).
% 2.93/1.63 thf(type_def_8, type, t: $tType).
% 2.93/1.63 thf(type_def_9, type, dtree: $tType).
% 2.93/1.63 thf(type_def_10, type, sum_sum: ($tType * $tType) > $tType).
% 2.93/1.63 thf(type_def_11, type, set: ($tType) > $tType).
% 2.93/1.63 thf(type_def_12, type, product_prod: ($tType * $tType) > $tType).
% 2.93/1.63 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 2.93/1.63 thf(func_def_1, type, sum_sum: ($tType * $tType) > $tType).
% 2.93/1.63 thf(func_def_2, type, dtree: $tType).
% 2.93/1.63 thf(func_def_3, type, set: ($tType) > $tType).
% 2.93/1.63 thf(func_def_4, type, t: $tType).
% 2.93/1.63 thf(func_def_5, type, n: $tType).
% 2.93/1.63 thf(func_def_6, type, itself: ($tType) > $tType).
% 2.93/1.63 thf(func_def_7, type, finite_finite: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.93/1.63 thf(func_def_8, type, node: n > set @ sum_sum @ t @ dtree > dtree).
% 2.93/1.63 thf(func_def_9, type, cont: dtree > set @ sum_sum @ t @ dtree).
% 2.93/1.63 thf(func_def_10, type, root: dtree > n).
% 2.93/1.63 thf(func_def_11, type, unfold: !>[X0: $tType]:((X0 > n) > (X0 > set @ sum_sum @ t @ X0) > X0 > dtree)).
% 2.93/1.63 thf(func_def_12, type, finite_finite2: !>[X0: $tType]:(set @ X0 > $o)).
% 2.93/1.63 thf(func_def_13, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X0) > X2 > X1)).
% 2.93/1.63 thf(func_def_14, type, id: !>[X0: $tType]:(X0 > X0)).
% 2.93/1.63 thf(func_def_15, type, inj_on: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > $o)).
% 2.93/1.63 thf(func_def_16, type, gram_L1451583632elle_P: set @ product_prod @ n @ set @ sum_sum @ t @ n).
% 2.93/1.63 thf(func_def_17, type, gram_L1451583635elle_S: n > set @ sum_sum @ t @ n).
% 2.93/1.63 thf(func_def_18, type, gram_L1231612515_deftr: n > dtree).
% 2.93/1.63 thf(func_def_19, type, gram_L1004374585hsubst: dtree > dtree > dtree).
% 2.93/1.63 thf(func_def_20, type, gram_L1905609002ubst_c: dtree > dtree > set @ sum_sum @ t @ dtree).
% 2.93/1.63 thf(func_def_21, type, gram_L1905609017ubst_r: dtree > n).
% 2.93/1.63 thf(func_def_22, type, gram_L1333338417e_inFr: set @ n > dtree > t > $o).
% 2.93/1.63 thf(func_def_23, type, gram_L805317441_inFr2: set @ n > dtree > t > $o).
% 2.93/1.63 thf(func_def_24, type, gram_L805317505_inFrr: set @ n > dtree > t > $o).
% 2.93/1.63 thf(func_def_25, type, gram_L830233218_inItr: set @ n > dtree > n > $o).
% 2.93/1.63 thf(func_def_26, type, gram_L716654942_subtr: set @ n > dtree > dtree > $o).
% 2.93/1.63 thf(func_def_27, type, gram_L1283001940subtr2: set @ n > dtree > dtree > $o).
% 2.93/1.63 thf(func_def_28, type, gram_L1614515765ubtrOf: dtree > n > dtree).
% 2.93/1.63 thf(func_def_29, type, gram_L864798063lle_wf: dtree > $o).
% 2.93/1.63 thf(func_def_30, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.93/1.63 thf(func_def_31, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.93/1.63 thf(func_def_32, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 2.93/1.63 thf(func_def_33, type, type: !>[X0: $tType]:(itself @ X0)).
% 2.93/1.63 thf(func_def_34, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.93/1.63 thf(func_def_35, type, image: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > set @ X1)).
% 2.93/1.63 thf(func_def_36, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 2.93/1.63 thf(func_def_37, type, vimage: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X1 > set @ X0)).
% 2.93/1.63 thf(func_def_38, type, sum_Inl: !>[X0: $tType, X1: $tType]:(X0 > sum_sum @ X0 @ X1)).
% 2.93/1.63 thf(func_def_39, type, sum_Inr: !>[X0: $tType, X1: $tType]:(X0 > sum_sum @ X1 @ X0)).
% 2.93/1.63 thf(func_def_40, type, sum_map_sum: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1) > (X2 > X3) > sum_sum @ X0 @ X2 > sum_sum @ X1 @ X3)).
% 2.93/1.63 thf(func_def_41, type, sum_rec_sum: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1)).
% 2.93/1.63 thf(func_def_42, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.93/1.63 thf(func_def_43, type, tr: dtree).
% 2.93/1.63 thf(func_def_44, type, tr0: dtree).
% 2.93/1.63 thf(func_def_62, type, sK0: !>[X0: $tType, X1: $tType, X2: $tType]:(set @ sum_sum @ X1 @ X2 > (X2 > X0) > X0 > X2)).
% 2.93/1.63 thf(func_def_63, type, sK1: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 2.93/1.63 thf(func_def_64, type, sK2: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > X0) > X1)).
% 2.93/1.63 thf(func_def_65, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > sum_sum @ X1 @ X0 > (X1 > X2) > X1)).
% 2.93/1.63 thf(func_def_66, type, sK4: !>[X0: $tType]:((X0 > X0) > X0)).
% 2.93/1.63 thf(func_def_67, type, sK5: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X1)).
% 2.93/1.63 thf(func_def_68, type, sK6: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X0)).
% 2.93/1.63 thf(func_def_69, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType]:($o > (sum_sum @ X0 @ X1 > X2) > X2 > X1)).
% 2.93/1.63 thf(func_def_70, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType]:($o > (sum_sum @ X0 @ X1 > X2) > X2 > X0)).
% 2.93/1.63 thf(func_def_71, type, sK9: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X1)).
% 2.93/1.63 thf(func_def_72, type, sK10: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X0)).
% 2.93/1.63 thf(func_def_73, type, sK11: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 2.93/1.63 thf(func_def_74, type, sK12: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > $o) > X1)).
% 2.93/1.63 thf(func_def_75, type, sK13: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > $o) > X0)).
% 2.93/1.63 thf(func_def_76, type, sK14: !>[X0: $tType, X1: $tType]:(set @ X1 > (X1 > X0) > X0 > X1)).
% 2.93/1.63 thf(func_def_77, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:(set @ sum_sum @ X0 @ X1 > (X1 > X2) > X2 > X1)).
% 2.93/1.63 thf(func_def_78, type, sK16: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X0)).
% 2.93/1.63 thf(func_def_79, type, sK17: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X1)).
% 2.93/1.63 thf(func_def_80, type, sK18: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.93/1.63 thf(func_def_81, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > sum_sum @ X0 @ X1 > (X1 > X2) > X1)).
% 2.93/1.63 thf(func_def_82, type, sK20: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > X0) > X0)).
% 2.93/1.63 thf(func_def_83, type, sK21: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 2.93/1.63 thf(func_def_85, type, ph23: !>[X0: $tType]:(X0)).
% 2.93/1.63 thf(f934,plain,(
% 2.93/1.63 $false),
% 2.93/1.63 inference(subsumption_resolution,[status(thm)],[f824,f815])).
% 2.93/1.63 thf(f815,plain,(
% 2.93/1.63 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X1 > X0,X4 : set @ sum_sum @ X2 @ X1] : (((vimage @ X2 @ sum_sum @ X2 @ X0 @ sum_Inl @ X2 @ X0 @ (image @ sum_sum @ X2 @ X1 @ sum_sum @ X2 @ X0 @ (sum_map_sum @ X2 @ X2 @ X1 @ X0 @ id @ X2 @ X3) @ X4)) = (vimage @ X2 @ sum_sum @ X2 @ X1 @ sum_Inl @ X2 @ X1 @ X4))) )),
% 2.93/1.63 inference(cnf_transformation,[status(thm)],[f620])).
% 2.93/1.63 thf(f620,plain,(
% 2.93/1.63 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X1 > X0,X4 : set @ sum_sum @ X2 @ X1] : ((vimage @ X2 @ sum_sum @ X2 @ X0 @ sum_Inl @ X2 @ X0 @ (image @ sum_sum @ X2 @ X1 @ sum_sum @ X2 @ X0 @ (sum_map_sum @ X2 @ X2 @ X1 @ X0 @ id @ X2 @ X3) @ X4)) = (vimage @ X2 @ sum_sum @ X2 @ X1 @ sum_Inl @ X2 @ X1 @ X4))),
% 2.93/1.63 inference(rectify,[status(thm)],[f3])).
% 2.93/1.63 thf(f3,axiom,(
% 2.93/1.63 ! [X1 : $tType,X2 : $tType,X0 : $tType,X5 : X2 > X1,X6 : set @ sum_sum @ X0 @ X2] : ((vimage @ X0 @ sum_sum @ X0 @ X1 @ sum_Inl @ X0 @ X1 @ (image @ sum_sum @ X0 @ X2 @ sum_sum @ X0 @ X1 @ (sum_map_sum @ X0 @ X0 @ X2 @ X1 @ id @ X0 @ X5) @ X6)) = (vimage @ X0 @ sum_sum @ X0 @ X2 @ sum_Inl @ X0 @ X2 @ X6))),
% 2.93/1.63 file('/export/starexec/sandbox2/tmp/tmp.wlnNTaEhLw/DTF2THF_23752.p',fact_2_Inl__m__oplus)).
% 2.93/1.63 thf(f824,plain,(
% 2.93/1.63 ((vimage @ t @ sum_sum @ t @ dtree @ sum_Inl @ t @ dtree @ (image @ sum_sum @ t @ dtree @ sum_sum @ t @ dtree @ (sum_map_sum @ t @ t @ dtree @ dtree @ id @ t @ (gram_L1004374585hsubst @ tr0)) @ (cont @ tr))) != (vimage @ t @ sum_sum @ t @ dtree @ sum_Inl @ t @ dtree @ (cont @ tr)))),
% 2.93/1.63 inference(cnf_transformation,[status(thm)],[f608])).
% 2.93/1.63 thf(f608,plain,(
% 2.93/1.63 ((vimage @ t @ sum_sum @ t @ dtree @ sum_Inl @ t @ dtree @ (image @ sum_sum @ t @ dtree @ sum_sum @ t @ dtree @ (sum_map_sum @ t @ t @ dtree @ dtree @ id @ t @ (gram_L1004374585hsubst @ tr0)) @ (cont @ tr))) != (vimage @ t @ sum_sum @ t @ dtree @ sum_Inl @ t @ dtree @ (cont @ tr)))),
% 2.93/1.63 inference(flattening,[status(thm)],[f266])).
% 2.93/1.63 thf(f266,negated_conjecture,(
% 2.93/1.63 ~((vimage @ t @ sum_sum @ t @ dtree @ sum_Inl @ t @ dtree @ (image @ sum_sum @ t @ dtree @ sum_sum @ t @ dtree @ (sum_map_sum @ t @ t @ dtree @ dtree @ id @ t @ (gram_L1004374585hsubst @ tr0)) @ (cont @ tr))) = (vimage @ t @ sum_sum @ t @ dtree @ sum_Inl @ t @ dtree @ (cont @ tr)))),
% 2.93/1.63 inference(negated_conjecture,[status(cth)],[f265])).
% 2.93/1.63 thf(f265,conjecture,(
% 2.93/1.63 ((vimage @ t @ sum_sum @ t @ dtree @ sum_Inl @ t @ dtree @ (image @ sum_sum @ t @ dtree @ sum_sum @ t @ dtree @ (sum_map_sum @ t @ t @ dtree @ dtree @ id @ t @ (gram_L1004374585hsubst @ tr0)) @ (cont @ tr))) = (vimage @ t @ sum_sum @ t @ dtree @ sum_Inl @ t @ dtree @ (cont @ tr)))),
% 2.93/1.63 file('/export/starexec/sandbox2/tmp/tmp.wlnNTaEhLw/DTF2THF_23752.p',conj_0)).
% 2.93/1.63 % SZS output end Proof for DTF2THF_23752
% 2.93/1.63 % (23863)------------------------------
% 2.93/1.63 % (23863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (23863)Termination reason: Refutation
% 2.93/1.63
% 2.93/1.63 % (23863)Memory used [KB]: 7036
% 2.93/1.63 % (23863)Time elapsed: 0.042 s
% 2.93/1.63 % (23863)Instructions burned: 80 (million)
% 2.93/1.63 % (23863)------------------------------
% 2.93/1.63 % (23863)------------------------------
% 2.93/1.63 % (23857)Success in time 0.065 s
%------------------------------------------------------------------------------