%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : COM189^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:41:53 AM UTC 2026
% Result : Theorem 3.02s 1.72s
% Output : Refutation 3.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM189^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.32 % Computer : n029.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue Feb 24 04:16:29 EST 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : COM189^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.44 % Domain : Computing Theory
% 0.19/0.44 % Problem : Grammars and languages 706
% 0.19/0.44 % Version : [Bla16] axioms : Especial.
% 0.19/0.44 % English :
% 0.19/0.44
% 0.19/0.44 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.19/0.44 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.19/0.44 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.19/0.44 % Source : [Bla16]
% 0.19/0.44 % Names : gram_lang__706.p [Bla16]
% 0.19/0.44
% 0.19/0.44 % Status : Theorem
% 0.19/0.44 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.33 v7.2.0, 0.50 v7.1.0
% 0.19/0.44 % Syntax : Number of formulae : 331 ( 116 unt; 52 typ; 0 def)
% 0.19/0.44 % Number of atoms : 755 ( 265 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 13 ( 2 avg)
% 0.19/0.44 % Number of connectives : 3930 ( 73 ~; 11 |; 65 &;3420 @)
% 0.19/0.44 % ( 0 <=>; 361 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 24 ( 8 avg)
% 0.19/0.44 % Number of types : 4 ( 3 usr)
% 0.19/0.44 % Number of type conns : 292 ( 292 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 52 ( 49 usr; 3 con; 0-6 aty)
% 0.19/0.44 % Number of variables : 1143 ( 62 ^;1001 !; 46 ?;1143 :)
% 0.19/0.44 % ( 34 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.44 % SPC : TH1_THM_EQU_NAR
% 0.19/0.44
% 0.19/0.44 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.19/0.44 % 2016-07-13 14:44:19.466
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 %----Could-be-implicit typings (6)
% 0.19/0.44 thf(ty_t_Sum__Type_Osum,type,
% 0.19/0.44 sum_sum: $tType > $tType > $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_DTree_Odtree,type,
% 0.19/0.44 dtree: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_Set_Oset,type,
% 0.19/0.44 set: $tType > $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_DTree_OT,type,
% 0.19/0.44 t: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_DTree_ON,type,
% 0.19/0.44 n: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_t_itself,type,
% 0.19/0.44 itself: $tType > $tType ).
% 0.19/0.44
% 0.19/0.44 %----Explicit typings (46)
% 0.19/0.44 thf(sy_cl_HOL_Otype,type,
% 0.19/0.44 type:
% 0.19/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Orderings_Obot,type,
% 0.19/0.44 bot:
% 0.19/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Orderings_Oord,type,
% 0.19/0.44 ord:
% 0.19/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Orderings_Otop,type,
% 0.19/0.44 top:
% 0.19/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Orderings_Oorder,type,
% 0.19/0.44 order:
% 0.19/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Orderings_Olinorder,type,
% 0.19/0.44 linorder:
% 0.19/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Orderings_Opreorder,type,
% 0.19/0.44 preorder:
% 0.19/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_cl_Orderings_Oorder__top,type,
% 0.19/0.44 order_top:
% 0.19/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_DTree_ONode,type,
% 0.19/0.44 node: n > ( set @ ( sum_sum @ t @ dtree ) ) > dtree ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_DTree_Ocont,type,
% 0.19/0.44 cont: dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_DTree_Ocorec,type,
% 0.19/0.44 corec:
% 0.19/0.44 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) ) ) > A > dtree ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_DTree_Odtree_Oroot,type,
% 0.19/0.44 root: dtree > n ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_DTree_Ounfold,type,
% 0.19/0.44 unfold:
% 0.19/0.44 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ A ) ) ) > A > dtree ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Fun_Ocomp,type,
% 0.19/0.44 comp:
% 0.19/0.44 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Fun_Oid,type,
% 0.19/0.44 id:
% 0.19/0.44 !>[A: $tType] : ( A > A ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OS,type,
% 0.19/0.44 gram_L1451583635elle_S: n > ( set @ ( sum_sum @ t @ n ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr,type,
% 0.19/0.44 gram_L1231612515_deftr: n > dtree ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst,type,
% 0.19/0.44 gram_L1004374585hsubst: dtree > dtree > dtree ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c,type,
% 0.19/0.44 gram_L1905609002ubst_c: dtree > dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r,type,
% 0.19/0.44 gram_L1905609017ubst_r: dtree > n ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr,type,
% 0.19/0.44 gram_L1333338417e_inFr: ( set @ n ) > dtree > t > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2,type,
% 0.19/0.44 gram_L805317441_inFr2: ( set @ n ) > dtree > t > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFrr,type,
% 0.19/0.44 gram_L805317505_inFrr: ( set @ n ) > dtree > t > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr,type,
% 0.19/0.44 gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oreg,type,
% 0.19/0.44 gram_L1918716148le_reg: ( n > dtree ) > dtree > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oregular,type,
% 0.19/0.44 gram_L646766332egular: dtree > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr,type,
% 0.19/0.44 gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr2,type,
% 0.19/0.44 gram_L1283001940subtr2: ( set @ n ) > dtree > dtree > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OsubtrOf,type,
% 0.19/0.44 gram_L1614515765ubtrOf: dtree > n > dtree ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf,type,
% 0.19/0.44 gram_L864798063lle_wf: dtree > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.19/0.45 minus_minus:
% 0.19/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_If,type,
% 0.19/0.45 if:
% 0.19/0.45 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.19/0.45 bot_bot:
% 0.19/0.45 !>[A: $tType] : A ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.19/0.45 ord_less_eq:
% 0.19/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.19/0.45 top_top:
% 0.19/0.45 !>[A: $tType] : A ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Pure_Otype,type,
% 0.19/0.45 type2:
% 0.19/0.45 !>[A: $tType] : ( itself @ A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Set_OCollect,type,
% 0.19/0.45 collect:
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Set_Oinsert,type,
% 0.19/0.45 insert:
% 0.19/0.45 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Set_Ovimage,type,
% 0.19/0.45 vimage:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Sum__Type_OInl,type,
% 0.19/0.45 sum_Inl:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Sum__Type_OInr,type,
% 0.19/0.45 sum_Inr:
% 0.19/0.45 !>[B: $tType,A: $tType] : ( B > ( sum_sum @ A @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum,type,
% 0.19/0.45 sum_rec_sum:
% 0.19/0.45 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Typedef_Otype__definition,type,
% 0.19/0.45 type_definition:
% 0.19/0.45 !>[B: $tType,A: $tType] : ( ( B > A ) > ( A > B ) > ( set @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member,type,
% 0.19/0.45 member:
% 0.19/0.45 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_f,type,
% 0.19/0.45 f: n > dtree ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_tr,type,
% 0.19/0.45 tr: dtree ).
% 0.19/0.45
% 0.19/0.45 %----Relevant facts (256)
% 0.19/0.45 thf(fact_0_assms,axiom,
% 0.19/0.45 gram_L1918716148le_reg @ f @ tr ).
% 0.19/0.45
% 0.19/0.45 % assms
% 0.19/0.45 thf(fact_1_hsubst__r__def,axiom,
% 0.19/0.45 gram_L1905609017ubst_r = root ).
% 0.19/0.45
% 0.19/0.45 % hsubst_r_def
% 0.19/0.45 thf(fact_2_root__deftr,axiom,
% 0.19/0.45 ! [N: n] :
% 0.19/0.45 ( ( root @ ( gram_L1231612515_deftr @ N ) )
% 0.19/0.45 = N ) ).
% 0.19/0.45
% 0.19/0.45 % root_deftr
% 0.19/0.45 thf(fact_3_root__hsubst,axiom,
% 0.19/0.45 ! [Tr0: dtree,Tr: dtree] :
% 0.19/0.45 ( ( root @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.19/0.45 = ( root @ Tr ) ) ).
% 0.19/0.45
% 0.19/0.45 % root_hsubst
% 0.19/0.45 thf(fact_4_inFr2__root__in,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.19/0.45 ( ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 )
% 0.19/0.45 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr2_root_in
% 0.19/0.45 thf(fact_5_inItr_OBase,axiom,
% 0.19/0.45 ! [Tr: dtree,Ns: set @ n] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.19/0.45 => ( gram_L830233218_inItr @ Ns @ Tr @ ( root @ Tr ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inItr.Base
% 0.19/0.45 thf(fact_6_inItr__root__in,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr: dtree,N: n] :
% 0.19/0.45 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.19/0.45 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.19/0.45
% 0.19/0.45 % inItr_root_in
% 0.19/0.45 thf(fact_7_regular__def2,axiom,
% 0.19/0.45 ( gram_L646766332egular
% 0.19/0.45 = ( ^ [Tr2: dtree] :
% 0.19/0.45 ? [F: n > dtree] :
% 0.19/0.45 ( ( gram_L1918716148le_reg @ F @ Tr2 )
% 0.19/0.45 & ! [N2: n] :
% 0.19/0.45 ( ( root @ ( F @ N2 ) )
% 0.19/0.45 = N2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % regular_def2
% 0.19/0.45 thf(fact_8_hsubst__eq,axiom,
% 0.19/0.45 ! [Tr: dtree,Tr0: dtree] :
% 0.19/0.45 ( ( ( root @ Tr )
% 0.19/0.45 = ( root @ Tr0 ) )
% 0.19/0.45 => ( ( gram_L1004374585hsubst @ Tr0 @ Tr )
% 0.19/0.45 = ( gram_L1004374585hsubst @ Tr0 @ Tr0 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % hsubst_eq
% 0.19/0.45 thf(fact_9_subtr2_ORefl,axiom,
% 0.19/0.45 ! [Tr: dtree,Ns: set @ n] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.19/0.45 => ( gram_L1283001940subtr2 @ Ns @ Tr @ Tr ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr2.Refl
% 0.19/0.45 thf(fact_10_subtr2__rootL__in,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.19/0.45 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.19/0.45 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr2_rootL_in
% 0.19/0.45 thf(fact_11_subtr2__rootR__in,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.19/0.45 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.19/0.45 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr2_rootR_in
% 0.19/0.45 thf(fact_12_inFr__root__in,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.19/0.45 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.19/0.45 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr_root_in
% 0.19/0.45 thf(fact_13_inFr__inFr2,axiom,
% 0.19/0.45 gram_L1333338417e_inFr = gram_L805317441_inFr2 ).
% 0.19/0.45
% 0.19/0.45 % inFr_inFr2
% 0.19/0.45 thf(fact_14_regular__def,axiom,
% 0.19/0.45 ( gram_L646766332egular
% 0.19/0.45 = ( ^ [Tr2: dtree] :
% 0.19/0.45 ? [F: n > dtree] : ( gram_L1918716148le_reg @ F @ Tr2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % regular_def
% 0.19/0.45 thf(fact_15_subtr2__trans,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr3: dtree] :
% 0.19/0.45 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.19/0.45 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr3 )
% 0.19/0.45 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr2_trans
% 0.19/0.45 thf(fact_16_inFr__hsubst__notin,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr: dtree,T2: t,Tr0: dtree] :
% 0.19/0.45 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.19/0.45 => ( ~ ( member @ n @ ( root @ Tr0 ) @ Ns )
% 0.19/0.45 => ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr_hsubst_notin
% 0.19/0.45 thf(fact_17_not__root__inFr,axiom,
% 0.19/0.45 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.19/0.45 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 0.19/0.45 => ~ ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % not_root_inFr
% 0.19/0.45 thf(fact_18_hsubst__def,axiom,
% 0.19/0.45 ( gram_L1004374585hsubst
% 0.19/0.45 = ( ^ [Tr02: dtree] : ( unfold @ dtree @ gram_L1905609017ubst_r @ ( gram_L1905609002ubst_c @ Tr02 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % hsubst_def
% 0.19/0.45 thf(fact_19_reg__def2,axiom,
% 0.19/0.45 ( gram_L1918716148le_reg
% 0.19/0.45 = ( ^ [F: n > dtree,Tr2: dtree] :
% 0.19/0.45 ! [Ns2: set @ n,Tr4: dtree] :
% 0.19/0.45 ( ( gram_L716654942_subtr @ Ns2 @ Tr4 @ Tr2 )
% 0.19/0.45 => ( Tr4
% 0.19/0.45 = ( F @ ( root @ Tr4 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % reg_def2
% 0.19/0.45 thf(fact_20_inItr__subtr,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr: dtree,N: n] :
% 0.19/0.45 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.19/0.45 => ? [Tr5: dtree] :
% 0.19/0.45 ( ( gram_L716654942_subtr @ Ns @ Tr5 @ Tr )
% 0.19/0.45 & ( ( root @ Tr5 )
% 0.19/0.45 = N ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inItr_subtr
% 0.19/0.45 thf(fact_21_root__o__subst,axiom,
% 0.19/0.45 ! [Tr0: dtree] :
% 0.19/0.45 ( ( comp @ dtree @ n @ dtree @ root @ ( gram_L1004374585hsubst @ Tr0 ) )
% 0.19/0.45 = root ) ).
% 0.19/0.45
% 0.19/0.45 % root_o_subst
% 0.19/0.45 thf(fact_22_wf__deftr,axiom,
% 0.19/0.45 ! [N: n] : ( gram_L864798063lle_wf @ ( gram_L1231612515_deftr @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % wf_deftr
% 0.19/0.45 thf(fact_23_wf__hsubst,axiom,
% 0.19/0.45 ! [Tr0: dtree,Tr: dtree] :
% 0.19/0.45 ( ( gram_L864798063lle_wf @ Tr0 )
% 0.19/0.45 => ( ( gram_L864798063lle_wf @ Tr )
% 0.19/0.45 => ( gram_L864798063lle_wf @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % wf_hsubst
% 0.19/0.45 thf(fact_24_subtr__inItr,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr: dtree,N: n,Tr1: dtree] :
% 0.19/0.45 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.19/0.45 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.19/0.45 => ( gram_L830233218_inItr @ Ns @ Tr1 @ N ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr_inItr
% 0.19/0.45 thf(fact_25_subtr__subtr2,axiom,
% 0.19/0.45 gram_L716654942_subtr = gram_L1283001940subtr2 ).
% 0.19/0.45
% 0.19/0.45 % subtr_subtr2
% 0.19/0.45 thf(fact_26_subtr__inFr,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr: dtree,T2: t,Tr1: dtree] :
% 0.19/0.45 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.19/0.45 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.19/0.45 => ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr_inFr
% 0.19/0.45 thf(fact_27_root__Node,axiom,
% 0.19/0.45 ! [N: n,As: set @ ( sum_sum @ t @ dtree )] :
% 0.19/0.45 ( ( root @ ( node @ N @ As ) )
% 0.19/0.45 = N ) ).
% 0.19/0.45
% 0.19/0.45 % root_Node
% 0.19/0.45 thf(fact_28_inFr2__mono,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr: dtree,T2: t,Ns3: set @ n] :
% 0.19/0.45 ( ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 0.19/0.45 => ( gram_L805317441_inFr2 @ Ns3 @ Tr @ T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr2_mono
% 0.19/0.45 thf(fact_29_subtr__trans,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr3: dtree] :
% 0.19/0.45 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.19/0.45 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr3 )
% 0.19/0.45 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr_trans
% 0.19/0.45 thf(fact_30_subtr__mono,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Ns3: set @ n] :
% 0.19/0.45 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 0.19/0.45 => ( gram_L716654942_subtr @ Ns3 @ Tr1 @ Tr22 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr_mono
% 0.19/0.45 thf(fact_31_wf__subtr,axiom,
% 0.19/0.45 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 0.19/0.45 ( ( gram_L864798063lle_wf @ Tr1 )
% 0.19/0.45 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.19/0.45 => ( gram_L864798063lle_wf @ Tr ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % wf_subtr
% 0.19/0.45 thf(fact_32_unfold_I1_J,axiom,
% 0.19/0.45 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ A ) ),B2: A] :
% 0.19/0.45 ( ( root @ ( unfold @ A @ Rt @ Ct @ B2 ) )
% 0.19/0.45 = ( Rt @ B2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % unfold(1)
% 0.19/0.45 thf(fact_33_subtr_ORefl,axiom,
% 0.19/0.45 ! [Tr: dtree,Ns: set @ n] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.19/0.45 => ( gram_L716654942_subtr @ Ns @ Tr @ Tr ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr.Refl
% 0.19/0.45 thf(fact_34_subtr__rootL__in,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.19/0.45 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.19/0.45 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr_rootL_in
% 0.19/0.45 thf(fact_35_subtr__rootR__in,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.19/0.45 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.19/0.45 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr_rootR_in
% 0.19/0.45 thf(fact_36_inFr__mono,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr: dtree,T2: t,Ns3: set @ n] :
% 0.19/0.45 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 0.19/0.45 => ( gram_L1333338417e_inFr @ Ns3 @ Tr @ T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr_mono
% 0.19/0.45 thf(fact_37_subtr2__mono,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Ns3: set @ n] :
% 0.19/0.45 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 0.19/0.45 => ( gram_L1283001940subtr2 @ Ns3 @ Tr1 @ Tr22 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr2_mono
% 0.19/0.45 thf(fact_38_inItr__mono,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr: dtree,N: n,Ns3: set @ n] :
% 0.19/0.45 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 0.19/0.45 => ( gram_L830233218_inItr @ Ns3 @ Tr @ N ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inItr_mono
% 0.19/0.45 thf(fact_39_comp__apply,axiom,
% 0.19/0.45 ! [C: $tType,A: $tType,B: $tType] :
% 0.19/0.45 ( ( comp @ B @ A @ C )
% 0.19/0.45 = ( ^ [F: B > A,G: C > B,X: C] : ( F @ ( G @ X ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % comp_apply
% 0.19/0.45 thf(fact_40_subset__antisym,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A2 )
% 0.19/0.45 => ( A2 = B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_antisym
% 0.19/0.45 thf(fact_41_subsetI,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ! [X2: A] :
% 0.19/0.45 ( ( member @ A @ X2 @ A2 )
% 0.19/0.45 => ( member @ A @ X2 @ B3 ) )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % subsetI
% 0.19/0.45 thf(fact_42_order__refl,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_refl
% 0.19/0.45 thf(fact_43_reg__def,axiom,
% 0.19/0.45 ( gram_L1918716148le_reg
% 0.19/0.45 = ( ^ [F: n > dtree,Tr2: dtree] :
% 0.19/0.45 ! [Tr4: dtree] :
% 0.19/0.45 ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr4 @ Tr2 )
% 0.19/0.45 => ( Tr4
% 0.19/0.45 = ( F @ ( root @ Tr4 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % reg_def
% 0.19/0.45 thf(fact_44_rewriteR__comp__comp2,axiom,
% 0.19/0.45 ! [C: $tType,B: $tType,E: $tType,D: $tType,A: $tType,G2: C > B,H: A > C,R1: D > B,R2: A > D,F2: B > E,L: D > E] :
% 0.19/0.45 ( ( ( comp @ C @ B @ A @ G2 @ H )
% 0.19/0.45 = ( comp @ D @ B @ A @ R1 @ R2 ) )
% 0.19/0.45 => ( ( ( comp @ B @ E @ D @ F2 @ R1 )
% 0.19/0.45 = L )
% 0.19/0.45 => ( ( comp @ C @ E @ A @ ( comp @ B @ E @ C @ F2 @ G2 ) @ H )
% 0.19/0.45 = ( comp @ D @ E @ A @ L @ R2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % rewriteR_comp_comp2
% 0.19/0.45 thf(fact_45_mem__Collect__eq,axiom,
% 0.19/0.45 ! [A: $tType,A3: A,P: A > $o] :
% 0.19/0.45 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.19/0.45 = ( P @ A3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % mem_Collect_eq
% 0.19/0.45 thf(fact_46_Collect__mem__eq,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] :
% 0.19/0.45 ( ( collect @ A
% 0.19/0.45 @ ^ [X: A] : ( member @ A @ X @ A2 ) )
% 0.19/0.45 = A2 ) ).
% 0.19/0.45
% 0.19/0.45 % Collect_mem_eq
% 0.19/0.45 thf(fact_47_Collect__cong,axiom,
% 0.19/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.45 ( ! [X2: A] :
% 0.19/0.45 ( ( P @ X2 )
% 0.19/0.45 = ( Q @ X2 ) )
% 0.19/0.45 => ( ( collect @ A @ P )
% 0.19/0.45 = ( collect @ A @ Q ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Collect_cong
% 0.19/0.45 thf(fact_48_ext,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,F2: A > B,G2: A > B] :
% 0.19/0.45 ( ! [X2: A] :
% 0.19/0.45 ( ( F2 @ X2 )
% 0.19/0.45 = ( G2 @ X2 ) )
% 0.19/0.45 => ( F2 = G2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % ext
% 0.19/0.45 thf(fact_49_rewriteL__comp__comp2,axiom,
% 0.19/0.45 ! [A: $tType,C: $tType,B: $tType,D: $tType,E: $tType,F2: C > B,G2: A > C,L1: D > B,L2: A > D,H: E > A,R: E > D] :
% 0.19/0.45 ( ( ( comp @ C @ B @ A @ F2 @ G2 )
% 0.19/0.45 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 0.19/0.45 => ( ( ( comp @ A @ D @ E @ L2 @ H )
% 0.19/0.45 = R )
% 0.19/0.45 => ( ( comp @ C @ B @ E @ F2 @ ( comp @ A @ C @ E @ G2 @ H ) )
% 0.19/0.45 = ( comp @ D @ B @ E @ L1 @ R ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % rewriteL_comp_comp2
% 0.19/0.45 thf(fact_50_rewriteR__comp__comp,axiom,
% 0.19/0.45 ! [C: $tType,D: $tType,B: $tType,A: $tType,G2: C > B,H: A > C,R: A > B,F2: B > D] :
% 0.19/0.45 ( ( ( comp @ C @ B @ A @ G2 @ H )
% 0.19/0.45 = R )
% 0.19/0.45 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F2 @ G2 ) @ H )
% 0.19/0.45 = ( comp @ B @ D @ A @ F2 @ R ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % rewriteR_comp_comp
% 0.19/0.45 thf(fact_51_rewriteL__comp__comp,axiom,
% 0.19/0.45 ! [C: $tType,B: $tType,A: $tType,D: $tType,F2: C > B,G2: A > C,L: A > B,H: D > A] :
% 0.19/0.45 ( ( ( comp @ C @ B @ A @ F2 @ G2 )
% 0.19/0.45 = L )
% 0.19/0.45 => ( ( comp @ C @ B @ D @ F2 @ ( comp @ A @ C @ D @ G2 @ H ) )
% 0.19/0.45 = ( comp @ A @ B @ D @ L @ H ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % rewriteL_comp_comp
% 0.19/0.45 thf(fact_52_top__apply,axiom,
% 0.19/0.45 ! [C: $tType,D: $tType] :
% 0.19/0.45 ( ( top @ C @ ( type2 @ C ) )
% 0.19/0.45 => ( ( top_top @ ( D > C ) )
% 0.19/0.45 = ( ^ [X: D] : ( top_top @ C ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % top_apply
% 0.19/0.45 thf(fact_53_UNIV__I,axiom,
% 0.19/0.45 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % UNIV_I
% 0.19/0.45 thf(fact_54_UNIV__eq__I,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] :
% 0.19/0.45 ( ! [X2: A] : ( member @ A @ X2 @ A2 )
% 0.19/0.45 => ( ( top_top @ ( set @ A ) )
% 0.19/0.45 = A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % UNIV_eq_I
% 0.19/0.45 thf(fact_55_UNIV__witness,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ? [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % UNIV_witness
% 0.19/0.45 thf(fact_56_top__greatest,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order_top @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ ( top_top @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % top_greatest
% 0.19/0.45 thf(fact_57_top_Oextremum__unique,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order_top @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A3: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A3 )
% 0.19/0.45 = ( A3
% 0.19/0.45 = ( top_top @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % top.extremum_unique
% 0.19/0.45 thf(fact_58_top_Oextremum__uniqueI,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order_top @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A3: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A3 )
% 0.19/0.45 => ( A3
% 0.19/0.45 = ( top_top @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % top.extremum_uniqueI
% 0.19/0.45 thf(fact_59_subset__UNIV,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_UNIV
% 0.19/0.45 thf(fact_60_le__funD,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType] :
% 0.19/0.45 ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 => ! [F2: A > B,G2: A > B,X3: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.19/0.45 => ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_funD
% 0.19/0.45 thf(fact_61_le__funE,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType] :
% 0.19/0.45 ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 => ! [F2: A > B,G2: A > B,X3: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.19/0.45 => ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_funE
% 0.19/0.45 thf(fact_62_le__funI,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType] :
% 0.19/0.45 ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 => ! [F2: A > B,G2: A > B] :
% 0.19/0.45 ( ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
% 0.19/0.45 => ( ord_less_eq @ ( A > B ) @ F2 @ G2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_funI
% 0.19/0.45 thf(fact_63_le__fun__def,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType] :
% 0.19/0.45 ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 => ( ( ord_less_eq @ ( A > B ) )
% 0.19/0.45 = ( ^ [F: A > B,G: A > B] :
% 0.19/0.45 ! [X: A] : ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_fun_def
% 0.19/0.45 thf(fact_64_order__subst1,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType] :
% 0.19/0.45 ( ( ( order @ B @ ( type2 @ B ) )
% 0.19/0.45 & ( order @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A3: A,F2: B > A,B2: B,C2: B] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A3 @ ( F2 @ B2 ) )
% 0.19/0.45 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.19/0.45 => ( ! [X2: B,Y: B] :
% 0.19/0.45 ( ( ord_less_eq @ B @ X2 @ Y )
% 0.19/0.45 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 0.19/0.45 => ( ord_less_eq @ A @ A3 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_subst1
% 0.19/0.45 thf(fact_65_order__subst2,axiom,
% 0.19/0.45 ! [A: $tType,C: $tType] :
% 0.19/0.45 ( ( ( order @ C @ ( type2 @ C ) )
% 0.19/0.45 & ( order @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A3: A,B2: A,F2: A > C,C2: C] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.19/0.45 => ( ( ord_less_eq @ C @ ( F2 @ B2 ) @ C2 )
% 0.19/0.45 => ( ! [X2: A,Y: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.19/0.45 => ( ord_less_eq @ C @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 0.19/0.45 => ( ord_less_eq @ C @ ( F2 @ A3 ) @ C2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_subst2
% 0.19/0.45 thf(fact_66_ord__eq__le__subst,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType] :
% 0.19/0.45 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 & ( ord @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A3: A,F2: B > A,B2: B,C2: B] :
% 0.19/0.45 ( ( A3
% 0.19/0.45 = ( F2 @ B2 ) )
% 0.19/0.45 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.19/0.45 => ( ! [X2: B,Y: B] :
% 0.19/0.45 ( ( ord_less_eq @ B @ X2 @ Y )
% 0.19/0.45 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 0.19/0.45 => ( ord_less_eq @ A @ A3 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ord_eq_le_subst
% 0.19/0.45 thf(fact_67_ord__le__eq__subst,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType] :
% 0.19/0.45 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 & ( ord @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A3: A,B2: A,F2: A > B,C2: B] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.19/0.45 => ( ( ( F2 @ B2 )
% 0.19/0.45 = C2 )
% 0.19/0.45 => ( ! [X2: A,Y: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.19/0.45 => ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 0.19/0.45 => ( ord_less_eq @ B @ ( F2 @ A3 ) @ C2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ord_le_eq_subst
% 0.19/0.45 thf(fact_68_eq__iff,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ( ( ^ [Y2: A,Z: A] : ( Y2 = Z ) )
% 0.19/0.45 = ( ^ [X: A,Y3: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X @ Y3 )
% 0.19/0.45 & ( ord_less_eq @ A @ Y3 @ X ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % eq_iff
% 0.19/0.45 thf(fact_69_antisym,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X3: A,Y4: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ Y4 @ X3 )
% 0.19/0.45 => ( X3 = Y4 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % antisym
% 0.19/0.45 thf(fact_70_linear,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X3: A,Y4: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.19/0.45 | ( ord_less_eq @ A @ Y4 @ X3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % linear
% 0.19/0.45 thf(fact_71_eq__refl,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X3: A,Y4: A] :
% 0.19/0.45 ( ( X3 = Y4 )
% 0.19/0.45 => ( ord_less_eq @ A @ X3 @ Y4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % eq_refl
% 0.19/0.45 thf(fact_72_le__cases,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X3: A,Y4: A] :
% 0.19/0.45 ( ~ ( ord_less_eq @ A @ X3 @ Y4 )
% 0.19/0.45 => ( ord_less_eq @ A @ Y4 @ X3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_cases
% 0.19/0.45 thf(fact_73_order_Otrans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A3: A,B2: A,C2: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.19/0.45 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order.trans
% 0.19/0.45 thf(fact_74_le__cases3,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X3: A,Y4: A,Z2: A] :
% 0.19/0.45 ( ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.19/0.45 => ~ ( ord_less_eq @ A @ Y4 @ Z2 ) )
% 0.19/0.45 => ( ( ( ord_less_eq @ A @ Y4 @ X3 )
% 0.19/0.45 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 0.19/0.45 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.19/0.45 => ~ ( ord_less_eq @ A @ Z2 @ Y4 ) )
% 0.19/0.45 => ( ( ( ord_less_eq @ A @ Z2 @ Y4 )
% 0.19/0.45 => ~ ( ord_less_eq @ A @ Y4 @ X3 ) )
% 0.19/0.45 => ( ( ( ord_less_eq @ A @ Y4 @ Z2 )
% 0.19/0.45 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 0.19/0.45 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 0.19/0.45 => ~ ( ord_less_eq @ A @ X3 @ Y4 ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_cases3
% 0.19/0.45 thf(fact_75_antisym__conv,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [Y4: A,X3: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ Y4 @ X3 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.19/0.45 = ( X3 = Y4 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % antisym_conv
% 0.19/0.45 thf(fact_76_ord__eq__le__trans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A3: A,B2: A,C2: A] :
% 0.19/0.45 ( ( A3 = B2 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.19/0.45 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ord_eq_le_trans
% 0.19/0.45 thf(fact_77_ord__le__eq__trans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A3: A,B2: A,C2: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.19/0.45 => ( ( B2 = C2 )
% 0.19/0.45 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ord_le_eq_trans
% 0.19/0.45 thf(fact_78_order__class_Oorder_Oantisym,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A3: A,B2: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.19/0.45 => ( A3 = B2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_class.order.antisym
% 0.19/0.45 thf(fact_79_order__trans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X3: A,Y4: A,Z2: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ Y4 @ Z2 )
% 0.19/0.45 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_trans
% 0.19/0.45 thf(fact_80_dual__order_Orefl,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.refl
% 0.19/0.45 thf(fact_81_linorder__wlog,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [P: A > A > $o,A3: A,B2: A] :
% 0.19/0.45 ( ! [A4: A,B4: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.19/0.45 => ( P @ A4 @ B4 ) )
% 0.19/0.45 => ( ! [A4: A,B4: A] :
% 0.19/0.45 ( ( P @ B4 @ A4 )
% 0.19/0.45 => ( P @ A4 @ B4 ) )
% 0.19/0.45 => ( P @ A3 @ B2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % linorder_wlog
% 0.19/0.45 thf(fact_82_dual__order_Otrans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [B2: A,A3: A,C2: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.19/0.45 => ( ord_less_eq @ A @ C2 @ A3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.trans
% 0.19/0.45 thf(fact_83_dual__order_Oantisym,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [B2: A,A3: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.19/0.45 => ( A3 = B2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.antisym
% 0.19/0.45 thf(fact_84_set__mp,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B3: set @ A,X3: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.19/0.45 => ( ( member @ A @ X3 @ A2 )
% 0.19/0.45 => ( member @ A @ X3 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % set_mp
% 0.19/0.45 thf(fact_85_in__mono,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B3: set @ A,X3: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.19/0.45 => ( ( member @ A @ X3 @ A2 )
% 0.19/0.45 => ( member @ A @ X3 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % in_mono
% 0.19/0.45 thf(fact_86_subsetD,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B3: set @ A,C2: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.19/0.45 => ( ( member @ A @ C2 @ A2 )
% 0.19/0.45 => ( member @ A @ C2 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subsetD
% 0.19/0.45 thf(fact_87_subsetCE,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B3: set @ A,C2: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.19/0.45 => ( ( member @ A @ C2 @ A2 )
% 0.19/0.45 => ( member @ A @ C2 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subsetCE
% 0.19/0.45 thf(fact_88_equalityE,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ( A2 = B3 )
% 0.19/0.45 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.19/0.45 => ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % equalityE
% 0.19/0.45 thf(fact_89_subset__eq,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) )
% 0.19/0.45 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.19/0.45 ! [X: A] :
% 0.19/0.45 ( ( member @ A @ X @ A5 )
% 0.19/0.45 => ( member @ A @ X @ B5 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_eq
% 0.19/0.45 thf(fact_90_equalityD1,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ( A2 = B3 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % equalityD1
% 0.19/0.45 thf(fact_91_equalityD2,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ( A2 = B3 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ B3 @ A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % equalityD2
% 0.19/0.45 thf(fact_92_set__rev__mp,axiom,
% 0.19/0.45 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ( member @ A @ X3 @ A2 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.19/0.45 => ( member @ A @ X3 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % set_rev_mp
% 0.19/0.45 thf(fact_93_subset__iff,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) )
% 0.19/0.45 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.19/0.45 ! [T3: A] :
% 0.19/0.45 ( ( member @ A @ T3 @ A5 )
% 0.19/0.45 => ( member @ A @ T3 @ B5 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_iff
% 0.19/0.45 thf(fact_94_rev__subsetD,axiom,
% 0.19/0.45 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ( member @ A @ C2 @ A2 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.19/0.45 => ( member @ A @ C2 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % rev_subsetD
% 0.19/0.45 thf(fact_95_subset__refl,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 0.19/0.45
% 0.19/0.45 % subset_refl
% 0.19/0.45 thf(fact_96_Collect__mono,axiom,
% 0.19/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.45 ( ! [X2: A] :
% 0.19/0.45 ( ( P @ X2 )
% 0.19/0.45 => ( Q @ X2 ) )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Collect_mono
% 0.19/0.45 thf(fact_97_subset__trans,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B3: set @ A,C3: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C3 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_trans
% 0.19/0.45 thf(fact_98_set__eq__subset,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ^ [Y2: set @ A,Z: set @ A] : ( Y2 = Z ) )
% 0.19/0.45 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.19/0.45 & ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % set_eq_subset
% 0.19/0.45 thf(fact_99_contra__subsetD,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B3: set @ A,C2: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.19/0.45 => ( ~ ( member @ A @ C2 @ B3 )
% 0.19/0.45 => ~ ( member @ A @ C2 @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % contra_subsetD
% 0.19/0.45 thf(fact_100_Collect__mono__iff,axiom,
% 0.19/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.19/0.45 = ( ! [X: A] :
% 0.19/0.45 ( ( P @ X )
% 0.19/0.45 => ( Q @ X ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Collect_mono_iff
% 0.19/0.45 thf(fact_101_comp__def,axiom,
% 0.19/0.45 ! [A: $tType,C: $tType,B: $tType] :
% 0.19/0.45 ( ( comp @ B @ C @ A )
% 0.19/0.45 = ( ^ [F: B > C,G: A > B,X: A] : ( F @ ( G @ X ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % comp_def
% 0.19/0.45 thf(fact_102_comp__assoc,axiom,
% 0.19/0.45 ! [B: $tType,D: $tType,C: $tType,A: $tType,F2: D > B,G2: C > D,H: A > C] :
% 0.19/0.45 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F2 @ G2 ) @ H )
% 0.19/0.45 = ( comp @ D @ B @ A @ F2 @ ( comp @ C @ D @ A @ G2 @ H ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % comp_assoc
% 0.19/0.45 thf(fact_103_comp__eq__dest,axiom,
% 0.19/0.45 ! [C: $tType,B: $tType,D: $tType,A: $tType,A3: C > B,B2: A > C,C2: D > B,D2: A > D,V: A] :
% 0.19/0.45 ( ( ( comp @ C @ B @ A @ A3 @ B2 )
% 0.19/0.45 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 0.19/0.45 => ( ( A3 @ ( B2 @ V ) )
% 0.19/0.45 = ( C2 @ ( D2 @ V ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % comp_eq_dest
% 0.19/0.45 thf(fact_104_comp__eq__elim,axiom,
% 0.19/0.45 ! [C: $tType,B: $tType,D: $tType,A: $tType,A3: C > B,B2: A > C,C2: D > B,D2: A > D] :
% 0.19/0.45 ( ( ( comp @ C @ B @ A @ A3 @ B2 )
% 0.19/0.45 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 0.19/0.45 => ! [V2: A] :
% 0.19/0.45 ( ( A3 @ ( B2 @ V2 ) )
% 0.19/0.45 = ( C2 @ ( D2 @ V2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % comp_eq_elim
% 0.19/0.45 thf(fact_105_comp__eq__dest__lhs,axiom,
% 0.19/0.45 ! [C: $tType,B: $tType,A: $tType,A3: C > B,B2: A > C,C2: A > B,V: A] :
% 0.19/0.45 ( ( ( comp @ C @ B @ A @ A3 @ B2 )
% 0.19/0.45 = C2 )
% 0.19/0.45 => ( ( A3 @ ( B2 @ V ) )
% 0.19/0.45 = ( C2 @ V ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % comp_eq_dest_lhs
% 0.19/0.45 thf(fact_106_iso__tuple__UNIV__I,axiom,
% 0.19/0.45 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % iso_tuple_UNIV_I
% 0.19/0.45 thf(fact_107_comp__cong,axiom,
% 0.19/0.45 ! [C: $tType,B: $tType,D: $tType,A: $tType,E: $tType,F2: B > A,G2: C > B,X3: C,F3: D > A,G3: E > D,X4: E] :
% 0.19/0.45 ( ( ( F2 @ ( G2 @ X3 ) )
% 0.19/0.45 = ( F3 @ ( G3 @ X4 ) ) )
% 0.19/0.45 => ( ( comp @ B @ A @ C @ F2 @ G2 @ X3 )
% 0.19/0.45 = ( comp @ D @ A @ E @ F3 @ G3 @ X4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % comp_cong
% 0.19/0.45 thf(fact_108_comp__apply__eq,axiom,
% 0.19/0.45 ! [B: $tType,D: $tType,A: $tType,C: $tType,F2: B > A,G2: C > B,X3: C,H: D > A,K: C > D] :
% 0.19/0.45 ( ( ( F2 @ ( G2 @ X3 ) )
% 0.19/0.45 = ( H @ ( K @ X3 ) ) )
% 0.19/0.45 => ( ( comp @ B @ A @ C @ F2 @ G2 @ X3 )
% 0.19/0.45 = ( comp @ D @ A @ C @ H @ K @ X3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % comp_apply_eq
% 0.19/0.45 thf(fact_109_fun_Omap__comp,axiom,
% 0.19/0.45 ! [B: $tType,C: $tType,A: $tType,D: $tType,G2: B > C,F2: A > B,V: D > A] :
% 0.19/0.45 ( ( comp @ B @ C @ D @ G2 @ ( comp @ A @ B @ D @ F2 @ V ) )
% 0.19/0.45 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G2 @ F2 ) @ V ) ) ).
% 0.19/0.45
% 0.19/0.45 % fun.map_comp
% 0.19/0.45 thf(fact_110_type__copy__map__cong0,axiom,
% 0.19/0.45 ! [B: $tType,D: $tType,E: $tType,A: $tType,C: $tType,M: B > A,G2: C > B,X3: C,N3: D > A,H: C > D,F2: A > E] :
% 0.19/0.45 ( ( ( M @ ( G2 @ X3 ) )
% 0.19/0.45 = ( N3 @ ( H @ X3 ) ) )
% 0.19/0.45 => ( ( comp @ B @ E @ C @ ( comp @ A @ E @ B @ F2 @ M ) @ G2 @ X3 )
% 0.19/0.45 = ( comp @ D @ E @ C @ ( comp @ A @ E @ D @ F2 @ N3 ) @ H @ X3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % type_copy_map_cong0
% 0.19/0.45 thf(fact_111_corec_I1_J,axiom,
% 0.19/0.45 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) ),B2: A] :
% 0.19/0.45 ( ( root @ ( corec @ A @ Rt @ Ct @ B2 ) )
% 0.19/0.45 = ( Rt @ B2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % corec(1)
% 0.19/0.45 thf(fact_112_root__o__deftr,axiom,
% 0.19/0.45 ( ( comp @ dtree @ n @ n @ root @ gram_L1231612515_deftr )
% 0.19/0.45 = ( id @ n ) ) ).
% 0.19/0.45
% 0.19/0.45 % root_o_deftr
% 0.19/0.45 thf(fact_113_Node__root__cont,axiom,
% 0.19/0.45 ! [Tr: dtree] :
% 0.19/0.45 ( ( node @ ( root @ Tr ) @ ( cont @ Tr ) )
% 0.19/0.45 = Tr ) ).
% 0.19/0.45
% 0.19/0.45 % Node_root_cont
% 0.19/0.45 thf(fact_114_id__apply,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( id @ A )
% 0.19/0.45 = ( ^ [X: A] : X ) ) ).
% 0.19/0.45
% 0.19/0.45 % id_apply
% 0.19/0.45 thf(fact_115_fun_Omap__id,axiom,
% 0.19/0.45 ! [A: $tType,D: $tType,T2: D > A] :
% 0.19/0.45 ( ( comp @ A @ A @ D @ ( id @ A ) @ T2 )
% 0.19/0.45 = T2 ) ).
% 0.19/0.45
% 0.19/0.45 % fun.map_id
% 0.19/0.45 thf(fact_116_id__comp,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,G2: A > B] :
% 0.19/0.45 ( ( comp @ B @ B @ A @ ( id @ B ) @ G2 )
% 0.19/0.45 = G2 ) ).
% 0.19/0.45
% 0.19/0.45 % id_comp
% 0.19/0.45 thf(fact_117_comp__id,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,F2: A > B] :
% 0.19/0.45 ( ( comp @ A @ B @ A @ F2 @ ( id @ A ) )
% 0.19/0.45 = F2 ) ).
% 0.19/0.45
% 0.19/0.45 % comp_id
% 0.19/0.45 thf(fact_118_fun_Omap__id0,axiom,
% 0.19/0.45 ! [A: $tType,D: $tType] :
% 0.19/0.45 ( ( comp @ A @ A @ D @ ( id @ A ) )
% 0.19/0.45 = ( id @ ( D > A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % fun.map_id0
% 0.19/0.45 thf(fact_119_id__def,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( id @ A )
% 0.19/0.45 = ( ^ [X: A] : X ) ) ).
% 0.19/0.45
% 0.19/0.45 % id_def
% 0.19/0.45 thf(fact_120_eq__id__iff,axiom,
% 0.19/0.45 ! [A: $tType,F2: A > A] :
% 0.19/0.45 ( ( ! [X: A] :
% 0.19/0.45 ( ( F2 @ X )
% 0.19/0.45 = X ) )
% 0.19/0.45 = ( F2
% 0.19/0.45 = ( id @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % eq_id_iff
% 0.19/0.45 thf(fact_121_DEADID_Oin__rel,axiom,
% 0.19/0.45 ! [B: $tType] :
% 0.19/0.45 ( ( ^ [Y2: B,Z: B] : ( Y2 = Z ) )
% 0.19/0.45 = ( ^ [A6: B,B6: B] :
% 0.19/0.45 ? [Z3: B] :
% 0.19/0.45 ( ( member @ B @ Z3 @ ( top_top @ ( set @ B ) ) )
% 0.19/0.45 & ( ( id @ B @ Z3 )
% 0.19/0.45 = A6 )
% 0.19/0.45 & ( ( id @ B @ Z3 )
% 0.19/0.45 = B6 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % DEADID.in_rel
% 0.19/0.45 thf(fact_122_comp__eq__id__dest,axiom,
% 0.19/0.45 ! [C: $tType,B: $tType,A: $tType,A3: C > B,B2: A > C,C2: A > B,V: A] :
% 0.19/0.45 ( ( ( comp @ C @ B @ A @ A3 @ B2 )
% 0.19/0.45 = ( comp @ B @ B @ A @ ( id @ B ) @ C2 ) )
% 0.19/0.45 => ( ( A3 @ ( B2 @ V ) )
% 0.19/0.45 = ( C2 @ V ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % comp_eq_id_dest
% 0.19/0.45 thf(fact_123_pointfree__idE,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,F2: B > A,G2: A > B,X3: A] :
% 0.19/0.45 ( ( ( comp @ B @ A @ A @ F2 @ G2 )
% 0.19/0.45 = ( id @ A ) )
% 0.19/0.45 => ( ( F2 @ ( G2 @ X3 ) )
% 0.19/0.45 = X3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % pointfree_idE
% 0.19/0.45 thf(fact_124_dtree__cong,axiom,
% 0.19/0.45 ! [Tr: dtree,Tr6: dtree] :
% 0.19/0.45 ( ( ( root @ Tr )
% 0.19/0.45 = ( root @ Tr6 ) )
% 0.19/0.45 => ( ( ( cont @ Tr )
% 0.19/0.45 = ( cont @ Tr6 ) )
% 0.19/0.45 => ( Tr = Tr6 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dtree_cong
% 0.19/0.45 thf(fact_125_top__set__def,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( top_top @ ( set @ A ) )
% 0.19/0.45 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % top_set_def
% 0.19/0.45 thf(fact_126_hsubst__c__def,axiom,
% 0.19/0.45 ( gram_L1905609002ubst_c
% 0.19/0.45 = ( ^ [Tr02: dtree,Tr2: dtree] :
% 0.19/0.45 ( if @ ( set @ ( sum_sum @ t @ dtree ) )
% 0.19/0.45 @ ( ( root @ Tr2 )
% 0.19/0.45 = ( root @ Tr02 ) )
% 0.19/0.45 @ ( cont @ Tr02 )
% 0.19/0.45 @ ( cont @ Tr2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % hsubst_c_def
% 0.19/0.45 thf(fact_127_deftr__def,axiom,
% 0.19/0.45 ( gram_L1231612515_deftr
% 0.19/0.45 = ( unfold @ n @ ( id @ n ) @ gram_L1451583635elle_S ) ) ).
% 0.19/0.45
% 0.19/0.45 % deftr_def
% 0.19/0.45 thf(fact_128_wf__inj,axiom,
% 0.19/0.45 ! [Tr: dtree,Tr1: dtree,Tr22: dtree] :
% 0.19/0.45 ( ( gram_L864798063lle_wf @ Tr )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr ) )
% 0.19/0.45 => ( ( ( root @ Tr1 )
% 0.19/0.45 = ( root @ Tr22 ) )
% 0.19/0.45 = ( Tr1 = Tr22 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % wf_inj
% 0.19/0.45 thf(fact_129_subtr__UNIV__inductL,axiom,
% 0.19/0.45 ! [Tr1: dtree,Tr22: dtree,Phi: dtree > dtree > $o] :
% 0.19/0.45 ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr1 @ Tr22 )
% 0.19/0.45 => ( ! [Tr7: dtree] : ( Phi @ Tr7 @ Tr7 )
% 0.19/0.45 => ( ! [Tr12: dtree,Tr23: dtree,Tr32: dtree] :
% 0.19/0.45 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 0.19/0.45 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr23 @ Tr32 )
% 0.19/0.45 => ( ( Phi @ Tr23 @ Tr32 )
% 0.19/0.45 => ( Phi @ Tr12 @ Tr32 ) ) ) )
% 0.19/0.45 => ( Phi @ Tr1 @ Tr22 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr_UNIV_inductL
% 0.19/0.45 thf(fact_130_type__copy__map__id0,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,Rep: A > B,Abs: B > A,M: B > B] :
% 0.19/0.45 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 0.19/0.45 => ( ( M
% 0.19/0.45 = ( id @ B ) )
% 0.19/0.45 => ( ( comp @ B @ A @ A @ ( comp @ B @ A @ B @ Abs @ M ) @ Rep )
% 0.19/0.45 = ( id @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % type_copy_map_id0
% 0.19/0.45 thf(fact_131_type__copy__Abs__o__Rep,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,Rep: A > B,Abs: B > A] :
% 0.19/0.45 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 0.19/0.45 => ( ( comp @ B @ A @ A @ Abs @ Rep )
% 0.19/0.45 = ( id @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % type_copy_Abs_o_Rep
% 0.19/0.45 thf(fact_132_top1I,axiom,
% 0.19/0.45 ! [A: $tType,X3: A] : ( top_top @ ( A > $o ) @ X3 ) ).
% 0.19/0.45
% 0.19/0.45 % top1I
% 0.19/0.45 thf(fact_133_type__copy__wit,axiom,
% 0.19/0.45 ! [A: $tType,C: $tType,B: $tType,Rep: A > B,Abs: B > A,X3: C,S: B > ( set @ C ),Y4: B] :
% 0.19/0.45 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 0.19/0.45 => ( ( member @ C @ X3 @ ( comp @ B @ ( set @ C ) @ A @ S @ Rep @ ( Abs @ Y4 ) ) )
% 0.19/0.45 => ( member @ C @ X3 @ ( S @ Y4 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % type_copy_wit
% 0.19/0.45 thf(fact_134_top__conj_I2_J,axiom,
% 0.19/0.45 ! [A: $tType,P: $o,X3: A] :
% 0.19/0.45 ( ( P
% 0.19/0.45 & ( top_top @ ( A > $o ) @ X3 ) )
% 0.19/0.45 = P ) ).
% 0.19/0.45
% 0.19/0.45 % top_conj(2)
% 0.19/0.45 thf(fact_135_top__conj_I1_J,axiom,
% 0.19/0.45 ! [A: $tType,X3: A,P: $o] :
% 0.19/0.45 ( ( ( top_top @ ( A > $o ) @ X3 )
% 0.19/0.45 & P )
% 0.19/0.45 = P ) ).
% 0.19/0.45
% 0.19/0.45 % top_conj(1)
% 0.19/0.45 thf(fact_136_type__copy__ex__RepI,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,Rep: A > B,Abs: B > A,F4: B > $o] :
% 0.19/0.45 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 0.19/0.45 => ( ( ^ [P2: B > $o] :
% 0.19/0.45 ? [X5: B] : ( P2 @ X5 )
% 0.19/0.45 @ F4 )
% 0.19/0.45 = ( ? [B6: A] : ( F4 @ ( Rep @ B6 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % type_copy_ex_RepI
% 0.19/0.45 thf(fact_137_type__copy__obj__one__point__absE,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,Rep: A > B,Abs: B > A,S2: A] :
% 0.19/0.45 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 0.19/0.45 => ~ ! [X2: B] :
% 0.19/0.45 ( S2
% 0.19/0.45 != ( Abs @ X2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % type_copy_obj_one_point_absE
% 0.19/0.45 thf(fact_138_wf__cont,axiom,
% 0.19/0.45 ! [Tr: dtree,Tr6: dtree] :
% 0.19/0.45 ( ( gram_L864798063lle_wf @ Tr )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr6 ) @ ( cont @ Tr ) )
% 0.19/0.45 => ( gram_L864798063lle_wf @ Tr6 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % wf_cont
% 0.19/0.45 thf(fact_139_type__copy__map__comp0__undo,axiom,
% 0.19/0.45 ! [E: $tType,A: $tType,C: $tType,B: $tType,D: $tType,F5: $tType,Rep: A > B,Abs: B > A,Rep2: C > D,Abs2: D > C,Rep3: E > F5,Abs3: F5 > E,M: F5 > D,M1: B > D,M2: F5 > B] :
% 0.19/0.45 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 0.19/0.45 => ( ( type_definition @ C @ D @ Rep2 @ Abs2 @ ( top_top @ ( set @ D ) ) )
% 0.19/0.45 => ( ( type_definition @ E @ F5 @ Rep3 @ Abs3 @ ( top_top @ ( set @ F5 ) ) )
% 0.19/0.45 => ( ( ( comp @ F5 @ C @ E @ ( comp @ D @ C @ F5 @ Abs2 @ M ) @ Rep3 )
% 0.19/0.45 = ( comp @ A @ C @ E @ ( comp @ B @ C @ A @ ( comp @ D @ C @ B @ Abs2 @ M1 ) @ Rep ) @ ( comp @ F5 @ A @ E @ ( comp @ B @ A @ F5 @ Abs @ M2 ) @ Rep3 ) ) )
% 0.19/0.45 => ( ( comp @ B @ D @ F5 @ M1 @ M2 )
% 0.19/0.45 = M ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % type_copy_map_comp0_undo
% 0.19/0.45 thf(fact_140_type__copy__map__comp0,axiom,
% 0.19/0.45 ! [F5: $tType,D: $tType,B: $tType,A: $tType,C: $tType,E: $tType,Rep: A > B,Abs: B > A,M: C > D,M1: B > D,M2: C > B,F2: D > F5,G2: E > C] :
% 0.19/0.45 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 0.19/0.45 => ( ( M
% 0.19/0.45 = ( comp @ B @ D @ C @ M1 @ M2 ) )
% 0.19/0.45 => ( ( comp @ C @ F5 @ E @ ( comp @ D @ F5 @ C @ F2 @ M ) @ G2 )
% 0.19/0.45 = ( comp @ A @ F5 @ E @ ( comp @ B @ F5 @ A @ ( comp @ D @ F5 @ B @ F2 @ M1 ) @ Rep ) @ ( comp @ C @ A @ E @ ( comp @ B @ A @ C @ Abs @ M2 ) @ G2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % type_copy_map_comp0
% 0.19/0.45 thf(fact_141_subtr_OStep,axiom,
% 0.19/0.45 ! [Tr3: dtree,Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr3 ) @ Ns )
% 0.19/0.45 => ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr3 ) )
% 0.19/0.45 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr.Step
% 0.19/0.45 thf(fact_142_subtr_Ocases,axiom,
% 0.19/0.45 ! [A1: set @ n,A22: dtree,A32: dtree] :
% 0.19/0.45 ( ( gram_L716654942_subtr @ A1 @ A22 @ A32 )
% 0.19/0.45 => ( ( ( A32 = A22 )
% 0.19/0.45 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.19/0.45 => ~ ( ( member @ n @ ( root @ A32 ) @ A1 )
% 0.19/0.45 => ! [Tr23: dtree] :
% 0.19/0.45 ( ( gram_L716654942_subtr @ A1 @ A22 @ Tr23 )
% 0.19/0.45 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ A32 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr.cases
% 0.19/0.45 thf(fact_143_subtr_Osimps,axiom,
% 0.19/0.45 ( gram_L716654942_subtr
% 0.19/0.45 = ( ^ [A12: set @ n,A23: dtree,A33: dtree] :
% 0.19/0.45 ( ? [Tr2: dtree,Ns2: set @ n] :
% 0.19/0.45 ( ( A12 = Ns2 )
% 0.19/0.45 & ( A23 = Tr2 )
% 0.19/0.45 & ( A33 = Tr2 )
% 0.19/0.45 & ( member @ n @ ( root @ Tr2 ) @ Ns2 ) )
% 0.19/0.45 | ? [Tr33: dtree,Ns2: set @ n,Tr13: dtree,Tr24: dtree] :
% 0.19/0.45 ( ( A12 = Ns2 )
% 0.19/0.45 & ( A23 = Tr13 )
% 0.19/0.45 & ( A33 = Tr33 )
% 0.19/0.45 & ( member @ n @ ( root @ Tr33 ) @ Ns2 )
% 0.19/0.45 & ( gram_L716654942_subtr @ Ns2 @ Tr13 @ Tr24 )
% 0.19/0.45 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr24 ) @ ( cont @ Tr33 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr.simps
% 0.19/0.45 thf(fact_144_subtr__StepL,axiom,
% 0.19/0.45 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr3: dtree] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 0.19/0.45 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr3 )
% 0.19/0.45 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr_StepL
% 0.19/0.45 thf(fact_145_subtr_Oinducts,axiom,
% 0.19/0.45 ! [X1: set @ n,X22: dtree,X32: dtree,P: ( set @ n ) > dtree > dtree > $o] :
% 0.19/0.45 ( ( gram_L716654942_subtr @ X1 @ X22 @ X32 )
% 0.19/0.45 => ( ! [Tr7: dtree,Ns4: set @ n] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr7 ) @ Ns4 )
% 0.19/0.45 => ( P @ Ns4 @ Tr7 @ Tr7 ) )
% 0.19/0.45 => ( ! [Tr32: dtree,Ns4: set @ n,Tr12: dtree,Tr23: dtree] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr32 ) @ Ns4 )
% 0.19/0.45 => ( ( gram_L716654942_subtr @ Ns4 @ Tr12 @ Tr23 )
% 0.19/0.45 => ( ( P @ Ns4 @ Tr12 @ Tr23 )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ Tr32 ) )
% 0.19/0.45 => ( P @ Ns4 @ Tr12 @ Tr32 ) ) ) ) )
% 0.19/0.45 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr.inducts
% 0.19/0.45 thf(fact_146_subtr__inductL,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Phi: ( set @ n ) > dtree > dtree > $o] :
% 0.19/0.45 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.19/0.45 => ( ! [Ns4: set @ n,Tr7: dtree] : ( Phi @ Ns4 @ Tr7 @ Tr7 )
% 0.19/0.45 => ( ! [Ns4: set @ n,Tr12: dtree,Tr23: dtree,Tr32: dtree] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr12 ) @ Ns4 )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 0.19/0.45 => ( ( gram_L716654942_subtr @ Ns4 @ Tr23 @ Tr32 )
% 0.19/0.45 => ( ( Phi @ Ns4 @ Tr23 @ Tr32 )
% 0.19/0.45 => ( Phi @ Ns4 @ Tr12 @ Tr32 ) ) ) ) )
% 0.19/0.45 => ( Phi @ Ns @ Tr1 @ Tr22 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr_inductL
% 0.19/0.45 thf(fact_147_inFr_OInd,axiom,
% 0.19/0.45 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,T2: t] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.19/0.45 => ( ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 )
% 0.19/0.45 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr.Ind
% 0.19/0.45 thf(fact_148_subtr2_OStep,axiom,
% 0.19/0.45 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr3: dtree] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 0.19/0.45 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr3 )
% 0.19/0.45 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr2.Step
% 0.19/0.45 thf(fact_149_subtr2_Ocases,axiom,
% 0.19/0.45 ! [A1: set @ n,A22: dtree,A32: dtree] :
% 0.19/0.45 ( ( gram_L1283001940subtr2 @ A1 @ A22 @ A32 )
% 0.19/0.45 => ( ( ( A32 = A22 )
% 0.19/0.45 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.19/0.45 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.19/0.45 => ! [Tr23: dtree] :
% 0.19/0.45 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A22 ) @ ( cont @ Tr23 ) )
% 0.19/0.45 => ~ ( gram_L1283001940subtr2 @ A1 @ Tr23 @ A32 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr2.cases
% 0.19/0.45 thf(fact_150_subtr2_Osimps,axiom,
% 0.19/0.45 ( gram_L1283001940subtr2
% 0.19/0.45 = ( ^ [A12: set @ n,A23: dtree,A33: dtree] :
% 0.19/0.45 ( ? [Tr2: dtree,Ns2: set @ n] :
% 0.19/0.45 ( ( A12 = Ns2 )
% 0.19/0.45 & ( A23 = Tr2 )
% 0.19/0.45 & ( A33 = Tr2 )
% 0.19/0.45 & ( member @ n @ ( root @ Tr2 ) @ Ns2 ) )
% 0.19/0.45 | ? [Tr13: dtree,Ns2: set @ n,Tr24: dtree,Tr33: dtree] :
% 0.19/0.45 ( ( A12 = Ns2 )
% 0.19/0.45 & ( A23 = Tr13 )
% 0.19/0.45 & ( A33 = Tr33 )
% 0.19/0.45 & ( member @ n @ ( root @ Tr13 ) @ Ns2 )
% 0.19/0.45 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr24 ) )
% 0.19/0.45 & ( gram_L1283001940subtr2 @ Ns2 @ Tr24 @ Tr33 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr2.simps
% 0.19/0.45 thf(fact_151_subtr2__StepR,axiom,
% 0.19/0.45 ! [Tr3: dtree,Ns: set @ n,Tr22: dtree,Tr1: dtree] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr3 ) @ Ns )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr3 ) )
% 0.19/0.45 => ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.19/0.45 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr2_StepR
% 0.19/0.45 thf(fact_152_subtr2_Oinducts,axiom,
% 0.19/0.45 ! [X1: set @ n,X22: dtree,X32: dtree,P: ( set @ n ) > dtree > dtree > $o] :
% 0.19/0.45 ( ( gram_L1283001940subtr2 @ X1 @ X22 @ X32 )
% 0.19/0.45 => ( ! [Tr7: dtree,Ns4: set @ n] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr7 ) @ Ns4 )
% 0.19/0.45 => ( P @ Ns4 @ Tr7 @ Tr7 ) )
% 0.19/0.45 => ( ! [Tr12: dtree,Ns4: set @ n,Tr23: dtree,Tr32: dtree] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr12 ) @ Ns4 )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 0.19/0.45 => ( ( gram_L1283001940subtr2 @ Ns4 @ Tr23 @ Tr32 )
% 0.19/0.45 => ( ( P @ Ns4 @ Tr23 @ Tr32 )
% 0.19/0.45 => ( P @ Ns4 @ Tr12 @ Tr32 ) ) ) ) )
% 0.19/0.45 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtr2.inducts
% 0.19/0.45 thf(fact_153_inItr_OInd,axiom,
% 0.19/0.45 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,N: n] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.19/0.45 => ( ( gram_L830233218_inItr @ Ns @ Tr1 @ N )
% 0.19/0.45 => ( gram_L830233218_inItr @ Ns @ Tr @ N ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inItr.Ind
% 0.19/0.45 thf(fact_154_inItr_Ocases,axiom,
% 0.19/0.45 ! [A1: set @ n,A22: dtree,A32: n] :
% 0.19/0.45 ( ( gram_L830233218_inItr @ A1 @ A22 @ A32 )
% 0.19/0.45 => ( ( ( A32
% 0.19/0.45 = ( root @ A22 ) )
% 0.19/0.45 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 0.19/0.45 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.19/0.45 => ! [Tr12: dtree] :
% 0.19/0.45 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A22 ) )
% 0.19/0.45 => ~ ( gram_L830233218_inItr @ A1 @ Tr12 @ A32 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inItr.cases
% 0.19/0.45 thf(fact_155_inItr_Osimps,axiom,
% 0.19/0.45 ( gram_L830233218_inItr
% 0.19/0.45 = ( ^ [A12: set @ n,A23: dtree,A33: n] :
% 0.19/0.45 ( ? [Tr2: dtree,Ns2: set @ n] :
% 0.19/0.45 ( ( A12 = Ns2 )
% 0.19/0.45 & ( A23 = Tr2 )
% 0.19/0.45 & ( A33
% 0.19/0.45 = ( root @ Tr2 ) )
% 0.19/0.45 & ( member @ n @ ( root @ Tr2 ) @ Ns2 ) )
% 0.19/0.45 | ? [Tr2: dtree,Ns2: set @ n,Tr13: dtree,N2: n] :
% 0.19/0.45 ( ( A12 = Ns2 )
% 0.19/0.45 & ( A23 = Tr2 )
% 0.19/0.45 & ( A33 = N2 )
% 0.19/0.45 & ( member @ n @ ( root @ Tr2 ) @ Ns2 )
% 0.19/0.45 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr2 ) )
% 0.19/0.45 & ( gram_L830233218_inItr @ Ns2 @ Tr13 @ N2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inItr.simps
% 0.19/0.45 thf(fact_156_inItr_Oinducts,axiom,
% 0.19/0.45 ! [X1: set @ n,X22: dtree,X32: n,P: ( set @ n ) > dtree > n > $o] :
% 0.19/0.45 ( ( gram_L830233218_inItr @ X1 @ X22 @ X32 )
% 0.19/0.45 => ( ! [Tr7: dtree,Ns4: set @ n] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr7 ) @ Ns4 )
% 0.19/0.45 => ( P @ Ns4 @ Tr7 @ ( root @ Tr7 ) ) )
% 0.19/0.45 => ( ! [Tr7: dtree,Ns4: set @ n,Tr12: dtree,N4: n] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr7 ) @ Ns4 )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 0.19/0.45 => ( ( gram_L830233218_inItr @ Ns4 @ Tr12 @ N4 )
% 0.19/0.45 => ( ( P @ Ns4 @ Tr12 @ N4 )
% 0.19/0.45 => ( P @ Ns4 @ Tr7 @ N4 ) ) ) ) )
% 0.19/0.45 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inItr.inducts
% 0.19/0.45 thf(fact_157_inFr2__Ind,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 0.19/0.45 ( ( gram_L805317441_inFr2 @ Ns @ Tr1 @ T2 )
% 0.19/0.45 => ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.19/0.45 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr2_Ind
% 0.19/0.45 thf(fact_158_type__copy__Rep__o__Abs,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,Rep: A > B,Abs: B > A] :
% 0.19/0.45 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 0.19/0.45 => ( ( comp @ A @ B @ B @ Rep @ Abs )
% 0.19/0.45 = ( id @ B ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % type_copy_Rep_o_Abs
% 0.19/0.45 thf(fact_159_subtrOf__root,axiom,
% 0.19/0.45 ! [Tr: dtree,Tr6: dtree] :
% 0.19/0.45 ( ( gram_L864798063lle_wf @ Tr )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr6 ) @ ( cont @ Tr ) )
% 0.19/0.45 => ( ( gram_L1614515765ubtrOf @ Tr @ ( root @ Tr6 ) )
% 0.19/0.45 = Tr6 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subtrOf_root
% 0.19/0.45 thf(fact_160_inFrr__def,axiom,
% 0.19/0.45 ( gram_L805317505_inFrr
% 0.19/0.45 = ( ^ [Ns2: set @ n,Tr2: dtree,T3: t] :
% 0.19/0.45 ? [Tr4: dtree] :
% 0.19/0.45 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr4 ) @ ( cont @ Tr2 ) )
% 0.19/0.45 & ( gram_L1333338417e_inFr @ Ns2 @ Tr4 @ T3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFrr_def
% 0.19/0.45 thf(fact_161_sum_Oinject_I2_J,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,X22: B,Y22: B] :
% 0.19/0.45 ( ( ( sum_Inr @ B @ A @ X22 )
% 0.19/0.45 = ( sum_Inr @ B @ A @ Y22 ) )
% 0.19/0.45 = ( X22 = Y22 ) ) ).
% 0.19/0.45
% 0.19/0.45 % sum.inject(2)
% 0.19/0.45 thf(fact_162_old_Osum_Oinject_I2_J,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,B2: B,B7: B] :
% 0.19/0.45 ( ( ( sum_Inr @ B @ A @ B2 )
% 0.19/0.45 = ( sum_Inr @ B @ A @ B7 ) )
% 0.19/0.45 = ( B2 = B7 ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.sum.inject(2)
% 0.19/0.45 thf(fact_163_Inr__inject,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,X3: B,Y4: B] :
% 0.19/0.45 ( ( ( sum_Inr @ B @ A @ X3 )
% 0.19/0.45 = ( sum_Inr @ B @ A @ Y4 ) )
% 0.19/0.45 => ( X3 = Y4 ) ) ).
% 0.19/0.45
% 0.19/0.45 % Inr_inject
% 0.19/0.45 thf(fact_164_top__empty__eq,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( top_top @ ( A > $o ) )
% 0.19/0.45 = ( ^ [X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % top_empty_eq
% 0.19/0.45 thf(fact_165_old_Osum_Osimps_I8_J,axiom,
% 0.19/0.45 ! [A: $tType,T: $tType,B: $tType,F1: A > T,F22: B > T,B2: B] :
% 0.19/0.45 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inr @ B @ A @ B2 ) )
% 0.19/0.45 = ( F22 @ B2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.sum.simps(8)
% 0.19/0.45 thf(fact_166_inFr2_OInd,axiom,
% 0.19/0.45 ! [Tr1: dtree,Tr: dtree,Ns1: set @ n,T2: t] :
% 0.19/0.45 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.19/0.45 => ( ( gram_L805317441_inFr2 @ Ns1 @ Tr1 @ T2 )
% 0.19/0.45 => ( gram_L805317441_inFr2 @ ( insert @ n @ ( root @ Tr ) @ Ns1 ) @ Tr @ T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr2.Ind
% 0.19/0.45 thf(fact_167_insert__absorb2,axiom,
% 0.19/0.45 ! [A: $tType,X3: A,A2: set @ A] :
% 0.19/0.45 ( ( insert @ A @ X3 @ ( insert @ A @ X3 @ A2 ) )
% 0.19/0.45 = ( insert @ A @ X3 @ A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % insert_absorb2
% 0.19/0.45 thf(fact_168_insert__iff,axiom,
% 0.19/0.45 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 0.19/0.45 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 0.19/0.45 = ( ( A3 = B2 )
% 0.19/0.45 | ( member @ A @ A3 @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % insert_iff
% 0.19/0.45 thf(fact_169_insertCI,axiom,
% 0.19/0.45 ! [A: $tType,A3: A,B3: set @ A,B2: A] :
% 0.19/0.45 ( ( ~ ( member @ A @ A3 @ B3 )
% 0.19/0.45 => ( A3 = B2 ) )
% 0.19/0.45 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % insertCI
% 0.19/0.45 thf(fact_170_insert__subset,axiom,
% 0.19/0.45 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) @ B3 )
% 0.19/0.45 = ( ( member @ A @ X3 @ B3 )
% 0.19/0.45 & ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % insert_subset
% 0.19/0.45 thf(fact_171_subset__insertI2,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B3: set @ A,B2: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_insertI2
% 0.19/0.45 thf(fact_172_subset__insertI,axiom,
% 0.19/0.45 ! [A: $tType,B3: set @ A,A3: A] : ( ord_less_eq @ ( set @ A ) @ B3 @ ( insert @ A @ A3 @ B3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_insertI
% 0.19/0.45 thf(fact_173_subset__insert,axiom,
% 0.19/0.45 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ~ ( member @ A @ X3 @ A2 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ B3 ) )
% 0.19/0.45 = ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_insert
% 0.19/0.45 thf(fact_174_insert__mono,axiom,
% 0.19/0.45 ! [A: $tType,C3: set @ A,D3: set @ A,A3: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ C3 @ D3 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A3 @ C3 ) @ ( insert @ A @ A3 @ D3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % insert_mono
% 0.19/0.45 thf(fact_175_mk__disjoint__insert,axiom,
% 0.19/0.45 ! [A: $tType,A3: A,A2: set @ A] :
% 0.19/0.45 ( ( member @ A @ A3 @ A2 )
% 0.19/0.45 => ? [B8: set @ A] :
% 0.19/0.45 ( ( A2
% 0.19/0.45 = ( insert @ A @ A3 @ B8 ) )
% 0.19/0.45 & ~ ( member @ A @ A3 @ B8 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % mk_disjoint_insert
% 0.19/0.45 thf(fact_176_insert__commute,axiom,
% 0.19/0.45 ! [A: $tType,X3: A,Y4: A,A2: set @ A] :
% 0.19/0.45 ( ( insert @ A @ X3 @ ( insert @ A @ Y4 @ A2 ) )
% 0.19/0.45 = ( insert @ A @ Y4 @ ( insert @ A @ X3 @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % insert_commute
% 0.19/0.45 thf(fact_177_insert__eq__iff,axiom,
% 0.19/0.45 ! [A: $tType,A3: A,A2: set @ A,B2: A,B3: set @ A] :
% 0.19/0.45 ( ~ ( member @ A @ A3 @ A2 )
% 0.19/0.45 => ( ~ ( member @ A @ B2 @ B3 )
% 0.19/0.45 => ( ( ( insert @ A @ A3 @ A2 )
% 0.19/0.45 = ( insert @ A @ B2 @ B3 ) )
% 0.19/0.45 = ( ( ( A3 = B2 )
% 0.19/0.45 => ( A2 = B3 ) )
% 0.19/0.45 & ( ( A3 != B2 )
% 0.19/0.45 => ? [C4: set @ A] :
% 0.19/0.45 ( ( A2
% 0.19/0.45 = ( insert @ A @ B2 @ C4 ) )
% 0.19/0.45 & ~ ( member @ A @ B2 @ C4 )
% 0.19/0.45 & ( B3
% 0.19/0.45 = ( insert @ A @ A3 @ C4 ) )
% 0.19/0.45 & ~ ( member @ A @ A3 @ C4 ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % insert_eq_iff
% 0.19/0.45 thf(fact_178_insert__absorb,axiom,
% 0.19/0.45 ! [A: $tType,A3: A,A2: set @ A] :
% 0.19/0.45 ( ( member @ A @ A3 @ A2 )
% 0.19/0.45 => ( ( insert @ A @ A3 @ A2 )
% 0.19/0.45 = A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % insert_absorb
% 0.19/0.45 thf(fact_179_insert__ident,axiom,
% 0.19/0.45 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ~ ( member @ A @ X3 @ A2 )
% 0.19/0.45 => ( ~ ( member @ A @ X3 @ B3 )
% 0.19/0.45 => ( ( ( insert @ A @ X3 @ A2 )
% 0.19/0.45 = ( insert @ A @ X3 @ B3 ) )
% 0.19/0.45 = ( A2 = B3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % insert_ident
% 0.19/0.45 thf(fact_180_Set_Oset__insert,axiom,
% 0.19/0.45 ! [A: $tType,X3: A,A2: set @ A] :
% 0.19/0.45 ( ( member @ A @ X3 @ A2 )
% 0.19/0.45 => ~ ! [B8: set @ A] :
% 0.19/0.45 ( ( A2
% 0.19/0.45 = ( insert @ A @ X3 @ B8 ) )
% 0.19/0.45 => ( member @ A @ X3 @ B8 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Set.set_insert
% 0.19/0.45 thf(fact_181_insertI2,axiom,
% 0.19/0.45 ! [A: $tType,A3: A,B3: set @ A,B2: A] :
% 0.19/0.45 ( ( member @ A @ A3 @ B3 )
% 0.19/0.45 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % insertI2
% 0.19/0.45 thf(fact_182_insertI1,axiom,
% 0.19/0.45 ! [A: $tType,A3: A,B3: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % insertI1
% 0.19/0.45 thf(fact_183_insertE,axiom,
% 0.19/0.45 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 0.19/0.45 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 0.19/0.45 => ( ( A3 != B2 )
% 0.19/0.45 => ( member @ A @ A3 @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % insertE
% 0.19/0.45 thf(fact_184_insert__UNIV,axiom,
% 0.19/0.45 ! [A: $tType,X3: A] :
% 0.19/0.45 ( ( insert @ A @ X3 @ ( top_top @ ( set @ A ) ) )
% 0.19/0.45 = ( top_top @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % insert_UNIV
% 0.19/0.45 thf(fact_185_inFr__Ind__minus,axiom,
% 0.19/0.45 ! [Ns1: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 0.19/0.45 ( ( gram_L1333338417e_inFr @ Ns1 @ Tr1 @ T2 )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.19/0.45 => ( gram_L1333338417e_inFr @ ( insert @ n @ ( root @ Tr ) @ Ns1 ) @ Tr @ T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr_Ind_minus
% 0.19/0.45 thf(fact_186_insert__subsetI,axiom,
% 0.19/0.45 ! [A: $tType,X3: A,A2: set @ A,X6: set @ A] :
% 0.19/0.45 ( ( member @ A @ X3 @ A2 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ A ) @ X6 @ A2 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ X6 ) @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % insert_subsetI
% 0.19/0.45 thf(fact_187_inFr2_Ocases,axiom,
% 0.19/0.45 ! [A1: set @ n,A22: dtree,A32: t] :
% 0.19/0.45 ( ( gram_L805317441_inFr2 @ A1 @ A22 @ A32 )
% 0.19/0.45 => ( ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.19/0.45 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A32 ) @ ( cont @ A22 ) ) )
% 0.19/0.45 => ~ ! [Tr12: dtree,Tr7: dtree,Ns12: set @ n] :
% 0.19/0.45 ( ( A1
% 0.19/0.45 = ( insert @ n @ ( root @ Tr7 ) @ Ns12 ) )
% 0.19/0.45 => ( ( A22 = Tr7 )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 0.19/0.45 => ~ ( gram_L805317441_inFr2 @ Ns12 @ Tr12 @ A32 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr2.cases
% 0.19/0.45 thf(fact_188_inFr2_Osimps,axiom,
% 0.19/0.45 ( gram_L805317441_inFr2
% 0.19/0.45 = ( ^ [A12: set @ n,A23: dtree,A33: t] :
% 0.19/0.45 ( ? [Tr2: dtree,Ns2: set @ n,T3: t] :
% 0.19/0.45 ( ( A12 = Ns2 )
% 0.19/0.45 & ( A23 = Tr2 )
% 0.19/0.45 & ( A33 = T3 )
% 0.19/0.45 & ( member @ n @ ( root @ Tr2 ) @ Ns2 )
% 0.19/0.45 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr2 ) ) )
% 0.19/0.45 | ? [Tr13: dtree,Tr2: dtree,Ns13: set @ n,T3: t] :
% 0.19/0.45 ( ( A12
% 0.19/0.45 = ( insert @ n @ ( root @ Tr2 ) @ Ns13 ) )
% 0.19/0.45 & ( A23 = Tr2 )
% 0.19/0.45 & ( A33 = T3 )
% 0.19/0.45 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr2 ) )
% 0.19/0.45 & ( gram_L805317441_inFr2 @ Ns13 @ Tr13 @ T3 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr2.simps
% 0.19/0.45 thf(fact_189_Inl__Inr__False,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,X3: A,Y4: B] :
% 0.19/0.45 ( ( sum_Inl @ A @ B @ X3 )
% 0.19/0.45 != ( sum_Inr @ B @ A @ Y4 ) ) ).
% 0.19/0.45
% 0.19/0.45 % Inl_Inr_False
% 0.19/0.45 thf(fact_190_Inr__Inl__False,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,X3: B,Y4: A] :
% 0.19/0.45 ( ( sum_Inr @ B @ A @ X3 )
% 0.19/0.45 != ( sum_Inl @ A @ B @ Y4 ) ) ).
% 0.19/0.45
% 0.19/0.45 % Inr_Inl_False
% 0.19/0.45 thf(fact_191_obj__sumE__f,axiom,
% 0.19/0.45 ! [A: $tType,C: $tType,B: $tType,S2: B,F2: ( sum_sum @ A @ C ) > B,P: $o] :
% 0.19/0.45 ( ! [X2: A] :
% 0.19/0.45 ( ( S2
% 0.19/0.45 = ( F2 @ ( sum_Inl @ A @ C @ X2 ) ) )
% 0.19/0.45 => P )
% 0.19/0.45 => ( ! [X2: C] :
% 0.19/0.45 ( ( S2
% 0.19/0.45 = ( F2 @ ( sum_Inr @ C @ A @ X2 ) ) )
% 0.19/0.45 => P )
% 0.19/0.45 => ! [X7: sum_sum @ A @ C] :
% 0.19/0.45 ( ( S2
% 0.19/0.45 = ( F2 @ X7 ) )
% 0.19/0.45 => P ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % obj_sumE_f
% 0.19/0.45 thf(fact_192_old_Osum_Oinducts,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,P: ( sum_sum @ A @ B ) > $o,Sum: sum_sum @ A @ B] :
% 0.19/0.45 ( ! [A4: A] : ( P @ ( sum_Inl @ A @ B @ A4 ) )
% 0.19/0.45 => ( ! [B4: B] : ( P @ ( sum_Inr @ B @ A @ B4 ) )
% 0.19/0.45 => ( P @ Sum ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.sum.inducts
% 0.19/0.45 thf(fact_193_old_Osum_Oexhaust,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,Y4: sum_sum @ A @ B] :
% 0.19/0.45 ( ! [A4: A] :
% 0.19/0.45 ( Y4
% 0.19/0.45 != ( sum_Inl @ A @ B @ A4 ) )
% 0.19/0.45 => ~ ! [B4: B] :
% 0.19/0.45 ( Y4
% 0.19/0.45 != ( sum_Inr @ B @ A @ B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.sum.exhaust
% 0.19/0.45 thf(fact_194_split__sum__all,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType] :
% 0.19/0.45 ( ( ^ [P2: ( sum_sum @ A @ B ) > $o] :
% 0.19/0.45 ! [X5: sum_sum @ A @ B] : ( P2 @ X5 ) )
% 0.19/0.45 = ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 0.19/0.45 ( ! [X: A] : ( P3 @ ( sum_Inl @ A @ B @ X ) )
% 0.19/0.45 & ! [X: B] : ( P3 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_sum_all
% 0.19/0.45 thf(fact_195_split__sum__ex,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType] :
% 0.19/0.45 ( ( ^ [P2: ( sum_sum @ A @ B ) > $o] :
% 0.19/0.45 ? [X5: sum_sum @ A @ B] : ( P2 @ X5 ) )
% 0.19/0.45 = ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 0.19/0.45 ( ? [X: A] : ( P3 @ ( sum_Inl @ A @ B @ X ) )
% 0.19/0.45 | ? [X: B] : ( P3 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_sum_ex
% 0.19/0.45 thf(fact_196_Inr__not__Inl,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,B2: B,A3: A] :
% 0.19/0.45 ( ( sum_Inr @ B @ A @ B2 )
% 0.19/0.45 != ( sum_Inl @ A @ B @ A3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % Inr_not_Inl
% 0.19/0.45 thf(fact_197_sumE,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,S2: sum_sum @ A @ B] :
% 0.19/0.45 ( ! [X2: A] :
% 0.19/0.45 ( S2
% 0.19/0.45 != ( sum_Inl @ A @ B @ X2 ) )
% 0.19/0.45 => ~ ! [Y: B] :
% 0.19/0.45 ( S2
% 0.19/0.45 != ( sum_Inr @ B @ A @ Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % sumE
% 0.19/0.45 thf(fact_198_old_Osum_Odistinct_I1_J,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,A3: A,B7: B] :
% 0.19/0.45 ( ( sum_Inl @ A @ B @ A3 )
% 0.19/0.45 != ( sum_Inr @ B @ A @ B7 ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.sum.distinct(1)
% 0.19/0.45 thf(fact_199_old_Osum_Odistinct_I2_J,axiom,
% 0.19/0.45 ! [B9: $tType,A7: $tType,B10: B9,A8: A7] :
% 0.19/0.45 ( ( sum_Inr @ B9 @ A7 @ B10 )
% 0.19/0.45 != ( sum_Inl @ A7 @ B9 @ A8 ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.sum.distinct(2)
% 0.19/0.45 thf(fact_200_sum_Odistinct_I1_J,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,X1: A,X22: B] :
% 0.19/0.45 ( ( sum_Inl @ A @ B @ X1 )
% 0.19/0.45 != ( sum_Inr @ B @ A @ X22 ) ) ).
% 0.19/0.45
% 0.19/0.45 % sum.distinct(1)
% 0.19/0.45 thf(fact_201_inFr_OBase,axiom,
% 0.19/0.45 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 0.19/0.45 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr.Base
% 0.19/0.45 thf(fact_202_inFr2_OBase,axiom,
% 0.19/0.45 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 0.19/0.45 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr2.Base
% 0.19/0.45 thf(fact_203_inFr__subtr,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.19/0.45 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.19/0.45 => ? [Tr5: dtree] :
% 0.19/0.45 ( ( gram_L716654942_subtr @ Ns @ Tr5 @ Tr )
% 0.19/0.45 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr5 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr_subtr
% 0.19/0.45 thf(fact_204_inFr_Ocases,axiom,
% 0.19/0.45 ! [A1: set @ n,A22: dtree,A32: t] :
% 0.19/0.45 ( ( gram_L1333338417e_inFr @ A1 @ A22 @ A32 )
% 0.19/0.45 => ( ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.19/0.45 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A32 ) @ ( cont @ A22 ) ) )
% 0.19/0.45 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 0.19/0.45 => ! [Tr12: dtree] :
% 0.19/0.45 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A22 ) )
% 0.19/0.45 => ~ ( gram_L1333338417e_inFr @ A1 @ Tr12 @ A32 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr.cases
% 0.19/0.45 thf(fact_205_inFr_Osimps,axiom,
% 0.19/0.45 ( gram_L1333338417e_inFr
% 0.19/0.45 = ( ^ [A12: set @ n,A23: dtree,A33: t] :
% 0.19/0.45 ( ? [Tr2: dtree,Ns2: set @ n,T3: t] :
% 0.19/0.45 ( ( A12 = Ns2 )
% 0.19/0.45 & ( A23 = Tr2 )
% 0.19/0.45 & ( A33 = T3 )
% 0.19/0.45 & ( member @ n @ ( root @ Tr2 ) @ Ns2 )
% 0.19/0.45 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr2 ) ) )
% 0.19/0.45 | ? [Tr2: dtree,Ns2: set @ n,Tr13: dtree,T3: t] :
% 0.19/0.45 ( ( A12 = Ns2 )
% 0.19/0.45 & ( A23 = Tr2 )
% 0.19/0.45 & ( A33 = T3 )
% 0.19/0.45 & ( member @ n @ ( root @ Tr2 ) @ Ns2 )
% 0.19/0.45 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr2 ) )
% 0.19/0.45 & ( gram_L1333338417e_inFr @ Ns2 @ Tr13 @ T3 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr.simps
% 0.19/0.45 thf(fact_206_inFr_Oinducts,axiom,
% 0.19/0.45 ! [X1: set @ n,X22: dtree,X32: t,P: ( set @ n ) > dtree > t > $o] :
% 0.19/0.45 ( ( gram_L1333338417e_inFr @ X1 @ X22 @ X32 )
% 0.19/0.45 => ( ! [Tr7: dtree,Ns4: set @ n,T4: t] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr7 ) @ Ns4 )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr7 ) )
% 0.19/0.45 => ( P @ Ns4 @ Tr7 @ T4 ) ) )
% 0.19/0.45 => ( ! [Tr7: dtree,Ns4: set @ n,Tr12: dtree,T4: t] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr7 ) @ Ns4 )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 0.19/0.45 => ( ( gram_L1333338417e_inFr @ Ns4 @ Tr12 @ T4 )
% 0.19/0.45 => ( ( P @ Ns4 @ Tr12 @ T4 )
% 0.19/0.45 => ( P @ Ns4 @ Tr7 @ T4 ) ) ) ) )
% 0.19/0.45 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr.inducts
% 0.19/0.45 thf(fact_207_inFr2_Oinducts,axiom,
% 0.19/0.45 ! [X1: set @ n,X22: dtree,X32: t,P: ( set @ n ) > dtree > t > $o] :
% 0.19/0.45 ( ( gram_L805317441_inFr2 @ X1 @ X22 @ X32 )
% 0.19/0.45 => ( ! [Tr7: dtree,Ns4: set @ n,T4: t] :
% 0.19/0.45 ( ( member @ n @ ( root @ Tr7 ) @ Ns4 )
% 0.19/0.45 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr7 ) )
% 0.19/0.45 => ( P @ Ns4 @ Tr7 @ T4 ) ) )
% 0.19/0.45 => ( ! [Tr12: dtree,Tr7: dtree,Ns12: set @ n,T4: t] :
% 0.19/0.45 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 0.19/0.45 => ( ( gram_L805317441_inFr2 @ Ns12 @ Tr12 @ T4 )
% 0.19/0.45 => ( ( P @ Ns12 @ Tr12 @ T4 )
% 0.19/0.45 => ( P @ ( insert @ n @ ( root @ Tr7 ) @ Ns12 ) @ Tr7 @ T4 ) ) ) )
% 0.19/0.45 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr2.inducts
% 0.19/0.45 thf(fact_208_obj__sumE,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,S2: sum_sum @ A @ B] :
% 0.19/0.45 ( ! [X2: A] :
% 0.19/0.45 ( S2
% 0.19/0.45 != ( sum_Inl @ A @ B @ X2 ) )
% 0.19/0.45 => ~ ! [X2: B] :
% 0.19/0.45 ( S2
% 0.19/0.45 != ( sum_Inr @ B @ A @ X2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % obj_sumE
% 0.19/0.45 thf(fact_209_Inl__cont__hsubst__neq,axiom,
% 0.19/0.45 ! [Tr: dtree,Tr0: dtree] :
% 0.19/0.45 ( ( ( root @ Tr )
% 0.19/0.45 != ( root @ Tr0 ) )
% 0.19/0.45 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.19/0.45 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Inl_cont_hsubst_neq
% 0.19/0.45 thf(fact_210_vimage__eq,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,A3: A,F2: A > B,B3: set @ B] :
% 0.19/0.45 ( ( member @ A @ A3 @ ( vimage @ A @ B @ F2 @ B3 ) )
% 0.19/0.45 = ( member @ B @ ( F2 @ A3 ) @ B3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % vimage_eq
% 0.19/0.45 thf(fact_211_vimageI,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,F2: B > A,A3: B,B2: A,B3: set @ A] :
% 0.19/0.45 ( ( ( F2 @ A3 )
% 0.19/0.45 = B2 )
% 0.19/0.45 => ( ( member @ A @ B2 @ B3 )
% 0.19/0.45 => ( member @ B @ A3 @ ( vimage @ B @ A @ F2 @ B3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % vimageI
% 0.19/0.45 thf(fact_212_vimage__UNIV,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,F2: A > B] :
% 0.19/0.45 ( ( vimage @ A @ B @ F2 @ ( top_top @ ( set @ B ) ) )
% 0.19/0.45 = ( top_top @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % vimage_UNIV
% 0.19/0.45 thf(fact_213_vimage__id,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( vimage @ A @ A @ ( id @ A ) )
% 0.19/0.45 = ( id @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % vimage_id
% 0.19/0.45 thf(fact_214_Inl__cont__hsubst__eq,axiom,
% 0.19/0.45 ! [Tr: dtree,Tr0: dtree] :
% 0.19/0.45 ( ( ( root @ Tr )
% 0.19/0.45 = ( root @ Tr0 ) )
% 0.19/0.45 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.19/0.45 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Inl_cont_hsubst_eq
% 0.19/0.45 thf(fact_215_set_Ocompositionality,axiom,
% 0.19/0.45 ! [C: $tType,B: $tType,A: $tType,F2: C > B,G2: B > A,Set: set @ A] :
% 0.19/0.45 ( ( vimage @ C @ B @ F2 @ ( vimage @ B @ A @ G2 @ Set ) )
% 0.19/0.45 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G2 @ F2 ) @ Set ) ) ).
% 0.19/0.45
% 0.19/0.45 % set.compositionality
% 0.19/0.45 thf(fact_216_vimage__comp,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,C: $tType,F2: A > B,G2: B > C,X3: set @ C] :
% 0.19/0.45 ( ( vimage @ A @ B @ F2 @ ( vimage @ B @ C @ G2 @ X3 ) )
% 0.19/0.45 = ( vimage @ A @ C @ ( comp @ B @ C @ A @ G2 @ F2 ) @ X3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % vimage_comp
% 0.19/0.45 thf(fact_217_set_Ocomp,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,C: $tType,F2: C > B,G2: B > A] :
% 0.19/0.45 ( ( comp @ ( set @ B ) @ ( set @ C ) @ ( set @ A ) @ ( vimage @ C @ B @ F2 ) @ ( vimage @ B @ A @ G2 ) )
% 0.19/0.45 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G2 @ F2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % set.comp
% 0.19/0.45 thf(fact_218_vimage__mono,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,A2: set @ A,B3: set @ A,F2: B > A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ B ) @ ( vimage @ B @ A @ F2 @ A2 ) @ ( vimage @ B @ A @ F2 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % vimage_mono
% 0.19/0.45 thf(fact_219_vimage__Collect,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,P: B > $o,F2: A > B,Q: A > $o] :
% 0.19/0.45 ( ! [X2: A] :
% 0.19/0.45 ( ( P @ ( F2 @ X2 ) )
% 0.19/0.45 = ( Q @ X2 ) )
% 0.19/0.45 => ( ( vimage @ A @ B @ F2 @ ( collect @ B @ P ) )
% 0.19/0.45 = ( collect @ A @ Q ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % vimage_Collect
% 0.19/0.45 thf(fact_220_vimageI2,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,F2: B > A,A3: B,A2: set @ A] :
% 0.19/0.45 ( ( member @ A @ ( F2 @ A3 ) @ A2 )
% 0.19/0.45 => ( member @ B @ A3 @ ( vimage @ B @ A @ F2 @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % vimageI2
% 0.19/0.45 thf(fact_221_vimageE,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,A3: A,F2: A > B,B3: set @ B] :
% 0.19/0.45 ( ( member @ A @ A3 @ ( vimage @ A @ B @ F2 @ B3 ) )
% 0.19/0.45 => ( member @ B @ ( F2 @ A3 ) @ B3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % vimageE
% 0.19/0.45 thf(fact_222_vimageD,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,A3: A,F2: A > B,A2: set @ B] :
% 0.19/0.45 ( ( member @ A @ A3 @ ( vimage @ A @ B @ F2 @ A2 ) )
% 0.19/0.45 => ( member @ B @ ( F2 @ A3 ) @ A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % vimageD
% 0.19/0.45 thf(fact_223_not__arg__cong__Inr,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,X3: A,Y4: A] :
% 0.19/0.45 ( ( X3 != Y4 )
% 0.19/0.45 => ( ( sum_Inr @ A @ B @ X3 )
% 0.19/0.45 != ( sum_Inr @ A @ B @ Y4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % not_arg_cong_Inr
% 0.19/0.45 thf(fact_224_Inl__Inr__image__cong,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,A2: set @ ( sum_sum @ A @ B ),B3: set @ ( sum_sum @ A @ B )] :
% 0.19/0.45 ( ( ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ A2 )
% 0.19/0.45 = ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ B3 ) )
% 0.19/0.45 => ( ( ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ A2 )
% 0.19/0.45 = ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ B3 ) )
% 0.19/0.45 => ( A2 = B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Inl_Inr_image_cong
% 0.19/0.45 thf(fact_225_inFr__hsubst__imp,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr0: dtree,Tr: dtree,T2: t] :
% 0.19/0.45 ( ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T2 )
% 0.19/0.45 => ( ( member @ t @ T2 @ ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) )
% 0.19/0.45 | ( gram_L805317505_inFrr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr0 @ T2 )
% 0.19/0.45 | ( gram_L1333338417e_inFr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr @ T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr_hsubst_imp
% 0.19/0.45 thf(fact_226_bot__apply,axiom,
% 0.19/0.45 ! [C: $tType,D: $tType] :
% 0.19/0.45 ( ( bot @ C @ ( type2 @ C ) )
% 0.19/0.45 => ( ( bot_bot @ ( D > C ) )
% 0.19/0.45 = ( ^ [X: D] : ( bot_bot @ C ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % bot_apply
% 0.19/0.45 thf(fact_227_empty__iff,axiom,
% 0.19/0.45 ! [A: $tType,C2: A] :
% 0.19/0.45 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % empty_iff
% 0.19/0.45 thf(fact_228_all__not__in__conv,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] :
% 0.19/0.45 ( ( ! [X: A] :
% 0.19/0.45 ~ ( member @ A @ X @ A2 ) )
% 0.19/0.45 = ( A2
% 0.19/0.45 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % all_not_in_conv
% 0.19/0.45 thf(fact_229_Collect__empty__eq,axiom,
% 0.19/0.45 ! [A: $tType,P: A > $o] :
% 0.19/0.45 ( ( ( collect @ A @ P )
% 0.19/0.45 = ( bot_bot @ ( set @ A ) ) )
% 0.19/0.45 = ( ! [X: A] :
% 0.19/0.45 ~ ( P @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Collect_empty_eq
% 0.19/0.45 thf(fact_230_empty__Collect__eq,axiom,
% 0.19/0.45 ! [A: $tType,P: A > $o] :
% 0.19/0.45 ( ( ( bot_bot @ ( set @ A ) )
% 0.19/0.45 = ( collect @ A @ P ) )
% 0.19/0.45 = ( ! [X: A] :
% 0.19/0.45 ~ ( P @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % empty_Collect_eq
% 0.19/0.45 thf(fact_231_DiffI,axiom,
% 0.19/0.45 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ( member @ A @ C2 @ A2 )
% 0.19/0.45 => ( ~ ( member @ A @ C2 @ B3 )
% 0.19/0.45 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % DiffI
% 0.19/0.45 thf(fact_232_Diff__iff,axiom,
% 0.19/0.45 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 0.19/0.45 = ( ( member @ A @ C2 @ A2 )
% 0.19/0.45 & ~ ( member @ A @ C2 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Diff_iff
% 0.19/0.45 thf(fact_233_Diff__idemp,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) @ B3 )
% 0.19/0.45 = ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % Diff_idemp
% 0.19/0.45 thf(fact_234_subset__empty,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.19/0.45 = ( A2
% 0.19/0.45 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_empty
% 0.19/0.45 thf(fact_235_empty__subsetI,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 ) ).
% 0.19/0.45
% 0.19/0.45 % empty_subsetI
% 0.19/0.45 thf(fact_236_singletonI,axiom,
% 0.19/0.45 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % singletonI
% 0.19/0.45 thf(fact_237_Diff__empty,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] :
% 0.19/0.45 ( ( minus_minus @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.19/0.45 = A2 ) ).
% 0.19/0.45
% 0.19/0.45 % Diff_empty
% 0.19/0.45 thf(fact_238_empty__Diff,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] :
% 0.19/0.45 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 )
% 0.19/0.45 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % empty_Diff
% 0.19/0.45 thf(fact_239_Diff__cancel,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] :
% 0.19/0.45 ( ( minus_minus @ ( set @ A ) @ A2 @ A2 )
% 0.19/0.45 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Diff_cancel
% 0.19/0.45 thf(fact_240_Diff__insert0,axiom,
% 0.19/0.45 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ~ ( member @ A @ X3 @ A2 )
% 0.19/0.45 => ( ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ B3 ) )
% 0.19/0.45 = ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Diff_insert0
% 0.19/0.45 thf(fact_241_insert__Diff1,axiom,
% 0.19/0.45 ! [A: $tType,X3: A,B3: set @ A,A2: set @ A] :
% 0.19/0.45 ( ( member @ A @ X3 @ B3 )
% 0.19/0.45 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) @ B3 )
% 0.19/0.45 = ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % insert_Diff1
% 0.19/0.45 thf(fact_242_vimage__empty,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,F2: A > B] :
% 0.19/0.45 ( ( vimage @ A @ B @ F2 @ ( bot_bot @ ( set @ B ) ) )
% 0.19/0.45 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % vimage_empty
% 0.19/0.45 thf(fact_243_singleton__insert__inj__eq,axiom,
% 0.19/0.45 ! [A: $tType,B2: A,A3: A,A2: set @ A] :
% 0.19/0.45 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 0.19/0.45 = ( insert @ A @ A3 @ A2 ) )
% 0.19/0.45 = ( ( A3 = B2 )
% 0.19/0.45 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % singleton_insert_inj_eq
% 0.19/0.45 thf(fact_244_singleton__insert__inj__eq_H,axiom,
% 0.19/0.45 ! [A: $tType,A3: A,A2: set @ A,B2: A] :
% 0.19/0.45 ( ( ( insert @ A @ A3 @ A2 )
% 0.19/0.45 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.19/0.45 = ( ( A3 = B2 )
% 0.19/0.45 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % singleton_insert_inj_eq'
% 0.19/0.45 thf(fact_245_Diff__eq__empty__iff,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ( ( minus_minus @ ( set @ A ) @ A2 @ B3 )
% 0.19/0.45 = ( bot_bot @ ( set @ A ) ) )
% 0.19/0.45 = ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % Diff_eq_empty_iff
% 0.19/0.45 thf(fact_246_insert__Diff__single,axiom,
% 0.19/0.45 ! [A: $tType,A3: A,A2: set @ A] :
% 0.19/0.45 ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.19/0.45 = ( insert @ A @ A3 @ A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % insert_Diff_single
% 0.19/0.45 thf(fact_247_Diff__UNIV,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] :
% 0.19/0.45 ( ( minus_minus @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 0.19/0.45 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Diff_UNIV
% 0.19/0.45 thf(fact_248_vimage__singleton__eq,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,A3: A,F2: A > B,B2: B] :
% 0.19/0.45 ( ( member @ A @ A3 @ ( vimage @ A @ B @ F2 @ ( insert @ B @ B2 @ ( bot_bot @ ( set @ B ) ) ) ) )
% 0.19/0.45 = ( ( F2 @ A3 )
% 0.19/0.45 = B2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % vimage_singleton_eq
% 0.19/0.45 thf(fact_249_vimage__Diff,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,F2: A > B,A2: set @ B,B3: set @ B] :
% 0.19/0.45 ( ( vimage @ A @ B @ F2 @ ( minus_minus @ ( set @ B ) @ A2 @ B3 ) )
% 0.19/0.45 = ( minus_minus @ ( set @ A ) @ ( vimage @ A @ B @ F2 @ A2 ) @ ( vimage @ A @ B @ F2 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % vimage_Diff
% 0.19/0.45 thf(fact_250_inFr__hsubst__minus,axiom,
% 0.19/0.45 ! [Ns: set @ n,Tr0: dtree,Tr: dtree,T2: t] :
% 0.19/0.45 ( ( gram_L1333338417e_inFr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr @ T2 )
% 0.19/0.45 => ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % inFr_hsubst_minus
% 0.19/0.45 thf(fact_251_empty__not__UNIV,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( bot_bot @ ( set @ A ) )
% 0.19/0.45 != ( top_top @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % empty_not_UNIV
% 0.19/0.45 thf(fact_252_DiffE,axiom,
% 0.19/0.45 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 0.19/0.45 => ~ ( ( member @ A @ C2 @ A2 )
% 0.19/0.45 => ( member @ A @ C2 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % DiffE
% 0.19/0.45 thf(fact_253_DiffD1,axiom,
% 0.19/0.45 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 0.19/0.45 => ( member @ A @ C2 @ A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % DiffD1
% 0.19/0.45 thf(fact_254_DiffD2,axiom,
% 0.19/0.45 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 0.19/0.45 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 0.19/0.45 => ~ ( member @ A @ C2 @ B3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % DiffD2
% 0.19/0.45 thf(fact_255_emptyE,axiom,
% 0.19/0.45 ! [A: $tType,A3: A] :
% 0.19/0.45 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % emptyE
% 0.19/0.45
% 0.19/0.45 %----Type constructors (19)
% 0.19/0.45 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 0.19/0.45 ! [A7: $tType,A9: $tType] :
% 0.19/0.45 ( ( order_top @ A9 @ ( type2 @ A9 ) )
% 0.19/0.45 => ( order_top @ ( A7 > A9 ) @ ( type2 @ ( A7 > A9 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.19/0.45 ! [A7: $tType,A9: $tType] :
% 0.19/0.45 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 0.19/0.45 => ( preorder @ ( A7 > A9 ) @ ( type2 @ ( A7 > A9 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.19/0.45 ! [A7: $tType,A9: $tType] :
% 0.19/0.45 ( ( order @ A9 @ ( type2 @ A9 ) )
% 0.19/0.45 => ( order @ ( A7 > A9 ) @ ( type2 @ ( A7 > A9 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_fun___Orderings_Otop,axiom,
% 0.19/0.45 ! [A7: $tType,A9: $tType] :
% 0.19/0.45 ( ( top @ A9 @ ( type2 @ A9 ) )
% 0.19/0.45 => ( top @ ( A7 > A9 ) @ ( type2 @ ( A7 > A9 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_fun___Orderings_Oord,axiom,
% 0.19/0.45 ! [A7: $tType,A9: $tType] :
% 0.19/0.45 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 0.19/0.45 => ( ord @ ( A7 > A9 ) @ ( type2 @ ( A7 > A9 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_fun___Orderings_Obot,axiom,
% 0.19/0.45 ! [A7: $tType,A9: $tType] :
% 0.19/0.45 ( ( bot @ A9 @ ( type2 @ A9 ) )
% 0.19/0.45 => ( bot @ ( A7 > A9 ) @ ( type2 @ ( A7 > A9 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Orderings_Oorder__top_1,axiom,
% 0.19/0.45 ! [A7: $tType] : ( order_top @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 0.19/0.45 ! [A7: $tType] : ( preorder @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Orderings_Oorder_3,axiom,
% 0.19/0.45 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Orderings_Otop_4,axiom,
% 0.19/0.45 ! [A7: $tType] : ( top @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Orderings_Oord_5,axiom,
% 0.19/0.45 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Orderings_Obot_6,axiom,
% 0.19/0.45 ! [A7: $tType] : ( bot @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Orderings_Oorder__top_7,axiom,
% 0.19/0.45 order_top @ $o @ ( type2 @ $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Orderings_Opreorder_8,axiom,
% 0.19/0.45 preorder @ $o @ ( type2 @ $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.19/0.45 linorder @ $o @ ( type2 @ $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 0.19/0.45 order @ $o @ ( type2 @ $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Orderings_Otop_10,axiom,
% 0.19/0.45 top @ $o @ ( type2 @ $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Orderings_Oord_11,axiom,
% 0.19/0.45 ord @ $o @ ( type2 @ $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Orderings_Obot_12,axiom,
% 0.19/0.45 bot @ $o @ ( type2 @ $o ) ).
% 0.19/0.45
% 0.19/0.45 %----Helper facts (3)
% 0.19/0.45 thf(help_If_3_1_T,axiom,
% 0.19/0.45 ! [P: $o] :
% 0.19/0.45 ( ( P = $true )
% 0.19/0.45 | ( P = $false ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(help_If_2_1_T,axiom,
% 0.19/0.45 ! [A: $tType,X3: A,Y4: A] :
% 0.19/0.45 ( ( if @ A @ $false @ X3 @ Y4 )
% 0.19/0.45 = Y4 ) ).
% 0.19/0.45
% 0.19/0.45 thf(help_If_1_1_T,axiom,
% 0.19/0.45 ! [A: $tType,X3: A,Y4: A] :
% 0.19/0.45 ( ( if @ A @ $true @ X3 @ Y4 )
% 0.19/0.45 = X3 ) ).
% 0.19/0.45
% 0.19/0.45 %----Conjectures (1)
% 0.19/0.45 thf(conj_0,conjecture,
% 0.19/0.45 ( ( f @ ( root @ tr ) )
% 0.19/0.45 = tr ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 2.72/1.49 ---- Embedded in THF ---
% 2.72/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.72/1.49 %%% Generated on Tue Feb 24 04:16:30 EST 2026
% 2.72/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 2.72/1.49 %%% Logic specification used:
% 2.72/1.49 %%% thf(spec, logic, $$dhol).
% 2.72/1.49
% 2.72/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.dpsNr913pg/DTF2DTF23682.p
% 2.72/1.49 thf(ty_t_Sum__Type_Osum, type, sum_sum: ($tType > ($tType > $tType))).
% 2.72/1.49 thf(ty_t_DTree_Odtree, type, dtree: $tType).
% 2.72/1.49 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.72/1.49 thf(ty_t_DTree_OT, type, t: $tType).
% 2.72/1.49 thf(ty_t_DTree_ON, type, n: $tType).
% 2.72/1.49 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.72/1.49 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.72/1.49 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.72/1.49 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.72/1.49 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.72/1.49 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.72/1.49 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.72/1.49 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.72/1.49 thf(sy_cl_Orderings_Oorder__top, type, order_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.72/1.49 thf(sy_c_DTree_ONode, type, node: (n > ((set @ ((sum_sum @ t) @ dtree)) > dtree))).
% 2.72/1.49 thf(sy_c_DTree_Ocont, type, cont: (dtree > (set @ ((sum_sum @ t) @ dtree)))).
% 2.72/1.49 thf(sy_c_DTree_Ocorec, type, corec: (!> [A:$tType]: (((A > n) > ((A > (set @ ((sum_sum @ t) @ ((sum_sum @ dtree) @ A)))) > (A > dtree)))))).
% 2.72/1.49 thf(sy_c_DTree_Odtree_Oroot, type, root: (dtree > n)).
% 2.72/1.49 thf(sy_c_DTree_Ounfold, type, unfold: (!> [A:$tType]: (((A > n) > ((A > (set @ ((sum_sum @ t) @ A))) > (A > dtree)))))).
% 2.72/1.49 thf(sy_c_Fun_Ocomp, type, comp: (!> [B:$tType,C:$tType,A:$tType]: (((B > C) > ((A > B) > (A > C)))))).
% 2.72/1.49 thf(sy_c_Fun_Oid, type, id: (!> [A:$tType]: ((A > A)))).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OS, type, gram_L1451583635elle_S: (n > (set @ ((sum_sum @ t) @ n)))).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr, type, gram_L1231612515_deftr: (n > dtree)).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst, type, gram_L1004374585hsubst: (dtree > (dtree > dtree))).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c, type, gram_L1905609002ubst_c: (dtree > (dtree > (set @ ((sum_sum @ t) @ dtree))))).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r, type, gram_L1905609017ubst_r: (dtree > n)).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr, type, gram_L1333338417e_inFr: ((set @ n) > (dtree > (t > $o)))).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2, type, gram_L805317441_inFr2: ((set @ n) > (dtree > (t > $o)))).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFrr, type, gram_L805317505_inFrr: ((set @ n) > (dtree > (t > $o)))).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr, type, gram_L830233218_inItr: ((set @ n) > (dtree > (n > $o)))).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oreg, type, gram_L1918716148le_reg: ((n > dtree) > (dtree > $o))).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oregular, type, gram_L646766332egular: (dtree > $o)).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr, type, gram_L716654942_subtr: ((set @ n) > (dtree > (dtree > $o)))).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr2, type, gram_L1283001940subtr2: ((set @ n) > (dtree > (dtree > $o)))).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OsubtrOf, type, gram_L1614515765ubtrOf: (dtree > (n > dtree))).
% 2.72/1.49 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf, type, gram_L864798063lle_wf: (dtree > $o)).
% 2.72/1.49 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.72/1.49 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.72/1.49 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.72/1.49 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.72/1.49 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.72/1.49 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.72/1.49 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.72/1.49 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.72/1.49 thf(sy_c_Set_Ovimage, type, vimage: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ B) > (set @ A)))))).
% 2.72/1.49 thf(sy_c_Sum__Type_OInl, type, sum_Inl: (!> [A:$tType,B:$tType]: ((A > ((sum_sum @ A) @ B))))).
% 2.72/1.49 thf(sy_c_Sum__Type_OInr, type, sum_Inr: (!> [B:$tType,A:$tType]: ((B > ((sum_sum @ A) @ B))))).
% 2.72/1.49 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum, type, sum_rec_sum: (!> [A:$tType,T:$tType,B:$tType]: (((A > T) > ((B > T) > (((sum_sum @ A) @ B) > T)))))).
% 2.72/1.49 thf(sy_c_Typedef_Otype__definition, type, type_definition: (!> [B:$tType,A:$tType]: (((B > A) > ((A > B) > ((set @ A) > $o)))))).
% 2.72/1.49 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.72/1.49 thf(sy_v_f, type, f: (n > dtree)).
% 2.72/1.49 thf(sy_v_tr, type, tr: dtree).
% 2.72/1.49 thf(fact_0_assms, axiom, ((gram_L1918716148le_reg @ f) @ tr)).
% 2.72/1.49 thf(fact_1_hsubst__r__def, axiom, (gram_L1905609017ubst_r = root)).
% 2.72/1.49 thf(fact_2_root__deftr, axiom, (! [N:n]: (((root @ (gram_L1231612515_deftr @ N)) = N)))).
% 2.72/1.49 thf(fact_3_root__hsubst, axiom, (! [Tr0:dtree,Tr:dtree]: (((root @ ((gram_L1004374585hsubst @ Tr0) @ Tr)) = (root @ Tr))))).
% 2.72/1.49 thf(fact_4_inFr2__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t]: (((((gram_L805317441_inFr2 @ Ns) @ Tr) @ T2) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 2.72/1.49 thf(fact_5_inItr_OBase, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L830233218_inItr @ Ns) @ Tr) @ (root @ Tr)))))).
% 2.72/1.49 thf(fact_6_inItr__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,N:n]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 2.72/1.49 thf(fact_7_regular__def2, axiom, (gram_L646766332egular = (^ [Tr2:dtree]: ((? [F:(n > dtree)]: ((((gram_L1918716148le_reg @ F) @ Tr2) & (! [N2:n]: (((root @ (F @ N2)) = N2)))))))))).
% 2.72/1.49 thf(fact_8_hsubst__eq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) = (root @ Tr0)) => (((gram_L1004374585hsubst @ Tr0) @ Tr) = ((gram_L1004374585hsubst @ Tr0) @ Tr0)))))).
% 2.72/1.49 thf(fact_9_subtr2_ORefl, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L1283001940subtr2 @ Ns) @ Tr) @ Tr))))).
% 2.72/1.49 thf(fact_10_subtr2__rootL__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr1)) @ Ns))))).
% 2.72/1.49 thf(fact_11_subtr2__rootR__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr22)) @ Ns))))).
% 2.72/1.49 thf(fact_12_inFr__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 2.72/1.49 thf(fact_13_inFr__inFr2, axiom, (gram_L1333338417e_inFr = gram_L805317441_inFr2)).
% 2.72/1.49 thf(fact_14_regular__def, axiom, (gram_L646766332egular = (^ [Tr2:dtree]: ((? [F:(n > dtree)]: (((gram_L1918716148le_reg @ F) @ Tr2))))))).
% 2.72/1.49 thf(fact_15_subtr2__trans, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree,Tr3:dtree]: (((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => ((((gram_L1283001940subtr2 @ Ns) @ Tr22) @ Tr3) => (((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr3)))))).
% 2.72/1.49 thf(fact_16_inFr__hsubst__notin, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t,Tr0:dtree]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2) => ((~ ((((member @ n) @ (root @ Tr0)) @ Ns))) => (((gram_L1333338417e_inFr @ Ns) @ ((gram_L1004374585hsubst @ Tr0) @ Tr)) @ T2)))))).
% 2.72/1.49 thf(fact_17_not__root__inFr, axiom, (! [Tr:dtree,Ns:(set @ n),T2:t]: (((~ ((((member @ n) @ (root @ Tr)) @ Ns))) => (~ ((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2))))))).
% 2.72/1.49 thf(fact_18_hsubst__def, axiom, (gram_L1004374585hsubst = (^ [Tr02:dtree]: ((((unfold @ dtree) @ gram_L1905609017ubst_r) @ (gram_L1905609002ubst_c @ Tr02)))))).
% 2.72/1.49 thf(fact_19_reg__def2, axiom, (gram_L1918716148le_reg = (^ [F:(n > dtree),Tr2:dtree]: ((! [Ns2:(set @ n),Tr4:dtree]: (((((gram_L716654942_subtr @ Ns2) @ Tr4) @ Tr2) => (Tr4 = (F @ (root @ Tr4)))))))))).
% 2.72/1.49 thf(fact_20_inItr__subtr, axiom, (! [Ns:(set @ n),Tr:dtree,N:n]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N) => (? [Tr5:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr5) @ Tr) & ((root @ Tr5) = N)))))))).
% 2.72/1.49 thf(fact_21_root__o__subst, axiom, (! [Tr0:dtree]: (((((((comp @ dtree) @ n) @ dtree) @ root) @ (gram_L1004374585hsubst @ Tr0)) = root)))).
% 2.72/1.49 thf(fact_22_wf__deftr, axiom, (! [N:n]: ((gram_L864798063lle_wf @ (gram_L1231612515_deftr @ N))))).
% 2.72/1.49 thf(fact_23_wf__hsubst, axiom, (! [Tr0:dtree,Tr:dtree]: (((gram_L864798063lle_wf @ Tr0) => ((gram_L864798063lle_wf @ Tr) => (gram_L864798063lle_wf @ ((gram_L1004374585hsubst @ Tr0) @ Tr))))))).
% 2.72/1.49 thf(fact_24_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)))))).
% 2.72/1.49 thf(fact_25_subtr__subtr2, axiom, (gram_L716654942_subtr = gram_L1283001940subtr2)).
% 2.72/1.49 thf(fact_26_subtr__inFr, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t,Tr1:dtree]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => (((gram_L1333338417e_inFr @ Ns) @ Tr1) @ T2)))))).
% 2.72/1.49 thf(fact_27_root__Node, axiom, (! [N:n,As:(set @ ((sum_sum @ t) @ dtree))]: (((root @ ((node @ N) @ As)) = N)))).
% 2.72/1.49 thf(fact_28_inFr2__mono, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t,Ns3:(set @ n)]: (((((gram_L805317441_inFr2 @ Ns) @ Tr) @ T2) => ((((ord_less_eq @ (set @ n)) @ Ns) @ Ns3) => (((gram_L805317441_inFr2 @ Ns3) @ Tr) @ T2)))))).
% 2.72/1.49 thf(fact_29_subtr__trans, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree,Tr3:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => ((((gram_L716654942_subtr @ Ns) @ Tr22) @ Tr3) => (((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr3)))))).
% 2.72/1.49 thf(fact_30_subtr__mono, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree,Ns3:(set @ n)]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => ((((ord_less_eq @ (set @ n)) @ Ns) @ Ns3) => (((gram_L716654942_subtr @ Ns3) @ Tr1) @ Tr22)))))).
% 2.72/1.49 thf(fact_31_wf__subtr, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr:dtree]: (((gram_L864798063lle_wf @ Tr1) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => (gram_L864798063lle_wf @ Tr)))))).
% 2.72/1.49 thf(fact_32_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))))).
% 2.72/1.49 thf(fact_33_subtr_ORefl, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L716654942_subtr @ Ns) @ Tr) @ Tr))))).
% 2.72/1.49 thf(fact_34_subtr__rootL__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr1)) @ Ns))))).
% 2.72/1.49 thf(fact_35_subtr__rootR__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr22)) @ Ns))))).
% 2.72/1.49 thf(fact_36_inFr__mono, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t,Ns3:(set @ n)]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2) => ((((ord_less_eq @ (set @ n)) @ Ns) @ Ns3) => (((gram_L1333338417e_inFr @ Ns3) @ Tr) @ T2)))))).
% 2.72/1.49 thf(fact_37_subtr2__mono, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree,Ns3:(set @ n)]: (((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => ((((ord_less_eq @ (set @ n)) @ Ns) @ Ns3) => (((gram_L1283001940subtr2 @ Ns3) @ Tr1) @ Tr22)))))).
% 2.72/1.49 thf(fact_38_inItr__mono, axiom, (! [Ns:(set @ n),Tr:dtree,N:n,Ns3:(set @ n)]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N) => ((((ord_less_eq @ (set @ n)) @ Ns) @ Ns3) => (((gram_L830233218_inItr @ Ns3) @ Tr) @ N)))))).
% 2.72/1.49 thf(fact_39_comp__apply, axiom, (! [C:$tType,A:$tType,B:$tType]: (((((comp @ B) @ A) @ C) = (^ [F:(B > A),G:(C > B),X:C]: ((F @ (G @ X)))))))).
% 2.72/1.49 thf(fact_40_subset__antisym, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ A2) => (A2 = B3)))))).
% 2.72/1.49 thf(fact_41_subsetI, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((! [X2:A]: (((((member @ A) @ X2) @ A2) => (((member @ A) @ X2) @ B3)))) => (((ord_less_eq @ (set @ A)) @ A2) @ B3))))).
% 2.72/1.49 thf(fact_42_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 2.72/1.49 thf(fact_43_reg__def, axiom, (gram_L1918716148le_reg = (^ [F:(n > dtree),Tr2:dtree]: ((! [Tr4:dtree]: (((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ Tr4) @ Tr2) => (Tr4 = (F @ (root @ Tr4)))))))))).
% 2.72/1.49 thf(fact_44_rewriteR__comp__comp2, axiom, (! [C:$tType,B:$tType,E:$tType,D:$tType,A:$tType,G2:(C > B),H:(A > C),R1:(D > B),R2:(A > D),F2:(B > E),L:(D > E)]: ((((((((comp @ C) @ B) @ A) @ G2) @ H) = (((((comp @ D) @ B) @ A) @ R1) @ R2)) => (((((((comp @ B) @ E) @ D) @ F2) @ R1) = L) => ((((((comp @ C) @ E) @ A) @ (((((comp @ B) @ E) @ C) @ F2) @ G2)) @ H) = (((((comp @ D) @ E) @ A) @ L) @ R2))))))).
% 2.72/1.49 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 2.72/1.49 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A2)))) = A2)))).
% 2.72/1.49 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) = (Q @ X2)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.72/1.49 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F2:(A > B),G2:(A > B)]: (((! [X2:A]: (((F2 @ X2) = (G2 @ X2)))) => (F2 = G2))))).
% 2.72/1.49 thf(fact_49_rewriteL__comp__comp2, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,E:$tType,F2:(C > B),G2:(A > C),L1:(D > B),L2:(A > D),H:(E > A),R:(E > D)]: ((((((((comp @ C) @ B) @ A) @ F2) @ G2) = (((((comp @ D) @ B) @ A) @ L1) @ L2)) => (((((((comp @ A) @ D) @ E) @ L2) @ H) = R) => ((((((comp @ C) @ B) @ E) @ F2) @ (((((comp @ A) @ C) @ E) @ G2) @ H)) = (((((comp @ D) @ B) @ E) @ L1) @ R))))))).
% 2.72/1.49 thf(fact_50_rewriteR__comp__comp, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,G2:(C > B),H:(A > C),R:(A > B),F2:(B > D)]: ((((((((comp @ C) @ B) @ A) @ G2) @ H) = R) => ((((((comp @ C) @ D) @ A) @ (((((comp @ B) @ D) @ C) @ F2) @ G2)) @ H) = (((((comp @ B) @ D) @ A) @ F2) @ R)))))).
% 2.72/1.49 thf(fact_51_rewriteL__comp__comp, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,F2:(C > B),G2:(A > C),L:(A > B),H:(D > A)]: ((((((((comp @ C) @ B) @ A) @ F2) @ G2) = L) => ((((((comp @ C) @ B) @ D) @ F2) @ (((((comp @ A) @ C) @ D) @ G2) @ H)) = (((((comp @ A) @ B) @ D) @ L) @ H)))))).
% 2.72/1.49 thf(fact_52_top__apply, axiom, (! [C:$tType,D:$tType]: ((((top @ C) @ (type2 @ C)) => ((top_top @ (D > C)) = (^ [X:D]: ((top_top @ C)))))))).
% 2.72/1.49 thf(fact_53_UNIV__I, axiom, (! [A:$tType,X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))).
% 2.72/1.49 thf(fact_54_UNIV__eq__I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X2:A]: ((((member @ A) @ X2) @ A2))) => ((top_top @ (set @ A)) = A2))))).
% 2.72/1.49 thf(fact_55_UNIV__witness, axiom, (! [A:$tType]: ((? [X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A)))))))).
% 2.72/1.49 thf(fact_56_top__greatest, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ (top_top @ A)))))))).
% 2.72/1.49 thf(fact_57_top_Oextremum__unique, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A3:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A3) = (A3 = (top_top @ A))))))))).
% 2.72/1.49 thf(fact_58_top_Oextremum__uniqueI, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A3:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A3) => (A3 = (top_top @ A))))))))).
% 2.72/1.49 thf(fact_59_subset__UNIV, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ (top_top @ (set @ A)))))).
% 2.72/1.49 thf(fact_60_le__funD, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F2:(A > B),G2:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F2) @ G2) => (((ord_less_eq @ B) @ (F2 @ X3)) @ (G2 @ X3))))))))).
% 2.72/1.49 thf(fact_61_le__funE, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F2:(A > B),G2:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F2) @ G2) => (((ord_less_eq @ B) @ (F2 @ X3)) @ (G2 @ X3))))))))).
% 2.72/1.49 thf(fact_62_le__funI, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F2:(A > B),G2:(A > B)]: (((! [X2:A]: ((((ord_less_eq @ B) @ (F2 @ X2)) @ (G2 @ X2)))) => (((ord_less_eq @ (A > B)) @ F2) @ G2)))))))).
% 2.72/1.49 thf(fact_63_le__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less_eq @ (A > B)) = (^ [F:(A > B),G:(A > B)]: ((! [X:A]: ((((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))))).
% 2.72/1.49 thf(fact_64_order__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A3:A,F2:(B > A),B2:B,C2:B]: (((((ord_less_eq @ A) @ A3) @ (F2 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X2:B,Y:B]: (((((ord_less_eq @ B) @ X2) @ Y) => (((ord_less_eq @ A) @ (F2 @ X2)) @ (F2 @ Y))))) => (((ord_less_eq @ A) @ A3) @ (F2 @ C2))))))))))).
% 2.72/1.49 thf(fact_65_order__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A3:A,B2:A,F2:(A > C),C2:C]: (((((ord_less_eq @ A) @ A3) @ B2) => ((((ord_less_eq @ C) @ (F2 @ B2)) @ C2) => ((! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) => (((ord_less_eq @ C) @ (F2 @ X2)) @ (F2 @ Y))))) => (((ord_less_eq @ C) @ (F2 @ A3)) @ C2)))))))))).
% 2.72/1.49 thf(fact_66_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A3:A,F2:(B > A),B2:B,C2:B]: (((A3 = (F2 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X2:B,Y:B]: (((((ord_less_eq @ B) @ X2) @ Y) => (((ord_less_eq @ A) @ (F2 @ X2)) @ (F2 @ Y))))) => (((ord_less_eq @ A) @ A3) @ (F2 @ C2))))))))))).
% 2.72/1.49 thf(fact_67_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A3:A,B2:A,F2:(A > B),C2:B]: (((((ord_less_eq @ A) @ A3) @ B2) => (((F2 @ B2) = C2) => ((! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) => (((ord_less_eq @ B) @ (F2 @ X2)) @ (F2 @ Y))))) => (((ord_less_eq @ B) @ (F2 @ A3)) @ C2)))))))))).
% 2.72/1.49 thf(fact_68_eq__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((^ [Y2:A,Z:A]: ((Y2 = Z))) = (^ [X:A,Y3:A]: (((((ord_less_eq @ A) @ X) @ Y3) & (((ord_less_eq @ A) @ Y3) @ X))))))))).
% 2.72/1.49 thf(fact_69_antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X3:A,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => ((((ord_less_eq @ A) @ Y4) @ X3) => (X3 = Y4))))))))).
% 2.72/1.49 thf(fact_70_linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) | (((ord_less_eq @ A) @ Y4) @ X3)))))))).
% 2.72/1.49 thf(fact_71_eq__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y4:A]: (((X3 = Y4) => (((ord_less_eq @ A) @ X3) @ Y4)))))))).
% 2.72/1.49 thf(fact_72_le__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y4:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y4))) => (((ord_less_eq @ A) @ Y4) @ X3)))))))).
% 2.72/1.49 thf(fact_73_order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A3:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A3) @ C2))))))))).
% 2.72/1.49 thf(fact_74_le__cases3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Y4:A,Z2:A]: ((((((ord_less_eq @ A) @ X3) @ Y4) => (~ ((((ord_less_eq @ A) @ Y4) @ Z2)))) => (((((ord_less_eq @ A) @ Y4) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Z2)))) => (((((ord_less_eq @ A) @ X3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y4)))) => (((((ord_less_eq @ A) @ Z2) @ Y4) => (~ ((((ord_less_eq @ A) @ Y4) @ X3)))) => (((((ord_less_eq @ A) @ Y4) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X3)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Y4))))))))))))))))).
% 2.72/1.49 thf(fact_75_antisym__conv, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y4:A,X3:A]: (((((ord_less_eq @ A) @ Y4) @ X3) => ((((ord_less_eq @ A) @ X3) @ Y4) = (X3 = Y4))))))))).
% 2.72/1.49 thf(fact_76_ord__eq__le__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A3:A,B2:A,C2:A]: (((A3 = B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A3) @ C2))))))))).
% 2.72/1.49 thf(fact_77_ord__le__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A3:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((B2 = C2) => (((ord_less_eq @ A) @ A3) @ C2))))))))).
% 2.72/1.49 thf(fact_78_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A3:A,B2:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((((ord_less_eq @ A) @ B2) @ A3) => (A3 = B2))))))))).
% 2.72/1.49 thf(fact_79_order__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X3:A,Y4:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => ((((ord_less_eq @ A) @ Y4) @ Z2) => (((ord_less_eq @ A) @ X3) @ Z2))))))))).
% 2.72/1.49 thf(fact_80_dual__order_Orefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ A3))))))).
% 2.72/1.49 thf(fact_81_linorder__wlog, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),A3:A,B2:A]: (((! [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((P @ A4) @ B4)))) => ((! [A4:A,B4:A]: ((((P @ B4) @ A4) => ((P @ A4) @ B4)))) => ((P @ A3) @ B2))))))))).
% 2.72/1.49 thf(fact_82_dual__order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A3:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A3) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ C2) @ A3))))))))).
% 2.72/1.49 thf(fact_83_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A3:A]: (((((ord_less_eq @ A) @ B2) @ A3) => ((((ord_less_eq @ A) @ A3) @ B2) => (A3 = B2))))))))).
% 2.72/1.49 thf(fact_84_set__mp, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((((member @ A) @ X3) @ A2) => (((member @ A) @ X3) @ B3)))))).
% 2.72/1.49 thf(fact_85_in__mono, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((((member @ A) @ X3) @ A2) => (((member @ A) @ X3) @ B3)))))).
% 2.72/1.49 thf(fact_86_subsetD, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ B3)))))).
% 2.72/1.49 thf(fact_87_subsetCE, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ B3)))))).
% 2.72/1.49 thf(fact_88_equalityE, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((A2 = B3) => (~ (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => (~ ((((ord_less_eq @ (set @ A)) @ B3) @ A2)))))))))).
% 2.72/1.49 thf(fact_89_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((! [X:A]: (((((member @ A) @ X) @ A5) => (((member @ A) @ X) @ B5)))))))))).
% 2.72/1.49 thf(fact_90_equalityD1, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((A2 = B3) => (((ord_less_eq @ (set @ A)) @ A2) @ B3))))).
% 2.72/1.49 thf(fact_91_equalityD2, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((A2 = B3) => (((ord_less_eq @ (set @ A)) @ B3) @ A2))))).
% 2.72/1.49 thf(fact_92_set__rev__mp, axiom, (! [A:$tType,X3:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ X3) @ A2) => ((((ord_less_eq @ (set @ A)) @ A2) @ B3) => (((member @ A) @ X3) @ B3)))))).
% 2.72/1.49 thf(fact_93_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((! [T3:A]: (((((member @ A) @ T3) @ A5) => (((member @ A) @ T3) @ B5)))))))))).
% 2.72/1.49 thf(fact_94_rev__subsetD, axiom, (! [A:$tType,C2:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ A2) => ((((ord_less_eq @ (set @ A)) @ A2) @ B3) => (((member @ A) @ C2) @ B3)))))).
% 2.72/1.49 thf(fact_95_subset__refl, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ A2)))).
% 2.72/1.49 thf(fact_96_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) => (Q @ X2)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.72/1.49 thf(fact_97_subset__trans, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ C3) => (((ord_less_eq @ (set @ A)) @ A2) @ C3)))))).
% 2.72/1.49 thf(fact_98_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y2:(set @ A),Z:(set @ A)]: ((Y2 = Z))) = (^ [A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) & (((ord_less_eq @ (set @ A)) @ B5) @ A5)))))))).
% 2.72/1.49 thf(fact_99_contra__subsetD, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => ((~ ((((member @ A) @ C2) @ B3))) => (~ ((((member @ A) @ C2) @ A2)))))))).
% 2.72/1.49 thf(fact_100_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X:A]: (((P @ X) => (Q @ X)))))))).
% 2.72/1.49 thf(fact_101_comp__def, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((comp @ B) @ C) @ A) = (^ [F:(B > C),G:(A > B),X:A]: ((F @ (G @ X)))))))).
% 2.72/1.49 thf(fact_102_comp__assoc, axiom, (! [B:$tType,D:$tType,C:$tType,A:$tType,F2:(D > B),G2:(C > D),H:(A > C)]: (((((((comp @ C) @ B) @ A) @ (((((comp @ D) @ B) @ C) @ F2) @ G2)) @ H) = (((((comp @ D) @ B) @ A) @ F2) @ (((((comp @ C) @ D) @ A) @ G2) @ H)))))).
% 2.72/1.49 thf(fact_103_comp__eq__dest, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A3:(C > B),B2:(A > C),C2:(D > B),D2:(A > D),V:A]: ((((((((comp @ C) @ B) @ A) @ A3) @ B2) = (((((comp @ D) @ B) @ A) @ C2) @ D2)) => ((A3 @ (B2 @ V)) = (C2 @ (D2 @ V))))))).
% 2.72/1.49 thf(fact_104_comp__eq__elim, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A3:(C > B),B2:(A > C),C2:(D > B),D2:(A > D)]: ((((((((comp @ C) @ B) @ A) @ A3) @ B2) = (((((comp @ D) @ B) @ A) @ C2) @ D2)) => (! [V2:A]: (((A3 @ (B2 @ V2)) = (C2 @ (D2 @ V2))))))))).
% 2.72/1.49 thf(fact_105_comp__eq__dest__lhs, axiom, (! [C:$tType,B:$tType,A:$tType,A3:(C > B),B2:(A > C),C2:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A3) @ B2) = C2) => ((A3 @ (B2 @ V)) = (C2 @ V)))))).
% 2.72/1.49 thf(fact_106_iso__tuple__UNIV__I, axiom, (! [A:$tType,X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))).
% 2.72/1.49 thf(fact_107_comp__cong, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,E:$tType,F2:(B > A),G2:(C > B),X3:C,F3:(D > A),G3:(E > D),X4:E]: ((((F2 @ (G2 @ X3)) = (F3 @ (G3 @ X4))) => (((((((comp @ B) @ A) @ C) @ F2) @ G2) @ X3) = ((((((comp @ D) @ A) @ E) @ F3) @ G3) @ X4)))))).
% 2.72/1.49 thf(fact_108_comp__apply__eq, axiom, (! [B:$tType,D:$tType,A:$tType,C:$tType,F2:(B > A),G2:(C > B),X3:C,H:(D > A),K:(C > D)]: ((((F2 @ (G2 @ X3)) = (H @ (K @ X3))) => (((((((comp @ B) @ A) @ C) @ F2) @ G2) @ X3) = ((((((comp @ D) @ A) @ C) @ H) @ K) @ X3)))))).
% 2.72/1.49 thf(fact_109_fun_Omap__comp, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,G2:(B > C),F2:(A > B),V:(D > A)]: (((((((comp @ B) @ C) @ D) @ G2) @ (((((comp @ A) @ B) @ D) @ F2) @ V)) = (((((comp @ A) @ C) @ D) @ (((((comp @ B) @ C) @ A) @ G2) @ F2)) @ V))))).
% 2.72/1.49 thf(fact_110_type__copy__map__cong0, axiom, (! [B:$tType,D:$tType,E:$tType,A:$tType,C:$tType,M:(B > A),G2:(C > B),X3:C,N3:(D > A),H:(C > D),F2:(A > E)]: ((((M @ (G2 @ X3)) = (N3 @ (H @ X3))) => (((((((comp @ B) @ E) @ C) @ (((((comp @ A) @ E) @ B) @ F2) @ M)) @ G2) @ X3) = ((((((comp @ D) @ E) @ C) @ (((((comp @ A) @ E) @ D) @ F2) @ N3)) @ H) @ X3)))))).
% 2.72/1.49 thf(fact_111_corec_I1_J, axiom, (! [A:$tType,Rt:(A > n),Ct:(A > (set @ ((sum_sum @ t) @ ((sum_sum @ dtree) @ A)))),B2:A]: (((root @ ((((corec @ A) @ Rt) @ Ct) @ B2)) = (Rt @ B2))))).
% 2.72/1.49 thf(fact_112_root__o__deftr, axiom, ((((((comp @ dtree) @ n) @ n) @ root) @ gram_L1231612515_deftr) = (id @ n))).
% 2.72/1.49 thf(fact_113_Node__root__cont, axiom, (! [Tr:dtree]: ((((node @ (root @ Tr)) @ (cont @ Tr)) = Tr)))).
% 2.72/1.49 thf(fact_114_id__apply, axiom, (! [A:$tType]: (((id @ A) = (^ [X:A]: (X)))))).
% 2.72/1.49 thf(fact_115_fun_Omap__id, axiom, (! [A:$tType,D:$tType,T2:(D > A)]: (((((((comp @ A) @ A) @ D) @ (id @ A)) @ T2) = T2)))).
% 2.72/1.49 thf(fact_116_id__comp, axiom, (! [B:$tType,A:$tType,G2:(A > B)]: (((((((comp @ B) @ B) @ A) @ (id @ B)) @ G2) = G2)))).
% 2.72/1.49 thf(fact_117_comp__id, axiom, (! [B:$tType,A:$tType,F2:(A > B)]: (((((((comp @ A) @ B) @ A) @ F2) @ (id @ A)) = F2)))).
% 2.72/1.49 thf(fact_118_fun_Omap__id0, axiom, (! [A:$tType,D:$tType]: ((((((comp @ A) @ A) @ D) @ (id @ A)) = (id @ (D > A)))))).
% 2.72/1.49 thf(fact_119_id__def, axiom, (! [A:$tType]: (((id @ A) = (^ [X:A]: (X)))))).
% 2.72/1.49 thf(fact_120_eq__id__iff, axiom, (! [A:$tType,F2:(A > A)]: (((! [X:A]: (((F2 @ X) = X))) = (F2 = (id @ A)))))).
% 2.72/1.49 thf(fact_121_DEADID_Oin__rel, axiom, (! [B:$tType]: (((^ [Y2:B,Z:B]: ((Y2 = Z))) = (^ [A6:B,B6:B]: ((? [Z3:B]: (((((member @ B) @ Z3) @ (top_top @ (set @ B))) & ((((id @ B) @ Z3) = A6) & (((id @ B) @ Z3) = B6))))))))))).
% 2.72/1.49 thf(fact_122_comp__eq__id__dest, axiom, (! [C:$tType,B:$tType,A:$tType,A3:(C > B),B2:(A > C),C2:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A3) @ B2) = (((((comp @ B) @ B) @ A) @ (id @ B)) @ C2)) => ((A3 @ (B2 @ V)) = (C2 @ V)))))).
% 2.72/1.49 thf(fact_123_pointfree__idE, axiom, (! [B:$tType,A:$tType,F2:(B > A),G2:(A > B),X3:A]: ((((((((comp @ B) @ A) @ A) @ F2) @ G2) = (id @ A)) => ((F2 @ (G2 @ X3)) = X3))))).
% 2.72/1.49 thf(fact_124_dtree__cong, axiom, (! [Tr:dtree,Tr6:dtree]: ((((root @ Tr) = (root @ Tr6)) => (((cont @ Tr) = (cont @ Tr6)) => (Tr = Tr6)))))).
% 2.72/1.49 thf(fact_125_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 2.72/1.49 thf(fact_126_hsubst__c__def, axiom, (gram_L1905609002ubst_c = (^ [Tr02:dtree,Tr2:dtree]: (((((if @ (set @ ((sum_sum @ t) @ dtree))) @ ((root @ Tr2) = (root @ Tr02))) @ (cont @ Tr02)) @ (cont @ Tr2)))))).
% 2.72/1.49 thf(fact_127_deftr__def, axiom, (gram_L1231612515_deftr = (((unfold @ n) @ (id @ n)) @ gram_L1451583635elle_S))).
% 2.72/1.49 thf(fact_128_wf__inj, axiom, (! [Tr:dtree,Tr1:dtree,Tr22:dtree]: (((gram_L864798063lle_wf @ Tr) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr22)) @ (cont @ Tr)) => (((root @ Tr1) = (root @ Tr22)) = (Tr1 = Tr22)))))))).
% 2.72/1.49 thf(fact_129_subtr__UNIV__inductL, axiom, (! [Tr1:dtree,Tr22:dtree,Phi:(dtree > (dtree > $o))]: (((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ Tr1) @ Tr22) => ((! [Tr7:dtree]: (((Phi @ Tr7) @ Tr7))) => ((! [Tr12:dtree,Tr23:dtree,Tr32:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr23)) => ((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ Tr23) @ Tr32) => (((Phi @ Tr23) @ Tr32) => ((Phi @ Tr12) @ Tr32)))))) => ((Phi @ Tr1) @ Tr22))))))).
% 2.72/1.49 thf(fact_130_type__copy__map__id0, axiom, (! [B:$tType,A:$tType,Rep:(A > B),Abs:(B > A),M:(B > B)]: (((((((type_definition @ A) @ B) @ Rep) @ Abs) @ (top_top @ (set @ B))) => ((M = (id @ B)) => ((((((comp @ B) @ A) @ A) @ (((((comp @ B) @ A) @ B) @ Abs) @ M)) @ Rep) = (id @ A))))))).
% 2.72/1.49 thf(fact_131_type__copy__Abs__o__Rep, axiom, (! [B:$tType,A:$tType,Rep:(A > B),Abs:(B > A)]: (((((((type_definition @ A) @ B) @ Rep) @ Abs) @ (top_top @ (set @ B))) => ((((((comp @ B) @ A) @ A) @ Abs) @ Rep) = (id @ A)))))).
% 2.72/1.49 thf(fact_132_top1I, axiom, (! [A:$tType,X3:A]: (((top_top @ (A > $o)) @ X3)))).
% 2.72/1.49 thf(fact_133_type__copy__wit, axiom, (! [A:$tType,C:$tType,B:$tType,Rep:(A > B),Abs:(B > A),X3:C,S:(B > (set @ C)),Y4:B]: (((((((type_definition @ A) @ B) @ Rep) @ Abs) @ (top_top @ (set @ B))) => ((((member @ C) @ X3) @ ((((((comp @ B) @ (set @ C)) @ A) @ S) @ Rep) @ (Abs @ Y4))) => (((member @ C) @ X3) @ (S @ Y4))))))).
% 2.72/1.49 thf(fact_134_top__conj_I2_J, axiom, (! [A:$tType,P:$o,X3:A]: (((P & ((top_top @ (A > $o)) @ X3)) = P)))).
% 2.72/1.49 thf(fact_135_top__conj_I1_J, axiom, (! [A:$tType,X3:A,P:$o]: (((((top_top @ (A > $o)) @ X3) & P) = P)))).
% 2.72/1.49 thf(fact_136_type__copy__ex__RepI, axiom, (! [B:$tType,A:$tType,Rep:(A > B),Abs:(B > A),F4:(B > $o)]: (((((((type_definition @ A) @ B) @ Rep) @ Abs) @ (top_top @ (set @ B))) => (((^ [P2:(B > $o)]: ((? [X5:B]: ((P2 @ X5))))) @ F4) = (? [B6:A]: ((F4 @ (Rep @ B6))))))))).
% 2.72/1.49 thf(fact_137_type__copy__obj__one__point__absE, axiom, (! [A:$tType,B:$tType,Rep:(A > B),Abs:(B > A),S2:A]: (((((((type_definition @ A) @ B) @ Rep) @ Abs) @ (top_top @ (set @ B))) => (~ ((! [X2:B]: ((S2 != (Abs @ X2)))))))))).
% 2.72/1.49 thf(fact_138_wf__cont, axiom, (! [Tr:dtree,Tr6:dtree]: (((gram_L864798063lle_wf @ Tr) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr6)) @ (cont @ Tr)) => (gram_L864798063lle_wf @ Tr6)))))).
% 2.72/1.49 thf(fact_139_type__copy__map__comp0__undo, axiom, (! [E:$tType,A:$tType,C:$tType,B:$tType,D:$tType,F5:$tType,Rep:(A > B),Abs:(B > A),Rep2:(C > D),Abs2:(D > C),Rep3:(E > F5),Abs3:(F5 > E),M:(F5 > D),M1:(B > D),M2:(F5 > B)]: (((((((type_definition @ A) @ B) @ Rep) @ Abs) @ (top_top @ (set @ B))) => ((((((type_definition @ C) @ D) @ Rep2) @ Abs2) @ (top_top @ (set @ D))) => ((((((type_definition @ E) @ F5) @ Rep3) @ Abs3) @ (top_top @ (set @ F5))) => (((((((comp @ F5) @ C) @ E) @ (((((comp @ D) @ C) @ F5) @ Abs2) @ M)) @ Rep3) = (((((comp @ A) @ C) @ E) @ (((((comp @ B) @ C) @ A) @ (((((comp @ D) @ C) @ B) @ Abs2) @ M1)) @ Rep)) @ (((((comp @ F5) @ A) @ E) @ (((((comp @ B) @ A) @ F5) @ Abs) @ M2)) @ Rep3))) => ((((((comp @ B) @ D) @ F5) @ M1) @ M2) = M)))))))).
% 2.72/1.49 thf(fact_140_type__copy__map__comp0, axiom, (! [F5:$tType,D:$tType,B:$tType,A:$tType,C:$tType,E:$tType,Rep:(A > B),Abs:(B > A),M:(C > D),M1:(B > D),M2:(C > B),F2:(D > F5),G2:(E > C)]: (((((((type_definition @ A) @ B) @ Rep) @ Abs) @ (top_top @ (set @ B))) => ((M = (((((comp @ B) @ D) @ C) @ M1) @ M2)) => ((((((comp @ C) @ F5) @ E) @ (((((comp @ D) @ F5) @ C) @ F2) @ M)) @ G2) = (((((comp @ A) @ F5) @ E) @ (((((comp @ B) @ F5) @ A) @ (((((comp @ D) @ F5) @ B) @ F2) @ M1)) @ Rep)) @ (((((comp @ C) @ A) @ E) @ (((((comp @ B) @ A) @ C) @ Abs) @ M2)) @ G2)))))))).
% 2.72/1.49 thf(fact_141_subtr_OStep, axiom, (! [Tr3:dtree,Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((member @ n) @ (root @ Tr3)) @ Ns) => ((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr22)) @ (cont @ Tr3)) => (((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr3))))))).
% 2.72/1.49 thf(fact_142_subtr_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:dtree]: (((((gram_L716654942_subtr @ A1) @ A22) @ A32) => (((A32 = A22) => (~ ((((member @ n) @ (root @ A22)) @ A1)))) => (~ (((((member @ n) @ (root @ A32)) @ A1) => (! [Tr23:dtree]: (((((gram_L716654942_subtr @ A1) @ A22) @ Tr23) => (~ ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr23)) @ (cont @ A32))))))))))))))).
% 2.72/1.49 thf(fact_143_subtr_Osimps, axiom, (gram_L716654942_subtr = (^ [A12:(set @ n),A23:dtree,A33:dtree]: (((? [Tr2:dtree,Ns2:(set @ n)]: (((A12 = Ns2) & ((A23 = Tr2) & ((A33 = Tr2) & (((member @ n) @ (root @ Tr2)) @ Ns2)))))) | (? [Tr33:dtree,Ns2:(set @ n),Tr13:dtree,Tr24:dtree]: (((A12 = Ns2) & ((A23 = Tr13) & ((A33 = Tr33) & ((((member @ n) @ (root @ Tr33)) @ Ns2) & ((((gram_L716654942_subtr @ Ns2) @ Tr13) @ Tr24) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr24)) @ (cont @ Tr33)))))))))))))).
% 2.72/1.49 thf(fact_144_subtr__StepL, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr22:dtree,Tr3:dtree]: (((((member @ n) @ (root @ Tr1)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr22)) => ((((gram_L716654942_subtr @ Ns) @ Tr22) @ Tr3) => (((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr3))))))).
% 2.72/1.49 thf(fact_145_subtr_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:dtree,P:((set @ n) > (dtree > (dtree > $o)))]: (((((gram_L716654942_subtr @ X1) @ X22) @ X32) => ((! [Tr7:dtree,Ns4:(set @ n)]: (((((member @ n) @ (root @ Tr7)) @ Ns4) => (((P @ Ns4) @ Tr7) @ Tr7)))) => ((! [Tr32:dtree,Ns4:(set @ n),Tr12:dtree,Tr23:dtree]: (((((member @ n) @ (root @ Tr32)) @ Ns4) => ((((gram_L716654942_subtr @ Ns4) @ Tr12) @ Tr23) => ((((P @ Ns4) @ Tr12) @ Tr23) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr23)) @ (cont @ Tr32)) => (((P @ Ns4) @ Tr12) @ Tr32))))))) => (((P @ X1) @ X22) @ X32))))))).
% 2.72/1.49 thf(fact_146_subtr__inductL, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree,Phi:((set @ n) > (dtree > (dtree > $o)))]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => ((! [Ns4:(set @ n),Tr7:dtree]: ((((Phi @ Ns4) @ Tr7) @ Tr7))) => ((! [Ns4:(set @ n),Tr12:dtree,Tr23:dtree,Tr32:dtree]: (((((member @ n) @ (root @ Tr12)) @ Ns4) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr23)) => ((((gram_L716654942_subtr @ Ns4) @ Tr23) @ Tr32) => ((((Phi @ Ns4) @ Tr23) @ Tr32) => (((Phi @ Ns4) @ Tr12) @ Tr32))))))) => (((Phi @ Ns) @ Tr1) @ Tr22))))))).
% 2.72/1.49 thf(fact_147_inFr_OInd, axiom, (! [Tr:dtree,Ns:(set @ n),Tr1:dtree,T2:t]: (((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => ((((gram_L1333338417e_inFr @ Ns) @ Tr1) @ T2) => (((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2))))))).
% 2.72/1.49 thf(fact_148_subtr2_OStep, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr22:dtree,Tr3:dtree]: (((((member @ n) @ (root @ Tr1)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr22)) => ((((gram_L1283001940subtr2 @ Ns) @ Tr22) @ Tr3) => (((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr3))))))).
% 2.72/1.49 thf(fact_149_subtr2_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:dtree]: (((((gram_L1283001940subtr2 @ A1) @ A22) @ A32) => (((A32 = A22) => (~ ((((member @ n) @ (root @ A22)) @ A1)))) => (~ (((((member @ n) @ (root @ A22)) @ A1) => (! [Tr23:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ A22)) @ (cont @ Tr23)) => (~ ((((gram_L1283001940subtr2 @ A1) @ Tr23) @ A32)))))))))))))).
% 2.72/1.49 thf(fact_150_subtr2_Osimps, axiom, (gram_L1283001940subtr2 = (^ [A12:(set @ n),A23:dtree,A33:dtree]: (((? [Tr2:dtree,Ns2:(set @ n)]: (((A12 = Ns2) & ((A23 = Tr2) & ((A33 = Tr2) & (((member @ n) @ (root @ Tr2)) @ Ns2)))))) | (? [Tr13:dtree,Ns2:(set @ n),Tr24:dtree,Tr33:dtree]: (((A12 = Ns2) & ((A23 = Tr13) & ((A33 = Tr33) & ((((member @ n) @ (root @ Tr13)) @ Ns2) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr24)) & (((gram_L1283001940subtr2 @ Ns2) @ Tr24) @ Tr33))))))))))))).
% 2.72/1.49 thf(fact_151_subtr2__StepR, axiom, (! [Tr3:dtree,Ns:(set @ n),Tr22:dtree,Tr1:dtree]: (((((member @ n) @ (root @ Tr3)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr22)) @ (cont @ Tr3)) => ((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => (((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr3))))))).
% 2.72/1.49 thf(fact_152_subtr2_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:dtree,P:((set @ n) > (dtree > (dtree > $o)))]: (((((gram_L1283001940subtr2 @ X1) @ X22) @ X32) => ((! [Tr7:dtree,Ns4:(set @ n)]: (((((member @ n) @ (root @ Tr7)) @ Ns4) => (((P @ Ns4) @ Tr7) @ Tr7)))) => ((! [Tr12:dtree,Ns4:(set @ n),Tr23:dtree,Tr32:dtree]: (((((member @ n) @ (root @ Tr12)) @ Ns4) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr23)) => ((((gram_L1283001940subtr2 @ Ns4) @ Tr23) @ Tr32) => ((((P @ Ns4) @ Tr23) @ Tr32) => (((P @ Ns4) @ Tr12) @ Tr32))))))) => (((P @ X1) @ X22) @ X32))))))).
% 2.72/1.49 thf(fact_153_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))))))).
% 2.72/1.49 thf(fact_154_inItr_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:n]: (((((gram_L830233218_inItr @ A1) @ A22) @ A32) => (((A32 = (root @ A22)) => (~ ((((member @ n) @ (root @ A22)) @ A1)))) => (~ (((((member @ n) @ (root @ A22)) @ A1) => (! [Tr12:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ A22)) => (~ ((((gram_L830233218_inItr @ A1) @ Tr12) @ A32)))))))))))))).
% 2.72/1.49 thf(fact_155_inItr_Osimps, axiom, (gram_L830233218_inItr = (^ [A12:(set @ n),A23:dtree,A33:n]: (((? [Tr2:dtree,Ns2:(set @ n)]: (((A12 = Ns2) & ((A23 = Tr2) & ((A33 = (root @ Tr2)) & (((member @ n) @ (root @ Tr2)) @ Ns2)))))) | (? [Tr2:dtree,Ns2:(set @ n),Tr13:dtree,N2:n]: (((A12 = Ns2) & ((A23 = Tr2) & ((A33 = N2) & ((((member @ n) @ (root @ Tr2)) @ Ns2) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr2)) & (((gram_L830233218_inItr @ Ns2) @ Tr13) @ N2))))))))))))).
% 2.72/1.49 thf(fact_156_inItr_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:n,P:((set @ n) > (dtree > (n > $o)))]: (((((gram_L830233218_inItr @ X1) @ X22) @ X32) => ((! [Tr7:dtree,Ns4:(set @ n)]: (((((member @ n) @ (root @ Tr7)) @ Ns4) => (((P @ Ns4) @ Tr7) @ (root @ Tr7))))) => ((! [Tr7:dtree,Ns4:(set @ n),Tr12:dtree,N4:n]: (((((member @ n) @ (root @ Tr7)) @ Ns4) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr7)) => ((((gram_L830233218_inItr @ Ns4) @ Tr12) @ N4) => ((((P @ Ns4) @ Tr12) @ N4) => (((P @ Ns4) @ Tr7) @ N4))))))) => (((P @ X1) @ X22) @ X32))))))).
% 2.72/1.49 thf(fact_157_inFr2__Ind, axiom, (! [Ns:(set @ n),Tr1:dtree,T2:t,Tr:dtree]: (((((gram_L805317441_inFr2 @ Ns) @ Tr1) @ T2) => ((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => (((gram_L805317441_inFr2 @ Ns) @ Tr) @ T2))))))).
% 2.72/1.49 thf(fact_158_type__copy__Rep__o__Abs, axiom, (! [A:$tType,B:$tType,Rep:(A > B),Abs:(B > A)]: (((((((type_definition @ A) @ B) @ Rep) @ Abs) @ (top_top @ (set @ B))) => ((((((comp @ A) @ B) @ B) @ Rep) @ Abs) = (id @ B)))))).
% 2.72/1.49 thf(fact_159_subtrOf__root, axiom, (! [Tr:dtree,Tr6:dtree]: (((gram_L864798063lle_wf @ Tr) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr6)) @ (cont @ Tr)) => (((gram_L1614515765ubtrOf @ Tr) @ (root @ Tr6)) = Tr6)))))).
% 2.72/1.49 thf(fact_160_inFrr__def, axiom, (gram_L805317505_inFrr = (^ [Ns2:(set @ n),Tr2:dtree,T3:t]: ((? [Tr4:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr4)) @ (cont @ Tr2)) & (((gram_L1333338417e_inFr @ Ns2) @ Tr4) @ T3)))))))).
% 2.72/1.49 thf(fact_161_sum_Oinject_I2_J, axiom, (! [A:$tType,B:$tType,X22:B,Y22:B]: ((((((sum_Inr @ B) @ A) @ X22) = (((sum_Inr @ B) @ A) @ Y22)) = (X22 = Y22))))).
% 2.72/1.49 thf(fact_162_old_Osum_Oinject_I2_J, axiom, (! [A:$tType,B:$tType,B2:B,B7:B]: ((((((sum_Inr @ B) @ A) @ B2) = (((sum_Inr @ B) @ A) @ B7)) = (B2 = B7))))).
% 2.72/1.49 thf(fact_163_Inr__inject, axiom, (! [A:$tType,B:$tType,X3:B,Y4:B]: ((((((sum_Inr @ B) @ A) @ X3) = (((sum_Inr @ B) @ A) @ Y4)) => (X3 = Y4))))).
% 2.72/1.49 thf(fact_164_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A))))))))).
% 2.72/1.49 thf(fact_165_old_Osum_Osimps_I8_J, axiom, (! [A:$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))))).
% 2.72/1.49 thf(fact_166_inFr2_OInd, axiom, (! [Tr1:dtree,Tr:dtree,Ns1:(set @ n),T2:t]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => ((((gram_L805317441_inFr2 @ Ns1) @ Tr1) @ T2) => (((gram_L805317441_inFr2 @ (((insert @ n) @ (root @ Tr)) @ Ns1)) @ Tr) @ T2)))))).
% 2.72/1.49 thf(fact_167_insert__absorb2, axiom, (! [A:$tType,X3:A,A2:(set @ A)]: (((((insert @ A) @ X3) @ (((insert @ A) @ X3) @ A2)) = (((insert @ A) @ X3) @ A2))))).
% 2.72/1.49 thf(fact_168_insert__iff, axiom, (! [A:$tType,A3:A,B2:A,A2:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B2) @ A2)) = ((A3 = B2) | (((member @ A) @ A3) @ A2)))))).
% 2.72/1.49 thf(fact_169_insertCI, axiom, (! [A:$tType,A3:A,B3:(set @ A),B2:A]: ((((~ ((((member @ A) @ A3) @ B3))) => (A3 = B2)) => (((member @ A) @ A3) @ (((insert @ A) @ B2) @ B3)))))).
% 2.72/1.49 thf(fact_170_insert__subset, axiom, (! [A:$tType,X3:A,A2:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X3) @ A2)) @ B3) = ((((member @ A) @ X3) @ B3) & (((ord_less_eq @ (set @ A)) @ A2) @ B3)))))).
% 2.72/1.49 thf(fact_171_subset__insertI2, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),B2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B2) @ B3)))))).
% 2.72/1.49 thf(fact_172_subset__insertI, axiom, (! [A:$tType,B3:(set @ A),A3:A]: ((((ord_less_eq @ (set @ A)) @ B3) @ (((insert @ A) @ A3) @ B3))))).
% 2.72/1.49 thf(fact_173_subset__insert, axiom, (! [A:$tType,X3:A,A2:(set @ A),B3:(set @ A)]: (((~ ((((member @ A) @ X3) @ A2))) => ((((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ X3) @ B3)) = (((ord_less_eq @ (set @ A)) @ A2) @ B3)))))).
% 2.72/1.49 thf(fact_174_insert__mono, axiom, (! [A:$tType,C3:(set @ A),D3:(set @ A),A3:A]: (((((ord_less_eq @ (set @ A)) @ C3) @ D3) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ A3) @ C3)) @ (((insert @ A) @ A3) @ D3)))))).
% 2.72/1.49 thf(fact_175_mk__disjoint__insert, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ A2) => (? [B8:(set @ A)]: (((A2 = (((insert @ A) @ A3) @ B8)) & (~ ((((member @ A) @ A3) @ B8)))))))))).
% 2.72/1.49 thf(fact_176_insert__commute, axiom, (! [A:$tType,X3:A,Y4:A,A2:(set @ A)]: (((((insert @ A) @ X3) @ (((insert @ A) @ Y4) @ A2)) = (((insert @ A) @ Y4) @ (((insert @ A) @ X3) @ A2)))))).
% 2.72/1.49 thf(fact_177_insert__eq__iff, axiom, (! [A:$tType,A3:A,A2:(set @ A),B2:A,B3:(set @ A)]: (((~ ((((member @ A) @ A3) @ A2))) => ((~ ((((member @ A) @ B2) @ B3))) => (((((insert @ A) @ A3) @ A2) = (((insert @ A) @ B2) @ B3)) = (((A3 = B2) => (A2 = B3)) & ((A3 != B2) => (? [C4:(set @ A)]: (((A2 = (((insert @ A) @ B2) @ C4)) & ((~ ((((member @ A) @ B2) @ C4))) & ((B3 = (((insert @ A) @ A3) @ C4)) & (~ ((((member @ A) @ A3) @ C4)))))))))))))))).
% 2.72/1.49 thf(fact_178_insert__absorb, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ A2) => ((((insert @ A) @ A3) @ A2) = A2))))).
% 2.72/1.49 thf(fact_179_insert__ident, axiom, (! [A:$tType,X3:A,A2:(set @ A),B3:(set @ A)]: (((~ ((((member @ A) @ X3) @ A2))) => ((~ ((((member @ A) @ X3) @ B3))) => (((((insert @ A) @ X3) @ A2) = (((insert @ A) @ X3) @ B3)) = (A2 = B3))))))).
% 2.72/1.49 thf(fact_180_Set_Oset__insert, axiom, (! [A:$tType,X3:A,A2:(set @ A)]: (((((member @ A) @ X3) @ A2) => (~ ((! [B8:(set @ A)]: (((A2 = (((insert @ A) @ X3) @ B8)) => (((member @ A) @ X3) @ B8)))))))))).
% 2.72/1.49 thf(fact_181_insertI2, axiom, (! [A:$tType,A3:A,B3:(set @ A),B2:A]: (((((member @ A) @ A3) @ B3) => (((member @ A) @ A3) @ (((insert @ A) @ B2) @ B3)))))).
% 2.72/1.49 thf(fact_182_insertI1, axiom, (! [A:$tType,A3:A,B3:(set @ A)]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ B3))))).
% 2.72/1.49 thf(fact_183_insertE, axiom, (! [A:$tType,A3:A,B2:A,A2:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B2) @ A2)) => ((A3 != B2) => (((member @ A) @ A3) @ A2)))))).
% 2.72/1.49 thf(fact_184_insert__UNIV, axiom, (! [A:$tType,X3:A]: (((((insert @ A) @ X3) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))).
% 2.72/1.49 thf(fact_185_inFr__Ind__minus, axiom, (! [Ns1:(set @ n),Tr1:dtree,T2:t,Tr:dtree]: (((((gram_L1333338417e_inFr @ Ns1) @ Tr1) @ T2) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => (((gram_L1333338417e_inFr @ (((insert @ n) @ (root @ Tr)) @ Ns1)) @ Tr) @ T2)))))).
% 2.72/1.49 thf(fact_186_insert__subsetI, axiom, (! [A:$tType,X3:A,A2:(set @ A),X6:(set @ A)]: (((((member @ A) @ X3) @ A2) => ((((ord_less_eq @ (set @ A)) @ X6) @ A2) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X3) @ X6)) @ A2)))))).
% 2.72/1.49 thf(fact_187_inFr2_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:t]: (((((gram_L805317441_inFr2 @ A1) @ A22) @ A32) => (((((member @ n) @ (root @ A22)) @ A1) => (~ ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ A32)) @ (cont @ A22))))) => (~ ((! [Tr12:dtree,Tr7:dtree,Ns12:(set @ n)]: (((A1 = (((insert @ n) @ (root @ Tr7)) @ Ns12)) => ((A22 = Tr7) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr7)) => (~ ((((gram_L805317441_inFr2 @ Ns12) @ Tr12) @ A32))))))))))))))).
% 2.72/1.49 thf(fact_188_inFr2_Osimps, axiom, (gram_L805317441_inFr2 = (^ [A12:(set @ n),A23:dtree,A33:t]: (((? [Tr2:dtree,Ns2:(set @ n),T3:t]: (((A12 = Ns2) & ((A23 = Tr2) & ((A33 = T3) & ((((member @ n) @ (root @ Tr2)) @ Ns2) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T3)) @ (cont @ Tr2)))))))) | (? [Tr13:dtree,Tr2:dtree,Ns13:(set @ n),T3:t]: (((A12 = (((insert @ n) @ (root @ Tr2)) @ Ns13)) & ((A23 = Tr2) & ((A33 = T3) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr2)) & (((gram_L805317441_inFr2 @ Ns13) @ Tr13) @ T3)))))))))))).
% 2.72/1.49 thf(fact_189_Inl__Inr__False, axiom, (! [A:$tType,B:$tType,X3:A,Y4:B]: (((((sum_Inl @ A) @ B) @ X3) != (((sum_Inr @ B) @ A) @ Y4))))).
% 2.72/1.49 thf(fact_190_Inr__Inl__False, axiom, (! [B:$tType,A:$tType,X3:B,Y4:A]: (((((sum_Inr @ B) @ A) @ X3) != (((sum_Inl @ A) @ B) @ Y4))))).
% 2.72/1.49 thf(fact_191_obj__sumE__f, axiom, (! [A:$tType,C:$tType,B:$tType,S2:B,F2:(((sum_sum @ A) @ C) > B),P:$o]: (((! [X2:A]: (((S2 = (F2 @ (((sum_Inl @ A) @ C) @ X2))) => P))) => ((! [X2:C]: (((S2 = (F2 @ (((sum_Inr @ C) @ A) @ X2))) => P))) => (! [X7:((sum_sum @ A) @ C)]: (((S2 = (F2 @ X7)) => P)))))))).
% 2.72/1.49 thf(fact_192_old_Osum_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((sum_sum @ A) @ B) > $o),Sum:((sum_sum @ A) @ B)]: (((! [A4:A]: ((P @ (((sum_Inl @ A) @ B) @ A4)))) => ((! [B4:B]: ((P @ (((sum_Inr @ B) @ A) @ B4)))) => (P @ Sum)))))).
% 2.72/1.49 thf(fact_193_old_Osum_Oexhaust, axiom, (! [A:$tType,B:$tType,Y4:((sum_sum @ A) @ B)]: (((! [A4:A]: ((Y4 != (((sum_Inl @ A) @ B) @ A4)))) => (~ ((! [B4:B]: ((Y4 != (((sum_Inr @ B) @ A) @ B4)))))))))).
% 2.72/1.49 thf(fact_194_split__sum__all, axiom, (! [B:$tType,A:$tType]: (((^ [P2:(((sum_sum @ A) @ B) > $o)]: ((! [X5:((sum_sum @ A) @ B)]: ((P2 @ X5))))) = (^ [P3:(((sum_sum @ A) @ B) > $o)]: (((! [X:A]: ((P3 @ (((sum_Inl @ A) @ B) @ X)))) & (! [X:B]: ((P3 @ (((sum_Inr @ B) @ A) @ X))))))))))).
% 2.72/1.49 thf(fact_195_split__sum__ex, axiom, (! [B:$tType,A:$tType]: (((^ [P2:(((sum_sum @ A) @ B) > $o)]: ((? [X5:((sum_sum @ A) @ B)]: ((P2 @ X5))))) = (^ [P3:(((sum_sum @ A) @ B) > $o)]: (((? [X:A]: ((P3 @ (((sum_Inl @ A) @ B) @ X)))) | (? [X:B]: ((P3 @ (((sum_Inr @ B) @ A) @ X))))))))))).
% 2.72/1.49 thf(fact_196_Inr__not__Inl, axiom, (! [B:$tType,A:$tType,B2:B,A3:A]: (((((sum_Inr @ B) @ A) @ B2) != (((sum_Inl @ A) @ B) @ A3))))).
% 2.72/1.49 thf(fact_197_sumE, axiom, (! [A:$tType,B:$tType,S2:((sum_sum @ A) @ B)]: (((! [X2:A]: ((S2 != (((sum_Inl @ A) @ B) @ X2)))) => (~ ((! [Y:B]: ((S2 != (((sum_Inr @ B) @ A) @ Y)))))))))).
% 2.72/1.49 thf(fact_198_old_Osum_Odistinct_I1_J, axiom, (! [A:$tType,B:$tType,A3:A,B7:B]: (((((sum_Inl @ A) @ B) @ A3) != (((sum_Inr @ B) @ A) @ B7))))).
% 2.72/1.49 thf(fact_199_old_Osum_Odistinct_I2_J, axiom, (! [B9:$tType,A7:$tType,B10:B9,A8:A7]: (((((sum_Inr @ B9) @ A7) @ B10) != (((sum_Inl @ A7) @ B9) @ A8))))).
% 2.72/1.49 thf(fact_200_sum_Odistinct_I1_J, axiom, (! [A:$tType,B:$tType,X1:A,X22:B]: (((((sum_Inl @ A) @ B) @ X1) != (((sum_Inr @ B) @ A) @ X22))))).
% 2.72/1.49 thf(fact_201_inFr_OBase, axiom, (! [Tr:dtree,Ns:(set @ n),T2:t]: (((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T2)) @ (cont @ Tr)) => (((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2)))))).
% 2.72/1.49 thf(fact_202_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)))))).
% 2.72/1.49 thf(fact_203_inFr__subtr, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2) => (? [Tr5:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr5) @ Tr) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T2)) @ (cont @ Tr5))))))))).
% 2.72/1.49 thf(fact_204_inFr_Ocases, axiom, (! [A1:(set @ n),A22:dtree,A32:t]: (((((gram_L1333338417e_inFr @ A1) @ A22) @ A32) => (((((member @ n) @ (root @ A22)) @ A1) => (~ ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ A32)) @ (cont @ A22))))) => (~ (((((member @ n) @ (root @ A22)) @ A1) => (! [Tr12:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ A22)) => (~ ((((gram_L1333338417e_inFr @ A1) @ Tr12) @ A32)))))))))))))).
% 2.72/1.49 thf(fact_205_inFr_Osimps, axiom, (gram_L1333338417e_inFr = (^ [A12:(set @ n),A23:dtree,A33:t]: (((? [Tr2:dtree,Ns2:(set @ n),T3:t]: (((A12 = Ns2) & ((A23 = Tr2) & ((A33 = T3) & ((((member @ n) @ (root @ Tr2)) @ Ns2) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T3)) @ (cont @ Tr2)))))))) | (? [Tr2:dtree,Ns2:(set @ n),Tr13:dtree,T3:t]: (((A12 = Ns2) & ((A23 = Tr2) & ((A33 = T3) & ((((member @ n) @ (root @ Tr2)) @ Ns2) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr2)) & (((gram_L1333338417e_inFr @ Ns2) @ Tr13) @ T3))))))))))))).
% 2.72/1.49 thf(fact_206_inFr_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:t,P:((set @ n) > (dtree > (t > $o)))]: (((((gram_L1333338417e_inFr @ X1) @ X22) @ X32) => ((! [Tr7:dtree,Ns4:(set @ n),T4:t]: (((((member @ n) @ (root @ Tr7)) @ Ns4) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T4)) @ (cont @ Tr7)) => (((P @ Ns4) @ Tr7) @ T4))))) => ((! [Tr7:dtree,Ns4:(set @ n),Tr12:dtree,T4:t]: (((((member @ n) @ (root @ Tr7)) @ Ns4) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr7)) => ((((gram_L1333338417e_inFr @ Ns4) @ Tr12) @ T4) => ((((P @ Ns4) @ Tr12) @ T4) => (((P @ Ns4) @ Tr7) @ T4))))))) => (((P @ X1) @ X22) @ X32))))))).
% 2.72/1.49 thf(fact_207_inFr2_Oinducts, axiom, (! [X1:(set @ n),X22:dtree,X32:t,P:((set @ n) > (dtree > (t > $o)))]: (((((gram_L805317441_inFr2 @ X1) @ X22) @ X32) => ((! [Tr7:dtree,Ns4:(set @ n),T4:t]: (((((member @ n) @ (root @ Tr7)) @ Ns4) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T4)) @ (cont @ Tr7)) => (((P @ Ns4) @ Tr7) @ T4))))) => ((! [Tr12:dtree,Tr7:dtree,Ns12:(set @ n),T4:t]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr7)) => ((((gram_L805317441_inFr2 @ Ns12) @ Tr12) @ T4) => ((((P @ Ns12) @ Tr12) @ T4) => (((P @ (((insert @ n) @ (root @ Tr7)) @ Ns12)) @ Tr7) @ T4)))))) => (((P @ X1) @ X22) @ X32))))))).
% 2.72/1.49 thf(fact_208_obj__sumE, axiom, (! [A:$tType,B:$tType,S2:((sum_sum @ A) @ B)]: (((! [X2:A]: ((S2 != (((sum_Inl @ A) @ B) @ X2)))) => (~ ((! [X2:B]: ((S2 != (((sum_Inr @ B) @ A) @ X2)))))))))).
% 2.72/1.49 thf(fact_209_Inl__cont__hsubst__neq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) != (root @ Tr0)) => (((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ ((gram_L1004374585hsubst @ Tr0) @ Tr))) = ((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ Tr))))))).
% 2.72/1.49 thf(fact_210_vimage__eq, axiom, (! [A:$tType,B:$tType,A3:A,F2:(A > B),B3:(set @ B)]: (((((member @ A) @ A3) @ ((((vimage @ A) @ B) @ F2) @ B3)) = (((member @ B) @ (F2 @ A3)) @ B3))))).
% 2.72/1.49 thf(fact_211_vimageI, axiom, (! [B:$tType,A:$tType,F2:(B > A),A3:B,B2:A,B3:(set @ A)]: ((((F2 @ A3) = B2) => ((((member @ A) @ B2) @ B3) => (((member @ B) @ A3) @ ((((vimage @ B) @ A) @ F2) @ B3))))))).
% 2.72/1.49 thf(fact_212_vimage__UNIV, axiom, (! [B:$tType,A:$tType,F2:(A > B)]: ((((((vimage @ A) @ B) @ F2) @ (top_top @ (set @ B))) = (top_top @ (set @ A)))))).
% 2.72/1.49 thf(fact_213_vimage__id, axiom, (! [A:$tType]: (((((vimage @ A) @ A) @ (id @ A)) = (id @ (set @ A)))))).
% 2.72/1.49 thf(fact_214_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))))))).
% 2.72/1.49 thf(fact_215_set_Ocompositionality, axiom, (! [C:$tType,B:$tType,A:$tType,F2:(C > B),G2:(B > A),Set:(set @ A)]: ((((((vimage @ C) @ B) @ F2) @ ((((vimage @ B) @ A) @ G2) @ Set)) = ((((vimage @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G2) @ F2)) @ Set))))).
% 2.72/1.49 thf(fact_216_vimage__comp, axiom, (! [A:$tType,B:$tType,C:$tType,F2:(A > B),G2:(B > C),X3:(set @ C)]: ((((((vimage @ A) @ B) @ F2) @ ((((vimage @ B) @ C) @ G2) @ X3)) = ((((vimage @ A) @ C) @ (((((comp @ B) @ C) @ A) @ G2) @ F2)) @ X3))))).
% 2.72/1.49 thf(fact_217_set_Ocomp, axiom, (! [A:$tType,B:$tType,C:$tType,F2:(C > B),G2:(B > A)]: (((((((comp @ (set @ B)) @ (set @ C)) @ (set @ A)) @ (((vimage @ C) @ B) @ F2)) @ (((vimage @ B) @ A) @ G2)) = (((vimage @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G2) @ F2)))))).
% 2.72/1.49 thf(fact_218_vimage__mono, axiom, (! [B:$tType,A:$tType,A2:(set @ A),B3:(set @ A),F2:(B > A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B3) => (((ord_less_eq @ (set @ B)) @ ((((vimage @ B) @ A) @ F2) @ A2)) @ ((((vimage @ B) @ A) @ F2) @ B3)))))).
% 2.72/1.49 thf(fact_219_vimage__Collect, axiom, (! [B:$tType,A:$tType,P:(B > $o),F2:(A > B),Q:(A > $o)]: (((! [X2:A]: (((P @ (F2 @ X2)) = (Q @ X2)))) => (((((vimage @ A) @ B) @ F2) @ ((collect @ B) @ P)) = ((collect @ A) @ Q)))))).
% 2.72/1.49 thf(fact_220_vimageI2, axiom, (! [B:$tType,A:$tType,F2:(B > A),A3:B,A2:(set @ A)]: (((((member @ A) @ (F2 @ A3)) @ A2) => (((member @ B) @ A3) @ ((((vimage @ B) @ A) @ F2) @ A2)))))).
% 2.72/1.49 thf(fact_221_vimageE, axiom, (! [A:$tType,B:$tType,A3:A,F2:(A > B),B3:(set @ B)]: (((((member @ A) @ A3) @ ((((vimage @ A) @ B) @ F2) @ B3)) => (((member @ B) @ (F2 @ A3)) @ B3))))).
% 2.72/1.49 thf(fact_222_vimageD, axiom, (! [A:$tType,B:$tType,A3:A,F2:(A > B),A2:(set @ B)]: (((((member @ A) @ A3) @ ((((vimage @ A) @ B) @ F2) @ A2)) => (((member @ B) @ (F2 @ A3)) @ A2))))).
% 2.72/1.49 thf(fact_223_not__arg__cong__Inr, axiom, (! [B:$tType,A:$tType,X3:A,Y4:A]: (((X3 != Y4) => ((((sum_Inr @ A) @ B) @ X3) != (((sum_Inr @ A) @ B) @ Y4)))))).
% 2.72/1.49 thf(fact_224_Inl__Inr__image__cong, axiom, (! [B:$tType,A:$tType,A2:(set @ ((sum_sum @ A) @ B)),B3:(set @ ((sum_sum @ A) @ B))]: (((((((vimage @ A) @ ((sum_sum @ A) @ B)) @ ((sum_Inl @ A) @ B)) @ A2) = ((((vimage @ A) @ ((sum_sum @ A) @ B)) @ ((sum_Inl @ A) @ B)) @ B3)) => ((((((vimage @ B) @ ((sum_sum @ A) @ B)) @ ((sum_Inr @ B) @ A)) @ A2) = ((((vimage @ B) @ ((sum_sum @ A) @ B)) @ ((sum_Inr @ B) @ A)) @ B3)) => (A2 = B3)))))).
% 2.72/1.49 thf(fact_225_inFr__hsubst__imp, axiom, (! [Ns:(set @ n),Tr0:dtree,Tr:dtree,T2:t]: (((((gram_L1333338417e_inFr @ Ns) @ ((gram_L1004374585hsubst @ Tr0) @ Tr)) @ T2) => ((((member @ t) @ T2) @ ((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ Tr0))) | ((((gram_L805317505_inFrr @ (((minus_minus @ (set @ n)) @ Ns) @ (((insert @ n) @ (root @ Tr0)) @ (bot_bot @ (set @ n))))) @ Tr0) @ T2) | (((gram_L1333338417e_inFr @ (((minus_minus @ (set @ n)) @ Ns) @ (((insert @ n) @ (root @ Tr0)) @ (bot_bot @ (set @ n))))) @ Tr) @ T2))))))).
% 2.72/1.49 thf(fact_226_bot__apply, axiom, (! [C:$tType,D:$tType]: ((((bot @ C) @ (type2 @ C)) => ((bot_bot @ (D > C)) = (^ [X:D]: ((bot_bot @ C)))))))).
% 2.72/1.49 thf(fact_227_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 2.72/1.49 thf(fact_228_all__not__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X:A]: ((~ ((((member @ A) @ X) @ A2))))) = (A2 = (bot_bot @ (set @ A))))))).
% 2.72/1.49 thf(fact_229_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X:A]: ((~ ((P @ X))))))))).
% 2.72/1.49 thf(fact_230_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X:A]: ((~ ((P @ X))))))))).
% 2.72/1.49 thf(fact_231_DiffI, axiom, (! [A:$tType,C2:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ A2) => ((~ ((((member @ A) @ C2) @ B3))) => (((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B3))))))).
% 2.72/1.49 thf(fact_232_Diff__iff, axiom, (! [A:$tType,C2:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B3)) = ((((member @ A) @ C2) @ A2) & (~ ((((member @ A) @ C2) @ B3)))))))).
% 2.72/1.49 thf(fact_233_Diff__idemp, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B3)) @ B3) = (((minus_minus @ (set @ A)) @ A2) @ B3))))).
% 2.72/1.49 thf(fact_234_subset__empty, axiom, (! [A:$tType,A2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = (A2 = (bot_bot @ (set @ A))))))).
% 2.72/1.49 thf(fact_235_empty__subsetI, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A2)))).
% 2.72/1.49 thf(fact_236_singletonI, axiom, (! [A:$tType,A3:A]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 2.72/1.49 thf(fact_237_Diff__empty, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = A2)))).
% 2.72/1.49 thf(fact_238_empty__Diff, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ (bot_bot @ (set @ A))) @ A2) = (bot_bot @ (set @ A)))))).
% 2.72/1.49 thf(fact_239_Diff__cancel, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ A2) = (bot_bot @ (set @ A)))))).
% 2.72/1.49 thf(fact_240_Diff__insert0, axiom, (! [A:$tType,X3:A,A2:(set @ A),B3:(set @ A)]: (((~ ((((member @ A) @ X3) @ A2))) => ((((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ X3) @ B3)) = (((minus_minus @ (set @ A)) @ A2) @ B3)))))).
% 2.72/1.49 thf(fact_241_insert__Diff1, axiom, (! [A:$tType,X3:A,B3:(set @ A),A2:(set @ A)]: (((((member @ A) @ X3) @ B3) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X3) @ A2)) @ B3) = (((minus_minus @ (set @ A)) @ A2) @ B3)))))).
% 2.72/1.49 thf(fact_242_vimage__empty, axiom, (! [B:$tType,A:$tType,F2:(A > B)]: ((((((vimage @ A) @ B) @ F2) @ (bot_bot @ (set @ B))) = (bot_bot @ (set @ A)))))).
% 2.72/1.49 thf(fact_243_singleton__insert__inj__eq, axiom, (! [A:$tType,B2:A,A3:A,A2:(set @ A)]: ((((((insert @ A) @ B2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A3) @ A2)) = ((A3 = B2) & (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.72/1.49 thf(fact_244_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A3:A,A2:(set @ A),B2:A]: ((((((insert @ A) @ A3) @ A2) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = ((A3 = B2) & (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.72/1.49 thf(fact_245_Diff__eq__empty__iff, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: ((((((minus_minus @ (set @ A)) @ A2) @ B3) = (bot_bot @ (set @ A))) = (((ord_less_eq @ (set @ A)) @ A2) @ B3))))).
% 2.72/1.49 thf(fact_246_insert__Diff__single, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((insert @ A) @ A3) @ (((minus_minus @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) = (((insert @ A) @ A3) @ A2))))).
% 2.72/1.49 thf(fact_247_Diff__UNIV, axiom, (! [A:$tType,A2:(set @ A)]: (((((minus_minus @ (set @ A)) @ A2) @ (top_top @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 2.72/1.49 thf(fact_248_vimage__singleton__eq, axiom, (! [A:$tType,B:$tType,A3:A,F2:(A > B),B2:B]: (((((member @ A) @ A3) @ ((((vimage @ A) @ B) @ F2) @ (((insert @ B) @ B2) @ (bot_bot @ (set @ B))))) = ((F2 @ A3) = B2))))).
% 2.72/1.49 thf(fact_249_vimage__Diff, axiom, (! [A:$tType,B:$tType,F2:(A > B),A2:(set @ B),B3:(set @ B)]: ((((((vimage @ A) @ B) @ F2) @ (((minus_minus @ (set @ B)) @ A2) @ B3)) = (((minus_minus @ (set @ A)) @ ((((vimage @ A) @ B) @ F2) @ A2)) @ ((((vimage @ A) @ B) @ F2) @ B3)))))).
% 2.72/1.49 thf(fact_250_inFr__hsubst__minus, axiom, (! [Ns:(set @ n),Tr0:dtree,Tr:dtree,T2:t]: (((((gram_L1333338417e_inFr @ (((minus_minus @ (set @ n)) @ Ns) @ (((insert @ n) @ (root @ Tr0)) @ (bot_bot @ (set @ n))))) @ Tr) @ T2) => (((gram_L1333338417e_inFr @ Ns) @ ((gram_L1004374585hsubst @ Tr0) @ Tr)) @ T2))))).
% 2.72/1.49 thf(fact_251_empty__not__UNIV, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) != (top_top @ (set @ A)))))).
% 2.72/1.49 thf(fact_252_DiffE, axiom, (! [A:$tType,C2:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B3)) => (~ (((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ B3)))))))).
% 2.72/1.49 thf(fact_253_DiffD1, axiom, (! [A:$tType,C2:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B3)) => (((member @ A) @ C2) @ A2))))).
% 2.72/1.49 thf(fact_254_DiffD2, axiom, (! [A:$tType,C2:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A2) @ B3)) => (~ ((((member @ A) @ C2) @ B3))))))).
% 2.72/1.49 thf(fact_255_emptyE, axiom, (! [A:$tType,A3:A]: ((~ ((((member @ A) @ A3) @ (bot_bot @ (set @ A)))))))).
% 2.72/1.49 thf(tcon_fun___Orderings_Oorder__top, axiom, (! [A7:$tType,A9:$tType]: ((((order_top @ A9) @ (type2 @ A9)) => ((order_top @ (A7 > A9)) @ (type2 @ (A7 > A9))))))).
% 2.72/1.49 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A9:$tType]: ((((preorder @ A9) @ (type2 @ A9)) => ((preorder @ (A7 > A9)) @ (type2 @ (A7 > A9))))))).
% 2.72/1.49 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A9:$tType]: ((((order @ A9) @ (type2 @ A9)) => ((order @ (A7 > A9)) @ (type2 @ (A7 > A9))))))).
% 2.72/1.49 thf(tcon_fun___Orderings_Otop, axiom, (! [A7:$tType,A9:$tType]: ((((top @ A9) @ (type2 @ A9)) => ((top @ (A7 > A9)) @ (type2 @ (A7 > A9))))))).
% 2.72/1.49 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A9:$tType]: ((((ord @ A9) @ (type2 @ A9)) => ((ord @ (A7 > A9)) @ (type2 @ (A7 > A9))))))).
% 2.72/1.49 thf(tcon_fun___Orderings_Obot, axiom, (! [A7:$tType,A9:$tType]: ((((bot @ A9) @ (type2 @ A9)) => ((bot @ (A7 > A9)) @ (type2 @ (A7 > A9))))))).
% 2.72/1.49 thf(tcon_Set_Oset___Orderings_Oorder__top_1, axiom, (! [A7:$tType]: (((order_top @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.72/1.49 thf(tcon_Set_Oset___Orderings_Opreorder_2, axiom, (! [A7:$tType]: (((preorder @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.72/1.49 thf(tcon_Set_Oset___Orderings_Oorder_3, axiom, (! [A7:$tType]: (((order @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.72/1.49 thf(tcon_Set_Oset___Orderings_Otop_4, axiom, (! [A7:$tType]: (((top @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.72/1.49 thf(tcon_Set_Oset___Orderings_Oord_5, axiom, (! [A7:$tType]: (((ord @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.72/1.49 thf(tcon_Set_Oset___Orderings_Obot_6, axiom, (! [A7:$tType]: (((bot @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.72/1.49 thf(tcon_HOL_Obool___Orderings_Oorder__top_7, axiom, ((order_top @ $o) @ (type2 @ $o))).
% 2.72/1.49 thf(tcon_HOL_Obool___Orderings_Opreorder_8, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.72/1.49 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.72/1.49 thf(tcon_HOL_Obool___Orderings_Oorder_9, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.72/1.49 thf(tcon_HOL_Obool___Orderings_Otop_10, axiom, ((top @ $o) @ (type2 @ $o))).
% 2.72/1.49 thf(tcon_HOL_Obool___Orderings_Oord_11, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.72/1.49 thf(tcon_HOL_Obool___Orderings_Obot_12, axiom, ((bot @ $o) @ (type2 @ $o))).
% 2.72/1.49 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.72/1.49 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y4:A]: ((((((if @ A) @ $false) @ X3) @ Y4) = Y4)))).
% 2.72/1.49 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y4:A]: ((((((if @ A) @ $true) @ X3) @ Y4) = X3)))).
% 2.72/1.49 thf(conj_0, conjecture, ((f @ (root @ tr)) = tr)).
% 2.72/1.49 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.dpsNr913pg/DTF2DTF23682.p
% 2.72/1.49 ------------------------
% 3.00/1.51 ---- Cleaned THF ---
% 3.00/1.51 thf(ty_t_Sum__Type_Osum,type,
% 3.00/1.51 sum_sum: $tType > $tType > $tType ).
% 3.00/1.51
% 3.00/1.51 thf(ty_t_DTree_Odtree,type,
% 3.00/1.51 dtree: $tType ).
% 3.00/1.51
% 3.00/1.51 thf(ty_t_Set_Oset,type,
% 3.00/1.51 set: $tType > $tType ).
% 3.00/1.51
% 3.00/1.51 thf(ty_t_DTree_OT,type,
% 3.00/1.51 t: $tType ).
% 3.00/1.51
% 3.00/1.51 thf(ty_t_DTree_ON,type,
% 3.00/1.51 n: $tType ).
% 3.00/1.51
% 3.00/1.51 thf(ty_t_itself,type,
% 3.00/1.51 itself: $tType > $tType ).
% 3.00/1.51
% 3.00/1.51 thf(sy_cl_HOL_Otype,type,
% 3.00/1.51 type:
% 3.00/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_cl_Orderings_Obot,type,
% 3.00/1.51 bot:
% 3.00/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_cl_Orderings_Oord,type,
% 3.00/1.51 ord:
% 3.00/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_cl_Orderings_Otop,type,
% 3.00/1.51 top:
% 3.00/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_cl_Orderings_Oorder,type,
% 3.00/1.51 order:
% 3.00/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_cl_Orderings_Olinorder,type,
% 3.00/1.51 linorder:
% 3.00/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_cl_Orderings_Opreorder,type,
% 3.00/1.51 preorder:
% 3.00/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_cl_Orderings_Oorder__top,type,
% 3.00/1.51 order_top:
% 3.00/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_DTree_ONode,type,
% 3.00/1.51 node: n > ( set @ ( sum_sum @ t @ dtree ) ) > dtree ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_DTree_Ocont,type,
% 3.00/1.51 cont: dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_DTree_Ocorec,type,
% 3.00/1.51 corec:
% 3.00/1.51 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) ) ) > A > dtree ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_DTree_Odtree_Oroot,type,
% 3.00/1.51 root: dtree > n ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_DTree_Ounfold,type,
% 3.00/1.51 unfold:
% 3.00/1.51 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ A ) ) ) > A > dtree ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Fun_Ocomp,type,
% 3.00/1.51 comp:
% 3.00/1.51 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Fun_Oid,type,
% 3.00/1.51 id:
% 3.00/1.51 !>[A: $tType] : ( A > A ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OS,type,
% 3.00/1.51 gram_L1451583635elle_S: n > ( set @ ( sum_sum @ t @ n ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr,type,
% 3.00/1.51 gram_L1231612515_deftr: n > dtree ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst,type,
% 3.00/1.51 gram_L1004374585hsubst: dtree > dtree > dtree ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c,type,
% 3.00/1.51 gram_L1905609002ubst_c: dtree > dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r,type,
% 3.00/1.51 gram_L1905609017ubst_r: dtree > n ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr,type,
% 3.00/1.51 gram_L1333338417e_inFr: ( set @ n ) > dtree > t > $o ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2,type,
% 3.00/1.51 gram_L805317441_inFr2: ( set @ n ) > dtree > t > $o ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFrr,type,
% 3.00/1.51 gram_L805317505_inFrr: ( set @ n ) > dtree > t > $o ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr,type,
% 3.00/1.51 gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oreg,type,
% 3.00/1.51 gram_L1918716148le_reg: ( n > dtree ) > dtree > $o ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oregular,type,
% 3.00/1.51 gram_L646766332egular: dtree > $o ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr,type,
% 3.00/1.51 gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr2,type,
% 3.00/1.51 gram_L1283001940subtr2: ( set @ n ) > dtree > dtree > $o ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OsubtrOf,type,
% 3.00/1.51 gram_L1614515765ubtrOf: dtree > n > dtree ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf,type,
% 3.00/1.51 gram_L864798063lle_wf: dtree > $o ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 3.00/1.51 minus_minus:
% 3.00/1.51 !>[A: $tType] : ( A > A > A ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_If,type,
% 3.00/1.51 if:
% 3.00/1.51 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Orderings_Obot__class_Obot,type,
% 3.00/1.51 bot_bot:
% 3.00/1.51 !>[A: $tType] : A ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.00/1.51 ord_less_eq:
% 3.00/1.51 !>[A: $tType] : ( A > A > $o ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Orderings_Otop__class_Otop,type,
% 3.00/1.51 top_top:
% 3.00/1.51 !>[A: $tType] : A ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Pure_Otype,type,
% 3.00/1.51 type2:
% 3.00/1.51 !>[A: $tType] : ( itself @ A ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Set_OCollect,type,
% 3.00/1.51 collect:
% 3.00/1.51 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Set_Oinsert,type,
% 3.00/1.51 insert:
% 3.00/1.51 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Set_Ovimage,type,
% 3.00/1.51 vimage:
% 3.00/1.51 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Sum__Type_OInl,type,
% 3.00/1.51 sum_Inl:
% 3.00/1.51 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Sum__Type_OInr,type,
% 3.00/1.51 sum_Inr:
% 3.00/1.51 !>[B: $tType,A: $tType] : ( B > ( sum_sum @ A @ B ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum,type,
% 3.00/1.51 sum_rec_sum:
% 3.00/1.51 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_Typedef_Otype__definition,type,
% 3.00/1.51 type_definition:
% 3.00/1.51 !>[B: $tType,A: $tType] : ( ( B > A ) > ( A > B ) > ( set @ A ) > $o ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_c_member,type,
% 3.00/1.51 member:
% 3.00/1.51 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.00/1.51
% 3.00/1.51 thf(sy_v_f,type,
% 3.00/1.51 f: n > dtree ).
% 3.00/1.51
% 3.00/1.51 thf(sy_v_tr,type,
% 3.00/1.51 tr: dtree ).
% 3.00/1.51
% 3.00/1.51 thf(fact_0_assms,axiom,
% 3.00/1.51 gram_L1918716148le_reg @ f @ tr ).
% 3.00/1.51
% 3.00/1.51 thf(fact_1_hsubst__r__def,axiom,
% 3.00/1.51 gram_L1905609017ubst_r = root ).
% 3.00/1.51
% 3.00/1.51 thf(fact_2_root__deftr,axiom,
% 3.00/1.51 ! [N: n] :
% 3.00/1.51 ( ( root @ ( gram_L1231612515_deftr @ N ) )
% 3.00/1.51 = N ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_3_root__hsubst,axiom,
% 3.00/1.51 ! [Tr0: dtree,Tr: dtree] :
% 3.00/1.51 ( ( root @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 3.00/1.51 = ( root @ Tr ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_4_inFr2__root__in,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 3.00/1.51 ( ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 )
% 3.00/1.51 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_5_inItr_OBase,axiom,
% 3.00/1.51 ! [Tr: dtree,Ns: set @ n] :
% 3.00/1.51 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.00/1.51 => ( gram_L830233218_inItr @ Ns @ Tr @ ( root @ Tr ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_6_inItr__root__in,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr: dtree,N: n] :
% 3.00/1.51 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 3.00/1.51 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_7_regular__def2,axiom,
% 3.00/1.51 ( gram_L646766332egular
% 3.00/1.51 = ( ^ [Tr2: dtree] :
% 3.00/1.51 ? [F: n > dtree] :
% 3.00/1.51 ( ( gram_L1918716148le_reg @ F @ Tr2 )
% 3.00/1.51 & ! [N2: n] :
% 3.00/1.51 ( ( root @ ( F @ N2 ) )
% 3.00/1.51 = N2 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_8_hsubst__eq,axiom,
% 3.00/1.51 ! [Tr: dtree,Tr0: dtree] :
% 3.00/1.51 ( ( ( root @ Tr )
% 3.00/1.51 = ( root @ Tr0 ) )
% 3.00/1.51 => ( ( gram_L1004374585hsubst @ Tr0 @ Tr )
% 3.00/1.51 = ( gram_L1004374585hsubst @ Tr0 @ Tr0 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_9_subtr2_ORefl,axiom,
% 3.00/1.51 ! [Tr: dtree,Ns: set @ n] :
% 3.00/1.51 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.00/1.51 => ( gram_L1283001940subtr2 @ Ns @ Tr @ Tr ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_10_subtr2__rootL__in,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 3.00/1.51 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 3.00/1.51 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_11_subtr2__rootR__in,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 3.00/1.51 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 3.00/1.51 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_12_inFr__root__in,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 3.00/1.51 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 3.00/1.51 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_13_inFr__inFr2,axiom,
% 3.00/1.51 gram_L1333338417e_inFr = gram_L805317441_inFr2 ).
% 3.00/1.51
% 3.00/1.51 thf(fact_14_regular__def,axiom,
% 3.00/1.51 ( gram_L646766332egular
% 3.00/1.51 = ( ^ [Tr2: dtree] :
% 3.00/1.51 ? [F: n > dtree] : ( gram_L1918716148le_reg @ F @ Tr2 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_15_subtr2__trans,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr3: dtree] :
% 3.00/1.51 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 3.00/1.51 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr3 )
% 3.00/1.51 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_16_inFr__hsubst__notin,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr: dtree,T2: t,Tr0: dtree] :
% 3.00/1.51 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 3.00/1.51 => ( ~ ( member @ n @ ( root @ Tr0 ) @ Ns )
% 3.00/1.51 => ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T2 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_17_not__root__inFr,axiom,
% 3.00/1.51 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 3.00/1.51 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 3.00/1.51 => ~ ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_18_hsubst__def,axiom,
% 3.00/1.51 ( gram_L1004374585hsubst
% 3.00/1.51 = ( ^ [Tr02: dtree] : ( unfold @ dtree @ gram_L1905609017ubst_r @ ( gram_L1905609002ubst_c @ Tr02 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_19_reg__def2,axiom,
% 3.00/1.51 ( gram_L1918716148le_reg
% 3.00/1.51 = ( ^ [F: n > dtree,Tr2: dtree] :
% 3.00/1.51 ! [Ns2: set @ n,Tr4: dtree] :
% 3.00/1.51 ( ( gram_L716654942_subtr @ Ns2 @ Tr4 @ Tr2 )
% 3.00/1.51 => ( Tr4
% 3.00/1.51 = ( F @ ( root @ Tr4 ) ) ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_20_inItr__subtr,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr: dtree,N: n] :
% 3.00/1.51 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 3.00/1.51 => ? [Tr5: dtree] :
% 3.00/1.51 ( ( gram_L716654942_subtr @ Ns @ Tr5 @ Tr )
% 3.00/1.51 & ( ( root @ Tr5 )
% 3.00/1.51 = N ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_21_root__o__subst,axiom,
% 3.00/1.51 ! [Tr0: dtree] :
% 3.00/1.51 ( ( comp @ dtree @ n @ dtree @ root @ ( gram_L1004374585hsubst @ Tr0 ) )
% 3.00/1.51 = root ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_22_wf__deftr,axiom,
% 3.00/1.51 ! [N: n] : ( gram_L864798063lle_wf @ ( gram_L1231612515_deftr @ N ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_23_wf__hsubst,axiom,
% 3.00/1.51 ! [Tr0: dtree,Tr: dtree] :
% 3.00/1.51 ( ( gram_L864798063lle_wf @ Tr0 )
% 3.00/1.51 => ( ( gram_L864798063lle_wf @ Tr )
% 3.00/1.51 => ( gram_L864798063lle_wf @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_24_subtr__inItr,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr: dtree,N: n,Tr1: dtree] :
% 3.00/1.51 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 3.00/1.51 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 3.00/1.51 => ( gram_L830233218_inItr @ Ns @ Tr1 @ N ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_25_subtr__subtr2,axiom,
% 3.00/1.51 gram_L716654942_subtr = gram_L1283001940subtr2 ).
% 3.00/1.51
% 3.00/1.51 thf(fact_26_subtr__inFr,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr: dtree,T2: t,Tr1: dtree] :
% 3.00/1.51 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 3.00/1.51 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 3.00/1.51 => ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_27_root__Node,axiom,
% 3.00/1.51 ! [N: n,As: set @ ( sum_sum @ t @ dtree )] :
% 3.00/1.51 ( ( root @ ( node @ N @ As ) )
% 3.00/1.51 = N ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_28_inFr2__mono,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr: dtree,T2: t,Ns3: set @ n] :
% 3.00/1.51 ( ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 )
% 3.00/1.51 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 3.00/1.51 => ( gram_L805317441_inFr2 @ Ns3 @ Tr @ T2 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_29_subtr__trans,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr3: dtree] :
% 3.00/1.51 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 3.00/1.51 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr3 )
% 3.00/1.51 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_30_subtr__mono,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Ns3: set @ n] :
% 3.00/1.51 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 3.00/1.51 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 3.00/1.51 => ( gram_L716654942_subtr @ Ns3 @ Tr1 @ Tr22 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_31_wf__subtr,axiom,
% 3.00/1.51 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 3.00/1.51 ( ( gram_L864798063lle_wf @ Tr1 )
% 3.00/1.51 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 3.00/1.51 => ( gram_L864798063lle_wf @ Tr ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_32_unfold_I1_J,axiom,
% 3.00/1.51 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ A ) ),B2: A] :
% 3.00/1.51 ( ( root @ ( unfold @ A @ Rt @ Ct @ B2 ) )
% 3.00/1.51 = ( Rt @ B2 ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_33_subtr_ORefl,axiom,
% 3.00/1.51 ! [Tr: dtree,Ns: set @ n] :
% 3.00/1.51 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.00/1.51 => ( gram_L716654942_subtr @ Ns @ Tr @ Tr ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_34_subtr__rootL__in,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 3.00/1.51 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 3.00/1.51 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_35_subtr__rootR__in,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 3.00/1.51 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 3.00/1.51 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_36_inFr__mono,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr: dtree,T2: t,Ns3: set @ n] :
% 3.00/1.51 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 3.00/1.51 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 3.00/1.51 => ( gram_L1333338417e_inFr @ Ns3 @ Tr @ T2 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_37_subtr2__mono,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Ns3: set @ n] :
% 3.00/1.51 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 3.00/1.51 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 3.00/1.51 => ( gram_L1283001940subtr2 @ Ns3 @ Tr1 @ Tr22 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_38_inItr__mono,axiom,
% 3.00/1.51 ! [Ns: set @ n,Tr: dtree,N: n,Ns3: set @ n] :
% 3.00/1.51 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 3.00/1.51 => ( ( ord_less_eq @ ( set @ n ) @ Ns @ Ns3 )
% 3.00/1.51 => ( gram_L830233218_inItr @ Ns3 @ Tr @ N ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_39_comp__apply,axiom,
% 3.00/1.51 ! [C: $tType,A: $tType,B: $tType] :
% 3.00/1.51 ( ( comp @ B @ A @ C )
% 3.00/1.51 = ( ^ [F: B > A,G: C > B,X: C] : ( F @ ( G @ X ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_40_subset__antisym,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 3.00/1.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 3.00/1.51 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A2 )
% 3.00/1.51 => ( A2 = B3 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_41_subsetI,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 3.00/1.51 ( ! [X2: A] :
% 3.00/1.51 ( ( member @ A @ X2 @ A2 )
% 3.00/1.51 => ( member @ A @ X2 @ B3 ) )
% 3.00/1.51 => ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_42_order__refl,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( preorder @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_43_reg__def,axiom,
% 3.00/1.51 ( gram_L1918716148le_reg
% 3.00/1.51 = ( ^ [F: n > dtree,Tr2: dtree] :
% 3.00/1.51 ! [Tr4: dtree] :
% 3.00/1.51 ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr4 @ Tr2 )
% 3.00/1.51 => ( Tr4
% 3.00/1.51 = ( F @ ( root @ Tr4 ) ) ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_44_rewriteR__comp__comp2,axiom,
% 3.00/1.51 ! [C: $tType,B: $tType,E: $tType,D: $tType,A: $tType,G2: C > B,H: A > C,R1: D > B,R2: A > D,F2: B > E,L: D > E] :
% 3.00/1.51 ( ( ( comp @ C @ B @ A @ G2 @ H )
% 3.00/1.51 = ( comp @ D @ B @ A @ R1 @ R2 ) )
% 3.00/1.51 => ( ( ( comp @ B @ E @ D @ F2 @ R1 )
% 3.00/1.51 = L )
% 3.00/1.51 => ( ( comp @ C @ E @ A @ ( comp @ B @ E @ C @ F2 @ G2 ) @ H )
% 3.00/1.51 = ( comp @ D @ E @ A @ L @ R2 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_45_mem__Collect__eq,axiom,
% 3.00/1.51 ! [A: $tType,A3: A,P: A > $o] :
% 3.00/1.51 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 3.00/1.51 = ( P @ A3 ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_46_Collect__mem__eq,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A] :
% 3.00/1.51 ( ( collect @ A
% 3.00/1.51 @ ^ [X: A] : ( member @ A @ X @ A2 ) )
% 3.00/1.51 = A2 ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_47_Collect__cong,axiom,
% 3.00/1.51 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.00/1.51 ( ! [X2: A] :
% 3.00/1.51 ( ( P @ X2 )
% 3.00/1.51 = ( Q @ X2 ) )
% 3.00/1.51 => ( ( collect @ A @ P )
% 3.00/1.51 = ( collect @ A @ Q ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_48_ext,axiom,
% 3.00/1.51 ! [B: $tType,A: $tType,F2: A > B,G2: A > B] :
% 3.00/1.51 ( ! [X2: A] :
% 3.00/1.51 ( ( F2 @ X2 )
% 3.00/1.51 = ( G2 @ X2 ) )
% 3.00/1.51 => ( F2 = G2 ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_49_rewriteL__comp__comp2,axiom,
% 3.00/1.51 ! [A: $tType,C: $tType,B: $tType,D: $tType,E: $tType,F2: C > B,G2: A > C,L1: D > B,L2: A > D,H: E > A,R: E > D] :
% 3.00/1.51 ( ( ( comp @ C @ B @ A @ F2 @ G2 )
% 3.00/1.51 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 3.00/1.51 => ( ( ( comp @ A @ D @ E @ L2 @ H )
% 3.00/1.51 = R )
% 3.00/1.51 => ( ( comp @ C @ B @ E @ F2 @ ( comp @ A @ C @ E @ G2 @ H ) )
% 3.00/1.51 = ( comp @ D @ B @ E @ L1 @ R ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_50_rewriteR__comp__comp,axiom,
% 3.00/1.51 ! [C: $tType,D: $tType,B: $tType,A: $tType,G2: C > B,H: A > C,R: A > B,F2: B > D] :
% 3.00/1.51 ( ( ( comp @ C @ B @ A @ G2 @ H )
% 3.00/1.51 = R )
% 3.00/1.51 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F2 @ G2 ) @ H )
% 3.00/1.51 = ( comp @ B @ D @ A @ F2 @ R ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_51_rewriteL__comp__comp,axiom,
% 3.00/1.51 ! [C: $tType,B: $tType,A: $tType,D: $tType,F2: C > B,G2: A > C,L: A > B,H: D > A] :
% 3.00/1.51 ( ( ( comp @ C @ B @ A @ F2 @ G2 )
% 3.00/1.51 = L )
% 3.00/1.51 => ( ( comp @ C @ B @ D @ F2 @ ( comp @ A @ C @ D @ G2 @ H ) )
% 3.00/1.51 = ( comp @ A @ B @ D @ L @ H ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_52_top__apply,axiom,
% 3.00/1.51 ! [C: $tType,D: $tType] :
% 3.00/1.51 ( ( top @ C @ ( type2 @ C ) )
% 3.00/1.51 => ( ( top_top @ ( D > C ) )
% 3.00/1.51 = ( ^ [X: D] : ( top_top @ C ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_53_UNIV__I,axiom,
% 3.00/1.51 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_54_UNIV__eq__I,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A] :
% 3.00/1.51 ( ! [X2: A] : ( member @ A @ X2 @ A2 )
% 3.00/1.51 => ( ( top_top @ ( set @ A ) )
% 3.00/1.51 = A2 ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_55_UNIV__witness,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ? [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_56_top__greatest,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( order_top @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ ( top_top @ A ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_57_top_Oextremum__unique,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( order_top @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [A3: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A3 )
% 3.00/1.51 = ( A3
% 3.00/1.51 = ( top_top @ A ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_58_top_Oextremum__uniqueI,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( order_top @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [A3: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A3 )
% 3.00/1.51 => ( A3
% 3.00/1.51 = ( top_top @ A ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_59_subset__UNIV,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_60_le__funD,axiom,
% 3.00/1.51 ! [B: $tType,A: $tType] :
% 3.00/1.51 ( ( ord @ B @ ( type2 @ B ) )
% 3.00/1.51 => ! [F2: A > B,G2: A > B,X3: A] :
% 3.00/1.51 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 3.00/1.51 => ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_61_le__funE,axiom,
% 3.00/1.51 ! [B: $tType,A: $tType] :
% 3.00/1.51 ( ( ord @ B @ ( type2 @ B ) )
% 3.00/1.51 => ! [F2: A > B,G2: A > B,X3: A] :
% 3.00/1.51 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 3.00/1.51 => ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_62_le__funI,axiom,
% 3.00/1.51 ! [B: $tType,A: $tType] :
% 3.00/1.51 ( ( ord @ B @ ( type2 @ B ) )
% 3.00/1.51 => ! [F2: A > B,G2: A > B] :
% 3.00/1.51 ( ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
% 3.00/1.51 => ( ord_less_eq @ ( A > B ) @ F2 @ G2 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_63_le__fun__def,axiom,
% 3.00/1.51 ! [B: $tType,A: $tType] :
% 3.00/1.51 ( ( ord @ B @ ( type2 @ B ) )
% 3.00/1.51 => ( ( ord_less_eq @ ( A > B ) )
% 3.00/1.51 = ( ^ [F: A > B,G: A > B] :
% 3.00/1.51 ! [X: A] : ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_64_order__subst1,axiom,
% 3.00/1.51 ! [A: $tType,B: $tType] :
% 3.00/1.51 ( ( ( order @ B @ ( type2 @ B ) )
% 3.00/1.51 & ( order @ A @ ( type2 @ A ) ) )
% 3.00/1.51 => ! [A3: A,F2: B > A,B2: B,C2: B] :
% 3.00/1.51 ( ( ord_less_eq @ A @ A3 @ ( F2 @ B2 ) )
% 3.00/1.51 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 3.00/1.51 => ( ! [X2: B,Y: B] :
% 3.00/1.51 ( ( ord_less_eq @ B @ X2 @ Y )
% 3.00/1.51 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 3.00/1.51 => ( ord_less_eq @ A @ A3 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_65_order__subst2,axiom,
% 3.00/1.51 ! [A: $tType,C: $tType] :
% 3.00/1.51 ( ( ( order @ C @ ( type2 @ C ) )
% 3.00/1.51 & ( order @ A @ ( type2 @ A ) ) )
% 3.00/1.51 => ! [A3: A,B2: A,F2: A > C,C2: C] :
% 3.00/1.51 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.00/1.51 => ( ( ord_less_eq @ C @ ( F2 @ B2 ) @ C2 )
% 3.00/1.51 => ( ! [X2: A,Y: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ X2 @ Y )
% 3.00/1.51 => ( ord_less_eq @ C @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 3.00/1.51 => ( ord_less_eq @ C @ ( F2 @ A3 ) @ C2 ) ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_66_ord__eq__le__subst,axiom,
% 3.00/1.51 ! [A: $tType,B: $tType] :
% 3.00/1.51 ( ( ( ord @ B @ ( type2 @ B ) )
% 3.00/1.51 & ( ord @ A @ ( type2 @ A ) ) )
% 3.00/1.51 => ! [A3: A,F2: B > A,B2: B,C2: B] :
% 3.00/1.51 ( ( A3
% 3.00/1.51 = ( F2 @ B2 ) )
% 3.00/1.51 => ( ( ord_less_eq @ B @ B2 @ C2 )
% 3.00/1.51 => ( ! [X2: B,Y: B] :
% 3.00/1.51 ( ( ord_less_eq @ B @ X2 @ Y )
% 3.00/1.51 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 3.00/1.51 => ( ord_less_eq @ A @ A3 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_67_ord__le__eq__subst,axiom,
% 3.00/1.51 ! [A: $tType,B: $tType] :
% 3.00/1.51 ( ( ( ord @ B @ ( type2 @ B ) )
% 3.00/1.51 & ( ord @ A @ ( type2 @ A ) ) )
% 3.00/1.51 => ! [A3: A,B2: A,F2: A > B,C2: B] :
% 3.00/1.51 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.00/1.51 => ( ( ( F2 @ B2 )
% 3.00/1.51 = C2 )
% 3.00/1.51 => ( ! [X2: A,Y: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ X2 @ Y )
% 3.00/1.51 => ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( F2 @ Y ) ) )
% 3.00/1.51 => ( ord_less_eq @ B @ ( F2 @ A3 ) @ C2 ) ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_68_eq__iff,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( order @ A @ ( type2 @ A ) )
% 3.00/1.51 => ( ( ^ [Y2: A,Z: A] : ( Y2 = Z ) )
% 3.00/1.51 = ( ^ [X: A,Y3: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ X @ Y3 )
% 3.00/1.51 & ( ord_less_eq @ A @ Y3 @ X ) ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_69_antisym,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( order @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [X3: A,Y4: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 3.00/1.51 => ( ( ord_less_eq @ A @ Y4 @ X3 )
% 3.00/1.51 => ( X3 = Y4 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_70_linear,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( linorder @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [X3: A,Y4: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 3.00/1.51 | ( ord_less_eq @ A @ Y4 @ X3 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_71_eq__refl,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( preorder @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [X3: A,Y4: A] :
% 3.00/1.51 ( ( X3 = Y4 )
% 3.00/1.51 => ( ord_less_eq @ A @ X3 @ Y4 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_72_le__cases,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( linorder @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [X3: A,Y4: A] :
% 3.00/1.51 ( ~ ( ord_less_eq @ A @ X3 @ Y4 )
% 3.00/1.51 => ( ord_less_eq @ A @ Y4 @ X3 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_73_order_Otrans,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( order @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [A3: A,B2: A,C2: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.00/1.51 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 3.00/1.51 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_74_le__cases3,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( linorder @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [X3: A,Y4: A,Z2: A] :
% 3.00/1.51 ( ( ( ord_less_eq @ A @ X3 @ Y4 )
% 3.00/1.51 => ~ ( ord_less_eq @ A @ Y4 @ Z2 ) )
% 3.00/1.51 => ( ( ( ord_less_eq @ A @ Y4 @ X3 )
% 3.00/1.51 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 3.00/1.51 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 3.00/1.51 => ~ ( ord_less_eq @ A @ Z2 @ Y4 ) )
% 3.00/1.51 => ( ( ( ord_less_eq @ A @ Z2 @ Y4 )
% 3.00/1.51 => ~ ( ord_less_eq @ A @ Y4 @ X3 ) )
% 3.00/1.51 => ( ( ( ord_less_eq @ A @ Y4 @ Z2 )
% 3.00/1.51 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 3.00/1.51 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 3.00/1.51 => ~ ( ord_less_eq @ A @ X3 @ Y4 ) ) ) ) ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_75_antisym__conv,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( order @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [Y4: A,X3: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ Y4 @ X3 )
% 3.00/1.51 => ( ( ord_less_eq @ A @ X3 @ Y4 )
% 3.00/1.51 = ( X3 = Y4 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_76_ord__eq__le__trans,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( ord @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [A3: A,B2: A,C2: A] :
% 3.00/1.51 ( ( A3 = B2 )
% 3.00/1.51 => ( ( ord_less_eq @ A @ B2 @ C2 )
% 3.00/1.51 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_77_ord__le__eq__trans,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( ord @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [A3: A,B2: A,C2: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.00/1.51 => ( ( B2 = C2 )
% 3.00/1.51 => ( ord_less_eq @ A @ A3 @ C2 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_78_order__class_Oorder_Oantisym,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( order @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [A3: A,B2: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.00/1.51 => ( ( ord_less_eq @ A @ B2 @ A3 )
% 3.00/1.51 => ( A3 = B2 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_79_order__trans,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( preorder @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [X3: A,Y4: A,Z2: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 3.00/1.51 => ( ( ord_less_eq @ A @ Y4 @ Z2 )
% 3.00/1.51 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_80_dual__order_Orefl,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( order @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_81_linorder__wlog,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( linorder @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [P: A > A > $o,A3: A,B2: A] :
% 3.00/1.51 ( ! [A4: A,B4: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ A4 @ B4 )
% 3.00/1.51 => ( P @ A4 @ B4 ) )
% 3.00/1.51 => ( ! [A4: A,B4: A] :
% 3.00/1.51 ( ( P @ B4 @ A4 )
% 3.00/1.51 => ( P @ A4 @ B4 ) )
% 3.00/1.51 => ( P @ A3 @ B2 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_82_dual__order_Otrans,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( order @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [B2: A,A3: A,C2: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ B2 @ A3 )
% 3.00/1.51 => ( ( ord_less_eq @ A @ C2 @ B2 )
% 3.00/1.51 => ( ord_less_eq @ A @ C2 @ A3 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_83_dual__order_Oantisym,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( order @ A @ ( type2 @ A ) )
% 3.00/1.51 => ! [B2: A,A3: A] :
% 3.00/1.51 ( ( ord_less_eq @ A @ B2 @ A3 )
% 3.00/1.51 => ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.00/1.51 => ( A3 = B2 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_84_set__mp,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A,B3: set @ A,X3: A] :
% 3.00/1.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 3.00/1.51 => ( ( member @ A @ X3 @ A2 )
% 3.00/1.51 => ( member @ A @ X3 @ B3 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_85_in__mono,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A,B3: set @ A,X3: A] :
% 3.00/1.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 3.00/1.51 => ( ( member @ A @ X3 @ A2 )
% 3.00/1.51 => ( member @ A @ X3 @ B3 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_86_subsetD,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A,B3: set @ A,C2: A] :
% 3.00/1.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 3.00/1.51 => ( ( member @ A @ C2 @ A2 )
% 3.00/1.51 => ( member @ A @ C2 @ B3 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_87_subsetCE,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A,B3: set @ A,C2: A] :
% 3.00/1.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 3.00/1.51 => ( ( member @ A @ C2 @ A2 )
% 3.00/1.51 => ( member @ A @ C2 @ B3 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_88_equalityE,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 3.00/1.51 ( ( A2 = B3 )
% 3.00/1.51 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 3.00/1.51 => ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A2 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_89_subset__eq,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( ord_less_eq @ ( set @ A ) )
% 3.00/1.51 = ( ^ [A5: set @ A,B5: set @ A] :
% 3.00/1.51 ! [X: A] :
% 3.00/1.51 ( ( member @ A @ X @ A5 )
% 3.00/1.51 => ( member @ A @ X @ B5 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_90_equalityD1,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 3.00/1.51 ( ( A2 = B3 )
% 3.00/1.51 => ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_91_equalityD2,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 3.00/1.51 ( ( A2 = B3 )
% 3.00/1.51 => ( ord_less_eq @ ( set @ A ) @ B3 @ A2 ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_92_set__rev__mp,axiom,
% 3.00/1.51 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 3.00/1.51 ( ( member @ A @ X3 @ A2 )
% 3.00/1.51 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 3.00/1.51 => ( member @ A @ X3 @ B3 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_93_subset__iff,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( ord_less_eq @ ( set @ A ) )
% 3.00/1.51 = ( ^ [A5: set @ A,B5: set @ A] :
% 3.00/1.51 ! [T3: A] :
% 3.00/1.51 ( ( member @ A @ T3 @ A5 )
% 3.00/1.51 => ( member @ A @ T3 @ B5 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_94_rev__subsetD,axiom,
% 3.00/1.51 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 3.00/1.51 ( ( member @ A @ C2 @ A2 )
% 3.00/1.51 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 3.00/1.51 => ( member @ A @ C2 @ B3 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_95_subset__refl,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_96_Collect__mono,axiom,
% 3.00/1.51 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.00/1.51 ( ! [X2: A] :
% 3.00/1.51 ( ( P @ X2 )
% 3.00/1.51 => ( Q @ X2 ) )
% 3.00/1.51 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_97_subset__trans,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A,B3: set @ A,C3: set @ A] :
% 3.00/1.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 3.00/1.51 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C3 )
% 3.00/1.51 => ( ord_less_eq @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_98_set__eq__subset,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( ^ [Y2: set @ A,Z: set @ A] : ( Y2 = Z ) )
% 3.00/1.51 = ( ^ [A5: set @ A,B5: set @ A] :
% 3.00/1.51 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 3.00/1.51 & ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_99_contra__subsetD,axiom,
% 3.00/1.51 ! [A: $tType,A2: set @ A,B3: set @ A,C2: A] :
% 3.00/1.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 3.00/1.51 => ( ~ ( member @ A @ C2 @ B3 )
% 3.00/1.51 => ~ ( member @ A @ C2 @ A2 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_100_Collect__mono__iff,axiom,
% 3.00/1.51 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.00/1.51 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 3.00/1.51 = ( ! [X: A] :
% 3.00/1.51 ( ( P @ X )
% 3.00/1.51 => ( Q @ X ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_101_comp__def,axiom,
% 3.00/1.51 ! [A: $tType,C: $tType,B: $tType] :
% 3.00/1.51 ( ( comp @ B @ C @ A )
% 3.00/1.51 = ( ^ [F: B > C,G: A > B,X: A] : ( F @ ( G @ X ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_102_comp__assoc,axiom,
% 3.00/1.51 ! [B: $tType,D: $tType,C: $tType,A: $tType,F2: D > B,G2: C > D,H: A > C] :
% 3.00/1.51 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F2 @ G2 ) @ H )
% 3.00/1.51 = ( comp @ D @ B @ A @ F2 @ ( comp @ C @ D @ A @ G2 @ H ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_103_comp__eq__dest,axiom,
% 3.00/1.51 ! [C: $tType,B: $tType,D: $tType,A: $tType,A3: C > B,B2: A > C,C2: D > B,D2: A > D,V: A] :
% 3.00/1.51 ( ( ( comp @ C @ B @ A @ A3 @ B2 )
% 3.00/1.51 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 3.00/1.51 => ( ( A3 @ ( B2 @ V ) )
% 3.00/1.51 = ( C2 @ ( D2 @ V ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_104_comp__eq__elim,axiom,
% 3.00/1.51 ! [C: $tType,B: $tType,D: $tType,A: $tType,A3: C > B,B2: A > C,C2: D > B,D2: A > D] :
% 3.00/1.51 ( ( ( comp @ C @ B @ A @ A3 @ B2 )
% 3.00/1.51 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 3.00/1.51 => ! [V2: A] :
% 3.00/1.51 ( ( A3 @ ( B2 @ V2 ) )
% 3.00/1.51 = ( C2 @ ( D2 @ V2 ) ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_105_comp__eq__dest__lhs,axiom,
% 3.00/1.51 ! [C: $tType,B: $tType,A: $tType,A3: C > B,B2: A > C,C2: A > B,V: A] :
% 3.00/1.51 ( ( ( comp @ C @ B @ A @ A3 @ B2 )
% 3.00/1.51 = C2 )
% 3.00/1.51 => ( ( A3 @ ( B2 @ V ) )
% 3.00/1.51 = ( C2 @ V ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_106_iso__tuple__UNIV__I,axiom,
% 3.00/1.51 ! [A: $tType,X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_107_comp__cong,axiom,
% 3.00/1.51 ! [C: $tType,B: $tType,D: $tType,A: $tType,E: $tType,F2: B > A,G2: C > B,X3: C,F3: D > A,G3: E > D,X4: E] :
% 3.00/1.51 ( ( ( F2 @ ( G2 @ X3 ) )
% 3.00/1.51 = ( F3 @ ( G3 @ X4 ) ) )
% 3.00/1.51 => ( ( comp @ B @ A @ C @ F2 @ G2 @ X3 )
% 3.00/1.51 = ( comp @ D @ A @ E @ F3 @ G3 @ X4 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_108_comp__apply__eq,axiom,
% 3.00/1.51 ! [B: $tType,D: $tType,A: $tType,C: $tType,F2: B > A,G2: C > B,X3: C,H: D > A,K: C > D] :
% 3.00/1.51 ( ( ( F2 @ ( G2 @ X3 ) )
% 3.00/1.51 = ( H @ ( K @ X3 ) ) )
% 3.00/1.51 => ( ( comp @ B @ A @ C @ F2 @ G2 @ X3 )
% 3.00/1.51 = ( comp @ D @ A @ C @ H @ K @ X3 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_109_fun_Omap__comp,axiom,
% 3.00/1.51 ! [B: $tType,C: $tType,A: $tType,D: $tType,G2: B > C,F2: A > B,V: D > A] :
% 3.00/1.51 ( ( comp @ B @ C @ D @ G2 @ ( comp @ A @ B @ D @ F2 @ V ) )
% 3.00/1.51 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G2 @ F2 ) @ V ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_110_type__copy__map__cong0,axiom,
% 3.00/1.51 ! [B: $tType,D: $tType,E: $tType,A: $tType,C: $tType,M: B > A,G2: C > B,X3: C,N3: D > A,H: C > D,F2: A > E] :
% 3.00/1.51 ( ( ( M @ ( G2 @ X3 ) )
% 3.00/1.51 = ( N3 @ ( H @ X3 ) ) )
% 3.00/1.51 => ( ( comp @ B @ E @ C @ ( comp @ A @ E @ B @ F2 @ M ) @ G2 @ X3 )
% 3.00/1.51 = ( comp @ D @ E @ C @ ( comp @ A @ E @ D @ F2 @ N3 ) @ H @ X3 ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_111_corec_I1_J,axiom,
% 3.00/1.51 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ A ) ) ),B2: A] :
% 3.00/1.51 ( ( root @ ( corec @ A @ Rt @ Ct @ B2 ) )
% 3.00/1.51 = ( Rt @ B2 ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_112_root__o__deftr,axiom,
% 3.00/1.51 ( ( comp @ dtree @ n @ n @ root @ gram_L1231612515_deftr )
% 3.00/1.51 = ( id @ n ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_113_Node__root__cont,axiom,
% 3.00/1.51 ! [Tr: dtree] :
% 3.00/1.51 ( ( node @ ( root @ Tr ) @ ( cont @ Tr ) )
% 3.00/1.51 = Tr ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_114_id__apply,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( id @ A )
% 3.00/1.51 = ( ^ [X: A] : X ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_115_fun_Omap__id,axiom,
% 3.00/1.51 ! [A: $tType,D: $tType,T2: D > A] :
% 3.00/1.51 ( ( comp @ A @ A @ D @ ( id @ A ) @ T2 )
% 3.00/1.51 = T2 ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_116_id__comp,axiom,
% 3.00/1.51 ! [B: $tType,A: $tType,G2: A > B] :
% 3.00/1.51 ( ( comp @ B @ B @ A @ ( id @ B ) @ G2 )
% 3.00/1.51 = G2 ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_117_comp__id,axiom,
% 3.00/1.51 ! [B: $tType,A: $tType,F2: A > B] :
% 3.00/1.51 ( ( comp @ A @ B @ A @ F2 @ ( id @ A ) )
% 3.00/1.51 = F2 ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_118_fun_Omap__id0,axiom,
% 3.00/1.51 ! [A: $tType,D: $tType] :
% 3.00/1.51 ( ( comp @ A @ A @ D @ ( id @ A ) )
% 3.00/1.51 = ( id @ ( D > A ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_119_id__def,axiom,
% 3.00/1.51 ! [A: $tType] :
% 3.00/1.51 ( ( id @ A )
% 3.00/1.51 = ( ^ [X: A] : X ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_120_eq__id__iff,axiom,
% 3.00/1.51 ! [A: $tType,F2: A > A] :
% 3.00/1.51 ( ( ! [X: A] :
% 3.00/1.51 ( ( F2 @ X )
% 3.00/1.51 = X ) )
% 3.00/1.51 = ( F2
% 3.00/1.51 = ( id @ A ) ) ) ).
% 3.00/1.51
% 3.00/1.51 thf(fact_121_DEADID_Oin__rel,axiom,
% 3.00/1.51 ! [B: $tType] :
% 3.00/1.51 ( ( ^ [Y2: B,Z: B] : ( Y2 = Z ) )
% 3.00/1.51 = ( ^ [A6: B,B6: B] :
% 3.00/1.52 ? [Z3: B] :
% 3.00/1.52 ( ( member @ B @ Z3 @ ( top_top @ ( set @ B ) ) )
% 3.00/1.52 & ( ( id @ B @ Z3 )
% 3.00/1.52 = A6 )
% 3.00/1.52 & ( ( id @ B @ Z3 )
% 3.00/1.52 = B6 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_122_comp__eq__id__dest,axiom,
% 3.00/1.52 ! [C: $tType,B: $tType,A: $tType,A3: C > B,B2: A > C,C2: A > B,V: A] :
% 3.00/1.52 ( ( ( comp @ C @ B @ A @ A3 @ B2 )
% 3.00/1.52 = ( comp @ B @ B @ A @ ( id @ B ) @ C2 ) )
% 3.00/1.52 => ( ( A3 @ ( B2 @ V ) )
% 3.00/1.52 = ( C2 @ V ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_123_pointfree__idE,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,F2: B > A,G2: A > B,X3: A] :
% 3.00/1.52 ( ( ( comp @ B @ A @ A @ F2 @ G2 )
% 3.00/1.52 = ( id @ A ) )
% 3.00/1.52 => ( ( F2 @ ( G2 @ X3 ) )
% 3.00/1.52 = X3 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_124_dtree__cong,axiom,
% 3.00/1.52 ! [Tr: dtree,Tr6: dtree] :
% 3.00/1.52 ( ( ( root @ Tr )
% 3.00/1.52 = ( root @ Tr6 ) )
% 3.00/1.52 => ( ( ( cont @ Tr )
% 3.00/1.52 = ( cont @ Tr6 ) )
% 3.00/1.52 => ( Tr = Tr6 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_125_top__set__def,axiom,
% 3.00/1.52 ! [A: $tType] :
% 3.00/1.52 ( ( top_top @ ( set @ A ) )
% 3.00/1.52 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_126_hsubst__c__def,axiom,
% 3.00/1.52 ( gram_L1905609002ubst_c
% 3.00/1.52 = ( ^ [Tr02: dtree,Tr2: dtree] :
% 3.00/1.52 ( if @ ( set @ ( sum_sum @ t @ dtree ) )
% 3.00/1.52 @ ( ( root @ Tr2 )
% 3.00/1.52 = ( root @ Tr02 ) )
% 3.00/1.52 @ ( cont @ Tr02 )
% 3.00/1.52 @ ( cont @ Tr2 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_127_deftr__def,axiom,
% 3.00/1.52 ( gram_L1231612515_deftr
% 3.00/1.52 = ( unfold @ n @ ( id @ n ) @ gram_L1451583635elle_S ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_128_wf__inj,axiom,
% 3.00/1.52 ! [Tr: dtree,Tr1: dtree,Tr22: dtree] :
% 3.00/1.52 ( ( gram_L864798063lle_wf @ Tr )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr ) )
% 3.00/1.52 => ( ( ( root @ Tr1 )
% 3.00/1.52 = ( root @ Tr22 ) )
% 3.00/1.52 = ( Tr1 = Tr22 ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_129_subtr__UNIV__inductL,axiom,
% 3.00/1.52 ! [Tr1: dtree,Tr22: dtree,Phi: dtree > dtree > $o] :
% 3.00/1.52 ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr1 @ Tr22 )
% 3.00/1.52 => ( ! [Tr7: dtree] : ( Phi @ Tr7 @ Tr7 )
% 3.00/1.52 => ( ! [Tr12: dtree,Tr23: dtree,Tr32: dtree] :
% 3.00/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 3.00/1.52 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr23 @ Tr32 )
% 3.00/1.52 => ( ( Phi @ Tr23 @ Tr32 )
% 3.00/1.52 => ( Phi @ Tr12 @ Tr32 ) ) ) )
% 3.00/1.52 => ( Phi @ Tr1 @ Tr22 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_130_type__copy__map__id0,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,Rep: A > B,Abs: B > A,M: B > B] :
% 3.00/1.52 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 3.00/1.52 => ( ( M
% 3.00/1.52 = ( id @ B ) )
% 3.00/1.52 => ( ( comp @ B @ A @ A @ ( comp @ B @ A @ B @ Abs @ M ) @ Rep )
% 3.00/1.52 = ( id @ A ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_131_type__copy__Abs__o__Rep,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,Rep: A > B,Abs: B > A] :
% 3.00/1.52 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 3.00/1.52 => ( ( comp @ B @ A @ A @ Abs @ Rep )
% 3.00/1.52 = ( id @ A ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_132_top1I,axiom,
% 3.00/1.52 ! [A: $tType,X3: A] : ( top_top @ ( A > $o ) @ X3 ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_133_type__copy__wit,axiom,
% 3.00/1.52 ! [A: $tType,C: $tType,B: $tType,Rep: A > B,Abs: B > A,X3: C,S: B > ( set @ C ),Y4: B] :
% 3.00/1.52 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 3.00/1.52 => ( ( member @ C @ X3 @ ( comp @ B @ ( set @ C ) @ A @ S @ Rep @ ( Abs @ Y4 ) ) )
% 3.00/1.52 => ( member @ C @ X3 @ ( S @ Y4 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_134_top__conj_I2_J,axiom,
% 3.00/1.52 ! [A: $tType,P: $o,X3: A] :
% 3.00/1.52 ( ( P
% 3.00/1.52 & ( top_top @ ( A > $o ) @ X3 ) )
% 3.00/1.52 = P ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_135_top__conj_I1_J,axiom,
% 3.00/1.52 ! [A: $tType,X3: A,P: $o] :
% 3.00/1.52 ( ( ( top_top @ ( A > $o ) @ X3 )
% 3.00/1.52 & P )
% 3.00/1.52 = P ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_136_type__copy__ex__RepI,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,Rep: A > B,Abs: B > A,F4: B > $o] :
% 3.00/1.52 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 3.00/1.52 => ( ( ^ [P2: B > $o] :
% 3.00/1.52 ? [X5: B] : ( P2 @ X5 )
% 3.00/1.52 @ F4 )
% 3.00/1.52 = ( ? [B6: A] : ( F4 @ ( Rep @ B6 ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_137_type__copy__obj__one__point__absE,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,Rep: A > B,Abs: B > A,S2: A] :
% 3.00/1.52 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 3.00/1.52 => ~ ! [X2: B] :
% 3.00/1.52 ( S2
% 3.00/1.52 != ( Abs @ X2 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_138_wf__cont,axiom,
% 3.00/1.52 ! [Tr: dtree,Tr6: dtree] :
% 3.00/1.52 ( ( gram_L864798063lle_wf @ Tr )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr6 ) @ ( cont @ Tr ) )
% 3.00/1.52 => ( gram_L864798063lle_wf @ Tr6 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_139_type__copy__map__comp0__undo,axiom,
% 3.00/1.52 ! [E: $tType,A: $tType,C: $tType,B: $tType,D: $tType,F5: $tType,Rep: A > B,Abs: B > A,Rep2: C > D,Abs2: D > C,Rep3: E > F5,Abs3: F5 > E,M: F5 > D,M1: B > D,M2: F5 > B] :
% 3.00/1.52 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 3.00/1.52 => ( ( type_definition @ C @ D @ Rep2 @ Abs2 @ ( top_top @ ( set @ D ) ) )
% 3.00/1.52 => ( ( type_definition @ E @ F5 @ Rep3 @ Abs3 @ ( top_top @ ( set @ F5 ) ) )
% 3.00/1.52 => ( ( ( comp @ F5 @ C @ E @ ( comp @ D @ C @ F5 @ Abs2 @ M ) @ Rep3 )
% 3.00/1.52 = ( comp @ A @ C @ E @ ( comp @ B @ C @ A @ ( comp @ D @ C @ B @ Abs2 @ M1 ) @ Rep ) @ ( comp @ F5 @ A @ E @ ( comp @ B @ A @ F5 @ Abs @ M2 ) @ Rep3 ) ) )
% 3.00/1.52 => ( ( comp @ B @ D @ F5 @ M1 @ M2 )
% 3.00/1.52 = M ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_140_type__copy__map__comp0,axiom,
% 3.00/1.52 ! [F5: $tType,D: $tType,B: $tType,A: $tType,C: $tType,E: $tType,Rep: A > B,Abs: B > A,M: C > D,M1: B > D,M2: C > B,F2: D > F5,G2: E > C] :
% 3.00/1.52 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 3.00/1.52 => ( ( M
% 3.00/1.52 = ( comp @ B @ D @ C @ M1 @ M2 ) )
% 3.00/1.52 => ( ( comp @ C @ F5 @ E @ ( comp @ D @ F5 @ C @ F2 @ M ) @ G2 )
% 3.00/1.52 = ( comp @ A @ F5 @ E @ ( comp @ B @ F5 @ A @ ( comp @ D @ F5 @ B @ F2 @ M1 ) @ Rep ) @ ( comp @ C @ A @ E @ ( comp @ B @ A @ C @ Abs @ M2 ) @ G2 ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_141_subtr_OStep,axiom,
% 3.00/1.52 ! [Tr3: dtree,Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr3 ) @ Ns )
% 3.00/1.52 => ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr3 ) )
% 3.00/1.52 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_142_subtr_Ocases,axiom,
% 3.00/1.52 ! [A1: set @ n,A22: dtree,A32: dtree] :
% 3.00/1.52 ( ( gram_L716654942_subtr @ A1 @ A22 @ A32 )
% 3.00/1.52 => ( ( ( A32 = A22 )
% 3.00/1.52 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 3.00/1.52 => ~ ( ( member @ n @ ( root @ A32 ) @ A1 )
% 3.00/1.52 => ! [Tr23: dtree] :
% 3.00/1.52 ( ( gram_L716654942_subtr @ A1 @ A22 @ Tr23 )
% 3.00/1.52 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ A32 ) ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_143_subtr_Osimps,axiom,
% 3.00/1.52 ( gram_L716654942_subtr
% 3.00/1.52 = ( ^ [A12: set @ n,A23: dtree,A33: dtree] :
% 3.00/1.52 ( ? [Tr2: dtree,Ns2: set @ n] :
% 3.00/1.52 ( ( A12 = Ns2 )
% 3.00/1.52 & ( A23 = Tr2 )
% 3.00/1.52 & ( A33 = Tr2 )
% 3.00/1.52 & ( member @ n @ ( root @ Tr2 ) @ Ns2 ) )
% 3.00/1.52 | ? [Tr33: dtree,Ns2: set @ n,Tr13: dtree,Tr24: dtree] :
% 3.00/1.52 ( ( A12 = Ns2 )
% 3.00/1.52 & ( A23 = Tr13 )
% 3.00/1.52 & ( A33 = Tr33 )
% 3.00/1.52 & ( member @ n @ ( root @ Tr33 ) @ Ns2 )
% 3.00/1.52 & ( gram_L716654942_subtr @ Ns2 @ Tr13 @ Tr24 )
% 3.00/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr24 ) @ ( cont @ Tr33 ) ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_144_subtr__StepL,axiom,
% 3.00/1.52 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr3: dtree] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 3.00/1.52 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr3 )
% 3.00/1.52 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_145_subtr_Oinducts,axiom,
% 3.00/1.52 ! [X1: set @ n,X22: dtree,X32: dtree,P: ( set @ n ) > dtree > dtree > $o] :
% 3.00/1.52 ( ( gram_L716654942_subtr @ X1 @ X22 @ X32 )
% 3.00/1.52 => ( ! [Tr7: dtree,Ns4: set @ n] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr7 ) @ Ns4 )
% 3.00/1.52 => ( P @ Ns4 @ Tr7 @ Tr7 ) )
% 3.00/1.52 => ( ! [Tr32: dtree,Ns4: set @ n,Tr12: dtree,Tr23: dtree] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr32 ) @ Ns4 )
% 3.00/1.52 => ( ( gram_L716654942_subtr @ Ns4 @ Tr12 @ Tr23 )
% 3.00/1.52 => ( ( P @ Ns4 @ Tr12 @ Tr23 )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ Tr32 ) )
% 3.00/1.52 => ( P @ Ns4 @ Tr12 @ Tr32 ) ) ) ) )
% 3.00/1.52 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_146_subtr__inductL,axiom,
% 3.00/1.52 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Phi: ( set @ n ) > dtree > dtree > $o] :
% 3.00/1.52 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 3.00/1.52 => ( ! [Ns4: set @ n,Tr7: dtree] : ( Phi @ Ns4 @ Tr7 @ Tr7 )
% 3.00/1.52 => ( ! [Ns4: set @ n,Tr12: dtree,Tr23: dtree,Tr32: dtree] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr12 ) @ Ns4 )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 3.00/1.52 => ( ( gram_L716654942_subtr @ Ns4 @ Tr23 @ Tr32 )
% 3.00/1.52 => ( ( Phi @ Ns4 @ Tr23 @ Tr32 )
% 3.00/1.52 => ( Phi @ Ns4 @ Tr12 @ Tr32 ) ) ) ) )
% 3.00/1.52 => ( Phi @ Ns @ Tr1 @ Tr22 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_147_inFr_OInd,axiom,
% 3.00/1.52 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,T2: t] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 3.00/1.52 => ( ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 )
% 3.00/1.52 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_148_subtr2_OStep,axiom,
% 3.00/1.52 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr3: dtree] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 3.00/1.52 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr3 )
% 3.00/1.52 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_149_subtr2_Ocases,axiom,
% 3.00/1.52 ! [A1: set @ n,A22: dtree,A32: dtree] :
% 3.00/1.52 ( ( gram_L1283001940subtr2 @ A1 @ A22 @ A32 )
% 3.00/1.52 => ( ( ( A32 = A22 )
% 3.00/1.52 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 3.00/1.52 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 3.00/1.52 => ! [Tr23: dtree] :
% 3.00/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A22 ) @ ( cont @ Tr23 ) )
% 3.00/1.52 => ~ ( gram_L1283001940subtr2 @ A1 @ Tr23 @ A32 ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_150_subtr2_Osimps,axiom,
% 3.00/1.52 ( gram_L1283001940subtr2
% 3.00/1.52 = ( ^ [A12: set @ n,A23: dtree,A33: dtree] :
% 3.00/1.52 ( ? [Tr2: dtree,Ns2: set @ n] :
% 3.00/1.52 ( ( A12 = Ns2 )
% 3.00/1.52 & ( A23 = Tr2 )
% 3.00/1.52 & ( A33 = Tr2 )
% 3.00/1.52 & ( member @ n @ ( root @ Tr2 ) @ Ns2 ) )
% 3.00/1.52 | ? [Tr13: dtree,Ns2: set @ n,Tr24: dtree,Tr33: dtree] :
% 3.00/1.52 ( ( A12 = Ns2 )
% 3.00/1.52 & ( A23 = Tr13 )
% 3.00/1.52 & ( A33 = Tr33 )
% 3.00/1.52 & ( member @ n @ ( root @ Tr13 ) @ Ns2 )
% 3.00/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr24 ) )
% 3.00/1.52 & ( gram_L1283001940subtr2 @ Ns2 @ Tr24 @ Tr33 ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_151_subtr2__StepR,axiom,
% 3.00/1.52 ! [Tr3: dtree,Ns: set @ n,Tr22: dtree,Tr1: dtree] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr3 ) @ Ns )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr3 ) )
% 3.00/1.52 => ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 3.00/1.52 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_152_subtr2_Oinducts,axiom,
% 3.00/1.52 ! [X1: set @ n,X22: dtree,X32: dtree,P: ( set @ n ) > dtree > dtree > $o] :
% 3.00/1.52 ( ( gram_L1283001940subtr2 @ X1 @ X22 @ X32 )
% 3.00/1.52 => ( ! [Tr7: dtree,Ns4: set @ n] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr7 ) @ Ns4 )
% 3.00/1.52 => ( P @ Ns4 @ Tr7 @ Tr7 ) )
% 3.00/1.52 => ( ! [Tr12: dtree,Ns4: set @ n,Tr23: dtree,Tr32: dtree] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr12 ) @ Ns4 )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 3.00/1.52 => ( ( gram_L1283001940subtr2 @ Ns4 @ Tr23 @ Tr32 )
% 3.00/1.52 => ( ( P @ Ns4 @ Tr23 @ Tr32 )
% 3.00/1.52 => ( P @ Ns4 @ Tr12 @ Tr32 ) ) ) ) )
% 3.00/1.52 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_153_inItr_OInd,axiom,
% 3.00/1.52 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,N: n] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 3.00/1.52 => ( ( gram_L830233218_inItr @ Ns @ Tr1 @ N )
% 3.00/1.52 => ( gram_L830233218_inItr @ Ns @ Tr @ N ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_154_inItr_Ocases,axiom,
% 3.00/1.52 ! [A1: set @ n,A22: dtree,A32: n] :
% 3.00/1.52 ( ( gram_L830233218_inItr @ A1 @ A22 @ A32 )
% 3.00/1.52 => ( ( ( A32
% 3.00/1.52 = ( root @ A22 ) )
% 3.00/1.52 => ~ ( member @ n @ ( root @ A22 ) @ A1 ) )
% 3.00/1.52 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 3.00/1.52 => ! [Tr12: dtree] :
% 3.00/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A22 ) )
% 3.00/1.52 => ~ ( gram_L830233218_inItr @ A1 @ Tr12 @ A32 ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_155_inItr_Osimps,axiom,
% 3.00/1.52 ( gram_L830233218_inItr
% 3.00/1.52 = ( ^ [A12: set @ n,A23: dtree,A33: n] :
% 3.00/1.52 ( ? [Tr2: dtree,Ns2: set @ n] :
% 3.00/1.52 ( ( A12 = Ns2 )
% 3.00/1.52 & ( A23 = Tr2 )
% 3.00/1.52 & ( A33
% 3.00/1.52 = ( root @ Tr2 ) )
% 3.00/1.52 & ( member @ n @ ( root @ Tr2 ) @ Ns2 ) )
% 3.00/1.52 | ? [Tr2: dtree,Ns2: set @ n,Tr13: dtree,N2: n] :
% 3.00/1.52 ( ( A12 = Ns2 )
% 3.00/1.52 & ( A23 = Tr2 )
% 3.00/1.52 & ( A33 = N2 )
% 3.00/1.52 & ( member @ n @ ( root @ Tr2 ) @ Ns2 )
% 3.00/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr2 ) )
% 3.00/1.52 & ( gram_L830233218_inItr @ Ns2 @ Tr13 @ N2 ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_156_inItr_Oinducts,axiom,
% 3.00/1.52 ! [X1: set @ n,X22: dtree,X32: n,P: ( set @ n ) > dtree > n > $o] :
% 3.00/1.52 ( ( gram_L830233218_inItr @ X1 @ X22 @ X32 )
% 3.00/1.52 => ( ! [Tr7: dtree,Ns4: set @ n] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr7 ) @ Ns4 )
% 3.00/1.52 => ( P @ Ns4 @ Tr7 @ ( root @ Tr7 ) ) )
% 3.00/1.52 => ( ! [Tr7: dtree,Ns4: set @ n,Tr12: dtree,N4: n] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr7 ) @ Ns4 )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 3.00/1.52 => ( ( gram_L830233218_inItr @ Ns4 @ Tr12 @ N4 )
% 3.00/1.52 => ( ( P @ Ns4 @ Tr12 @ N4 )
% 3.00/1.52 => ( P @ Ns4 @ Tr7 @ N4 ) ) ) ) )
% 3.00/1.52 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_157_inFr2__Ind,axiom,
% 3.00/1.52 ! [Ns: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 3.00/1.52 ( ( gram_L805317441_inFr2 @ Ns @ Tr1 @ T2 )
% 3.00/1.52 => ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 3.00/1.52 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_158_type__copy__Rep__o__Abs,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,Rep: A > B,Abs: B > A] :
% 3.00/1.52 ( ( type_definition @ A @ B @ Rep @ Abs @ ( top_top @ ( set @ B ) ) )
% 3.00/1.52 => ( ( comp @ A @ B @ B @ Rep @ Abs )
% 3.00/1.52 = ( id @ B ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_159_subtrOf__root,axiom,
% 3.00/1.52 ! [Tr: dtree,Tr6: dtree] :
% 3.00/1.52 ( ( gram_L864798063lle_wf @ Tr )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr6 ) @ ( cont @ Tr ) )
% 3.00/1.52 => ( ( gram_L1614515765ubtrOf @ Tr @ ( root @ Tr6 ) )
% 3.00/1.52 = Tr6 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_160_inFrr__def,axiom,
% 3.00/1.52 ( gram_L805317505_inFrr
% 3.00/1.52 = ( ^ [Ns2: set @ n,Tr2: dtree,T3: t] :
% 3.00/1.52 ? [Tr4: dtree] :
% 3.00/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr4 ) @ ( cont @ Tr2 ) )
% 3.00/1.52 & ( gram_L1333338417e_inFr @ Ns2 @ Tr4 @ T3 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_161_sum_Oinject_I2_J,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,X22: B,Y22: B] :
% 3.00/1.52 ( ( ( sum_Inr @ B @ A @ X22 )
% 3.00/1.52 = ( sum_Inr @ B @ A @ Y22 ) )
% 3.00/1.52 = ( X22 = Y22 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_162_old_Osum_Oinject_I2_J,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,B2: B,B7: B] :
% 3.00/1.52 ( ( ( sum_Inr @ B @ A @ B2 )
% 3.00/1.52 = ( sum_Inr @ B @ A @ B7 ) )
% 3.00/1.52 = ( B2 = B7 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_163_Inr__inject,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,X3: B,Y4: B] :
% 3.00/1.52 ( ( ( sum_Inr @ B @ A @ X3 )
% 3.00/1.52 = ( sum_Inr @ B @ A @ Y4 ) )
% 3.00/1.52 => ( X3 = Y4 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_164_top__empty__eq,axiom,
% 3.00/1.52 ! [A: $tType] :
% 3.00/1.52 ( ( top_top @ ( A > $o ) )
% 3.00/1.52 = ( ^ [X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_165_old_Osum_Osimps_I8_J,axiom,
% 3.00/1.52 ! [A: $tType,T: $tType,B: $tType,F1: A > T,F22: B > T,B2: B] :
% 3.00/1.52 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inr @ B @ A @ B2 ) )
% 3.00/1.52 = ( F22 @ B2 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_166_inFr2_OInd,axiom,
% 3.00/1.52 ! [Tr1: dtree,Tr: dtree,Ns1: set @ n,T2: t] :
% 3.00/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 3.00/1.52 => ( ( gram_L805317441_inFr2 @ Ns1 @ Tr1 @ T2 )
% 3.00/1.52 => ( gram_L805317441_inFr2 @ ( insert @ n @ ( root @ Tr ) @ Ns1 ) @ Tr @ T2 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_167_insert__absorb2,axiom,
% 3.00/1.52 ! [A: $tType,X3: A,A2: set @ A] :
% 3.00/1.52 ( ( insert @ A @ X3 @ ( insert @ A @ X3 @ A2 ) )
% 3.00/1.52 = ( insert @ A @ X3 @ A2 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_168_insert__iff,axiom,
% 3.00/1.52 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 3.00/1.52 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 3.00/1.52 = ( ( A3 = B2 )
% 3.00/1.52 | ( member @ A @ A3 @ A2 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_169_insertCI,axiom,
% 3.00/1.52 ! [A: $tType,A3: A,B3: set @ A,B2: A] :
% 3.00/1.52 ( ( ~ ( member @ A @ A3 @ B3 )
% 3.00/1.52 => ( A3 = B2 ) )
% 3.00/1.52 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_170_insert__subset,axiom,
% 3.00/1.52 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 3.00/1.52 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) @ B3 )
% 3.00/1.52 = ( ( member @ A @ X3 @ B3 )
% 3.00/1.52 & ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_171_subset__insertI2,axiom,
% 3.00/1.52 ! [A: $tType,A2: set @ A,B3: set @ A,B2: A] :
% 3.00/1.52 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 3.00/1.52 => ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_172_subset__insertI,axiom,
% 3.00/1.52 ! [A: $tType,B3: set @ A,A3: A] : ( ord_less_eq @ ( set @ A ) @ B3 @ ( insert @ A @ A3 @ B3 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_173_subset__insert,axiom,
% 3.00/1.52 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 3.00/1.52 ( ~ ( member @ A @ X3 @ A2 )
% 3.00/1.52 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ B3 ) )
% 3.00/1.52 = ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_174_insert__mono,axiom,
% 3.00/1.52 ! [A: $tType,C3: set @ A,D3: set @ A,A3: A] :
% 3.00/1.52 ( ( ord_less_eq @ ( set @ A ) @ C3 @ D3 )
% 3.00/1.52 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A3 @ C3 ) @ ( insert @ A @ A3 @ D3 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_175_mk__disjoint__insert,axiom,
% 3.00/1.52 ! [A: $tType,A3: A,A2: set @ A] :
% 3.00/1.52 ( ( member @ A @ A3 @ A2 )
% 3.00/1.52 => ? [B8: set @ A] :
% 3.00/1.52 ( ( A2
% 3.00/1.52 = ( insert @ A @ A3 @ B8 ) )
% 3.00/1.52 & ~ ( member @ A @ A3 @ B8 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_176_insert__commute,axiom,
% 3.00/1.52 ! [A: $tType,X3: A,Y4: A,A2: set @ A] :
% 3.00/1.52 ( ( insert @ A @ X3 @ ( insert @ A @ Y4 @ A2 ) )
% 3.00/1.52 = ( insert @ A @ Y4 @ ( insert @ A @ X3 @ A2 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_177_insert__eq__iff,axiom,
% 3.00/1.52 ! [A: $tType,A3: A,A2: set @ A,B2: A,B3: set @ A] :
% 3.00/1.52 ( ~ ( member @ A @ A3 @ A2 )
% 3.00/1.52 => ( ~ ( member @ A @ B2 @ B3 )
% 3.00/1.52 => ( ( ( insert @ A @ A3 @ A2 )
% 3.00/1.52 = ( insert @ A @ B2 @ B3 ) )
% 3.00/1.52 = ( ( ( A3 = B2 )
% 3.00/1.52 => ( A2 = B3 ) )
% 3.00/1.52 & ( ( A3 != B2 )
% 3.00/1.52 => ? [C4: set @ A] :
% 3.00/1.52 ( ( A2
% 3.00/1.52 = ( insert @ A @ B2 @ C4 ) )
% 3.00/1.52 & ~ ( member @ A @ B2 @ C4 )
% 3.00/1.52 & ( B3
% 3.00/1.52 = ( insert @ A @ A3 @ C4 ) )
% 3.00/1.52 & ~ ( member @ A @ A3 @ C4 ) ) ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_178_insert__absorb,axiom,
% 3.00/1.52 ! [A: $tType,A3: A,A2: set @ A] :
% 3.00/1.52 ( ( member @ A @ A3 @ A2 )
% 3.00/1.52 => ( ( insert @ A @ A3 @ A2 )
% 3.00/1.52 = A2 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_179_insert__ident,axiom,
% 3.00/1.52 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 3.00/1.52 ( ~ ( member @ A @ X3 @ A2 )
% 3.00/1.52 => ( ~ ( member @ A @ X3 @ B3 )
% 3.00/1.52 => ( ( ( insert @ A @ X3 @ A2 )
% 3.00/1.52 = ( insert @ A @ X3 @ B3 ) )
% 3.00/1.52 = ( A2 = B3 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_180_Set_Oset__insert,axiom,
% 3.00/1.52 ! [A: $tType,X3: A,A2: set @ A] :
% 3.00/1.52 ( ( member @ A @ X3 @ A2 )
% 3.00/1.52 => ~ ! [B8: set @ A] :
% 3.00/1.52 ( ( A2
% 3.00/1.52 = ( insert @ A @ X3 @ B8 ) )
% 3.00/1.52 => ( member @ A @ X3 @ B8 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_181_insertI2,axiom,
% 3.00/1.52 ! [A: $tType,A3: A,B3: set @ A,B2: A] :
% 3.00/1.52 ( ( member @ A @ A3 @ B3 )
% 3.00/1.52 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_182_insertI1,axiom,
% 3.00/1.52 ! [A: $tType,A3: A,B3: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B3 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_183_insertE,axiom,
% 3.00/1.52 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 3.00/1.52 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 3.00/1.52 => ( ( A3 != B2 )
% 3.00/1.52 => ( member @ A @ A3 @ A2 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_184_insert__UNIV,axiom,
% 3.00/1.52 ! [A: $tType,X3: A] :
% 3.00/1.52 ( ( insert @ A @ X3 @ ( top_top @ ( set @ A ) ) )
% 3.00/1.52 = ( top_top @ ( set @ A ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_185_inFr__Ind__minus,axiom,
% 3.00/1.52 ! [Ns1: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 3.00/1.52 ( ( gram_L1333338417e_inFr @ Ns1 @ Tr1 @ T2 )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 3.00/1.52 => ( gram_L1333338417e_inFr @ ( insert @ n @ ( root @ Tr ) @ Ns1 ) @ Tr @ T2 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_186_insert__subsetI,axiom,
% 3.00/1.52 ! [A: $tType,X3: A,A2: set @ A,X6: set @ A] :
% 3.00/1.52 ( ( member @ A @ X3 @ A2 )
% 3.00/1.52 => ( ( ord_less_eq @ ( set @ A ) @ X6 @ A2 )
% 3.00/1.52 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ X6 ) @ A2 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_187_inFr2_Ocases,axiom,
% 3.00/1.52 ! [A1: set @ n,A22: dtree,A32: t] :
% 3.00/1.52 ( ( gram_L805317441_inFr2 @ A1 @ A22 @ A32 )
% 3.00/1.52 => ( ( ( member @ n @ ( root @ A22 ) @ A1 )
% 3.00/1.52 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A32 ) @ ( cont @ A22 ) ) )
% 3.00/1.52 => ~ ! [Tr12: dtree,Tr7: dtree,Ns12: set @ n] :
% 3.00/1.52 ( ( A1
% 3.00/1.52 = ( insert @ n @ ( root @ Tr7 ) @ Ns12 ) )
% 3.00/1.52 => ( ( A22 = Tr7 )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 3.00/1.52 => ~ ( gram_L805317441_inFr2 @ Ns12 @ Tr12 @ A32 ) ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_188_inFr2_Osimps,axiom,
% 3.00/1.52 ( gram_L805317441_inFr2
% 3.00/1.52 = ( ^ [A12: set @ n,A23: dtree,A33: t] :
% 3.00/1.52 ( ? [Tr2: dtree,Ns2: set @ n,T3: t] :
% 3.00/1.52 ( ( A12 = Ns2 )
% 3.00/1.52 & ( A23 = Tr2 )
% 3.00/1.52 & ( A33 = T3 )
% 3.00/1.52 & ( member @ n @ ( root @ Tr2 ) @ Ns2 )
% 3.00/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr2 ) ) )
% 3.00/1.52 | ? [Tr13: dtree,Tr2: dtree,Ns13: set @ n,T3: t] :
% 3.00/1.52 ( ( A12
% 3.00/1.52 = ( insert @ n @ ( root @ Tr2 ) @ Ns13 ) )
% 3.00/1.52 & ( A23 = Tr2 )
% 3.00/1.52 & ( A33 = T3 )
% 3.00/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr2 ) )
% 3.00/1.52 & ( gram_L805317441_inFr2 @ Ns13 @ Tr13 @ T3 ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_189_Inl__Inr__False,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,X3: A,Y4: B] :
% 3.00/1.52 ( ( sum_Inl @ A @ B @ X3 )
% 3.00/1.52 != ( sum_Inr @ B @ A @ Y4 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_190_Inr__Inl__False,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,X3: B,Y4: A] :
% 3.00/1.52 ( ( sum_Inr @ B @ A @ X3 )
% 3.00/1.52 != ( sum_Inl @ A @ B @ Y4 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_191_obj__sumE__f,axiom,
% 3.00/1.52 ! [A: $tType,C: $tType,B: $tType,S2: B,F2: ( sum_sum @ A @ C ) > B,P: $o] :
% 3.00/1.52 ( ! [X2: A] :
% 3.00/1.52 ( ( S2
% 3.00/1.52 = ( F2 @ ( sum_Inl @ A @ C @ X2 ) ) )
% 3.00/1.52 => P )
% 3.00/1.52 => ( ! [X2: C] :
% 3.00/1.52 ( ( S2
% 3.00/1.52 = ( F2 @ ( sum_Inr @ C @ A @ X2 ) ) )
% 3.00/1.52 => P )
% 3.00/1.52 => ! [X7: sum_sum @ A @ C] :
% 3.00/1.52 ( ( S2
% 3.00/1.52 = ( F2 @ X7 ) )
% 3.00/1.52 => P ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_192_old_Osum_Oinducts,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,P: ( sum_sum @ A @ B ) > $o,Sum: sum_sum @ A @ B] :
% 3.00/1.52 ( ! [A4: A] : ( P @ ( sum_Inl @ A @ B @ A4 ) )
% 3.00/1.52 => ( ! [B4: B] : ( P @ ( sum_Inr @ B @ A @ B4 ) )
% 3.00/1.52 => ( P @ Sum ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_193_old_Osum_Oexhaust,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,Y4: sum_sum @ A @ B] :
% 3.00/1.52 ( ! [A4: A] :
% 3.00/1.52 ( Y4
% 3.00/1.52 != ( sum_Inl @ A @ B @ A4 ) )
% 3.00/1.52 => ~ ! [B4: B] :
% 3.00/1.52 ( Y4
% 3.00/1.52 != ( sum_Inr @ B @ A @ B4 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_194_split__sum__all,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType] :
% 3.00/1.52 ( ( ^ [P2: ( sum_sum @ A @ B ) > $o] :
% 3.00/1.52 ! [X5: sum_sum @ A @ B] : ( P2 @ X5 ) )
% 3.00/1.52 = ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 3.00/1.52 ( ! [X: A] : ( P3 @ ( sum_Inl @ A @ B @ X ) )
% 3.00/1.52 & ! [X: B] : ( P3 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_195_split__sum__ex,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType] :
% 3.00/1.52 ( ( ^ [P2: ( sum_sum @ A @ B ) > $o] :
% 3.00/1.52 ? [X5: sum_sum @ A @ B] : ( P2 @ X5 ) )
% 3.00/1.52 = ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 3.00/1.52 ( ? [X: A] : ( P3 @ ( sum_Inl @ A @ B @ X ) )
% 3.00/1.52 | ? [X: B] : ( P3 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_196_Inr__not__Inl,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,B2: B,A3: A] :
% 3.00/1.52 ( ( sum_Inr @ B @ A @ B2 )
% 3.00/1.52 != ( sum_Inl @ A @ B @ A3 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_197_sumE,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,S2: sum_sum @ A @ B] :
% 3.00/1.52 ( ! [X2: A] :
% 3.00/1.52 ( S2
% 3.00/1.52 != ( sum_Inl @ A @ B @ X2 ) )
% 3.00/1.52 => ~ ! [Y: B] :
% 3.00/1.52 ( S2
% 3.00/1.52 != ( sum_Inr @ B @ A @ Y ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_198_old_Osum_Odistinct_I1_J,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,A3: A,B7: B] :
% 3.00/1.52 ( ( sum_Inl @ A @ B @ A3 )
% 3.00/1.52 != ( sum_Inr @ B @ A @ B7 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_199_old_Osum_Odistinct_I2_J,axiom,
% 3.00/1.52 ! [B9: $tType,A7: $tType,B10: B9,A8: A7] :
% 3.00/1.52 ( ( sum_Inr @ B9 @ A7 @ B10 )
% 3.00/1.52 != ( sum_Inl @ A7 @ B9 @ A8 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_200_sum_Odistinct_I1_J,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,X1: A,X22: B] :
% 3.00/1.52 ( ( sum_Inl @ A @ B @ X1 )
% 3.00/1.52 != ( sum_Inr @ B @ A @ X22 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_201_inFr_OBase,axiom,
% 3.00/1.52 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 3.00/1.52 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_202_inFr2_OBase,axiom,
% 3.00/1.52 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 3.00/1.52 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_203_inFr__subtr,axiom,
% 3.00/1.52 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 3.00/1.52 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 3.00/1.52 => ? [Tr5: dtree] :
% 3.00/1.52 ( ( gram_L716654942_subtr @ Ns @ Tr5 @ Tr )
% 3.00/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr5 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_204_inFr_Ocases,axiom,
% 3.00/1.52 ! [A1: set @ n,A22: dtree,A32: t] :
% 3.00/1.52 ( ( gram_L1333338417e_inFr @ A1 @ A22 @ A32 )
% 3.00/1.52 => ( ( ( member @ n @ ( root @ A22 ) @ A1 )
% 3.00/1.52 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A32 ) @ ( cont @ A22 ) ) )
% 3.00/1.52 => ~ ( ( member @ n @ ( root @ A22 ) @ A1 )
% 3.00/1.52 => ! [Tr12: dtree] :
% 3.00/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A22 ) )
% 3.00/1.52 => ~ ( gram_L1333338417e_inFr @ A1 @ Tr12 @ A32 ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_205_inFr_Osimps,axiom,
% 3.00/1.52 ( gram_L1333338417e_inFr
% 3.00/1.52 = ( ^ [A12: set @ n,A23: dtree,A33: t] :
% 3.00/1.52 ( ? [Tr2: dtree,Ns2: set @ n,T3: t] :
% 3.00/1.52 ( ( A12 = Ns2 )
% 3.00/1.52 & ( A23 = Tr2 )
% 3.00/1.52 & ( A33 = T3 )
% 3.00/1.52 & ( member @ n @ ( root @ Tr2 ) @ Ns2 )
% 3.00/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr2 ) ) )
% 3.00/1.52 | ? [Tr2: dtree,Ns2: set @ n,Tr13: dtree,T3: t] :
% 3.00/1.52 ( ( A12 = Ns2 )
% 3.00/1.52 & ( A23 = Tr2 )
% 3.00/1.52 & ( A33 = T3 )
% 3.00/1.52 & ( member @ n @ ( root @ Tr2 ) @ Ns2 )
% 3.00/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr2 ) )
% 3.00/1.52 & ( gram_L1333338417e_inFr @ Ns2 @ Tr13 @ T3 ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_206_inFr_Oinducts,axiom,
% 3.00/1.52 ! [X1: set @ n,X22: dtree,X32: t,P: ( set @ n ) > dtree > t > $o] :
% 3.00/1.52 ( ( gram_L1333338417e_inFr @ X1 @ X22 @ X32 )
% 3.00/1.52 => ( ! [Tr7: dtree,Ns4: set @ n,T4: t] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr7 ) @ Ns4 )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr7 ) )
% 3.00/1.52 => ( P @ Ns4 @ Tr7 @ T4 ) ) )
% 3.00/1.52 => ( ! [Tr7: dtree,Ns4: set @ n,Tr12: dtree,T4: t] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr7 ) @ Ns4 )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 3.00/1.52 => ( ( gram_L1333338417e_inFr @ Ns4 @ Tr12 @ T4 )
% 3.00/1.52 => ( ( P @ Ns4 @ Tr12 @ T4 )
% 3.00/1.52 => ( P @ Ns4 @ Tr7 @ T4 ) ) ) ) )
% 3.00/1.52 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_207_inFr2_Oinducts,axiom,
% 3.00/1.52 ! [X1: set @ n,X22: dtree,X32: t,P: ( set @ n ) > dtree > t > $o] :
% 3.00/1.52 ( ( gram_L805317441_inFr2 @ X1 @ X22 @ X32 )
% 3.00/1.52 => ( ! [Tr7: dtree,Ns4: set @ n,T4: t] :
% 3.00/1.52 ( ( member @ n @ ( root @ Tr7 ) @ Ns4 )
% 3.00/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr7 ) )
% 3.00/1.52 => ( P @ Ns4 @ Tr7 @ T4 ) ) )
% 3.00/1.52 => ( ! [Tr12: dtree,Tr7: dtree,Ns12: set @ n,T4: t] :
% 3.00/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr7 ) )
% 3.00/1.52 => ( ( gram_L805317441_inFr2 @ Ns12 @ Tr12 @ T4 )
% 3.00/1.52 => ( ( P @ Ns12 @ Tr12 @ T4 )
% 3.00/1.52 => ( P @ ( insert @ n @ ( root @ Tr7 ) @ Ns12 ) @ Tr7 @ T4 ) ) ) )
% 3.00/1.52 => ( P @ X1 @ X22 @ X32 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_208_obj__sumE,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,S2: sum_sum @ A @ B] :
% 3.00/1.52 ( ! [X2: A] :
% 3.00/1.52 ( S2
% 3.00/1.52 != ( sum_Inl @ A @ B @ X2 ) )
% 3.00/1.52 => ~ ! [X2: B] :
% 3.00/1.52 ( S2
% 3.00/1.52 != ( sum_Inr @ B @ A @ X2 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_209_Inl__cont__hsubst__neq,axiom,
% 3.00/1.52 ! [Tr: dtree,Tr0: dtree] :
% 3.00/1.52 ( ( ( root @ Tr )
% 3.00/1.52 != ( root @ Tr0 ) )
% 3.00/1.52 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 3.00/1.52 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_210_vimage__eq,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,A3: A,F2: A > B,B3: set @ B] :
% 3.00/1.52 ( ( member @ A @ A3 @ ( vimage @ A @ B @ F2 @ B3 ) )
% 3.00/1.52 = ( member @ B @ ( F2 @ A3 ) @ B3 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_211_vimageI,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,F2: B > A,A3: B,B2: A,B3: set @ A] :
% 3.00/1.52 ( ( ( F2 @ A3 )
% 3.00/1.52 = B2 )
% 3.00/1.52 => ( ( member @ A @ B2 @ B3 )
% 3.00/1.52 => ( member @ B @ A3 @ ( vimage @ B @ A @ F2 @ B3 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_212_vimage__UNIV,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,F2: A > B] :
% 3.00/1.52 ( ( vimage @ A @ B @ F2 @ ( top_top @ ( set @ B ) ) )
% 3.00/1.52 = ( top_top @ ( set @ A ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_213_vimage__id,axiom,
% 3.00/1.52 ! [A: $tType] :
% 3.00/1.52 ( ( vimage @ A @ A @ ( id @ A ) )
% 3.00/1.52 = ( id @ ( set @ A ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_214_Inl__cont__hsubst__eq,axiom,
% 3.00/1.52 ! [Tr: dtree,Tr0: dtree] :
% 3.00/1.52 ( ( ( root @ Tr )
% 3.00/1.52 = ( root @ Tr0 ) )
% 3.00/1.52 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 3.00/1.52 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_215_set_Ocompositionality,axiom,
% 3.00/1.52 ! [C: $tType,B: $tType,A: $tType,F2: C > B,G2: B > A,Set: set @ A] :
% 3.00/1.52 ( ( vimage @ C @ B @ F2 @ ( vimage @ B @ A @ G2 @ Set ) )
% 3.00/1.52 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G2 @ F2 ) @ Set ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_216_vimage__comp,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,C: $tType,F2: A > B,G2: B > C,X3: set @ C] :
% 3.00/1.52 ( ( vimage @ A @ B @ F2 @ ( vimage @ B @ C @ G2 @ X3 ) )
% 3.00/1.52 = ( vimage @ A @ C @ ( comp @ B @ C @ A @ G2 @ F2 ) @ X3 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_217_set_Ocomp,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,C: $tType,F2: C > B,G2: B > A] :
% 3.00/1.52 ( ( comp @ ( set @ B ) @ ( set @ C ) @ ( set @ A ) @ ( vimage @ C @ B @ F2 ) @ ( vimage @ B @ A @ G2 ) )
% 3.00/1.52 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G2 @ F2 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_218_vimage__mono,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,A2: set @ A,B3: set @ A,F2: B > A] :
% 3.00/1.52 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B3 )
% 3.00/1.52 => ( ord_less_eq @ ( set @ B ) @ ( vimage @ B @ A @ F2 @ A2 ) @ ( vimage @ B @ A @ F2 @ B3 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_219_vimage__Collect,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,P: B > $o,F2: A > B,Q: A > $o] :
% 3.00/1.52 ( ! [X2: A] :
% 3.00/1.52 ( ( P @ ( F2 @ X2 ) )
% 3.00/1.52 = ( Q @ X2 ) )
% 3.00/1.52 => ( ( vimage @ A @ B @ F2 @ ( collect @ B @ P ) )
% 3.00/1.52 = ( collect @ A @ Q ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_220_vimageI2,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,F2: B > A,A3: B,A2: set @ A] :
% 3.00/1.52 ( ( member @ A @ ( F2 @ A3 ) @ A2 )
% 3.00/1.52 => ( member @ B @ A3 @ ( vimage @ B @ A @ F2 @ A2 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_221_vimageE,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,A3: A,F2: A > B,B3: set @ B] :
% 3.00/1.52 ( ( member @ A @ A3 @ ( vimage @ A @ B @ F2 @ B3 ) )
% 3.00/1.52 => ( member @ B @ ( F2 @ A3 ) @ B3 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_222_vimageD,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,A3: A,F2: A > B,A2: set @ B] :
% 3.00/1.52 ( ( member @ A @ A3 @ ( vimage @ A @ B @ F2 @ A2 ) )
% 3.00/1.52 => ( member @ B @ ( F2 @ A3 ) @ A2 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_223_not__arg__cong__Inr,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,X3: A,Y4: A] :
% 3.00/1.52 ( ( X3 != Y4 )
% 3.00/1.52 => ( ( sum_Inr @ A @ B @ X3 )
% 3.00/1.52 != ( sum_Inr @ A @ B @ Y4 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_224_Inl__Inr__image__cong,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,A2: set @ ( sum_sum @ A @ B ),B3: set @ ( sum_sum @ A @ B )] :
% 3.00/1.52 ( ( ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ A2 )
% 3.00/1.52 = ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ B3 ) )
% 3.00/1.52 => ( ( ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ A2 )
% 3.00/1.52 = ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ B3 ) )
% 3.00/1.52 => ( A2 = B3 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_225_inFr__hsubst__imp,axiom,
% 3.00/1.52 ! [Ns: set @ n,Tr0: dtree,Tr: dtree,T2: t] :
% 3.00/1.52 ( ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T2 )
% 3.00/1.52 => ( ( member @ t @ T2 @ ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) )
% 3.00/1.52 | ( gram_L805317505_inFrr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr0 @ T2 )
% 3.00/1.52 | ( gram_L1333338417e_inFr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr @ T2 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_226_bot__apply,axiom,
% 3.00/1.52 ! [C: $tType,D: $tType] :
% 3.00/1.52 ( ( bot @ C @ ( type2 @ C ) )
% 3.00/1.52 => ( ( bot_bot @ ( D > C ) )
% 3.00/1.52 = ( ^ [X: D] : ( bot_bot @ C ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_227_empty__iff,axiom,
% 3.00/1.52 ! [A: $tType,C2: A] :
% 3.00/1.52 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_228_all__not__in__conv,axiom,
% 3.00/1.52 ! [A: $tType,A2: set @ A] :
% 3.00/1.52 ( ( ! [X: A] :
% 3.00/1.52 ~ ( member @ A @ X @ A2 ) )
% 3.00/1.52 = ( A2
% 3.00/1.52 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_229_Collect__empty__eq,axiom,
% 3.00/1.52 ! [A: $tType,P: A > $o] :
% 3.00/1.52 ( ( ( collect @ A @ P )
% 3.00/1.52 = ( bot_bot @ ( set @ A ) ) )
% 3.00/1.52 = ( ! [X: A] :
% 3.00/1.52 ~ ( P @ X ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_230_empty__Collect__eq,axiom,
% 3.00/1.52 ! [A: $tType,P: A > $o] :
% 3.00/1.52 ( ( ( bot_bot @ ( set @ A ) )
% 3.00/1.52 = ( collect @ A @ P ) )
% 3.00/1.52 = ( ! [X: A] :
% 3.00/1.52 ~ ( P @ X ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_231_DiffI,axiom,
% 3.00/1.52 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 3.00/1.52 ( ( member @ A @ C2 @ A2 )
% 3.00/1.52 => ( ~ ( member @ A @ C2 @ B3 )
% 3.00/1.52 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_232_Diff__iff,axiom,
% 3.00/1.52 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 3.00/1.52 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 3.00/1.52 = ( ( member @ A @ C2 @ A2 )
% 3.00/1.52 & ~ ( member @ A @ C2 @ B3 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_233_Diff__idemp,axiom,
% 3.00/1.52 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 3.00/1.52 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) @ B3 )
% 3.00/1.52 = ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_234_subset__empty,axiom,
% 3.00/1.52 ! [A: $tType,A2: set @ A] :
% 3.00/1.52 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 3.00/1.52 = ( A2
% 3.00/1.52 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_235_empty__subsetI,axiom,
% 3.00/1.52 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_236_singletonI,axiom,
% 3.00/1.52 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_237_Diff__empty,axiom,
% 3.00/1.52 ! [A: $tType,A2: set @ A] :
% 3.00/1.52 ( ( minus_minus @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 3.00/1.52 = A2 ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_238_empty__Diff,axiom,
% 3.00/1.52 ! [A: $tType,A2: set @ A] :
% 3.00/1.52 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 )
% 3.00/1.52 = ( bot_bot @ ( set @ A ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_239_Diff__cancel,axiom,
% 3.00/1.52 ! [A: $tType,A2: set @ A] :
% 3.00/1.52 ( ( minus_minus @ ( set @ A ) @ A2 @ A2 )
% 3.00/1.52 = ( bot_bot @ ( set @ A ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_240_Diff__insert0,axiom,
% 3.00/1.52 ! [A: $tType,X3: A,A2: set @ A,B3: set @ A] :
% 3.00/1.52 ( ~ ( member @ A @ X3 @ A2 )
% 3.00/1.52 => ( ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ X3 @ B3 ) )
% 3.00/1.52 = ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_241_insert__Diff1,axiom,
% 3.00/1.52 ! [A: $tType,X3: A,B3: set @ A,A2: set @ A] :
% 3.00/1.52 ( ( member @ A @ X3 @ B3 )
% 3.00/1.52 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A2 ) @ B3 )
% 3.00/1.52 = ( minus_minus @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_242_vimage__empty,axiom,
% 3.00/1.52 ! [B: $tType,A: $tType,F2: A > B] :
% 3.00/1.52 ( ( vimage @ A @ B @ F2 @ ( bot_bot @ ( set @ B ) ) )
% 3.00/1.52 = ( bot_bot @ ( set @ A ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_243_singleton__insert__inj__eq,axiom,
% 3.00/1.52 ! [A: $tType,B2: A,A3: A,A2: set @ A] :
% 3.00/1.52 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 3.00/1.52 = ( insert @ A @ A3 @ A2 ) )
% 3.00/1.52 = ( ( A3 = B2 )
% 3.00/1.52 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_244_singleton__insert__inj__eq_H,axiom,
% 3.00/1.52 ! [A: $tType,A3: A,A2: set @ A,B2: A] :
% 3.00/1.52 ( ( ( insert @ A @ A3 @ A2 )
% 3.00/1.52 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.00/1.52 = ( ( A3 = B2 )
% 3.00/1.52 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_245_Diff__eq__empty__iff,axiom,
% 3.00/1.52 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 3.00/1.52 ( ( ( minus_minus @ ( set @ A ) @ A2 @ B3 )
% 3.00/1.52 = ( bot_bot @ ( set @ A ) ) )
% 3.00/1.52 = ( ord_less_eq @ ( set @ A ) @ A2 @ B3 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_246_insert__Diff__single,axiom,
% 3.00/1.52 ! [A: $tType,A3: A,A2: set @ A] :
% 3.00/1.52 ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.00/1.52 = ( insert @ A @ A3 @ A2 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_247_Diff__UNIV,axiom,
% 3.00/1.52 ! [A: $tType,A2: set @ A] :
% 3.00/1.52 ( ( minus_minus @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 3.00/1.52 = ( bot_bot @ ( set @ A ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_248_vimage__singleton__eq,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,A3: A,F2: A > B,B2: B] :
% 3.00/1.52 ( ( member @ A @ A3 @ ( vimage @ A @ B @ F2 @ ( insert @ B @ B2 @ ( bot_bot @ ( set @ B ) ) ) ) )
% 3.00/1.52 = ( ( F2 @ A3 )
% 3.00/1.52 = B2 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_249_vimage__Diff,axiom,
% 3.00/1.52 ! [A: $tType,B: $tType,F2: A > B,A2: set @ B,B3: set @ B] :
% 3.00/1.52 ( ( vimage @ A @ B @ F2 @ ( minus_minus @ ( set @ B ) @ A2 @ B3 ) )
% 3.00/1.52 = ( minus_minus @ ( set @ A ) @ ( vimage @ A @ B @ F2 @ A2 ) @ ( vimage @ A @ B @ F2 @ B3 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_250_inFr__hsubst__minus,axiom,
% 3.00/1.52 ! [Ns: set @ n,Tr0: dtree,Tr: dtree,T2: t] :
% 3.00/1.52 ( ( gram_L1333338417e_inFr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr @ T2 )
% 3.00/1.52 => ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T2 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_251_empty__not__UNIV,axiom,
% 3.00/1.52 ! [A: $tType] :
% 3.00/1.52 ( ( bot_bot @ ( set @ A ) )
% 3.00/1.52 != ( top_top @ ( set @ A ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_252_DiffE,axiom,
% 3.00/1.52 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 3.00/1.52 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 3.00/1.52 => ~ ( ( member @ A @ C2 @ A2 )
% 3.00/1.52 => ( member @ A @ C2 @ B3 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_253_DiffD1,axiom,
% 3.00/1.52 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 3.00/1.52 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 3.00/1.52 => ( member @ A @ C2 @ A2 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_254_DiffD2,axiom,
% 3.00/1.52 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 3.00/1.52 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A2 @ B3 ) )
% 3.00/1.52 => ~ ( member @ A @ C2 @ B3 ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(fact_255_emptyE,axiom,
% 3.00/1.52 ! [A: $tType,A3: A] :
% 3.00/1.52 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 3.00/1.52 ! [A7: $tType,A9: $tType] :
% 3.00/1.52 ( ( order_top @ A9 @ ( type2 @ A9 ) )
% 3.00/1.52 => ( order_top @ ( A7 > A9 ) @ ( type2 @ ( A7 > A9 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_fun___Orderings_Opreorder,axiom,
% 3.00/1.52 ! [A7: $tType,A9: $tType] :
% 3.00/1.52 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 3.00/1.52 => ( preorder @ ( A7 > A9 ) @ ( type2 @ ( A7 > A9 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_fun___Orderings_Oorder,axiom,
% 3.00/1.52 ! [A7: $tType,A9: $tType] :
% 3.00/1.52 ( ( order @ A9 @ ( type2 @ A9 ) )
% 3.00/1.52 => ( order @ ( A7 > A9 ) @ ( type2 @ ( A7 > A9 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_fun___Orderings_Otop,axiom,
% 3.00/1.52 ! [A7: $tType,A9: $tType] :
% 3.00/1.52 ( ( top @ A9 @ ( type2 @ A9 ) )
% 3.00/1.52 => ( top @ ( A7 > A9 ) @ ( type2 @ ( A7 > A9 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_fun___Orderings_Oord,axiom,
% 3.00/1.52 ! [A7: $tType,A9: $tType] :
% 3.00/1.52 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 3.00/1.52 => ( ord @ ( A7 > A9 ) @ ( type2 @ ( A7 > A9 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_fun___Orderings_Obot,axiom,
% 3.00/1.52 ! [A7: $tType,A9: $tType] :
% 3.00/1.52 ( ( bot @ A9 @ ( type2 @ A9 ) )
% 3.00/1.52 => ( bot @ ( A7 > A9 ) @ ( type2 @ ( A7 > A9 ) ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_Set_Oset___Orderings_Oorder__top_1,axiom,
% 3.00/1.52 ! [A7: $tType] : ( order_top @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 3.00/1.52 ! [A7: $tType] : ( preorder @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_Set_Oset___Orderings_Oorder_3,axiom,
% 3.00/1.52 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_Set_Oset___Orderings_Otop_4,axiom,
% 3.00/1.52 ! [A7: $tType] : ( top @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_Set_Oset___Orderings_Oord_5,axiom,
% 3.00/1.52 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_Set_Oset___Orderings_Obot_6,axiom,
% 3.00/1.52 ! [A7: $tType] : ( bot @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_HOL_Obool___Orderings_Oorder__top_7,axiom,
% 3.00/1.52 order_top @ $o @ ( type2 @ $o ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_HOL_Obool___Orderings_Opreorder_8,axiom,
% 3.00/1.52 preorder @ $o @ ( type2 @ $o ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 3.00/1.52 linorder @ $o @ ( type2 @ $o ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 3.00/1.52 order @ $o @ ( type2 @ $o ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_HOL_Obool___Orderings_Otop_10,axiom,
% 3.00/1.52 top @ $o @ ( type2 @ $o ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_HOL_Obool___Orderings_Oord_11,axiom,
% 3.00/1.52 ord @ $o @ ( type2 @ $o ) ).
% 3.00/1.52
% 3.00/1.52 thf(tcon_HOL_Obool___Orderings_Obot_12,axiom,
% 3.00/1.52 bot @ $o @ ( type2 @ $o ) ).
% 3.00/1.52
% 3.00/1.52 thf(help_If_3_1_T,axiom,
% 3.00/1.52 ! [P: $o] :
% 3.00/1.52 ( ( P = $true )
% 3.00/1.52 | ( P = $false ) ) ).
% 3.00/1.52
% 3.00/1.52 thf(help_If_2_1_T,axiom,
% 3.00/1.52 ! [A: $tType,X3: A,Y4: A] :
% 3.00/1.52 ( ( if @ A @ $false @ X3 @ Y4 )
% 3.00/1.52 = Y4 ) ).
% 3.00/1.52
% 3.00/1.52 thf(help_If_1_1_T,axiom,
% 3.00/1.52 ! [A: $tType,X3: A,Y4: A] :
% 3.00/1.52 ( ( if @ A @ $true @ X3 @ Y4 )
% 3.00/1.52 = X3 ) ).
% 3.00/1.52
% 3.00/1.52 thf(conj_0,conjecture,
% 3.00/1.52 ( ( f @ ( root @ tr ) )
% 3.00/1.52 = tr ) ).
% 3.00/1.52 ------------------------
% 3.00/1.54 % (23860)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/183Mi)
% 3.00/1.54 % (23866)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/18Mi)
% 3.00/1.54 % (23862)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_23682 for (2999ds/27Mi)
% 3.00/1.54 % (23861)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_23682 for (2999ds/4Mi)
% 3.00/1.54 % (23863)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/2Mi)
% 3.00/1.54 % (23865)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_23682 for (2999ds/275Mi)
% 3.00/1.54 % (23863)Instruction limit reached!
% 3.00/1.54 % (23863)------------------------------
% 3.00/1.54 % (23863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.54 % (23863)Termination reason: Unknown
% 3.00/1.54 % (23863)Termination phase: shuffling
% 3.00/1.54
% 3.00/1.54 % (23863)Memory used [KB]: 1407
% 3.00/1.54 % (23863)Time elapsed: 0.003 s
% 3.00/1.54 % (23863)Instructions burned: 3 (million)
% 3.00/1.54 % (23863)------------------------------
% 3.00/1.54 % (23863)------------------------------
% 3.00/1.54 % (23861)Instruction limit reached!
% 3.00/1.54 % (23861)------------------------------
% 3.00/1.54 % (23861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.54 % (23861)Termination reason: Unknown
% 3.00/1.54 % (23861)Termination phase: shuffling
% 3.00/1.54
% 3.00/1.54 % (23861)Memory used [KB]: 1407
% 3.00/1.54 % (23861)Time elapsed: 0.004 s
% 3.00/1.54 % (23861)Instructions burned: 5 (million)
% 3.00/1.54 % (23861)------------------------------
% 3.00/1.54 % (23861)------------------------------
% 3.00/1.54 % (23864)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_23682 for (2999ds/2Mi)
% 3.00/1.55 % (23864)Instruction limit reached!
% 3.00/1.55 % (23864)------------------------------
% 3.00/1.55 % (23864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.55 % (23864)Termination reason: Unknown
% 3.00/1.55 % (23864)Termination phase: shuffling
% 3.00/1.55
% 3.00/1.55 % (23864)Memory used [KB]: 1407
% 3.00/1.55 % (23864)Time elapsed: 0.003 s
% 3.00/1.55 % (23864)Instructions burned: 2 (million)
% 3.00/1.55 % (23864)------------------------------
% 3.00/1.55 % (23864)------------------------------
% 3.00/1.55 % (23866)Instruction limit reached!
% 3.00/1.55 % (23866)------------------------------
% 3.00/1.55 % (23866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.55 % (23866)Termination reason: Unknown
% 3.00/1.55 % (23866)Termination phase: shuffling
% 3.00/1.55
% 3.00/1.55 % (23866)Memory used [KB]: 1918
% 3.00/1.55 % (23866)Time elapsed: 0.008 s
% 3.00/1.55 % (23866)Instructions burned: 20 (million)
% 3.00/1.55 % (23866)------------------------------
% 3.00/1.55 % (23866)------------------------------
% 3.00/1.56 % (23862)Instruction limit reached!
% 3.00/1.56 % (23862)------------------------------
% 3.00/1.56 % (23862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.56 % (23862)Termination reason: Unknown
% 3.00/1.56 % (23862)Termination phase: Property scanning
% 3.00/1.56
% 3.00/1.56 % (23862)Memory used [KB]: 1918
% 3.00/1.56 % (23862)Time elapsed: 0.016 s
% 3.00/1.56 % (23862)Instructions burned: 27 (million)
% 3.00/1.56 % (23862)------------------------------
% 3.00/1.56 % (23862)------------------------------
% 3.00/1.56 % (23874)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_23682 for (2999ds/15Mi)
% 3.00/1.56 % (23871)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/3Mi)
% 3.00/1.56 % (23871)Instruction limit reached!
% 3.00/1.56 % (23871)------------------------------
% 3.00/1.56 % (23871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.56 % (23871)Termination reason: Unknown
% 3.00/1.56 % (23871)Termination phase: shuffling
% 3.00/1.56
% 3.00/1.56 % (23871)Memory used [KB]: 1407
% 3.00/1.56 % (23871)Time elapsed: 0.003 s
% 3.00/1.56 % (23871)Instructions burned: 3 (million)
% 3.00/1.56 % (23871)------------------------------
% 3.00/1.56 % (23871)------------------------------
% 3.00/1.56 % (23873)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_23682 for (2999ds/37Mi)
% 3.00/1.56 % (23865)Refutation not found, incomplete strategy
% 3.00/1.56 % (23865)------------------------------
% 3.00/1.56 % (23865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.56 % (23865)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.56
% 3.00/1.56
% 3.00/1.56 % (23865)Memory used [KB]: 6396
% 3.00/1.56 % (23865)Time elapsed: 0.021 s
% 3.00/1.56 % (23874)Instruction limit reached!
% 3.00/1.56 % (23874)------------------------------
% 3.00/1.56 % (23874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.56 % (23874)Termination reason: Unknown
% 3.00/1.56 % (23874)Termination phase: shuffling
% 3.00/1.56
% 3.00/1.56 % (23874)Memory used [KB]: 1791
% 3.00/1.56 % (23874)Time elapsed: 0.007 s
% 3.00/1.56 % (23874)Instructions burned: 17 (million)
% 3.00/1.56 % (23874)------------------------------
% 3.00/1.56 % (23874)------------------------------
% 3.00/1.56 % (23865)Instructions burned: 41 (million)
% 3.00/1.56 % (23865)------------------------------
% 3.00/1.56 % (23865)------------------------------
% 3.00/1.57 % (23875)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_23682 for (2999ds/3Mi)
% 3.00/1.57 % (23875)Instruction limit reached!
% 3.00/1.57 % (23875)------------------------------
% 3.00/1.57 % (23875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.57 % (23875)Termination reason: Unknown
% 3.00/1.57 % (23875)Termination phase: shuffling
% 3.00/1.57
% 3.00/1.57 % (23875)Memory used [KB]: 1407
% 3.00/1.57 % (23875)Time elapsed: 0.004 s
% 3.00/1.57 % (23875)Instructions burned: 4 (million)
% 3.00/1.57 % (23875)------------------------------
% 3.00/1.57 % (23875)------------------------------
% 3.00/1.57 % (23878)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_23682 for (2999ds/1041Mi)
% 3.00/1.57 % (23880)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/7Mi)
% 3.00/1.57 % (23880)Instruction limit reached!
% 3.00/1.57 % (23880)------------------------------
% 3.00/1.57 % (23880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.57 % (23880)Termination reason: Unknown
% 3.00/1.57 % (23880)Termination phase: shuffling
% 3.00/1.57
% 3.00/1.57 % (23880)Memory used [KB]: 1535
% 3.00/1.57 % (23880)Time elapsed: 0.004 s
% 3.00/1.57 % (23880)Instructions burned: 9 (million)
% 3.00/1.57 % (23880)------------------------------
% 3.00/1.57 % (23880)------------------------------
% 3.00/1.57 % (23882)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/16Mi)
% 3.00/1.57 % (23883)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_23682 for (2999ds/3Mi)
% 3.00/1.58 % (23873)Instruction limit reached!
% 3.00/1.58 % (23873)------------------------------
% 3.00/1.58 % (23873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.58 % (23873)Termination reason: Unknown
% 3.00/1.58 % (23873)Termination phase: shuffling
% 3.00/1.58
% 3.00/1.58 % (23873)Memory used [KB]: 2174
% 3.00/1.58 % (23873)Time elapsed: 0.015 s
% 3.00/1.58 % (23873)Instructions burned: 39 (million)
% 3.00/1.58 % (23873)------------------------------
% 3.00/1.58 % (23873)------------------------------
% 3.00/1.58 % (23883)Instruction limit reached!
% 3.00/1.58 % (23883)------------------------------
% 3.00/1.58 % (23883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.58 % (23883)Termination reason: Unknown
% 3.00/1.58 % (23883)Termination phase: shuffling
% 3.00/1.58
% 3.00/1.58 % (23883)Memory used [KB]: 1407
% 3.00/1.58 % (23883)Time elapsed: 0.003 s
% 3.00/1.58 % (23883)Instructions burned: 4 (million)
% 3.00/1.58 % (23883)------------------------------
% 3.00/1.58 % (23883)------------------------------
% 3.00/1.58 % (23885)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_23682 for (2999ds/3Mi)
% 3.00/1.58 % (23885)Instruction limit reached!
% 3.00/1.58 % (23885)------------------------------
% 3.00/1.58 % (23885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.58 % (23885)Termination reason: Unknown
% 3.00/1.58 % (23885)Termination phase: shuffling
% 3.00/1.58
% 3.00/1.58 % (23885)Memory used [KB]: 1407
% 3.00/1.58 % (23885)Time elapsed: 0.002 s
% 3.00/1.58 % (23885)Instructions burned: 3 (million)
% 3.00/1.58 % (23885)------------------------------
% 3.00/1.58 % (23885)------------------------------
% 3.00/1.58 % (23882)Instruction limit reached!
% 3.00/1.58 % (23882)------------------------------
% 3.00/1.58 % (23882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.58 % (23882)Termination reason: Unknown
% 3.00/1.58 % (23882)Termination phase: shuffling
% 3.00/1.58
% 3.00/1.58 % (23882)Memory used [KB]: 1791
% 3.00/1.58 % (23882)Time elapsed: 0.007 s
% 3.00/1.58 % (23882)Instructions burned: 17 (million)
% 3.00/1.58 % (23882)------------------------------
% 3.00/1.58 % (23882)------------------------------
% 3.00/1.58 % (23886)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/7Mi)
% 3.00/1.58 % (23888)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/4Mi)
% 3.00/1.59 % (23887)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/3Mi)
% 3.00/1.59 % (23886)Instruction limit reached!
% 3.00/1.59 % (23886)------------------------------
% 3.00/1.59 % (23886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.59 % (23886)Termination reason: Unknown
% 3.00/1.59 % (23886)Termination phase: shuffling
% 3.00/1.59
% 3.00/1.59 % (23886)Memory used [KB]: 1535
% 3.00/1.59 % (23886)Time elapsed: 0.004 s
% 3.00/1.59 % (23886)Instructions burned: 9 (million)
% 3.00/1.59 % (23886)------------------------------
% 3.00/1.59 % (23886)------------------------------
% 3.00/1.59 % (23887)Instruction limit reached!
% 3.00/1.59 % (23887)------------------------------
% 3.00/1.59 % (23887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.59 % (23887)Termination reason: Unknown
% 3.00/1.59 % (23887)Termination phase: shuffling
% 3.00/1.59
% 3.00/1.59 % (23887)Memory used [KB]: 1407
% 3.00/1.59 % (23887)Time elapsed: 0.003 s
% 3.00/1.59 % (23887)Instructions burned: 4 (million)
% 3.00/1.59 % (23887)------------------------------
% 3.00/1.59 % (23887)------------------------------
% 3.00/1.59 % (23888)Instruction limit reached!
% 3.00/1.59 % (23888)------------------------------
% 3.00/1.59 % (23888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.59 % (23888)Termination reason: Unknown
% 3.00/1.59 % (23888)Termination phase: shuffling
% 3.00/1.59
% 3.00/1.59 % (23888)Memory used [KB]: 1535
% 3.00/1.59 % (23888)Time elapsed: 0.003 s
% 3.00/1.59 % (23888)Instructions burned: 6 (million)
% 3.00/1.59 % (23888)------------------------------
% 3.00/1.59 % (23888)------------------------------
% 3.00/1.59 % (23889)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/18Mi)
% 3.00/1.59 % (23890)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/710Mi)
% 3.00/1.59 % (23889)Instruction limit reached!
% 3.00/1.59 % (23889)------------------------------
% 3.00/1.59 % (23889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.59 % (23889)Termination reason: Unknown
% 3.00/1.59 % (23889)Termination phase: shuffling
% 3.00/1.59
% 3.00/1.59 % (23889)Memory used [KB]: 1791
% 3.00/1.59 % (23889)Time elapsed: 0.008 s
% 3.00/1.59 % (23889)Instructions burned: 18 (million)
% 3.00/1.59 % (23889)------------------------------
% 3.00/1.59 % (23889)------------------------------
% 3.00/1.60 % (23891)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/6Mi)
% 3.00/1.60 % (23893)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/21Mi)
% 3.02/1.60 % (23892)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_23682 for (2999ds/902Mi)
% 3.02/1.60 % (23891)Instruction limit reached!
% 3.02/1.60 % (23891)------------------------------
% 3.02/1.60 % (23891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.60 % (23891)Termination reason: Unknown
% 3.02/1.60 % (23891)Termination phase: shuffling
% 3.02/1.60
% 3.02/1.60 % (23891)Memory used [KB]: 1535
% 3.02/1.60 % (23891)Time elapsed: 0.003 s
% 3.02/1.60 % (23891)Instructions burned: 6 (million)
% 3.02/1.60 % (23891)------------------------------
% 3.02/1.60 % (23891)------------------------------
% 3.02/1.60 % (23860)Instruction limit reached!
% 3.02/1.60 % (23860)------------------------------
% 3.02/1.60 % (23860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.60 % (23860)Termination reason: Unknown
% 3.02/1.60 % (23893)Instruction limit reached!
% 3.02/1.60 % (23893)------------------------------
% 3.02/1.60 % (23893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.60 % (23860)Termination phase: Saturation
% 3.02/1.60
% 3.02/1.60 % (23893)Termination reason: Unknown
% 3.02/1.60 % (23860)Memory used [KB]: 7291
% 3.02/1.60 % (23893)Termination phase: shuffling
% 3.02/1.60
% 3.02/1.60 % (23860)Time elapsed: 0.068 s
% 3.02/1.60 % (23893)Memory used [KB]: 1918
% 3.02/1.60 % (23860)Instructions burned: 183 (million)
% 3.02/1.60 % (23893)Time elapsed: 0.008 s
% 3.02/1.60 % (23860)------------------------------
% 3.02/1.60 % (23860)------------------------------
% 3.02/1.60 % (23893)Instructions burned: 21 (million)
% 3.02/1.60 % (23893)------------------------------
% 3.02/1.60 % (23893)------------------------------
% 3.02/1.61 % (23895)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/5Mi)
% 3.02/1.61 % (23896)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/6Mi)
% 3.02/1.61 % (23895)Instruction limit reached!
% 3.02/1.61 % (23895)------------------------------
% 3.02/1.61 % (23895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.61 % (23895)Termination reason: Unknown
% 3.02/1.61 % (23895)Termination phase: shuffling
% 3.02/1.61
% 3.02/1.61 % (23895)Memory used [KB]: 1535
% 3.02/1.61 % (23895)Time elapsed: 0.003 s
% 3.02/1.61 % (23895)Instructions burned: 7 (million)
% 3.02/1.61 % (23895)------------------------------
% 3.02/1.61 % (23895)------------------------------
% 3.02/1.61 % (23896)Instruction limit reached!
% 3.02/1.61 % (23896)------------------------------
% 3.02/1.61 % (23896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.61 % (23896)Termination reason: Unknown
% 3.02/1.61 % (23896)Termination phase: shuffling
% 3.02/1.61
% 3.02/1.61 % (23896)Memory used [KB]: 1535
% 3.02/1.61 % (23896)Time elapsed: 0.003 s
% 3.02/1.61 % (23896)Instructions burned: 7 (million)
% 3.02/1.61 % (23896)------------------------------
% 3.02/1.61 % (23896)------------------------------
% 3.02/1.61 % (23897)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/377Mi)
% 3.02/1.61 % (23898)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/779Mi)
% 3.02/1.62 % (23899)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/19Mi)
% 3.02/1.62 % (23900)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/879Mi)
% 3.02/1.62 % (23899)Instruction limit reached!
% 3.02/1.62 % (23899)------------------------------
% 3.02/1.62 % (23899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.62 % (23899)Termination reason: Unknown
% 3.02/1.62 % (23899)Termination phase: shuffling
% 3.02/1.62
% 3.02/1.62 % (23899)Memory used [KB]: 1791
% 3.02/1.62 % (23899)Time elapsed: 0.009 s
% 3.02/1.62 % (23899)Instructions burned: 19 (million)
% 3.02/1.62 % (23899)------------------------------
% 3.02/1.62 % (23899)------------------------------
% 3.02/1.63 % (23901)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_23682 for (2999ds/17Mi)
% 3.02/1.64 % (23892)Refutation not found, incomplete strategy
% 3.02/1.64 % (23892)------------------------------
% 3.02/1.64 % (23892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.64 % (23892)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.64
% 3.02/1.64
% 3.02/1.64 % (23892)Memory used [KB]: 7291
% 3.02/1.64 % (23892)Time elapsed: 0.041 s
% 3.02/1.64 % (23892)Instructions burned: 123 (million)
% 3.02/1.64 % (23892)------------------------------
% 3.02/1.64 % (23892)------------------------------
% 3.02/1.64 % (23901)Instruction limit reached!
% 3.02/1.64 % (23901)------------------------------
% 3.02/1.64 % (23901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.64 % (23901)Termination reason: Unknown
% 3.02/1.64 % (23901)Termination phase: shuffling
% 3.02/1.64
% 3.02/1.64 % (23901)Memory used [KB]: 1791
% 3.02/1.64 % (23901)Time elapsed: 0.007 s
% 3.02/1.64 % (23901)Instructions burned: 18 (million)
% 3.02/1.64 % (23901)------------------------------
% 3.02/1.64 % (23901)------------------------------
% 3.02/1.65 % (23903)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_23682 for (2998ds/30Mi)
% 3.02/1.66 % (23902)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23682 for (2998ds/3Mi)
% 3.02/1.66 % (23902)Instruction limit reached!
% 3.02/1.66 % (23902)------------------------------
% 3.02/1.66 % (23902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.66 % (23902)Termination reason: Unknown
% 3.02/1.66 % (23902)Termination phase: shuffling
% 3.02/1.66
% 3.02/1.66 % (23902)Memory used [KB]: 1407
% 3.02/1.66 % (23902)Time elapsed: 0.003 s
% 3.02/1.66 % (23902)Instructions burned: 4 (million)
% 3.02/1.66 % (23902)------------------------------
% 3.02/1.66 % (23902)------------------------------
% 3.02/1.66 % (23903)Instruction limit reached!
% 3.02/1.66 % (23903)------------------------------
% 3.02/1.66 % (23903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.66 % (23903)Termination reason: Unknown
% 3.02/1.66 % (23903)Termination phase: Property scanning
% 3.02/1.66
% 3.02/1.66 % (23903)Memory used [KB]: 2046
% 3.02/1.66 % (23903)Time elapsed: 0.012 s
% 3.02/1.66 % (23903)Instructions burned: 33 (million)
% 3.02/1.66 % (23903)------------------------------
% 3.02/1.66 % (23903)------------------------------
% 3.02/1.67 % (23905)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_23682 for (2998ds/100Mi)
% 3.02/1.67 % (23904)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_23682 for (2998ds/127Mi)
% 3.02/1.70 % (23905)Instruction limit reached!
% 3.02/1.70 % (23905)------------------------------
% 3.02/1.70 % (23905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.70 % (23905)Termination reason: Unknown
% 3.02/1.70 % (23905)Termination phase: Property scanning
% 3.02/1.70
% 3.02/1.70 % (23905)Memory used [KB]: 2686
% 3.02/1.70 % (23905)Time elapsed: 0.029 s
% 3.02/1.70 % (23905)Instructions burned: 102 (million)
% 3.02/1.70 % (23905)------------------------------
% 3.02/1.70 % (23905)------------------------------
% 3.02/1.71 % (23908)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_23682 for (2998ds/3Mi)
% 3.02/1.71 % (23908)Instruction limit reached!
% 3.02/1.71 % (23908)------------------------------
% 3.02/1.71 % (23908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.71 % (23908)Termination reason: Unknown
% 3.02/1.71 % (23908)Termination phase: shuffling
% 3.02/1.71
% 3.02/1.71 % (23908)Memory used [KB]: 1407
% 3.02/1.71 % (23908)Time elapsed: 0.002 s
% 3.02/1.71 % (23908)Instructions burned: 3 (million)
% 3.02/1.71 % (23908)------------------------------
% 3.02/1.71 % (23908)------------------------------
% 3.02/1.72 % (23912)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_23682 for (2998ds/20Mi)
% 3.02/1.72 % (23904)Instruction limit reached!
% 3.02/1.72 % (23904)------------------------------
% 3.02/1.72 % (23904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.72 % (23904)Termination reason: Unknown
% 3.02/1.72 % (23904)Termination phase: Saturation
% 3.02/1.72
% 3.02/1.72 % (23904)Memory used [KB]: 7036
% 3.02/1.72 % (23904)Time elapsed: 0.052 s
% 3.02/1.72 % (23904)Instructions burned: 127 (million)
% 3.02/1.72 % (23904)------------------------------
% 3.02/1.72 % (23904)------------------------------
% 3.02/1.72 % (23898)First to succeed.
% 3.02/1.72 % (23912)Instruction limit reached!
% 3.02/1.72 % (23912)------------------------------
% 3.02/1.72 % (23912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.72 % (23912)Termination reason: Unknown
% 3.02/1.72 % (23912)Termination phase: shuffling
% 3.02/1.72
% 3.02/1.72 % (23912)Memory used [KB]: 1791
% 3.02/1.72 % (23912)Time elapsed: 0.008 s
% 3.02/1.72 % (23912)Instructions burned: 20 (million)
% 3.02/1.72 % (23912)------------------------------
% 3.02/1.72 % (23912)------------------------------
% 3.02/1.72 % (23898)Refutation found. Thanks to Tanya!
% 3.02/1.72 % SZS status Theorem for DTF2THF_23682
% 3.02/1.72 % SZS output start Proof for DTF2THF_23682
% 3.02/1.72 thf(type_def_5, type, itself: ($tType) > $tType).
% 3.02/1.72 thf(type_def_7, type, n: $tType).
% 3.02/1.72 thf(type_def_8, type, t: $tType).
% 3.02/1.72 thf(type_def_9, type, dtree: $tType).
% 3.02/1.72 thf(type_def_10, type, sum_sum: ($tType * $tType) > $tType).
% 3.02/1.72 thf(type_def_11, type, set: ($tType) > $tType).
% 3.02/1.72 thf(func_def_0, type, sum_sum: ($tType * $tType) > $tType).
% 3.02/1.72 thf(func_def_1, type, dtree: $tType).
% 3.02/1.72 thf(func_def_2, type, set: ($tType) > $tType).
% 3.02/1.72 thf(func_def_3, type, t: $tType).
% 3.02/1.72 thf(func_def_4, type, n: $tType).
% 3.02/1.72 thf(func_def_5, type, itself: ($tType) > $tType).
% 3.02/1.72 thf(func_def_6, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.02/1.72 thf(func_def_7, type, bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.02/1.72 thf(func_def_8, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.02/1.72 thf(func_def_9, type, top: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.02/1.72 thf(func_def_10, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.02/1.72 thf(func_def_11, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.02/1.72 thf(func_def_12, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.02/1.72 thf(func_def_13, type, order_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.02/1.72 thf(func_def_14, type, node: n > set @ sum_sum @ t @ dtree > dtree).
% 3.02/1.72 thf(func_def_15, type, cont: dtree > set @ sum_sum @ t @ dtree).
% 3.02/1.72 thf(func_def_16, type, corec: !>[X0: $tType]:((X0 > n) > (X0 > set @ sum_sum @ t @ sum_sum @ dtree @ X0) > X0 > dtree)).
% 3.02/1.72 thf(func_def_17, type, root: dtree > n).
% 3.02/1.72 thf(func_def_18, type, unfold: !>[X0: $tType]:((X0 > n) > (X0 > set @ sum_sum @ t @ X0) > X0 > dtree)).
% 3.02/1.72 thf(func_def_19, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X0) > X2 > X1)).
% 3.02/1.72 thf(func_def_20, type, id: !>[X0: $tType]:(X0 > X0)).
% 3.02/1.72 thf(func_def_21, type, gram_L1451583635elle_S: n > set @ sum_sum @ t @ n).
% 3.02/1.72 thf(func_def_22, type, gram_L1231612515_deftr: n > dtree).
% 3.02/1.72 thf(func_def_23, type, gram_L1004374585hsubst: dtree > dtree > dtree).
% 3.02/1.72 thf(func_def_24, type, gram_L1905609002ubst_c: dtree > dtree > set @ sum_sum @ t @ dtree).
% 3.02/1.72 thf(func_def_25, type, gram_L1905609017ubst_r: dtree > n).
% 3.02/1.72 thf(func_def_26, type, gram_L1333338417e_inFr: set @ n > dtree > t > $o).
% 3.02/1.72 thf(func_def_27, type, gram_L805317441_inFr2: set @ n > dtree > t > $o).
% 3.02/1.72 thf(func_def_28, type, gram_L805317505_inFrr: set @ n > dtree > t > $o).
% 3.02/1.72 thf(func_def_29, type, gram_L830233218_inItr: set @ n > dtree > n > $o).
% 3.02/1.72 thf(func_def_30, type, gram_L1918716148le_reg: (n > dtree) > dtree > $o).
% 3.02/1.72 thf(func_def_31, type, gram_L646766332egular: dtree > $o).
% 3.02/1.72 thf(func_def_32, type, gram_L716654942_subtr: set @ n > dtree > dtree > $o).
% 3.02/1.72 thf(func_def_33, type, gram_L1283001940subtr2: set @ n > dtree > dtree > $o).
% 3.02/1.72 thf(func_def_34, type, gram_L1614515765ubtrOf: dtree > n > dtree).
% 3.02/1.72 thf(func_def_35, type, gram_L864798063lle_wf: dtree > $o).
% 3.02/1.72 thf(func_def_36, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.02/1.72 thf(func_def_37, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 3.02/1.72 thf(func_def_38, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.02/1.72 thf(func_def_39, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.02/1.72 thf(func_def_40, type, top_top: !>[X0: $tType]:(X0)).
% 3.02/1.73 thf(func_def_41, type, type2: !>[X0: $tType]:(itself @ X0)).
% 3.02/1.73 thf(func_def_42, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.02/1.73 thf(func_def_43, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 3.02/1.73 thf(func_def_44, type, vimage: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X1 > set @ X0)).
% 3.02/1.73 thf(func_def_45, type, sum_Inl: !>[X0: $tType, X1: $tType]:(X0 > sum_sum @ X0 @ X1)).
% 3.02/1.73 thf(func_def_46, type, sum_Inr: !>[X0: $tType, X1: $tType]:(X0 > sum_sum @ X1 @ X0)).
% 3.02/1.73 thf(func_def_47, type, sum_rec_sum: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1)).
% 3.02/1.73 thf(func_def_48, type, type_definition: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > X0) > set @ X1 > $o)).
% 3.02/1.73 thf(func_def_49, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.02/1.73 thf(func_def_50, type, f: n > dtree).
% 3.02/1.73 thf(func_def_51, type, tr: dtree).
% 3.02/1.73 thf(func_def_73, type, sK1: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > $o) > X1)).
% 3.02/1.73 thf(func_def_74, type, sK2: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > $o) > X0)).
% 3.02/1.73 thf(func_def_75, type, sK3: (dtree > dtree > $o) > dtree).
% 3.02/1.73 thf(func_def_76, type, sK4: (dtree > dtree > $o) > dtree).
% 3.02/1.73 thf(func_def_77, type, sK5: (dtree > dtree > $o) > dtree).
% 3.02/1.73 thf(func_def_78, type, sK6: (dtree > dtree > $o) > dtree).
% 3.02/1.73 thf(func_def_79, type, sK7: set @ n > t > dtree > dtree).
% 3.02/1.73 thf(func_def_80, type, sK8: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 3.02/1.73 thf(func_def_81, type, sK9: !>[X0: $tType]:(set @ X0 > X0)).
% 3.02/1.73 thf(func_def_82, type, sK10: !>[X0: $tType, X1: $tType]:(sum_sum @ X1 @ X0 > X1)).
% 3.02/1.73 thf(func_def_83, type, sK11: !>[X0: $tType, X1: $tType]:(sum_sum @ X1 @ X0 > X0)).
% 3.02/1.73 thf(func_def_84, type, sK12: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 3.02/1.73 thf(func_def_85, type, sK13: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 3.02/1.73 thf(func_def_86, type, sK14: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 3.02/1.73 thf(func_def_87, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > (sum_sum @ X1 @ X2 > X0) > $o > X1)).
% 3.02/1.73 thf(func_def_88, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType]:(X1 > (sum_sum @ X0 @ X2 > X1) > $o > X2)).
% 3.02/1.73 thf(func_def_89, type, sK17: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 3.02/1.73 thf(func_def_90, type, sK18: !>[X0: $tType]:(set @ X0 > X0 > set @ X0 > X0 > set @ X0)).
% 3.02/1.73 thf(func_def_91, type, sK19: !>[X0: $tType]:((X0 > X0) > X0)).
% 3.02/1.73 thf(func_def_92, type, sK20: !>[X0: $tType]:(set @ X0 > X0)).
% 3.02/1.73 thf(func_def_93, type, sK21: t > dtree > set @ n > dtree).
% 3.02/1.73 thf(func_def_94, type, sK22: !>[X0: $tType]:(X0)).
% 3.02/1.73 thf(func_def_95, type, sK23: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.02/1.73 thf(func_def_96, type, sK24: dtree > dtree > set @ n > dtree).
% 3.02/1.73 thf(func_def_97, type, ph25: !>[X0: $tType]:(X0)).
% 3.02/1.73 thf(f2792,plain,(
% 3.02/1.73 $false),
% 3.02/1.73 inference(trivial_inequality_removal,[status(thm)],[f2789])).
% 3.02/1.73 thf(f2789,plain,(
% 3.02/1.73 ($false = $true)),
% 3.02/1.73 inference(superposition,[status(thm)],[f1813,f2785])).
% 3.02/1.73 thf(f2785,plain,(
% 3.02/1.73 ((member @ n @ (root @ tr) @ top_top @ set @ n) = $false)),
% 3.02/1.73 inference(subsumption_resolution,[status(thm)],[f2783,f2050])).
% 3.02/1.73 thf(f2050,plain,(
% 3.02/1.73 (tr != (f @ (root @ tr)))),
% 3.02/1.73 inference(equality_proxy_clausification,[status(thm)],[f2049])).
% 3.02/1.73 thf(f2049,plain,(
% 3.02/1.73 ((tr = (f @ (root @ tr))) = $false)),
% 3.02/1.73 inference(not_proxy_clausification,[status(thm)],[f1226])).
% 3.02/1.73 thf(f1226,plain,(
% 3.02/1.73 ((~ (tr = (f @ (root @ tr)))) = $true)),
% 3.02/1.73 inference(cnf_transformation,[status(thm)],[f742])).
% 3.02/1.73 thf(f742,plain,(
% 3.02/1.73 ((~ (tr = (f @ (root @ tr)))) = $true)),
% 3.02/1.73 inference(fool_elimination,[status(thm)],[f280])).
% 3.02/1.73 thf(f280,negated_conjecture,(
% 3.02/1.73 ~(tr = (f @ (root @ tr)))),
% 3.02/1.73 inference(negated_conjecture,[status(cth)],[f279])).
% 3.02/1.73 thf(f279,conjecture,(
% 3.02/1.73 (tr = (f @ (root @ tr)))),
% 3.02/1.73 file('/export/starexec/sandbox2/tmp/tmp.dpsNr913pg/DTF2THF_23682.p',conj_0)).
% 3.02/1.73 thf(f2783,plain,(
% 3.02/1.73 ((member @ n @ (root @ tr) @ top_top @ set @ n) = $false) | (tr = (f @ (root @ tr)))),
% 3.02/1.73 inference(trivial_inequality_removal,[status(thm)],[f2776])).
% 3.02/1.73 thf(f2776,plain,(
% 3.02/1.73 ((member @ n @ (root @ tr) @ top_top @ set @ n) = $false) | (tr = (f @ (root @ tr))) | ($false = $true)),
% 3.02/1.73 inference(superposition,[status(thm)],[f1631,f2480])).
% 3.02/1.73 thf(f2480,plain,(
% 3.02/1.73 ( ! [X1 : dtree] : (($false = (gram_L716654942_subtr @ top_top @ set @ n @ X1 @ tr)) | ((f @ (root @ X1)) = X1)) )),
% 3.02/1.73 inference(equality_proxy_clausification,[status(thm)],[f2479])).
% 3.02/1.73 thf(f2479,plain,(
% 3.02/1.73 ( ! [X1 : dtree] : (($true = ((f @ (root @ X1)) = X1)) | ($false = (gram_L716654942_subtr @ top_top @ set @ n @ X1 @ tr))) )),
% 3.02/1.73 inference(binary_proxy_clausification,[status(thm)],[f2478])).
% 3.02/1.73 thf(f2478,plain,(
% 3.02/1.73 ( ! [X1 : dtree] : ((((gram_L716654942_subtr @ top_top @ set @ n @ X1 @ tr) => ((f @ (root @ X1)) = X1)) = $true)) )),
% 3.02/1.73 inference(beta_eta_normalization,[status(thm)],[f2477])).
% 3.02/1.73 thf(f2477,plain,(
% 3.02/1.73 ( ! [X1 : dtree] : ((((^[Y0 : dtree]: ((gram_L716654942_subtr @ top_top @ set @ n @ Y0 @ tr) => ((f @ (root @ Y0)) = Y0))) @ X1) = $true)) )),
% 3.02/1.73 inference(pi_clausification,[status(thm)],[f1235])).
% 3.02/1.73 thf(f1235,plain,(
% 3.02/1.73 ((!! @ dtree @ (^[Y0 : dtree]: ((gram_L716654942_subtr @ top_top @ set @ n @ Y0 @ tr) => ((f @ (root @ Y0)) = Y0)))) = $true)),
% 3.02/1.73 inference(beta_eta_normalization,[status(thm)],[f1232])).
% 3.02/1.73 thf(f1232,plain,(
% 3.02/1.73 (((^[Y0 : n > dtree]: ((^[Y1 : dtree]: (!! @ dtree @ (^[Y2 : dtree]: ((gram_L716654942_subtr @ top_top @ set @ n @ Y2 @ Y1) => ((Y0 @ (root @ Y2)) = Y2))))))) @ f @ tr) = $true)),
% 3.02/1.73 inference(definition_unfolding,[status(thm)],[f1223,f1141])).
% 3.02/1.73 thf(f1141,plain,(
% 3.02/1.73 (gram_L1918716148le_reg = (^[Y0 : n > dtree]: ((^[Y1 : dtree]: (!! @ dtree @ (^[Y2 : dtree]: ((gram_L716654942_subtr @ top_top @ set @ n @ Y2 @ Y1) => ((Y0 @ (root @ Y2)) = Y2))))))))),
% 3.02/1.73 inference(cnf_transformation,[status(thm)],[f477])).
% 3.02/1.73 thf(f477,plain,(
% 3.02/1.73 (gram_L1918716148le_reg = (^[Y0 : n > dtree]: ((^[Y1 : dtree]: (!! @ dtree @ (^[Y2 : dtree]: ((gram_L716654942_subtr @ top_top @ set @ n @ Y2 @ Y1) => ((Y0 @ (root @ Y2)) = Y2))))))))),
% 3.02/1.73 inference(fool_elimination,[status(thm)],[f476])).
% 3.02/1.73 thf(f476,plain,(
% 3.02/1.73 ((^[X0 : n > dtree, X1 : dtree] : (! [X2 : dtree] : ((gram_L716654942_subtr @ top_top @ set @ n @ X2 @ X1) => ((X0 @ (root @ X2)) = X2)))) = gram_L1918716148le_reg)),
% 3.02/1.73 inference(rectify,[status(thm)],[f44])).
% 3.02/1.73 thf(f44,axiom,(
% 3.02/1.73 ((^[X10 : n > dtree, X9 : dtree] : (! [X17 : dtree] : ((gram_L716654942_subtr @ top_top @ set @ n @ X17 @ X9) => ((X10 @ (root @ X17)) = X17)))) = gram_L1918716148le_reg)),
% 3.02/1.73 file('/export/starexec/sandbox2/tmp/tmp.dpsNr913pg/DTF2THF_23682.p',fact_43_reg__def)).
% 3.02/1.73 thf(f1223,plain,(
% 3.02/1.73 ((gram_L1918716148le_reg @ f @ tr) = $true)),
% 3.02/1.73 inference(cnf_transformation,[status(thm)],[f794])).
% 3.02/1.73 thf(f794,plain,(
% 3.02/1.73 ((gram_L1918716148le_reg @ f @ tr) = $true)),
% 3.02/1.73 inference(fool_elimination,[status(thm)],[f793])).
% 3.02/1.73 thf(f793,plain,(
% 3.02/1.73 (gram_L1918716148le_reg @ f @ tr)),
% 3.02/1.73 inference(rectify,[status(thm)],[f1])).
% 3.02/1.73 thf(f1,axiom,(
% 3.02/1.73 (gram_L1918716148le_reg @ f @ tr)),
% 3.02/1.73 file('/export/starexec/sandbox2/tmp/tmp.dpsNr913pg/DTF2THF_23682.p',fact_0_assms)).
% 3.02/1.73 thf(f1631,plain,(
% 3.02/1.73 ( ! [X2 : dtree,X1 : set @ n] : (($true = (gram_L716654942_subtr @ X1 @ X2 @ X2)) | ($false = (member @ n @ (root @ X2) @ X1))) )),
% 3.02/1.73 inference(binary_proxy_clausification,[status(thm)],[f1630])).
% 3.02/1.73 thf(f1630,plain,(
% 3.02/1.73 ( ! [X2 : dtree,X1 : set @ n] : (($true = ((member @ n @ (root @ X2) @ X1) => (gram_L716654942_subtr @ X1 @ X2 @ X2)))) )),
% 3.02/1.73 inference(beta_eta_normalization,[status(thm)],[f1629])).
% 3.02/1.73 thf(f1629,plain,(
% 3.02/1.73 ( ! [X2 : dtree,X1 : set @ n] : (($true = ((^[Y0 : dtree]: ((member @ n @ (root @ Y0) @ X1) => (gram_L716654942_subtr @ X1 @ Y0 @ Y0))) @ X2))) )),
% 3.02/1.73 inference(pi_clausification,[status(thm)],[f1628])).
% 3.02/1.73 thf(f1628,plain,(
% 3.02/1.73 ( ! [X1 : set @ n] : (((!! @ dtree @ (^[Y0 : dtree]: ((member @ n @ (root @ Y0) @ X1) => (gram_L716654942_subtr @ X1 @ Y0 @ Y0)))) = $true)) )),
% 3.02/1.73 inference(beta_eta_normalization,[status(thm)],[f1627])).
% 3.02/1.73 thf(f1627,plain,(
% 3.02/1.73 ( ! [X1 : set @ n] : ((((^[Y0 : set @ n]: (!! @ dtree @ (^[Y1 : dtree]: ((member @ n @ (root @ Y1) @ Y0) => (gram_L716654942_subtr @ Y0 @ Y1 @ Y1))))) @ X1) = $true)) )),
% 3.02/1.73 inference(pi_clausification,[status(thm)],[f1086])).
% 3.02/1.73 thf(f1086,plain,(
% 3.02/1.73 ((!! @ set @ n @ (^[Y0 : set @ n]: (!! @ dtree @ (^[Y1 : dtree]: ((member @ n @ (root @ Y1) @ Y0) => (gram_L716654942_subtr @ Y0 @ Y1 @ Y1)))))) = $true)),
% 3.02/1.73 inference(cnf_transformation,[status(thm)],[f816])).
% 3.02/1.73 thf(f816,plain,(
% 3.02/1.73 ((!! @ set @ n @ (^[Y0 : set @ n]: (!! @ dtree @ (^[Y1 : dtree]: ((member @ n @ (root @ Y1) @ Y0) => (gram_L716654942_subtr @ Y0 @ Y1 @ Y1)))))) = $true)),
% 3.02/1.73 inference(fool_elimination,[status(thm)],[f815])).
% 3.02/1.73 thf(f815,plain,(
% 3.02/1.73 ! [X0 : dtree,X1 : set @ n] : ((member @ n @ (root @ X0) @ X1) => (gram_L716654942_subtr @ X1 @ X0 @ X0))),
% 3.02/1.73 inference(rectify,[status(thm)],[f34])).
% 3.02/1.73 thf(f34,axiom,(
% 3.02/1.73 ! [X6 : dtree,X7 : set @ n] : ((member @ n @ (root @ X6) @ X7) => (gram_L716654942_subtr @ X7 @ X6 @ X6))),
% 3.02/1.73 file('/export/starexec/sandbox2/tmp/tmp.dpsNr913pg/DTF2THF_23682.p',fact_33_subtr_ORefl)).
% 3.02/1.73 thf(f1813,plain,(
% 3.02/1.73 ( ! [X0 : $tType,X1 : X0] : (($true = (member @ X0 @ X1 @ top_top @ set @ X0))) )),
% 3.02/1.73 inference(beta_eta_normalization,[status(thm)],[f1812])).
% 3.02/1.73 thf(f1812,plain,(
% 3.02/1.73 ( ! [X0 : $tType,X1 : X0] : ((((^[Y0 : X0]: (member @ X0 @ Y0 @ top_top @ set @ X0)) @ X1) = $true)) )),
% 3.02/1.73 inference(pi_clausification,[status(thm)],[f1169])).
% 3.02/1.73 thf(f1169,plain,(
% 3.02/1.73 ( ! [X0 : $tType] : (((!! @ X0 @ (^[Y0 : X0]: (member @ X0 @ Y0 @ top_top @ set @ X0))) = $true)) )),
% 3.02/1.73 inference(cnf_transformation,[status(thm)],[f886])).
% 3.02/1.73 thf(f886,plain,(
% 3.02/1.73 ! [X0 : $tType] : ((!! @ X0 @ (^[Y0 : X0]: (member @ X0 @ Y0 @ top_top @ set @ X0))) = $true)),
% 3.02/1.73 inference(closure,[status(thm)],[f747])).
% 3.02/1.73 thf(f747,plain,(
% 3.02/1.73 ( ! [X0 : $tType] : (((!! @ X0 @ (^[Y0 : X0]: (member @ X0 @ Y0 @ top_top @ set @ X0))) = $true)) )),
% 3.02/1.73 inference(fool_elimination,[status(thm)],[f746])).
% 3.02/1.73 thf(f746,plain,(
% 3.02/1.73 ! [X0 : $tType,X1 : X0] : (member @ X0 @ X1 @ top_top @ set @ X0)),
% 3.02/1.73 inference(rectify,[status(thm)],[f107])).
% 3.02/1.73 thf(f107,axiom,(
% 3.02/1.73 ! [X0 : $tType,X29 : X0] : (member @ X0 @ X29 @ top_top @ set @ X0)),
% 3.02/1.73 file('/export/starexec/sandbox2/tmp/tmp.dpsNr913pg/DTF2THF_23682.p',fact_106_iso__tuple__UNIV__I)).
% 3.02/1.73 % SZS output end Proof for DTF2THF_23682
% 3.02/1.73 % (23898)------------------------------
% 3.02/1.73 % (23898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.73 % (23898)Termination reason: Refutation
% 3.02/1.73
% 3.02/1.73 % (23898)Memory used [KB]: 7931
% 3.02/1.73 % (23898)Time elapsed: 0.112 s
% 3.02/1.73 % (23898)Instructions burned: 367 (million)
% 3.02/1.73 % (23898)------------------------------
% 3.02/1.73 % (23898)------------------------------
% 3.02/1.73 % (23855)Success in time 0.214 s
%------------------------------------------------------------------------------