%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : COM192^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n031.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 08:41:54 AM UTC 2026
% Result : Theorem 2.91s 1.62s
% Output : Refutation 2.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM192^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n031.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 04:18:17 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : COM192^1 : TPTP v9.2.1. Released v7.0.0.
% 0.20/0.47 % Domain : Computing Theory
% 0.20/0.47 % Problem : Grammars and languages 1005
% 0.20/0.47 % Version : [Bla16] axioms : Especial.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.20/0.47 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.20/0.47 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bla16]
% 0.20/0.47 % Names : gram_lang__1005.p [Bla16]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.33 v9.1.0, 0.00 v8.1.0, 0.25 v7.5.0, 0.67 v7.2.0, 0.75 v7.1.0
% 0.20/0.47 % Syntax : Number of formulae : 323 ( 127 unt; 51 typ; 0 def)
% 0.20/0.47 % Number of atoms : 593 ( 316 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 6 ( 2 avg)
% 0.20/0.47 % Number of connectives : 4456 ( 38 ~; 4 |; 47 &;4118 @)
% 0.20/0.47 % ( 0 <=>; 249 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 21 ( 8 avg)
% 0.20/0.47 % Number of types : 4 ( 3 usr)
% 0.20/0.47 % Number of type conns : 365 ( 365 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 51 ( 48 usr; 6 con; 0-7 aty)
% 0.20/0.47 % Number of variables : 1152 ( 34 ^;1048 !; 34 ?;1152 :)
% 0.20/0.47 % ( 36 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.47 % SPC : TH1_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.20/0.47 % 2016-07-13 14:46:10.588
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 %----Could-be-implicit typings (8)
% 0.20/0.47 thf(ty_t_Product__Type_Oprod,type,
% 0.20/0.47 product_prod: $tType > $tType > $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_t_Sum__Type_Osum,type,
% 0.20/0.47 sum_sum: $tType > $tType > $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_t_Option_Ooption,type,
% 0.20/0.47 option: $tType > $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_t_DTree_Odtree,type,
% 0.20/0.47 dtree: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_t_Set_Oset,type,
% 0.20/0.47 set: $tType > $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_t_DTree_OT,type,
% 0.20/0.47 t: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_t_DTree_ON,type,
% 0.20/0.47 n: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_t_itself,type,
% 0.20/0.47 itself: $tType > $tType ).
% 0.20/0.47
% 0.20/0.47 %----Explicit typings (43)
% 0.20/0.47 thf(sy_cl_HOL_Otype,type,
% 0.20/0.47 type:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Orderings_Otop,type,
% 0.20/0.47 top:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Finite__Set_Ofinite,type,
% 0.20/0.47 finite_finite:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_cl_Nat_Osemiring__char__0,type,
% 0.20/0.47 semiring_char_0:
% 0.20/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_DTree_ONode,type,
% 0.20/0.47 node: n > ( set @ ( sum_sum @ t @ dtree ) ) > dtree ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_DTree_Ocont,type,
% 0.20/0.47 cont: dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_DTree_Ocorec,type,
% 0.20/0.47 corec:
% 0.20/0.47 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) ) ) > A > dtree ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_DTree_Odtree_Oroot,type,
% 0.20/0.47 root: dtree > n ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_DTree_Ounfold,type,
% 0.20/0.47 unfold:
% 0.20/0.47 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ A ) ) ) > A > dtree ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Finite__Set_Ofinite,type,
% 0.20/0.47 finite_finite2:
% 0.20/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Fun_Ocomp,type,
% 0.20/0.47 comp:
% 0.20/0.47 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Fun_Oid,type,
% 0.20/0.47 id:
% 0.20/0.47 !>[A: $tType] : ( A > A ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Fun_Oinj__on,type,
% 0.20/0.47 inj_on:
% 0.20/0.47 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH,type,
% 0.20/0.47 gram_L1451583624elle_H: dtree > n > dtree ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__c,type,
% 0.20/0.47 gram_L1221482011le_H_c: dtree > n > ( set @ ( sum_sum @ t @ n ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__r,type,
% 0.20/0.47 gram_L1221482026le_H_r: dtree > n > n ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OS,type,
% 0.20/0.47 gram_L1451583635elle_S: n > ( set @ ( sum_sum @ t @ n ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr,type,
% 0.20/0.47 gram_L1231612515_deftr: n > dtree ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst,type,
% 0.20/0.47 gram_L1004374585hsubst: dtree > dtree > dtree ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c,type,
% 0.20/0.47 gram_L1905609002ubst_c: dtree > dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r,type,
% 0.20/0.47 gram_L1905609017ubst_r: dtree > n ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2,type,
% 0.20/0.47 gram_L805317441_inFr2: ( set @ n ) > dtree > t > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr,type,
% 0.20/0.47 gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Opick,type,
% 0.20/0.47 gram_L315592705e_pick: dtree > n > dtree ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr,type,
% 0.20/0.47 gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OsubtrOf,type,
% 0.20/0.47 gram_L1614515765ubtrOf: dtree > n > dtree ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf,type,
% 0.20/0.47 gram_L864798063lle_wf: dtree > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_If,type,
% 0.20/0.47 if:
% 0.20/0.47 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.20/0.47 top_top:
% 0.20/0.47 !>[A: $tType] : A ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Pure_Otype,type,
% 0.20/0.47 type2:
% 0.20/0.47 !>[A: $tType] : ( itself @ A ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_OCollect,type,
% 0.20/0.47 collect:
% 0.20/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Oimage,type,
% 0.20/0.47 image:
% 0.20/0.47 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Ovimage,type,
% 0.20/0.47 vimage:
% 0.20/0.47 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Sum__Type_OInl,type,
% 0.20/0.47 sum_Inl:
% 0.20/0.47 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Sum__Type_OInr,type,
% 0.20/0.47 sum_Inr:
% 0.20/0.47 !>[B: $tType,A: $tType] : ( B > ( sum_sum @ A @ B ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Sum__Type_Omap__sum,type,
% 0.20/0.47 sum_map_sum:
% 0.20/0.47 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C ) > ( B > D ) > ( sum_sum @ A @ B ) > ( sum_sum @ C @ D ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum,type,
% 0.20/0.47 sum_rec_sum:
% 0.20/0.47 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Sum__Type_Osum_Ocase__sum,type,
% 0.20/0.47 sum_case_sum:
% 0.20/0.47 !>[A: $tType,C: $tType,B: $tType] : ( ( A > C ) > ( B > C ) > ( sum_sum @ A @ B ) > C ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member,type,
% 0.20/0.47 member:
% 0.20/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_a,type,
% 0.20/0.47 a: t ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_n,type,
% 0.20/0.47 n2: n ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_t__tr,type,
% 0.20/0.47 t_tr: sum_sum @ t @ dtree ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_tr0,type,
% 0.20/0.47 tr0: dtree ).
% 0.20/0.47
% 0.20/0.47 %----Relevant facts (256)
% 0.20/0.47 thf(fact_0_n,axiom,
% 0.20/0.47 gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ n2 ).
% 0.20/0.47
% 0.20/0.47 % n
% 0.20/0.47 thf(fact_1_root__H__pick,axiom,
% 0.20/0.47 ! [N: n] :
% 0.20/0.47 ( ( root @ ( gram_L1451583624elle_H @ tr0 @ N ) )
% 0.20/0.47 = ( root @ ( gram_L315592705e_pick @ tr0 @ N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % root_H_pick
% 0.20/0.47 thf(fact_2_t__tr,axiom,
% 0.20/0.47 member @ ( sum_sum @ t @ dtree ) @ t_tr @ ( cont @ ( gram_L315592705e_pick @ tr0 @ n2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % t_tr
% 0.20/0.47 thf(fact_3_root__pick,axiom,
% 0.20/0.47 ! [N: n] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ N )
% 0.20/0.47 => ( ( root @ ( gram_L315592705e_pick @ tr0 @ N ) )
% 0.20/0.47 = N ) ) ).
% 0.20/0.47
% 0.20/0.47 % root_pick
% 0.20/0.47 thf(fact_4_H__r__def,axiom,
% 0.20/0.47 ! [N: n] :
% 0.20/0.47 ( ( gram_L1221482026le_H_r @ tr0 @ N )
% 0.20/0.47 = ( root @ ( gram_L315592705e_pick @ tr0 @ N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % H_r_def
% 0.20/0.47 thf(fact_5_root__H,axiom,
% 0.20/0.47 ! [N: n] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ N )
% 0.20/0.47 => ( ( root @ ( gram_L1451583624elle_H @ tr0 @ N ) )
% 0.20/0.47 = N ) ) ).
% 0.20/0.47
% 0.20/0.47 % root_H
% 0.20/0.47 thf(fact_6_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__H,axiom,
% 0.20/0.47 ! [Tr0: dtree,N: n] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.20/0.47 => ( ( root @ ( gram_L1451583624elle_H @ Tr0 @ N ) )
% 0.20/0.47 = N ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gram_Lang_Mirabelle_ojxrtuoybn.root_H
% 0.20/0.47 thf(fact_7_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__pick,axiom,
% 0.20/0.47 ! [Tr0: dtree,N: n] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.20/0.47 => ( ( root @ ( gram_L315592705e_pick @ Tr0 @ N ) )
% 0.20/0.47 = N ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gram_Lang_Mirabelle_ojxrtuoybn.root_pick
% 0.20/0.47 thf(fact_8_inItr_OBase,axiom,
% 0.20/0.47 ! [Tr: dtree,Ns: set @ n] :
% 0.20/0.47 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.20/0.47 => ( gram_L830233218_inItr @ Ns @ Tr @ ( root @ Tr ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inItr.Base
% 0.20/0.47 thf(fact_9_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__H__pick,axiom,
% 0.20/0.47 ! [Tr0: dtree,N: n] :
% 0.20/0.47 ( ( root @ ( gram_L1451583624elle_H @ Tr0 @ N ) )
% 0.20/0.47 = ( root @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gram_Lang_Mirabelle_ojxrtuoybn.root_H_pick
% 0.20/0.47 thf(fact_10_inItr__root__in,axiom,
% 0.20/0.47 ! [Ns: set @ n,Tr: dtree,N: n] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.20/0.47 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.20/0.47
% 0.20/0.47 % inItr_root_in
% 0.20/0.47 thf(fact_11_wf__pick,axiom,
% 0.20/0.47 ! [N: n] :
% 0.20/0.47 ( ( gram_L864798063lle_wf @ tr0 )
% 0.20/0.47 => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ N )
% 0.20/0.47 => ( gram_L864798063lle_wf @ ( gram_L315592705e_pick @ tr0 @ N ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % wf_pick
% 0.20/0.47 thf(fact_12_pick,axiom,
% 0.20/0.47 ! [N: n] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ N )
% 0.20/0.47 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ tr0 @ N ) @ tr0 )
% 0.20/0.47 & ( ( root @ ( gram_L315592705e_pick @ tr0 @ N ) )
% 0.20/0.47 = N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % pick
% 0.20/0.47 thf(fact_13_comp__id,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F: A > B] :
% 0.20/0.47 ( ( comp @ A @ B @ A @ F @ ( id @ A ) )
% 0.20/0.47 = F ) ).
% 0.20/0.47
% 0.20/0.47 % comp_id
% 0.20/0.47 thf(fact_14_id__comp,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,G: A > B] :
% 0.20/0.47 ( ( comp @ B @ B @ A @ ( id @ B ) @ G )
% 0.20/0.47 = G ) ).
% 0.20/0.47
% 0.20/0.47 % id_comp
% 0.20/0.47 thf(fact_15_fun_Omap__id,axiom,
% 0.20/0.47 ! [A: $tType,D: $tType,T2: D > A] :
% 0.20/0.47 ( ( comp @ A @ A @ D @ ( id @ A ) @ T2 )
% 0.20/0.47 = T2 ) ).
% 0.20/0.47
% 0.20/0.47 % fun.map_id
% 0.20/0.47 thf(fact_16_subtr__H,axiom,
% 0.20/0.47 ! [N: n,Tr1: dtree] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ N )
% 0.20/0.47 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr1 @ ( gram_L1451583624elle_H @ tr0 @ N ) )
% 0.20/0.47 => ? [N1: n] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ N1 )
% 0.20/0.47 & ( Tr1
% 0.20/0.47 = ( gram_L1451583624elle_H @ tr0 @ N1 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr_H
% 0.20/0.47 thf(fact_17_subtr__pick,axiom,
% 0.20/0.47 ! [N: n] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ N )
% 0.20/0.47 => ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ tr0 @ N ) @ tr0 ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr_pick
% 0.20/0.47 thf(fact_18_sum_Oinject_I1_J,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,X1: A,Y1: A] :
% 0.20/0.47 ( ( ( sum_Inl @ A @ B @ X1 )
% 0.20/0.47 = ( sum_Inl @ A @ B @ Y1 ) )
% 0.20/0.47 = ( X1 = Y1 ) ) ).
% 0.20/0.47
% 0.20/0.47 % sum.inject(1)
% 0.20/0.47 thf(fact_19_old_Osum_Oinject_I1_J,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,A2: A,A3: A] :
% 0.20/0.47 ( ( ( sum_Inl @ A @ B @ A2 )
% 0.20/0.47 = ( sum_Inl @ A @ B @ A3 ) )
% 0.20/0.47 = ( A2 = A3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.sum.inject(1)
% 0.20/0.47 thf(fact_20_id__apply,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( id @ A )
% 0.20/0.47 = ( ^ [X: A] : X ) ) ).
% 0.20/0.47
% 0.20/0.47 % id_apply
% 0.20/0.47 thf(fact_21_comp__apply,axiom,
% 0.20/0.47 ! [C: $tType,A: $tType,B: $tType] :
% 0.20/0.47 ( ( comp @ B @ A @ C )
% 0.20/0.47 = ( ^ [F2: B > A,G2: C > B,X: C] : ( F2 @ ( G2 @ X ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % comp_apply
% 0.20/0.47 thf(fact_22_UNIV__I,axiom,
% 0.20/0.47 ! [A: $tType,X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_I
% 0.20/0.47 thf(fact_23_wf__subtr,axiom,
% 0.20/0.47 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 0.20/0.47 ( ( gram_L864798063lle_wf @ Tr1 )
% 0.20/0.47 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.20/0.47 => ( gram_L864798063lle_wf @ Tr ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % wf_subtr
% 0.20/0.47 thf(fact_24_subtr__trans,axiom,
% 0.20/0.47 ! [Ns: set @ n,Tr1: dtree,Tr2: dtree,Tr3: dtree] :
% 0.20/0.47 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr2 )
% 0.20/0.47 => ( ( gram_L716654942_subtr @ Ns @ Tr2 @ Tr3 )
% 0.20/0.47 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr_trans
% 0.20/0.47 thf(fact_25_subtr__rootR__in,axiom,
% 0.20/0.47 ! [Ns: set @ n,Tr1: dtree,Tr2: dtree] :
% 0.20/0.47 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr2 )
% 0.20/0.47 => ( member @ n @ ( root @ Tr2 ) @ Ns ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr_rootR_in
% 0.20/0.47 thf(fact_26_subtr__rootL__in,axiom,
% 0.20/0.47 ! [Ns: set @ n,Tr1: dtree,Tr2: dtree] :
% 0.20/0.47 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr2 )
% 0.20/0.47 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr_rootL_in
% 0.20/0.47 thf(fact_27_subtr_ORefl,axiom,
% 0.20/0.47 ! [Tr: dtree,Ns: set @ n] :
% 0.20/0.47 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.20/0.47 => ( gram_L716654942_subtr @ Ns @ Tr @ Tr ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr.Refl
% 0.20/0.47 thf(fact_28_subtr__inItr,axiom,
% 0.20/0.47 ! [Ns: set @ n,Tr: dtree,N: n,Tr1: dtree] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.20/0.47 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.20/0.47 => ( gram_L830233218_inItr @ Ns @ Tr1 @ N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr_inItr
% 0.20/0.47 thf(fact_29_inItr__subtr,axiom,
% 0.20/0.47 ! [Ns: set @ n,Tr: dtree,N: n] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.20/0.47 => ? [Tr4: dtree] :
% 0.20/0.47 ( ( gram_L716654942_subtr @ Ns @ Tr4 @ Tr )
% 0.20/0.47 & ( ( root @ Tr4 )
% 0.20/0.47 = N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inItr_subtr
% 0.20/0.47 thf(fact_30_UNIV__witness,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_witness
% 0.20/0.47 thf(fact_31_UNIV__eq__I,axiom,
% 0.20/0.47 ! [A: $tType,A4: set @ A] :
% 0.20/0.47 ( ! [X3: A] : ( member @ A @ X3 @ A4 )
% 0.20/0.47 => ( ( top_top @ ( set @ A ) )
% 0.20/0.47 = A4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % UNIV_eq_I
% 0.20/0.47 thf(fact_32_fun_Omap__comp,axiom,
% 0.20/0.47 ! [B: $tType,C: $tType,A: $tType,D: $tType,G: B > C,F: A > B,V: D > A] :
% 0.20/0.47 ( ( comp @ B @ C @ D @ G @ ( comp @ A @ B @ D @ F @ V ) )
% 0.20/0.47 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G @ F ) @ V ) ) ).
% 0.20/0.47
% 0.20/0.47 % fun.map_comp
% 0.20/0.47 thf(fact_33_comp__eq__dest__lhs,axiom,
% 0.20/0.47 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B2: A > C,C2: A > B,V: A] :
% 0.20/0.47 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.20/0.47 = C2 )
% 0.20/0.47 => ( ( A2 @ ( B2 @ V ) )
% 0.20/0.47 = ( C2 @ V ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % comp_eq_dest_lhs
% 0.20/0.47 thf(fact_34_comp__eq__elim,axiom,
% 0.20/0.47 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C2: D > B,D2: A > D] :
% 0.20/0.47 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.20/0.47 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 0.20/0.47 => ! [V2: A] :
% 0.20/0.47 ( ( A2 @ ( B2 @ V2 ) )
% 0.20/0.47 = ( C2 @ ( D2 @ V2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % comp_eq_elim
% 0.20/0.47 thf(fact_35_comp__eq__dest,axiom,
% 0.20/0.47 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C2: D > B,D2: A > D,V: A] :
% 0.20/0.47 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.20/0.47 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 0.20/0.47 => ( ( A2 @ ( B2 @ V ) )
% 0.20/0.47 = ( C2 @ ( D2 @ V ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % comp_eq_dest
% 0.20/0.47 thf(fact_36_comp__assoc,axiom,
% 0.20/0.47 ! [B: $tType,D: $tType,C: $tType,A: $tType,F: D > B,G: C > D,H: A > C] :
% 0.20/0.47 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F @ G ) @ H )
% 0.20/0.47 = ( comp @ D @ B @ A @ F @ ( comp @ C @ D @ A @ G @ H ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % comp_assoc
% 0.20/0.47 thf(fact_37_comp__def,axiom,
% 0.20/0.47 ! [A: $tType,C: $tType,B: $tType] :
% 0.20/0.47 ( ( comp @ B @ C @ A )
% 0.20/0.47 = ( ^ [F2: B > C,G2: A > B,X: A] : ( F2 @ ( G2 @ X ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % comp_def
% 0.20/0.47 thf(fact_38_eq__id__iff,axiom,
% 0.20/0.47 ! [A: $tType,F: A > A] :
% 0.20/0.47 ( ( ! [X: A] :
% 0.20/0.47 ( ( F @ X )
% 0.20/0.47 = X ) )
% 0.20/0.47 = ( F
% 0.20/0.47 = ( id @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % eq_id_iff
% 0.20/0.47 thf(fact_39_id__def,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( id @ A )
% 0.20/0.47 = ( ^ [X: A] : X ) ) ).
% 0.20/0.47
% 0.20/0.47 % id_def
% 0.20/0.47 thf(fact_40_Inl__inject,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,X2: A,Y: A] :
% 0.20/0.47 ( ( ( sum_Inl @ A @ B @ X2 )
% 0.20/0.47 = ( sum_Inl @ A @ B @ Y ) )
% 0.20/0.47 => ( X2 = Y ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inl_inject
% 0.20/0.47 thf(fact_41_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr__pick,axiom,
% 0.20/0.47 ! [Tr0: dtree,N: n] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.20/0.47 => ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ Tr0 @ N ) @ Tr0 ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gram_Lang_Mirabelle_ojxrtuoybn.subtr_pick
% 0.20/0.47 thf(fact_42_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr__H,axiom,
% 0.20/0.47 ! [Tr0: dtree,N: n,Tr1: dtree] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.20/0.47 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr1 @ ( gram_L1451583624elle_H @ Tr0 @ N ) )
% 0.20/0.47 => ? [N1: n] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N1 )
% 0.20/0.47 & ( Tr1
% 0.20/0.47 = ( gram_L1451583624elle_H @ Tr0 @ N1 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gram_Lang_Mirabelle_ojxrtuoybn.subtr_H
% 0.20/0.47 thf(fact_43_Gram__Lang__Mirabelle__ojxrtuoybn_Owf__pick,axiom,
% 0.20/0.47 ! [Tr0: dtree,N: n] :
% 0.20/0.47 ( ( gram_L864798063lle_wf @ Tr0 )
% 0.20/0.47 => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.20/0.47 => ( gram_L864798063lle_wf @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gram_Lang_Mirabelle_ojxrtuoybn.wf_pick
% 0.20/0.47 thf(fact_44_Gram__Lang__Mirabelle__ojxrtuoybn_Opick,axiom,
% 0.20/0.47 ! [Tr0: dtree,N: n] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.20/0.47 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ Tr0 @ N ) @ Tr0 )
% 0.20/0.47 & ( ( root @ ( gram_L315592705e_pick @ Tr0 @ N ) )
% 0.20/0.47 = N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gram_Lang_Mirabelle_ojxrtuoybn.pick
% 0.20/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A: $tType,A2: A,P: A > $o] :
% 0.20/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.20/0.47 = ( P @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_46_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A: $tType,A4: set @ A] :
% 0.20/0.47 ( ( collect @ A
% 0.20/0.47 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 0.20/0.47 = A4 ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_47_Collect__cong,axiom,
% 0.20/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.20/0.47 ( ! [X3: A] :
% 0.20/0.47 ( ( P @ X3 )
% 0.20/0.47 = ( Q @ X3 ) )
% 0.20/0.47 => ( ( collect @ A @ P )
% 0.20/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_cong
% 0.20/0.47 thf(fact_48_ext,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.20/0.47 ( ! [X3: A] :
% 0.20/0.47 ( ( F @ X3 )
% 0.20/0.47 = ( G @ X3 ) )
% 0.20/0.47 => ( F = G ) ) ).
% 0.20/0.47
% 0.20/0.47 % ext
% 0.20/0.47 thf(fact_49_Gram__Lang__Mirabelle__ojxrtuoybn_OH__r__def,axiom,
% 0.20/0.47 ( gram_L1221482026le_H_r
% 0.20/0.47 = ( ^ [Tr02: dtree,N2: n] : ( root @ ( gram_L315592705e_pick @ Tr02 @ N2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gram_Lang_Mirabelle_ojxrtuoybn.H_r_def
% 0.20/0.47 thf(fact_50_fun_Omap__id0,axiom,
% 0.20/0.47 ! [A: $tType,D: $tType] :
% 0.20/0.47 ( ( comp @ A @ A @ D @ ( id @ A ) )
% 0.20/0.47 = ( id @ ( D > A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % fun.map_id0
% 0.20/0.47 thf(fact_51_comp__eq__id__dest,axiom,
% 0.20/0.47 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B2: A > C,C2: A > B,V: A] :
% 0.20/0.47 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.20/0.47 = ( comp @ B @ B @ A @ ( id @ B ) @ C2 ) )
% 0.20/0.47 => ( ( A2 @ ( B2 @ V ) )
% 0.20/0.47 = ( C2 @ V ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % comp_eq_id_dest
% 0.20/0.47 thf(fact_52_map__sum_Ocompositionality,axiom,
% 0.20/0.47 ! [D: $tType,F3: $tType,E: $tType,C: $tType,B: $tType,A: $tType,F: C > E,G: D > F3,H: A > C,I: B > D,Sum: sum_sum @ A @ B] :
% 0.20/0.47 ( ( sum_map_sum @ C @ E @ D @ F3 @ F @ G @ ( sum_map_sum @ A @ C @ B @ D @ H @ I @ Sum ) )
% 0.20/0.47 = ( sum_map_sum @ A @ E @ B @ F3 @ ( comp @ C @ E @ A @ F @ H ) @ ( comp @ D @ F3 @ B @ G @ I ) @ Sum ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_sum.compositionality
% 0.20/0.47 thf(fact_53_sum_Omap__comp,axiom,
% 0.20/0.47 ! [D: $tType,F3: $tType,E: $tType,C: $tType,B: $tType,A: $tType,G1: C > E,G22: D > F3,F1: A > C,F22: B > D,V: sum_sum @ A @ B] :
% 0.20/0.47 ( ( sum_map_sum @ C @ E @ D @ F3 @ G1 @ G22 @ ( sum_map_sum @ A @ C @ B @ D @ F1 @ F22 @ V ) )
% 0.20/0.47 = ( sum_map_sum @ A @ E @ B @ F3 @ ( comp @ C @ E @ A @ G1 @ F1 ) @ ( comp @ D @ F3 @ B @ G22 @ F22 ) @ V ) ) ).
% 0.20/0.47
% 0.20/0.47 % sum.map_comp
% 0.20/0.47 thf(fact_54_map__sum_Ocomp,axiom,
% 0.20/0.47 ! [A: $tType,C: $tType,E: $tType,F3: $tType,D: $tType,B: $tType,F: C > E,G: D > F3,H: A > C,I: B > D] :
% 0.20/0.47 ( ( comp @ ( sum_sum @ C @ D ) @ ( sum_sum @ E @ F3 ) @ ( sum_sum @ A @ B ) @ ( sum_map_sum @ C @ E @ D @ F3 @ F @ G ) @ ( sum_map_sum @ A @ C @ B @ D @ H @ I ) )
% 0.20/0.47 = ( sum_map_sum @ A @ E @ B @ F3 @ ( comp @ C @ E @ A @ F @ H ) @ ( comp @ D @ F3 @ B @ G @ I ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_sum.comp
% 0.20/0.47 thf(fact_55_sum_Omap__id0,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( sum_map_sum @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) )
% 0.20/0.47 = ( id @ ( sum_sum @ A @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % sum.map_id0
% 0.20/0.47 thf(fact_56_sum_Omap__id,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,T2: sum_sum @ A @ B] :
% 0.20/0.47 ( ( sum_map_sum @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) @ T2 )
% 0.20/0.47 = T2 ) ).
% 0.20/0.47
% 0.20/0.47 % sum.map_id
% 0.20/0.47 thf(fact_57_map__sum_Osimps_I1_J,axiom,
% 0.20/0.47 ! [B: $tType,D: $tType,C: $tType,A: $tType,F1: A > C,F22: B > D,A2: A] :
% 0.20/0.47 ( ( sum_map_sum @ A @ C @ B @ D @ F1 @ F22 @ ( sum_Inl @ A @ B @ A2 ) )
% 0.20/0.47 = ( sum_Inl @ C @ D @ ( F1 @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_sum.simps(1)
% 0.20/0.47 thf(fact_58_H__def,axiom,
% 0.20/0.47 ( ( gram_L1451583624elle_H @ tr0 )
% 0.20/0.47 = ( unfold @ n @ ( gram_L1221482026le_H_r @ tr0 ) @ ( gram_L1221482011le_H_c @ tr0 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % H_def
% 0.20/0.47 thf(fact_59_root__o__deftr,axiom,
% 0.20/0.47 ( ( comp @ dtree @ n @ n @ root @ gram_L1231612515_deftr )
% 0.20/0.47 = ( id @ n ) ) ).
% 0.20/0.47
% 0.20/0.47 % root_o_deftr
% 0.20/0.47 thf(fact_60_iso__tuple__UNIV__I,axiom,
% 0.20/0.47 ! [A: $tType,X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % iso_tuple_UNIV_I
% 0.20/0.47 thf(fact_61_top__apply,axiom,
% 0.20/0.47 ! [C: $tType,D: $tType] :
% 0.20/0.47 ( ( top @ C @ ( type2 @ C ) )
% 0.20/0.47 => ( ( top_top @ ( D > C ) )
% 0.20/0.47 = ( ^ [X: D] : ( top_top @ C ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_apply
% 0.20/0.47 thf(fact_62_H__c__def,axiom,
% 0.20/0.47 ! [N: n] :
% 0.20/0.47 ( ( gram_L1221482011le_H_c @ tr0 @ N )
% 0.20/0.47 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ N ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % H_c_def
% 0.20/0.47 thf(fact_63_old_Osum_Osimps_I7_J,axiom,
% 0.20/0.47 ! [B: $tType,T: $tType,A: $tType,F1: A > T,F22: B > T,A2: A] :
% 0.20/0.47 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inl @ A @ B @ A2 ) )
% 0.20/0.47 = ( F1 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.sum.simps(7)
% 0.20/0.47 thf(fact_64_map__sum__o__inj_I1_J,axiom,
% 0.20/0.47 ! [D: $tType,C: $tType,B: $tType,A: $tType,F: A > B,G: D > C] :
% 0.20/0.47 ( ( comp @ ( sum_sum @ A @ D ) @ ( sum_sum @ B @ C ) @ A @ ( sum_map_sum @ A @ B @ D @ C @ F @ G ) @ ( sum_Inl @ A @ D ) )
% 0.20/0.47 = ( comp @ B @ ( sum_sum @ B @ C ) @ A @ ( sum_Inl @ B @ C ) @ F ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_sum_o_inj(1)
% 0.20/0.47 thf(fact_65_map__sum__InlD,axiom,
% 0.20/0.47 ! [D: $tType,B: $tType,C: $tType,A: $tType,F: C > A,G: D > B,Z: sum_sum @ C @ D,X2: A] :
% 0.20/0.47 ( ( ( sum_map_sum @ C @ A @ D @ B @ F @ G @ Z )
% 0.20/0.47 = ( sum_Inl @ A @ B @ X2 ) )
% 0.20/0.47 => ? [Y2: C] :
% 0.20/0.47 ( ( Z
% 0.20/0.47 = ( sum_Inl @ C @ D @ Y2 ) )
% 0.20/0.47 & ( ( F @ Y2 )
% 0.20/0.47 = X2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_sum_InlD
% 0.20/0.47 thf(fact_66_map__sum__if__distrib__then_I1_J,axiom,
% 0.20/0.47 ! [D: $tType,B: $tType,C: $tType,A: $tType,E2: $o,F: A > B,G: C > D,X2: A,Y: sum_sum @ A @ C] :
% 0.20/0.47 ( ( E2
% 0.20/0.47 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E2 @ ( sum_Inl @ A @ C @ X2 ) @ Y ) )
% 0.20/0.47 = ( sum_Inl @ B @ D @ ( F @ X2 ) ) ) )
% 0.20/0.47 & ( ~ E2
% 0.20/0.47 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E2 @ ( sum_Inl @ A @ C @ X2 ) @ Y ) )
% 0.20/0.47 = ( sum_map_sum @ A @ B @ C @ D @ F @ G @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_sum_if_distrib_then(1)
% 0.20/0.47 thf(fact_67_map__sum__if__distrib__else_I1_J,axiom,
% 0.20/0.47 ! [C: $tType,D: $tType,B: $tType,A: $tType,E2: $o,F: A > B,G: C > D,X2: sum_sum @ A @ C,Y: A] :
% 0.20/0.47 ( ( E2
% 0.20/0.47 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E2 @ X2 @ ( sum_Inl @ A @ C @ Y ) ) )
% 0.20/0.47 = ( sum_map_sum @ A @ B @ C @ D @ F @ G @ X2 ) ) )
% 0.20/0.47 & ( ~ E2
% 0.20/0.47 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E2 @ X2 @ ( sum_Inl @ A @ C @ Y ) ) )
% 0.20/0.47 = ( sum_Inl @ B @ D @ ( F @ Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_sum_if_distrib_else(1)
% 0.20/0.47 thf(fact_68_image__eqI,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,B2: A,F: B > A,X2: B,A4: set @ B] :
% 0.20/0.47 ( ( B2
% 0.20/0.47 = ( F @ X2 ) )
% 0.20/0.47 => ( ( member @ B @ X2 @ A4 )
% 0.20/0.47 => ( member @ A @ B2 @ ( image @ B @ A @ F @ A4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % image_eqI
% 0.20/0.47 thf(fact_69_image__id,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( image @ A @ A @ ( id @ A ) )
% 0.20/0.47 = ( id @ ( set @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % image_id
% 0.20/0.47 thf(fact_70_root__deftr,axiom,
% 0.20/0.47 ! [N: n] :
% 0.20/0.47 ( ( root @ ( gram_L1231612515_deftr @ N ) )
% 0.20/0.47 = N ) ).
% 0.20/0.47
% 0.20/0.47 % root_deftr
% 0.20/0.47 thf(fact_71_Inl__oplus__iff,axiom,
% 0.20/0.47 ! [B: $tType,C: $tType,A: $tType,Tr: A,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.20/0.47 ( ( 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 ) )
% 0.20/0.47 = ( member @ ( sum_sum @ A @ C ) @ ( sum_Inl @ A @ C @ Tr ) @ Tns ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inl_oplus_iff
% 0.20/0.47 thf(fact_72_imageI,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,X2: A,A4: set @ A,F: A > B] :
% 0.20/0.47 ( ( member @ A @ X2 @ A4 )
% 0.20/0.47 => ( member @ B @ ( F @ X2 ) @ ( image @ A @ B @ F @ A4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % imageI
% 0.20/0.47 thf(fact_73_image__iff,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,Z: A,F: B > A,A4: set @ B] :
% 0.20/0.47 ( ( member @ A @ Z @ ( image @ B @ A @ F @ A4 ) )
% 0.20/0.47 = ( ? [X: B] :
% 0.20/0.47 ( ( member @ B @ X @ A4 )
% 0.20/0.47 & ( Z
% 0.20/0.47 = ( F @ X ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % image_iff
% 0.20/0.47 thf(fact_74_bex__imageD,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,F: B > A,A4: set @ B,P: A > $o] :
% 0.20/0.47 ( ? [X4: A] :
% 0.20/0.47 ( ( member @ A @ X4 @ ( image @ B @ A @ F @ A4 ) )
% 0.20/0.47 & ( P @ X4 ) )
% 0.20/0.47 => ? [X3: B] :
% 0.20/0.47 ( ( member @ B @ X3 @ A4 )
% 0.20/0.47 & ( P @ ( F @ X3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % bex_imageD
% 0.20/0.47 thf(fact_75_image__cong,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,M: set @ A,N3: set @ A,F: A > B,G: A > B] :
% 0.20/0.47 ( ( M = N3 )
% 0.20/0.47 => ( ! [X3: A] :
% 0.20/0.47 ( ( member @ A @ X3 @ N3 )
% 0.20/0.47 => ( ( F @ X3 )
% 0.20/0.47 = ( G @ X3 ) ) )
% 0.20/0.47 => ( ( image @ A @ B @ F @ M )
% 0.20/0.47 = ( image @ A @ B @ G @ N3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % image_cong
% 0.20/0.47 thf(fact_76_ball__imageD,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,F: B > A,A4: set @ B,P: A > $o] :
% 0.20/0.47 ( ! [X3: A] :
% 0.20/0.47 ( ( member @ A @ X3 @ ( image @ B @ A @ F @ A4 ) )
% 0.20/0.47 => ( P @ X3 ) )
% 0.20/0.47 => ! [X4: B] :
% 0.20/0.47 ( ( member @ B @ X4 @ A4 )
% 0.20/0.47 => ( P @ ( F @ X4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ball_imageD
% 0.20/0.47 thf(fact_77_rev__image__eqI,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,X2: A,A4: set @ A,B2: B,F: A > B] :
% 0.20/0.47 ( ( member @ A @ X2 @ A4 )
% 0.20/0.47 => ( ( B2
% 0.20/0.47 = ( F @ X2 ) )
% 0.20/0.47 => ( member @ B @ B2 @ ( image @ A @ B @ F @ A4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % rev_image_eqI
% 0.20/0.47 thf(fact_78_surjD,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,F: B > A,Y: A] :
% 0.20/0.47 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.20/0.47 = ( top_top @ ( set @ A ) ) )
% 0.20/0.47 => ? [X3: B] :
% 0.20/0.47 ( Y
% 0.20/0.47 = ( F @ X3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjD
% 0.20/0.47 thf(fact_79_surjE,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,F: B > A,Y: A] :
% 0.20/0.47 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.20/0.47 = ( top_top @ ( set @ A ) ) )
% 0.20/0.47 => ~ ! [X3: B] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( F @ X3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjE
% 0.20/0.47 thf(fact_80_surjI,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,G: B > A,F: A > B] :
% 0.20/0.47 ( ! [X3: A] :
% 0.20/0.47 ( ( G @ ( F @ X3 ) )
% 0.20/0.47 = X3 )
% 0.20/0.47 => ( ( image @ B @ A @ G @ ( top_top @ ( set @ B ) ) )
% 0.20/0.47 = ( top_top @ ( set @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surjI
% 0.20/0.47 thf(fact_81_rangeI,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,F: B > A,X2: B] : ( member @ A @ ( F @ X2 ) @ ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % rangeI
% 0.20/0.47 thf(fact_82_surj__def,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F: B > A] :
% 0.20/0.47 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.20/0.47 = ( top_top @ ( set @ A ) ) )
% 0.20/0.47 = ( ! [Y3: A] :
% 0.20/0.47 ? [X: B] :
% 0.20/0.47 ( Y3
% 0.20/0.47 = ( F @ X ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_def
% 0.20/0.47 thf(fact_83_range__eqI,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,B2: A,F: B > A,X2: B] :
% 0.20/0.47 ( ( B2
% 0.20/0.47 = ( F @ X2 ) )
% 0.20/0.47 => ( member @ A @ B2 @ ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % range_eqI
% 0.20/0.47 thf(fact_84_image__comp,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,C: $tType,F: B > A,G: C > B,R: set @ C] :
% 0.20/0.47 ( ( image @ B @ A @ F @ ( image @ C @ B @ G @ R ) )
% 0.20/0.47 = ( image @ C @ A @ ( comp @ B @ A @ C @ F @ G ) @ R ) ) ).
% 0.20/0.47
% 0.20/0.47 % image_comp
% 0.20/0.47 thf(fact_85_image__eq__imp__comp,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,D: $tType,C: $tType,F: B > A,A4: set @ B,G: C > A,B3: set @ C,H: A > D] :
% 0.20/0.47 ( ( ( image @ B @ A @ F @ A4 )
% 0.20/0.47 = ( image @ C @ A @ G @ B3 ) )
% 0.20/0.47 => ( ( image @ B @ D @ ( comp @ A @ D @ B @ H @ F ) @ A4 )
% 0.20/0.47 = ( image @ C @ D @ ( comp @ A @ D @ C @ H @ G ) @ B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % image_eq_imp_comp
% 0.20/0.47 thf(fact_86_top__set__def,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( top_top @ ( set @ A ) )
% 0.20/0.47 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_set_def
% 0.20/0.47 thf(fact_87_comp__surj,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,C: $tType,F: B > A,G: A > C] :
% 0.20/0.47 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.20/0.47 = ( top_top @ ( set @ A ) ) )
% 0.20/0.47 => ( ( ( image @ A @ C @ G @ ( top_top @ ( set @ A ) ) )
% 0.20/0.47 = ( top_top @ ( set @ C ) ) )
% 0.20/0.47 => ( ( image @ B @ C @ ( comp @ A @ C @ B @ G @ F ) @ ( top_top @ ( set @ B ) ) )
% 0.20/0.47 = ( top_top @ ( set @ C ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % comp_surj
% 0.20/0.47 thf(fact_88_fun_Oset__map,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,D: $tType,F: A > B,V: D > A] :
% 0.20/0.47 ( ( image @ D @ B @ ( comp @ A @ B @ D @ F @ V ) @ ( top_top @ ( set @ D ) ) )
% 0.20/0.47 = ( image @ A @ B @ F @ ( image @ D @ A @ V @ ( top_top @ ( set @ D ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % fun.set_map
% 0.20/0.47 thf(fact_89_fun_Omap__cong,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,D: $tType,X2: D > A,Ya: D > A,F: A > B,G: A > B] :
% 0.20/0.47 ( ( X2 = Ya )
% 0.20/0.47 => ( ! [Z2: A] :
% 0.20/0.47 ( ( member @ A @ Z2 @ ( image @ D @ A @ Ya @ ( top_top @ ( set @ D ) ) ) )
% 0.20/0.47 => ( ( F @ Z2 )
% 0.20/0.47 = ( G @ Z2 ) ) )
% 0.20/0.47 => ( ( comp @ A @ B @ D @ F @ X2 )
% 0.20/0.47 = ( comp @ A @ B @ D @ G @ Ya ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % fun.map_cong
% 0.20/0.47 thf(fact_90_fun_Omap__cong0,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,D: $tType,X2: D > A,F: A > B,G: A > B] :
% 0.20/0.47 ( ! [Z2: A] :
% 0.20/0.47 ( ( member @ A @ Z2 @ ( image @ D @ A @ X2 @ ( top_top @ ( set @ D ) ) ) )
% 0.20/0.47 => ( ( F @ Z2 )
% 0.20/0.47 = ( G @ Z2 ) ) )
% 0.20/0.47 => ( ( comp @ A @ B @ D @ F @ X2 )
% 0.20/0.47 = ( comp @ A @ B @ D @ G @ X2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % fun.map_cong0
% 0.20/0.47 thf(fact_91_fun_Oinj__map__strong,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,D: $tType,X2: D > A,Xa: D > A,F: A > B,Fa: A > B] :
% 0.20/0.47 ( ! [Z2: A,Za: A] :
% 0.20/0.47 ( ( member @ A @ Z2 @ ( image @ D @ A @ X2 @ ( top_top @ ( set @ D ) ) ) )
% 0.20/0.47 => ( ( member @ A @ Za @ ( image @ D @ A @ Xa @ ( top_top @ ( set @ D ) ) ) )
% 0.20/0.47 => ( ( ( F @ Z2 )
% 0.20/0.47 = ( Fa @ Za ) )
% 0.20/0.47 => ( Z2 = Za ) ) ) )
% 0.20/0.47 => ( ( ( comp @ A @ B @ D @ F @ X2 )
% 0.20/0.47 = ( comp @ A @ B @ D @ Fa @ Xa ) )
% 0.20/0.47 => ( X2 = Xa ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % fun.inj_map_strong
% 0.20/0.47 thf(fact_92_surj__id,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( image @ A @ A @ ( id @ A ) @ ( top_top @ ( set @ A ) ) )
% 0.20/0.47 = ( top_top @ ( set @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_id
% 0.20/0.47 thf(fact_93_Inl__oplus__elim,axiom,
% 0.20/0.47 ! [B: $tType,C: $tType,A: $tType,Tr: A,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.20/0.47 ( ( 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 ) )
% 0.20/0.47 => ( member @ ( sum_sum @ A @ C ) @ ( sum_Inl @ A @ C @ Tr ) @ Tns ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inl_oplus_elim
% 0.20/0.47 thf(fact_94_wf__deftr,axiom,
% 0.20/0.47 ! [N: n] : ( gram_L864798063lle_wf @ ( gram_L1231612515_deftr @ N ) ) ).
% 0.20/0.47
% 0.20/0.47 % wf_deftr
% 0.20/0.47 thf(fact_95_Gram__Lang__Mirabelle__ojxrtuoybn_OH__def,axiom,
% 0.20/0.47 ( gram_L1451583624elle_H
% 0.20/0.47 = ( ^ [Tr02: dtree] : ( unfold @ n @ ( gram_L1221482026le_H_r @ Tr02 ) @ ( gram_L1221482011le_H_c @ Tr02 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gram_Lang_Mirabelle_ojxrtuoybn.H_def
% 0.20/0.47 thf(fact_96_comp__apply__eq,axiom,
% 0.20/0.47 ! [B: $tType,D: $tType,A: $tType,C: $tType,F: B > A,G: C > B,X2: C,H: D > A,K: C > D] :
% 0.20/0.47 ( ( ( F @ ( G @ X2 ) )
% 0.20/0.47 = ( H @ ( K @ X2 ) ) )
% 0.20/0.47 => ( ( comp @ B @ A @ C @ F @ G @ X2 )
% 0.20/0.47 = ( comp @ D @ A @ C @ H @ K @ X2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % comp_apply_eq
% 0.20/0.47 thf(fact_97_rewriteL__comp__comp,axiom,
% 0.20/0.47 ! [C: $tType,B: $tType,A: $tType,D: $tType,F: C > B,G: A > C,L: A > B,H: D > A] :
% 0.20/0.47 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.20/0.47 = L )
% 0.20/0.47 => ( ( comp @ C @ B @ D @ F @ ( comp @ A @ C @ D @ G @ H ) )
% 0.20/0.47 = ( comp @ A @ B @ D @ L @ H ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % rewriteL_comp_comp
% 0.20/0.47 thf(fact_98_rewriteR__comp__comp,axiom,
% 0.20/0.47 ! [C: $tType,D: $tType,B: $tType,A: $tType,G: C > B,H: A > C,R: A > B,F: B > D] :
% 0.20/0.47 ( ( ( comp @ C @ B @ A @ G @ H )
% 0.20/0.47 = R )
% 0.20/0.47 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F @ G ) @ H )
% 0.20/0.47 = ( comp @ B @ D @ A @ F @ R ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % rewriteR_comp_comp
% 0.20/0.47 thf(fact_99_rewriteL__comp__comp2,axiom,
% 0.20/0.47 ! [A: $tType,C: $tType,B: $tType,D: $tType,E: $tType,F: C > B,G: A > C,L1: D > B,L2: A > D,H: E > A,R: E > D] :
% 0.20/0.47 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.20/0.47 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 0.20/0.47 => ( ( ( comp @ A @ D @ E @ L2 @ H )
% 0.20/0.47 = R )
% 0.20/0.47 => ( ( comp @ C @ B @ E @ F @ ( comp @ A @ C @ E @ G @ H ) )
% 0.20/0.47 = ( comp @ D @ B @ E @ L1 @ R ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % rewriteL_comp_comp2
% 0.20/0.47 thf(fact_100_rewriteR__comp__comp2,axiom,
% 0.20/0.47 ! [C: $tType,B: $tType,E: $tType,D: $tType,A: $tType,G: C > B,H: A > C,R1: D > B,R2: A > D,F: B > E,L: D > E] :
% 0.20/0.47 ( ( ( comp @ C @ B @ A @ G @ H )
% 0.20/0.47 = ( comp @ D @ B @ A @ R1 @ R2 ) )
% 0.20/0.47 => ( ( ( comp @ B @ E @ D @ F @ R1 )
% 0.20/0.47 = L )
% 0.20/0.47 => ( ( comp @ C @ E @ A @ ( comp @ B @ E @ C @ F @ G ) @ H )
% 0.20/0.47 = ( comp @ D @ E @ A @ L @ R2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % rewriteR_comp_comp2
% 0.20/0.47 thf(fact_101_Gram__Lang__Mirabelle__ojxrtuoybn_OH__c__def,axiom,
% 0.20/0.47 ( gram_L1221482011le_H_c
% 0.20/0.47 = ( ^ [Tr02: dtree,N2: n] : ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ ( gram_L315592705e_pick @ Tr02 @ N2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gram_Lang_Mirabelle_ojxrtuoybn.H_c_def
% 0.20/0.47 thf(fact_102_subtr__deftr,axiom,
% 0.20/0.47 ! [Ns: set @ n,Tr5: dtree,N: n] :
% 0.20/0.47 ( ( gram_L716654942_subtr @ Ns @ Tr5 @ ( gram_L1231612515_deftr @ N ) )
% 0.20/0.47 => ( Tr5
% 0.20/0.47 = ( gram_L1231612515_deftr @ ( root @ Tr5 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr_deftr
% 0.20/0.47 thf(fact_103_pointfree__idE,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F: B > A,G: A > B,X2: A] :
% 0.20/0.47 ( ( ( comp @ B @ A @ A @ F @ G )
% 0.20/0.47 = ( id @ A ) )
% 0.20/0.47 => ( ( F @ ( G @ X2 ) )
% 0.20/0.47 = X2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % pointfree_idE
% 0.20/0.47 thf(fact_104_deftr__def,axiom,
% 0.20/0.47 ( gram_L1231612515_deftr
% 0.20/0.47 = ( unfold @ n @ ( id @ n ) @ gram_L1451583635elle_S ) ) ).
% 0.20/0.47
% 0.20/0.47 % deftr_def
% 0.20/0.47 thf(fact_105_surj__fun__eq,axiom,
% 0.20/0.47 ! [B: $tType,C: $tType,A: $tType,F: B > A,X5: set @ B,G1: A > C,G22: A > C] :
% 0.20/0.47 ( ( ( image @ B @ A @ F @ X5 )
% 0.20/0.47 = ( top_top @ ( set @ A ) ) )
% 0.20/0.47 => ( ! [X3: B] :
% 0.20/0.47 ( ( member @ B @ X3 @ X5 )
% 0.20/0.47 => ( ( comp @ A @ C @ B @ G1 @ F @ X3 )
% 0.20/0.47 = ( comp @ A @ C @ B @ G22 @ F @ X3 ) ) )
% 0.20/0.47 => ( G1 = G22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_fun_eq
% 0.20/0.47 thf(fact_106_finite__H__c,axiom,
% 0.20/0.47 ! [N: n] : ( finite_finite2 @ ( sum_sum @ t @ n ) @ ( gram_L1221482011le_H_c @ tr0 @ N ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_H_c
% 0.20/0.47 thf(fact_107_unfold_I1_J,axiom,
% 0.20/0.47 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ A ) ),B2: A] :
% 0.20/0.47 ( ( root @ ( unfold @ A @ Rt @ Ct @ B2 ) )
% 0.20/0.47 = ( Rt @ B2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % unfold(1)
% 0.20/0.47 thf(fact_108_cont__H,axiom,
% 0.20/0.47 ! [N: n] :
% 0.20/0.47 ( ( cont @ ( gram_L1451583624elle_H @ tr0 @ N ) )
% 0.20/0.47 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ tr0 ) @ root ) ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ N ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % cont_H
% 0.20/0.47 thf(fact_109_dtree__cong,axiom,
% 0.20/0.47 ! [Tr: dtree,Tr5: dtree] :
% 0.20/0.47 ( ( ( root @ Tr )
% 0.20/0.47 = ( root @ Tr5 ) )
% 0.20/0.47 => ( ( ( cont @ Tr )
% 0.20/0.47 = ( cont @ Tr5 ) )
% 0.20/0.47 => ( Tr = Tr5 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dtree_cong
% 0.20/0.47 thf(fact_110_hsubst__c__def,axiom,
% 0.20/0.47 ( gram_L1905609002ubst_c
% 0.20/0.47 = ( ^ [Tr02: dtree,Tr6: dtree] :
% 0.20/0.47 ( if @ ( set @ ( sum_sum @ t @ dtree ) )
% 0.20/0.47 @ ( ( root @ Tr6 )
% 0.20/0.47 = ( root @ Tr02 ) )
% 0.20/0.47 @ ( cont @ Tr02 )
% 0.20/0.47 @ ( cont @ Tr6 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % hsubst_c_def
% 0.20/0.47 thf(fact_111_top1I,axiom,
% 0.20/0.47 ! [A: $tType,X2: A] : ( top_top @ ( A > $o ) @ X2 ) ).
% 0.20/0.47
% 0.20/0.47 % top1I
% 0.20/0.47 thf(fact_112_cont__deftr,axiom,
% 0.20/0.47 ! [N: n] :
% 0.20/0.47 ( ( cont @ ( gram_L1231612515_deftr @ N ) )
% 0.20/0.47 = ( image @ ( sum_sum @ t @ n ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ n @ dtree @ ( id @ t ) @ gram_L1231612515_deftr ) @ ( gram_L1451583635elle_S @ N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % cont_deftr
% 0.20/0.47 thf(fact_113_top__conj_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,P: $o,X2: A] :
% 0.20/0.47 ( ( P
% 0.20/0.47 & ( top_top @ ( A > $o ) @ X2 ) )
% 0.20/0.47 = P ) ).
% 0.20/0.47
% 0.20/0.47 % top_conj(2)
% 0.20/0.47 thf(fact_114_top__conj_I1_J,axiom,
% 0.20/0.47 ! [A: $tType,X2: A,P: $o] :
% 0.20/0.47 ( ( ( top_top @ ( A > $o ) @ X2 )
% 0.20/0.47 & P )
% 0.20/0.47 = P ) ).
% 0.20/0.47
% 0.20/0.47 % top_conj(1)
% 0.20/0.47 thf(fact_115_finite__S,axiom,
% 0.20/0.47 ! [N: n] : ( finite_finite2 @ ( sum_sum @ t @ n ) @ ( gram_L1451583635elle_S @ N ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_S
% 0.20/0.47 thf(fact_116_unfold_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,Ct: A > ( set @ ( sum_sum @ t @ A ) ),B2: A,Rt: A > n] :
% 0.20/0.47 ( ( finite_finite2 @ ( sum_sum @ t @ A ) @ ( Ct @ B2 ) )
% 0.20/0.47 => ( ( cont @ ( unfold @ A @ Rt @ Ct @ B2 ) )
% 0.20/0.47 = ( image @ ( sum_sum @ t @ A ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ A @ dtree @ ( id @ t ) @ ( unfold @ A @ Rt @ Ct ) ) @ ( Ct @ B2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % unfold(2)
% 0.20/0.47 thf(fact_117_Gram__Lang__Mirabelle__ojxrtuoybn_Ofinite__H__c,axiom,
% 0.20/0.47 ! [Tr0: dtree,N: n] : ( finite_finite2 @ ( sum_sum @ t @ n ) @ ( gram_L1221482011le_H_c @ Tr0 @ N ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gram_Lang_Mirabelle_ojxrtuoybn.finite_H_c
% 0.20/0.47 thf(fact_118_Gram__Lang__Mirabelle__ojxrtuoybn_Ocont__H,axiom,
% 0.20/0.47 ! [Tr0: dtree,N: n] :
% 0.20/0.47 ( ( cont @ ( gram_L1451583624elle_H @ Tr0 @ N ) )
% 0.20/0.47 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ Tr0 ) @ root ) ) @ ( cont @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gram_Lang_Mirabelle_ojxrtuoybn.cont_H
% 0.20/0.47 thf(fact_119_finite__Plus__UNIV__iff,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType] :
% 0.20/0.47 ( ( finite_finite2 @ ( sum_sum @ A @ B ) @ ( top_top @ ( set @ ( sum_sum @ A @ B ) ) ) )
% 0.20/0.47 = ( ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.20/0.47 & ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_Plus_UNIV_iff
% 0.20/0.47 thf(fact_120_finite__option__UNIV,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( finite_finite2 @ ( option @ A ) @ ( top_top @ ( set @ ( option @ A ) ) ) )
% 0.20/0.47 = ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_option_UNIV
% 0.20/0.47 thf(fact_121_finite__imageI,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F4: set @ A,H: A > B] :
% 0.20/0.47 ( ( finite_finite2 @ A @ F4 )
% 0.20/0.47 => ( finite_finite2 @ B @ ( image @ A @ B @ H @ F4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_imageI
% 0.20/0.47 thf(fact_122_cont__hsubst__neq,axiom,
% 0.20/0.47 ! [Tr: dtree,Tr0: dtree] :
% 0.20/0.47 ( ( ( root @ Tr )
% 0.20/0.47 != ( root @ Tr0 ) )
% 0.20/0.47 => ( ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.20/0.47 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ Tr0 ) ) @ ( cont @ Tr ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % cont_hsubst_neq
% 0.20/0.47 thf(fact_123_cont__hsubst__eq,axiom,
% 0.20/0.47 ! [Tr: dtree,Tr0: dtree] :
% 0.20/0.47 ( ( ( root @ Tr )
% 0.20/0.47 = ( root @ Tr0 ) )
% 0.20/0.47 => ( ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.20/0.47 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ Tr0 ) ) @ ( cont @ Tr0 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % cont_hsubst_eq
% 0.20/0.47 thf(fact_124_finite__code,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( finite_finite @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( finite_finite2 @ A )
% 0.20/0.47 = ( ^ [A5: set @ A] : $true ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_code
% 0.20/0.47 thf(fact_125_root__hsubst,axiom,
% 0.20/0.47 ! [Tr0: dtree,Tr: dtree] :
% 0.20/0.47 ( ( root @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.20/0.47 = ( root @ Tr ) ) ).
% 0.20/0.47
% 0.20/0.47 % root_hsubst
% 0.20/0.47 thf(fact_126_root__o__subst,axiom,
% 0.20/0.47 ! [Tr0: dtree] :
% 0.20/0.47 ( ( comp @ dtree @ n @ dtree @ root @ ( gram_L1004374585hsubst @ Tr0 ) )
% 0.20/0.47 = root ) ).
% 0.20/0.47
% 0.20/0.47 % root_o_subst
% 0.20/0.47 thf(fact_127_finite__cont,axiom,
% 0.20/0.47 ! [Tr: dtree] : ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ ( cont @ Tr ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_cont
% 0.20/0.47 thf(fact_128_finite__N,axiom,
% 0.20/0.47 finite_finite2 @ n @ ( top_top @ ( set @ n ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_N
% 0.20/0.47 thf(fact_129_hsubst__eq,axiom,
% 0.20/0.47 ! [Tr: dtree,Tr0: dtree] :
% 0.20/0.47 ( ( ( root @ Tr )
% 0.20/0.47 = ( root @ Tr0 ) )
% 0.20/0.47 => ( ( gram_L1004374585hsubst @ Tr0 @ Tr )
% 0.20/0.47 = ( gram_L1004374585hsubst @ Tr0 @ Tr0 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % hsubst_eq
% 0.20/0.47 thf(fact_130_wf__hsubst,axiom,
% 0.20/0.47 ! [Tr0: dtree,Tr: dtree] :
% 0.20/0.47 ( ( gram_L864798063lle_wf @ Tr0 )
% 0.20/0.47 => ( ( gram_L864798063lle_wf @ Tr )
% 0.20/0.47 => ( gram_L864798063lle_wf @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % wf_hsubst
% 0.20/0.47 thf(fact_131_finite__hsubst__c,axiom,
% 0.20/0.47 ! [Tr0: dtree,N: dtree] : ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ ( gram_L1905609002ubst_c @ Tr0 @ N ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_hsubst_c
% 0.20/0.47 thf(fact_132_finite,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( finite_finite @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A4: set @ A] : ( finite_finite2 @ A @ A4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite
% 0.20/0.47 thf(fact_133_finite__set__choice,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,A4: set @ A,P: A > B > $o] :
% 0.20/0.47 ( ( finite_finite2 @ A @ A4 )
% 0.20/0.47 => ( ! [X3: A] :
% 0.20/0.47 ( ( member @ A @ X3 @ A4 )
% 0.20/0.47 => ? [X12: B] : ( P @ X3 @ X12 ) )
% 0.20/0.47 => ? [F5: A > B] :
% 0.20/0.47 ! [X4: A] :
% 0.20/0.47 ( ( member @ A @ X4 @ A4 )
% 0.20/0.47 => ( P @ X4 @ ( F5 @ X4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_set_choice
% 0.20/0.47 thf(fact_134_finite__UNIV,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( finite_finite @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_UNIV
% 0.20/0.47 thf(fact_135_infinite__UNIV__char__0,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ~ ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % infinite_UNIV_char_0
% 0.20/0.47 thf(fact_136_ex__new__if__finite,axiom,
% 0.20/0.47 ! [A: $tType,A4: set @ A] :
% 0.20/0.47 ( ~ ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.20/0.47 => ( ( finite_finite2 @ A @ A4 )
% 0.20/0.47 => ? [A6: A] :
% 0.20/0.47 ~ ( member @ A @ A6 @ A4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ex_new_if_finite
% 0.20/0.47 thf(fact_137_finite__fun__UNIVD2,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType] :
% 0.20/0.47 ( ( finite_finite2 @ ( A > B ) @ ( top_top @ ( set @ ( A > B ) ) ) )
% 0.20/0.47 => ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_fun_UNIVD2
% 0.20/0.47 thf(fact_138_finite__Prod__UNIV,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.20/0.47 => ( ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) )
% 0.20/0.47 => ( finite_finite2 @ ( product_prod @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_Prod_UNIV
% 0.20/0.47 thf(fact_139_finite__prod,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType] :
% 0.20/0.47 ( ( finite_finite2 @ ( product_prod @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) )
% 0.20/0.47 = ( ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.20/0.47 & ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_prod
% 0.20/0.47 thf(fact_140_Finite__Set_Ofinite__set,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( finite_finite2 @ ( set @ A ) @ ( top_top @ ( set @ ( set @ A ) ) ) )
% 0.20/0.47 = ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Finite_Set.finite_set
% 0.20/0.47 thf(fact_141_hsubst__def,axiom,
% 0.20/0.47 ( gram_L1004374585hsubst
% 0.20/0.47 = ( ^ [Tr02: dtree] : ( unfold @ dtree @ gram_L1905609017ubst_r @ ( gram_L1905609002ubst_c @ Tr02 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % hsubst_def
% 0.20/0.47 thf(fact_142_top__empty__eq,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( top_top @ ( A > $o ) )
% 0.20/0.47 = ( ^ [X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % top_empty_eq
% 0.20/0.47 thf(fact_143_Node__root__cont,axiom,
% 0.20/0.47 ! [Tr: dtree] :
% 0.20/0.47 ( ( node @ ( root @ Tr ) @ ( cont @ Tr ) )
% 0.20/0.47 = Tr ) ).
% 0.20/0.47
% 0.20/0.47 % Node_root_cont
% 0.20/0.47 thf(fact_144_DEADID_Oin__rel,axiom,
% 0.20/0.47 ! [B: $tType] :
% 0.20/0.47 ( ( ^ [Y4: B,Z3: B] : ( Y4 = Z3 ) )
% 0.20/0.47 = ( ^ [A7: B,B4: B] :
% 0.20/0.47 ? [Z4: B] :
% 0.20/0.47 ( ( member @ B @ Z4 @ ( top_top @ ( set @ B ) ) )
% 0.20/0.47 & ( ( id @ B @ Z4 )
% 0.20/0.47 = A7 )
% 0.20/0.47 & ( ( id @ B @ Z4 )
% 0.20/0.47 = B4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % DEADID.in_rel
% 0.20/0.47 thf(fact_145_root__Node,axiom,
% 0.20/0.47 ! [N: n,As: set @ ( sum_sum @ t @ dtree )] :
% 0.20/0.47 ( ( root @ ( node @ N @ As ) )
% 0.20/0.47 = N ) ).
% 0.20/0.47
% 0.20/0.47 % root_Node
% 0.20/0.47 thf(fact_146_dtree__simps,axiom,
% 0.20/0.47 ! [As: set @ ( sum_sum @ t @ dtree ),As2: set @ ( sum_sum @ t @ dtree ),N: n,N4: n] :
% 0.20/0.47 ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As )
% 0.20/0.47 => ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As2 )
% 0.20/0.47 => ( ( ( node @ N @ As )
% 0.20/0.47 = ( node @ N4 @ As2 ) )
% 0.20/0.47 = ( ( N = N4 )
% 0.20/0.47 & ( As = As2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dtree_simps
% 0.20/0.47 thf(fact_147_cont__Node,axiom,
% 0.20/0.47 ! [As: set @ ( sum_sum @ t @ dtree ),N: n] :
% 0.20/0.47 ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As )
% 0.20/0.47 => ( ( cont @ ( node @ N @ As ) )
% 0.20/0.47 = As ) ) ).
% 0.20/0.47
% 0.20/0.47 % cont_Node
% 0.20/0.47 thf(fact_148_dtree__cases,axiom,
% 0.20/0.47 ! [Tr: dtree] :
% 0.20/0.47 ~ ! [N5: n,As3: set @ ( sum_sum @ t @ dtree )] :
% 0.20/0.47 ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As3 )
% 0.20/0.47 => ( Tr
% 0.20/0.47 != ( node @ N5 @ As3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dtree_cases
% 0.20/0.47 thf(fact_149_type__copy__map__cong0,axiom,
% 0.20/0.47 ! [B: $tType,D: $tType,E: $tType,A: $tType,C: $tType,M: B > A,G: C > B,X2: C,N3: D > A,H: C > D,F: A > E] :
% 0.20/0.47 ( ( ( M @ ( G @ X2 ) )
% 0.20/0.47 = ( N3 @ ( H @ X2 ) ) )
% 0.20/0.47 => ( ( comp @ B @ E @ C @ ( comp @ A @ E @ B @ F @ M ) @ G @ X2 )
% 0.20/0.47 = ( comp @ D @ E @ C @ ( comp @ A @ E @ D @ F @ N3 ) @ H @ X2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % type_copy_map_cong0
% 0.20/0.47 thf(fact_150_hsubst__r__def,axiom,
% 0.20/0.47 gram_L1905609017ubst_r = root ).
% 0.20/0.47
% 0.20/0.47 % hsubst_r_def
% 0.20/0.47 thf(fact_151_Sup_OSUP__id__eq,axiom,
% 0.20/0.47 ! [A: $tType,Sup: ( set @ A ) > A,A4: set @ A] :
% 0.20/0.47 ( ( Sup @ ( image @ A @ A @ ( id @ A ) @ A4 ) )
% 0.20/0.47 = ( Sup @ A4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % Sup.SUP_id_eq
% 0.20/0.47 thf(fact_152_Inf_OINF__id__eq,axiom,
% 0.20/0.47 ! [A: $tType,Inf: ( set @ A ) > A,A4: set @ A] :
% 0.20/0.47 ( ( Inf @ ( image @ A @ A @ ( id @ A ) @ A4 ) )
% 0.20/0.47 = ( Inf @ A4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inf.INF_id_eq
% 0.20/0.47 thf(fact_153_Sup_OSUP__image,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,C: $tType,Sup: ( set @ A ) > A,G: B > A,F: C > B,A4: set @ C] :
% 0.20/0.47 ( ( Sup @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A4 ) ) )
% 0.20/0.47 = ( Sup @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Sup.SUP_image
% 0.20/0.47 thf(fact_154_Sup_OSUP__cong,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,A4: set @ B,B3: set @ B,C3: B > A,D3: B > A,Sup: ( set @ A ) > A] :
% 0.20/0.47 ( ( A4 = B3 )
% 0.20/0.47 => ( ! [X3: B] :
% 0.20/0.47 ( ( member @ B @ X3 @ B3 )
% 0.20/0.47 => ( ( C3 @ X3 )
% 0.20/0.47 = ( D3 @ X3 ) ) )
% 0.20/0.47 => ( ( Sup @ ( image @ B @ A @ C3 @ A4 ) )
% 0.20/0.47 = ( Sup @ ( image @ B @ A @ D3 @ B3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Sup.SUP_cong
% 0.20/0.47 thf(fact_155_Inf_OINF__cong,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,A4: set @ B,B3: set @ B,C3: B > A,D3: B > A,Inf: ( set @ A ) > A] :
% 0.20/0.47 ( ( A4 = B3 )
% 0.20/0.47 => ( ! [X3: B] :
% 0.20/0.47 ( ( member @ B @ X3 @ B3 )
% 0.20/0.47 => ( ( C3 @ X3 )
% 0.20/0.47 = ( D3 @ X3 ) ) )
% 0.20/0.47 => ( ( Inf @ ( image @ B @ A @ C3 @ A4 ) )
% 0.20/0.47 = ( Inf @ ( image @ B @ A @ D3 @ B3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inf.INF_cong
% 0.20/0.47 thf(fact_156_Inf_OINF__image,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,C: $tType,Inf: ( set @ A ) > A,G: B > A,F: C > B,A4: set @ C] :
% 0.20/0.47 ( ( Inf @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A4 ) ) )
% 0.20/0.47 = ( Inf @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inf.INF_image
% 0.20/0.47 thf(fact_157_Inl__cont__H,axiom,
% 0.20/0.47 ! [N: n] :
% 0.20/0.47 ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1451583624elle_H @ tr0 @ N ) ) )
% 0.20/0.47 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ N ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inl_cont_H
% 0.20/0.47 thf(fact_158_case__sum__o__map__sum__id,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,C: $tType,G: B > A,F: C > A,X2: sum_sum @ C @ B] :
% 0.20/0.47 ( ( comp @ ( sum_sum @ A @ B ) @ A @ ( sum_sum @ C @ B ) @ ( sum_case_sum @ A @ A @ B @ ( id @ A ) @ G ) @ ( sum_map_sum @ C @ A @ B @ B @ F @ ( id @ B ) ) @ X2 )
% 0.20/0.47 = ( sum_case_sum @ C @ A @ B @ ( comp @ C @ A @ C @ F @ ( id @ C ) ) @ G @ X2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_sum_o_map_sum_id
% 0.20/0.47 thf(fact_159_inFr2_OBase,axiom,
% 0.20/0.47 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.20/0.47 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.20/0.47 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 0.20/0.47 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inFr2.Base
% 0.20/0.47 thf(fact_160_vimage__eq,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 0.20/0.47 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 0.20/0.47 = ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % vimage_eq
% 0.20/0.47 thf(fact_161_vimageI,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F: B > A,A2: B,B2: A,B3: set @ A] :
% 0.20/0.47 ( ( ( F @ A2 )
% 0.20/0.47 = B2 )
% 0.20/0.47 => ( ( member @ A @ B2 @ B3 )
% 0.20/0.47 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ B3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % vimageI
% 0.20/0.47 thf(fact_162_vimage__UNIV,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F: A > B] :
% 0.20/0.47 ( ( vimage @ A @ B @ F @ ( top_top @ ( set @ B ) ) )
% 0.20/0.47 = ( top_top @ ( set @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % vimage_UNIV
% 0.20/0.47 thf(fact_163_vimage__id,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( vimage @ A @ A @ ( id @ A ) )
% 0.20/0.47 = ( id @ ( set @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % vimage_id
% 0.20/0.47 thf(fact_164_Inl__m__oplus,axiom,
% 0.20/0.47 ! [B: $tType,C: $tType,A: $tType,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.20/0.47 ( ( 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 ) )
% 0.20/0.47 = ( vimage @ A @ ( sum_sum @ A @ C ) @ ( sum_Inl @ A @ C ) @ Tns ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inl_m_oplus
% 0.20/0.47 thf(fact_165_Inl__cont__hsubst__neq,axiom,
% 0.20/0.47 ! [Tr: dtree,Tr0: dtree] :
% 0.20/0.47 ( ( ( root @ Tr )
% 0.20/0.47 != ( root @ Tr0 ) )
% 0.20/0.47 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.20/0.47 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inl_cont_hsubst_neq
% 0.20/0.47 thf(fact_166_Inl__cont__hsubst__eq,axiom,
% 0.20/0.47 ! [Tr: dtree,Tr0: dtree] :
% 0.20/0.47 ( ( ( root @ Tr )
% 0.20/0.47 = ( root @ Tr0 ) )
% 0.20/0.47 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.20/0.47 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inl_cont_hsubst_eq
% 0.20/0.47 thf(fact_167_case__sum__step_I1_J,axiom,
% 0.20/0.47 ! [D: $tType,A: $tType,C: $tType,B: $tType,F6: B > A,G3: C > A,G: D > A,P2: sum_sum @ B @ C] :
% 0.20/0.47 ( ( sum_case_sum @ ( sum_sum @ B @ C ) @ A @ D @ ( sum_case_sum @ B @ A @ C @ F6 @ G3 ) @ G @ ( sum_Inl @ ( sum_sum @ B @ C ) @ D @ P2 ) )
% 0.20/0.47 = ( sum_case_sum @ B @ A @ C @ F6 @ G3 @ P2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_sum_step(1)
% 0.20/0.47 thf(fact_168_case__sum__inject,axiom,
% 0.20/0.47 ! [A: $tType,C: $tType,B: $tType,F1: A > C,F22: B > C,G1: A > C,G22: B > C] :
% 0.20/0.47 ( ( ( sum_case_sum @ A @ C @ B @ F1 @ F22 )
% 0.20/0.47 = ( sum_case_sum @ A @ C @ B @ G1 @ G22 ) )
% 0.20/0.47 => ~ ( ( F1 = G1 )
% 0.20/0.47 => ( F22 != G22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_sum_inject
% 0.20/0.47 thf(fact_169_vimage__Collect,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,P: B > $o,F: A > B,Q: A > $o] :
% 0.20/0.47 ( ! [X3: A] :
% 0.20/0.47 ( ( P @ ( F @ X3 ) )
% 0.20/0.47 = ( Q @ X3 ) )
% 0.20/0.47 => ( ( vimage @ A @ B @ F @ ( collect @ B @ P ) )
% 0.20/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % vimage_Collect
% 0.20/0.47 thf(fact_170_vimageI2,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F: B > A,A2: B,A4: set @ A] :
% 0.20/0.47 ( ( member @ A @ ( F @ A2 ) @ A4 )
% 0.20/0.47 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ A4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % vimageI2
% 0.20/0.47 thf(fact_171_vimageE,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 0.20/0.47 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 0.20/0.47 => ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % vimageE
% 0.20/0.47 thf(fact_172_vimageD,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,A2: A,F: A > B,A4: set @ B] :
% 0.20/0.47 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ A4 ) )
% 0.20/0.47 => ( member @ B @ ( F @ A2 ) @ A4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % vimageD
% 0.20/0.47 thf(fact_173_old_Osum_Osimps_I5_J,axiom,
% 0.20/0.47 ! [B: $tType,C: $tType,A: $tType,F1: A > C,F22: B > C,X1: A] :
% 0.20/0.47 ( ( sum_case_sum @ A @ C @ B @ F1 @ F22 @ ( sum_Inl @ A @ B @ X1 ) )
% 0.20/0.47 = ( F1 @ X1 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.sum.simps(5)
% 0.20/0.47 thf(fact_174_set_Ocompositionality,axiom,
% 0.20/0.47 ! [C: $tType,B: $tType,A: $tType,F: C > B,G: B > A,Set: set @ A] :
% 0.20/0.47 ( ( vimage @ C @ B @ F @ ( vimage @ B @ A @ G @ Set ) )
% 0.20/0.47 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ Set ) ) ).
% 0.20/0.47
% 0.20/0.47 % set.compositionality
% 0.20/0.47 thf(fact_175_vimage__comp,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,C: $tType,F: A > B,G: B > C,X2: set @ C] :
% 0.20/0.47 ( ( vimage @ A @ B @ F @ ( vimage @ B @ C @ G @ X2 ) )
% 0.20/0.47 = ( vimage @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ X2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % vimage_comp
% 0.20/0.47 thf(fact_176_set_Ocomp,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,C: $tType,F: C > B,G: B > A] :
% 0.20/0.47 ( ( comp @ ( set @ B ) @ ( set @ C ) @ ( set @ A ) @ ( vimage @ C @ B @ F ) @ ( vimage @ B @ A @ G ) )
% 0.20/0.47 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % set.comp
% 0.20/0.47 thf(fact_177_surj__image__vimage__eq,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F: B > A,A4: set @ A] :
% 0.20/0.47 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.20/0.47 = ( top_top @ ( set @ A ) ) )
% 0.20/0.47 => ( ( image @ B @ A @ F @ ( vimage @ B @ A @ F @ A4 ) )
% 0.20/0.47 = A4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_image_vimage_eq
% 0.20/0.47 thf(fact_178_inFr2__root__in,axiom,
% 0.20/0.47 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.20/0.47 ( ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 )
% 0.20/0.47 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.20/0.47
% 0.20/0.47 % inFr2_root_in
% 0.20/0.47 thf(fact_179_case__sum__map__sum,axiom,
% 0.20/0.47 ! [C: $tType,A: $tType,B: $tType,E: $tType,D: $tType,L: B > A,R: C > A,F: D > B,G: E > C,X2: sum_sum @ D @ E] :
% 0.20/0.47 ( ( sum_case_sum @ B @ A @ C @ L @ R @ ( sum_map_sum @ D @ B @ E @ C @ F @ G @ X2 ) )
% 0.20/0.47 = ( sum_case_sum @ D @ A @ E @ ( comp @ B @ A @ D @ L @ F ) @ ( comp @ C @ A @ E @ R @ G ) @ X2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_sum_map_sum
% 0.20/0.47 thf(fact_180_finite__vimageD,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,H: A > B,F4: set @ B] :
% 0.20/0.47 ( ( finite_finite2 @ A @ ( vimage @ A @ B @ H @ F4 ) )
% 0.20/0.47 => ( ( ( image @ A @ B @ H @ ( top_top @ ( set @ A ) ) )
% 0.20/0.47 = ( top_top @ ( set @ B ) ) )
% 0.20/0.47 => ( finite_finite2 @ B @ F4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_vimageD
% 0.20/0.47 thf(fact_181_case__sum__o__inj_I1_J,axiom,
% 0.20/0.47 ! [C: $tType,B: $tType,A: $tType,F: A > B,G: C > B] :
% 0.20/0.47 ( ( comp @ ( sum_sum @ A @ C ) @ B @ A @ ( sum_case_sum @ A @ B @ C @ F @ G ) @ ( sum_Inl @ A @ C ) )
% 0.20/0.47 = F ) ).
% 0.20/0.47
% 0.20/0.47 % case_sum_o_inj(1)
% 0.20/0.47 thf(fact_182_o__case__sum,axiom,
% 0.20/0.47 ! [A: $tType,C: $tType,D: $tType,B: $tType,H: D > C,F: A > D,G: B > D] :
% 0.20/0.47 ( ( comp @ D @ C @ ( sum_sum @ A @ B ) @ H @ ( sum_case_sum @ A @ D @ B @ F @ G ) )
% 0.20/0.47 = ( sum_case_sum @ A @ C @ B @ ( comp @ D @ C @ A @ H @ F ) @ ( comp @ D @ C @ B @ H @ G ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % o_case_sum
% 0.20/0.47 thf(fact_183_Gram__Lang__Mirabelle__ojxrtuoybn_OInl__cont__H,axiom,
% 0.20/0.47 ! [Tr0: dtree,N: n] :
% 0.20/0.47 ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1451583624elle_H @ Tr0 @ N ) ) )
% 0.20/0.47 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gram_Lang_Mirabelle_ojxrtuoybn.Inl_cont_H
% 0.20/0.47 thf(fact_184_case__sum__o__map__sum,axiom,
% 0.20/0.47 ! [A: $tType,D: $tType,C: $tType,E: $tType,B: $tType,F: D > C,G: E > C,H1: A > D,H2: B > E] :
% 0.20/0.47 ( ( comp @ ( sum_sum @ D @ E ) @ C @ ( sum_sum @ A @ B ) @ ( sum_case_sum @ D @ C @ E @ F @ G ) @ ( sum_map_sum @ A @ D @ B @ E @ H1 @ H2 ) )
% 0.20/0.47 = ( sum_case_sum @ A @ C @ B @ ( comp @ D @ C @ A @ F @ H1 ) @ ( comp @ E @ C @ B @ G @ H2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_sum_o_map_sum
% 0.20/0.47 thf(fact_185_Inl__prodOf,axiom,
% 0.20/0.47 ! [Tr: dtree] :
% 0.20/0.47 ( ( 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 ) ) )
% 0.20/0.47 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inl_prodOf
% 0.20/0.47 thf(fact_186_corec_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,Ct: A > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) ),B2: A,Rt: A > n] :
% 0.20/0.47 ( ( finite_finite2 @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) @ ( Ct @ B2 ) )
% 0.20/0.47 => ( ( cont @ ( corec @ A @ Rt @ Ct @ B2 ) )
% 0.20/0.47 = ( image @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ ( sum_sum @ dtree @ A ) @ dtree @ ( id @ t ) @ ( sum_case_sum @ dtree @ dtree @ A @ ( id @ dtree ) @ ( corec @ A @ Rt @ Ct ) ) ) @ ( Ct @ B2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % corec(2)
% 0.20/0.47 thf(fact_187_Inr__m__oplus,axiom,
% 0.20/0.47 ! [A: $tType,C: $tType,B: $tType,F: C > A,Tns: set @ ( sum_sum @ B @ C )] :
% 0.20/0.47 ( ( 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 ) )
% 0.20/0.47 = ( image @ C @ A @ F @ ( vimage @ C @ ( sum_sum @ B @ C ) @ ( sum_Inr @ C @ B ) @ Tns ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inr_m_oplus
% 0.20/0.47 thf(fact_188_sum_Oinject_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,X22: B,Y22: B] :
% 0.20/0.47 ( ( ( sum_Inr @ B @ A @ X22 )
% 0.20/0.47 = ( sum_Inr @ B @ A @ Y22 ) )
% 0.20/0.47 = ( X22 = Y22 ) ) ).
% 0.20/0.47
% 0.20/0.47 % sum.inject(2)
% 0.20/0.47 thf(fact_189_old_Osum_Oinject_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,B2: B,B5: B] :
% 0.20/0.47 ( ( ( sum_Inr @ B @ A @ B2 )
% 0.20/0.47 = ( sum_Inr @ B @ A @ B5 ) )
% 0.20/0.47 = ( B2 = B5 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.sum.inject(2)
% 0.20/0.47 thf(fact_190_Inr__cont__H,axiom,
% 0.20/0.47 ! [N: n] :
% 0.20/0.47 ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1451583624elle_H @ tr0 @ N ) ) )
% 0.20/0.47 = ( image @ dtree @ dtree @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ tr0 ) @ root ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ N ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inr_cont_H
% 0.20/0.47 thf(fact_191_Inr__Inl__False,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,X2: B,Y: A] :
% 0.20/0.47 ( ( sum_Inr @ B @ A @ X2 )
% 0.20/0.47 != ( sum_Inl @ A @ B @ Y ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inr_Inl_False
% 0.20/0.47 thf(fact_192_Inl__Inr__False,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,X2: A,Y: B] :
% 0.20/0.47 ( ( sum_Inl @ A @ B @ X2 )
% 0.20/0.47 != ( sum_Inr @ B @ A @ Y ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inl_Inr_False
% 0.20/0.47 thf(fact_193_old_Osum_Osimps_I8_J,axiom,
% 0.20/0.47 ! [A: $tType,T: $tType,B: $tType,F1: A > T,F22: B > T,B2: B] :
% 0.20/0.47 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inr @ B @ A @ B2 ) )
% 0.20/0.47 = ( F22 @ B2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.sum.simps(8)
% 0.20/0.47 thf(fact_194_wf__inj,axiom,
% 0.20/0.47 ! [Tr: dtree,Tr1: dtree,Tr2: dtree] :
% 0.20/0.47 ( ( gram_L864798063lle_wf @ Tr )
% 0.20/0.47 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.20/0.47 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 0.20/0.47 => ( ( ( root @ Tr1 )
% 0.20/0.47 = ( root @ Tr2 ) )
% 0.20/0.47 = ( Tr1 = Tr2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % wf_inj
% 0.20/0.47 thf(fact_195_Inr__cont__hsubst__neq,axiom,
% 0.20/0.47 ! [Tr: dtree,Tr0: dtree] :
% 0.20/0.47 ( ( ( root @ Tr )
% 0.20/0.47 != ( root @ Tr0 ) )
% 0.20/0.47 => ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.20/0.47 = ( image @ dtree @ dtree @ ( gram_L1004374585hsubst @ Tr0 ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inr_cont_hsubst_neq
% 0.20/0.47 thf(fact_196_Inr__cont__hsubst__eq,axiom,
% 0.20/0.47 ! [Tr: dtree,Tr0: dtree] :
% 0.20/0.47 ( ( ( root @ Tr )
% 0.20/0.47 = ( root @ Tr0 ) )
% 0.20/0.47 => ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.20/0.47 = ( image @ dtree @ dtree @ ( gram_L1004374585hsubst @ Tr0 ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr0 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inr_cont_hsubst_eq
% 0.20/0.47 thf(fact_197_Inr__oplus__iff,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,C: $tType,Tr: B,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.20/0.47 ( ( 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 ) )
% 0.20/0.47 = ( ? [N2: C] :
% 0.20/0.47 ( ( member @ ( sum_sum @ A @ C ) @ ( sum_Inr @ C @ A @ N2 ) @ Tns )
% 0.20/0.47 & ( ( F @ N2 )
% 0.20/0.47 = Tr ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inr_oplus_iff
% 0.20/0.47 thf(fact_198_case__sum__step_I2_J,axiom,
% 0.20/0.47 ! [E: $tType,A: $tType,C: $tType,B: $tType,F: E > A,F6: B > A,G3: C > A,P2: sum_sum @ B @ C] :
% 0.20/0.47 ( ( sum_case_sum @ E @ A @ ( sum_sum @ B @ C ) @ F @ ( sum_case_sum @ B @ A @ C @ F6 @ G3 ) @ ( sum_Inr @ ( sum_sum @ B @ C ) @ E @ P2 ) )
% 0.20/0.47 = ( sum_case_sum @ B @ A @ C @ F6 @ G3 @ P2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_sum_step(2)
% 0.20/0.47 thf(fact_199_old_Osum_Osimps_I6_J,axiom,
% 0.20/0.47 ! [A: $tType,C: $tType,B: $tType,F1: A > C,F22: B > C,X22: B] :
% 0.20/0.47 ( ( sum_case_sum @ A @ C @ B @ F1 @ F22 @ ( sum_Inr @ B @ A @ X22 ) )
% 0.20/0.47 = ( F22 @ X22 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.sum.simps(6)
% 0.20/0.47 thf(fact_200_old_Osum_Oinducts,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,P: ( sum_sum @ A @ B ) > $o,Sum: sum_sum @ A @ B] :
% 0.20/0.47 ( ! [A6: A] : ( P @ ( sum_Inl @ A @ B @ A6 ) )
% 0.20/0.47 => ( ! [B6: B] : ( P @ ( sum_Inr @ B @ A @ B6 ) )
% 0.20/0.47 => ( P @ Sum ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.sum.inducts
% 0.20/0.47 thf(fact_201_old_Osum_Oexhaust,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,Y: sum_sum @ A @ B] :
% 0.20/0.47 ( ! [A6: A] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( sum_Inl @ A @ B @ A6 ) )
% 0.20/0.47 => ~ ! [B6: B] :
% 0.20/0.47 ( Y
% 0.20/0.47 != ( sum_Inr @ B @ A @ B6 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.sum.exhaust
% 0.20/0.47 thf(fact_202_split__sum__all,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 0.20/0.47 ! [X6: sum_sum @ A @ B] : ( P3 @ X6 ) )
% 0.20/0.47 = ( ^ [P4: ( sum_sum @ A @ B ) > $o] :
% 0.20/0.47 ( ! [X: A] : ( P4 @ ( sum_Inl @ A @ B @ X ) )
% 0.20/0.47 & ! [X: B] : ( P4 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % split_sum_all
% 0.20/0.47 thf(fact_203_split__sum__ex,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 0.20/0.47 ? [X6: sum_sum @ A @ B] : ( P3 @ X6 ) )
% 0.20/0.47 = ( ^ [P4: ( sum_sum @ A @ B ) > $o] :
% 0.20/0.47 ( ? [X: A] : ( P4 @ ( sum_Inl @ A @ B @ X ) )
% 0.20/0.47 | ? [X: B] : ( P4 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % split_sum_ex
% 0.20/0.47 thf(fact_204_Inr__not__Inl,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,B2: B,A2: A] :
% 0.20/0.47 ( ( sum_Inr @ B @ A @ B2 )
% 0.20/0.47 != ( sum_Inl @ A @ B @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inr_not_Inl
% 0.20/0.47 thf(fact_205_sumE,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 0.20/0.47 ( ! [X3: A] :
% 0.20/0.47 ( S
% 0.20/0.47 != ( sum_Inl @ A @ B @ X3 ) )
% 0.20/0.47 => ~ ! [Y2: B] :
% 0.20/0.47 ( S
% 0.20/0.47 != ( sum_Inr @ B @ A @ Y2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % sumE
% 0.20/0.47 thf(fact_206_old_Osum_Odistinct_I1_J,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,A2: A,B5: B] :
% 0.20/0.47 ( ( sum_Inl @ A @ B @ A2 )
% 0.20/0.47 != ( sum_Inr @ B @ A @ B5 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.sum.distinct(1)
% 0.20/0.47 thf(fact_207_old_Osum_Odistinct_I2_J,axiom,
% 0.20/0.47 ! [B7: $tType,A8: $tType,B8: B7,A9: A8] :
% 0.20/0.47 ( ( sum_Inr @ B7 @ A8 @ B8 )
% 0.20/0.47 != ( sum_Inl @ A8 @ B7 @ A9 ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.sum.distinct(2)
% 0.20/0.47 thf(fact_208_sum_Odistinct_I1_J,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,X1: A,X22: B] :
% 0.20/0.47 ( ( sum_Inl @ A @ B @ X1 )
% 0.20/0.47 != ( sum_Inr @ B @ A @ X22 ) ) ).
% 0.20/0.47
% 0.20/0.47 % sum.distinct(1)
% 0.20/0.47 thf(fact_209_obj__sumE__f,axiom,
% 0.20/0.47 ! [A: $tType,C: $tType,B: $tType,S: B,F: ( sum_sum @ A @ C ) > B,P: $o] :
% 0.20/0.47 ( ! [X3: A] :
% 0.20/0.47 ( ( S
% 0.20/0.47 = ( F @ ( sum_Inl @ A @ C @ X3 ) ) )
% 0.20/0.47 => P )
% 0.20/0.47 => ( ! [X3: C] :
% 0.20/0.47 ( ( S
% 0.20/0.47 = ( F @ ( sum_Inr @ C @ A @ X3 ) ) )
% 0.20/0.47 => P )
% 0.20/0.47 => ! [X4: sum_sum @ A @ C] :
% 0.20/0.47 ( ( S
% 0.20/0.47 = ( F @ X4 ) )
% 0.20/0.47 => P ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % obj_sumE_f
% 0.20/0.47 thf(fact_210_Inr__inject,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,X2: B,Y: B] :
% 0.20/0.47 ( ( ( sum_Inr @ B @ A @ X2 )
% 0.20/0.47 = ( sum_Inr @ B @ A @ Y ) )
% 0.20/0.47 => ( X2 = Y ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inr_inject
% 0.20/0.47 thf(fact_211_map__sum__if__distrib__else_I2_J,axiom,
% 0.20/0.47 ! [E: $tType,F3: $tType,H3: $tType,G4: $tType,E2: $o,F: E > F3,G: G4 > H3,X2: sum_sum @ E @ G4,Y: G4] :
% 0.20/0.47 ( ( E2
% 0.20/0.47 => ( ( sum_map_sum @ E @ F3 @ G4 @ H3 @ F @ G @ ( if @ ( sum_sum @ E @ G4 ) @ E2 @ X2 @ ( sum_Inr @ G4 @ E @ Y ) ) )
% 0.20/0.47 = ( sum_map_sum @ E @ F3 @ G4 @ H3 @ F @ G @ X2 ) ) )
% 0.20/0.47 & ( ~ E2
% 0.20/0.47 => ( ( sum_map_sum @ E @ F3 @ G4 @ H3 @ F @ G @ ( if @ ( sum_sum @ E @ G4 ) @ E2 @ X2 @ ( sum_Inr @ G4 @ E @ Y ) ) )
% 0.20/0.47 = ( sum_Inr @ H3 @ F3 @ ( G @ Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_sum_if_distrib_else(2)
% 0.20/0.47 thf(fact_212_map__sum__if__distrib__then_I2_J,axiom,
% 0.20/0.47 ! [H3: $tType,F3: $tType,G4: $tType,E: $tType,E2: $o,F: E > F3,G: G4 > H3,X2: G4,Y: sum_sum @ E @ G4] :
% 0.20/0.47 ( ( E2
% 0.20/0.47 => ( ( sum_map_sum @ E @ F3 @ G4 @ H3 @ F @ G @ ( if @ ( sum_sum @ E @ G4 ) @ E2 @ ( sum_Inr @ G4 @ E @ X2 ) @ Y ) )
% 0.20/0.47 = ( sum_Inr @ H3 @ F3 @ ( G @ X2 ) ) ) )
% 0.20/0.47 & ( ~ E2
% 0.20/0.47 => ( ( sum_map_sum @ E @ F3 @ G4 @ H3 @ F @ G @ ( if @ ( sum_sum @ E @ G4 ) @ E2 @ ( sum_Inr @ G4 @ E @ X2 ) @ Y ) )
% 0.20/0.47 = ( sum_map_sum @ E @ F3 @ G4 @ H3 @ F @ G @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_sum_if_distrib_then(2)
% 0.20/0.47 thf(fact_213_map__sum__InrD,axiom,
% 0.20/0.47 ! [C: $tType,A: $tType,D: $tType,B: $tType,F: C > A,G: D > B,Z: sum_sum @ C @ D,X2: B] :
% 0.20/0.47 ( ( ( sum_map_sum @ C @ A @ D @ B @ F @ G @ Z )
% 0.20/0.47 = ( sum_Inr @ B @ A @ X2 ) )
% 0.20/0.47 => ? [Y2: D] :
% 0.20/0.47 ( ( Z
% 0.20/0.47 = ( sum_Inr @ D @ C @ Y2 ) )
% 0.20/0.47 & ( ( G @ Y2 )
% 0.20/0.47 = X2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_sum_InrD
% 0.20/0.47 thf(fact_214_map__sum_Osimps_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,C: $tType,D: $tType,B: $tType,F1: A > C,F22: B > D,A2: B] :
% 0.20/0.47 ( ( sum_map_sum @ A @ C @ B @ D @ F1 @ F22 @ ( sum_Inr @ B @ A @ A2 ) )
% 0.20/0.47 = ( sum_Inr @ D @ C @ ( F22 @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_sum.simps(2)
% 0.20/0.47 thf(fact_215_Inl__Inr__image__cong,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,A4: set @ ( sum_sum @ A @ B ),B3: set @ ( sum_sum @ A @ B )] :
% 0.20/0.47 ( ( ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ A4 )
% 0.20/0.47 = ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ B3 ) )
% 0.20/0.47 => ( ( ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ A4 )
% 0.20/0.47 = ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ B3 ) )
% 0.20/0.47 => ( A4 = B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inl_Inr_image_cong
% 0.20/0.47 thf(fact_216_case__sum__if,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,C: $tType,P2: $o,F: B > A,G: C > A,X2: B,Y: C] :
% 0.20/0.47 ( ( P2
% 0.20/0.47 => ( ( sum_case_sum @ B @ A @ C @ F @ G @ ( if @ ( sum_sum @ B @ C ) @ P2 @ ( sum_Inl @ B @ C @ X2 ) @ ( sum_Inr @ C @ B @ Y ) ) )
% 0.20/0.47 = ( F @ X2 ) ) )
% 0.20/0.47 & ( ~ P2
% 0.20/0.47 => ( ( sum_case_sum @ B @ A @ C @ F @ G @ ( if @ ( sum_sum @ B @ C ) @ P2 @ ( sum_Inl @ B @ C @ X2 ) @ ( sum_Inr @ C @ B @ Y ) ) )
% 0.20/0.47 = ( G @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_sum_if
% 0.20/0.47 thf(fact_217_wf__cont,axiom,
% 0.20/0.47 ! [Tr: dtree,Tr5: dtree] :
% 0.20/0.47 ( ( gram_L864798063lle_wf @ Tr )
% 0.20/0.47 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr5 ) @ ( cont @ Tr ) )
% 0.20/0.47 => ( gram_L864798063lle_wf @ Tr5 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % wf_cont
% 0.20/0.47 thf(fact_218_case__sum__o__inj_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,C: $tType,F: A > B,G: C > B] :
% 0.20/0.47 ( ( comp @ ( sum_sum @ A @ C ) @ B @ C @ ( sum_case_sum @ A @ B @ C @ F @ G ) @ ( sum_Inr @ C @ A ) )
% 0.20/0.47 = G ) ).
% 0.20/0.47
% 0.20/0.47 % case_sum_o_inj(2)
% 0.20/0.47 thf(fact_219_root__prodOf,axiom,
% 0.20/0.47 ! [Tr5: dtree,Tr: dtree] :
% 0.20/0.47 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr5 ) @ ( cont @ Tr ) )
% 0.20/0.47 => ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ ( root @ Tr5 ) ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % root_prodOf
% 0.20/0.47 thf(fact_220_Gram__Lang__Mirabelle__ojxrtuoybn_OInr__cont__H,axiom,
% 0.20/0.47 ! [Tr0: dtree,N: n] :
% 0.20/0.47 ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1451583624elle_H @ Tr0 @ N ) ) )
% 0.20/0.47 = ( image @ dtree @ dtree @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ Tr0 ) @ root ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gram_Lang_Mirabelle_ojxrtuoybn.Inr_cont_H
% 0.20/0.47 thf(fact_221_Inr__oplus__elim,axiom,
% 0.20/0.47 ! [A: $tType,C: $tType,B: $tType,Tr: B,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.20/0.47 ( ( 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 ) )
% 0.20/0.47 => ? [N5: C] :
% 0.20/0.47 ( ( member @ ( sum_sum @ A @ C ) @ ( sum_Inr @ C @ A @ N5 ) @ Tns )
% 0.20/0.47 & ( ( F @ N5 )
% 0.20/0.47 = Tr ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inr_oplus_elim
% 0.20/0.47 thf(fact_222_subtr_OStep,axiom,
% 0.20/0.47 ! [Tr3: dtree,Ns: set @ n,Tr1: dtree,Tr2: dtree] :
% 0.20/0.47 ( ( member @ n @ ( root @ Tr3 ) @ Ns )
% 0.20/0.47 => ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr2 )
% 0.20/0.47 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr3 ) )
% 0.20/0.47 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr.Step
% 0.20/0.47 thf(fact_223_subtr_Ocases,axiom,
% 0.20/0.47 ! [A1: set @ n,A22: dtree,A32: dtree] :
% 0.20/0.47 ( ( gram_L716654942_subtr @ A1 @ A22 @ A32 )
% 0.20/0.47 => ( ( ( A32 = A22 )
% 0.20/0.47 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.20/0.47 => ~ ( ( member @ n @ ( root @ A32 ) @ A1 )
% 0.20/0.47 => ! [Tr22: dtree] :
% 0.20/0.47 ( ( gram_L716654942_subtr @ A1 @ A22 @ Tr22 )
% 0.20/0.47 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ A32 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr.cases
% 0.20/0.47 thf(fact_224_subtr_Osimps,axiom,
% 0.20/0.47 ( gram_L716654942_subtr
% 0.20/0.47 = ( ^ [A12: set @ n,A23: dtree,A33: dtree] :
% 0.20/0.47 ( ? [Tr6: dtree,Ns2: set @ n] :
% 0.20/0.47 ( ( A12 = Ns2 )
% 0.20/0.47 & ( A23 = Tr6 )
% 0.20/0.47 & ( A33 = Tr6 )
% 0.20/0.47 & ( member @ n @ ( root @ Tr6 ) @ Ns2 ) )
% 0.20/0.47 | ? [Tr32: dtree,Ns2: set @ n,Tr12: dtree,Tr23: dtree] :
% 0.20/0.47 ( ( A12 = Ns2 )
% 0.20/0.47 & ( A23 = Tr12 )
% 0.20/0.47 & ( A33 = Tr32 )
% 0.20/0.47 & ( member @ n @ ( root @ Tr32 ) @ Ns2 )
% 0.20/0.47 & ( gram_L716654942_subtr @ Ns2 @ Tr12 @ Tr23 )
% 0.20/0.47 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ Tr32 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr.simps
% 0.20/0.47 thf(fact_225_subtr__StepL,axiom,
% 0.20/0.47 ! [Tr1: dtree,Ns: set @ n,Tr2: dtree,Tr3: dtree] :
% 0.20/0.47 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 0.20/0.47 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr2 ) )
% 0.20/0.47 => ( ( gram_L716654942_subtr @ Ns @ Tr2 @ Tr3 )
% 0.20/0.47 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr_StepL
% 0.20/0.47 thf(fact_226_subtr_Oinducts,axiom,
% 0.20/0.47 ! [X1: set @ n,X22: dtree,X32: dtree,P: ( set @ n ) > dtree > dtree > $o] :
% 0.20/0.47 ( ( gram_L716654942_subtr @ X1 @ X22 @ X32 )
% 0.20/0.47 => ( ! [Tr7: dtree,Ns3: set @ n] :
% 0.20/0.47 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 0.20/0.47 => ( P @ Ns3 @ Tr7 @ Tr7 ) )
% 0.20/0.47 => ( ! [Tr33: dtree,Ns3: set @ n,Tr13: dtree,Tr22: dtree] :
% 0.20/0.47 ( ( member @ n @ ( root @ Tr33 ) @ Ns3 )
% 0.20/0.47 => ( ( gram_L716654942_subtr @ Ns3 @ Tr13 @ Tr22 )
% 0.20/0.47 => ( ( P @ Ns3 @ Tr13 @ Tr22 )
% 0.20/0.47 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr33 ) )
% 0.20/0.47 => ( P @ Ns3 @ Tr13 @ Tr33 ) ) ) ) )
% 0.20/0.47 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr.inducts
% 0.20/0.47 thf(fact_227_subtr__inductL,axiom,
% 0.20/0.47 ! [Ns: set @ n,Tr1: dtree,Tr2: dtree,Phi: ( set @ n ) > dtree > dtree > $o] :
% 0.20/0.47 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr2 )
% 0.20/0.47 => ( ! [Ns3: set @ n,Tr7: dtree] : ( Phi @ Ns3 @ Tr7 @ Tr7 )
% 0.20/0.47 => ( ! [Ns3: set @ n,Tr13: dtree,Tr22: dtree,Tr33: dtree] :
% 0.20/0.47 ( ( member @ n @ ( root @ Tr13 ) @ Ns3 )
% 0.20/0.47 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr22 ) )
% 0.20/0.47 => ( ( gram_L716654942_subtr @ Ns3 @ Tr22 @ Tr33 )
% 0.20/0.47 => ( ( Phi @ Ns3 @ Tr22 @ Tr33 )
% 0.20/0.47 => ( Phi @ Ns3 @ Tr13 @ Tr33 ) ) ) ) )
% 0.20/0.47 => ( Phi @ Ns @ Tr1 @ Tr2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr_inductL
% 0.20/0.47 thf(fact_228_inItr_OInd,axiom,
% 0.20/0.47 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,N: n] :
% 0.20/0.47 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.20/0.47 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.20/0.47 => ( ( gram_L830233218_inItr @ Ns @ Tr1 @ N )
% 0.20/0.47 => ( gram_L830233218_inItr @ Ns @ Tr @ N ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inItr.Ind
% 0.20/0.47 thf(fact_229_inItr_Ocases,axiom,
% 0.20/0.47 ! [A1: set @ n,A22: dtree,A32: n] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ A1 @ A22 @ A32 )
% 0.20/0.47 => ( ( ( A32
% 0.20/0.47 = ( root @ A22 ) )
% 0.20/0.47 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.20/0.47 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.20/0.47 => ! [Tr13: dtree] :
% 0.20/0.47 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ A22 ) )
% 0.20/0.47 => ~ ( gram_L830233218_inItr @ A1 @ Tr13 @ A32 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inItr.cases
% 0.20/0.47 thf(fact_230_inItr_Osimps,axiom,
% 0.20/0.47 ( gram_L830233218_inItr
% 0.20/0.47 = ( ^ [A12: set @ n,A23: dtree,A33: n] :
% 0.20/0.47 ( ? [Tr6: dtree,Ns2: set @ n] :
% 0.20/0.47 ( ( A12 = Ns2 )
% 0.20/0.47 & ( A23 = Tr6 )
% 0.20/0.47 & ( A33
% 0.20/0.47 = ( root @ Tr6 ) )
% 0.20/0.47 & ( member @ n @ ( root @ Tr6 ) @ Ns2 ) )
% 0.20/0.47 | ? [Tr6: dtree,Ns2: set @ n,Tr12: dtree,N2: n] :
% 0.20/0.47 ( ( A12 = Ns2 )
% 0.20/0.47 & ( A23 = Tr6 )
% 0.20/0.47 & ( A33 = N2 )
% 0.20/0.47 & ( member @ n @ ( root @ Tr6 ) @ Ns2 )
% 0.20/0.47 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr6 ) )
% 0.20/0.47 & ( gram_L830233218_inItr @ Ns2 @ Tr12 @ N2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inItr.simps
% 0.20/0.47 thf(fact_231_inItr_Oinducts,axiom,
% 0.20/0.47 ! [X1: set @ n,X22: dtree,X32: n,P: ( set @ n ) > dtree > n > $o] :
% 0.20/0.47 ( ( gram_L830233218_inItr @ X1 @ X22 @ X32 )
% 0.20/0.47 => ( ! [Tr7: dtree,Ns3: set @ n] :
% 0.20/0.47 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 0.20/0.47 => ( P @ Ns3 @ Tr7 @ ( root @ Tr7 ) ) )
% 0.20/0.47 => ( ! [Tr7: dtree,Ns3: set @ n,Tr13: dtree,N5: n] :
% 0.20/0.47 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 0.20/0.47 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr7 ) )
% 0.20/0.47 => ( ( gram_L830233218_inItr @ Ns3 @ Tr13 @ N5 )
% 0.20/0.47 => ( ( P @ Ns3 @ Tr13 @ N5 )
% 0.20/0.47 => ( P @ Ns3 @ Tr7 @ N5 ) ) ) ) )
% 0.20/0.47 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inItr.inducts
% 0.20/0.47 thf(fact_232_case__sum__expand__Inr,axiom,
% 0.20/0.47 ! [B: $tType,C: $tType,A: $tType,F: ( sum_sum @ A @ C ) > B,G: A > B,X2: sum_sum @ A @ C] :
% 0.20/0.47 ( ( ( comp @ ( sum_sum @ A @ C ) @ B @ A @ F @ ( sum_Inl @ A @ C ) )
% 0.20/0.47 = G )
% 0.20/0.47 => ( ( F @ X2 )
% 0.20/0.47 = ( sum_case_sum @ A @ B @ C @ G @ ( comp @ ( sum_sum @ A @ C ) @ B @ C @ F @ ( sum_Inr @ C @ A ) ) @ X2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_sum_expand_Inr
% 0.20/0.47 thf(fact_233_case__sum__expand__Inr_H,axiom,
% 0.20/0.47 ! [B: $tType,C: $tType,A: $tType,F: ( sum_sum @ A @ C ) > B,G: A > B,H: C > B] :
% 0.20/0.47 ( ( ( comp @ ( sum_sum @ A @ C ) @ B @ A @ F @ ( sum_Inl @ A @ C ) )
% 0.20/0.47 = G )
% 0.20/0.47 => ( ( H
% 0.20/0.47 = ( comp @ ( sum_sum @ A @ C ) @ B @ C @ F @ ( sum_Inr @ C @ A ) ) )
% 0.20/0.47 = ( ( sum_case_sum @ A @ B @ C @ G @ H )
% 0.20/0.47 = F ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_sum_expand_Inr'
% 0.20/0.47 thf(fact_234_case__sum__expand__Inr__pointfree,axiom,
% 0.20/0.47 ! [B: $tType,C: $tType,A: $tType,F: ( sum_sum @ A @ C ) > B,G: A > B] :
% 0.20/0.47 ( ( ( comp @ ( sum_sum @ A @ C ) @ B @ A @ F @ ( sum_Inl @ A @ C ) )
% 0.20/0.47 = G )
% 0.20/0.47 => ( ( sum_case_sum @ A @ B @ C @ G @ ( comp @ ( sum_sum @ A @ C ) @ B @ C @ F @ ( sum_Inr @ C @ A ) ) )
% 0.20/0.47 = F ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_sum_expand_Inr_pointfree
% 0.20/0.47 thf(fact_235_corec_I1_J,axiom,
% 0.20/0.47 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) ),B2: A] :
% 0.20/0.47 ( ( root @ ( corec @ A @ Rt @ Ct @ B2 ) )
% 0.20/0.47 = ( Rt @ B2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % corec(1)
% 0.20/0.47 thf(fact_236_subtr__UNIV__inductL,axiom,
% 0.20/0.47 ! [Tr1: dtree,Tr2: dtree,Phi: dtree > dtree > $o] :
% 0.20/0.47 ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr1 @ Tr2 )
% 0.20/0.47 => ( ! [Tr7: dtree] : ( Phi @ Tr7 @ Tr7 )
% 0.20/0.47 => ( ! [Tr13: dtree,Tr22: dtree,Tr33: dtree] :
% 0.20/0.47 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr22 ) )
% 0.20/0.47 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr22 @ Tr33 )
% 0.20/0.47 => ( ( Phi @ Tr22 @ Tr33 )
% 0.20/0.47 => ( Phi @ Tr13 @ Tr33 ) ) ) )
% 0.20/0.47 => ( Phi @ Tr1 @ Tr2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtr_UNIV_inductL
% 0.20/0.47 thf(fact_237_inFr2__Ind,axiom,
% 0.20/0.47 ! [Ns: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 0.20/0.47 ( ( gram_L805317441_inFr2 @ Ns @ Tr1 @ T2 )
% 0.20/0.47 => ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.20/0.47 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.20/0.47 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inFr2_Ind
% 0.20/0.47 thf(fact_238_map__sum__o__inj_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,C: $tType,D: $tType,F: A > B,G: D > C] :
% 0.20/0.47 ( ( comp @ ( sum_sum @ A @ D ) @ ( sum_sum @ B @ C ) @ D @ ( sum_map_sum @ A @ B @ D @ C @ F @ G ) @ ( sum_Inr @ D @ A ) )
% 0.20/0.47 = ( comp @ C @ ( sum_sum @ B @ C ) @ D @ ( sum_Inr @ C @ B ) @ G ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_sum_o_inj(2)
% 0.20/0.47 thf(fact_239_root__subtrOf,axiom,
% 0.20/0.47 ! [N: n,Tr: dtree] :
% 0.20/0.47 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.20/0.47 => ( ( root @ ( gram_L1614515765ubtrOf @ Tr @ N ) )
% 0.20/0.47 = N ) ) ).
% 0.20/0.47
% 0.20/0.47 % root_subtrOf
% 0.20/0.47 thf(fact_240_surj__subtrOf,axiom,
% 0.20/0.47 ! [Tr: dtree,Tr5: dtree] :
% 0.20/0.47 ( ( gram_L864798063lle_wf @ Tr )
% 0.20/0.47 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr5 ) @ ( cont @ Tr ) )
% 0.20/0.47 => ? [N5: n] :
% 0.20/0.47 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N5 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.20/0.47 & ( ( gram_L1614515765ubtrOf @ Tr @ N5 )
% 0.20/0.47 = Tr5 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_subtrOf
% 0.20/0.47 thf(fact_241_subtrOf__root,axiom,
% 0.20/0.47 ! [Tr: dtree,Tr5: dtree] :
% 0.20/0.47 ( ( gram_L864798063lle_wf @ Tr )
% 0.20/0.47 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr5 ) @ ( cont @ Tr ) )
% 0.20/0.47 => ( ( gram_L1614515765ubtrOf @ Tr @ ( root @ Tr5 ) )
% 0.20/0.47 = Tr5 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtrOf_root
% 0.20/0.47 thf(fact_242_Inr__subtrOf,axiom,
% 0.20/0.47 ! [N: n,Tr: dtree] :
% 0.20/0.47 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.20/0.47 => ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( gram_L1614515765ubtrOf @ Tr @ N ) ) @ ( cont @ Tr ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Inr_subtrOf
% 0.20/0.47 thf(fact_243_subtrOf,axiom,
% 0.20/0.47 ! [N: n,Tr: dtree] :
% 0.20/0.47 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.20/0.47 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( gram_L1614515765ubtrOf @ Tr @ N ) ) @ ( cont @ Tr ) )
% 0.20/0.47 & ( ( root @ ( gram_L1614515765ubtrOf @ Tr @ N ) )
% 0.20/0.47 = N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subtrOf
% 0.20/0.47 thf(fact_244_obj__sumE,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 0.20/0.47 ( ! [X3: A] :
% 0.20/0.47 ( S
% 0.20/0.47 != ( sum_Inl @ A @ B @ X3 ) )
% 0.20/0.47 => ~ ! [X3: B] :
% 0.20/0.47 ( S
% 0.20/0.47 != ( sum_Inr @ B @ A @ X3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % obj_sumE
% 0.20/0.47 thf(fact_245_wf__subtr__inj__on,axiom,
% 0.20/0.47 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 0.20/0.47 ( ( gram_L864798063lle_wf @ Tr1 )
% 0.20/0.47 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.20/0.47 => ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % wf_subtr_inj_on
% 0.20/0.47 thf(fact_246_inj__on__image__iff,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,A4: set @ A,G: A > B,F: A > A] :
% 0.20/0.47 ( ! [X3: A] :
% 0.20/0.47 ( ( member @ A @ X3 @ A4 )
% 0.20/0.47 => ! [Xa2: A] :
% 0.20/0.47 ( ( member @ A @ Xa2 @ A4 )
% 0.20/0.47 => ( ( ( G @ ( F @ X3 ) )
% 0.20/0.47 = ( G @ ( F @ Xa2 ) ) )
% 0.20/0.47 = ( ( G @ X3 )
% 0.20/0.47 = ( G @ Xa2 ) ) ) ) )
% 0.20/0.47 => ( ( inj_on @ A @ A @ F @ A4 )
% 0.20/0.47 => ( ( inj_on @ A @ B @ G @ ( image @ A @ A @ F @ A4 ) )
% 0.20/0.47 = ( inj_on @ A @ B @ G @ A4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_image_iff
% 0.20/0.47 thf(fact_247_finite__image__iff,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F: A > B,A4: set @ A] :
% 0.20/0.47 ( ( inj_on @ A @ B @ F @ A4 )
% 0.20/0.47 => ( ( finite_finite2 @ B @ ( image @ A @ B @ F @ A4 ) )
% 0.20/0.47 = ( finite_finite2 @ A @ A4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_image_iff
% 0.20/0.47 thf(fact_248_finite__imageD,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,F: B > A,A4: set @ B] :
% 0.20/0.47 ( ( finite_finite2 @ A @ ( image @ B @ A @ F @ A4 ) )
% 0.20/0.47 => ( ( inj_on @ B @ A @ F @ A4 )
% 0.20/0.47 => ( finite_finite2 @ B @ A4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_imageD
% 0.20/0.47 thf(fact_249_range__ex1__eq,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F: A > B,B2: B] :
% 0.20/0.47 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.20/0.47 => ( ( member @ B @ B2 @ ( image @ A @ B @ F @ ( top_top @ ( set @ A ) ) ) )
% 0.20/0.47 = ( ? [X: A] :
% 0.20/0.47 ( ( B2
% 0.20/0.47 = ( F @ X ) )
% 0.20/0.47 & ! [Y3: A] :
% 0.20/0.47 ( ( B2
% 0.20/0.47 = ( F @ Y3 ) )
% 0.20/0.47 => ( Y3 = X ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % range_ex1_eq
% 0.20/0.47 thf(fact_250_inj__image__eq__iff,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F: A > B,A4: set @ A,B3: set @ A] :
% 0.20/0.47 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.20/0.47 => ( ( ( image @ A @ B @ F @ A4 )
% 0.20/0.47 = ( image @ A @ B @ F @ B3 ) )
% 0.20/0.47 = ( A4 = B3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_image_eq_iff
% 0.20/0.47 thf(fact_251_inj__image__mem__iff,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F: A > B,A2: A,A4: set @ A] :
% 0.20/0.47 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.20/0.47 => ( ( member @ B @ ( F @ A2 ) @ ( image @ A @ B @ F @ A4 ) )
% 0.20/0.47 = ( member @ A @ A2 @ A4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_image_mem_iff
% 0.20/0.47 thf(fact_252_comp__inj__on,axiom,
% 0.20/0.47 ! [B: $tType,C: $tType,A: $tType,F: A > B,A4: set @ A,G: B > C] :
% 0.20/0.47 ( ( inj_on @ A @ B @ F @ A4 )
% 0.20/0.47 => ( ( inj_on @ B @ C @ G @ ( image @ A @ B @ F @ A4 ) )
% 0.20/0.47 => ( inj_on @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ A4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % comp_inj_on
% 0.20/0.47 thf(fact_253_inj__on__imageI,axiom,
% 0.20/0.47 ! [B: $tType,C: $tType,A: $tType,G: C > B,F: A > C,A4: set @ A] :
% 0.20/0.47 ( ( inj_on @ A @ B @ ( comp @ C @ B @ A @ G @ F ) @ A4 )
% 0.20/0.47 => ( inj_on @ C @ B @ G @ ( image @ A @ C @ F @ A4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % inj_on_imageI
% 0.20/0.47 thf(fact_254_comp__inj__on__iff,axiom,
% 0.20/0.47 ! [B: $tType,C: $tType,A: $tType,F: A > B,A4: set @ A,F6: B > C] :
% 0.20/0.47 ( ( inj_on @ A @ B @ F @ A4 )
% 0.20/0.47 => ( ( inj_on @ B @ C @ F6 @ ( image @ A @ B @ F @ A4 ) )
% 0.20/0.47 = ( inj_on @ A @ C @ ( comp @ B @ C @ A @ F6 @ F ) @ A4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % comp_inj_on_iff
% 0.20/0.47 thf(fact_255_finite__UNIV__inj__surj,axiom,
% 0.20/0.47 ! [A: $tType,F: A > A] :
% 0.20/0.47 ( ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.20/0.47 => ( ( inj_on @ A @ A @ F @ ( top_top @ ( set @ A ) ) )
% 0.20/0.47 => ( ( image @ A @ A @ F @ ( top_top @ ( set @ A ) ) )
% 0.20/0.47 = ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % finite_UNIV_inj_surj
% 0.20/0.47
% 0.20/0.47 %----Type constructors (9)
% 0.20/0.47 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 0.20/0.47 ! [A8: $tType,A10: $tType] :
% 0.20/0.47 ( ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.20/0.47 & ( finite_finite @ A10 @ ( type2 @ A10 ) ) )
% 0.20/0.47 => ( finite_finite @ ( A8 > A10 ) @ ( type2 @ ( A8 > A10 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_fun___Orderings_Otop,axiom,
% 0.20/0.47 ! [A8: $tType,A10: $tType] :
% 0.20/0.47 ( ( top @ A10 @ ( type2 @ A10 ) )
% 0.20/0.47 => ( top @ ( A8 > A10 ) @ ( type2 @ ( A8 > A10 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Set_Oset___Finite__Set_Ofinite_1,axiom,
% 0.20/0.47 ! [A8: $tType] :
% 0.20/0.47 ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.20/0.47 => ( finite_finite @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Set_Oset___Orderings_Otop_2,axiom,
% 0.20/0.47 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Finite__Set_Ofinite_3,axiom,
% 0.20/0.47 finite_finite @ $o @ ( type2 @ $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Orderings_Otop_4,axiom,
% 0.20/0.47 top @ $o @ ( type2 @ $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_5,axiom,
% 0.20/0.47 ! [A8: $tType,A10: $tType] :
% 0.20/0.47 ( ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.20/0.47 & ( finite_finite @ A10 @ ( type2 @ A10 ) ) )
% 0.20/0.47 => ( finite_finite @ ( sum_sum @ A8 @ A10 ) @ ( type2 @ ( sum_sum @ A8 @ A10 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Option_Ooption___Finite__Set_Ofinite_6,axiom,
% 0.20/0.47 ! [A8: $tType] :
% 0.20/0.47 ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.20/0.47 => ( finite_finite @ ( option @ A8 ) @ ( type2 @ ( option @ A8 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_7,axiom,
% 0.20/0.47 ! [A8: $tType,A10: $tType] :
% 0.20/0.47 ( ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.20/0.47 & ( finite_finite @ A10 @ ( type2 @ A10 ) ) )
% 0.20/0.47 => ( finite_finite @ ( product_prod @ A8 @ A10 ) @ ( type2 @ ( product_prod @ A8 @ A10 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %----Helper facts (3)
% 0.20/0.47 thf(help_If_3_1_T,axiom,
% 0.20/0.47 ! [P: $o] :
% 0.20/0.47 ( ( P = $true )
% 0.20/0.47 | ( P = $false ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(help_If_2_1_T,axiom,
% 0.20/0.47 ! [A: $tType,X2: A,Y: A] :
% 0.20/0.47 ( ( if @ A @ $false @ X2 @ Y )
% 0.20/0.47 = Y ) ).
% 0.20/0.47
% 0.20/0.47 thf(help_If_1_1_T,axiom,
% 0.20/0.47 ! [A: $tType,X2: A,Y: A] :
% 0.20/0.47 ( ( if @ A @ $true @ X2 @ Y )
% 0.20/0.47 = X2 ) ).
% 0.20/0.47
% 0.20/0.47 %----Conjectures (4)
% 0.20/0.47 thf(conj_0,hypothesis,
% 0.20/0.47 $true ).
% 0.20/0.47
% 0.20/0.47 thf(conj_1,hypothesis,
% 0.20/0.47 $true ).
% 0.20/0.47
% 0.20/0.47 thf(conj_2,hypothesis,
% 0.20/0.47 ( t_tr
% 0.20/0.47 = ( sum_Inl @ t @ dtree @ a ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(conj_3,conjecture,
% 0.20/0.47 ( ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ ( comp @ n @ n @ dtree @ ( comp @ dtree @ n @ n @ root @ ( gram_L1451583624elle_H @ tr0 ) ) @ root ) @ t_tr )
% 0.20/0.47 = ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root @ t_tr ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 0.32/1.50 ---- Embedded in THF ---
% 0.32/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.51 %%% Generated on Tue Feb 24 04:18:19 EST 2026
% 0.32/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.51 %%% Logic specification used:
% 0.32/1.51 %%% thf(spec, logic, $$dhol).
% 0.32/1.51
% 0.32/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.jDfwb26t2m/DTF2DTF25971.p
% 0.32/1.51 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 0.32/1.51 thf(ty_t_Sum__Type_Osum, type, sum_sum: ($tType > ($tType > $tType))).
% 0.32/1.51 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 0.32/1.51 thf(ty_t_DTree_Odtree, type, dtree: $tType).
% 0.32/1.51 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.32/1.51 thf(ty_t_DTree_OT, type, t: $tType).
% 0.32/1.51 thf(ty_t_DTree_ON, type, n: $tType).
% 0.32/1.51 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 0.32/1.51 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Nat_Osemiring__char__0, type, semiring_char_0: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_c_DTree_ONode, type, node: (n > ((set @ ((sum_sum @ t) @ dtree)) > dtree))).
% 0.32/1.51 thf(sy_c_DTree_Ocont, type, cont: (dtree > (set @ ((sum_sum @ t) @ dtree)))).
% 0.32/1.51 thf(sy_c_DTree_Ocorec, type, corec: (!> [A:$tType]: (((A > n) > ((A > (set @ ((sum_sum @ t) @ ((sum_sum @ dtree) @ A)))) > (A > dtree)))))).
% 0.32/1.51 thf(sy_c_DTree_Odtree_Oroot, type, root: (dtree > n)).
% 0.32/1.51 thf(sy_c_DTree_Ounfold, type, unfold: (!> [A:$tType]: (((A > n) > ((A > (set @ ((sum_sum @ t) @ A))) > (A > dtree)))))).
% 0.32/1.51 thf(sy_c_Finite__Set_Ofinite, type, finite_finite2: (!> [A:$tType]: (((set @ A) > $o)))).
% 0.32/1.51 thf(sy_c_Fun_Ocomp, type, comp: (!> [B:$tType,C:$tType,A:$tType]: (((B > C) > ((A > B) > (A > C)))))).
% 0.32/1.51 thf(sy_c_Fun_Oid, type, id: (!> [A:$tType]: ((A > A)))).
% 0.32/1.51 thf(sy_c_Fun_Oinj__on, type, inj_on: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > $o))))).
% 0.32/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH, type, gram_L1451583624elle_H: (dtree > (n > dtree))).
% 0.32/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__c, type, gram_L1221482011le_H_c: (dtree > (n > (set @ ((sum_sum @ t) @ n))))).
% 0.32/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__r, type, gram_L1221482026le_H_r: (dtree > (n > n))).
% 0.32/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OS, type, gram_L1451583635elle_S: (n > (set @ ((sum_sum @ t) @ n)))).
% 0.32/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr, type, gram_L1231612515_deftr: (n > dtree)).
% 0.32/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst, type, gram_L1004374585hsubst: (dtree > (dtree > dtree))).
% 0.32/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c, type, gram_L1905609002ubst_c: (dtree > (dtree > (set @ ((sum_sum @ t) @ dtree))))).
% 0.32/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r, type, gram_L1905609017ubst_r: (dtree > n)).
% 0.32/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2, type, gram_L805317441_inFr2: ((set @ n) > (dtree > (t > $o)))).
% 0.32/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr, type, gram_L830233218_inItr: ((set @ n) > (dtree > (n > $o)))).
% 0.32/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Opick, type, gram_L315592705e_pick: (dtree > (n > dtree))).
% 0.32/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr, type, gram_L716654942_subtr: ((set @ n) > (dtree > (dtree > $o)))).
% 0.32/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OsubtrOf, type, gram_L1614515765ubtrOf: (dtree > (n > dtree))).
% 0.32/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf, type, gram_L864798063lle_wf: (dtree > $o)).
% 0.32/1.51 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 0.32/1.51 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 0.32/1.51 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 0.32/1.51 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.32/1.51 thf(sy_c_Set_Oimage, type, image: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > (set @ B)))))).
% 0.32/1.51 thf(sy_c_Set_Ovimage, type, vimage: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ B) > (set @ A)))))).
% 0.32/1.51 thf(sy_c_Sum__Type_OInl, type, sum_Inl: (!> [A:$tType,B:$tType]: ((A > ((sum_sum @ A) @ B))))).
% 0.32/1.51 thf(sy_c_Sum__Type_OInr, type, sum_Inr: (!> [B:$tType,A:$tType]: ((B > ((sum_sum @ A) @ B))))).
% 0.32/1.51 thf(sy_c_Sum__Type_Omap__sum, type, sum_map_sum: (!> [A:$tType,C:$tType,B:$tType,D:$tType]: (((A > C) > ((B > D) > (((sum_sum @ A) @ B) > ((sum_sum @ C) @ D))))))).
% 0.32/1.51 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum, type, sum_rec_sum: (!> [A:$tType,T:$tType,B:$tType]: (((A > T) > ((B > T) > (((sum_sum @ A) @ B) > T)))))).
% 0.32/1.51 thf(sy_c_Sum__Type_Osum_Ocase__sum, type, sum_case_sum: (!> [A:$tType,C:$tType,B:$tType]: (((A > C) > ((B > C) > (((sum_sum @ A) @ B) > C)))))).
% 0.32/1.51 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.32/1.51 thf(sy_v_a, type, a: t).
% 0.32/1.51 thf(sy_v_n, type, n2: n).
% 0.32/1.51 thf(sy_v_t__tr, type, t_tr: ((sum_sum @ t) @ dtree)).
% 0.32/1.51 thf(sy_v_tr0, type, tr0: dtree).
% 0.32/1.51 thf(fact_0_n, axiom, (((gram_L830233218_inItr @ (top_top @ (set @ n))) @ tr0) @ n2)).
% 0.32/1.51 thf(fact_1_root__H__pick, axiom, (! [N:n]: (((root @ ((gram_L1451583624elle_H @ tr0) @ N)) = (root @ ((gram_L315592705e_pick @ tr0) @ N)))))).
% 0.32/1.51 thf(fact_2_t__tr, axiom, (((member @ ((sum_sum @ t) @ dtree)) @ t_tr) @ (cont @ ((gram_L315592705e_pick @ tr0) @ n2)))).
% 0.32/1.51 thf(fact_3_root__pick, axiom, (! [N:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ tr0) @ N) => ((root @ ((gram_L315592705e_pick @ tr0) @ N)) = N))))).
% 0.32/1.51 thf(fact_4_H__r__def, axiom, (! [N:n]: ((((gram_L1221482026le_H_r @ tr0) @ N) = (root @ ((gram_L315592705e_pick @ tr0) @ N)))))).
% 0.32/1.51 thf(fact_5_root__H, axiom, (! [N:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ tr0) @ N) => ((root @ ((gram_L1451583624elle_H @ tr0) @ N)) = N))))).
% 0.32/1.51 thf(fact_6_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__H, axiom, (! [Tr0:dtree,N:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N) => ((root @ ((gram_L1451583624elle_H @ Tr0) @ N)) = N))))).
% 0.32/1.51 thf(fact_7_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__pick, axiom, (! [Tr0:dtree,N:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N) => ((root @ ((gram_L315592705e_pick @ Tr0) @ N)) = N))))).
% 0.32/1.51 thf(fact_8_inItr_OBase, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L830233218_inItr @ Ns) @ Tr) @ (root @ Tr)))))).
% 0.32/1.51 thf(fact_9_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__H__pick, axiom, (! [Tr0:dtree,N:n]: (((root @ ((gram_L1451583624elle_H @ Tr0) @ N)) = (root @ ((gram_L315592705e_pick @ Tr0) @ N)))))).
% 0.32/1.51 thf(fact_10_inItr__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,N:n]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 0.32/1.51 thf(fact_11_wf__pick, axiom, (! [N:n]: (((gram_L864798063lle_wf @ tr0) => ((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ tr0) @ N) => (gram_L864798063lle_wf @ ((gram_L315592705e_pick @ tr0) @ N))))))).
% 0.32/1.51 thf(fact_12_pick, axiom, (! [N:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ tr0) @ N) => ((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ ((gram_L315592705e_pick @ tr0) @ N)) @ tr0) & ((root @ ((gram_L315592705e_pick @ tr0) @ N)) = N)))))).
% 0.32/1.51 thf(fact_13_comp__id, axiom, (! [B:$tType,A:$tType,F:(A > B)]: (((((((comp @ A) @ B) @ A) @ F) @ (id @ A)) = F)))).
% 0.32/1.51 thf(fact_14_id__comp, axiom, (! [B:$tType,A:$tType,G:(A > B)]: (((((((comp @ B) @ B) @ A) @ (id @ B)) @ G) = G)))).
% 0.32/1.51 thf(fact_15_fun_Omap__id, axiom, (! [A:$tType,D:$tType,T2:(D > A)]: (((((((comp @ A) @ A) @ D) @ (id @ A)) @ T2) = T2)))).
% 0.32/1.51 thf(fact_16_subtr__H, axiom, (! [N:n,Tr1:dtree]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ tr0) @ N) => ((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ Tr1) @ ((gram_L1451583624elle_H @ tr0) @ N)) => (? [N1:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ tr0) @ N1) & (Tr1 = ((gram_L1451583624elle_H @ tr0) @ N1)))))))))).
% 0.32/1.51 thf(fact_17_subtr__pick, axiom, (! [N:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ tr0) @ N) => (((gram_L716654942_subtr @ (top_top @ (set @ n))) @ ((gram_L315592705e_pick @ tr0) @ N)) @ tr0))))).
% 0.32/1.51 thf(fact_18_sum_Oinject_I1_J, axiom, (! [B:$tType,A:$tType,X1:A,Y1:A]: ((((((sum_Inl @ A) @ B) @ X1) = (((sum_Inl @ A) @ B) @ Y1)) = (X1 = Y1))))).
% 0.32/1.51 thf(fact_19_old_Osum_Oinject_I1_J, axiom, (! [B:$tType,A:$tType,A2:A,A3:A]: ((((((sum_Inl @ A) @ B) @ A2) = (((sum_Inl @ A) @ B) @ A3)) = (A2 = A3))))).
% 0.32/1.51 thf(fact_20_id__apply, axiom, (! [A:$tType]: (((id @ A) = (^ [X:A]: (X)))))).
% 0.32/1.51 thf(fact_21_comp__apply, axiom, (! [C:$tType,A:$tType,B:$tType]: (((((comp @ B) @ A) @ C) = (^ [F2:(B > A),G2:(C > B),X:C]: ((F2 @ (G2 @ X)))))))).
% 0.32/1.51 thf(fact_22_UNIV__I, axiom, (! [A:$tType,X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A)))))).
% 0.32/1.51 thf(fact_23_wf__subtr, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr:dtree]: (((gram_L864798063lle_wf @ Tr1) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => (gram_L864798063lle_wf @ Tr)))))).
% 0.32/1.51 thf(fact_24_subtr__trans, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr2:dtree,Tr3:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr2) => ((((gram_L716654942_subtr @ Ns) @ Tr2) @ Tr3) => (((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr3)))))).
% 0.32/1.51 thf(fact_25_subtr__rootR__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr2:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr2) => (((member @ n) @ (root @ Tr2)) @ Ns))))).
% 0.32/1.51 thf(fact_26_subtr__rootL__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr2:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr2) => (((member @ n) @ (root @ Tr1)) @ Ns))))).
% 0.32/1.51 thf(fact_27_subtr_ORefl, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L716654942_subtr @ Ns) @ Tr) @ Tr))))).
% 0.32/1.51 thf(fact_28_subtr__inItr, axiom, (! [Ns:(set @ n),Tr:dtree,N:n,Tr1:dtree]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => (((gram_L830233218_inItr @ Ns) @ Tr1) @ N)))))).
% 0.32/1.51 thf(fact_29_inItr__subtr, axiom, (! [Ns:(set @ n),Tr:dtree,N:n]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N) => (? [Tr4:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr4) @ Tr) & ((root @ Tr4) = N)))))))).
% 0.32/1.51 thf(fact_30_UNIV__witness, axiom, (! [A:$tType]: ((? [X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))))).
% 0.32/1.51 thf(fact_31_UNIV__eq__I, axiom, (! [A:$tType,A4:(set @ A)]: (((! [X3:A]: ((((member @ A) @ X3) @ A4))) => ((top_top @ (set @ A)) = A4))))).
% 0.32/1.51 thf(fact_32_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))))).
% 0.32/1.51 thf(fact_33_comp__eq__dest__lhs, axiom, (! [C:$tType,B:$tType,A:$tType,A2:(C > B),B2:(A > C),C2:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = C2) => ((A2 @ (B2 @ V)) = (C2 @ V)))))).
% 0.32/1.51 thf(fact_34_comp__eq__elim, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A2:(C > B),B2:(A > C),C2:(D > B),D2:(A > D)]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = (((((comp @ D) @ B) @ A) @ C2) @ D2)) => (! [V2:A]: (((A2 @ (B2 @ V2)) = (C2 @ (D2 @ V2))))))))).
% 0.32/1.51 thf(fact_35_comp__eq__dest, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A2:(C > B),B2:(A > C),C2:(D > B),D2:(A > D),V:A]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = (((((comp @ D) @ B) @ A) @ C2) @ D2)) => ((A2 @ (B2 @ V)) = (C2 @ (D2 @ V))))))).
% 0.32/1.51 thf(fact_36_comp__assoc, axiom, (! [B:$tType,D:$tType,C:$tType,A:$tType,F:(D > B),G:(C > D),H:(A > C)]: (((((((comp @ C) @ B) @ A) @ (((((comp @ D) @ B) @ C) @ F) @ G)) @ H) = (((((comp @ D) @ B) @ A) @ F) @ (((((comp @ C) @ D) @ A) @ G) @ H)))))).
% 0.32/1.51 thf(fact_37_comp__def, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((comp @ B) @ C) @ A) = (^ [F2:(B > C),G2:(A > B),X:A]: ((F2 @ (G2 @ X)))))))).
% 0.32/1.51 thf(fact_38_eq__id__iff, axiom, (! [A:$tType,F:(A > A)]: (((! [X:A]: (((F @ X) = X))) = (F = (id @ A)))))).
% 0.32/1.51 thf(fact_39_id__def, axiom, (! [A:$tType]: (((id @ A) = (^ [X:A]: (X)))))).
% 0.32/1.51 thf(fact_40_Inl__inject, axiom, (! [B:$tType,A:$tType,X2:A,Y:A]: ((((((sum_Inl @ A) @ B) @ X2) = (((sum_Inl @ A) @ B) @ Y)) => (X2 = Y))))).
% 0.32/1.51 thf(fact_41_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr__pick, axiom, (! [Tr0:dtree,N:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N) => (((gram_L716654942_subtr @ (top_top @ (set @ n))) @ ((gram_L315592705e_pick @ Tr0) @ N)) @ Tr0))))).
% 0.32/1.51 thf(fact_42_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr__H, axiom, (! [Tr0:dtree,N:n,Tr1:dtree]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N) => ((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ Tr1) @ ((gram_L1451583624elle_H @ Tr0) @ N)) => (? [N1:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N1) & (Tr1 = ((gram_L1451583624elle_H @ Tr0) @ N1)))))))))).
% 0.32/1.51 thf(fact_43_Gram__Lang__Mirabelle__ojxrtuoybn_Owf__pick, axiom, (! [Tr0:dtree,N:n]: (((gram_L864798063lle_wf @ Tr0) => ((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N) => (gram_L864798063lle_wf @ ((gram_L315592705e_pick @ Tr0) @ N))))))).
% 0.32/1.51 thf(fact_44_Gram__Lang__Mirabelle__ojxrtuoybn_Opick, axiom, (! [Tr0:dtree,N:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N) => ((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ ((gram_L315592705e_pick @ Tr0) @ N)) @ Tr0) & ((root @ ((gram_L315592705e_pick @ Tr0) @ N)) = N)))))).
% 0.32/1.51 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 0.32/1.51 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A4)))) = A4)))).
% 0.32/1.51 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.32/1.51 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 0.32/1.51 thf(fact_49_Gram__Lang__Mirabelle__ojxrtuoybn_OH__r__def, axiom, (gram_L1221482026le_H_r = (^ [Tr02:dtree,N2:n]: ((root @ ((gram_L315592705e_pick @ Tr02) @ N2)))))).
% 0.32/1.51 thf(fact_50_fun_Omap__id0, axiom, (! [A:$tType,D:$tType]: ((((((comp @ A) @ A) @ D) @ (id @ A)) = (id @ (D > A)))))).
% 0.32/1.51 thf(fact_51_comp__eq__id__dest, axiom, (! [C:$tType,B:$tType,A:$tType,A2:(C > B),B2:(A > C),C2:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = (((((comp @ B) @ B) @ A) @ (id @ B)) @ C2)) => ((A2 @ (B2 @ V)) = (C2 @ V)))))).
% 0.32/1.51 thf(fact_52_map__sum_Ocompositionality, axiom, (! [D:$tType,F3:$tType,E:$tType,C:$tType,B:$tType,A:$tType,F:(C > E),G:(D > F3),H:(A > C),I:(B > D),Sum:((sum_sum @ A) @ B)]: (((((((((sum_map_sum @ C) @ E) @ D) @ F3) @ F) @ G) @ (((((((sum_map_sum @ A) @ C) @ B) @ D) @ H) @ I) @ Sum)) = (((((((sum_map_sum @ A) @ E) @ B) @ F3) @ (((((comp @ C) @ E) @ A) @ F) @ H)) @ (((((comp @ D) @ F3) @ B) @ G) @ I)) @ Sum))))).
% 0.32/1.51 thf(fact_53_sum_Omap__comp, axiom, (! [D:$tType,F3:$tType,E:$tType,C:$tType,B:$tType,A:$tType,G1:(C > E),G22:(D > F3),F1:(A > C),F22:(B > D),V:((sum_sum @ A) @ B)]: (((((((((sum_map_sum @ C) @ E) @ D) @ F3) @ G1) @ G22) @ (((((((sum_map_sum @ A) @ C) @ B) @ D) @ F1) @ F22) @ V)) = (((((((sum_map_sum @ A) @ E) @ B) @ F3) @ (((((comp @ C) @ E) @ A) @ G1) @ F1)) @ (((((comp @ D) @ F3) @ B) @ G22) @ F22)) @ V))))).
% 0.32/1.51 thf(fact_54_map__sum_Ocomp, axiom, (! [A:$tType,C:$tType,E:$tType,F3:$tType,D:$tType,B:$tType,F:(C > E),G:(D > F3),H:(A > C),I:(B > D)]: (((((((comp @ ((sum_sum @ C) @ D)) @ ((sum_sum @ E) @ F3)) @ ((sum_sum @ A) @ B)) @ ((((((sum_map_sum @ C) @ E) @ D) @ F3) @ F) @ G)) @ ((((((sum_map_sum @ A) @ C) @ B) @ D) @ H) @ I)) = ((((((sum_map_sum @ A) @ E) @ B) @ F3) @ (((((comp @ C) @ E) @ A) @ F) @ H)) @ (((((comp @ D) @ F3) @ B) @ G) @ I)))))).
% 0.32/1.51 thf(fact_55_sum_Omap__id0, axiom, (! [B:$tType,A:$tType]: ((((((((sum_map_sum @ A) @ A) @ B) @ B) @ (id @ A)) @ (id @ B)) = (id @ ((sum_sum @ A) @ B)))))).
% 0.32/1.51 thf(fact_56_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)))).
% 0.32/1.51 thf(fact_57_map__sum_Osimps_I1_J, axiom, (! [B:$tType,D:$tType,C:$tType,A:$tType,F1:(A > C),F22:(B > D),A2:A]: (((((((((sum_map_sum @ A) @ C) @ B) @ D) @ F1) @ F22) @ (((sum_Inl @ A) @ B) @ A2)) = (((sum_Inl @ C) @ D) @ (F1 @ A2)))))).
% 0.32/1.51 thf(fact_58_H__def, axiom, ((gram_L1451583624elle_H @ tr0) = (((unfold @ n) @ (gram_L1221482026le_H_r @ tr0)) @ (gram_L1221482011le_H_c @ tr0)))).
% 0.32/1.51 thf(fact_59_root__o__deftr, axiom, ((((((comp @ dtree) @ n) @ n) @ root) @ gram_L1231612515_deftr) = (id @ n))).
% 0.32/1.51 thf(fact_60_iso__tuple__UNIV__I, axiom, (! [A:$tType,X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A)))))).
% 0.32/1.51 thf(fact_61_top__apply, axiom, (! [C:$tType,D:$tType]: ((((top @ C) @ (type2 @ C)) => ((top_top @ (D > C)) = (^ [X:D]: ((top_top @ C)))))))).
% 0.32/1.51 thf(fact_62_H__c__def, axiom, (! [N:n]: ((((gram_L1221482011le_H_c @ tr0) @ N) = ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ ((gram_L315592705e_pick @ tr0) @ N))))))).
% 0.32/1.51 thf(fact_63_old_Osum_Osimps_I7_J, axiom, (! [B:$tType,T:$tType,A:$tType,F1:(A > T),F22:(B > T),A2:A]: ((((((((sum_rec_sum @ A) @ T) @ B) @ F1) @ F22) @ (((sum_Inl @ A) @ B) @ A2)) = (F1 @ A2))))).
% 0.32/1.51 thf(fact_64_map__sum__o__inj_I1_J, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,F:(A > B),G:(D > C)]: (((((((comp @ ((sum_sum @ A) @ D)) @ ((sum_sum @ B) @ C)) @ A) @ ((((((sum_map_sum @ A) @ B) @ D) @ C) @ F) @ G)) @ ((sum_Inl @ A) @ D)) = (((((comp @ B) @ ((sum_sum @ B) @ C)) @ A) @ ((sum_Inl @ B) @ C)) @ F))))).
% 0.32/1.51 thf(fact_65_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)))))))).
% 0.32/1.51 thf(fact_66_map__sum__if__distrib__then_I1_J, axiom, (! [D:$tType,B:$tType,C:$tType,A:$tType,E2:$o,F:(A > B),G:(C > D),X2:A,Y:((sum_sum @ A) @ C)]: (((E2 => ((((((((sum_map_sum @ A) @ B) @ C) @ D) @ F) @ G) @ ((((if @ ((sum_sum @ A) @ C)) @ E2) @ (((sum_Inl @ A) @ C) @ X2)) @ Y)) = (((sum_Inl @ B) @ D) @ (F @ X2)))) & ((~ (E2)) => ((((((((sum_map_sum @ A) @ B) @ C) @ D) @ F) @ G) @ ((((if @ ((sum_sum @ A) @ C)) @ E2) @ (((sum_Inl @ A) @ C) @ X2)) @ Y)) = (((((((sum_map_sum @ A) @ B) @ C) @ D) @ F) @ G) @ Y))))))).
% 0.32/1.51 thf(fact_67_map__sum__if__distrib__else_I1_J, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,E2:$o,F:(A > B),G:(C > D),X2:((sum_sum @ A) @ C),Y:A]: (((E2 => ((((((((sum_map_sum @ A) @ B) @ C) @ D) @ F) @ G) @ ((((if @ ((sum_sum @ A) @ C)) @ E2) @ X2) @ (((sum_Inl @ A) @ C) @ Y))) = (((((((sum_map_sum @ A) @ B) @ C) @ D) @ F) @ G) @ X2))) & ((~ (E2)) => ((((((((sum_map_sum @ A) @ B) @ C) @ D) @ F) @ G) @ ((((if @ ((sum_sum @ A) @ C)) @ E2) @ X2) @ (((sum_Inl @ A) @ C) @ Y))) = (((sum_Inl @ B) @ D) @ (F @ Y)))))))).
% 0.32/1.51 thf(fact_68_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))))))).
% 0.32/1.51 thf(fact_69_image__id, axiom, (! [A:$tType]: (((((image @ A) @ A) @ (id @ A)) = (id @ (set @ A)))))).
% 0.32/1.51 thf(fact_70_root__deftr, axiom, (! [N:n]: (((root @ (gram_L1231612515_deftr @ N)) = N)))).
% 0.32/1.51 thf(fact_71_Inl__oplus__iff, axiom, (! [B:$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))))).
% 0.32/1.51 thf(fact_72_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)))))).
% 0.32/1.51 thf(fact_73_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))))))))).
% 0.32/1.51 thf(fact_74_bex__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A4:(set @ B),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((((image @ B) @ A) @ F) @ A4)) & (P @ X4)))) => (? [X3:B]: (((((member @ B) @ X3) @ A4) & (P @ (F @ X3))))))))).
% 0.32/1.51 thf(fact_75_image__cong, axiom, (! [B:$tType,A:$tType,M:(set @ A),N3:(set @ A),F:(A > B),G:(A > B)]: (((M = N3) => ((! [X3:A]: (((((member @ A) @ X3) @ N3) => ((F @ X3) = (G @ X3))))) => (((((image @ A) @ B) @ F) @ M) = ((((image @ A) @ B) @ G) @ N3))))))).
% 0.32/1.51 thf(fact_76_ball__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A4:(set @ B),P:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ ((((image @ B) @ A) @ F) @ A4)) => (P @ X3)))) => (! [X4:B]: (((((member @ B) @ X4) @ A4) => (P @ (F @ X4))))))))).
% 0.32/1.51 thf(fact_77_rev__image__eqI, axiom, (! [B:$tType,A:$tType,X2:A,A4:(set @ A),B2:B,F:(A > B)]: (((((member @ A) @ X2) @ A4) => ((B2 = (F @ X2)) => (((member @ B) @ B2) @ ((((image @ A) @ B) @ F) @ A4))))))).
% 0.32/1.51 thf(fact_78_surjD, axiom, (! [A:$tType,B:$tType,F:(B > A),Y:A]: (((((((image @ B) @ A) @ F) @ (top_top @ (set @ B))) = (top_top @ (set @ A))) => (? [X3:B]: ((Y = (F @ X3)))))))).
% 0.32/1.51 thf(fact_79_surjE, axiom, (! [A:$tType,B:$tType,F:(B > A),Y:A]: (((((((image @ B) @ A) @ F) @ (top_top @ (set @ B))) = (top_top @ (set @ A))) => (~ ((! [X3:B]: ((Y != (F @ X3)))))))))).
% 0.32/1.51 thf(fact_80_surjI, axiom, (! [B:$tType,A:$tType,G:(B > A),F:(A > B)]: (((! [X3:A]: (((G @ (F @ X3)) = X3))) => (((((image @ B) @ A) @ G) @ (top_top @ (set @ B))) = (top_top @ (set @ A))))))).
% 0.32/1.51 thf(fact_81_rangeI, axiom, (! [A:$tType,B:$tType,F:(B > A),X2:B]: ((((member @ A) @ (F @ X2)) @ ((((image @ B) @ A) @ F) @ (top_top @ (set @ B))))))).
% 0.32/1.51 thf(fact_82_surj__def, axiom, (! [B:$tType,A:$tType,F:(B > A)]: (((((((image @ B) @ A) @ F) @ (top_top @ (set @ B))) = (top_top @ (set @ A))) = (! [Y3:A]: ((? [X:B]: ((Y3 = (F @ X)))))))))).
% 0.32/1.51 thf(fact_83_range__eqI, axiom, (! [A:$tType,B:$tType,B2:A,F:(B > A),X2:B]: (((B2 = (F @ X2)) => (((member @ A) @ B2) @ ((((image @ B) @ A) @ F) @ (top_top @ (set @ B)))))))).
% 0.32/1.51 thf(fact_84_image__comp, axiom, (! [B:$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))))).
% 0.32/1.51 thf(fact_85_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),H:(A > D)]: (((((((image @ B) @ A) @ F) @ A4) = ((((image @ C) @ A) @ G) @ B3)) => (((((image @ B) @ D) @ (((((comp @ A) @ D) @ B) @ H) @ F)) @ A4) = ((((image @ C) @ D) @ (((((comp @ A) @ D) @ C) @ H) @ G)) @ B3)))))).
% 0.32/1.51 thf(fact_86_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 0.32/1.51 thf(fact_87_comp__surj, axiom, (! [B:$tType,A:$tType,C:$tType,F:(B > A),G:(A > C)]: (((((((image @ B) @ A) @ F) @ (top_top @ (set @ B))) = (top_top @ (set @ A))) => ((((((image @ A) @ C) @ G) @ (top_top @ (set @ A))) = (top_top @ (set @ C))) => (((((image @ B) @ C) @ (((((comp @ A) @ C) @ B) @ G) @ F)) @ (top_top @ (set @ B))) = (top_top @ (set @ C)))))))).
% 0.32/1.51 thf(fact_88_fun_Oset__map, axiom, (! [B:$tType,A:$tType,D:$tType,F:(A > B),V:(D > A)]: ((((((image @ D) @ B) @ (((((comp @ A) @ B) @ D) @ F) @ V)) @ (top_top @ (set @ D))) = ((((image @ A) @ B) @ F) @ ((((image @ D) @ A) @ V) @ (top_top @ (set @ D)))))))).
% 0.32/1.51 thf(fact_89_fun_Omap__cong, axiom, (! [B:$tType,A:$tType,D:$tType,X2:(D > A),Ya:(D > A),F:(A > B),G:(A > B)]: (((X2 = Ya) => ((! [Z2:A]: (((((member @ A) @ Z2) @ ((((image @ D) @ A) @ Ya) @ (top_top @ (set @ D)))) => ((F @ Z2) = (G @ Z2))))) => ((((((comp @ A) @ B) @ D) @ F) @ X2) = (((((comp @ A) @ B) @ D) @ G) @ Ya))))))).
% 0.32/1.51 thf(fact_90_fun_Omap__cong0, axiom, (! [B:$tType,A:$tType,D:$tType,X2:(D > A),F:(A > B),G:(A > B)]: (((! [Z2:A]: (((((member @ A) @ Z2) @ ((((image @ D) @ A) @ X2) @ (top_top @ (set @ D)))) => ((F @ Z2) = (G @ Z2))))) => ((((((comp @ A) @ B) @ D) @ F) @ X2) = (((((comp @ A) @ B) @ D) @ G) @ X2)))))).
% 0.32/1.51 thf(fact_91_fun_Oinj__map__strong, axiom, (! [B:$tType,A:$tType,D:$tType,X2:(D > A),Xa:(D > A),F:(A > B),Fa:(A > B)]: (((! [Z2:A,Za:A]: (((((member @ A) @ Z2) @ ((((image @ D) @ A) @ X2) @ (top_top @ (set @ D)))) => ((((member @ A) @ Za) @ ((((image @ D) @ A) @ Xa) @ (top_top @ (set @ D)))) => (((F @ Z2) = (Fa @ Za)) => (Z2 = Za)))))) => (((((((comp @ A) @ B) @ D) @ F) @ X2) = (((((comp @ A) @ B) @ D) @ Fa) @ Xa)) => (X2 = Xa)))))).
% 0.32/1.51 thf(fact_92_surj__id, axiom, (! [A:$tType]: ((((((image @ A) @ A) @ (id @ A)) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))).
% 0.32/1.51 thf(fact_93_Inl__oplus__elim, axiom, (! [B:$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))))).
% 0.32/1.51 thf(fact_94_wf__deftr, axiom, (! [N:n]: ((gram_L864798063lle_wf @ (gram_L1231612515_deftr @ N))))).
% 0.32/1.51 thf(fact_95_Gram__Lang__Mirabelle__ojxrtuoybn_OH__def, axiom, (gram_L1451583624elle_H = (^ [Tr02:dtree]: ((((unfold @ n) @ (gram_L1221482026le_H_r @ Tr02)) @ (gram_L1221482011le_H_c @ Tr02)))))).
% 0.32/1.51 thf(fact_96_comp__apply__eq, axiom, (! [B:$tType,D:$tType,A:$tType,C:$tType,F:(B > A),G:(C > B),X2:C,H:(D > A),K:(C > D)]: ((((F @ (G @ X2)) = (H @ (K @ X2))) => (((((((comp @ B) @ A) @ C) @ F) @ G) @ X2) = ((((((comp @ D) @ A) @ C) @ H) @ K) @ X2)))))).
% 0.32/1.51 thf(fact_97_rewriteL__comp__comp, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,F:(C > B),G:(A > C),L:(A > B),H:(D > A)]: ((((((((comp @ C) @ B) @ A) @ F) @ G) = L) => ((((((comp @ C) @ B) @ D) @ F) @ (((((comp @ A) @ C) @ D) @ G) @ H)) = (((((comp @ A) @ B) @ D) @ L) @ H)))))).
% 0.32/1.51 thf(fact_98_rewriteR__comp__comp, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,G:(C > B),H:(A > C),R:(A > B),F:(B > D)]: ((((((((comp @ C) @ B) @ A) @ G) @ H) = R) => ((((((comp @ C) @ D) @ A) @ (((((comp @ B) @ D) @ C) @ F) @ G)) @ H) = (((((comp @ B) @ D) @ A) @ F) @ R)))))).
% 0.32/1.51 thf(fact_99_rewriteL__comp__comp2, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,E:$tType,F:(C > B),G:(A > C),L1:(D > B),L2:(A > D),H:(E > A),R:(E > D)]: ((((((((comp @ C) @ B) @ A) @ F) @ G) = (((((comp @ D) @ B) @ A) @ L1) @ L2)) => (((((((comp @ A) @ D) @ E) @ L2) @ H) = R) => ((((((comp @ C) @ B) @ E) @ F) @ (((((comp @ A) @ C) @ E) @ G) @ H)) = (((((comp @ D) @ B) @ E) @ L1) @ R))))))).
% 0.32/1.51 thf(fact_100_rewriteR__comp__comp2, axiom, (! [C:$tType,B:$tType,E:$tType,D:$tType,A:$tType,G:(C > B),H:(A > C),R1:(D > B),R2:(A > D),F:(B > E),L:(D > E)]: ((((((((comp @ C) @ B) @ A) @ G) @ H) = (((((comp @ D) @ B) @ A) @ R1) @ R2)) => (((((((comp @ B) @ E) @ D) @ F) @ R1) = L) => ((((((comp @ C) @ E) @ A) @ (((((comp @ B) @ E) @ C) @ F) @ G)) @ H) = (((((comp @ D) @ E) @ A) @ L) @ R2))))))).
% 0.32/1.51 thf(fact_101_Gram__Lang__Mirabelle__ojxrtuoybn_OH__c__def, axiom, (gram_L1221482011le_H_c = (^ [Tr02:dtree,N2:n]: (((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ ((gram_L315592705e_pick @ Tr02) @ N2))))))).
% 0.32/1.51 thf(fact_102_subtr__deftr, axiom, (! [Ns:(set @ n),Tr5:dtree,N:n]: (((((gram_L716654942_subtr @ Ns) @ Tr5) @ (gram_L1231612515_deftr @ N)) => (Tr5 = (gram_L1231612515_deftr @ (root @ Tr5))))))).
% 0.32/1.51 thf(fact_103_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))))).
% 0.32/1.51 thf(fact_104_deftr__def, axiom, (gram_L1231612515_deftr = (((unfold @ n) @ (id @ n)) @ gram_L1451583635elle_S))).
% 0.32/1.51 thf(fact_105_surj__fun__eq, axiom, (! [B:$tType,C:$tType,A:$tType,F:(B > A),X5:(set @ B),G1:(A > C),G22:(A > C)]: (((((((image @ B) @ A) @ F) @ X5) = (top_top @ (set @ A))) => ((! [X3:B]: (((((member @ B) @ X3) @ X5) => (((((((comp @ A) @ C) @ B) @ G1) @ F) @ X3) = ((((((comp @ A) @ C) @ B) @ G22) @ F) @ X3))))) => (G1 = G22)))))).
% 0.32/1.51 thf(fact_106_finite__H__c, axiom, (! [N:n]: (((finite_finite2 @ ((sum_sum @ t) @ n)) @ ((gram_L1221482011le_H_c @ tr0) @ N))))).
% 0.32/1.51 thf(fact_107_unfold_I1_J, axiom, (! [A:$tType,Rt:(A > n),Ct:(A > (set @ ((sum_sum @ t) @ A))),B2:A]: (((root @ ((((unfold @ A) @ Rt) @ Ct) @ B2)) = (Rt @ B2))))).
% 0.32/1.51 thf(fact_108_cont__H, axiom, (! [N:n]: (((cont @ ((gram_L1451583624elle_H @ tr0) @ N)) = ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ dtree)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ dtree) @ (id @ t)) @ (((((comp @ n) @ dtree) @ dtree) @ (gram_L1451583624elle_H @ tr0)) @ root))) @ (cont @ ((gram_L315592705e_pick @ tr0) @ N))))))).
% 0.32/1.51 thf(fact_109_dtree__cong, axiom, (! [Tr:dtree,Tr5:dtree]: ((((root @ Tr) = (root @ Tr5)) => (((cont @ Tr) = (cont @ Tr5)) => (Tr = Tr5)))))).
% 0.32/1.51 thf(fact_110_hsubst__c__def, axiom, (gram_L1905609002ubst_c = (^ [Tr02:dtree,Tr6:dtree]: (((((if @ (set @ ((sum_sum @ t) @ dtree))) @ ((root @ Tr6) = (root @ Tr02))) @ (cont @ Tr02)) @ (cont @ Tr6)))))).
% 0.32/1.51 thf(fact_111_top1I, axiom, (! [A:$tType,X2:A]: (((top_top @ (A > $o)) @ X2)))).
% 0.32/1.51 thf(fact_112_cont__deftr, axiom, (! [N:n]: (((cont @ (gram_L1231612515_deftr @ N)) = ((((image @ ((sum_sum @ t) @ n)) @ ((sum_sum @ t) @ dtree)) @ ((((((sum_map_sum @ t) @ t) @ n) @ dtree) @ (id @ t)) @ gram_L1231612515_deftr)) @ (gram_L1451583635elle_S @ N)))))).
% 0.32/1.51 thf(fact_113_top__conj_I2_J, axiom, (! [A:$tType,P:$o,X2:A]: (((P & ((top_top @ (A > $o)) @ X2)) = P)))).
% 0.32/1.51 thf(fact_114_top__conj_I1_J, axiom, (! [A:$tType,X2:A,P:$o]: (((((top_top @ (A > $o)) @ X2) & P) = P)))).
% 0.32/1.51 thf(fact_115_finite__S, axiom, (! [N:n]: (((finite_finite2 @ ((sum_sum @ t) @ n)) @ (gram_L1451583635elle_S @ N))))).
% 0.32/1.51 thf(fact_116_unfold_I2_J, axiom, (! [A:$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))))))).
% 0.32/1.51 thf(fact_117_Gram__Lang__Mirabelle__ojxrtuoybn_Ofinite__H__c, axiom, (! [Tr0:dtree,N:n]: (((finite_finite2 @ ((sum_sum @ t) @ n)) @ ((gram_L1221482011le_H_c @ Tr0) @ N))))).
% 0.32/1.51 thf(fact_118_Gram__Lang__Mirabelle__ojxrtuoybn_Ocont__H, axiom, (! [Tr0:dtree,N:n]: (((cont @ ((gram_L1451583624elle_H @ Tr0) @ N)) = ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ dtree)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ dtree) @ (id @ t)) @ (((((comp @ n) @ dtree) @ dtree) @ (gram_L1451583624elle_H @ Tr0)) @ root))) @ (cont @ ((gram_L315592705e_pick @ Tr0) @ N))))))).
% 0.32/1.51 thf(fact_119_finite__Plus__UNIV__iff, axiom, (! [A:$tType,B:$tType]: ((((finite_finite2 @ ((sum_sum @ A) @ B)) @ (top_top @ (set @ ((sum_sum @ A) @ B)))) = (((finite_finite2 @ A) @ (top_top @ (set @ A))) & ((finite_finite2 @ B) @ (top_top @ (set @ B)))))))).
% 0.32/1.51 thf(fact_120_finite__option__UNIV, axiom, (! [A:$tType]: ((((finite_finite2 @ (option @ A)) @ (top_top @ (set @ (option @ A)))) = ((finite_finite2 @ A) @ (top_top @ (set @ A))))))).
% 0.32/1.51 thf(fact_121_finite__imageI, axiom, (! [B:$tType,A:$tType,F4:(set @ A),H:(A > B)]: ((((finite_finite2 @ A) @ F4) => ((finite_finite2 @ B) @ ((((image @ A) @ B) @ H) @ F4)))))).
% 0.32/1.51 thf(fact_122_cont__hsubst__neq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) != (root @ Tr0)) => ((cont @ ((gram_L1004374585hsubst @ Tr0) @ Tr)) = ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ dtree)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ dtree) @ (id @ t)) @ (gram_L1004374585hsubst @ Tr0))) @ (cont @ Tr))))))).
% 0.32/1.51 thf(fact_123_cont__hsubst__eq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) = (root @ Tr0)) => ((cont @ ((gram_L1004374585hsubst @ Tr0) @ Tr)) = ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ dtree)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ dtree) @ (id @ t)) @ (gram_L1004374585hsubst @ Tr0))) @ (cont @ Tr0))))))).
% 0.32/1.51 thf(fact_124_finite__code, axiom, (! [A:$tType]: ((((finite_finite @ A) @ (type2 @ A)) => ((finite_finite2 @ A) = (^ [A5:(set @ A)]: ($true))))))).
% 0.32/1.51 thf(fact_125_root__hsubst, axiom, (! [Tr0:dtree,Tr:dtree]: (((root @ ((gram_L1004374585hsubst @ Tr0) @ Tr)) = (root @ Tr))))).
% 0.32/1.51 thf(fact_126_root__o__subst, axiom, (! [Tr0:dtree]: (((((((comp @ dtree) @ n) @ dtree) @ root) @ (gram_L1004374585hsubst @ Tr0)) = root)))).
% 0.32/1.51 thf(fact_127_finite__cont, axiom, (! [Tr:dtree]: (((finite_finite2 @ ((sum_sum @ t) @ dtree)) @ (cont @ Tr))))).
% 0.32/1.51 thf(fact_128_finite__N, axiom, ((finite_finite2 @ n) @ (top_top @ (set @ n)))).
% 0.32/1.51 thf(fact_129_hsubst__eq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) = (root @ Tr0)) => (((gram_L1004374585hsubst @ Tr0) @ Tr) = ((gram_L1004374585hsubst @ Tr0) @ Tr0)))))).
% 0.32/1.51 thf(fact_130_wf__hsubst, axiom, (! [Tr0:dtree,Tr:dtree]: (((gram_L864798063lle_wf @ Tr0) => ((gram_L864798063lle_wf @ Tr) => (gram_L864798063lle_wf @ ((gram_L1004374585hsubst @ Tr0) @ Tr))))))).
% 0.32/1.51 thf(fact_131_finite__hsubst__c, axiom, (! [Tr0:dtree,N:dtree]: (((finite_finite2 @ ((sum_sum @ t) @ dtree)) @ ((gram_L1905609002ubst_c @ Tr0) @ N))))).
% 0.32/1.51 thf(fact_132_finite, axiom, (! [A:$tType]: ((((finite_finite @ A) @ (type2 @ A)) => (! [A4:(set @ A)]: (((finite_finite2 @ A) @ A4))))))).
% 0.32/1.51 thf(fact_133_finite__set__choice, axiom, (! [B:$tType,A:$tType,A4:(set @ A),P:(A > (B > $o))]: ((((finite_finite2 @ A) @ A4) => ((! [X3:A]: (((((member @ A) @ X3) @ A4) => (? [X12:B]: (((P @ X3) @ X12)))))) => (? [F5:(A > B)]: ((! [X4:A]: (((((member @ A) @ X4) @ A4) => ((P @ X4) @ (F5 @ X4)))))))))))).
% 0.32/1.51 thf(fact_134_finite__UNIV, axiom, (! [A:$tType]: ((((finite_finite @ A) @ (type2 @ A)) => ((finite_finite2 @ A) @ (top_top @ (set @ A))))))).
% 0.32/1.51 thf(fact_135_infinite__UNIV__char__0, axiom, (! [A:$tType]: ((((semiring_char_0 @ A) @ (type2 @ A)) => (~ (((finite_finite2 @ A) @ (top_top @ (set @ A))))))))).
% 0.32/1.51 thf(fact_136_ex__new__if__finite, axiom, (! [A:$tType,A4:(set @ A)]: (((~ (((finite_finite2 @ A) @ (top_top @ (set @ A))))) => (((finite_finite2 @ A) @ A4) => (? [A6:A]: ((~ ((((member @ A) @ A6) @ A4)))))))))).
% 0.32/1.51 thf(fact_137_finite__fun__UNIVD2, axiom, (! [A:$tType,B:$tType]: ((((finite_finite2 @ (A > B)) @ (top_top @ (set @ (A > B)))) => ((finite_finite2 @ B) @ (top_top @ (set @ B))))))).
% 0.32/1.51 thf(fact_138_finite__Prod__UNIV, axiom, (! [B:$tType,A:$tType]: ((((finite_finite2 @ A) @ (top_top @ (set @ A))) => (((finite_finite2 @ B) @ (top_top @ (set @ B))) => ((finite_finite2 @ ((product_prod @ A) @ B)) @ (top_top @ (set @ ((product_prod @ A) @ B))))))))).
% 0.32/1.51 thf(fact_139_finite__prod, axiom, (! [A:$tType,B:$tType]: ((((finite_finite2 @ ((product_prod @ A) @ B)) @ (top_top @ (set @ ((product_prod @ A) @ B)))) = (((finite_finite2 @ A) @ (top_top @ (set @ A))) & ((finite_finite2 @ B) @ (top_top @ (set @ B)))))))).
% 0.32/1.51 thf(fact_140_Finite__Set_Ofinite__set, axiom, (! [A:$tType]: ((((finite_finite2 @ (set @ A)) @ (top_top @ (set @ (set @ A)))) = ((finite_finite2 @ A) @ (top_top @ (set @ A))))))).
% 0.32/1.51 thf(fact_141_hsubst__def, axiom, (gram_L1004374585hsubst = (^ [Tr02:dtree]: ((((unfold @ dtree) @ gram_L1905609017ubst_r) @ (gram_L1905609002ubst_c @ Tr02)))))).
% 0.32/1.51 thf(fact_142_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A))))))))).
% 0.32/1.51 thf(fact_143_Node__root__cont, axiom, (! [Tr:dtree]: ((((node @ (root @ Tr)) @ (cont @ Tr)) = Tr)))).
% 0.32/1.51 thf(fact_144_DEADID_Oin__rel, axiom, (! [B:$tType]: (((^ [Y4:B,Z3:B]: ((Y4 = Z3))) = (^ [A7:B,B4:B]: ((? [Z4:B]: (((((member @ B) @ Z4) @ (top_top @ (set @ B))) & ((((id @ B) @ Z4) = A7) & (((id @ B) @ Z4) = B4))))))))))).
% 0.32/1.51 thf(fact_145_root__Node, axiom, (! [N:n,As:(set @ ((sum_sum @ t) @ dtree))]: (((root @ ((node @ N) @ As)) = N)))).
% 0.32/1.51 thf(fact_146_dtree__simps, axiom, (! [As:(set @ ((sum_sum @ t) @ dtree)),As2:(set @ ((sum_sum @ t) @ dtree)),N:n,N4:n]: ((((finite_finite2 @ ((sum_sum @ t) @ dtree)) @ As) => (((finite_finite2 @ ((sum_sum @ t) @ dtree)) @ As2) => ((((node @ N) @ As) = ((node @ N4) @ As2)) = ((N = N4) & (As = As2)))))))).
% 0.32/1.51 thf(fact_147_cont__Node, axiom, (! [As:(set @ ((sum_sum @ t) @ dtree)),N:n]: ((((finite_finite2 @ ((sum_sum @ t) @ dtree)) @ As) => ((cont @ ((node @ N) @ As)) = As))))).
% 0.32/1.51 thf(fact_148_dtree__cases, axiom, (! [Tr:dtree]: ((~ ((! [N5:n,As3:(set @ ((sum_sum @ t) @ dtree))]: ((((finite_finite2 @ ((sum_sum @ t) @ dtree)) @ As3) => (Tr != ((node @ N5) @ As3)))))))))).
% 0.32/1.51 thf(fact_149_type__copy__map__cong0, axiom, (! [B:$tType,D:$tType,E:$tType,A:$tType,C:$tType,M:(B > A),G:(C > B),X2:C,N3:(D > A),H:(C > D),F:(A > E)]: ((((M @ (G @ X2)) = (N3 @ (H @ X2))) => (((((((comp @ B) @ E) @ C) @ (((((comp @ A) @ E) @ B) @ F) @ M)) @ G) @ X2) = ((((((comp @ D) @ E) @ C) @ (((((comp @ A) @ E) @ D) @ F) @ N3)) @ H) @ X2)))))).
% 0.32/1.51 thf(fact_150_hsubst__r__def, axiom, (gram_L1905609017ubst_r = root)).
% 0.32/1.51 thf(fact_151_Sup_OSUP__id__eq, axiom, (! [A:$tType,Sup:((set @ A) > A),A4:(set @ A)]: (((Sup @ ((((image @ A) @ A) @ (id @ A)) @ A4)) = (Sup @ A4))))).
% 0.32/1.51 thf(fact_152_Inf_OINF__id__eq, axiom, (! [A:$tType,Inf:((set @ A) > A),A4:(set @ A)]: (((Inf @ ((((image @ A) @ A) @ (id @ A)) @ A4)) = (Inf @ A4))))).
% 0.32/1.51 thf(fact_153_Sup_OSUP__image, axiom, (! [B:$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)))))).
% 0.32/1.51 thf(fact_154_Sup_OSUP__cong, axiom, (! [A:$tType,B:$tType,A4:(set @ B),B3:(set @ B),C3:(B > A),D3:(B > A),Sup:((set @ A) > A)]: (((A4 = B3) => ((! [X3:B]: (((((member @ B) @ X3) @ B3) => ((C3 @ X3) = (D3 @ X3))))) => ((Sup @ ((((image @ B) @ A) @ C3) @ A4)) = (Sup @ ((((image @ B) @ A) @ D3) @ B3)))))))).
% 0.32/1.51 thf(fact_155_Inf_OINF__cong, axiom, (! [A:$tType,B:$tType,A4:(set @ B),B3:(set @ B),C3:(B > A),D3:(B > A),Inf:((set @ A) > A)]: (((A4 = B3) => ((! [X3:B]: (((((member @ B) @ X3) @ B3) => ((C3 @ X3) = (D3 @ X3))))) => ((Inf @ ((((image @ B) @ A) @ C3) @ A4)) = (Inf @ ((((image @ B) @ A) @ D3) @ B3)))))))).
% 0.32/1.51 thf(fact_156_Inf_OINF__image, axiom, (! [B:$tType,A:$tType,C:$tType,Inf:((set @ A) > A),G:(B > A),F:(C > B),A4:(set @ C)]: (((Inf @ ((((image @ B) @ A) @ G) @ ((((image @ C) @ B) @ F) @ A4))) = (Inf @ ((((image @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)) @ A4)))))).
% 0.32/1.51 thf(fact_157_Inl__cont__H, axiom, (! [N:n]: ((((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ ((gram_L1451583624elle_H @ tr0) @ N))) = ((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ ((gram_L315592705e_pick @ tr0) @ N))))))).
% 0.32/1.51 thf(fact_158_case__sum__o__map__sum__id, axiom, (! [A:$tType,B:$tType,C:$tType,G:(B > A),F:(C > A),X2:((sum_sum @ C) @ B)]: ((((((((comp @ ((sum_sum @ A) @ B)) @ A) @ ((sum_sum @ C) @ B)) @ (((((sum_case_sum @ A) @ A) @ B) @ (id @ A)) @ G)) @ ((((((sum_map_sum @ C) @ A) @ B) @ B) @ F) @ (id @ B))) @ X2) = ((((((sum_case_sum @ C) @ A) @ B) @ (((((comp @ C) @ A) @ C) @ F) @ (id @ C))) @ G) @ X2))))).
% 0.32/1.51 thf(fact_159_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)))))).
% 0.32/1.51 thf(fact_160_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))))).
% 0.32/1.51 thf(fact_161_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))))))).
% 0.32/1.51 thf(fact_162_vimage__UNIV, axiom, (! [B:$tType,A:$tType,F:(A > B)]: ((((((vimage @ A) @ B) @ F) @ (top_top @ (set @ B))) = (top_top @ (set @ A)))))).
% 0.32/1.51 thf(fact_163_vimage__id, axiom, (! [A:$tType]: (((((vimage @ A) @ A) @ (id @ A)) = (id @ (set @ A)))))).
% 0.32/1.51 thf(fact_164_Inl__m__oplus, axiom, (! [B:$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))))).
% 0.32/1.51 thf(fact_165_Inl__cont__hsubst__neq, 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 @ Tr))))))).
% 0.32/1.51 thf(fact_166_Inl__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))))))).
% 0.32/1.51 thf(fact_167_case__sum__step_I1_J, axiom, (! [D:$tType,A:$tType,C:$tType,B:$tType,F6:(B > A),G3:(C > A),G:(D > A),P2:((sum_sum @ B) @ C)]: ((((((((sum_case_sum @ ((sum_sum @ B) @ C)) @ A) @ D) @ (((((sum_case_sum @ B) @ A) @ C) @ F6) @ G3)) @ G) @ (((sum_Inl @ ((sum_sum @ B) @ C)) @ D) @ P2)) = ((((((sum_case_sum @ B) @ A) @ C) @ F6) @ G3) @ P2))))).
% 0.32/1.51 thf(fact_168_case__sum__inject, axiom, (! [A:$tType,C:$tType,B:$tType,F1:(A > C),F22:(B > C),G1:(A > C),G22:(B > C)]: ((((((((sum_case_sum @ A) @ C) @ B) @ F1) @ F22) = (((((sum_case_sum @ A) @ C) @ B) @ G1) @ G22)) => (~ (((F1 = G1) => (F22 != G22)))))))).
% 0.32/1.51 thf(fact_169_vimage__Collect, axiom, (! [B:$tType,A:$tType,P:(B > $o),F:(A > B),Q:(A > $o)]: (((! [X3:A]: (((P @ (F @ X3)) = (Q @ X3)))) => (((((vimage @ A) @ B) @ F) @ ((collect @ B) @ P)) = ((collect @ A) @ Q)))))).
% 0.32/1.51 thf(fact_170_vimageI2, axiom, (! [B:$tType,A:$tType,F:(B > A),A2:B,A4:(set @ A)]: (((((member @ A) @ (F @ A2)) @ A4) => (((member @ B) @ A2) @ ((((vimage @ B) @ A) @ F) @ A4)))))).
% 0.32/1.51 thf(fact_171_vimageE, axiom, (! [A:$tType,B:$tType,A2:A,F:(A > B),B3:(set @ B)]: (((((member @ A) @ A2) @ ((((vimage @ A) @ B) @ F) @ B3)) => (((member @ B) @ (F @ A2)) @ B3))))).
% 0.32/1.51 thf(fact_172_vimageD, axiom, (! [A:$tType,B:$tType,A2:A,F:(A > B),A4:(set @ B)]: (((((member @ A) @ A2) @ ((((vimage @ A) @ B) @ F) @ A4)) => (((member @ B) @ (F @ A2)) @ A4))))).
% 0.32/1.51 thf(fact_173_old_Osum_Osimps_I5_J, axiom, (! [B:$tType,C:$tType,A:$tType,F1:(A > C),F22:(B > C),X1:A]: ((((((((sum_case_sum @ A) @ C) @ B) @ F1) @ F22) @ (((sum_Inl @ A) @ B) @ X1)) = (F1 @ X1))))).
% 0.32/1.51 thf(fact_174_set_Ocompositionality, axiom, (! [C:$tType,B:$tType,A:$tType,F:(C > B),G:(B > A),Set:(set @ A)]: ((((((vimage @ C) @ B) @ F) @ ((((vimage @ B) @ A) @ G) @ Set)) = ((((vimage @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)) @ Set))))).
% 0.32/1.51 thf(fact_175_vimage__comp, axiom, (! [A:$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))))).
% 0.32/1.51 thf(fact_176_set_Ocomp, axiom, (! [A:$tType,B:$tType,C:$tType,F:(C > B),G:(B > A)]: (((((((comp @ (set @ B)) @ (set @ C)) @ (set @ A)) @ (((vimage @ C) @ B) @ F)) @ (((vimage @ B) @ A) @ G)) = (((vimage @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)))))).
% 0.32/1.51 thf(fact_177_surj__image__vimage__eq, axiom, (! [B:$tType,A:$tType,F:(B > A),A4:(set @ A)]: (((((((image @ B) @ A) @ F) @ (top_top @ (set @ B))) = (top_top @ (set @ A))) => (((((image @ B) @ A) @ F) @ ((((vimage @ B) @ A) @ F) @ A4)) = A4))))).
% 0.32/1.51 thf(fact_178_inFr2__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t]: (((((gram_L805317441_inFr2 @ Ns) @ Tr) @ T2) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 0.32/1.51 thf(fact_179_case__sum__map__sum, axiom, (! [C:$tType,A:$tType,B:$tType,E:$tType,D:$tType,L:(B > A),R:(C > A),F:(D > B),G:(E > C),X2:((sum_sum @ D) @ E)]: ((((((((sum_case_sum @ B) @ A) @ C) @ L) @ R) @ (((((((sum_map_sum @ D) @ B) @ E) @ C) @ F) @ G) @ X2)) = ((((((sum_case_sum @ D) @ A) @ E) @ (((((comp @ B) @ A) @ D) @ L) @ F)) @ (((((comp @ C) @ A) @ E) @ R) @ G)) @ X2))))).
% 0.32/1.51 thf(fact_180_finite__vimageD, axiom, (! [A:$tType,B:$tType,H:(A > B),F4:(set @ B)]: ((((finite_finite2 @ A) @ ((((vimage @ A) @ B) @ H) @ F4)) => ((((((image @ A) @ B) @ H) @ (top_top @ (set @ A))) = (top_top @ (set @ B))) => ((finite_finite2 @ B) @ F4)))))).
% 0.32/1.51 thf(fact_181_case__sum__o__inj_I1_J, axiom, (! [C:$tType,B:$tType,A:$tType,F:(A > B),G:(C > B)]: (((((((comp @ ((sum_sum @ A) @ C)) @ B) @ A) @ (((((sum_case_sum @ A) @ B) @ C) @ F) @ G)) @ ((sum_Inl @ A) @ C)) = F)))).
% 0.32/1.51 thf(fact_182_o__case__sum, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,H:(D > C),F:(A > D),G:(B > D)]: (((((((comp @ D) @ C) @ ((sum_sum @ A) @ B)) @ H) @ (((((sum_case_sum @ A) @ D) @ B) @ F) @ G)) = (((((sum_case_sum @ A) @ C) @ B) @ (((((comp @ D) @ C) @ A) @ H) @ F)) @ (((((comp @ D) @ C) @ B) @ H) @ G)))))).
% 0.32/1.51 thf(fact_183_Gram__Lang__Mirabelle__ojxrtuoybn_OInl__cont__H, axiom, (! [Tr0:dtree,N:n]: ((((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ ((gram_L1451583624elle_H @ Tr0) @ N))) = ((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ ((gram_L315592705e_pick @ Tr0) @ N))))))).
% 0.32/1.51 thf(fact_184_case__sum__o__map__sum, axiom, (! [A:$tType,D:$tType,C:$tType,E:$tType,B:$tType,F:(D > C),G:(E > C),H1:(A > D),H2:(B > E)]: (((((((comp @ ((sum_sum @ D) @ E)) @ C) @ ((sum_sum @ A) @ B)) @ (((((sum_case_sum @ D) @ C) @ E) @ F) @ G)) @ ((((((sum_map_sum @ A) @ D) @ B) @ E) @ H1) @ H2)) = (((((sum_case_sum @ A) @ C) @ B) @ (((((comp @ D) @ C) @ A) @ F) @ H1)) @ (((((comp @ E) @ C) @ B) @ G) @ H2)))))).
% 0.32/1.51 thf(fact_185_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)))))).
% 0.32/1.51 thf(fact_186_corec_I2_J, axiom, (! [A:$tType,Ct:(A > (set @ ((sum_sum @ t) @ ((sum_sum @ dtree) @ A)))),B2:A,Rt:(A > n)]: ((((finite_finite2 @ ((sum_sum @ t) @ ((sum_sum @ dtree) @ A))) @ (Ct @ B2)) => ((cont @ ((((corec @ A) @ Rt) @ Ct) @ B2)) = ((((image @ ((sum_sum @ t) @ ((sum_sum @ dtree) @ A))) @ ((sum_sum @ t) @ dtree)) @ ((((((sum_map_sum @ t) @ t) @ ((sum_sum @ dtree) @ A)) @ dtree) @ (id @ t)) @ (((((sum_case_sum @ dtree) @ dtree) @ A) @ (id @ dtree)) @ (((corec @ A) @ Rt) @ Ct)))) @ (Ct @ B2))))))).
% 0.32/1.51 thf(fact_187_Inr__m__oplus, axiom, (! [A:$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)))))).
% 0.32/1.51 thf(fact_188_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))))).
% 0.32/1.51 thf(fact_189_old_Osum_Oinject_I2_J, axiom, (! [A:$tType,B:$tType,B2:B,B5:B]: ((((((sum_Inr @ B) @ A) @ B2) = (((sum_Inr @ B) @ A) @ B5)) = (B2 = B5))))).
% 0.32/1.51 thf(fact_190_Inr__cont__H, axiom, (! [N:n]: ((((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ ((gram_L1451583624elle_H @ tr0) @ N))) = ((((image @ dtree) @ dtree) @ (((((comp @ n) @ dtree) @ dtree) @ (gram_L1451583624elle_H @ tr0)) @ root)) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ ((gram_L315592705e_pick @ tr0) @ N)))))))).
% 0.32/1.51 thf(fact_191_Inr__Inl__False, axiom, (! [B:$tType,A:$tType,X2:B,Y:A]: (((((sum_Inr @ B) @ A) @ X2) != (((sum_Inl @ A) @ B) @ Y))))).
% 0.32/1.51 thf(fact_192_Inl__Inr__False, axiom, (! [A:$tType,B:$tType,X2:A,Y:B]: (((((sum_Inl @ A) @ B) @ X2) != (((sum_Inr @ B) @ A) @ Y))))).
% 0.32/1.51 thf(fact_193_old_Osum_Osimps_I8_J, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > T),F22:(B > T),B2:B]: ((((((((sum_rec_sum @ A) @ T) @ B) @ F1) @ F22) @ (((sum_Inr @ B) @ A) @ B2)) = (F22 @ B2))))).
% 0.32/1.51 thf(fact_194_wf__inj, axiom, (! [Tr:dtree,Tr1:dtree,Tr2:dtree]: (((gram_L864798063lle_wf @ Tr) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr2)) @ (cont @ Tr)) => (((root @ Tr1) = (root @ Tr2)) = (Tr1 = Tr2)))))))).
% 0.32/1.51 thf(fact_195_Inr__cont__hsubst__neq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) != (root @ Tr0)) => (((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ ((gram_L1004374585hsubst @ Tr0) @ Tr))) = ((((image @ dtree) @ dtree) @ (gram_L1004374585hsubst @ Tr0)) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr)))))))).
% 0.32/1.51 thf(fact_196_Inr__cont__hsubst__eq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) = (root @ Tr0)) => (((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ ((gram_L1004374585hsubst @ Tr0) @ Tr))) = ((((image @ dtree) @ dtree) @ (gram_L1004374585hsubst @ Tr0)) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr0)))))))).
% 0.32/1.51 thf(fact_197_Inr__oplus__iff, axiom, (! [B:$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)))))))).
% 0.32/1.51 thf(fact_198_case__sum__step_I2_J, axiom, (! [E:$tType,A:$tType,C:$tType,B:$tType,F:(E > A),F6:(B > A),G3:(C > A),P2:((sum_sum @ B) @ C)]: ((((((((sum_case_sum @ E) @ A) @ ((sum_sum @ B) @ C)) @ F) @ (((((sum_case_sum @ B) @ A) @ C) @ F6) @ G3)) @ (((sum_Inr @ ((sum_sum @ B) @ C)) @ E) @ P2)) = ((((((sum_case_sum @ B) @ A) @ C) @ F6) @ G3) @ P2))))).
% 0.32/1.51 thf(fact_199_old_Osum_Osimps_I6_J, axiom, (! [A:$tType,C:$tType,B:$tType,F1:(A > C),F22:(B > C),X22:B]: ((((((((sum_case_sum @ A) @ C) @ B) @ F1) @ F22) @ (((sum_Inr @ B) @ A) @ X22)) = (F22 @ X22))))).
% 0.32/1.51 thf(fact_200_old_Osum_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((sum_sum @ A) @ B) > $o),Sum:((sum_sum @ A) @ B)]: (((! [A6:A]: ((P @ (((sum_Inl @ A) @ B) @ A6)))) => ((! [B6:B]: ((P @ (((sum_Inr @ B) @ A) @ B6)))) => (P @ Sum)))))).
% 0.32/1.51 thf(fact_201_old_Osum_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((sum_sum @ A) @ B)]: (((! [A6:A]: ((Y != (((sum_Inl @ A) @ B) @ A6)))) => (~ ((! [B6:B]: ((Y != (((sum_Inr @ B) @ A) @ B6)))))))))).
% 0.32/1.51 thf(fact_202_split__sum__all, axiom, (! [B:$tType,A:$tType]: (((^ [P3:(((sum_sum @ A) @ B) > $o)]: ((! [X6:((sum_sum @ A) @ B)]: ((P3 @ X6))))) = (^ [P4:(((sum_sum @ A) @ B) > $o)]: (((! [X:A]: ((P4 @ (((sum_Inl @ A) @ B) @ X)))) & (! [X:B]: ((P4 @ (((sum_Inr @ B) @ A) @ X))))))))))).
% 0.32/1.51 thf(fact_203_split__sum__ex, axiom, (! [B:$tType,A:$tType]: (((^ [P3:(((sum_sum @ A) @ B) > $o)]: ((? [X6:((sum_sum @ A) @ B)]: ((P3 @ X6))))) = (^ [P4:(((sum_sum @ A) @ B) > $o)]: (((? [X:A]: ((P4 @ (((sum_Inl @ A) @ B) @ X)))) | (? [X:B]: ((P4 @ (((sum_Inr @ B) @ A) @ X))))))))))).
% 0.32/1.51 thf(fact_204_Inr__not__Inl, axiom, (! [B:$tType,A:$tType,B2:B,A2:A]: (((((sum_Inr @ B) @ A) @ B2) != (((sum_Inl @ A) @ B) @ A2))))).
% 0.32/1.51 thf(fact_205_sumE, axiom, (! [A:$tType,B:$tType,S:((sum_sum @ A) @ B)]: (((! [X3:A]: ((S != (((sum_Inl @ A) @ B) @ X3)))) => (~ ((! [Y2:B]: ((S != (((sum_Inr @ B) @ A) @ Y2)))))))))).
% 0.32/1.51 thf(fact_206_old_Osum_Odistinct_I1_J, axiom, (! [A:$tType,B:$tType,A2:A,B5:B]: (((((sum_Inl @ A) @ B) @ A2) != (((sum_Inr @ B) @ A) @ B5))))).
% 0.32/1.51 thf(fact_207_old_Osum_Odistinct_I2_J, axiom, (! [B7:$tType,A8:$tType,B8:B7,A9:A8]: (((((sum_Inr @ B7) @ A8) @ B8) != (((sum_Inl @ A8) @ B7) @ A9))))).
% 0.32/1.51 thf(fact_208_sum_Odistinct_I1_J, axiom, (! [A:$tType,B:$tType,X1:A,X22:B]: (((((sum_Inl @ A) @ B) @ X1) != (((sum_Inr @ B) @ A) @ X22))))).
% 0.32/1.51 thf(fact_209_obj__sumE__f, axiom, (! [A:$tType,C:$tType,B:$tType,S:B,F:(((sum_sum @ A) @ C) > B),P:$o]: (((! [X3:A]: (((S = (F @ (((sum_Inl @ A) @ C) @ X3))) => P))) => ((! [X3:C]: (((S = (F @ (((sum_Inr @ C) @ A) @ X3))) => P))) => (! [X4:((sum_sum @ A) @ C)]: (((S = (F @ X4)) => P)))))))).
% 0.32/1.51 thf(fact_210_Inr__inject, axiom, (! [A:$tType,B:$tType,X2:B,Y:B]: ((((((sum_Inr @ B) @ A) @ X2) = (((sum_Inr @ B) @ A) @ Y)) => (X2 = Y))))).
% 0.32/1.51 thf(fact_211_map__sum__if__distrib__else_I2_J, axiom, (! [E:$tType,F3:$tType,H3:$tType,G4:$tType,E2:$o,F:(E > F3),G:(G4 > H3),X2:((sum_sum @ E) @ G4),Y:G4]: (((E2 => ((((((((sum_map_sum @ E) @ F3) @ G4) @ H3) @ F) @ G) @ ((((if @ ((sum_sum @ E) @ G4)) @ E2) @ X2) @ (((sum_Inr @ G4) @ E) @ Y))) = (((((((sum_map_sum @ E) @ F3) @ G4) @ H3) @ F) @ G) @ X2))) & ((~ (E2)) => ((((((((sum_map_sum @ E) @ F3) @ G4) @ H3) @ F) @ G) @ ((((if @ ((sum_sum @ E) @ G4)) @ E2) @ X2) @ (((sum_Inr @ G4) @ E) @ Y))) = (((sum_Inr @ H3) @ F3) @ (G @ Y)))))))).
% 0.32/1.51 thf(fact_212_map__sum__if__distrib__then_I2_J, axiom, (! [H3:$tType,F3:$tType,G4:$tType,E:$tType,E2:$o,F:(E > F3),G:(G4 > H3),X2:G4,Y:((sum_sum @ E) @ G4)]: (((E2 => ((((((((sum_map_sum @ E) @ F3) @ G4) @ H3) @ F) @ G) @ ((((if @ ((sum_sum @ E) @ G4)) @ E2) @ (((sum_Inr @ G4) @ E) @ X2)) @ Y)) = (((sum_Inr @ H3) @ F3) @ (G @ X2)))) & ((~ (E2)) => ((((((((sum_map_sum @ E) @ F3) @ G4) @ H3) @ F) @ G) @ ((((if @ ((sum_sum @ E) @ G4)) @ E2) @ (((sum_Inr @ G4) @ E) @ X2)) @ Y)) = (((((((sum_map_sum @ E) @ F3) @ G4) @ H3) @ F) @ G) @ Y))))))).
% 0.32/1.51 thf(fact_213_map__sum__InrD, axiom, (! [C:$tType,A:$tType,D:$tType,B:$tType,F:(C > A),G:(D > B),Z:((sum_sum @ C) @ D),X2:B]: ((((((((((sum_map_sum @ C) @ A) @ D) @ B) @ F) @ G) @ Z) = (((sum_Inr @ B) @ A) @ X2)) => (? [Y2:D]: (((Z = (((sum_Inr @ D) @ C) @ Y2)) & ((G @ Y2) = X2)))))))).
% 0.32/1.51 thf(fact_214_map__sum_Osimps_I2_J, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,F1:(A > C),F22:(B > D),A2:B]: (((((((((sum_map_sum @ A) @ C) @ B) @ D) @ F1) @ F22) @ (((sum_Inr @ B) @ A) @ A2)) = (((sum_Inr @ D) @ C) @ (F22 @ A2)))))).
% 0.32/1.51 thf(fact_215_Inl__Inr__image__cong, axiom, (! [B:$tType,A:$tType,A4:(set @ ((sum_sum @ A) @ B)),B3:(set @ ((sum_sum @ A) @ B))]: (((((((vimage @ A) @ ((sum_sum @ A) @ B)) @ ((sum_Inl @ A) @ B)) @ A4) = ((((vimage @ A) @ ((sum_sum @ A) @ B)) @ ((sum_Inl @ A) @ B)) @ B3)) => ((((((vimage @ B) @ ((sum_sum @ A) @ B)) @ ((sum_Inr @ B) @ A)) @ A4) = ((((vimage @ B) @ ((sum_sum @ A) @ B)) @ ((sum_Inr @ B) @ A)) @ B3)) => (A4 = B3)))))).
% 0.32/1.51 thf(fact_216_case__sum__if, axiom, (! [B:$tType,A:$tType,C:$tType,P2:$o,F:(B > A),G:(C > A),X2:B,Y:C]: (((P2 => (((((((sum_case_sum @ B) @ A) @ C) @ F) @ G) @ ((((if @ ((sum_sum @ B) @ C)) @ P2) @ (((sum_Inl @ B) @ C) @ X2)) @ (((sum_Inr @ C) @ B) @ Y))) = (F @ X2))) & ((~ (P2)) => (((((((sum_case_sum @ B) @ A) @ C) @ F) @ G) @ ((((if @ ((sum_sum @ B) @ C)) @ P2) @ (((sum_Inl @ B) @ C) @ X2)) @ (((sum_Inr @ C) @ B) @ Y))) = (G @ Y))))))).
% 0.32/1.51 thf(fact_217_wf__cont, axiom, (! [Tr:dtree,Tr5:dtree]: (((gram_L864798063lle_wf @ Tr) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr5)) @ (cont @ Tr)) => (gram_L864798063lle_wf @ Tr5)))))).
% 0.32/1.51 thf(fact_218_case__sum__o__inj_I2_J, axiom, (! [A:$tType,B:$tType,C:$tType,F:(A > B),G:(C > B)]: (((((((comp @ ((sum_sum @ A) @ C)) @ B) @ C) @ (((((sum_case_sum @ A) @ B) @ C) @ F) @ G)) @ ((sum_Inr @ C) @ A)) = G)))).
% 0.32/1.51 thf(fact_219_root__prodOf, axiom, (! [Tr5:dtree,Tr:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr5)) @ (cont @ Tr)) => (((member @ ((sum_sum @ t) @ n)) @ (((sum_Inr @ n) @ t) @ (root @ Tr5))) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr))))))).
% 0.32/1.51 thf(fact_220_Gram__Lang__Mirabelle__ojxrtuoybn_OInr__cont__H, axiom, (! [Tr0:dtree,N:n]: ((((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ ((gram_L1451583624elle_H @ Tr0) @ N))) = ((((image @ dtree) @ dtree) @ (((((comp @ n) @ dtree) @ dtree) @ (gram_L1451583624elle_H @ Tr0)) @ root)) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ ((gram_L315592705e_pick @ Tr0) @ N)))))))).
% 0.32/1.51 thf(fact_221_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)) => (? [N5:C]: (((((member @ ((sum_sum @ A) @ C)) @ (((sum_Inr @ C) @ A) @ N5)) @ Tns) & ((F @ N5) = Tr)))))))).
% 0.32/1.51 thf(fact_222_subtr_OStep, axiom, (! [Tr3:dtree,Ns:(set @ n),Tr1:dtree,Tr2:dtree]: (((((member @ n) @ (root @ Tr3)) @ Ns) => ((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr2) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr2)) @ (cont @ Tr3)) => (((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr3))))))).
% 0.32/1.51 thf(fact_223_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) => (! [Tr22:dtree]: (((((gram_L716654942_subtr @ A1) @ A22) @ Tr22) => (~ ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr22)) @ (cont @ A32))))))))))))))).
% 0.32/1.51 thf(fact_224_subtr_Osimps, axiom, (gram_L716654942_subtr = (^ [A12:(set @ n),A23:dtree,A33:dtree]: (((? [Tr6:dtree,Ns2:(set @ n)]: (((A12 = Ns2) & ((A23 = Tr6) & ((A33 = Tr6) & (((member @ n) @ (root @ Tr6)) @ Ns2)))))) | (? [Tr32:dtree,Ns2:(set @ n),Tr12:dtree,Tr23:dtree]: (((A12 = Ns2) & ((A23 = Tr12) & ((A33 = Tr32) & ((((member @ n) @ (root @ Tr32)) @ Ns2) & ((((gram_L716654942_subtr @ Ns2) @ Tr12) @ Tr23) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr23)) @ (cont @ Tr32)))))))))))))).
% 0.32/1.51 thf(fact_225_subtr__StepL, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr2:dtree,Tr3:dtree]: (((((member @ n) @ (root @ Tr1)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr2)) => ((((gram_L716654942_subtr @ Ns) @ Tr2) @ Tr3) => (((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr3))))))).
% 0.32/1.51 thf(fact_226_subtr_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:dtree,P:((set @ n) > (dtree > (dtree > $o)))]: (((((gram_L716654942_subtr @ X1) @ X22) @ X32) => ((! [Tr7:dtree,Ns3:(set @ n)]: (((((member @ n) @ (root @ Tr7)) @ Ns3) => (((P @ Ns3) @ Tr7) @ Tr7)))) => ((! [Tr33:dtree,Ns3:(set @ n),Tr13:dtree,Tr22:dtree]: (((((member @ n) @ (root @ Tr33)) @ Ns3) => ((((gram_L716654942_subtr @ Ns3) @ Tr13) @ Tr22) => ((((P @ Ns3) @ Tr13) @ Tr22) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr22)) @ (cont @ Tr33)) => (((P @ Ns3) @ Tr13) @ Tr33))))))) => (((P @ X1) @ X22) @ X32))))))).
% 0.32/1.51 thf(fact_227_subtr__inductL, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr2:dtree,Phi:((set @ n) > (dtree > (dtree > $o)))]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr2) => ((! [Ns3:(set @ n),Tr7:dtree]: ((((Phi @ Ns3) @ Tr7) @ Tr7))) => ((! [Ns3:(set @ n),Tr13:dtree,Tr22:dtree,Tr33:dtree]: (((((member @ n) @ (root @ Tr13)) @ Ns3) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr22)) => ((((gram_L716654942_subtr @ Ns3) @ Tr22) @ Tr33) => ((((Phi @ Ns3) @ Tr22) @ Tr33) => (((Phi @ Ns3) @ Tr13) @ Tr33))))))) => (((Phi @ Ns) @ Tr1) @ Tr2))))))).
% 0.32/1.51 thf(fact_228_inItr_OInd, axiom, (! [Tr:dtree,Ns:(set @ n),Tr1:dtree,N:n]: (((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => ((((gram_L830233218_inItr @ Ns) @ Tr1) @ N) => (((gram_L830233218_inItr @ Ns) @ Tr) @ N))))))).
% 0.32/1.51 thf(fact_229_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) => (! [Tr13:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ A22)) => (~ ((((gram_L830233218_inItr @ A1) @ Tr13) @ A32)))))))))))))).
% 0.32/1.51 thf(fact_230_inItr_Osimps, axiom, (gram_L830233218_inItr = (^ [A12:(set @ n),A23:dtree,A33:n]: (((? [Tr6:dtree,Ns2:(set @ n)]: (((A12 = Ns2) & ((A23 = Tr6) & ((A33 = (root @ Tr6)) & (((member @ n) @ (root @ Tr6)) @ Ns2)))))) | (? [Tr6:dtree,Ns2:(set @ n),Tr12:dtree,N2:n]: (((A12 = Ns2) & ((A23 = Tr6) & ((A33 = N2) & ((((member @ n) @ (root @ Tr6)) @ Ns2) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr6)) & (((gram_L830233218_inItr @ Ns2) @ Tr12) @ N2))))))))))))).
% 0.32/1.51 thf(fact_231_inItr_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:n,P:((set @ n) > (dtree > (n > $o)))]: (((((gram_L830233218_inItr @ X1) @ X22) @ X32) => ((! [Tr7:dtree,Ns3:(set @ n)]: (((((member @ n) @ (root @ Tr7)) @ Ns3) => (((P @ Ns3) @ Tr7) @ (root @ Tr7))))) => ((! [Tr7:dtree,Ns3:(set @ n),Tr13:dtree,N5:n]: (((((member @ n) @ (root @ Tr7)) @ Ns3) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr7)) => ((((gram_L830233218_inItr @ Ns3) @ Tr13) @ N5) => ((((P @ Ns3) @ Tr13) @ N5) => (((P @ Ns3) @ Tr7) @ N5))))))) => (((P @ X1) @ X22) @ X32))))))).
% 0.32/1.51 thf(fact_232_case__sum__expand__Inr, axiom, (! [B:$tType,C:$tType,A:$tType,F:(((sum_sum @ A) @ C) > B),G:(A > B),X2:((sum_sum @ A) @ C)]: ((((((((comp @ ((sum_sum @ A) @ C)) @ B) @ A) @ F) @ ((sum_Inl @ A) @ C)) = G) => ((F @ X2) = ((((((sum_case_sum @ A) @ B) @ C) @ G) @ (((((comp @ ((sum_sum @ A) @ C)) @ B) @ C) @ F) @ ((sum_Inr @ C) @ A))) @ X2)))))).
% 0.32/1.51 thf(fact_233_case__sum__expand__Inr_H, axiom, (! [B:$tType,C:$tType,A:$tType,F:(((sum_sum @ A) @ C) > B),G:(A > B),H:(C > B)]: ((((((((comp @ ((sum_sum @ A) @ C)) @ B) @ A) @ F) @ ((sum_Inl @ A) @ C)) = G) => ((H = (((((comp @ ((sum_sum @ A) @ C)) @ B) @ C) @ F) @ ((sum_Inr @ C) @ A))) = ((((((sum_case_sum @ A) @ B) @ C) @ G) @ H) = F)))))).
% 0.32/1.51 thf(fact_234_case__sum__expand__Inr__pointfree, axiom, (! [B:$tType,C:$tType,A:$tType,F:(((sum_sum @ A) @ C) > B),G:(A > B)]: ((((((((comp @ ((sum_sum @ A) @ C)) @ B) @ A) @ F) @ ((sum_Inl @ A) @ C)) = G) => ((((((sum_case_sum @ A) @ B) @ C) @ G) @ (((((comp @ ((sum_sum @ A) @ C)) @ B) @ C) @ F) @ ((sum_Inr @ C) @ A))) = F))))).
% 0.32/1.51 thf(fact_235_corec_I1_J, axiom, (! [A:$tType,Rt:(A > n),Ct:(A > (set @ ((sum_sum @ t) @ ((sum_sum @ dtree) @ A)))),B2:A]: (((root @ ((((corec @ A) @ Rt) @ Ct) @ B2)) = (Rt @ B2))))).
% 0.32/1.51 thf(fact_236_subtr__UNIV__inductL, axiom, (! [Tr1:dtree,Tr2:dtree,Phi:(dtree > (dtree > $o))]: (((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ Tr1) @ Tr2) => ((! [Tr7:dtree]: (((Phi @ Tr7) @ Tr7))) => ((! [Tr13:dtree,Tr22:dtree,Tr33:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr22)) => ((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ Tr22) @ Tr33) => (((Phi @ Tr22) @ Tr33) => ((Phi @ Tr13) @ Tr33)))))) => ((Phi @ Tr1) @ Tr2))))))).
% 0.32/1.51 thf(fact_237_inFr2__Ind, axiom, (! [Ns:(set @ n),Tr1:dtree,T2:t,Tr:dtree]: (((((gram_L805317441_inFr2 @ Ns) @ Tr1) @ T2) => ((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => (((gram_L805317441_inFr2 @ Ns) @ Tr) @ T2))))))).
% 0.32/1.51 thf(fact_238_map__sum__o__inj_I2_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,F:(A > B),G:(D > C)]: (((((((comp @ ((sum_sum @ A) @ D)) @ ((sum_sum @ B) @ C)) @ D) @ ((((((sum_map_sum @ A) @ B) @ D) @ C) @ F) @ G)) @ ((sum_Inr @ D) @ A)) = (((((comp @ C) @ ((sum_sum @ B) @ C)) @ D) @ ((sum_Inr @ C) @ B)) @ G))))).
% 0.32/1.51 thf(fact_239_root__subtrOf, axiom, (! [N:n,Tr:dtree]: (((((member @ ((sum_sum @ t) @ n)) @ (((sum_Inr @ n) @ t) @ N)) @ ((((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) @ N)) = N))))).
% 0.32/1.51 thf(fact_240_surj__subtrOf, axiom, (! [Tr:dtree,Tr5:dtree]: (((gram_L864798063lle_wf @ Tr) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr5)) @ (cont @ Tr)) => (? [N5:n]: (((((member @ ((sum_sum @ t) @ n)) @ (((sum_Inr @ n) @ t) @ N5)) @ ((((image @ ((sum_sum @ t) @ dtree)) @ ((sum_sum @ t) @ n)) @ ((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root)) @ (cont @ Tr))) & (((gram_L1614515765ubtrOf @ Tr) @ N5) = Tr5))))))))).
% 0.32/1.51 thf(fact_241_subtrOf__root, axiom, (! [Tr:dtree,Tr5:dtree]: (((gram_L864798063lle_wf @ Tr) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr5)) @ (cont @ Tr)) => (((gram_L1614515765ubtrOf @ Tr) @ (root @ Tr5)) = Tr5)))))).
% 0.32/1.51 thf(fact_242_Inr__subtrOf, axiom, (! [N:n,Tr:dtree]: (((((member @ ((sum_sum @ t) @ n)) @ (((sum_Inr @ n) @ t) @ N)) @ ((((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) @ N))) @ (cont @ Tr)))))).
% 0.32/1.51 thf(fact_243_subtrOf, axiom, (! [N:n,Tr:dtree]: (((((member @ ((sum_sum @ t) @ n)) @ (((sum_Inr @ n) @ t) @ N)) @ ((((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) @ N))) @ (cont @ Tr)) & ((root @ ((gram_L1614515765ubtrOf @ Tr) @ N)) = N)))))).
% 0.32/1.51 thf(fact_244_obj__sumE, axiom, (! [A:$tType,B:$tType,S:((sum_sum @ A) @ B)]: (((! [X3:A]: ((S != (((sum_Inl @ A) @ B) @ X3)))) => (~ ((! [X3:B]: ((S != (((sum_Inr @ B) @ A) @ X3)))))))))).
% 0.32/1.51 thf(fact_245_wf__subtr__inj__on, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr:dtree]: (((gram_L864798063lle_wf @ Tr1) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => ((((inj_on @ dtree) @ n) @ root) @ ((((vimage @ dtree) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inr @ dtree) @ t)) @ (cont @ Tr)))))))).
% 0.32/1.51 thf(fact_246_inj__on__image__iff, axiom, (! [B:$tType,A:$tType,A4:(set @ A),G:(A > B),F:(A > A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A4) => (! [Xa2:A]: (((((member @ A) @ Xa2) @ A4) => (((G @ (F @ X3)) = (G @ (F @ Xa2))) = ((G @ X3) = (G @ Xa2))))))))) => (((((inj_on @ A) @ A) @ F) @ A4) => (((((inj_on @ A) @ B) @ G) @ ((((image @ A) @ A) @ F) @ A4)) = ((((inj_on @ A) @ B) @ G) @ A4))))))).
% 0.32/1.51 thf(fact_247_finite__image__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),A4:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ A4) => (((finite_finite2 @ B) @ ((((image @ A) @ B) @ F) @ A4)) = ((finite_finite2 @ A) @ A4)))))).
% 0.32/1.51 thf(fact_248_finite__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A4:(set @ B)]: ((((finite_finite2 @ A) @ ((((image @ B) @ A) @ F) @ A4)) => (((((inj_on @ B) @ A) @ F) @ A4) => ((finite_finite2 @ B) @ A4)))))).
% 0.32/1.51 thf(fact_249_range__ex1__eq, axiom, (! [B:$tType,A:$tType,F:(A > B),B2:B]: ((((((inj_on @ A) @ B) @ F) @ (top_top @ (set @ A))) => ((((member @ B) @ B2) @ ((((image @ A) @ B) @ F) @ (top_top @ (set @ A)))) = (? [X:A]: (((B2 = (F @ X)) & (! [Y3:A]: (((B2 = (F @ Y3)) => (Y3 = X)))))))))))).
% 0.32/1.51 thf(fact_250_inj__image__eq__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),A4:(set @ A),B3:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ (top_top @ (set @ A))) => ((((((image @ A) @ B) @ F) @ A4) = ((((image @ A) @ B) @ F) @ B3)) = (A4 = B3)))))).
% 0.32/1.51 thf(fact_251_inj__image__mem__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),A2:A,A4:(set @ A)]: ((((((inj_on @ A) @ B) @ F) @ (top_top @ (set @ A))) => ((((member @ B) @ (F @ A2)) @ ((((image @ A) @ B) @ F) @ A4)) = (((member @ A) @ A2) @ A4)))))).
% 0.32/1.51 thf(fact_252_comp__inj__on, axiom, (! [B:$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)))))).
% 0.32/1.51 thf(fact_253_inj__on__imageI, axiom, (! [B:$tType,C:$tType,A:$tType,G:(C > B),F:(A > C),A4:(set @ A)]: ((((((inj_on @ A) @ B) @ (((((comp @ C) @ B) @ A) @ G) @ F)) @ A4) => ((((inj_on @ C) @ B) @ G) @ ((((image @ A) @ C) @ F) @ A4)))))).
% 0.32/1.51 thf(fact_254_comp__inj__on__iff, axiom, (! [B:$tType,C:$tType,A:$tType,F:(A > B),A4:(set @ A),F6:(B > C)]: ((((((inj_on @ A) @ B) @ F) @ A4) => (((((inj_on @ B) @ C) @ F6) @ ((((image @ A) @ B) @ F) @ A4)) = ((((inj_on @ A) @ C) @ (((((comp @ B) @ C) @ A) @ F6) @ F)) @ A4)))))).
% 0.32/1.51 thf(fact_255_finite__UNIV__inj__surj, axiom, (! [A:$tType,F:(A > A)]: ((((finite_finite2 @ A) @ (top_top @ (set @ A))) => (((((inj_on @ A) @ A) @ F) @ (top_top @ (set @ A))) => (((((image @ A) @ A) @ F) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))))).
% 0.32/1.51 thf(tcon_fun___Finite__Set_Ofinite, axiom, (! [A8:$tType,A10:$tType]: (((((finite_finite @ A8) @ (type2 @ A8)) & ((finite_finite @ A10) @ (type2 @ A10))) => ((finite_finite @ (A8 > A10)) @ (type2 @ (A8 > A10))))))).
% 0.32/1.51 thf(tcon_fun___Orderings_Otop, axiom, (! [A8:$tType,A10:$tType]: ((((top @ A10) @ (type2 @ A10)) => ((top @ (A8 > A10)) @ (type2 @ (A8 > A10))))))).
% 0.32/1.51 thf(tcon_Set_Oset___Finite__Set_Ofinite_1, axiom, (! [A8:$tType]: ((((finite_finite @ A8) @ (type2 @ A8)) => ((finite_finite @ (set @ A8)) @ (type2 @ (set @ A8))))))).
% 0.32/1.51 thf(tcon_Set_Oset___Orderings_Otop_2, axiom, (! [A8:$tType]: (((top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.32/1.51 thf(tcon_HOL_Obool___Finite__Set_Ofinite_3, axiom, ((finite_finite @ $o) @ (type2 @ $o))).
% 0.32/1.51 thf(tcon_HOL_Obool___Orderings_Otop_4, axiom, ((top @ $o) @ (type2 @ $o))).
% 0.32/1.51 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_5, axiom, (! [A8:$tType,A10:$tType]: (((((finite_finite @ A8) @ (type2 @ A8)) & ((finite_finite @ A10) @ (type2 @ A10))) => ((finite_finite @ ((sum_sum @ A8) @ A10)) @ (type2 @ ((sum_sum @ A8) @ A10))))))).
% 0.32/1.51 thf(tcon_Option_Ooption___Finite__Set_Ofinite_6, axiom, (! [A8:$tType]: ((((finite_finite @ A8) @ (type2 @ A8)) => ((finite_finite @ (option @ A8)) @ (type2 @ (option @ A8))))))).
% 0.32/1.51 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_7, axiom, (! [A8:$tType,A10:$tType]: (((((finite_finite @ A8) @ (type2 @ A8)) & ((finite_finite @ A10) @ (type2 @ A10))) => ((finite_finite @ ((product_prod @ A8) @ A10)) @ (type2 @ ((product_prod @ A8) @ A10))))))).
% 0.32/1.51 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 0.32/1.51 thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $false) @ X2) @ Y) = Y)))).
% 0.32/1.51 thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y:A]: ((((((if @ A) @ $true) @ X2) @ Y) = X2)))).
% 0.32/1.51 thf(conj_0, hypothesis, $true).
% 0.32/1.51 thf(conj_1, hypothesis, $true).
% 0.32/1.51 thf(conj_2, hypothesis, (t_tr = (((sum_Inl @ t) @ dtree) @ a))).
% 0.32/1.51 thf(conj_3, conjecture, ((((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ (((((comp @ n) @ n) @ dtree) @ (((((comp @ dtree) @ n) @ n) @ root) @ (gram_L1451583624elle_H @ tr0))) @ root)) @ t_tr) = (((((((sum_map_sum @ t) @ t) @ dtree) @ n) @ (id @ t)) @ root) @ t_tr))).
% 0.32/1.51 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.jDfwb26t2m/DTF2DTF25971.p
% 0.32/1.51 ------------------------
% 0.32/1.53 ---- Cleaned THF ---
% 0.32/1.53 thf(ty_t_Product__Type_Oprod,type,
% 0.32/1.53 product_prod: $tType > $tType > $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_t_Sum__Type_Osum,type,
% 0.32/1.53 sum_sum: $tType > $tType > $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_t_Option_Ooption,type,
% 0.32/1.53 option: $tType > $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_t_DTree_Odtree,type,
% 0.32/1.53 dtree: $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_t_Set_Oset,type,
% 0.32/1.53 set: $tType > $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_t_DTree_OT,type,
% 0.32/1.53 t: $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_t_DTree_ON,type,
% 0.32/1.53 n: $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_t_itself,type,
% 0.32/1.53 itself: $tType > $tType ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_HOL_Otype,type,
% 0.32/1.53 type:
% 0.32/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Orderings_Otop,type,
% 0.32/1.53 top:
% 0.32/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Finite__Set_Ofinite,type,
% 0.32/1.53 finite_finite:
% 0.32/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Nat_Osemiring__char__0,type,
% 0.32/1.53 semiring_char_0:
% 0.32/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_DTree_ONode,type,
% 0.32/1.53 node: n > ( set @ ( sum_sum @ t @ dtree ) ) > dtree ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_DTree_Ocont,type,
% 0.32/1.53 cont: dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_DTree_Ocorec,type,
% 0.32/1.53 corec:
% 0.32/1.53 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) ) ) > A > dtree ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_DTree_Odtree_Oroot,type,
% 0.32/1.53 root: dtree > n ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_DTree_Ounfold,type,
% 0.32/1.53 unfold:
% 0.32/1.53 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ A ) ) ) > A > dtree ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Finite__Set_Ofinite,type,
% 0.32/1.53 finite_finite2:
% 0.32/1.53 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Fun_Ocomp,type,
% 0.32/1.53 comp:
% 0.32/1.53 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Fun_Oid,type,
% 0.32/1.53 id:
% 0.32/1.53 !>[A: $tType] : ( A > A ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Fun_Oinj__on,type,
% 0.32/1.53 inj_on:
% 0.32/1.53 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH,type,
% 0.32/1.53 gram_L1451583624elle_H: dtree > n > dtree ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__c,type,
% 0.32/1.53 gram_L1221482011le_H_c: dtree > n > ( set @ ( sum_sum @ t @ n ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__r,type,
% 0.32/1.53 gram_L1221482026le_H_r: dtree > n > n ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OS,type,
% 0.32/1.53 gram_L1451583635elle_S: n > ( set @ ( sum_sum @ t @ n ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr,type,
% 0.32/1.53 gram_L1231612515_deftr: n > dtree ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst,type,
% 0.32/1.53 gram_L1004374585hsubst: dtree > dtree > dtree ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c,type,
% 0.32/1.53 gram_L1905609002ubst_c: dtree > dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r,type,
% 0.32/1.53 gram_L1905609017ubst_r: dtree > n ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2,type,
% 0.32/1.53 gram_L805317441_inFr2: ( set @ n ) > dtree > t > $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr,type,
% 0.32/1.53 gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Opick,type,
% 0.32/1.53 gram_L315592705e_pick: dtree > n > dtree ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr,type,
% 0.32/1.53 gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OsubtrOf,type,
% 0.32/1.53 gram_L1614515765ubtrOf: dtree > n > dtree ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf,type,
% 0.32/1.53 gram_L864798063lle_wf: dtree > $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_If,type,
% 0.32/1.53 if:
% 0.32/1.53 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.32/1.53 top_top:
% 0.32/1.53 !>[A: $tType] : A ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Pure_Otype,type,
% 0.32/1.53 type2:
% 0.32/1.53 !>[A: $tType] : ( itself @ A ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Set_OCollect,type,
% 0.32/1.53 collect:
% 0.32/1.53 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Set_Oimage,type,
% 0.32/1.53 image:
% 0.32/1.53 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Set_Ovimage,type,
% 0.32/1.53 vimage:
% 0.32/1.53 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Sum__Type_OInl,type,
% 0.32/1.53 sum_Inl:
% 0.32/1.53 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Sum__Type_OInr,type,
% 0.32/1.53 sum_Inr:
% 0.32/1.53 !>[B: $tType,A: $tType] : ( B > ( sum_sum @ A @ B ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Sum__Type_Omap__sum,type,
% 0.32/1.53 sum_map_sum:
% 0.32/1.53 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C ) > ( B > D ) > ( sum_sum @ A @ B ) > ( sum_sum @ C @ D ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum,type,
% 0.32/1.53 sum_rec_sum:
% 0.32/1.53 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Sum__Type_Osum_Ocase__sum,type,
% 0.32/1.53 sum_case_sum:
% 0.32/1.53 !>[A: $tType,C: $tType,B: $tType] : ( ( A > C ) > ( B > C ) > ( sum_sum @ A @ B ) > C ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_member,type,
% 0.32/1.53 member:
% 0.32/1.53 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_a,type,
% 0.32/1.53 a: t ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_n,type,
% 0.32/1.53 n2: n ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_t__tr,type,
% 0.32/1.53 t_tr: sum_sum @ t @ dtree ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_tr0,type,
% 0.32/1.53 tr0: dtree ).
% 0.32/1.53
% 0.32/1.53 thf(fact_0_n,axiom,
% 0.32/1.53 gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ n2 ).
% 0.32/1.53
% 0.32/1.53 thf(fact_1_root__H__pick,axiom,
% 0.32/1.53 ! [N: n] :
% 0.32/1.53 ( ( root @ ( gram_L1451583624elle_H @ tr0 @ N ) )
% 0.32/1.53 = ( root @ ( gram_L315592705e_pick @ tr0 @ N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_2_t__tr,axiom,
% 0.32/1.53 member @ ( sum_sum @ t @ dtree ) @ t_tr @ ( cont @ ( gram_L315592705e_pick @ tr0 @ n2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_3_root__pick,axiom,
% 0.32/1.53 ! [N: n] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ N )
% 0.32/1.53 => ( ( root @ ( gram_L315592705e_pick @ tr0 @ N ) )
% 0.32/1.53 = N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_4_H__r__def,axiom,
% 0.32/1.53 ! [N: n] :
% 0.32/1.53 ( ( gram_L1221482026le_H_r @ tr0 @ N )
% 0.32/1.53 = ( root @ ( gram_L315592705e_pick @ tr0 @ N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_5_root__H,axiom,
% 0.32/1.53 ! [N: n] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ N )
% 0.32/1.53 => ( ( root @ ( gram_L1451583624elle_H @ tr0 @ N ) )
% 0.32/1.53 = N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_6_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__H,axiom,
% 0.32/1.53 ! [Tr0: dtree,N: n] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.32/1.53 => ( ( root @ ( gram_L1451583624elle_H @ Tr0 @ N ) )
% 0.32/1.53 = N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_7_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__pick,axiom,
% 0.32/1.53 ! [Tr0: dtree,N: n] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.32/1.53 => ( ( root @ ( gram_L315592705e_pick @ Tr0 @ N ) )
% 0.32/1.53 = N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_8_inItr_OBase,axiom,
% 0.32/1.53 ! [Tr: dtree,Ns: set @ n] :
% 0.32/1.53 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.32/1.53 => ( gram_L830233218_inItr @ Ns @ Tr @ ( root @ Tr ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_9_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__H__pick,axiom,
% 0.32/1.53 ! [Tr0: dtree,N: n] :
% 0.32/1.53 ( ( root @ ( gram_L1451583624elle_H @ Tr0 @ N ) )
% 0.32/1.53 = ( root @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_10_inItr__root__in,axiom,
% 0.32/1.53 ! [Ns: set @ n,Tr: dtree,N: n] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.32/1.53 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_11_wf__pick,axiom,
% 0.32/1.53 ! [N: n] :
% 0.32/1.53 ( ( gram_L864798063lle_wf @ tr0 )
% 0.32/1.53 => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ N )
% 0.32/1.53 => ( gram_L864798063lle_wf @ ( gram_L315592705e_pick @ tr0 @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_12_pick,axiom,
% 0.32/1.53 ! [N: n] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ N )
% 0.32/1.53 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ tr0 @ N ) @ tr0 )
% 0.32/1.53 & ( ( root @ ( gram_L315592705e_pick @ tr0 @ N ) )
% 0.32/1.53 = N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_13_comp__id,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,F: A > B] :
% 0.32/1.53 ( ( comp @ A @ B @ A @ F @ ( id @ A ) )
% 0.32/1.53 = F ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_14_id__comp,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,G: A > B] :
% 0.32/1.53 ( ( comp @ B @ B @ A @ ( id @ B ) @ G )
% 0.32/1.53 = G ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_15_fun_Omap__id,axiom,
% 0.32/1.53 ! [A: $tType,D: $tType,T2: D > A] :
% 0.32/1.53 ( ( comp @ A @ A @ D @ ( id @ A ) @ T2 )
% 0.32/1.53 = T2 ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_16_subtr__H,axiom,
% 0.32/1.53 ! [N: n,Tr1: dtree] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ N )
% 0.32/1.53 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr1 @ ( gram_L1451583624elle_H @ tr0 @ N ) )
% 0.32/1.53 => ? [N1: n] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ N1 )
% 0.32/1.53 & ( Tr1
% 0.32/1.53 = ( gram_L1451583624elle_H @ tr0 @ N1 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_17_subtr__pick,axiom,
% 0.32/1.53 ! [N: n] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ N )
% 0.32/1.53 => ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ tr0 @ N ) @ tr0 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_18_sum_Oinject_I1_J,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,X1: A,Y1: A] :
% 0.32/1.53 ( ( ( sum_Inl @ A @ B @ X1 )
% 0.32/1.53 = ( sum_Inl @ A @ B @ Y1 ) )
% 0.32/1.53 = ( X1 = Y1 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_19_old_Osum_Oinject_I1_J,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,A2: A,A3: A] :
% 0.32/1.53 ( ( ( sum_Inl @ A @ B @ A2 )
% 0.32/1.53 = ( sum_Inl @ A @ B @ A3 ) )
% 0.32/1.53 = ( A2 = A3 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_20_id__apply,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( id @ A )
% 0.32/1.53 = ( ^ [X: A] : X ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_21_comp__apply,axiom,
% 0.32/1.53 ! [C: $tType,A: $tType,B: $tType] :
% 0.32/1.53 ( ( comp @ B @ A @ C )
% 0.32/1.53 = ( ^ [F2: B > A,G2: C > B,X: C] : ( F2 @ ( G2 @ X ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_22_UNIV__I,axiom,
% 0.32/1.53 ! [A: $tType,X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_23_wf__subtr,axiom,
% 0.32/1.53 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 0.32/1.53 ( ( gram_L864798063lle_wf @ Tr1 )
% 0.32/1.53 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.32/1.53 => ( gram_L864798063lle_wf @ Tr ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_24_subtr__trans,axiom,
% 0.32/1.53 ! [Ns: set @ n,Tr1: dtree,Tr2: dtree,Tr3: dtree] :
% 0.32/1.53 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr2 )
% 0.32/1.53 => ( ( gram_L716654942_subtr @ Ns @ Tr2 @ Tr3 )
% 0.32/1.53 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_25_subtr__rootR__in,axiom,
% 0.32/1.53 ! [Ns: set @ n,Tr1: dtree,Tr2: dtree] :
% 0.32/1.53 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr2 )
% 0.32/1.53 => ( member @ n @ ( root @ Tr2 ) @ Ns ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_26_subtr__rootL__in,axiom,
% 0.32/1.53 ! [Ns: set @ n,Tr1: dtree,Tr2: dtree] :
% 0.32/1.53 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr2 )
% 0.32/1.53 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_27_subtr_ORefl,axiom,
% 0.32/1.53 ! [Tr: dtree,Ns: set @ n] :
% 0.32/1.53 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.32/1.53 => ( gram_L716654942_subtr @ Ns @ Tr @ Tr ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_28_subtr__inItr,axiom,
% 0.32/1.53 ! [Ns: set @ n,Tr: dtree,N: n,Tr1: dtree] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.32/1.53 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.32/1.53 => ( gram_L830233218_inItr @ Ns @ Tr1 @ N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_29_inItr__subtr,axiom,
% 0.32/1.53 ! [Ns: set @ n,Tr: dtree,N: n] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.32/1.53 => ? [Tr4: dtree] :
% 0.32/1.53 ( ( gram_L716654942_subtr @ Ns @ Tr4 @ Tr )
% 0.32/1.53 & ( ( root @ Tr4 )
% 0.32/1.53 = N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_30_UNIV__witness,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_31_UNIV__eq__I,axiom,
% 0.32/1.53 ! [A: $tType,A4: set @ A] :
% 0.32/1.53 ( ! [X3: A] : ( member @ A @ X3 @ A4 )
% 0.32/1.53 => ( ( top_top @ ( set @ A ) )
% 0.32/1.53 = A4 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_32_fun_Omap__comp,axiom,
% 0.32/1.53 ! [B: $tType,C: $tType,A: $tType,D: $tType,G: B > C,F: A > B,V: D > A] :
% 0.32/1.53 ( ( comp @ B @ C @ D @ G @ ( comp @ A @ B @ D @ F @ V ) )
% 0.32/1.53 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G @ F ) @ V ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_33_comp__eq__dest__lhs,axiom,
% 0.32/1.53 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B2: A > C,C2: A > B,V: A] :
% 0.32/1.53 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.32/1.53 = C2 )
% 0.32/1.53 => ( ( A2 @ ( B2 @ V ) )
% 0.32/1.53 = ( C2 @ V ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_34_comp__eq__elim,axiom,
% 0.32/1.53 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C2: D > B,D2: A > D] :
% 0.32/1.53 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.32/1.53 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 0.32/1.53 => ! [V2: A] :
% 0.32/1.53 ( ( A2 @ ( B2 @ V2 ) )
% 0.32/1.53 = ( C2 @ ( D2 @ V2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_35_comp__eq__dest,axiom,
% 0.32/1.53 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C2: D > B,D2: A > D,V: A] :
% 0.32/1.53 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.32/1.53 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 0.32/1.53 => ( ( A2 @ ( B2 @ V ) )
% 0.32/1.53 = ( C2 @ ( D2 @ V ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_36_comp__assoc,axiom,
% 0.32/1.53 ! [B: $tType,D: $tType,C: $tType,A: $tType,F: D > B,G: C > D,H: A > C] :
% 0.32/1.53 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F @ G ) @ H )
% 0.32/1.53 = ( comp @ D @ B @ A @ F @ ( comp @ C @ D @ A @ G @ H ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_37_comp__def,axiom,
% 0.32/1.53 ! [A: $tType,C: $tType,B: $tType] :
% 0.32/1.53 ( ( comp @ B @ C @ A )
% 0.32/1.53 = ( ^ [F2: B > C,G2: A > B,X: A] : ( F2 @ ( G2 @ X ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_38_eq__id__iff,axiom,
% 0.32/1.53 ! [A: $tType,F: A > A] :
% 0.32/1.53 ( ( ! [X: A] :
% 0.32/1.53 ( ( F @ X )
% 0.32/1.53 = X ) )
% 0.32/1.53 = ( F
% 0.32/1.53 = ( id @ A ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_39_id__def,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( id @ A )
% 0.32/1.53 = ( ^ [X: A] : X ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_40_Inl__inject,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,X2: A,Y: A] :
% 0.32/1.53 ( ( ( sum_Inl @ A @ B @ X2 )
% 0.32/1.53 = ( sum_Inl @ A @ B @ Y ) )
% 0.32/1.53 => ( X2 = Y ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_41_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr__pick,axiom,
% 0.32/1.53 ! [Tr0: dtree,N: n] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.32/1.53 => ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ Tr0 @ N ) @ Tr0 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_42_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr__H,axiom,
% 0.32/1.53 ! [Tr0: dtree,N: n,Tr1: dtree] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.32/1.53 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr1 @ ( gram_L1451583624elle_H @ Tr0 @ N ) )
% 0.32/1.53 => ? [N1: n] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N1 )
% 0.32/1.53 & ( Tr1
% 0.32/1.53 = ( gram_L1451583624elle_H @ Tr0 @ N1 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_43_Gram__Lang__Mirabelle__ojxrtuoybn_Owf__pick,axiom,
% 0.32/1.53 ! [Tr0: dtree,N: n] :
% 0.32/1.53 ( ( gram_L864798063lle_wf @ Tr0 )
% 0.32/1.53 => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.32/1.53 => ( gram_L864798063lle_wf @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_44_Gram__Lang__Mirabelle__ojxrtuoybn_Opick,axiom,
% 0.32/1.53 ! [Tr0: dtree,N: n] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.32/1.53 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ Tr0 @ N ) @ Tr0 )
% 0.32/1.53 & ( ( root @ ( gram_L315592705e_pick @ Tr0 @ N ) )
% 0.32/1.53 = N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_45_mem__Collect__eq,axiom,
% 0.32/1.53 ! [A: $tType,A2: A,P: A > $o] :
% 0.32/1.53 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.32/1.53 = ( P @ A2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_46_Collect__mem__eq,axiom,
% 0.32/1.53 ! [A: $tType,A4: set @ A] :
% 0.32/1.53 ( ( collect @ A
% 0.32/1.53 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 0.32/1.53 = A4 ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_47_Collect__cong,axiom,
% 0.32/1.53 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ( P @ X3 )
% 0.32/1.53 = ( Q @ X3 ) )
% 0.32/1.53 => ( ( collect @ A @ P )
% 0.32/1.53 = ( collect @ A @ Q ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_48_ext,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ( F @ X3 )
% 0.32/1.53 = ( G @ X3 ) )
% 0.32/1.53 => ( F = G ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_49_Gram__Lang__Mirabelle__ojxrtuoybn_OH__r__def,axiom,
% 0.32/1.53 ( gram_L1221482026le_H_r
% 0.32/1.53 = ( ^ [Tr02: dtree,N2: n] : ( root @ ( gram_L315592705e_pick @ Tr02 @ N2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_50_fun_Omap__id0,axiom,
% 0.32/1.53 ! [A: $tType,D: $tType] :
% 0.32/1.53 ( ( comp @ A @ A @ D @ ( id @ A ) )
% 0.32/1.53 = ( id @ ( D > A ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_51_comp__eq__id__dest,axiom,
% 0.32/1.53 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B2: A > C,C2: A > B,V: A] :
% 0.32/1.53 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.32/1.53 = ( comp @ B @ B @ A @ ( id @ B ) @ C2 ) )
% 0.32/1.53 => ( ( A2 @ ( B2 @ V ) )
% 0.32/1.53 = ( C2 @ V ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_52_map__sum_Ocompositionality,axiom,
% 0.32/1.53 ! [D: $tType,F3: $tType,E: $tType,C: $tType,B: $tType,A: $tType,F: C > E,G: D > F3,H: A > C,I: B > D,Sum: sum_sum @ A @ B] :
% 0.32/1.53 ( ( sum_map_sum @ C @ E @ D @ F3 @ F @ G @ ( sum_map_sum @ A @ C @ B @ D @ H @ I @ Sum ) )
% 0.32/1.53 = ( sum_map_sum @ A @ E @ B @ F3 @ ( comp @ C @ E @ A @ F @ H ) @ ( comp @ D @ F3 @ B @ G @ I ) @ Sum ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_53_sum_Omap__comp,axiom,
% 0.32/1.53 ! [D: $tType,F3: $tType,E: $tType,C: $tType,B: $tType,A: $tType,G1: C > E,G22: D > F3,F1: A > C,F22: B > D,V: sum_sum @ A @ B] :
% 0.32/1.53 ( ( sum_map_sum @ C @ E @ D @ F3 @ G1 @ G22 @ ( sum_map_sum @ A @ C @ B @ D @ F1 @ F22 @ V ) )
% 0.32/1.53 = ( sum_map_sum @ A @ E @ B @ F3 @ ( comp @ C @ E @ A @ G1 @ F1 ) @ ( comp @ D @ F3 @ B @ G22 @ F22 ) @ V ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_54_map__sum_Ocomp,axiom,
% 0.32/1.53 ! [A: $tType,C: $tType,E: $tType,F3: $tType,D: $tType,B: $tType,F: C > E,G: D > F3,H: A > C,I: B > D] :
% 0.32/1.53 ( ( comp @ ( sum_sum @ C @ D ) @ ( sum_sum @ E @ F3 ) @ ( sum_sum @ A @ B ) @ ( sum_map_sum @ C @ E @ D @ F3 @ F @ G ) @ ( sum_map_sum @ A @ C @ B @ D @ H @ I ) )
% 0.32/1.53 = ( sum_map_sum @ A @ E @ B @ F3 @ ( comp @ C @ E @ A @ F @ H ) @ ( comp @ D @ F3 @ B @ G @ I ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_55_sum_Omap__id0,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType] :
% 0.32/1.53 ( ( sum_map_sum @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) )
% 0.32/1.53 = ( id @ ( sum_sum @ A @ B ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_56_sum_Omap__id,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,T2: sum_sum @ A @ B] :
% 0.32/1.53 ( ( sum_map_sum @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) @ T2 )
% 0.32/1.53 = T2 ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_57_map__sum_Osimps_I1_J,axiom,
% 0.32/1.53 ! [B: $tType,D: $tType,C: $tType,A: $tType,F1: A > C,F22: B > D,A2: A] :
% 0.32/1.53 ( ( sum_map_sum @ A @ C @ B @ D @ F1 @ F22 @ ( sum_Inl @ A @ B @ A2 ) )
% 0.32/1.53 = ( sum_Inl @ C @ D @ ( F1 @ A2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_58_H__def,axiom,
% 0.32/1.53 ( ( gram_L1451583624elle_H @ tr0 )
% 0.32/1.53 = ( unfold @ n @ ( gram_L1221482026le_H_r @ tr0 ) @ ( gram_L1221482011le_H_c @ tr0 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_59_root__o__deftr,axiom,
% 0.32/1.53 ( ( comp @ dtree @ n @ n @ root @ gram_L1231612515_deftr )
% 0.32/1.53 = ( id @ n ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_60_iso__tuple__UNIV__I,axiom,
% 0.32/1.53 ! [A: $tType,X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_61_top__apply,axiom,
% 0.32/1.53 ! [C: $tType,D: $tType] :
% 0.32/1.53 ( ( top @ C @ ( type2 @ C ) )
% 0.32/1.53 => ( ( top_top @ ( D > C ) )
% 0.32/1.53 = ( ^ [X: D] : ( top_top @ C ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_62_H__c__def,axiom,
% 0.32/1.53 ! [N: n] :
% 0.32/1.53 ( ( gram_L1221482011le_H_c @ tr0 @ N )
% 0.32/1.53 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_63_old_Osum_Osimps_I7_J,axiom,
% 0.32/1.53 ! [B: $tType,T: $tType,A: $tType,F1: A > T,F22: B > T,A2: A] :
% 0.32/1.53 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inl @ A @ B @ A2 ) )
% 0.32/1.53 = ( F1 @ A2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_64_map__sum__o__inj_I1_J,axiom,
% 0.32/1.53 ! [D: $tType,C: $tType,B: $tType,A: $tType,F: A > B,G: D > C] :
% 0.32/1.53 ( ( comp @ ( sum_sum @ A @ D ) @ ( sum_sum @ B @ C ) @ A @ ( sum_map_sum @ A @ B @ D @ C @ F @ G ) @ ( sum_Inl @ A @ D ) )
% 0.32/1.53 = ( comp @ B @ ( sum_sum @ B @ C ) @ A @ ( sum_Inl @ B @ C ) @ F ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_65_map__sum__InlD,axiom,
% 0.32/1.53 ! [D: $tType,B: $tType,C: $tType,A: $tType,F: C > A,G: D > B,Z: sum_sum @ C @ D,X2: A] :
% 0.32/1.53 ( ( ( sum_map_sum @ C @ A @ D @ B @ F @ G @ Z )
% 0.32/1.53 = ( sum_Inl @ A @ B @ X2 ) )
% 0.32/1.53 => ? [Y2: C] :
% 0.32/1.53 ( ( Z
% 0.32/1.53 = ( sum_Inl @ C @ D @ Y2 ) )
% 0.32/1.53 & ( ( F @ Y2 )
% 0.32/1.53 = X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_66_map__sum__if__distrib__then_I1_J,axiom,
% 0.32/1.53 ! [D: $tType,B: $tType,C: $tType,A: $tType,E2: $o,F: A > B,G: C > D,X2: A,Y: sum_sum @ A @ C] :
% 0.32/1.53 ( ( E2
% 0.32/1.53 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E2 @ ( sum_Inl @ A @ C @ X2 ) @ Y ) )
% 0.32/1.53 = ( sum_Inl @ B @ D @ ( F @ X2 ) ) ) )
% 0.32/1.53 & ( ~ E2
% 0.32/1.53 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E2 @ ( sum_Inl @ A @ C @ X2 ) @ Y ) )
% 0.32/1.53 = ( sum_map_sum @ A @ B @ C @ D @ F @ G @ Y ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_67_map__sum__if__distrib__else_I1_J,axiom,
% 0.32/1.53 ! [C: $tType,D: $tType,B: $tType,A: $tType,E2: $o,F: A > B,G: C > D,X2: sum_sum @ A @ C,Y: A] :
% 0.32/1.53 ( ( E2
% 0.32/1.53 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E2 @ X2 @ ( sum_Inl @ A @ C @ Y ) ) )
% 0.32/1.53 = ( sum_map_sum @ A @ B @ C @ D @ F @ G @ X2 ) ) )
% 0.32/1.53 & ( ~ E2
% 0.32/1.53 => ( ( sum_map_sum @ A @ B @ C @ D @ F @ G @ ( if @ ( sum_sum @ A @ C ) @ E2 @ X2 @ ( sum_Inl @ A @ C @ Y ) ) )
% 0.32/1.53 = ( sum_Inl @ B @ D @ ( F @ Y ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_68_image__eqI,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,B2: A,F: B > A,X2: B,A4: set @ B] :
% 0.32/1.53 ( ( B2
% 0.32/1.53 = ( F @ X2 ) )
% 0.32/1.53 => ( ( member @ B @ X2 @ A4 )
% 0.32/1.53 => ( member @ A @ B2 @ ( image @ B @ A @ F @ A4 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_69_image__id,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( image @ A @ A @ ( id @ A ) )
% 0.32/1.53 = ( id @ ( set @ A ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_70_root__deftr,axiom,
% 0.32/1.53 ! [N: n] :
% 0.32/1.53 ( ( root @ ( gram_L1231612515_deftr @ N ) )
% 0.32/1.53 = N ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_71_Inl__oplus__iff,axiom,
% 0.32/1.53 ! [B: $tType,C: $tType,A: $tType,Tr: A,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.32/1.53 ( ( 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 ) )
% 0.32/1.53 = ( member @ ( sum_sum @ A @ C ) @ ( sum_Inl @ A @ C @ Tr ) @ Tns ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_72_imageI,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,X2: A,A4: set @ A,F: A > B] :
% 0.32/1.53 ( ( member @ A @ X2 @ A4 )
% 0.32/1.53 => ( member @ B @ ( F @ X2 ) @ ( image @ A @ B @ F @ A4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_73_image__iff,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,Z: A,F: B > A,A4: set @ B] :
% 0.32/1.53 ( ( member @ A @ Z @ ( image @ B @ A @ F @ A4 ) )
% 0.32/1.53 = ( ? [X: B] :
% 0.32/1.53 ( ( member @ B @ X @ A4 )
% 0.32/1.53 & ( Z
% 0.32/1.53 = ( F @ X ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_74_bex__imageD,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,F: B > A,A4: set @ B,P: A > $o] :
% 0.32/1.53 ( ? [X4: A] :
% 0.32/1.53 ( ( member @ A @ X4 @ ( image @ B @ A @ F @ A4 ) )
% 0.32/1.53 & ( P @ X4 ) )
% 0.32/1.53 => ? [X3: B] :
% 0.32/1.53 ( ( member @ B @ X3 @ A4 )
% 0.32/1.53 & ( P @ ( F @ X3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_75_image__cong,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,M: set @ A,N3: set @ A,F: A > B,G: A > B] :
% 0.32/1.53 ( ( M = N3 )
% 0.32/1.53 => ( ! [X3: A] :
% 0.32/1.53 ( ( member @ A @ X3 @ N3 )
% 0.32/1.53 => ( ( F @ X3 )
% 0.32/1.53 = ( G @ X3 ) ) )
% 0.32/1.53 => ( ( image @ A @ B @ F @ M )
% 0.32/1.53 = ( image @ A @ B @ G @ N3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_76_ball__imageD,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,F: B > A,A4: set @ B,P: A > $o] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ( member @ A @ X3 @ ( image @ B @ A @ F @ A4 ) )
% 0.32/1.53 => ( P @ X3 ) )
% 0.32/1.53 => ! [X4: B] :
% 0.32/1.53 ( ( member @ B @ X4 @ A4 )
% 0.32/1.53 => ( P @ ( F @ X4 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_77_rev__image__eqI,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,X2: A,A4: set @ A,B2: B,F: A > B] :
% 0.32/1.53 ( ( member @ A @ X2 @ A4 )
% 0.32/1.53 => ( ( B2
% 0.32/1.53 = ( F @ X2 ) )
% 0.32/1.53 => ( member @ B @ B2 @ ( image @ A @ B @ F @ A4 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_78_surjD,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,F: B > A,Y: A] :
% 0.32/1.53 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.32/1.53 = ( top_top @ ( set @ A ) ) )
% 0.32/1.53 => ? [X3: B] :
% 0.32/1.53 ( Y
% 0.32/1.53 = ( F @ X3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_79_surjE,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,F: B > A,Y: A] :
% 0.32/1.53 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.32/1.53 = ( top_top @ ( set @ A ) ) )
% 0.32/1.53 => ~ ! [X3: B] :
% 0.32/1.53 ( Y
% 0.32/1.53 != ( F @ X3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_80_surjI,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,G: B > A,F: A > B] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ( G @ ( F @ X3 ) )
% 0.32/1.53 = X3 )
% 0.32/1.53 => ( ( image @ B @ A @ G @ ( top_top @ ( set @ B ) ) )
% 0.32/1.53 = ( top_top @ ( set @ A ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_81_rangeI,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,F: B > A,X2: B] : ( member @ A @ ( F @ X2 ) @ ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_82_surj__def,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,F: B > A] :
% 0.32/1.53 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.32/1.53 = ( top_top @ ( set @ A ) ) )
% 0.32/1.53 = ( ! [Y3: A] :
% 0.32/1.53 ? [X: B] :
% 0.32/1.53 ( Y3
% 0.32/1.53 = ( F @ X ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_83_range__eqI,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,B2: A,F: B > A,X2: B] :
% 0.32/1.53 ( ( B2
% 0.32/1.53 = ( F @ X2 ) )
% 0.32/1.53 => ( member @ A @ B2 @ ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_84_image__comp,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,C: $tType,F: B > A,G: C > B,R: set @ C] :
% 0.32/1.53 ( ( image @ B @ A @ F @ ( image @ C @ B @ G @ R ) )
% 0.32/1.53 = ( image @ C @ A @ ( comp @ B @ A @ C @ F @ G ) @ R ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_85_image__eq__imp__comp,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,D: $tType,C: $tType,F: B > A,A4: set @ B,G: C > A,B3: set @ C,H: A > D] :
% 0.32/1.53 ( ( ( image @ B @ A @ F @ A4 )
% 0.32/1.53 = ( image @ C @ A @ G @ B3 ) )
% 0.32/1.53 => ( ( image @ B @ D @ ( comp @ A @ D @ B @ H @ F ) @ A4 )
% 0.32/1.53 = ( image @ C @ D @ ( comp @ A @ D @ C @ H @ G ) @ B3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_86_top__set__def,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( top_top @ ( set @ A ) )
% 0.32/1.53 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_87_comp__surj,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,C: $tType,F: B > A,G: A > C] :
% 0.32/1.53 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.32/1.53 = ( top_top @ ( set @ A ) ) )
% 0.32/1.53 => ( ( ( image @ A @ C @ G @ ( top_top @ ( set @ A ) ) )
% 0.32/1.53 = ( top_top @ ( set @ C ) ) )
% 0.32/1.53 => ( ( image @ B @ C @ ( comp @ A @ C @ B @ G @ F ) @ ( top_top @ ( set @ B ) ) )
% 0.32/1.53 = ( top_top @ ( set @ C ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_88_fun_Oset__map,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,D: $tType,F: A > B,V: D > A] :
% 0.32/1.53 ( ( image @ D @ B @ ( comp @ A @ B @ D @ F @ V ) @ ( top_top @ ( set @ D ) ) )
% 0.32/1.53 = ( image @ A @ B @ F @ ( image @ D @ A @ V @ ( top_top @ ( set @ D ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_89_fun_Omap__cong,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,D: $tType,X2: D > A,Ya: D > A,F: A > B,G: A > B] :
% 0.32/1.53 ( ( X2 = Ya )
% 0.32/1.53 => ( ! [Z2: A] :
% 0.32/1.53 ( ( member @ A @ Z2 @ ( image @ D @ A @ Ya @ ( top_top @ ( set @ D ) ) ) )
% 0.32/1.53 => ( ( F @ Z2 )
% 0.32/1.53 = ( G @ Z2 ) ) )
% 0.32/1.53 => ( ( comp @ A @ B @ D @ F @ X2 )
% 0.32/1.53 = ( comp @ A @ B @ D @ G @ Ya ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_90_fun_Omap__cong0,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,D: $tType,X2: D > A,F: A > B,G: A > B] :
% 0.32/1.53 ( ! [Z2: A] :
% 0.32/1.53 ( ( member @ A @ Z2 @ ( image @ D @ A @ X2 @ ( top_top @ ( set @ D ) ) ) )
% 0.32/1.53 => ( ( F @ Z2 )
% 0.32/1.53 = ( G @ Z2 ) ) )
% 0.32/1.53 => ( ( comp @ A @ B @ D @ F @ X2 )
% 0.32/1.53 = ( comp @ A @ B @ D @ G @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_91_fun_Oinj__map__strong,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,D: $tType,X2: D > A,Xa: D > A,F: A > B,Fa: A > B] :
% 0.32/1.53 ( ! [Z2: A,Za: A] :
% 0.32/1.53 ( ( member @ A @ Z2 @ ( image @ D @ A @ X2 @ ( top_top @ ( set @ D ) ) ) )
% 0.32/1.53 => ( ( member @ A @ Za @ ( image @ D @ A @ Xa @ ( top_top @ ( set @ D ) ) ) )
% 0.32/1.53 => ( ( ( F @ Z2 )
% 0.32/1.53 = ( Fa @ Za ) )
% 0.32/1.53 => ( Z2 = Za ) ) ) )
% 0.32/1.53 => ( ( ( comp @ A @ B @ D @ F @ X2 )
% 0.32/1.53 = ( comp @ A @ B @ D @ Fa @ Xa ) )
% 0.32/1.53 => ( X2 = Xa ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_92_surj__id,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( image @ A @ A @ ( id @ A ) @ ( top_top @ ( set @ A ) ) )
% 0.32/1.53 = ( top_top @ ( set @ A ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_93_Inl__oplus__elim,axiom,
% 0.32/1.53 ! [B: $tType,C: $tType,A: $tType,Tr: A,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.32/1.53 ( ( 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 ) )
% 0.32/1.53 => ( member @ ( sum_sum @ A @ C ) @ ( sum_Inl @ A @ C @ Tr ) @ Tns ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_94_wf__deftr,axiom,
% 0.32/1.53 ! [N: n] : ( gram_L864798063lle_wf @ ( gram_L1231612515_deftr @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_95_Gram__Lang__Mirabelle__ojxrtuoybn_OH__def,axiom,
% 0.32/1.53 ( gram_L1451583624elle_H
% 0.32/1.53 = ( ^ [Tr02: dtree] : ( unfold @ n @ ( gram_L1221482026le_H_r @ Tr02 ) @ ( gram_L1221482011le_H_c @ Tr02 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_96_comp__apply__eq,axiom,
% 0.32/1.53 ! [B: $tType,D: $tType,A: $tType,C: $tType,F: B > A,G: C > B,X2: C,H: D > A,K: C > D] :
% 0.32/1.53 ( ( ( F @ ( G @ X2 ) )
% 0.32/1.53 = ( H @ ( K @ X2 ) ) )
% 0.32/1.53 => ( ( comp @ B @ A @ C @ F @ G @ X2 )
% 0.32/1.53 = ( comp @ D @ A @ C @ H @ K @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_97_rewriteL__comp__comp,axiom,
% 0.32/1.53 ! [C: $tType,B: $tType,A: $tType,D: $tType,F: C > B,G: A > C,L: A > B,H: D > A] :
% 0.32/1.53 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.32/1.53 = L )
% 0.32/1.53 => ( ( comp @ C @ B @ D @ F @ ( comp @ A @ C @ D @ G @ H ) )
% 0.32/1.53 = ( comp @ A @ B @ D @ L @ H ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_98_rewriteR__comp__comp,axiom,
% 0.32/1.53 ! [C: $tType,D: $tType,B: $tType,A: $tType,G: C > B,H: A > C,R: A > B,F: B > D] :
% 0.32/1.53 ( ( ( comp @ C @ B @ A @ G @ H )
% 0.32/1.53 = R )
% 0.32/1.53 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F @ G ) @ H )
% 0.32/1.53 = ( comp @ B @ D @ A @ F @ R ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_99_rewriteL__comp__comp2,axiom,
% 0.32/1.53 ! [A: $tType,C: $tType,B: $tType,D: $tType,E: $tType,F: C > B,G: A > C,L1: D > B,L2: A > D,H: E > A,R: E > D] :
% 0.32/1.53 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.32/1.53 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 0.32/1.53 => ( ( ( comp @ A @ D @ E @ L2 @ H )
% 0.32/1.53 = R )
% 0.32/1.53 => ( ( comp @ C @ B @ E @ F @ ( comp @ A @ C @ E @ G @ H ) )
% 0.32/1.53 = ( comp @ D @ B @ E @ L1 @ R ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_100_rewriteR__comp__comp2,axiom,
% 0.32/1.53 ! [C: $tType,B: $tType,E: $tType,D: $tType,A: $tType,G: C > B,H: A > C,R1: D > B,R2: A > D,F: B > E,L: D > E] :
% 0.32/1.53 ( ( ( comp @ C @ B @ A @ G @ H )
% 0.32/1.53 = ( comp @ D @ B @ A @ R1 @ R2 ) )
% 0.32/1.53 => ( ( ( comp @ B @ E @ D @ F @ R1 )
% 0.32/1.53 = L )
% 0.32/1.53 => ( ( comp @ C @ E @ A @ ( comp @ B @ E @ C @ F @ G ) @ H )
% 0.32/1.53 = ( comp @ D @ E @ A @ L @ R2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_101_Gram__Lang__Mirabelle__ojxrtuoybn_OH__c__def,axiom,
% 0.32/1.53 ( gram_L1221482011le_H_c
% 0.32/1.53 = ( ^ [Tr02: dtree,N2: n] : ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ ( gram_L315592705e_pick @ Tr02 @ N2 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_102_subtr__deftr,axiom,
% 0.32/1.53 ! [Ns: set @ n,Tr5: dtree,N: n] :
% 0.32/1.53 ( ( gram_L716654942_subtr @ Ns @ Tr5 @ ( gram_L1231612515_deftr @ N ) )
% 0.32/1.53 => ( Tr5
% 0.32/1.53 = ( gram_L1231612515_deftr @ ( root @ Tr5 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_103_pointfree__idE,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,F: B > A,G: A > B,X2: A] :
% 0.32/1.53 ( ( ( comp @ B @ A @ A @ F @ G )
% 0.32/1.53 = ( id @ A ) )
% 0.32/1.53 => ( ( F @ ( G @ X2 ) )
% 0.32/1.53 = X2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_104_deftr__def,axiom,
% 0.32/1.53 ( gram_L1231612515_deftr
% 0.32/1.53 = ( unfold @ n @ ( id @ n ) @ gram_L1451583635elle_S ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_105_surj__fun__eq,axiom,
% 0.32/1.53 ! [B: $tType,C: $tType,A: $tType,F: B > A,X5: set @ B,G1: A > C,G22: A > C] :
% 0.32/1.53 ( ( ( image @ B @ A @ F @ X5 )
% 0.32/1.53 = ( top_top @ ( set @ A ) ) )
% 0.32/1.53 => ( ! [X3: B] :
% 0.32/1.53 ( ( member @ B @ X3 @ X5 )
% 0.32/1.53 => ( ( comp @ A @ C @ B @ G1 @ F @ X3 )
% 0.32/1.53 = ( comp @ A @ C @ B @ G22 @ F @ X3 ) ) )
% 0.32/1.53 => ( G1 = G22 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_106_finite__H__c,axiom,
% 0.32/1.53 ! [N: n] : ( finite_finite2 @ ( sum_sum @ t @ n ) @ ( gram_L1221482011le_H_c @ tr0 @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_107_unfold_I1_J,axiom,
% 0.32/1.53 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ A ) ),B2: A] :
% 0.32/1.53 ( ( root @ ( unfold @ A @ Rt @ Ct @ B2 ) )
% 0.32/1.53 = ( Rt @ B2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_108_cont__H,axiom,
% 0.32/1.53 ! [N: n] :
% 0.32/1.53 ( ( cont @ ( gram_L1451583624elle_H @ tr0 @ N ) )
% 0.32/1.53 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ tr0 ) @ root ) ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_109_dtree__cong,axiom,
% 0.32/1.53 ! [Tr: dtree,Tr5: dtree] :
% 0.32/1.53 ( ( ( root @ Tr )
% 0.32/1.53 = ( root @ Tr5 ) )
% 0.32/1.53 => ( ( ( cont @ Tr )
% 0.32/1.53 = ( cont @ Tr5 ) )
% 0.32/1.53 => ( Tr = Tr5 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_110_hsubst__c__def,axiom,
% 0.32/1.53 ( gram_L1905609002ubst_c
% 0.32/1.53 = ( ^ [Tr02: dtree,Tr6: dtree] :
% 0.32/1.53 ( if @ ( set @ ( sum_sum @ t @ dtree ) )
% 0.32/1.53 @ ( ( root @ Tr6 )
% 0.32/1.53 = ( root @ Tr02 ) )
% 0.32/1.53 @ ( cont @ Tr02 )
% 0.32/1.53 @ ( cont @ Tr6 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_111_top1I,axiom,
% 0.32/1.53 ! [A: $tType,X2: A] : ( top_top @ ( A > $o ) @ X2 ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_112_cont__deftr,axiom,
% 0.32/1.53 ! [N: n] :
% 0.32/1.53 ( ( cont @ ( gram_L1231612515_deftr @ N ) )
% 0.32/1.53 = ( image @ ( sum_sum @ t @ n ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ n @ dtree @ ( id @ t ) @ gram_L1231612515_deftr ) @ ( gram_L1451583635elle_S @ N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_113_top__conj_I2_J,axiom,
% 0.32/1.53 ! [A: $tType,P: $o,X2: A] :
% 0.32/1.53 ( ( P
% 0.32/1.53 & ( top_top @ ( A > $o ) @ X2 ) )
% 0.32/1.53 = P ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_114_top__conj_I1_J,axiom,
% 0.32/1.53 ! [A: $tType,X2: A,P: $o] :
% 0.32/1.53 ( ( ( top_top @ ( A > $o ) @ X2 )
% 0.32/1.53 & P )
% 0.32/1.53 = P ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_115_finite__S,axiom,
% 0.32/1.53 ! [N: n] : ( finite_finite2 @ ( sum_sum @ t @ n ) @ ( gram_L1451583635elle_S @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_116_unfold_I2_J,axiom,
% 0.32/1.53 ! [A: $tType,Ct: A > ( set @ ( sum_sum @ t @ A ) ),B2: A,Rt: A > n] :
% 0.32/1.53 ( ( finite_finite2 @ ( sum_sum @ t @ A ) @ ( Ct @ B2 ) )
% 0.32/1.53 => ( ( cont @ ( unfold @ A @ Rt @ Ct @ B2 ) )
% 0.32/1.53 = ( image @ ( sum_sum @ t @ A ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ A @ dtree @ ( id @ t ) @ ( unfold @ A @ Rt @ Ct ) ) @ ( Ct @ B2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_117_Gram__Lang__Mirabelle__ojxrtuoybn_Ofinite__H__c,axiom,
% 0.32/1.53 ! [Tr0: dtree,N: n] : ( finite_finite2 @ ( sum_sum @ t @ n ) @ ( gram_L1221482011le_H_c @ Tr0 @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_118_Gram__Lang__Mirabelle__ojxrtuoybn_Ocont__H,axiom,
% 0.32/1.53 ! [Tr0: dtree,N: n] :
% 0.32/1.53 ( ( cont @ ( gram_L1451583624elle_H @ Tr0 @ N ) )
% 0.32/1.53 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ Tr0 ) @ root ) ) @ ( cont @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_119_finite__Plus__UNIV__iff,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType] :
% 0.32/1.53 ( ( finite_finite2 @ ( sum_sum @ A @ B ) @ ( top_top @ ( set @ ( sum_sum @ A @ B ) ) ) )
% 0.32/1.53 = ( ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.32/1.53 & ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_120_finite__option__UNIV,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( finite_finite2 @ ( option @ A ) @ ( top_top @ ( set @ ( option @ A ) ) ) )
% 0.32/1.53 = ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_121_finite__imageI,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,F4: set @ A,H: A > B] :
% 0.32/1.53 ( ( finite_finite2 @ A @ F4 )
% 0.32/1.53 => ( finite_finite2 @ B @ ( image @ A @ B @ H @ F4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_122_cont__hsubst__neq,axiom,
% 0.32/1.53 ! [Tr: dtree,Tr0: dtree] :
% 0.32/1.53 ( ( ( root @ Tr )
% 0.32/1.53 != ( root @ Tr0 ) )
% 0.32/1.53 => ( ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.32/1.53 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ Tr0 ) ) @ ( cont @ Tr ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_123_cont__hsubst__eq,axiom,
% 0.32/1.53 ! [Tr: dtree,Tr0: dtree] :
% 0.32/1.53 ( ( ( root @ Tr )
% 0.32/1.53 = ( root @ Tr0 ) )
% 0.32/1.53 => ( ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.32/1.53 = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ Tr0 ) ) @ ( cont @ Tr0 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_124_finite__code,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( finite_finite @ A @ ( type2 @ A ) )
% 0.32/1.53 => ( ( finite_finite2 @ A )
% 0.32/1.53 = ( ^ [A5: set @ A] : $true ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_125_root__hsubst,axiom,
% 0.32/1.53 ! [Tr0: dtree,Tr: dtree] :
% 0.32/1.53 ( ( root @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.32/1.53 = ( root @ Tr ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_126_root__o__subst,axiom,
% 0.32/1.53 ! [Tr0: dtree] :
% 0.32/1.53 ( ( comp @ dtree @ n @ dtree @ root @ ( gram_L1004374585hsubst @ Tr0 ) )
% 0.32/1.53 = root ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_127_finite__cont,axiom,
% 0.32/1.53 ! [Tr: dtree] : ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ ( cont @ Tr ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_128_finite__N,axiom,
% 0.32/1.53 finite_finite2 @ n @ ( top_top @ ( set @ n ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_129_hsubst__eq,axiom,
% 0.32/1.53 ! [Tr: dtree,Tr0: dtree] :
% 0.32/1.53 ( ( ( root @ Tr )
% 0.32/1.53 = ( root @ Tr0 ) )
% 0.32/1.53 => ( ( gram_L1004374585hsubst @ Tr0 @ Tr )
% 0.32/1.53 = ( gram_L1004374585hsubst @ Tr0 @ Tr0 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_130_wf__hsubst,axiom,
% 0.32/1.53 ! [Tr0: dtree,Tr: dtree] :
% 0.32/1.53 ( ( gram_L864798063lle_wf @ Tr0 )
% 0.32/1.53 => ( ( gram_L864798063lle_wf @ Tr )
% 0.32/1.53 => ( gram_L864798063lle_wf @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_131_finite__hsubst__c,axiom,
% 0.32/1.53 ! [Tr0: dtree,N: dtree] : ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ ( gram_L1905609002ubst_c @ Tr0 @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_132_finite,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( finite_finite @ A @ ( type2 @ A ) )
% 0.32/1.53 => ! [A4: set @ A] : ( finite_finite2 @ A @ A4 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_133_finite__set__choice,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,A4: set @ A,P: A > B > $o] :
% 0.32/1.53 ( ( finite_finite2 @ A @ A4 )
% 0.32/1.53 => ( ! [X3: A] :
% 0.32/1.53 ( ( member @ A @ X3 @ A4 )
% 0.32/1.53 => ? [X12: B] : ( P @ X3 @ X12 ) )
% 0.32/1.53 => ? [F5: A > B] :
% 0.32/1.53 ! [X4: A] :
% 0.32/1.53 ( ( member @ A @ X4 @ A4 )
% 0.32/1.53 => ( P @ X4 @ ( F5 @ X4 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_134_finite__UNIV,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( finite_finite @ A @ ( type2 @ A ) )
% 0.32/1.53 => ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_135_infinite__UNIV__char__0,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.32/1.53 => ~ ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_136_ex__new__if__finite,axiom,
% 0.32/1.53 ! [A: $tType,A4: set @ A] :
% 0.32/1.53 ( ~ ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.32/1.53 => ( ( finite_finite2 @ A @ A4 )
% 0.32/1.53 => ? [A6: A] :
% 0.32/1.53 ~ ( member @ A @ A6 @ A4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_137_finite__fun__UNIVD2,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType] :
% 0.32/1.53 ( ( finite_finite2 @ ( A > B ) @ ( top_top @ ( set @ ( A > B ) ) ) )
% 0.32/1.53 => ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_138_finite__Prod__UNIV,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType] :
% 0.32/1.53 ( ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.32/1.53 => ( ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) )
% 0.32/1.53 => ( finite_finite2 @ ( product_prod @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_139_finite__prod,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType] :
% 0.32/1.53 ( ( finite_finite2 @ ( product_prod @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ A @ B ) ) ) )
% 0.32/1.53 = ( ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.32/1.53 & ( finite_finite2 @ B @ ( top_top @ ( set @ B ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_140_Finite__Set_Ofinite__set,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( finite_finite2 @ ( set @ A ) @ ( top_top @ ( set @ ( set @ A ) ) ) )
% 0.32/1.53 = ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_141_hsubst__def,axiom,
% 0.32/1.53 ( gram_L1004374585hsubst
% 0.32/1.53 = ( ^ [Tr02: dtree] : ( unfold @ dtree @ gram_L1905609017ubst_r @ ( gram_L1905609002ubst_c @ Tr02 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_142_top__empty__eq,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( top_top @ ( A > $o ) )
% 0.32/1.53 = ( ^ [X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_143_Node__root__cont,axiom,
% 0.32/1.53 ! [Tr: dtree] :
% 0.32/1.53 ( ( node @ ( root @ Tr ) @ ( cont @ Tr ) )
% 0.32/1.53 = Tr ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_144_DEADID_Oin__rel,axiom,
% 0.32/1.53 ! [B: $tType] :
% 0.32/1.53 ( ( ^ [Y4: B,Z3: B] : ( Y4 = Z3 ) )
% 0.32/1.53 = ( ^ [A7: B,B4: B] :
% 0.32/1.53 ? [Z4: B] :
% 0.32/1.53 ( ( member @ B @ Z4 @ ( top_top @ ( set @ B ) ) )
% 0.32/1.53 & ( ( id @ B @ Z4 )
% 0.32/1.53 = A7 )
% 0.32/1.53 & ( ( id @ B @ Z4 )
% 0.32/1.53 = B4 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_145_root__Node,axiom,
% 0.32/1.53 ! [N: n,As: set @ ( sum_sum @ t @ dtree )] :
% 0.32/1.53 ( ( root @ ( node @ N @ As ) )
% 0.32/1.53 = N ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_146_dtree__simps,axiom,
% 0.32/1.53 ! [As: set @ ( sum_sum @ t @ dtree ),As2: set @ ( sum_sum @ t @ dtree ),N: n,N4: n] :
% 0.32/1.53 ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As )
% 0.32/1.53 => ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As2 )
% 0.32/1.53 => ( ( ( node @ N @ As )
% 0.32/1.53 = ( node @ N4 @ As2 ) )
% 0.32/1.53 = ( ( N = N4 )
% 0.32/1.53 & ( As = As2 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_147_cont__Node,axiom,
% 0.32/1.53 ! [As: set @ ( sum_sum @ t @ dtree ),N: n] :
% 0.32/1.53 ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As )
% 0.32/1.53 => ( ( cont @ ( node @ N @ As ) )
% 0.32/1.53 = As ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_148_dtree__cases,axiom,
% 0.32/1.53 ! [Tr: dtree] :
% 0.32/1.53 ~ ! [N5: n,As3: set @ ( sum_sum @ t @ dtree )] :
% 0.32/1.53 ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ As3 )
% 0.32/1.53 => ( Tr
% 0.32/1.53 != ( node @ N5 @ As3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_149_type__copy__map__cong0,axiom,
% 0.32/1.53 ! [B: $tType,D: $tType,E: $tType,A: $tType,C: $tType,M: B > A,G: C > B,X2: C,N3: D > A,H: C > D,F: A > E] :
% 0.32/1.53 ( ( ( M @ ( G @ X2 ) )
% 0.32/1.53 = ( N3 @ ( H @ X2 ) ) )
% 0.32/1.53 => ( ( comp @ B @ E @ C @ ( comp @ A @ E @ B @ F @ M ) @ G @ X2 )
% 0.32/1.53 = ( comp @ D @ E @ C @ ( comp @ A @ E @ D @ F @ N3 ) @ H @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_150_hsubst__r__def,axiom,
% 0.32/1.53 gram_L1905609017ubst_r = root ).
% 0.32/1.53
% 0.32/1.53 thf(fact_151_Sup_OSUP__id__eq,axiom,
% 0.32/1.53 ! [A: $tType,Sup: ( set @ A ) > A,A4: set @ A] :
% 0.32/1.53 ( ( Sup @ ( image @ A @ A @ ( id @ A ) @ A4 ) )
% 0.32/1.53 = ( Sup @ A4 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_152_Inf_OINF__id__eq,axiom,
% 0.32/1.53 ! [A: $tType,Inf: ( set @ A ) > A,A4: set @ A] :
% 0.32/1.53 ( ( Inf @ ( image @ A @ A @ ( id @ A ) @ A4 ) )
% 0.32/1.53 = ( Inf @ A4 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_153_Sup_OSUP__image,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,C: $tType,Sup: ( set @ A ) > A,G: B > A,F: C > B,A4: set @ C] :
% 0.32/1.53 ( ( Sup @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A4 ) ) )
% 0.32/1.53 = ( Sup @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_154_Sup_OSUP__cong,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,A4: set @ B,B3: set @ B,C3: B > A,D3: B > A,Sup: ( set @ A ) > A] :
% 0.32/1.53 ( ( A4 = B3 )
% 0.32/1.53 => ( ! [X3: B] :
% 0.32/1.53 ( ( member @ B @ X3 @ B3 )
% 0.32/1.53 => ( ( C3 @ X3 )
% 0.32/1.53 = ( D3 @ X3 ) ) )
% 0.32/1.53 => ( ( Sup @ ( image @ B @ A @ C3 @ A4 ) )
% 0.32/1.53 = ( Sup @ ( image @ B @ A @ D3 @ B3 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_155_Inf_OINF__cong,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,A4: set @ B,B3: set @ B,C3: B > A,D3: B > A,Inf: ( set @ A ) > A] :
% 0.32/1.53 ( ( A4 = B3 )
% 0.32/1.53 => ( ! [X3: B] :
% 0.32/1.53 ( ( member @ B @ X3 @ B3 )
% 0.32/1.53 => ( ( C3 @ X3 )
% 0.32/1.53 = ( D3 @ X3 ) ) )
% 0.32/1.53 => ( ( Inf @ ( image @ B @ A @ C3 @ A4 ) )
% 0.32/1.53 = ( Inf @ ( image @ B @ A @ D3 @ B3 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_156_Inf_OINF__image,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,C: $tType,Inf: ( set @ A ) > A,G: B > A,F: C > B,A4: set @ C] :
% 0.32/1.53 ( ( Inf @ ( image @ B @ A @ G @ ( image @ C @ B @ F @ A4 ) ) )
% 0.32/1.53 = ( Inf @ ( image @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ A4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_157_Inl__cont__H,axiom,
% 0.32/1.53 ! [N: n] :
% 0.32/1.53 ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1451583624elle_H @ tr0 @ N ) ) )
% 0.32/1.53 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_158_case__sum__o__map__sum__id,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,C: $tType,G: B > A,F: C > A,X2: sum_sum @ C @ B] :
% 0.32/1.53 ( ( comp @ ( sum_sum @ A @ B ) @ A @ ( sum_sum @ C @ B ) @ ( sum_case_sum @ A @ A @ B @ ( id @ A ) @ G ) @ ( sum_map_sum @ C @ A @ B @ B @ F @ ( id @ B ) ) @ X2 )
% 0.32/1.53 = ( sum_case_sum @ C @ A @ B @ ( comp @ C @ A @ C @ F @ ( id @ C ) ) @ G @ X2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_159_inFr2_OBase,axiom,
% 0.32/1.53 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.32/1.53 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.32/1.53 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 0.32/1.53 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_160_vimage__eq,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 0.32/1.53 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 0.32/1.53 = ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_161_vimageI,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,F: B > A,A2: B,B2: A,B3: set @ A] :
% 0.32/1.53 ( ( ( F @ A2 )
% 0.32/1.53 = B2 )
% 0.32/1.53 => ( ( member @ A @ B2 @ B3 )
% 0.32/1.53 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ B3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_162_vimage__UNIV,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,F: A > B] :
% 0.32/1.53 ( ( vimage @ A @ B @ F @ ( top_top @ ( set @ B ) ) )
% 0.32/1.53 = ( top_top @ ( set @ A ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_163_vimage__id,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( vimage @ A @ A @ ( id @ A ) )
% 0.32/1.53 = ( id @ ( set @ A ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_164_Inl__m__oplus,axiom,
% 0.32/1.53 ! [B: $tType,C: $tType,A: $tType,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.32/1.53 ( ( 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 ) )
% 0.32/1.53 = ( vimage @ A @ ( sum_sum @ A @ C ) @ ( sum_Inl @ A @ C ) @ Tns ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_165_Inl__cont__hsubst__neq,axiom,
% 0.32/1.53 ! [Tr: dtree,Tr0: dtree] :
% 0.32/1.53 ( ( ( root @ Tr )
% 0.32/1.53 != ( root @ Tr0 ) )
% 0.32/1.53 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.32/1.53 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_166_Inl__cont__hsubst__eq,axiom,
% 0.32/1.53 ! [Tr: dtree,Tr0: dtree] :
% 0.32/1.53 ( ( ( root @ Tr )
% 0.32/1.53 = ( root @ Tr0 ) )
% 0.32/1.53 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.32/1.53 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_167_case__sum__step_I1_J,axiom,
% 0.32/1.53 ! [D: $tType,A: $tType,C: $tType,B: $tType,F6: B > A,G3: C > A,G: D > A,P2: sum_sum @ B @ C] :
% 0.32/1.53 ( ( sum_case_sum @ ( sum_sum @ B @ C ) @ A @ D @ ( sum_case_sum @ B @ A @ C @ F6 @ G3 ) @ G @ ( sum_Inl @ ( sum_sum @ B @ C ) @ D @ P2 ) )
% 0.32/1.53 = ( sum_case_sum @ B @ A @ C @ F6 @ G3 @ P2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_168_case__sum__inject,axiom,
% 0.32/1.53 ! [A: $tType,C: $tType,B: $tType,F1: A > C,F22: B > C,G1: A > C,G22: B > C] :
% 0.32/1.53 ( ( ( sum_case_sum @ A @ C @ B @ F1 @ F22 )
% 0.32/1.53 = ( sum_case_sum @ A @ C @ B @ G1 @ G22 ) )
% 0.32/1.53 => ~ ( ( F1 = G1 )
% 0.32/1.53 => ( F22 != G22 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_169_vimage__Collect,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,P: B > $o,F: A > B,Q: A > $o] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ( P @ ( F @ X3 ) )
% 0.32/1.53 = ( Q @ X3 ) )
% 0.32/1.53 => ( ( vimage @ A @ B @ F @ ( collect @ B @ P ) )
% 0.32/1.53 = ( collect @ A @ Q ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_170_vimageI2,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,F: B > A,A2: B,A4: set @ A] :
% 0.32/1.53 ( ( member @ A @ ( F @ A2 ) @ A4 )
% 0.32/1.53 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ A4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_171_vimageE,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 0.32/1.53 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 0.32/1.53 => ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_172_vimageD,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,A2: A,F: A > B,A4: set @ B] :
% 0.32/1.53 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ A4 ) )
% 0.32/1.53 => ( member @ B @ ( F @ A2 ) @ A4 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_173_old_Osum_Osimps_I5_J,axiom,
% 0.32/1.53 ! [B: $tType,C: $tType,A: $tType,F1: A > C,F22: B > C,X1: A] :
% 0.32/1.53 ( ( sum_case_sum @ A @ C @ B @ F1 @ F22 @ ( sum_Inl @ A @ B @ X1 ) )
% 0.32/1.53 = ( F1 @ X1 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_174_set_Ocompositionality,axiom,
% 0.32/1.53 ! [C: $tType,B: $tType,A: $tType,F: C > B,G: B > A,Set: set @ A] :
% 0.32/1.53 ( ( vimage @ C @ B @ F @ ( vimage @ B @ A @ G @ Set ) )
% 0.32/1.53 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ Set ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_175_vimage__comp,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,C: $tType,F: A > B,G: B > C,X2: set @ C] :
% 0.32/1.53 ( ( vimage @ A @ B @ F @ ( vimage @ B @ C @ G @ X2 ) )
% 0.32/1.53 = ( vimage @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ X2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_176_set_Ocomp,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,C: $tType,F: C > B,G: B > A] :
% 0.32/1.53 ( ( comp @ ( set @ B ) @ ( set @ C ) @ ( set @ A ) @ ( vimage @ C @ B @ F ) @ ( vimage @ B @ A @ G ) )
% 0.32/1.53 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_177_surj__image__vimage__eq,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,F: B > A,A4: set @ A] :
% 0.32/1.53 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.32/1.53 = ( top_top @ ( set @ A ) ) )
% 0.32/1.53 => ( ( image @ B @ A @ F @ ( vimage @ B @ A @ F @ A4 ) )
% 0.32/1.53 = A4 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_178_inFr2__root__in,axiom,
% 0.32/1.53 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.32/1.53 ( ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 )
% 0.32/1.53 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_179_case__sum__map__sum,axiom,
% 0.32/1.53 ! [C: $tType,A: $tType,B: $tType,E: $tType,D: $tType,L: B > A,R: C > A,F: D > B,G: E > C,X2: sum_sum @ D @ E] :
% 0.32/1.53 ( ( sum_case_sum @ B @ A @ C @ L @ R @ ( sum_map_sum @ D @ B @ E @ C @ F @ G @ X2 ) )
% 0.32/1.53 = ( sum_case_sum @ D @ A @ E @ ( comp @ B @ A @ D @ L @ F ) @ ( comp @ C @ A @ E @ R @ G ) @ X2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_180_finite__vimageD,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,H: A > B,F4: set @ B] :
% 0.32/1.53 ( ( finite_finite2 @ A @ ( vimage @ A @ B @ H @ F4 ) )
% 0.32/1.53 => ( ( ( image @ A @ B @ H @ ( top_top @ ( set @ A ) ) )
% 0.32/1.53 = ( top_top @ ( set @ B ) ) )
% 0.32/1.53 => ( finite_finite2 @ B @ F4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_181_case__sum__o__inj_I1_J,axiom,
% 0.32/1.53 ! [C: $tType,B: $tType,A: $tType,F: A > B,G: C > B] :
% 0.32/1.53 ( ( comp @ ( sum_sum @ A @ C ) @ B @ A @ ( sum_case_sum @ A @ B @ C @ F @ G ) @ ( sum_Inl @ A @ C ) )
% 0.32/1.53 = F ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_182_o__case__sum,axiom,
% 0.32/1.53 ! [A: $tType,C: $tType,D: $tType,B: $tType,H: D > C,F: A > D,G: B > D] :
% 0.32/1.53 ( ( comp @ D @ C @ ( sum_sum @ A @ B ) @ H @ ( sum_case_sum @ A @ D @ B @ F @ G ) )
% 0.32/1.53 = ( sum_case_sum @ A @ C @ B @ ( comp @ D @ C @ A @ H @ F ) @ ( comp @ D @ C @ B @ H @ G ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_183_Gram__Lang__Mirabelle__ojxrtuoybn_OInl__cont__H,axiom,
% 0.32/1.53 ! [Tr0: dtree,N: n] :
% 0.32/1.53 ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1451583624elle_H @ Tr0 @ N ) ) )
% 0.32/1.53 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_184_case__sum__o__map__sum,axiom,
% 0.32/1.53 ! [A: $tType,D: $tType,C: $tType,E: $tType,B: $tType,F: D > C,G: E > C,H1: A > D,H2: B > E] :
% 0.32/1.53 ( ( comp @ ( sum_sum @ D @ E ) @ C @ ( sum_sum @ A @ B ) @ ( sum_case_sum @ D @ C @ E @ F @ G ) @ ( sum_map_sum @ A @ D @ B @ E @ H1 @ H2 ) )
% 0.32/1.53 = ( sum_case_sum @ A @ C @ B @ ( comp @ D @ C @ A @ F @ H1 ) @ ( comp @ E @ C @ B @ G @ H2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_185_Inl__prodOf,axiom,
% 0.32/1.53 ! [Tr: dtree] :
% 0.32/1.53 ( ( 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 ) ) )
% 0.32/1.53 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_186_corec_I2_J,axiom,
% 0.32/1.53 ! [A: $tType,Ct: A > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) ),B2: A,Rt: A > n] :
% 0.32/1.53 ( ( finite_finite2 @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) @ ( Ct @ B2 ) )
% 0.32/1.53 => ( ( cont @ ( corec @ A @ Rt @ Ct @ B2 ) )
% 0.32/1.53 = ( image @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ ( sum_sum @ dtree @ A ) @ dtree @ ( id @ t ) @ ( sum_case_sum @ dtree @ dtree @ A @ ( id @ dtree ) @ ( corec @ A @ Rt @ Ct ) ) ) @ ( Ct @ B2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_187_Inr__m__oplus,axiom,
% 0.32/1.53 ! [A: $tType,C: $tType,B: $tType,F: C > A,Tns: set @ ( sum_sum @ B @ C )] :
% 0.32/1.53 ( ( 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 ) )
% 0.32/1.53 = ( image @ C @ A @ F @ ( vimage @ C @ ( sum_sum @ B @ C ) @ ( sum_Inr @ C @ B ) @ Tns ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_188_sum_Oinject_I2_J,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,X22: B,Y22: B] :
% 0.32/1.53 ( ( ( sum_Inr @ B @ A @ X22 )
% 0.32/1.53 = ( sum_Inr @ B @ A @ Y22 ) )
% 0.32/1.53 = ( X22 = Y22 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_189_old_Osum_Oinject_I2_J,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,B2: B,B5: B] :
% 0.32/1.53 ( ( ( sum_Inr @ B @ A @ B2 )
% 0.32/1.53 = ( sum_Inr @ B @ A @ B5 ) )
% 0.32/1.53 = ( B2 = B5 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_190_Inr__cont__H,axiom,
% 0.32/1.53 ! [N: n] :
% 0.32/1.53 ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1451583624elle_H @ tr0 @ N ) ) )
% 0.32/1.53 = ( image @ dtree @ dtree @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ tr0 ) @ root ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ N ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_191_Inr__Inl__False,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,X2: B,Y: A] :
% 0.32/1.53 ( ( sum_Inr @ B @ A @ X2 )
% 0.32/1.53 != ( sum_Inl @ A @ B @ Y ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_192_Inl__Inr__False,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,X2: A,Y: B] :
% 0.32/1.53 ( ( sum_Inl @ A @ B @ X2 )
% 0.32/1.53 != ( sum_Inr @ B @ A @ Y ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_193_old_Osum_Osimps_I8_J,axiom,
% 0.32/1.53 ! [A: $tType,T: $tType,B: $tType,F1: A > T,F22: B > T,B2: B] :
% 0.32/1.53 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inr @ B @ A @ B2 ) )
% 0.32/1.53 = ( F22 @ B2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_194_wf__inj,axiom,
% 0.32/1.53 ! [Tr: dtree,Tr1: dtree,Tr2: dtree] :
% 0.32/1.53 ( ( gram_L864798063lle_wf @ Tr )
% 0.32/1.53 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.32/1.53 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 0.32/1.53 => ( ( ( root @ Tr1 )
% 0.32/1.53 = ( root @ Tr2 ) )
% 0.32/1.53 = ( Tr1 = Tr2 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_195_Inr__cont__hsubst__neq,axiom,
% 0.32/1.53 ! [Tr: dtree,Tr0: dtree] :
% 0.32/1.53 ( ( ( root @ Tr )
% 0.32/1.53 != ( root @ Tr0 ) )
% 0.32/1.53 => ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.32/1.53 = ( image @ dtree @ dtree @ ( gram_L1004374585hsubst @ Tr0 ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_196_Inr__cont__hsubst__eq,axiom,
% 0.32/1.53 ! [Tr: dtree,Tr0: dtree] :
% 0.32/1.53 ( ( ( root @ Tr )
% 0.32/1.53 = ( root @ Tr0 ) )
% 0.32/1.53 => ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.32/1.53 = ( image @ dtree @ dtree @ ( gram_L1004374585hsubst @ Tr0 ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr0 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_197_Inr__oplus__iff,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,C: $tType,Tr: B,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.32/1.53 ( ( 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 ) )
% 0.32/1.53 = ( ? [N2: C] :
% 0.32/1.53 ( ( member @ ( sum_sum @ A @ C ) @ ( sum_Inr @ C @ A @ N2 ) @ Tns )
% 0.32/1.53 & ( ( F @ N2 )
% 0.32/1.53 = Tr ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_198_case__sum__step_I2_J,axiom,
% 0.32/1.53 ! [E: $tType,A: $tType,C: $tType,B: $tType,F: E > A,F6: B > A,G3: C > A,P2: sum_sum @ B @ C] :
% 0.32/1.53 ( ( sum_case_sum @ E @ A @ ( sum_sum @ B @ C ) @ F @ ( sum_case_sum @ B @ A @ C @ F6 @ G3 ) @ ( sum_Inr @ ( sum_sum @ B @ C ) @ E @ P2 ) )
% 0.32/1.53 = ( sum_case_sum @ B @ A @ C @ F6 @ G3 @ P2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_199_old_Osum_Osimps_I6_J,axiom,
% 0.32/1.53 ! [A: $tType,C: $tType,B: $tType,F1: A > C,F22: B > C,X22: B] :
% 0.32/1.53 ( ( sum_case_sum @ A @ C @ B @ F1 @ F22 @ ( sum_Inr @ B @ A @ X22 ) )
% 0.32/1.53 = ( F22 @ X22 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_200_old_Osum_Oinducts,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,P: ( sum_sum @ A @ B ) > $o,Sum: sum_sum @ A @ B] :
% 0.32/1.53 ( ! [A6: A] : ( P @ ( sum_Inl @ A @ B @ A6 ) )
% 0.32/1.53 => ( ! [B6: B] : ( P @ ( sum_Inr @ B @ A @ B6 ) )
% 0.32/1.53 => ( P @ Sum ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_201_old_Osum_Oexhaust,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,Y: sum_sum @ A @ B] :
% 0.32/1.53 ( ! [A6: A] :
% 0.32/1.53 ( Y
% 0.32/1.53 != ( sum_Inl @ A @ B @ A6 ) )
% 0.32/1.53 => ~ ! [B6: B] :
% 0.32/1.53 ( Y
% 0.32/1.53 != ( sum_Inr @ B @ A @ B6 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_202_split__sum__all,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType] :
% 0.32/1.53 ( ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 0.32/1.53 ! [X6: sum_sum @ A @ B] : ( P3 @ X6 ) )
% 0.32/1.53 = ( ^ [P4: ( sum_sum @ A @ B ) > $o] :
% 0.32/1.53 ( ! [X: A] : ( P4 @ ( sum_Inl @ A @ B @ X ) )
% 0.32/1.53 & ! [X: B] : ( P4 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_203_split__sum__ex,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType] :
% 0.32/1.53 ( ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 0.32/1.53 ? [X6: sum_sum @ A @ B] : ( P3 @ X6 ) )
% 0.32/1.53 = ( ^ [P4: ( sum_sum @ A @ B ) > $o] :
% 0.32/1.53 ( ? [X: A] : ( P4 @ ( sum_Inl @ A @ B @ X ) )
% 0.32/1.53 | ? [X: B] : ( P4 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_204_Inr__not__Inl,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,B2: B,A2: A] :
% 0.32/1.53 ( ( sum_Inr @ B @ A @ B2 )
% 0.32/1.53 != ( sum_Inl @ A @ B @ A2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_205_sumE,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( S
% 0.32/1.53 != ( sum_Inl @ A @ B @ X3 ) )
% 0.32/1.53 => ~ ! [Y2: B] :
% 0.32/1.53 ( S
% 0.32/1.53 != ( sum_Inr @ B @ A @ Y2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_206_old_Osum_Odistinct_I1_J,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,A2: A,B5: B] :
% 0.32/1.53 ( ( sum_Inl @ A @ B @ A2 )
% 0.32/1.53 != ( sum_Inr @ B @ A @ B5 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_207_old_Osum_Odistinct_I2_J,axiom,
% 0.32/1.53 ! [B7: $tType,A8: $tType,B8: B7,A9: A8] :
% 0.32/1.53 ( ( sum_Inr @ B7 @ A8 @ B8 )
% 0.32/1.53 != ( sum_Inl @ A8 @ B7 @ A9 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_208_sum_Odistinct_I1_J,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,X1: A,X22: B] :
% 0.32/1.53 ( ( sum_Inl @ A @ B @ X1 )
% 0.32/1.53 != ( sum_Inr @ B @ A @ X22 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_209_obj__sumE__f,axiom,
% 0.32/1.53 ! [A: $tType,C: $tType,B: $tType,S: B,F: ( sum_sum @ A @ C ) > B,P: $o] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ( S
% 0.32/1.53 = ( F @ ( sum_Inl @ A @ C @ X3 ) ) )
% 0.32/1.53 => P )
% 0.32/1.53 => ( ! [X3: C] :
% 0.32/1.53 ( ( S
% 0.32/1.53 = ( F @ ( sum_Inr @ C @ A @ X3 ) ) )
% 0.32/1.53 => P )
% 0.32/1.53 => ! [X4: sum_sum @ A @ C] :
% 0.32/1.53 ( ( S
% 0.32/1.53 = ( F @ X4 ) )
% 0.32/1.53 => P ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_210_Inr__inject,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,X2: B,Y: B] :
% 0.32/1.53 ( ( ( sum_Inr @ B @ A @ X2 )
% 0.32/1.53 = ( sum_Inr @ B @ A @ Y ) )
% 0.32/1.53 => ( X2 = Y ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_211_map__sum__if__distrib__else_I2_J,axiom,
% 0.32/1.53 ! [E: $tType,F3: $tType,H3: $tType,G4: $tType,E2: $o,F: E > F3,G: G4 > H3,X2: sum_sum @ E @ G4,Y: G4] :
% 0.32/1.53 ( ( E2
% 0.32/1.53 => ( ( sum_map_sum @ E @ F3 @ G4 @ H3 @ F @ G @ ( if @ ( sum_sum @ E @ G4 ) @ E2 @ X2 @ ( sum_Inr @ G4 @ E @ Y ) ) )
% 0.32/1.53 = ( sum_map_sum @ E @ F3 @ G4 @ H3 @ F @ G @ X2 ) ) )
% 0.32/1.53 & ( ~ E2
% 0.32/1.53 => ( ( sum_map_sum @ E @ F3 @ G4 @ H3 @ F @ G @ ( if @ ( sum_sum @ E @ G4 ) @ E2 @ X2 @ ( sum_Inr @ G4 @ E @ Y ) ) )
% 0.32/1.53 = ( sum_Inr @ H3 @ F3 @ ( G @ Y ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_212_map__sum__if__distrib__then_I2_J,axiom,
% 0.32/1.53 ! [H3: $tType,F3: $tType,G4: $tType,E: $tType,E2: $o,F: E > F3,G: G4 > H3,X2: G4,Y: sum_sum @ E @ G4] :
% 0.32/1.53 ( ( E2
% 0.32/1.53 => ( ( sum_map_sum @ E @ F3 @ G4 @ H3 @ F @ G @ ( if @ ( sum_sum @ E @ G4 ) @ E2 @ ( sum_Inr @ G4 @ E @ X2 ) @ Y ) )
% 0.32/1.53 = ( sum_Inr @ H3 @ F3 @ ( G @ X2 ) ) ) )
% 0.32/1.53 & ( ~ E2
% 0.32/1.53 => ( ( sum_map_sum @ E @ F3 @ G4 @ H3 @ F @ G @ ( if @ ( sum_sum @ E @ G4 ) @ E2 @ ( sum_Inr @ G4 @ E @ X2 ) @ Y ) )
% 0.32/1.53 = ( sum_map_sum @ E @ F3 @ G4 @ H3 @ F @ G @ Y ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_213_map__sum__InrD,axiom,
% 0.32/1.53 ! [C: $tType,A: $tType,D: $tType,B: $tType,F: C > A,G: D > B,Z: sum_sum @ C @ D,X2: B] :
% 0.32/1.53 ( ( ( sum_map_sum @ C @ A @ D @ B @ F @ G @ Z )
% 0.32/1.53 = ( sum_Inr @ B @ A @ X2 ) )
% 0.32/1.53 => ? [Y2: D] :
% 0.32/1.53 ( ( Z
% 0.32/1.53 = ( sum_Inr @ D @ C @ Y2 ) )
% 0.32/1.53 & ( ( G @ Y2 )
% 0.32/1.53 = X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_214_map__sum_Osimps_I2_J,axiom,
% 0.32/1.53 ! [A: $tType,C: $tType,D: $tType,B: $tType,F1: A > C,F22: B > D,A2: B] :
% 0.32/1.53 ( ( sum_map_sum @ A @ C @ B @ D @ F1 @ F22 @ ( sum_Inr @ B @ A @ A2 ) )
% 0.32/1.53 = ( sum_Inr @ D @ C @ ( F22 @ A2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_215_Inl__Inr__image__cong,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,A4: set @ ( sum_sum @ A @ B ),B3: set @ ( sum_sum @ A @ B )] :
% 0.32/1.53 ( ( ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ A4 )
% 0.32/1.53 = ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ B3 ) )
% 0.32/1.53 => ( ( ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ A4 )
% 0.32/1.53 = ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ B3 ) )
% 0.32/1.53 => ( A4 = B3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_216_case__sum__if,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,C: $tType,P2: $o,F: B > A,G: C > A,X2: B,Y: C] :
% 0.32/1.53 ( ( P2
% 0.32/1.53 => ( ( sum_case_sum @ B @ A @ C @ F @ G @ ( if @ ( sum_sum @ B @ C ) @ P2 @ ( sum_Inl @ B @ C @ X2 ) @ ( sum_Inr @ C @ B @ Y ) ) )
% 0.32/1.53 = ( F @ X2 ) ) )
% 0.32/1.53 & ( ~ P2
% 0.32/1.53 => ( ( sum_case_sum @ B @ A @ C @ F @ G @ ( if @ ( sum_sum @ B @ C ) @ P2 @ ( sum_Inl @ B @ C @ X2 ) @ ( sum_Inr @ C @ B @ Y ) ) )
% 0.32/1.53 = ( G @ Y ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_217_wf__cont,axiom,
% 0.32/1.53 ! [Tr: dtree,Tr5: dtree] :
% 0.32/1.53 ( ( gram_L864798063lle_wf @ Tr )
% 0.32/1.53 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr5 ) @ ( cont @ Tr ) )
% 0.32/1.53 => ( gram_L864798063lle_wf @ Tr5 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_218_case__sum__o__inj_I2_J,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,C: $tType,F: A > B,G: C > B] :
% 0.32/1.53 ( ( comp @ ( sum_sum @ A @ C ) @ B @ C @ ( sum_case_sum @ A @ B @ C @ F @ G ) @ ( sum_Inr @ C @ A ) )
% 0.32/1.53 = G ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_219_root__prodOf,axiom,
% 0.32/1.53 ! [Tr5: dtree,Tr: dtree] :
% 0.32/1.53 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr5 ) @ ( cont @ Tr ) )
% 0.32/1.53 => ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ ( root @ Tr5 ) ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_220_Gram__Lang__Mirabelle__ojxrtuoybn_OInr__cont__H,axiom,
% 0.32/1.53 ! [Tr0: dtree,N: n] :
% 0.32/1.53 ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1451583624elle_H @ Tr0 @ N ) ) )
% 0.32/1.53 = ( image @ dtree @ dtree @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ Tr0 ) @ root ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_221_Inr__oplus__elim,axiom,
% 0.32/1.53 ! [A: $tType,C: $tType,B: $tType,Tr: B,F: C > B,Tns: set @ ( sum_sum @ A @ C )] :
% 0.32/1.53 ( ( 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 ) )
% 0.32/1.53 => ? [N5: C] :
% 0.32/1.53 ( ( member @ ( sum_sum @ A @ C ) @ ( sum_Inr @ C @ A @ N5 ) @ Tns )
% 0.32/1.53 & ( ( F @ N5 )
% 0.32/1.53 = Tr ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_222_subtr_OStep,axiom,
% 0.32/1.53 ! [Tr3: dtree,Ns: set @ n,Tr1: dtree,Tr2: dtree] :
% 0.32/1.53 ( ( member @ n @ ( root @ Tr3 ) @ Ns )
% 0.32/1.53 => ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr2 )
% 0.32/1.53 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr3 ) )
% 0.32/1.53 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_223_subtr_Ocases,axiom,
% 0.32/1.53 ! [A1: set @ n,A22: dtree,A32: dtree] :
% 0.32/1.53 ( ( gram_L716654942_subtr @ A1 @ A22 @ A32 )
% 0.32/1.53 => ( ( ( A32 = A22 )
% 0.32/1.53 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.32/1.53 => ~ ( ( member @ n @ ( root @ A32 ) @ A1 )
% 0.32/1.53 => ! [Tr22: dtree] :
% 0.32/1.53 ( ( gram_L716654942_subtr @ A1 @ A22 @ Tr22 )
% 0.32/1.53 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ A32 ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_224_subtr_Osimps,axiom,
% 0.32/1.53 ( gram_L716654942_subtr
% 0.32/1.53 = ( ^ [A12: set @ n,A23: dtree,A33: dtree] :
% 0.32/1.53 ( ? [Tr6: dtree,Ns2: set @ n] :
% 0.32/1.53 ( ( A12 = Ns2 )
% 0.32/1.53 & ( A23 = Tr6 )
% 0.32/1.53 & ( A33 = Tr6 )
% 0.32/1.53 & ( member @ n @ ( root @ Tr6 ) @ Ns2 ) )
% 0.32/1.53 | ? [Tr32: dtree,Ns2: set @ n,Tr12: dtree,Tr23: dtree] :
% 0.32/1.53 ( ( A12 = Ns2 )
% 0.32/1.53 & ( A23 = Tr12 )
% 0.32/1.53 & ( A33 = Tr32 )
% 0.32/1.53 & ( member @ n @ ( root @ Tr32 ) @ Ns2 )
% 0.32/1.53 & ( gram_L716654942_subtr @ Ns2 @ Tr12 @ Tr23 )
% 0.32/1.53 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ Tr32 ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_225_subtr__StepL,axiom,
% 0.32/1.53 ! [Tr1: dtree,Ns: set @ n,Tr2: dtree,Tr3: dtree] :
% 0.32/1.53 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 0.32/1.53 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr2 ) )
% 0.32/1.53 => ( ( gram_L716654942_subtr @ Ns @ Tr2 @ Tr3 )
% 0.32/1.53 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_226_subtr_Oinducts,axiom,
% 0.32/1.53 ! [X1: set @ n,X22: dtree,X32: dtree,P: ( set @ n ) > dtree > dtree > $o] :
% 0.32/1.53 ( ( gram_L716654942_subtr @ X1 @ X22 @ X32 )
% 0.32/1.53 => ( ! [Tr7: dtree,Ns3: set @ n] :
% 0.32/1.53 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 0.32/1.53 => ( P @ Ns3 @ Tr7 @ Tr7 ) )
% 0.32/1.53 => ( ! [Tr33: dtree,Ns3: set @ n,Tr13: dtree,Tr22: dtree] :
% 0.32/1.53 ( ( member @ n @ ( root @ Tr33 ) @ Ns3 )
% 0.32/1.53 => ( ( gram_L716654942_subtr @ Ns3 @ Tr13 @ Tr22 )
% 0.32/1.53 => ( ( P @ Ns3 @ Tr13 @ Tr22 )
% 0.32/1.53 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr33 ) )
% 0.32/1.53 => ( P @ Ns3 @ Tr13 @ Tr33 ) ) ) ) )
% 0.32/1.53 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_227_subtr__inductL,axiom,
% 0.32/1.53 ! [Ns: set @ n,Tr1: dtree,Tr2: dtree,Phi: ( set @ n ) > dtree > dtree > $o] :
% 0.32/1.53 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr2 )
% 0.32/1.53 => ( ! [Ns3: set @ n,Tr7: dtree] : ( Phi @ Ns3 @ Tr7 @ Tr7 )
% 0.32/1.53 => ( ! [Ns3: set @ n,Tr13: dtree,Tr22: dtree,Tr33: dtree] :
% 0.32/1.53 ( ( member @ n @ ( root @ Tr13 ) @ Ns3 )
% 0.32/1.53 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr22 ) )
% 0.32/1.53 => ( ( gram_L716654942_subtr @ Ns3 @ Tr22 @ Tr33 )
% 0.32/1.53 => ( ( Phi @ Ns3 @ Tr22 @ Tr33 )
% 0.32/1.53 => ( Phi @ Ns3 @ Tr13 @ Tr33 ) ) ) ) )
% 0.32/1.53 => ( Phi @ Ns @ Tr1 @ Tr2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_228_inItr_OInd,axiom,
% 0.32/1.53 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,N: n] :
% 0.32/1.53 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.32/1.53 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.32/1.53 => ( ( gram_L830233218_inItr @ Ns @ Tr1 @ N )
% 0.32/1.53 => ( gram_L830233218_inItr @ Ns @ Tr @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_229_inItr_Ocases,axiom,
% 0.32/1.53 ! [A1: set @ n,A22: dtree,A32: n] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ A1 @ A22 @ A32 )
% 0.32/1.53 => ( ( ( A32
% 0.32/1.53 = ( root @ A22 ) )
% 0.32/1.53 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.32/1.53 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.32/1.53 => ! [Tr13: dtree] :
% 0.32/1.53 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ A22 ) )
% 0.32/1.53 => ~ ( gram_L830233218_inItr @ A1 @ Tr13 @ A32 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_230_inItr_Osimps,axiom,
% 0.32/1.53 ( gram_L830233218_inItr
% 0.32/1.53 = ( ^ [A12: set @ n,A23: dtree,A33: n] :
% 0.32/1.53 ( ? [Tr6: dtree,Ns2: set @ n] :
% 0.32/1.53 ( ( A12 = Ns2 )
% 0.32/1.53 & ( A23 = Tr6 )
% 0.32/1.53 & ( A33
% 0.32/1.53 = ( root @ Tr6 ) )
% 0.32/1.53 & ( member @ n @ ( root @ Tr6 ) @ Ns2 ) )
% 0.32/1.53 | ? [Tr6: dtree,Ns2: set @ n,Tr12: dtree,N2: n] :
% 0.32/1.53 ( ( A12 = Ns2 )
% 0.32/1.53 & ( A23 = Tr6 )
% 0.32/1.53 & ( A33 = N2 )
% 0.32/1.53 & ( member @ n @ ( root @ Tr6 ) @ Ns2 )
% 0.32/1.53 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr6 ) )
% 0.32/1.53 & ( gram_L830233218_inItr @ Ns2 @ Tr12 @ N2 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_231_inItr_Oinducts,axiom,
% 0.32/1.53 ! [X1: set @ n,X22: dtree,X32: n,P: ( set @ n ) > dtree > n > $o] :
% 0.32/1.53 ( ( gram_L830233218_inItr @ X1 @ X22 @ X32 )
% 0.32/1.53 => ( ! [Tr7: dtree,Ns3: set @ n] :
% 0.32/1.53 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 0.32/1.53 => ( P @ Ns3 @ Tr7 @ ( root @ Tr7 ) ) )
% 0.32/1.53 => ( ! [Tr7: dtree,Ns3: set @ n,Tr13: dtree,N5: n] :
% 0.32/1.53 ( ( member @ n @ ( root @ Tr7 ) @ Ns3 )
% 0.32/1.53 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr7 ) )
% 0.32/1.53 => ( ( gram_L830233218_inItr @ Ns3 @ Tr13 @ N5 )
% 0.32/1.53 => ( ( P @ Ns3 @ Tr13 @ N5 )
% 0.32/1.53 => ( P @ Ns3 @ Tr7 @ N5 ) ) ) ) )
% 0.32/1.53 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_232_case__sum__expand__Inr,axiom,
% 0.32/1.53 ! [B: $tType,C: $tType,A: $tType,F: ( sum_sum @ A @ C ) > B,G: A > B,X2: sum_sum @ A @ C] :
% 0.32/1.53 ( ( ( comp @ ( sum_sum @ A @ C ) @ B @ A @ F @ ( sum_Inl @ A @ C ) )
% 0.32/1.53 = G )
% 0.32/1.53 => ( ( F @ X2 )
% 0.32/1.53 = ( sum_case_sum @ A @ B @ C @ G @ ( comp @ ( sum_sum @ A @ C ) @ B @ C @ F @ ( sum_Inr @ C @ A ) ) @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_233_case__sum__expand__Inr_H,axiom,
% 0.32/1.53 ! [B: $tType,C: $tType,A: $tType,F: ( sum_sum @ A @ C ) > B,G: A > B,H: C > B] :
% 0.32/1.53 ( ( ( comp @ ( sum_sum @ A @ C ) @ B @ A @ F @ ( sum_Inl @ A @ C ) )
% 0.32/1.53 = G )
% 0.32/1.53 => ( ( H
% 0.32/1.53 = ( comp @ ( sum_sum @ A @ C ) @ B @ C @ F @ ( sum_Inr @ C @ A ) ) )
% 0.32/1.53 = ( ( sum_case_sum @ A @ B @ C @ G @ H )
% 0.32/1.53 = F ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_234_case__sum__expand__Inr__pointfree,axiom,
% 0.32/1.53 ! [B: $tType,C: $tType,A: $tType,F: ( sum_sum @ A @ C ) > B,G: A > B] :
% 0.32/1.53 ( ( ( comp @ ( sum_sum @ A @ C ) @ B @ A @ F @ ( sum_Inl @ A @ C ) )
% 0.32/1.53 = G )
% 0.32/1.53 => ( ( sum_case_sum @ A @ B @ C @ G @ ( comp @ ( sum_sum @ A @ C ) @ B @ C @ F @ ( sum_Inr @ C @ A ) ) )
% 0.32/1.53 = F ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_235_corec_I1_J,axiom,
% 0.32/1.53 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) ),B2: A] :
% 0.32/1.53 ( ( root @ ( corec @ A @ Rt @ Ct @ B2 ) )
% 0.32/1.53 = ( Rt @ B2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_236_subtr__UNIV__inductL,axiom,
% 0.32/1.53 ! [Tr1: dtree,Tr2: dtree,Phi: dtree > dtree > $o] :
% 0.32/1.53 ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr1 @ Tr2 )
% 0.32/1.53 => ( ! [Tr7: dtree] : ( Phi @ Tr7 @ Tr7 )
% 0.32/1.53 => ( ! [Tr13: dtree,Tr22: dtree,Tr33: dtree] :
% 0.32/1.53 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr22 ) )
% 0.32/1.53 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr22 @ Tr33 )
% 0.32/1.53 => ( ( Phi @ Tr22 @ Tr33 )
% 0.32/1.53 => ( Phi @ Tr13 @ Tr33 ) ) ) )
% 0.32/1.53 => ( Phi @ Tr1 @ Tr2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_237_inFr2__Ind,axiom,
% 0.32/1.53 ! [Ns: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 0.32/1.53 ( ( gram_L805317441_inFr2 @ Ns @ Tr1 @ T2 )
% 0.32/1.53 => ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.32/1.53 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.32/1.53 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_238_map__sum__o__inj_I2_J,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,C: $tType,D: $tType,F: A > B,G: D > C] :
% 0.32/1.53 ( ( comp @ ( sum_sum @ A @ D ) @ ( sum_sum @ B @ C ) @ D @ ( sum_map_sum @ A @ B @ D @ C @ F @ G ) @ ( sum_Inr @ D @ A ) )
% 0.32/1.53 = ( comp @ C @ ( sum_sum @ B @ C ) @ D @ ( sum_Inr @ C @ B ) @ G ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_239_root__subtrOf,axiom,
% 0.32/1.53 ! [N: n,Tr: dtree] :
% 0.32/1.53 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.32/1.53 => ( ( root @ ( gram_L1614515765ubtrOf @ Tr @ N ) )
% 0.32/1.53 = N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_240_surj__subtrOf,axiom,
% 0.32/1.53 ! [Tr: dtree,Tr5: dtree] :
% 0.32/1.53 ( ( gram_L864798063lle_wf @ Tr )
% 0.32/1.53 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr5 ) @ ( cont @ Tr ) )
% 0.32/1.53 => ? [N5: n] :
% 0.32/1.53 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N5 ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.32/1.53 & ( ( gram_L1614515765ubtrOf @ Tr @ N5 )
% 0.32/1.53 = Tr5 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_241_subtrOf__root,axiom,
% 0.32/1.53 ! [Tr: dtree,Tr5: dtree] :
% 0.32/1.53 ( ( gram_L864798063lle_wf @ Tr )
% 0.32/1.53 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr5 ) @ ( cont @ Tr ) )
% 0.32/1.53 => ( ( gram_L1614515765ubtrOf @ Tr @ ( root @ Tr5 ) )
% 0.32/1.53 = Tr5 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_242_Inr__subtrOf,axiom,
% 0.32/1.53 ! [N: n,Tr: dtree] :
% 0.32/1.53 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.32/1.53 => ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( gram_L1614515765ubtrOf @ Tr @ N ) ) @ ( cont @ Tr ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_243_subtrOf,axiom,
% 0.32/1.53 ! [N: n,Tr: dtree] :
% 0.32/1.53 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ Tr ) ) )
% 0.32/1.53 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( gram_L1614515765ubtrOf @ Tr @ N ) ) @ ( cont @ Tr ) )
% 0.32/1.53 & ( ( root @ ( gram_L1614515765ubtrOf @ Tr @ N ) )
% 0.32/1.53 = N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_244_obj__sumE,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( S
% 0.32/1.53 != ( sum_Inl @ A @ B @ X3 ) )
% 0.32/1.53 => ~ ! [X3: B] :
% 0.32/1.53 ( S
% 0.32/1.53 != ( sum_Inr @ B @ A @ X3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_245_wf__subtr__inj__on,axiom,
% 0.32/1.53 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 0.32/1.53 ( ( gram_L864798063lle_wf @ Tr1 )
% 0.32/1.53 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.32/1.53 => ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ Tr ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_246_inj__on__image__iff,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,A4: set @ A,G: A > B,F: A > A] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ( member @ A @ X3 @ A4 )
% 0.32/1.53 => ! [Xa2: A] :
% 0.32/1.53 ( ( member @ A @ Xa2 @ A4 )
% 0.32/1.53 => ( ( ( G @ ( F @ X3 ) )
% 0.32/1.53 = ( G @ ( F @ Xa2 ) ) )
% 0.32/1.53 = ( ( G @ X3 )
% 0.32/1.53 = ( G @ Xa2 ) ) ) ) )
% 0.32/1.53 => ( ( inj_on @ A @ A @ F @ A4 )
% 0.32/1.53 => ( ( inj_on @ A @ B @ G @ ( image @ A @ A @ F @ A4 ) )
% 0.32/1.53 = ( inj_on @ A @ B @ G @ A4 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_247_finite__image__iff,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,F: A > B,A4: set @ A] :
% 0.32/1.53 ( ( inj_on @ A @ B @ F @ A4 )
% 0.32/1.53 => ( ( finite_finite2 @ B @ ( image @ A @ B @ F @ A4 ) )
% 0.32/1.53 = ( finite_finite2 @ A @ A4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_248_finite__imageD,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType,F: B > A,A4: set @ B] :
% 0.32/1.53 ( ( finite_finite2 @ A @ ( image @ B @ A @ F @ A4 ) )
% 0.32/1.53 => ( ( inj_on @ B @ A @ F @ A4 )
% 0.32/1.53 => ( finite_finite2 @ B @ A4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_249_range__ex1__eq,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,F: A > B,B2: B] :
% 0.32/1.53 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.32/1.53 => ( ( member @ B @ B2 @ ( image @ A @ B @ F @ ( top_top @ ( set @ A ) ) ) )
% 0.32/1.53 = ( ? [X: A] :
% 0.32/1.53 ( ( B2
% 0.32/1.53 = ( F @ X ) )
% 0.32/1.53 & ! [Y3: A] :
% 0.32/1.53 ( ( B2
% 0.32/1.53 = ( F @ Y3 ) )
% 0.32/1.53 => ( Y3 = X ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_250_inj__image__eq__iff,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,F: A > B,A4: set @ A,B3: set @ A] :
% 0.32/1.53 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.32/1.53 => ( ( ( image @ A @ B @ F @ A4 )
% 0.32/1.53 = ( image @ A @ B @ F @ B3 ) )
% 0.32/1.53 = ( A4 = B3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_251_inj__image__mem__iff,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,F: A > B,A2: A,A4: set @ A] :
% 0.32/1.53 ( ( inj_on @ A @ B @ F @ ( top_top @ ( set @ A ) ) )
% 0.32/1.53 => ( ( member @ B @ ( F @ A2 ) @ ( image @ A @ B @ F @ A4 ) )
% 0.32/1.53 = ( member @ A @ A2 @ A4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_252_comp__inj__on,axiom,
% 0.32/1.53 ! [B: $tType,C: $tType,A: $tType,F: A > B,A4: set @ A,G: B > C] :
% 0.32/1.53 ( ( inj_on @ A @ B @ F @ A4 )
% 0.32/1.53 => ( ( inj_on @ B @ C @ G @ ( image @ A @ B @ F @ A4 ) )
% 0.32/1.53 => ( inj_on @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ A4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_253_inj__on__imageI,axiom,
% 0.32/1.53 ! [B: $tType,C: $tType,A: $tType,G: C > B,F: A > C,A4: set @ A] :
% 0.32/1.53 ( ( inj_on @ A @ B @ ( comp @ C @ B @ A @ G @ F ) @ A4 )
% 0.32/1.53 => ( inj_on @ C @ B @ G @ ( image @ A @ C @ F @ A4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_254_comp__inj__on__iff,axiom,
% 0.32/1.53 ! [B: $tType,C: $tType,A: $tType,F: A > B,A4: set @ A,F6: B > C] :
% 0.32/1.53 ( ( inj_on @ A @ B @ F @ A4 )
% 0.32/1.53 => ( ( inj_on @ B @ C @ F6 @ ( image @ A @ B @ F @ A4 ) )
% 0.32/1.53 = ( inj_on @ A @ C @ ( comp @ B @ C @ A @ F6 @ F ) @ A4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_255_finite__UNIV__inj__surj,axiom,
% 0.32/1.53 ! [A: $tType,F: A > A] :
% 0.32/1.53 ( ( finite_finite2 @ A @ ( top_top @ ( set @ A ) ) )
% 0.32/1.53 => ( ( inj_on @ A @ A @ F @ ( top_top @ ( set @ A ) ) )
% 0.32/1.53 => ( ( image @ A @ A @ F @ ( top_top @ ( set @ A ) ) )
% 0.32/1.53 = ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 0.32/1.53 ! [A8: $tType,A10: $tType] :
% 0.32/1.53 ( ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.32/1.53 & ( finite_finite @ A10 @ ( type2 @ A10 ) ) )
% 0.32/1.53 => ( finite_finite @ ( A8 > A10 ) @ ( type2 @ ( A8 > A10 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(tcon_fun___Orderings_Otop,axiom,
% 0.32/1.53 ! [A8: $tType,A10: $tType] :
% 0.32/1.53 ( ( top @ A10 @ ( type2 @ A10 ) )
% 0.32/1.53 => ( top @ ( A8 > A10 ) @ ( type2 @ ( A8 > A10 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(tcon_Set_Oset___Finite__Set_Ofinite_1,axiom,
% 0.32/1.53 ! [A8: $tType] :
% 0.32/1.53 ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.32/1.53 => ( finite_finite @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(tcon_Set_Oset___Orderings_Otop_2,axiom,
% 0.32/1.53 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(tcon_HOL_Obool___Finite__Set_Ofinite_3,axiom,
% 0.32/1.53 finite_finite @ $o @ ( type2 @ $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(tcon_HOL_Obool___Orderings_Otop_4,axiom,
% 0.32/1.53 top @ $o @ ( type2 @ $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(tcon_Sum__Type_Osum___Finite__Set_Ofinite_5,axiom,
% 0.32/1.54 ! [A8: $tType,A10: $tType] :
% 0.32/1.54 ( ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.32/1.54 & ( finite_finite @ A10 @ ( type2 @ A10 ) ) )
% 0.32/1.54 => ( finite_finite @ ( sum_sum @ A8 @ A10 ) @ ( type2 @ ( sum_sum @ A8 @ A10 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Option_Ooption___Finite__Set_Ofinite_6,axiom,
% 0.32/1.54 ! [A8: $tType] :
% 0.32/1.54 ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.32/1.54 => ( finite_finite @ ( option @ A8 ) @ ( type2 @ ( option @ A8 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_7,axiom,
% 0.32/1.54 ! [A8: $tType,A10: $tType] :
% 0.32/1.54 ( ( ( finite_finite @ A8 @ ( type2 @ A8 ) )
% 0.32/1.54 & ( finite_finite @ A10 @ ( type2 @ A10 ) ) )
% 0.32/1.54 => ( finite_finite @ ( product_prod @ A8 @ A10 ) @ ( type2 @ ( product_prod @ A8 @ A10 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(help_If_3_1_T,axiom,
% 0.32/1.54 ! [P: $o] :
% 0.32/1.54 ( ( P = $true )
% 0.32/1.54 | ( P = $false ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(help_If_2_1_T,axiom,
% 0.32/1.54 ! [A: $tType,X2: A,Y: A] :
% 0.32/1.54 ( ( if @ A @ $false @ X2 @ Y )
% 0.32/1.54 = Y ) ).
% 0.32/1.54
% 0.32/1.54 thf(help_If_1_1_T,axiom,
% 0.32/1.54 ! [A: $tType,X2: A,Y: A] :
% 0.32/1.54 ( ( if @ A @ $true @ X2 @ Y )
% 0.32/1.54 = X2 ) ).
% 0.32/1.54
% 0.32/1.54 thf(conj_0,hypothesis,
% 0.32/1.54 $true ).
% 0.32/1.54
% 0.32/1.54 thf(conj_1,hypothesis,
% 0.32/1.54 $true ).
% 0.32/1.54
% 0.32/1.54 thf(conj_2,hypothesis,
% 0.32/1.54 ( t_tr
% 0.32/1.54 = ( sum_Inl @ t @ dtree @ a ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(conj_3,conjecture,
% 0.32/1.54 ( ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ ( comp @ n @ n @ dtree @ ( comp @ dtree @ n @ n @ root @ ( gram_L1451583624elle_H @ tr0 ) ) @ root ) @ t_tr )
% 0.32/1.54 = ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root @ t_tr ) ) ).
% 0.32/1.54 ------------------------
% 0.32/1.55 % (26295)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_25971 for (2999ds/4Mi)
% 0.32/1.55 % (26296)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_25971 for (2999ds/27Mi)
% 0.32/1.56 % (26297)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/2Mi)
% 0.32/1.56 % (26298)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_25971 for (2999ds/2Mi)
% 0.32/1.56 % (26295)Instruction limit reached!
% 0.32/1.56 % (26295)------------------------------
% 0.32/1.56 % (26295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.56 % (26295)Termination reason: Unknown
% 0.32/1.56 % (26295)Termination phase: shuffling
% 0.32/1.56
% 0.32/1.56 % (26295)Memory used [KB]: 1535
% 0.32/1.56 % (26295)Time elapsed: 0.003 s
% 0.32/1.56 % (26295)Instructions burned: 5 (million)
% 0.32/1.56 % (26295)------------------------------
% 0.32/1.56 % (26295)------------------------------
% 0.32/1.56 % (26297)Instruction limit reached!
% 0.32/1.56 % (26297)------------------------------
% 0.32/1.56 % (26297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.56 % (26297)Termination reason: Unknown
% 0.32/1.56 % (26297)Termination phase: shuffling
% 0.32/1.56
% 0.32/1.56 % (26297)Memory used [KB]: 1407
% 0.32/1.56 % (26297)Time elapsed: 0.002 s
% 0.32/1.56 % (26297)Instructions burned: 3 (million)
% 0.32/1.56 % (26297)------------------------------
% 0.32/1.56 % (26297)------------------------------
% 0.32/1.56 % (26298)Instruction limit reached!
% 0.32/1.56 % (26298)------------------------------
% 0.32/1.56 % (26298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.56 % (26298)Termination reason: Unknown
% 0.32/1.56 % (26298)Termination phase: shuffling
% 0.32/1.56
% 0.32/1.56 % (26298)Memory used [KB]: 1407
% 0.32/1.56 % (26298)Time elapsed: 0.002 s
% 0.32/1.56 % (26298)Instructions burned: 3 (million)
% 0.32/1.56 % (26298)------------------------------
% 0.32/1.56 % (26298)------------------------------
% 0.32/1.56 % (26294)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/183Mi)
% 0.32/1.56 % (26299)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_25971 for (2999ds/275Mi)
% 0.32/1.56 % (26300)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/18Mi)
% 0.32/1.56 % (26296)Instruction limit reached!
% 0.32/1.56 % (26296)------------------------------
% 0.32/1.56 % (26296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.56 % (26296)Termination reason: Unknown
% 0.32/1.56 % (26296)Termination phase: Property scanning
% 0.32/1.56
% 0.32/1.56 % (26296)Memory used [KB]: 1791
% 0.32/1.56 % (26296)Time elapsed: 0.011 s
% 0.32/1.56 % (26296)Instructions burned: 30 (million)
% 0.32/1.56 % (26296)------------------------------
% 0.32/1.56 % (26296)------------------------------
% 0.32/1.57 % (26301)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/3Mi)
% 0.32/1.57 % (26302)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_25971 for (2999ds/37Mi)
% 0.32/1.57 % (26303)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_25971 for (2999ds/15Mi)
% 0.32/1.57 % (26301)Instruction limit reached!
% 0.32/1.57 % (26301)------------------------------
% 0.32/1.57 % (26301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.57 % (26301)Termination reason: Unknown
% 0.32/1.57 % (26301)Termination phase: shuffling
% 0.32/1.57
% 0.32/1.57 % (26301)Memory used [KB]: 1407
% 0.32/1.57 % (26301)Time elapsed: 0.003 s
% 0.32/1.57 % (26301)Instructions burned: 5 (million)
% 0.32/1.57 % (26301)------------------------------
% 0.32/1.57 % (26301)------------------------------
% 0.32/1.57 % (26303)Instruction limit reached!
% 0.32/1.57 % (26303)------------------------------
% 0.32/1.57 % (26303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.57 % (26303)Termination reason: Unknown
% 0.32/1.57 % (26303)Termination phase: shuffling
% 0.32/1.57
% 0.32/1.57 % (26303)Memory used [KB]: 1791
% 0.32/1.57 % (26303)Time elapsed: 0.008 s
% 0.32/1.57 % (26303)Instructions burned: 17 (million)
% 0.32/1.57 % (26303)------------------------------
% 0.32/1.57 % (26303)------------------------------
% 0.32/1.57 % (26304)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_25971 for (2999ds/3Mi)
% 0.32/1.57 % (26300)Instruction limit reached!
% 0.32/1.57 % (26300)------------------------------
% 0.32/1.57 % (26300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.57 % (26300)Termination reason: Unknown
% 0.32/1.57 % (26300)Termination phase: shuffling
% 0.32/1.57
% 0.32/1.57 % (26300)Memory used [KB]: 1791
% 0.32/1.57 % (26300)Time elapsed: 0.014 s
% 0.32/1.57 % (26300)Instructions burned: 19 (million)
% 0.32/1.57 % (26300)------------------------------
% 0.32/1.57 % (26300)------------------------------
% 0.32/1.57 % (26304)Instruction limit reached!
% 0.32/1.57 % (26304)------------------------------
% 0.32/1.57 % (26304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.57 % (26304)Termination reason: Unknown
% 0.32/1.57 % (26304)Termination phase: shuffling
% 0.32/1.57
% 0.32/1.57 % (26304)Memory used [KB]: 1407
% 0.32/1.57 % (26304)Time elapsed: 0.002 s
% 0.32/1.57 % (26304)Instructions burned: 3 (million)
% 0.32/1.57 % (26304)------------------------------
% 0.32/1.57 % (26304)------------------------------
% 0.32/1.58 % (26305)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_25971 for (2999ds/1041Mi)
% 0.32/1.58 % (26302)Instruction limit reached!
% 0.32/1.58 % (26302)------------------------------
% 0.32/1.58 % (26302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.58 % (26302)Termination reason: Unknown
% 0.32/1.58 % (26302)Termination phase: shuffling
% 0.32/1.58
% 0.32/1.58 % (26302)Memory used [KB]: 2174
% 0.32/1.58 % (26302)Time elapsed: 0.013 s
% 0.32/1.58 % (26302)Instructions burned: 37 (million)
% 0.32/1.58 % (26302)------------------------------
% 0.32/1.58 % (26302)------------------------------
% 0.32/1.58 % (26306)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/7Mi)
% 0.32/1.58 % (26307)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/16Mi)
% 0.32/1.59 % (26306)Instruction limit reached!
% 0.32/1.59 % (26306)------------------------------
% 0.32/1.59 % (26306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.59 % (26306)Termination reason: Unknown
% 0.32/1.59 % (26306)Termination phase: shuffling
% 0.32/1.59
% 0.32/1.59 % (26306)Memory used [KB]: 1535
% 0.32/1.59 % (26306)Time elapsed: 0.005 s
% 0.32/1.59 % (26306)Instructions burned: 9 (million)
% 0.32/1.59 % (26306)------------------------------
% 0.32/1.59 % (26306)------------------------------
% 0.32/1.59 % (26309)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/3Mi)
% 0.32/1.59 % (26309)Instruction limit reached!
% 0.32/1.59 % (26309)------------------------------
% 0.32/1.59 % (26309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.59 % (26309)Termination reason: Unknown
% 0.32/1.59 % (26309)Termination phase: shuffling
% 0.32/1.59
% 0.32/1.59 % (26309)Memory used [KB]: 1407
% 0.32/1.59 % (26309)Time elapsed: 0.003 s
% 0.32/1.59 % (26309)Instructions burned: 3 (million)
% 0.32/1.59 % (26309)------------------------------
% 0.32/1.59 % (26309)------------------------------
% 0.32/1.59 % (26307)Instruction limit reached!
% 0.32/1.59 % (26307)------------------------------
% 0.32/1.59 % (26307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.59 % (26307)Termination reason: Unknown
% 0.32/1.59 % (26307)Termination phase: shuffling
% 0.32/1.59
% 0.32/1.59 % (26307)Memory used [KB]: 1791
% 0.32/1.59 % (26307)Time elapsed: 0.007 s
% 0.32/1.59 % (26307)Instructions burned: 18 (million)
% 0.32/1.59 % (26307)------------------------------
% 0.32/1.59 % (26307)------------------------------
% 0.32/1.59 % (26308)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/3Mi)
% 0.32/1.59 % (26308)Instruction limit reached!
% 0.32/1.59 % (26308)------------------------------
% 0.32/1.59 % (26308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.59 % (26308)Termination reason: Unknown
% 0.32/1.59 % (26308)Termination phase: shuffling
% 0.32/1.59
% 0.32/1.59 % (26308)Memory used [KB]: 1407
% 0.32/1.59 % (26308)Time elapsed: 0.004 s
% 0.32/1.59 % (26308)Instructions burned: 4 (million)
% 0.32/1.59 % (26308)------------------------------
% 0.32/1.59 % (26308)------------------------------
% 0.32/1.60 % (26310)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/7Mi)
% 2.91/1.60 % (26311)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/3Mi)
% 2.91/1.60 % (26312)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/4Mi)
% 2.91/1.60 % (26310)Instruction limit reached!
% 2.91/1.60 % (26310)------------------------------
% 2.91/1.60 % (26310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.60 % (26310)Termination reason: Unknown
% 2.91/1.60 % (26310)Termination phase: shuffling
% 2.91/1.60
% 2.91/1.60 % (26310)Memory used [KB]: 1535
% 2.91/1.60 % (26310)Time elapsed: 0.004 s
% 2.91/1.60 % (26310)Instructions burned: 9 (million)
% 2.91/1.60 % (26310)------------------------------
% 2.91/1.60 % (26310)------------------------------
% 2.91/1.60 % (26311)Instruction limit reached!
% 2.91/1.60 % (26311)------------------------------
% 2.91/1.60 % (26311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.60 % (26311)Termination reason: Unknown
% 2.91/1.60 % (26311)Termination phase: shuffling
% 2.91/1.60
% 2.91/1.60 % (26311)Memory used [KB]: 1535
% 2.91/1.60 % (26311)Time elapsed: 0.003 s
% 2.91/1.60 % (26311)Instructions burned: 4 (million)
% 2.91/1.60 % (26311)------------------------------
% 2.91/1.60 % (26311)------------------------------
% 2.91/1.60 % (26312)Instruction limit reached!
% 2.91/1.60 % (26312)------------------------------
% 2.91/1.60 % (26312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.60 % (26312)Termination reason: Unknown
% 2.91/1.60 % (26312)Termination phase: shuffling
% 2.91/1.60
% 2.91/1.60 % (26312)Memory used [KB]: 1407
% 2.91/1.60 % (26312)Time elapsed: 0.003 s
% 2.91/1.60 % (26312)Instructions burned: 6 (million)
% 2.91/1.60 % (26312)------------------------------
% 2.91/1.60 % (26312)------------------------------
% 2.91/1.61 % (26313)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/18Mi)
% 2.91/1.61 % (26314)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/710Mi)
% 2.91/1.61 % (26315)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/6Mi)
% 2.91/1.61 % (26316)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_25971 for (2999ds/902Mi)
% 2.91/1.61 % (26315)Instruction limit reached!
% 2.91/1.61 % (26315)------------------------------
% 2.91/1.61 % (26315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.61 % (26315)Termination reason: Unknown
% 2.91/1.61 % (26315)Termination phase: shuffling
% 2.91/1.61
% 2.91/1.61 % (26315)Memory used [KB]: 1535
% 2.91/1.61 % (26315)Time elapsed: 0.004 s
% 2.91/1.61 % (26315)Instructions burned: 6 (million)
% 2.91/1.61 % (26315)------------------------------
% 2.91/1.61 % (26315)------------------------------
% 2.91/1.61 % (26313)Instruction limit reached!
% 2.91/1.61 % (26313)------------------------------
% 2.91/1.61 % (26313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.61 % (26313)Termination reason: Unknown
% 2.91/1.61 % (26313)Termination phase: shuffling
% 2.91/1.61
% 2.91/1.61 % (26313)Memory used [KB]: 1791
% 2.91/1.61 % (26313)Time elapsed: 0.008 s
% 2.91/1.61 % (26313)Instructions burned: 18 (million)
% 2.91/1.61 % (26313)------------------------------
% 2.91/1.61 % (26313)------------------------------
% 2.91/1.62 % (26299)First to succeed.
% 2.91/1.62 % (26299)Refutation found. Thanks to Tanya!
% 2.91/1.62 % SZS status Theorem for DTF2THF_25971
% 2.91/1.62 % SZS output start Proof for DTF2THF_25971
% 2.91/1.62 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.91/1.62 thf(type_def_7, type, n: $tType).
% 2.91/1.62 thf(type_def_8, type, t: $tType).
% 2.91/1.62 thf(type_def_9, type, dtree: $tType).
% 2.91/1.62 thf(type_def_10, type, sum_sum: ($tType * $tType) > $tType).
% 2.91/1.62 thf(type_def_11, type, set: ($tType) > $tType).
% 2.91/1.62 thf(type_def_12, type, option: ($tType) > $tType).
% 2.91/1.62 thf(type_def_13, type, product_prod: ($tType * $tType) > $tType).
% 2.91/1.62 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 2.91/1.62 thf(func_def_1, type, sum_sum: ($tType * $tType) > $tType).
% 2.91/1.62 thf(func_def_2, type, option: ($tType) > $tType).
% 2.91/1.62 thf(func_def_3, type, dtree: $tType).
% 2.91/1.62 thf(func_def_4, type, set: ($tType) > $tType).
% 2.91/1.62 thf(func_def_5, type, t: $tType).
% 2.91/1.62 thf(func_def_6, type, n: $tType).
% 2.91/1.62 thf(func_def_7, type, itself: ($tType) > $tType).
% 2.91/1.62 thf(func_def_8, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.91/1.62 thf(func_def_9, type, top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.91/1.62 thf(func_def_10, type, finite_finite: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.91/1.62 thf(func_def_11, type, semiring_char_0: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.91/1.62 thf(func_def_12, type, node: n > set @ sum_sum @ t @ dtree > dtree).
% 2.91/1.62 thf(func_def_13, type, cont: dtree > set @ sum_sum @ t @ dtree).
% 2.91/1.62 thf(func_def_14, type, corec: !>[X0: $tType]:((X0 > n) > (X0 > set @ sum_sum @ t @ sum_sum @ dtree @ X0) > X0 > dtree)).
% 2.91/1.62 thf(func_def_15, type, root: dtree > n).
% 2.91/1.62 thf(func_def_16, type, unfold: !>[X0: $tType]:((X0 > n) > (X0 > set @ sum_sum @ t @ X0) > X0 > dtree)).
% 2.91/1.62 thf(func_def_17, type, finite_finite2: !>[X0: $tType]:(set @ X0 > $o)).
% 2.91/1.62 thf(func_def_18, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X0) > X2 > X1)).
% 2.91/1.62 thf(func_def_19, type, id: !>[X0: $tType]:(X0 > X0)).
% 2.91/1.62 thf(func_def_20, type, inj_on: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > $o)).
% 2.91/1.62 thf(func_def_21, type, gram_L1451583624elle_H: dtree > n > dtree).
% 2.91/1.62 thf(func_def_22, type, gram_L1221482011le_H_c: dtree > n > set @ sum_sum @ t @ n).
% 2.91/1.62 thf(func_def_23, type, gram_L1221482026le_H_r: dtree > n > n).
% 2.91/1.62 thf(func_def_24, type, gram_L1451583635elle_S: n > set @ sum_sum @ t @ n).
% 2.91/1.62 thf(func_def_25, type, gram_L1231612515_deftr: n > dtree).
% 2.91/1.62 thf(func_def_26, type, gram_L1004374585hsubst: dtree > dtree > dtree).
% 2.91/1.62 thf(func_def_27, type, gram_L1905609002ubst_c: dtree > dtree > set @ sum_sum @ t @ dtree).
% 2.91/1.62 thf(func_def_28, type, gram_L1905609017ubst_r: dtree > n).
% 2.91/1.62 thf(func_def_29, type, gram_L805317441_inFr2: set @ n > dtree > t > $o).
% 2.91/1.62 thf(func_def_30, type, gram_L830233218_inItr: set @ n > dtree > n > $o).
% 2.91/1.62 thf(func_def_31, type, gram_L315592705e_pick: dtree > n > dtree).
% 2.91/1.62 thf(func_def_32, type, gram_L716654942_subtr: set @ n > dtree > dtree > $o).
% 2.91/1.62 thf(func_def_33, type, gram_L1614515765ubtrOf: dtree > n > dtree).
% 2.91/1.62 thf(func_def_34, type, gram_L864798063lle_wf: dtree > $o).
% 2.91/1.62 thf(func_def_35, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.91/1.62 thf(func_def_36, type, top_top: !>[X0: $tType]:(X0)).
% 2.91/1.62 thf(func_def_37, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.91/1.62 thf(func_def_38, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.91/1.62 thf(func_def_39, type, image: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > set @ X1)).
% 2.91/1.62 thf(func_def_40, type, vimage: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X1 > set @ X0)).
% 2.91/1.62 thf(func_def_41, type, sum_Inl: !>[X0: $tType, X1: $tType]:(X0 > sum_sum @ X0 @ X1)).
% 2.91/1.62 thf(func_def_42, type, sum_Inr: !>[X0: $tType, X1: $tType]:(X0 > sum_sum @ X1 @ X0)).
% 2.91/1.62 thf(func_def_43, type, sum_map_sum: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1) > (X2 > X3) > sum_sum @ X0 @ X2 > sum_sum @ X1 @ X3)).
% 2.91/1.62 thf(func_def_44, type, sum_rec_sum: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1)).
% 2.91/1.62 thf(func_def_45, type, sum_case_sum: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1)).
% 2.91/1.62 thf(func_def_46, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.91/1.62 thf(func_def_47, type, a: t).
% 2.91/1.62 thf(func_def_48, type, n2: n).
% 2.91/1.62 thf(func_def_49, type, t_tr: sum_sum @ t @ dtree).
% 2.91/1.62 thf(func_def_50, type, tr0: dtree).
% 2.91/1.62 thf(func_def_67, type, sP0: (set @ n > dtree > dtree > $o) > $o).
% 2.91/1.62 thf(func_def_68, type, sP1: (set @ n > dtree > n > $o) > $o).
% 2.91/1.62 thf(func_def_69, type, sK2: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 2.91/1.62 thf(func_def_70, type, sK3: !>[X0: $tType]:(set @ X0 > X0)).
% 2.91/1.62 thf(func_def_71, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > sum_sum @ X1 @ X0 > (X1 > X2) > X1)).
% 2.91/1.62 thf(func_def_72, type, sK5: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 2.91/1.62 thf(func_def_73, type, sK6: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > X1) > X1)).
% 2.91/1.62 thf(func_def_74, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 2.91/1.62 thf(func_def_75, type, sK8: n > dtree > set @ n > dtree).
% 2.91/1.62 thf(func_def_76, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X0) > (X1 > X0) > (X2 > X1) > (X2 > X1) > X1)).
% 2.91/1.62 thf(func_def_77, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X0) > (X1 > X0) > (X2 > X1) > (X2 > X1) > X1)).
% 2.91/1.62 thf(func_def_78, type, sK11: !>[X0: $tType]:(X0)).
% 2.91/1.62 thf(func_def_79, type, sK12: (set @ n > dtree > dtree > $o) > set @ n).
% 2.91/1.62 thf(func_def_80, type, sK13: (set @ n > dtree > dtree > $o) > dtree).
% 2.91/1.62 thf(func_def_81, type, sK14: (set @ n > dtree > dtree > $o) > set @ n).
% 2.91/1.62 thf(func_def_82, type, sK15: (set @ n > dtree > dtree > $o) > dtree).
% 2.91/1.62 thf(func_def_83, type, sK16: (set @ n > dtree > dtree > $o) > dtree).
% 2.91/1.62 thf(func_def_84, type, sK17: (set @ n > dtree > dtree > $o) > dtree).
% 2.91/1.62 thf(func_def_85, type, sK18: dtree > dtree > n).
% 2.91/1.62 thf(func_def_86, type, sK19: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > X1)).
% 2.91/1.62 thf(func_def_87, type, sK20: !>[X0: $tType]:((X0 > X0) > X0)).
% 2.91/1.62 thf(func_def_88, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType]:(set @ sum_sum @ X0 @ X1 > (X1 > X2) > X2 > X1)).
% 2.91/1.62 thf(func_def_89, type, sK22: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > X1)).
% 2.91/1.62 thf(func_def_90, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > sum_sum @ X0 @ X1 > (X1 > X2) > X1)).
% 2.91/1.62 thf(func_def_91, type, sK24: !>[X0: $tType, X1: $tType]:(set @ X1 > (X1 > X0) > X0 > X1)).
% 2.91/1.62 thf(func_def_92, type, sK25: dtree > n).
% 2.91/1.62 thf(func_def_93, type, sK26: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > X0) > X1)).
% 2.91/1.62 thf(func_def_94, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X0) > (X1 > X0) > (X2 > X1) > X1)).
% 2.91/1.62 thf(func_def_95, type, sK28: (set @ n > dtree > dtree > $o) > dtree).
% 2.91/1.62 thf(func_def_96, type, sK29: (set @ n > dtree > dtree > $o) > set @ n).
% 2.91/1.62 thf(func_def_97, type, sK30: (set @ n > dtree > dtree > $o) > dtree).
% 2.91/1.62 thf(func_def_98, type, sK31: (set @ n > dtree > dtree > $o) > dtree).
% 2.91/1.62 thf(func_def_99, type, sK32: (set @ n > dtree > dtree > $o) > dtree).
% 2.91/1.62 thf(func_def_100, type, sK33: (set @ n > dtree > dtree > $o) > set @ n).
% 2.91/1.62 thf(func_def_101, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType]:($o > (sum_sum @ X0 @ X1 > X2) > X2 > X1)).
% 2.91/1.62 thf(func_def_102, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType]:($o > (sum_sum @ X0 @ X1 > X2) > X2 > X0)).
% 2.91/1.62 thf(func_def_103, type, sK36: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > $o) > X0)).
% 2.91/1.62 thf(func_def_104, type, sK37: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > $o) > X1)).
% 2.91/1.62 thf(func_def_105, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1) > (X2 > X1) > set @ X0 > (X0 > X2) > X0)).
% 2.91/1.62 thf(func_def_106, type, sK39: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > X0) > X0)).
% 2.91/1.62 thf(func_def_107, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X0) > (X1 > X0) > (X2 > X1) > X1)).
% 2.91/1.62 thf(func_def_108, type, sK41: (set @ n > dtree > n > $o) > dtree).
% 2.91/1.62 thf(func_def_109, type, sK42: (set @ n > dtree > n > $o) > set @ n).
% 2.91/1.62 thf(func_def_110, type, sK43: (set @ n > dtree > n > $o) > dtree).
% 2.91/1.62 thf(func_def_111, type, sK44: (set @ n > dtree > n > $o) > n).
% 2.91/1.62 thf(func_def_112, type, sK45: (set @ n > dtree > n > $o) > dtree).
% 2.91/1.62 thf(func_def_113, type, sK46: (set @ n > dtree > n > $o) > set @ n).
% 2.91/1.62 thf(func_def_114, type, sK47: n > dtree > set @ n > dtree).
% 2.91/1.62 thf(func_def_115, type, sK48: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X0)).
% 2.91/1.62 thf(func_def_116, type, sK49: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X1)).
% 2.91/1.62 thf(func_def_117, type, sK50: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X1)).
% 2.91/1.62 thf(func_def_118, type, sK51: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X0)).
% 2.91/1.62 thf(func_def_119, type, sK52: (dtree > dtree > $o) > dtree).
% 2.91/1.62 thf(func_def_120, type, sK53: (dtree > dtree > $o) > dtree).
% 2.91/1.62 thf(func_def_121, type, sK54: (dtree > dtree > $o) > dtree).
% 2.91/1.62 thf(func_def_122, type, sK55: (dtree > dtree > $o) > dtree).
% 2.91/1.62 thf(func_def_123, type, sK56: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.91/1.62 thf(func_def_124, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType]:(set @ sum_sum @ X1 @ X2 > (X2 > X0) > X0 > X2)).
% 2.91/1.62 thf(func_def_125, type, sK58: dtree > dtree > set @ n > dtree).
% 2.91/1.62 thf(func_def_126, type, sK59: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X0)).
% 2.91/1.62 thf(func_def_127, type, sK60: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X1)).
% 2.91/1.62 thf(func_def_128, type, sK61: !>[X0: $tType, X1: $tType]:(X1 > (X0 > X1) > X0)).
% 2.91/1.62 thf(func_def_129, type, sK62: !>[X0: $tType, X1: $tType]:((X0 > X1) > X1)).
% 2.91/1.62 thf(func_def_131, type, ph64: !>[X0: $tType]:(X0)).
% 2.91/1.62 thf(f1125,plain,(
% 2.91/1.62 $false),
% 2.91/1.62 inference(subsumption_resolution,[status(thm)],[f1124,f897])).
% 2.91/1.62 thf(f897,plain,(
% 2.91/1.62 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : X3,X4 : X3 > X2,X5 : X0 > X1] : (((sum_map_sum @ X3 @ X2 @ X0 @ X1 @ X4 @ X5 @ (sum_Inl @ X3 @ X0 @ X6)) = (sum_Inl @ X2 @ X1 @ (X4 @ X6)))) )),
% 2.91/1.62 inference(cnf_transformation,[status(thm)],[f612])).
% 2.91/1.62 thf(f612,plain,(
% 2.91/1.62 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : X3 > X2,X5 : X0 > X1,X6 : X3] : ((sum_map_sum @ X3 @ X2 @ X0 @ X1 @ X4 @ X5 @ (sum_Inl @ X3 @ X0 @ X6)) = (sum_Inl @ X2 @ X1 @ (X4 @ X6)))),
% 2.91/1.62 inference(rectify,[status(thm)],[f58])).
% 2.91/1.62 thf(f58,axiom,(
% 2.91/1.62 ! [X1 : $tType,X3 : $tType,X2 : $tType,X0 : $tType,X44 : X0 > X2,X45 : X1 > X3,X16 : X0] : ((sum_map_sum @ X0 @ X2 @ X1 @ X3 @ X44 @ X45 @ (sum_Inl @ X0 @ X1 @ X16)) = (sum_Inl @ X2 @ X3 @ (X44 @ X16)))),
% 2.91/1.62 file('/export/starexec/sandbox/tmp/tmp.jDfwb26t2m/DTF2THF_25971.p',fact_57_map__sum_Osimps_I1_J)).
% 2.91/1.62 thf(f1124,plain,(
% 2.91/1.62 ((sum_map_sum @ t @ t @ dtree @ n @ id @ t @ (comp @ n @ n @ dtree @ (comp @ dtree @ n @ n @ root @ (gram_L1451583624elle_H @ tr0)) @ root) @ (sum_Inl @ t @ dtree @ a)) != (sum_Inl @ t @ n @ (id @ t @ a)))),
% 2.91/1.62 inference(forward_demodulation,[status(thm)],[f1084,f897])).
% 2.91/1.62 thf(f1084,plain,(
% 2.91/1.62 ((sum_map_sum @ t @ t @ dtree @ n @ id @ t @ (comp @ n @ n @ dtree @ (comp @ dtree @ n @ n @ root @ (gram_L1451583624elle_H @ tr0)) @ root) @ (sum_Inl @ t @ dtree @ a)) != (sum_map_sum @ t @ t @ dtree @ n @ id @ t @ root @ (sum_Inl @ t @ dtree @ a)))),
% 2.91/1.62 inference(definition_unfolding,[status(thm)],[f935,f925,f925])).
% 2.91/1.62 thf(f925,plain,(
% 2.91/1.62 (t_tr = (sum_Inl @ t @ dtree @ a))),
% 2.91/1.62 inference(cnf_transformation,[status(thm)],[f271])).
% 2.91/1.62 thf(f271,axiom,(
% 2.91/1.62 (t_tr = (sum_Inl @ t @ dtree @ a))),
% 2.91/1.62 file('/export/starexec/sandbox/tmp/tmp.jDfwb26t2m/DTF2THF_25971.p',conj_2)).
% 2.91/1.62 thf(f935,plain,(
% 2.91/1.62 ((sum_map_sum @ t @ t @ dtree @ n @ id @ t @ (comp @ n @ n @ dtree @ (comp @ dtree @ n @ n @ root @ (gram_L1451583624elle_H @ tr0)) @ root) @ t_tr) != (sum_map_sum @ t @ t @ dtree @ n @ id @ t @ root @ t_tr))),
% 2.91/1.62 inference(cnf_transformation,[status(thm)],[f579])).
% 2.91/1.62 thf(f579,plain,(
% 2.91/1.62 ((sum_map_sum @ t @ t @ dtree @ n @ id @ t @ (comp @ n @ n @ dtree @ (comp @ dtree @ n @ n @ root @ (gram_L1451583624elle_H @ tr0)) @ root) @ t_tr) != (sum_map_sum @ t @ t @ dtree @ n @ id @ t @ root @ t_tr))),
% 2.91/1.62 inference(flattening,[status(thm)],[f273])).
% 2.91/1.62 thf(f273,negated_conjecture,(
% 2.91/1.62 ~((sum_map_sum @ t @ t @ dtree @ n @ id @ t @ (comp @ n @ n @ dtree @ (comp @ dtree @ n @ n @ root @ (gram_L1451583624elle_H @ tr0)) @ root) @ t_tr) = (sum_map_sum @ t @ t @ dtree @ n @ id @ t @ root @ t_tr))),
% 2.91/1.62 inference(negated_conjecture,[status(cth)],[f272])).
% 2.91/1.62 thf(f272,conjecture,(
% 2.91/1.62 ((sum_map_sum @ t @ t @ dtree @ n @ id @ t @ (comp @ n @ n @ dtree @ (comp @ dtree @ n @ n @ root @ (gram_L1451583624elle_H @ tr0)) @ root) @ t_tr) = (sum_map_sum @ t @ t @ dtree @ n @ id @ t @ root @ t_tr))),
% 2.91/1.62 file('/export/starexec/sandbox/tmp/tmp.jDfwb26t2m/DTF2THF_25971.p',conj_3)).
% 2.91/1.62 % SZS output end Proof for DTF2THF_25971
% 2.91/1.62 % (26299)------------------------------
% 2.91/1.62 % (26299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.62 % (26299)Termination reason: Refutation
% 2.91/1.62
% 2.91/1.62 % (26299)Memory used [KB]: 7164
% 2.91/1.62 % (26299)Time elapsed: 0.060 s
% 2.91/1.62 % (26299)Instructions burned: 96 (million)
% 2.91/1.62 % (26299)------------------------------
% 2.91/1.62 % (26299)------------------------------
% 2.91/1.62 % (26293)Success in time 0.077 s
%------------------------------------------------------------------------------