%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : COM194^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.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 08:41:55 AM UTC 2026
% Result : Theorem 2.89s 1.61s
% Output : Refutation 2.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COM194^1 : TPTP v9.2.1. Released v7.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n025.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 04:17:27 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : COM194^1 : TPTP v9.2.1. Released v7.0.0.
% 0.30/0.46 % Domain : Computing Theory
% 0.30/0.46 % Problem : Grammars and languages 1238
% 0.30/0.46 % Version : [Bla16] axioms : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.30/0.46 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.30/0.46 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bla16]
% 0.30/0.46 % Names : gram_lang__1238.p [Bla16]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.33 v9.1.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.30/0.46 % Syntax : Number of formulae : 334 ( 135 unt; 62 typ; 0 def)
% 0.30/0.46 % Number of atoms : 677 ( 297 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 7 ( 2 avg)
% 0.30/0.46 % Number of connectives : 3834 ( 73 ~; 19 |; 77 &;3394 @)
% 0.30/0.46 % ( 0 <=>; 271 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 21 ( 7 avg)
% 0.30/0.46 % Number of types : 4 ( 3 usr)
% 0.30/0.46 % Number of type conns : 224 ( 224 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 62 ( 59 usr; 8 con; 0-6 aty)
% 0.30/0.46 % Number of variables : 989 ( 51 ^; 856 !; 52 ?; 989 :)
% 0.30/0.46 % ( 30 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.46 % SPC : TH1_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.30/0.46 % 2016-07-13 14:47:54.192
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 %----Could-be-implicit typings (7)
% 0.30/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.30/0.46 product_prod: $tType > $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Sum__Type_Osum,type,
% 0.30/0.46 sum_sum: $tType > $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_DTree_Odtree,type,
% 0.30/0.46 dtree: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Set_Oset,type,
% 0.30/0.46 set: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_DTree_OT,type,
% 0.30/0.46 t: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_DTree_ON,type,
% 0.30/0.46 n: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_itself,type,
% 0.30/0.46 itself: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 %----Explicit typings (55)
% 0.30/0.46 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.30/0.46 bounded_lattice:
% 0.30/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_HOL_Otype,type,
% 0.30/0.46 type:
% 0.30/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Obot,type,
% 0.30/0.46 bot:
% 0.30/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Otop,type,
% 0.30/0.46 top:
% 0.30/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 0.30/0.46 bounded_lattice_top:
% 0.30/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_DTree_ONode,type,
% 0.30/0.46 node: n > ( set @ ( sum_sum @ t @ dtree ) ) > dtree ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_DTree_Ocont,type,
% 0.30/0.46 cont: dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_DTree_Odtree_Oroot,type,
% 0.30/0.46 root: dtree > n ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_DTree_Ounfold,type,
% 0.30/0.46 unfold:
% 0.30/0.46 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ A ) ) ) > A > dtree ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Fun_Ocomp,type,
% 0.30/0.46 comp:
% 0.30/0.46 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OFr,type,
% 0.30/0.46 gram_L861583724lle_Fr: ( set @ n ) > dtree > ( set @ t ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OFrr,type,
% 0.30/0.46 gram_L1556062726le_Frr: ( set @ n ) > dtree > ( set @ t ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH,type,
% 0.30/0.46 gram_L1451583624elle_H: dtree > n > dtree ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__c,type,
% 0.30/0.46 gram_L1221482011le_H_c: dtree > n > ( set @ ( sum_sum @ t @ n ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__r,type,
% 0.30/0.46 gram_L1221482026le_H_r: dtree > n > n ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OL,type,
% 0.30/0.46 gram_L1451583628elle_L: ( set @ n ) > n > ( set @ ( set @ t ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OP,type,
% 0.30/0.46 gram_L1451583632elle_P: set @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr,type,
% 0.30/0.46 gram_L1231612515_deftr: n > dtree ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst,type,
% 0.30/0.46 gram_L1004374585hsubst: dtree > dtree > dtree ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c,type,
% 0.30/0.46 gram_L1905609002ubst_c: dtree > dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r,type,
% 0.30/0.46 gram_L1905609017ubst_r: dtree > n ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr,type,
% 0.30/0.46 gram_L1333338417e_inFr: ( set @ n ) > dtree > t > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2,type,
% 0.30/0.46 gram_L805317441_inFr2: ( set @ n ) > dtree > t > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFrr,type,
% 0.30/0.46 gram_L805317505_inFrr: ( set @ n ) > dtree > t > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr,type,
% 0.30/0.46 gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Opick,type,
% 0.30/0.46 gram_L315592705e_pick: dtree > n > dtree ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Orcut,type,
% 0.30/0.46 gram_L1828378864e_rcut: dtree > dtree ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oreg,type,
% 0.30/0.46 gram_L1918716148le_reg: ( n > dtree ) > dtree > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oregular,type,
% 0.30/0.46 gram_L646766332egular: dtree > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr,type,
% 0.30/0.46 gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr2,type,
% 0.30/0.46 gram_L1283001940subtr2: ( set @ n ) > dtree > dtree > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OsubtrOf,type,
% 0.30/0.46 gram_L1614515765ubtrOf: dtree > n > dtree ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf,type,
% 0.30/0.46 gram_L864798063lle_wf: dtree > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.30/0.46 minus_minus:
% 0.30/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_If,type,
% 0.30/0.46 if:
% 0.30/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.30/0.46 sup_sup:
% 0.30/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.30/0.46 bot_bot:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.30/0.46 top_top:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair,type,
% 0.30/0.46 product_Pair:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Pure_Otype,type,
% 0.30/0.46 type2:
% 0.30/0.46 !>[A: $tType] : ( itself @ A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect,type,
% 0.30/0.46 collect:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oinsert,type,
% 0.30/0.46 insert:
% 0.30/0.46 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Ois__singleton,type,
% 0.30/0.46 is_singleton:
% 0.30/0.46 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Ovimage,type,
% 0.30/0.46 vimage:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Sum__Type_OInl,type,
% 0.30/0.46 sum_Inl:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Sum__Type_OInr,type,
% 0.30/0.46 sum_Inr:
% 0.30/0.46 !>[B: $tType,A: $tType] : ( B > ( sum_sum @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum,type,
% 0.30/0.46 sum_rec_sum:
% 0.30/0.46 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member,type,
% 0.30/0.46 member:
% 0.30/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_K____,type,
% 0.30/0.46 k: n > ( set @ t ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_ftr____,type,
% 0.30/0.46 ftr: n > dtree ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_n,type,
% 0.30/0.46 n2: n ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_ns,type,
% 0.30/0.46 ns: set @ n ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_tns____,type,
% 0.30/0.46 tns: set @ ( sum_sum @ t @ n ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_tr_H____,type,
% 0.30/0.46 tr: dtree ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_tr____,type,
% 0.30/0.46 tr2: dtree ).
% 0.30/0.46
% 0.30/0.46 %----Relevant facts (256)
% 0.30/0.46 thf(fact_0_dtr,axiom,
% 0.30/0.46 gram_L864798063lle_wf @ tr2 ).
% 0.30/0.46
% 0.30/0.46 % dtr
% 0.30/0.46 thf(fact_1_tr_H__def,axiom,
% 0.30/0.46 ( tr
% 0.30/0.46 = ( gram_L1004374585hsubst @ tr2 @ tr2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % tr'_def
% 0.30/0.46 thf(fact_2_wf__hsubst,axiom,
% 0.30/0.46 ! [Tr0: dtree,Tr: dtree] :
% 0.30/0.46 ( ( gram_L864798063lle_wf @ Tr0 )
% 0.30/0.46 => ( ( gram_L864798063lle_wf @ Tr )
% 0.30/0.46 => ( gram_L864798063lle_wf @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % wf_hsubst
% 0.30/0.46 thf(fact_3_wf__rcut,axiom,
% 0.30/0.46 ! [Tr0: dtree] :
% 0.30/0.46 ( ( gram_L864798063lle_wf @ Tr0 )
% 0.30/0.46 => ( gram_L864798063lle_wf @ ( gram_L1828378864e_rcut @ Tr0 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % wf_rcut
% 0.30/0.46 thf(fact_4_wf__deftr,axiom,
% 0.30/0.46 ! [N: n] : ( gram_L864798063lle_wf @ ( gram_L1231612515_deftr @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % wf_deftr
% 0.30/0.46 thf(fact_5_rtr,axiom,
% 0.30/0.46 ( ( root @ tr2 )
% 0.30/0.46 = n2 ) ).
% 0.30/0.46
% 0.30/0.46 % rtr
% 0.30/0.46 thf(fact_6_n,axiom,
% 0.30/0.46 member @ n @ n2 @ ns ).
% 0.30/0.46
% 0.30/0.46 % n
% 0.30/0.46 thf(fact_7_root__hsubst,axiom,
% 0.30/0.46 ! [Tr0: dtree,Tr: dtree] :
% 0.30/0.46 ( ( root @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 0.30/0.46 = ( root @ Tr ) ) ).
% 0.30/0.46
% 0.30/0.46 % root_hsubst
% 0.30/0.46 thf(fact_8_wf__subtr,axiom,
% 0.30/0.46 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 0.30/0.46 ( ( gram_L864798063lle_wf @ Tr1 )
% 0.30/0.46 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.30/0.46 => ( gram_L864798063lle_wf @ Tr ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % wf_subtr
% 0.30/0.46 thf(fact_9_hsubst__def,axiom,
% 0.30/0.46 ( gram_L1004374585hsubst
% 0.30/0.46 = ( ^ [Tr02: dtree] : ( unfold @ dtree @ gram_L1905609017ubst_r @ ( gram_L1905609002ubst_c @ Tr02 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % hsubst_def
% 0.30/0.46 thf(fact_10_hsubst__eq,axiom,
% 0.30/0.46 ! [Tr: dtree,Tr0: dtree] :
% 0.30/0.46 ( ( ( root @ Tr )
% 0.30/0.46 = ( root @ Tr0 ) )
% 0.30/0.46 => ( ( gram_L1004374585hsubst @ Tr0 @ Tr )
% 0.30/0.46 = ( gram_L1004374585hsubst @ Tr0 @ Tr0 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % hsubst_eq
% 0.30/0.46 thf(fact_11_inFr__hsubst__notin,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr: dtree,T2: t,Tr0: dtree] :
% 0.30/0.46 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.30/0.46 => ( ~ ( member @ n @ ( root @ Tr0 ) @ Ns )
% 0.30/0.46 => ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr_hsubst_notin
% 0.30/0.46 thf(fact_12_root__o__subst,axiom,
% 0.30/0.46 ! [Tr0: dtree] :
% 0.30/0.46 ( ( comp @ dtree @ n @ dtree @ root @ ( gram_L1004374585hsubst @ Tr0 ) )
% 0.30/0.46 = root ) ).
% 0.30/0.46
% 0.30/0.46 % root_o_subst
% 0.30/0.46 thf(fact_13_wf__cont,axiom,
% 0.30/0.46 ! [Tr: dtree,Tr2: dtree] :
% 0.30/0.46 ( ( gram_L864798063lle_wf @ Tr )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 0.30/0.46 => ( gram_L864798063lle_wf @ Tr2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % wf_cont
% 0.30/0.46 thf(fact_14_wf__pick,axiom,
% 0.30/0.46 ! [Tr0: dtree,N: n] :
% 0.30/0.46 ( ( gram_L864798063lle_wf @ Tr0 )
% 0.30/0.46 => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.30/0.46 => ( gram_L864798063lle_wf @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % wf_pick
% 0.30/0.46 thf(fact_15_root__deftr,axiom,
% 0.30/0.46 ! [N: n] :
% 0.30/0.46 ( ( root @ ( gram_L1231612515_deftr @ N ) )
% 0.30/0.46 = N ) ).
% 0.30/0.46
% 0.30/0.46 % root_deftr
% 0.30/0.46 thf(fact_16_root__rcut,axiom,
% 0.30/0.46 ! [Tr0: dtree] :
% 0.30/0.46 ( ( root @ ( gram_L1828378864e_rcut @ Tr0 ) )
% 0.30/0.46 = ( root @ Tr0 ) ) ).
% 0.30/0.46
% 0.30/0.46 % root_rcut
% 0.30/0.46 thf(fact_17_wf__inj,axiom,
% 0.30/0.46 ! [Tr: dtree,Tr1: dtree,Tr22: dtree] :
% 0.30/0.46 ( ( gram_L864798063lle_wf @ Tr )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr ) )
% 0.30/0.46 => ( ( ( root @ Tr1 )
% 0.30/0.46 = ( root @ Tr22 ) )
% 0.30/0.46 = ( Tr1 = Tr22 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % wf_inj
% 0.30/0.46 thf(fact_18_pick,axiom,
% 0.30/0.46 ! [Tr0: dtree,N: n] :
% 0.30/0.46 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.30/0.46 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ Tr0 @ N ) @ Tr0 )
% 0.30/0.46 & ( ( root @ ( gram_L315592705e_pick @ Tr0 @ N ) )
% 0.30/0.46 = N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pick
% 0.30/0.46 thf(fact_19_inFr_OInd,axiom,
% 0.30/0.46 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,T2: t] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.30/0.46 => ( ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 )
% 0.30/0.46 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr.Ind
% 0.30/0.46 thf(fact_20_inItr_OInd,axiom,
% 0.30/0.46 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,N: n] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.30/0.46 => ( ( gram_L830233218_inItr @ Ns @ Tr1 @ N )
% 0.30/0.46 => ( gram_L830233218_inItr @ Ns @ Tr @ N ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inItr.Ind
% 0.30/0.46 thf(fact_21_root__pick,axiom,
% 0.30/0.46 ! [Tr0: dtree,N: n] :
% 0.30/0.46 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.30/0.46 => ( ( root @ ( gram_L315592705e_pick @ Tr0 @ N ) )
% 0.30/0.46 = N ) ) ).
% 0.30/0.46
% 0.30/0.46 % root_pick
% 0.30/0.46 thf(fact_22_inItr_OBase,axiom,
% 0.30/0.46 ! [Tr: dtree,Ns: set @ n] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.30/0.46 => ( gram_L830233218_inItr @ Ns @ Tr @ ( root @ Tr ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inItr.Base
% 0.30/0.46 thf(fact_23_subtr_ORefl,axiom,
% 0.30/0.46 ! [Tr: dtree,Ns: set @ n] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.30/0.46 => ( gram_L716654942_subtr @ Ns @ Tr @ Tr ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr.Refl
% 0.30/0.46 thf(fact_24_subtr_OStep,axiom,
% 0.30/0.46 ! [Tr3: dtree,Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr3 ) @ Ns )
% 0.30/0.46 => ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr3 ) )
% 0.30/0.46 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr.Step
% 0.30/0.46 thf(fact_25_subtr__inFr,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr: dtree,T2: t,Tr1: dtree] :
% 0.30/0.46 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.30/0.46 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.30/0.46 => ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr_inFr
% 0.30/0.46 thf(fact_26_subtr__pick,axiom,
% 0.30/0.46 ! [Tr0: dtree,N: n] :
% 0.30/0.46 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.30/0.46 => ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ Tr0 @ N ) @ Tr0 ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr_pick
% 0.30/0.46 thf(fact_27_inItr_Ocases,axiom,
% 0.30/0.46 ! [A1: set @ n,A2: dtree,A3: n] :
% 0.30/0.46 ( ( gram_L830233218_inItr @ A1 @ A2 @ A3 )
% 0.30/0.46 => ( ( ( A3
% 0.30/0.46 = ( root @ A2 ) )
% 0.30/0.46 => ~ ( member @ n @ ( root @ A2 ) @ A1 ) )
% 0.30/0.46 => ~ ( ( member @ n @ ( root @ A2 ) @ A1 )
% 0.30/0.46 => ! [Tr12: dtree] :
% 0.30/0.46 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A2 ) )
% 0.30/0.46 => ~ ( gram_L830233218_inItr @ A1 @ Tr12 @ A3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inItr.cases
% 0.30/0.46 thf(fact_28_inItr_Osimps,axiom,
% 0.30/0.46 ( gram_L830233218_inItr
% 0.30/0.46 = ( ^ [A12: set @ n,A22: dtree,A32: n] :
% 0.30/0.46 ( ? [Tr4: dtree,Ns2: set @ n] :
% 0.30/0.46 ( ( A12 = Ns2 )
% 0.30/0.46 & ( A22 = Tr4 )
% 0.30/0.46 & ( A32
% 0.30/0.46 = ( root @ Tr4 ) )
% 0.30/0.46 & ( member @ n @ ( root @ Tr4 ) @ Ns2 ) )
% 0.30/0.46 | ? [Tr4: dtree,Ns2: set @ n,Tr13: dtree,N2: n] :
% 0.30/0.46 ( ( A12 = Ns2 )
% 0.30/0.46 & ( A22 = Tr4 )
% 0.30/0.46 & ( A32 = N2 )
% 0.30/0.46 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.30/0.46 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr4 ) )
% 0.30/0.46 & ( gram_L830233218_inItr @ Ns2 @ Tr13 @ N2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inItr.simps
% 0.30/0.46 thf(fact_29_inItr__subtr,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr: dtree,N: n] :
% 0.30/0.46 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.30/0.46 => ? [Tr5: dtree] :
% 0.30/0.46 ( ( gram_L716654942_subtr @ Ns @ Tr5 @ Tr )
% 0.30/0.46 & ( ( root @ Tr5 )
% 0.30/0.46 = N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inItr_subtr
% 0.30/0.46 thf(fact_30_subtr_Ocases,axiom,
% 0.30/0.46 ! [A1: set @ n,A2: dtree,A3: dtree] :
% 0.30/0.46 ( ( gram_L716654942_subtr @ A1 @ A2 @ A3 )
% 0.30/0.46 => ( ( ( A3 = A2 )
% 0.30/0.46 => ~ ( member @ n @ ( root @ A2 ) @ A1 ) )
% 0.30/0.46 => ~ ( ( member @ n @ ( root @ A3 ) @ A1 )
% 0.30/0.46 => ! [Tr23: dtree] :
% 0.30/0.46 ( ( gram_L716654942_subtr @ A1 @ A2 @ Tr23 )
% 0.30/0.46 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ A3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr.cases
% 0.30/0.46 thf(fact_31_subtr_Osimps,axiom,
% 0.30/0.46 ( gram_L716654942_subtr
% 0.30/0.46 = ( ^ [A12: set @ n,A22: dtree,A32: dtree] :
% 0.30/0.46 ( ? [Tr4: dtree,Ns2: set @ n] :
% 0.30/0.46 ( ( A12 = Ns2 )
% 0.30/0.46 & ( A22 = Tr4 )
% 0.30/0.46 & ( A32 = Tr4 )
% 0.30/0.46 & ( member @ n @ ( root @ Tr4 ) @ Ns2 ) )
% 0.30/0.46 | ? [Tr32: dtree,Ns2: set @ n,Tr13: dtree,Tr24: dtree] :
% 0.30/0.46 ( ( A12 = Ns2 )
% 0.30/0.46 & ( A22 = Tr13 )
% 0.30/0.46 & ( A32 = Tr32 )
% 0.30/0.46 & ( member @ n @ ( root @ Tr32 ) @ Ns2 )
% 0.30/0.46 & ( gram_L716654942_subtr @ Ns2 @ Tr13 @ Tr24 )
% 0.30/0.46 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr24 ) @ ( cont @ Tr32 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr.simps
% 0.30/0.46 thf(fact_32_subtr__StepL,axiom,
% 0.30/0.46 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr3: dtree] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 0.30/0.46 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr3 )
% 0.30/0.46 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr_StepL
% 0.30/0.46 thf(fact_33_subtr__deftr,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr2: dtree,N: n] :
% 0.30/0.46 ( ( gram_L716654942_subtr @ Ns @ Tr2 @ ( gram_L1231612515_deftr @ N ) )
% 0.30/0.46 => ( Tr2
% 0.30/0.46 = ( gram_L1231612515_deftr @ ( root @ Tr2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr_deftr
% 0.30/0.46 thf(fact_34_subtr__inItr,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr: dtree,N: n,Tr1: dtree] :
% 0.30/0.46 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.30/0.46 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 0.30/0.46 => ( gram_L830233218_inItr @ Ns @ Tr1 @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr_inItr
% 0.30/0.46 thf(fact_35_subtr__trans,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr3: dtree] :
% 0.30/0.46 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.30/0.46 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr3 )
% 0.30/0.46 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr_trans
% 0.30/0.46 thf(fact_36_hsubst__c__def,axiom,
% 0.30/0.46 ( gram_L1905609002ubst_c
% 0.30/0.46 = ( ^ [Tr02: dtree,Tr4: dtree] :
% 0.30/0.46 ( if @ ( set @ ( sum_sum @ t @ dtree ) )
% 0.30/0.46 @ ( ( root @ Tr4 )
% 0.30/0.46 = ( root @ Tr02 ) )
% 0.30/0.46 @ ( cont @ Tr02 )
% 0.30/0.46 @ ( cont @ Tr4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % hsubst_c_def
% 0.30/0.46 thf(fact_37_hsubst__r__def,axiom,
% 0.30/0.46 gram_L1905609017ubst_r = root ).
% 0.30/0.46
% 0.30/0.46 % hsubst_r_def
% 0.30/0.46 thf(fact_38_inFr__root__in,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.30/0.46 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.30/0.46 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr_root_in
% 0.30/0.46 thf(fact_39_inItr_Oinducts,axiom,
% 0.30/0.46 ! [X1: set @ n,X2: dtree,X3: n,P: ( set @ n ) > dtree > n > $o] :
% 0.30/0.46 ( ( gram_L830233218_inItr @ X1 @ X2 @ X3 )
% 0.30/0.46 => ( ! [Tr6: dtree,Ns3: set @ n] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr6 ) @ Ns3 )
% 0.30/0.46 => ( P @ Ns3 @ Tr6 @ ( root @ Tr6 ) ) )
% 0.30/0.46 => ( ! [Tr6: dtree,Ns3: set @ n,Tr12: dtree,N3: n] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr6 ) @ Ns3 )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr6 ) )
% 0.30/0.46 => ( ( gram_L830233218_inItr @ Ns3 @ Tr12 @ N3 )
% 0.30/0.46 => ( ( P @ Ns3 @ Tr12 @ N3 )
% 0.30/0.46 => ( P @ Ns3 @ Tr6 @ N3 ) ) ) ) )
% 0.30/0.46 => ( P @ X1 @ X2 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inItr.inducts
% 0.30/0.46 thf(fact_40_inItr__root__in,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr: dtree,N: n] :
% 0.30/0.46 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 0.30/0.46 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.30/0.46
% 0.30/0.46 % inItr_root_in
% 0.30/0.46 thf(fact_41_not__root__inFr,axiom,
% 0.30/0.46 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.30/0.46 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 0.30/0.46 => ~ ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_root_inFr
% 0.30/0.46 thf(fact_42_subtr_Oinducts,axiom,
% 0.30/0.46 ! [X1: set @ n,X2: dtree,X3: dtree,P: ( set @ n ) > dtree > dtree > $o] :
% 0.30/0.46 ( ( gram_L716654942_subtr @ X1 @ X2 @ X3 )
% 0.30/0.46 => ( ! [Tr6: dtree,Ns3: set @ n] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr6 ) @ Ns3 )
% 0.30/0.46 => ( P @ Ns3 @ Tr6 @ Tr6 ) )
% 0.30/0.46 => ( ! [Tr33: dtree,Ns3: set @ n,Tr12: dtree,Tr23: dtree] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr33 ) @ Ns3 )
% 0.30/0.46 => ( ( gram_L716654942_subtr @ Ns3 @ Tr12 @ Tr23 )
% 0.30/0.46 => ( ( P @ Ns3 @ Tr12 @ Tr23 )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ Tr33 ) )
% 0.30/0.46 => ( P @ Ns3 @ Tr12 @ Tr33 ) ) ) ) )
% 0.30/0.46 => ( P @ X1 @ X2 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr.inducts
% 0.30/0.46 thf(fact_43_subtr__inductL,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Phi: ( set @ n ) > dtree > dtree > $o] :
% 0.30/0.46 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.30/0.46 => ( ! [Ns3: set @ n,Tr6: dtree] : ( Phi @ Ns3 @ Tr6 @ Tr6 )
% 0.30/0.46 => ( ! [Ns3: set @ n,Tr12: dtree,Tr23: dtree,Tr33: dtree] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr12 ) @ Ns3 )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 0.30/0.46 => ( ( gram_L716654942_subtr @ Ns3 @ Tr23 @ Tr33 )
% 0.30/0.46 => ( ( Phi @ Ns3 @ Tr23 @ Tr33 )
% 0.30/0.46 => ( Phi @ Ns3 @ Tr12 @ Tr33 ) ) ) ) )
% 0.30/0.46 => ( Phi @ Ns @ Tr1 @ Tr22 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr_inductL
% 0.30/0.46 thf(fact_44_subtr__rootL__in,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.30/0.46 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.30/0.46 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr_rootL_in
% 0.30/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,P: A > $o] :
% 0.30/0.46 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 0.30/0.46 = ( P @ A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X: A] : ( member @ A @ X @ A5 ) )
% 0.30/0.46 = A5 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_47_Collect__cong,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X4: A] :
% 0.30/0.46 ( ( P @ X4 )
% 0.30/0.46 = ( Q @ X4 ) )
% 0.30/0.46 => ( ( collect @ A @ P )
% 0.30/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_48_ext,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.30/0.46 ( ! [X4: A] :
% 0.30/0.46 ( ( F @ X4 )
% 0.30/0.46 = ( G @ X4 ) )
% 0.30/0.46 => ( F = G ) ) ).
% 0.30/0.46
% 0.30/0.46 % ext
% 0.30/0.46 thf(fact_49_subtr__rootR__in,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.30/0.46 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 0.30/0.46 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr_rootR_in
% 0.30/0.46 thf(fact_50_subtr__UNIV__inductL,axiom,
% 0.30/0.46 ! [Tr1: dtree,Tr22: dtree,Phi: dtree > dtree > $o] :
% 0.30/0.46 ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr1 @ Tr22 )
% 0.30/0.46 => ( ! [Tr6: dtree] : ( Phi @ Tr6 @ Tr6 )
% 0.30/0.46 => ( ! [Tr12: dtree,Tr23: dtree,Tr33: dtree] :
% 0.30/0.46 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 0.30/0.46 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr23 @ Tr33 )
% 0.30/0.46 => ( ( Phi @ Tr23 @ Tr33 )
% 0.30/0.46 => ( Phi @ Tr12 @ Tr33 ) ) ) )
% 0.30/0.46 => ( Phi @ Tr1 @ Tr22 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr_UNIV_inductL
% 0.30/0.46 thf(fact_51_subtrOf__root,axiom,
% 0.30/0.46 ! [Tr: dtree,Tr2: dtree] :
% 0.30/0.46 ( ( gram_L864798063lle_wf @ Tr )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 0.30/0.46 => ( ( gram_L1614515765ubtrOf @ Tr @ ( root @ Tr2 ) )
% 0.30/0.46 = Tr2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtrOf_root
% 0.30/0.46 thf(fact_52_H__r__def,axiom,
% 0.30/0.46 ( gram_L1221482026le_H_r
% 0.30/0.46 = ( ^ [Tr02: dtree,N2: n] : ( root @ ( gram_L315592705e_pick @ Tr02 @ N2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % H_r_def
% 0.30/0.46 thf(fact_53_inFrr__def,axiom,
% 0.30/0.46 ( gram_L805317505_inFrr
% 0.30/0.46 = ( ^ [Ns2: set @ n,Tr4: dtree,T3: t] :
% 0.30/0.46 ? [Tr7: dtree] :
% 0.30/0.46 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr7 ) @ ( cont @ Tr4 ) )
% 0.30/0.46 & ( gram_L1333338417e_inFr @ Ns2 @ Tr7 @ T3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFrr_def
% 0.30/0.46 thf(fact_54_sum_Oinject_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X2: B,Y2: B] :
% 0.30/0.46 ( ( ( sum_Inr @ B @ A @ X2 )
% 0.30/0.46 = ( sum_Inr @ B @ A @ Y2 ) )
% 0.30/0.46 = ( X2 = Y2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sum.inject(2)
% 0.30/0.46 thf(fact_55_old_Osum_Oinject_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,B2: B,B3: B] :
% 0.30/0.46 ( ( ( sum_Inr @ B @ A @ B2 )
% 0.30/0.46 = ( sum_Inr @ B @ A @ B3 ) )
% 0.30/0.46 = ( B2 = B3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.sum.inject(2)
% 0.30/0.46 thf(fact_56_unfold_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ A ) ),B2: A] :
% 0.30/0.46 ( ( root @ ( unfold @ A @ Rt @ Ct @ B2 ) )
% 0.30/0.46 = ( Rt @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % unfold(1)
% 0.30/0.46 thf(fact_57_comp__apply,axiom,
% 0.30/0.46 ! [C: $tType,A: $tType,B: $tType] :
% 0.30/0.46 ( ( comp @ B @ A @ C )
% 0.30/0.46 = ( ^ [F2: B > A,G2: C > B,X: C] : ( F2 @ ( G2 @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_apply
% 0.30/0.46 thf(fact_58_UNIV__I,axiom,
% 0.30/0.46 ! [A: $tType,X5: A] : ( member @ A @ X5 @ ( top_top @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UNIV_I
% 0.30/0.46 thf(fact_59_iso__tuple__UNIV__I,axiom,
% 0.30/0.46 ! [A: $tType,X5: A] : ( member @ A @ X5 @ ( top_top @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % iso_tuple_UNIV_I
% 0.30/0.46 thf(fact_60_top__apply,axiom,
% 0.30/0.46 ! [C: $tType,D: $tType] :
% 0.30/0.46 ( ( top @ C @ ( type2 @ C ) )
% 0.30/0.46 => ( ( top_top @ ( D > C ) )
% 0.30/0.46 = ( ^ [X: D] : ( top_top @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % top_apply
% 0.30/0.46 thf(fact_61_top__set__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( top_top @ ( set @ A ) )
% 0.30/0.46 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % top_set_def
% 0.30/0.46 thf(fact_62_UNIV__witness,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ? [X4: A] : ( member @ A @ X4 @ ( top_top @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UNIV_witness
% 0.30/0.46 thf(fact_63_UNIV__eq__I,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ! [X4: A] : ( member @ A @ X4 @ A5 )
% 0.30/0.46 => ( ( top_top @ ( set @ A ) )
% 0.30/0.46 = A5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % UNIV_eq_I
% 0.30/0.46 thf(fact_64_comp__eq__dest__lhs,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,A4: C > B,B2: A > C,C2: A > B,V: A] :
% 0.30/0.46 ( ( ( comp @ C @ B @ A @ A4 @ B2 )
% 0.30/0.46 = C2 )
% 0.30/0.46 => ( ( A4 @ ( B2 @ V ) )
% 0.30/0.46 = ( C2 @ V ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest_lhs
% 0.30/0.46 thf(fact_65_comp__eq__elim,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,D: $tType,A: $tType,A4: C > B,B2: A > C,C2: D > B,D2: A > D] :
% 0.30/0.46 ( ( ( comp @ C @ B @ A @ A4 @ B2 )
% 0.30/0.46 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 0.30/0.46 => ! [V2: A] :
% 0.30/0.46 ( ( A4 @ ( B2 @ V2 ) )
% 0.30/0.46 = ( C2 @ ( D2 @ V2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_elim
% 0.30/0.46 thf(fact_66_comp__eq__dest,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,D: $tType,A: $tType,A4: C > B,B2: A > C,C2: D > B,D2: A > D,V: A] :
% 0.30/0.46 ( ( ( comp @ C @ B @ A @ A4 @ B2 )
% 0.30/0.46 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 0.30/0.46 => ( ( A4 @ ( B2 @ V ) )
% 0.30/0.46 = ( C2 @ ( D2 @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_eq_dest
% 0.30/0.46 thf(fact_67_comp__assoc,axiom,
% 0.30/0.46 ! [B: $tType,D: $tType,C: $tType,A: $tType,F: D > B,G: C > D,H: A > C] :
% 0.30/0.46 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F @ G ) @ H )
% 0.30/0.46 = ( comp @ D @ B @ A @ F @ ( comp @ C @ D @ A @ G @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_assoc
% 0.30/0.46 thf(fact_68_comp__def,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,B: $tType] :
% 0.30/0.46 ( ( comp @ B @ C @ A )
% 0.30/0.46 = ( ^ [F2: B > C,G2: A > B,X: A] : ( F2 @ ( G2 @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % comp_def
% 0.30/0.46 thf(fact_69_Inr__inject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X5: B,Y: B] :
% 0.30/0.46 ( ( ( sum_Inr @ B @ A @ X5 )
% 0.30/0.46 = ( sum_Inr @ B @ A @ Y ) )
% 0.30/0.46 => ( X5 = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % Inr_inject
% 0.30/0.46 thf(fact_70_dtree__cong,axiom,
% 0.30/0.46 ! [Tr: dtree,Tr2: dtree] :
% 0.30/0.46 ( ( ( root @ Tr )
% 0.30/0.46 = ( root @ Tr2 ) )
% 0.30/0.46 => ( ( ( cont @ Tr )
% 0.30/0.46 = ( cont @ Tr2 ) )
% 0.30/0.46 => ( Tr = Tr2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dtree_cong
% 0.30/0.46 thf(fact_71_old_Osum_Osimps_I8_J,axiom,
% 0.30/0.46 ! [A: $tType,T: $tType,B: $tType,F1: A > T,F22: B > T,B2: B] :
% 0.30/0.46 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inr @ B @ A @ B2 ) )
% 0.30/0.46 = ( F22 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.sum.simps(8)
% 0.30/0.46 thf(fact_72_root__H,axiom,
% 0.30/0.46 ! [Tr0: dtree,N: n] :
% 0.30/0.46 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.30/0.46 => ( ( root @ ( gram_L1451583624elle_H @ Tr0 @ N ) )
% 0.30/0.46 = N ) ) ).
% 0.30/0.46
% 0.30/0.46 % root_H
% 0.30/0.46 thf(fact_73_Node__root__cont,axiom,
% 0.30/0.46 ! [Tr: dtree] :
% 0.30/0.46 ( ( node @ ( root @ Tr ) @ ( cont @ Tr ) )
% 0.30/0.46 = Tr ) ).
% 0.30/0.46
% 0.30/0.46 % Node_root_cont
% 0.30/0.46 thf(fact_74_wf__H,axiom,
% 0.30/0.46 ! [Tr0: dtree,N: n] :
% 0.30/0.46 ( ( gram_L864798063lle_wf @ Tr0 )
% 0.30/0.46 => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.30/0.46 => ( gram_L864798063lle_wf @ ( gram_L1451583624elle_H @ Tr0 @ N ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % wf_H
% 0.30/0.46 thf(fact_75_subtr__H,axiom,
% 0.30/0.46 ! [Tr0: dtree,N: n,Tr1: dtree] :
% 0.30/0.46 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 0.30/0.46 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr1 @ ( gram_L1451583624elle_H @ Tr0 @ N ) )
% 0.30/0.46 => ? [N1: n] :
% 0.30/0.46 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N1 )
% 0.30/0.46 & ( Tr1
% 0.30/0.46 = ( gram_L1451583624elle_H @ Tr0 @ N1 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr_H
% 0.30/0.46 thf(fact_76_inFr2__Ind,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 0.30/0.46 ( ( gram_L805317441_inFr2 @ Ns @ Tr1 @ T2 )
% 0.30/0.46 => ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.30/0.46 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr2_Ind
% 0.30/0.46 thf(fact_77_reg__def,axiom,
% 0.30/0.46 ( gram_L1918716148le_reg
% 0.30/0.46 = ( ^ [F2: n > dtree,Tr4: dtree] :
% 0.30/0.46 ! [Tr7: dtree] :
% 0.30/0.46 ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr7 @ Tr4 )
% 0.30/0.46 => ( Tr7
% 0.30/0.46 = ( F2 @ ( root @ Tr7 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % reg_def
% 0.30/0.46 thf(fact_78_top1I,axiom,
% 0.30/0.46 ! [A: $tType,X5: A] : ( top_top @ ( A > $o ) @ X5 ) ).
% 0.30/0.46
% 0.30/0.46 % top1I
% 0.30/0.46 thf(fact_79_root__Node,axiom,
% 0.30/0.46 ! [N: n,As: set @ ( sum_sum @ t @ dtree )] :
% 0.30/0.46 ( ( root @ ( node @ N @ As ) )
% 0.30/0.46 = N ) ).
% 0.30/0.46
% 0.30/0.46 % root_Node
% 0.30/0.46 thf(fact_80_rcut__eq,axiom,
% 0.30/0.46 ! [Tr0: dtree] :
% 0.30/0.46 ( ( ( gram_L1828378864e_rcut @ Tr0 )
% 0.30/0.46 = Tr0 )
% 0.30/0.46 = ( gram_L1918716148le_reg @ ( gram_L1451583624elle_H @ Tr0 ) @ Tr0 ) ) ).
% 0.30/0.46
% 0.30/0.46 % rcut_eq
% 0.30/0.46 thf(fact_81_rcut__reg,axiom,
% 0.30/0.46 ! [Tr0: dtree] :
% 0.30/0.46 ( ( gram_L1918716148le_reg @ ( gram_L1451583624elle_H @ Tr0 ) @ Tr0 )
% 0.30/0.46 => ( ( gram_L1828378864e_rcut @ Tr0 )
% 0.30/0.46 = Tr0 ) ) ).
% 0.30/0.46
% 0.30/0.46 % rcut_reg
% 0.30/0.46 thf(fact_82_reg__rcut,axiom,
% 0.30/0.46 ! [Tr0: dtree] : ( gram_L1918716148le_reg @ ( gram_L1451583624elle_H @ Tr0 ) @ ( gram_L1828378864e_rcut @ Tr0 ) ) ).
% 0.30/0.46
% 0.30/0.46 % reg_rcut
% 0.30/0.46 thf(fact_83_reg__root,axiom,
% 0.30/0.46 ! [F: n > dtree,Tr: dtree] :
% 0.30/0.46 ( ( gram_L1918716148le_reg @ F @ Tr )
% 0.30/0.46 => ( ( F @ ( root @ Tr ) )
% 0.30/0.46 = Tr ) ) ).
% 0.30/0.46
% 0.30/0.46 % reg_root
% 0.30/0.46 thf(fact_84_reg__subtr,axiom,
% 0.30/0.46 ! [F: n > dtree,Tr: dtree,Ns: set @ n,Tr2: dtree] :
% 0.30/0.46 ( ( gram_L1918716148le_reg @ F @ Tr )
% 0.30/0.46 => ( ( gram_L716654942_subtr @ Ns @ Tr2 @ Tr )
% 0.30/0.46 => ( gram_L1918716148le_reg @ F @ Tr2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % reg_subtr
% 0.30/0.46 thf(fact_85_inFr2__root__in,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.30/0.46 ( ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 )
% 0.30/0.46 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr2_root_in
% 0.30/0.46 thf(fact_86_inFr__inFr2,axiom,
% 0.30/0.46 gram_L1333338417e_inFr = gram_L805317441_inFr2 ).
% 0.30/0.46
% 0.30/0.46 % inFr_inFr2
% 0.30/0.46 thf(fact_87_reg__deftr,axiom,
% 0.30/0.46 ! [N: n] : ( gram_L1918716148le_reg @ gram_L1231612515_deftr @ ( gram_L1231612515_deftr @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % reg_deftr
% 0.30/0.46 thf(fact_88_reg__Inr__cont,axiom,
% 0.30/0.46 ! [F: n > dtree,Tr: dtree,Tr2: dtree] :
% 0.30/0.46 ( ( gram_L1918716148le_reg @ F @ Tr )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 0.30/0.46 => ( gram_L1918716148le_reg @ F @ Tr2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % reg_Inr_cont
% 0.30/0.46 thf(fact_89_reg__def2,axiom,
% 0.30/0.46 ( gram_L1918716148le_reg
% 0.30/0.46 = ( ^ [F2: n > dtree,Tr4: dtree] :
% 0.30/0.46 ! [Ns2: set @ n,Tr7: dtree] :
% 0.30/0.46 ( ( gram_L716654942_subtr @ Ns2 @ Tr7 @ Tr4 )
% 0.30/0.46 => ( Tr7
% 0.30/0.46 = ( F2 @ ( root @ Tr7 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % reg_def2
% 0.30/0.46 thf(fact_90_root__H__pick,axiom,
% 0.30/0.46 ! [Tr0: dtree,N: n] :
% 0.30/0.46 ( ( root @ ( gram_L1451583624elle_H @ Tr0 @ N ) )
% 0.30/0.46 = ( root @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % root_H_pick
% 0.30/0.46 thf(fact_91_rcut__def,axiom,
% 0.30/0.46 ( gram_L1828378864e_rcut
% 0.30/0.46 = ( ^ [Tr02: dtree] : ( gram_L1451583624elle_H @ Tr02 @ ( root @ Tr02 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rcut_def
% 0.30/0.46 thf(fact_92_H__def,axiom,
% 0.30/0.46 ( gram_L1451583624elle_H
% 0.30/0.46 = ( ^ [Tr02: dtree] : ( unfold @ n @ ( gram_L1221482026le_H_r @ Tr02 ) @ ( gram_L1221482011le_H_c @ Tr02 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % H_def
% 0.30/0.46 thf(fact_93_top__empty__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( top_top @ ( A > $o ) )
% 0.30/0.46 = ( ^ [X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % top_empty_eq
% 0.30/0.46 thf(fact_94_regular__def2,axiom,
% 0.30/0.46 ( gram_L646766332egular
% 0.30/0.46 = ( ^ [Tr4: dtree] :
% 0.30/0.46 ? [F2: n > dtree] :
% 0.30/0.46 ( ( gram_L1918716148le_reg @ F2 @ Tr4 )
% 0.30/0.46 & ! [N2: n] :
% 0.30/0.46 ( ( root @ ( F2 @ N2 ) )
% 0.30/0.46 = N2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % regular_def2
% 0.30/0.46 thf(fact_95_top__conj_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,P: $o,X5: A] :
% 0.30/0.46 ( ( P
% 0.30/0.46 & ( top_top @ ( A > $o ) @ X5 ) )
% 0.30/0.46 = P ) ).
% 0.30/0.46
% 0.30/0.46 % top_conj(2)
% 0.30/0.46 thf(fact_96_top__conj_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X5: A,P: $o] :
% 0.30/0.46 ( ( ( top_top @ ( A > $o ) @ X5 )
% 0.30/0.46 & P )
% 0.30/0.46 = P ) ).
% 0.30/0.46
% 0.30/0.46 % top_conj(1)
% 0.30/0.46 thf(fact_97_inFr2_OInd,axiom,
% 0.30/0.46 ! [Tr1: dtree,Tr: dtree,Ns1: set @ n,T2: t] :
% 0.30/0.46 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.30/0.46 => ( ( gram_L805317441_inFr2 @ Ns1 @ Tr1 @ T2 )
% 0.30/0.46 => ( gram_L805317441_inFr2 @ ( insert @ n @ ( root @ Tr ) @ Ns1 ) @ Tr @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr2.Ind
% 0.30/0.46 thf(fact_98_insertCI,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,B4: set @ A,B2: A] :
% 0.30/0.46 ( ( ~ ( member @ A @ A4 @ B4 )
% 0.30/0.46 => ( A4 = B2 ) )
% 0.30/0.46 => ( member @ A @ A4 @ ( insert @ A @ B2 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertCI
% 0.30/0.46 thf(fact_99_insert__iff,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,B2: A,A5: set @ A] :
% 0.30/0.46 ( ( member @ A @ A4 @ ( insert @ A @ B2 @ A5 ) )
% 0.30/0.46 = ( ( A4 = B2 )
% 0.30/0.46 | ( member @ A @ A4 @ A5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_iff
% 0.30/0.46 thf(fact_100_insert__absorb2,axiom,
% 0.30/0.46 ! [A: $tType,X5: A,A5: set @ A] :
% 0.30/0.46 ( ( insert @ A @ X5 @ ( insert @ A @ X5 @ A5 ) )
% 0.30/0.46 = ( insert @ A @ X5 @ A5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_absorb2
% 0.30/0.46 thf(fact_101_insertE,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,B2: A,A5: set @ A] :
% 0.30/0.46 ( ( member @ A @ A4 @ ( insert @ A @ B2 @ A5 ) )
% 0.30/0.46 => ( ( A4 != B2 )
% 0.30/0.46 => ( member @ A @ A4 @ A5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertE
% 0.30/0.46 thf(fact_102_insertI1,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,B4: set @ A] : ( member @ A @ A4 @ ( insert @ A @ A4 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI1
% 0.30/0.46 thf(fact_103_insertI2,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,B4: set @ A,B2: A] :
% 0.30/0.46 ( ( member @ A @ A4 @ B4 )
% 0.30/0.46 => ( member @ A @ A4 @ ( insert @ A @ B2 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI2
% 0.30/0.46 thf(fact_104_Set_Oset__insert,axiom,
% 0.30/0.46 ! [A: $tType,X5: A,A5: set @ A] :
% 0.30/0.46 ( ( member @ A @ X5 @ A5 )
% 0.30/0.46 => ~ ! [B5: set @ A] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( insert @ A @ X5 @ B5 ) )
% 0.30/0.46 => ( member @ A @ X5 @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Set.set_insert
% 0.30/0.46 thf(fact_105_insert__ident,axiom,
% 0.30/0.46 ! [A: $tType,X5: A,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ~ ( member @ A @ X5 @ A5 )
% 0.30/0.46 => ( ~ ( member @ A @ X5 @ B4 )
% 0.30/0.46 => ( ( ( insert @ A @ X5 @ A5 )
% 0.30/0.46 = ( insert @ A @ X5 @ B4 ) )
% 0.30/0.46 = ( A5 = B4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_ident
% 0.30/0.46 thf(fact_106_insert__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,A5: set @ A] :
% 0.30/0.46 ( ( member @ A @ A4 @ A5 )
% 0.30/0.46 => ( ( insert @ A @ A4 @ A5 )
% 0.30/0.46 = A5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_absorb
% 0.30/0.46 thf(fact_107_insert__eq__iff,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,A5: set @ A,B2: A,B4: set @ A] :
% 0.30/0.46 ( ~ ( member @ A @ A4 @ A5 )
% 0.30/0.46 => ( ~ ( member @ A @ B2 @ B4 )
% 0.30/0.46 => ( ( ( insert @ A @ A4 @ A5 )
% 0.30/0.46 = ( insert @ A @ B2 @ B4 ) )
% 0.30/0.46 = ( ( ( A4 = B2 )
% 0.30/0.46 => ( A5 = B4 ) )
% 0.30/0.46 & ( ( A4 != B2 )
% 0.30/0.46 => ? [C3: set @ A] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( insert @ A @ B2 @ C3 ) )
% 0.30/0.46 & ~ ( member @ A @ B2 @ C3 )
% 0.30/0.46 & ( B4
% 0.30/0.46 = ( insert @ A @ A4 @ C3 ) )
% 0.30/0.46 & ~ ( member @ A @ A4 @ C3 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_eq_iff
% 0.30/0.46 thf(fact_108_insert__commute,axiom,
% 0.30/0.46 ! [A: $tType,X5: A,Y: A,A5: set @ A] :
% 0.30/0.46 ( ( insert @ A @ X5 @ ( insert @ A @ Y @ A5 ) )
% 0.30/0.46 = ( insert @ A @ Y @ ( insert @ A @ X5 @ A5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_commute
% 0.30/0.46 thf(fact_109_mk__disjoint__insert,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,A5: set @ A] :
% 0.30/0.46 ( ( member @ A @ A4 @ A5 )
% 0.30/0.46 => ? [B5: set @ A] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( insert @ A @ A4 @ B5 ) )
% 0.30/0.46 & ~ ( member @ A @ A4 @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mk_disjoint_insert
% 0.30/0.46 thf(fact_110_insert__UNIV,axiom,
% 0.30/0.46 ! [A: $tType,X5: A] :
% 0.30/0.46 ( ( insert @ A @ X5 @ ( top_top @ ( set @ A ) ) )
% 0.30/0.46 = ( top_top @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_UNIV
% 0.30/0.46 thf(fact_111_regular__subtr,axiom,
% 0.30/0.46 ! [Tr: dtree,Ns: set @ n,Tr2: dtree] :
% 0.30/0.46 ( ( gram_L646766332egular @ Tr )
% 0.30/0.46 => ( ( gram_L716654942_subtr @ Ns @ Tr2 @ Tr )
% 0.30/0.46 => ( gram_L646766332egular @ Tr2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % regular_subtr
% 0.30/0.46 thf(fact_112_regular__def,axiom,
% 0.30/0.46 ( gram_L646766332egular
% 0.30/0.46 = ( ^ [Tr4: dtree] :
% 0.30/0.46 ? [F2: n > dtree] : ( gram_L1918716148le_reg @ F2 @ Tr4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % regular_def
% 0.30/0.46 thf(fact_113_regular__rcut,axiom,
% 0.30/0.46 ! [Tr0: dtree] : ( gram_L646766332egular @ ( gram_L1828378864e_rcut @ Tr0 ) ) ).
% 0.30/0.46
% 0.30/0.46 % regular_rcut
% 0.30/0.46 thf(fact_114_rewriteR__comp__comp2,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,E: $tType,D: $tType,A: $tType,G: C > B,H: A > C,R1: D > B,R2: A > D,F: B > E,L: D > E] :
% 0.30/0.46 ( ( ( comp @ C @ B @ A @ G @ H )
% 0.30/0.46 = ( comp @ D @ B @ A @ R1 @ R2 ) )
% 0.30/0.46 => ( ( ( comp @ B @ E @ D @ F @ R1 )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp @ C @ E @ A @ ( comp @ B @ E @ C @ F @ G ) @ H )
% 0.30/0.46 = ( comp @ D @ E @ A @ L @ R2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp2
% 0.30/0.46 thf(fact_115_rewriteL__comp__comp2,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,B: $tType,D: $tType,E: $tType,F: C > B,G: A > C,L1: D > B,L2: A > D,H: E > A,R: E > D] :
% 0.30/0.46 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.30/0.46 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 0.30/0.46 => ( ( ( comp @ A @ D @ E @ L2 @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp @ C @ B @ E @ F @ ( comp @ A @ C @ E @ G @ H ) )
% 0.30/0.46 = ( comp @ D @ B @ E @ L1 @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp2
% 0.30/0.46 thf(fact_116_rewriteR__comp__comp,axiom,
% 0.30/0.46 ! [C: $tType,D: $tType,B: $tType,A: $tType,G: C > B,H: A > C,R: A > B,F: B > D] :
% 0.30/0.46 ( ( ( comp @ C @ B @ A @ G @ H )
% 0.30/0.46 = R )
% 0.30/0.46 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F @ G ) @ H )
% 0.30/0.46 = ( comp @ B @ D @ A @ F @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteR_comp_comp
% 0.30/0.46 thf(fact_117_rewriteL__comp__comp,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,D: $tType,F: C > B,G: A > C,L: A > B,H: D > A] :
% 0.30/0.46 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.30/0.46 = L )
% 0.30/0.46 => ( ( comp @ C @ B @ D @ F @ ( comp @ A @ C @ D @ G @ H ) )
% 0.30/0.46 = ( comp @ A @ B @ D @ L @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rewriteL_comp_comp
% 0.30/0.46 thf(fact_118_inFr__Ind__minus,axiom,
% 0.30/0.46 ! [Ns1: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 0.30/0.46 ( ( gram_L1333338417e_inFr @ Ns1 @ Tr1 @ T2 )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 0.30/0.46 => ( gram_L1333338417e_inFr @ ( insert @ n @ ( root @ Tr ) @ Ns1 ) @ Tr @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr_Ind_minus
% 0.30/0.46 thf(fact_119_inFr2_Oinducts,axiom,
% 0.30/0.46 ! [X1: set @ n,X2: dtree,X3: t,P: ( set @ n ) > dtree > t > $o] :
% 0.30/0.46 ( ( gram_L805317441_inFr2 @ X1 @ X2 @ X3 )
% 0.30/0.46 => ( ! [Tr6: dtree,Ns3: set @ n,T4: t] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr6 ) @ Ns3 )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr6 ) )
% 0.30/0.46 => ( P @ Ns3 @ Tr6 @ T4 ) ) )
% 0.30/0.46 => ( ! [Tr12: dtree,Tr6: dtree,Ns12: set @ n,T4: t] :
% 0.30/0.46 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr6 ) )
% 0.30/0.46 => ( ( gram_L805317441_inFr2 @ Ns12 @ Tr12 @ T4 )
% 0.30/0.46 => ( ( P @ Ns12 @ Tr12 @ T4 )
% 0.30/0.46 => ( P @ ( insert @ n @ ( root @ Tr6 ) @ Ns12 ) @ Tr6 @ T4 ) ) ) )
% 0.30/0.46 => ( P @ X1 @ X2 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr2.inducts
% 0.30/0.46 thf(fact_120_inFr2_Osimps,axiom,
% 0.30/0.46 ( gram_L805317441_inFr2
% 0.30/0.46 = ( ^ [A12: set @ n,A22: dtree,A32: t] :
% 0.30/0.46 ( ? [Tr4: dtree,Ns2: set @ n,T3: t] :
% 0.30/0.46 ( ( A12 = Ns2 )
% 0.30/0.46 & ( A22 = Tr4 )
% 0.30/0.46 & ( A32 = T3 )
% 0.30/0.46 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.30/0.46 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr4 ) ) )
% 0.30/0.46 | ? [Tr13: dtree,Tr4: dtree,Ns13: set @ n,T3: t] :
% 0.30/0.46 ( ( A12
% 0.30/0.46 = ( insert @ n @ ( root @ Tr4 ) @ Ns13 ) )
% 0.30/0.46 & ( A22 = Tr4 )
% 0.30/0.46 & ( A32 = T3 )
% 0.30/0.46 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr4 ) )
% 0.30/0.46 & ( gram_L805317441_inFr2 @ Ns13 @ Tr13 @ T3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr2.simps
% 0.30/0.46 thf(fact_121_inFr2_Ocases,axiom,
% 0.30/0.46 ! [A1: set @ n,A2: dtree,A3: t] :
% 0.30/0.46 ( ( gram_L805317441_inFr2 @ A1 @ A2 @ A3 )
% 0.30/0.46 => ( ( ( member @ n @ ( root @ A2 ) @ A1 )
% 0.30/0.46 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A3 ) @ ( cont @ A2 ) ) )
% 0.30/0.46 => ~ ! [Tr12: dtree,Tr6: dtree,Ns12: set @ n] :
% 0.30/0.46 ( ( A1
% 0.30/0.46 = ( insert @ n @ ( root @ Tr6 ) @ Ns12 ) )
% 0.30/0.46 => ( ( A2 = Tr6 )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr6 ) )
% 0.30/0.46 => ~ ( gram_L805317441_inFr2 @ Ns12 @ Tr12 @ A3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr2.cases
% 0.30/0.46 thf(fact_122_subtr2_Oinducts,axiom,
% 0.30/0.46 ! [X1: set @ n,X2: dtree,X3: dtree,P: ( set @ n ) > dtree > dtree > $o] :
% 0.30/0.46 ( ( gram_L1283001940subtr2 @ X1 @ X2 @ X3 )
% 0.30/0.46 => ( ! [Tr6: dtree,Ns3: set @ n] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr6 ) @ Ns3 )
% 0.30/0.46 => ( P @ Ns3 @ Tr6 @ Tr6 ) )
% 0.30/0.46 => ( ! [Tr12: dtree,Ns3: set @ n,Tr23: dtree,Tr33: dtree] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr12 ) @ Ns3 )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 0.30/0.46 => ( ( gram_L1283001940subtr2 @ Ns3 @ Tr23 @ Tr33 )
% 0.30/0.46 => ( ( P @ Ns3 @ Tr23 @ Tr33 )
% 0.30/0.46 => ( P @ Ns3 @ Tr12 @ Tr33 ) ) ) ) )
% 0.30/0.46 => ( P @ X1 @ X2 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr2.inducts
% 0.30/0.46 thf(fact_123_subtr2__StepR,axiom,
% 0.30/0.46 ! [Tr3: dtree,Ns: set @ n,Tr22: dtree,Tr1: dtree] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr3 ) @ Ns )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr3 ) )
% 0.30/0.46 => ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.30/0.46 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr2_StepR
% 0.30/0.46 thf(fact_124_old_Osum_Oinject_I1_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A4: A,A6: A] :
% 0.30/0.46 ( ( ( sum_Inl @ A @ B @ A4 )
% 0.30/0.46 = ( sum_Inl @ A @ B @ A6 ) )
% 0.30/0.46 = ( A4 = A6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.sum.inject(1)
% 0.30/0.46 thf(fact_125_sum_Oinject_I1_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X1: A,Y1: A] :
% 0.30/0.46 ( ( ( sum_Inl @ A @ B @ X1 )
% 0.30/0.46 = ( sum_Inl @ A @ B @ Y1 ) )
% 0.30/0.46 = ( X1 = Y1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sum.inject(1)
% 0.30/0.46 thf(fact_126_Inr__Inl__False,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X5: B,Y: A] :
% 0.30/0.46 ( ( sum_Inr @ B @ A @ X5 )
% 0.30/0.46 != ( sum_Inl @ A @ B @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % Inr_Inl_False
% 0.30/0.46 thf(fact_127_Inl__Inr__False,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X5: A,Y: B] :
% 0.30/0.46 ( ( sum_Inl @ A @ B @ X5 )
% 0.30/0.46 != ( sum_Inr @ B @ A @ Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % Inl_Inr_False
% 0.30/0.46 thf(fact_128_old_Osum_Osimps_I7_J,axiom,
% 0.30/0.46 ! [B: $tType,T: $tType,A: $tType,F1: A > T,F22: B > T,A4: A] :
% 0.30/0.46 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inl @ A @ B @ A4 ) )
% 0.30/0.46 = ( F1 @ A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.sum.simps(7)
% 0.30/0.46 thf(fact_129_obj__sumE__f,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,B: $tType,S: B,F: ( sum_sum @ A @ C ) > B,P: $o] :
% 0.30/0.46 ( ! [X4: A] :
% 0.30/0.46 ( ( S
% 0.30/0.46 = ( F @ ( sum_Inl @ A @ C @ X4 ) ) )
% 0.30/0.46 => P )
% 0.30/0.46 => ( ! [X4: C] :
% 0.30/0.46 ( ( S
% 0.30/0.46 = ( F @ ( sum_Inr @ C @ A @ X4 ) ) )
% 0.30/0.46 => P )
% 0.30/0.46 => ! [X6: sum_sum @ A @ C] :
% 0.30/0.46 ( ( S
% 0.30/0.46 = ( F @ X6 ) )
% 0.30/0.46 => P ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % obj_sumE_f
% 0.30/0.46 thf(fact_130_old_Osum_Oinducts,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: ( sum_sum @ A @ B ) > $o,Sum: sum_sum @ A @ B] :
% 0.30/0.46 ( ! [A7: A] : ( P @ ( sum_Inl @ A @ B @ A7 ) )
% 0.30/0.46 => ( ! [B6: B] : ( P @ ( sum_Inr @ B @ A @ B6 ) )
% 0.30/0.46 => ( P @ Sum ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.sum.inducts
% 0.30/0.46 thf(fact_131_old_Osum_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Y: sum_sum @ A @ B] :
% 0.30/0.46 ( ! [A7: A] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( sum_Inl @ A @ B @ A7 ) )
% 0.30/0.46 => ~ ! [B6: B] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( sum_Inr @ B @ A @ B6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.sum.exhaust
% 0.30/0.46 thf(fact_132_split__sum__all,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ^ [P2: ( sum_sum @ A @ B ) > $o] :
% 0.30/0.46 ! [X7: sum_sum @ A @ B] : ( P2 @ X7 ) )
% 0.30/0.46 = ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 0.30/0.46 ( ! [X: A] : ( P3 @ ( sum_Inl @ A @ B @ X ) )
% 0.30/0.46 & ! [X: B] : ( P3 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_sum_all
% 0.30/0.46 thf(fact_133_split__sum__ex,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ^ [P2: ( sum_sum @ A @ B ) > $o] :
% 0.30/0.46 ? [X7: sum_sum @ A @ B] : ( P2 @ X7 ) )
% 0.30/0.46 = ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 0.30/0.46 ( ? [X: A] : ( P3 @ ( sum_Inl @ A @ B @ X ) )
% 0.30/0.46 | ? [X: B] : ( P3 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_sum_ex
% 0.30/0.46 thf(fact_134_Inr__not__Inl,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,B2: B,A4: A] :
% 0.30/0.46 ( ( sum_Inr @ B @ A @ B2 )
% 0.30/0.46 != ( sum_Inl @ A @ B @ A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Inr_not_Inl
% 0.30/0.46 thf(fact_135_sumE,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 0.30/0.46 ( ! [X4: A] :
% 0.30/0.46 ( S
% 0.30/0.46 != ( sum_Inl @ A @ B @ X4 ) )
% 0.30/0.46 => ~ ! [Y3: B] :
% 0.30/0.46 ( S
% 0.30/0.46 != ( sum_Inr @ B @ A @ Y3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sumE
% 0.30/0.46 thf(fact_136_old_Osum_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A4: A,B3: B] :
% 0.30/0.46 ( ( sum_Inl @ A @ B @ A4 )
% 0.30/0.46 != ( sum_Inr @ B @ A @ B3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.sum.distinct(1)
% 0.30/0.46 thf(fact_137_old_Osum_Odistinct_I2_J,axiom,
% 0.30/0.46 ! [B7: $tType,A8: $tType,B8: B7,A9: A8] :
% 0.30/0.46 ( ( sum_Inr @ B7 @ A8 @ B8 )
% 0.30/0.46 != ( sum_Inl @ A8 @ B7 @ A9 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.sum.distinct(2)
% 0.30/0.46 thf(fact_138_sum_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X1: A,X2: B] :
% 0.30/0.46 ( ( sum_Inl @ A @ B @ X1 )
% 0.30/0.46 != ( sum_Inr @ B @ A @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sum.distinct(1)
% 0.30/0.46 thf(fact_139_Inl__inject,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X5: A,Y: A] :
% 0.30/0.46 ( ( ( sum_Inl @ A @ B @ X5 )
% 0.30/0.46 = ( sum_Inl @ A @ B @ Y ) )
% 0.30/0.46 => ( X5 = Y ) ) ).
% 0.30/0.46
% 0.30/0.46 % Inl_inject
% 0.30/0.46 thf(fact_140_subtr2__trans,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr3: dtree] :
% 0.30/0.46 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.30/0.46 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr3 )
% 0.30/0.46 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr2_trans
% 0.30/0.46 thf(fact_141_subtr2_ORefl,axiom,
% 0.30/0.46 ! [Tr: dtree,Ns: set @ n] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.30/0.46 => ( gram_L1283001940subtr2 @ Ns @ Tr @ Tr ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr2.Refl
% 0.30/0.46 thf(fact_142_subtr2__rootL__in,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.30/0.46 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.30/0.46 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr2_rootL_in
% 0.30/0.46 thf(fact_143_subtr2__rootR__in,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 0.30/0.46 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 0.30/0.46 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr2_rootR_in
% 0.30/0.46 thf(fact_144_subtr__subtr2,axiom,
% 0.30/0.46 gram_L716654942_subtr = gram_L1283001940subtr2 ).
% 0.30/0.46
% 0.30/0.46 % subtr_subtr2
% 0.30/0.46 thf(fact_145_inFr_OBase,axiom,
% 0.30/0.46 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 0.30/0.46 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr.Base
% 0.30/0.46 thf(fact_146_inFr__subtr,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 0.30/0.46 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.30/0.46 => ? [Tr5: dtree] :
% 0.30/0.46 ( ( gram_L716654942_subtr @ Ns @ Tr5 @ Tr )
% 0.30/0.46 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr_subtr
% 0.30/0.46 thf(fact_147_inFr2_OBase,axiom,
% 0.30/0.46 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 0.30/0.46 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr2.Base
% 0.30/0.46 thf(fact_148_inFr_Ocases,axiom,
% 0.30/0.46 ! [A1: set @ n,A2: dtree,A3: t] :
% 0.30/0.46 ( ( gram_L1333338417e_inFr @ A1 @ A2 @ A3 )
% 0.30/0.46 => ( ( ( member @ n @ ( root @ A2 ) @ A1 )
% 0.30/0.46 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A3 ) @ ( cont @ A2 ) ) )
% 0.30/0.46 => ~ ( ( member @ n @ ( root @ A2 ) @ A1 )
% 0.30/0.46 => ! [Tr12: dtree] :
% 0.30/0.46 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A2 ) )
% 0.30/0.46 => ~ ( gram_L1333338417e_inFr @ A1 @ Tr12 @ A3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr.cases
% 0.30/0.46 thf(fact_149_inFr_Osimps,axiom,
% 0.30/0.46 ( gram_L1333338417e_inFr
% 0.30/0.46 = ( ^ [A12: set @ n,A22: dtree,A32: t] :
% 0.30/0.46 ( ? [Tr4: dtree,Ns2: set @ n,T3: t] :
% 0.30/0.46 ( ( A12 = Ns2 )
% 0.30/0.46 & ( A22 = Tr4 )
% 0.30/0.46 & ( A32 = T3 )
% 0.30/0.46 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.30/0.46 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr4 ) ) )
% 0.30/0.46 | ? [Tr4: dtree,Ns2: set @ n,Tr13: dtree,T3: t] :
% 0.30/0.46 ( ( A12 = Ns2 )
% 0.30/0.46 & ( A22 = Tr4 )
% 0.30/0.46 & ( A32 = T3 )
% 0.30/0.46 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 0.30/0.46 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr4 ) )
% 0.30/0.46 & ( gram_L1333338417e_inFr @ Ns2 @ Tr13 @ T3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr.simps
% 0.30/0.46 thf(fact_150_inFr_Oinducts,axiom,
% 0.30/0.46 ! [X1: set @ n,X2: dtree,X3: t,P: ( set @ n ) > dtree > t > $o] :
% 0.30/0.46 ( ( gram_L1333338417e_inFr @ X1 @ X2 @ X3 )
% 0.30/0.46 => ( ! [Tr6: dtree,Ns3: set @ n,T4: t] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr6 ) @ Ns3 )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr6 ) )
% 0.30/0.46 => ( P @ Ns3 @ Tr6 @ T4 ) ) )
% 0.30/0.46 => ( ! [Tr6: dtree,Ns3: set @ n,Tr12: dtree,T4: t] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr6 ) @ Ns3 )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr6 ) )
% 0.30/0.46 => ( ( gram_L1333338417e_inFr @ Ns3 @ Tr12 @ T4 )
% 0.30/0.46 => ( ( P @ Ns3 @ Tr12 @ T4 )
% 0.30/0.46 => ( P @ Ns3 @ Tr6 @ T4 ) ) ) ) )
% 0.30/0.46 => ( P @ X1 @ X2 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr.inducts
% 0.30/0.46 thf(fact_151_subtr2_OStep,axiom,
% 0.30/0.46 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr3: dtree] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 0.30/0.46 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 0.30/0.46 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr3 )
% 0.30/0.46 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr2.Step
% 0.30/0.46 thf(fact_152_subtr2_Ocases,axiom,
% 0.30/0.46 ! [A1: set @ n,A2: dtree,A3: dtree] :
% 0.30/0.46 ( ( gram_L1283001940subtr2 @ A1 @ A2 @ A3 )
% 0.30/0.46 => ( ( ( A3 = A2 )
% 0.30/0.46 => ~ ( member @ n @ ( root @ A2 ) @ A1 ) )
% 0.30/0.46 => ~ ( ( member @ n @ ( root @ A2 ) @ A1 )
% 0.30/0.46 => ! [Tr23: dtree] :
% 0.30/0.46 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A2 ) @ ( cont @ Tr23 ) )
% 0.30/0.46 => ~ ( gram_L1283001940subtr2 @ A1 @ Tr23 @ A3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr2.cases
% 0.30/0.46 thf(fact_153_subtr2_Osimps,axiom,
% 0.30/0.46 ( gram_L1283001940subtr2
% 0.30/0.46 = ( ^ [A12: set @ n,A22: dtree,A32: dtree] :
% 0.30/0.46 ( ? [Tr4: dtree,Ns2: set @ n] :
% 0.30/0.46 ( ( A12 = Ns2 )
% 0.30/0.46 & ( A22 = Tr4 )
% 0.30/0.46 & ( A32 = Tr4 )
% 0.30/0.46 & ( member @ n @ ( root @ Tr4 ) @ Ns2 ) )
% 0.30/0.46 | ? [Tr13: dtree,Ns2: set @ n,Tr24: dtree,Tr32: dtree] :
% 0.30/0.46 ( ( A12 = Ns2 )
% 0.30/0.46 & ( A22 = Tr13 )
% 0.30/0.46 & ( A32 = Tr32 )
% 0.30/0.46 & ( member @ n @ ( root @ Tr13 ) @ Ns2 )
% 0.30/0.46 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr24 ) )
% 0.30/0.46 & ( gram_L1283001940subtr2 @ Ns2 @ Tr24 @ Tr32 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr2.simps
% 0.30/0.46 thf(fact_154_obj__sumE,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 0.30/0.46 ( ! [X4: A] :
% 0.30/0.46 ( S
% 0.30/0.46 != ( sum_Inl @ A @ B @ X4 ) )
% 0.30/0.46 => ~ ! [X4: B] :
% 0.30/0.46 ( S
% 0.30/0.46 != ( sum_Inr @ B @ A @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % obj_sumE
% 0.30/0.46 thf(fact_155_Inl__cont__H,axiom,
% 0.30/0.46 ! [Tr0: dtree,N: n] :
% 0.30/0.46 ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1451583624elle_H @ Tr0 @ N ) ) )
% 0.30/0.46 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Inl_cont_H
% 0.30/0.46 thf(fact_156_Inl__cont__hsubst__eq,axiom,
% 0.30/0.46 ! [Tr: dtree,Tr0: dtree] :
% 0.30/0.46 ( ( ( root @ Tr )
% 0.30/0.46 = ( root @ Tr0 ) )
% 0.30/0.46 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.30/0.46 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Inl_cont_hsubst_eq
% 0.30/0.46 thf(fact_157_Inl__cont__hsubst__neq,axiom,
% 0.30/0.46 ! [Tr: dtree,Tr0: dtree] :
% 0.30/0.46 ( ( ( root @ Tr )
% 0.30/0.46 != ( root @ Tr0 ) )
% 0.30/0.46 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 0.30/0.46 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Inl_cont_hsubst_neq
% 0.30/0.46 thf(fact_158_vimageI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: B > A,A4: B,B2: A,B4: set @ A] :
% 0.30/0.46 ( ( ( F @ A4 )
% 0.30/0.46 = B2 )
% 0.30/0.46 => ( ( member @ A @ B2 @ B4 )
% 0.30/0.46 => ( member @ B @ A4 @ ( vimage @ B @ A @ F @ B4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % vimageI
% 0.30/0.46 thf(fact_159_vimage__eq,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A4: A,F: A > B,B4: set @ B] :
% 0.30/0.46 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ B4 ) )
% 0.30/0.46 = ( member @ B @ ( F @ A4 ) @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % vimage_eq
% 0.30/0.46 thf(fact_160_vimage__UNIV,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: A > B] :
% 0.30/0.46 ( ( vimage @ A @ B @ F @ ( top_top @ ( set @ B ) ) )
% 0.30/0.46 = ( top_top @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % vimage_UNIV
% 0.30/0.46 thf(fact_161_vimageD,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A4: A,F: A > B,A5: set @ B] :
% 0.30/0.46 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ A5 ) )
% 0.30/0.46 => ( member @ B @ ( F @ A4 ) @ A5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % vimageD
% 0.30/0.46 thf(fact_162_vimageE,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A4: A,F: A > B,B4: set @ B] :
% 0.30/0.46 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ B4 ) )
% 0.30/0.46 => ( member @ B @ ( F @ A4 ) @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % vimageE
% 0.30/0.46 thf(fact_163_vimageI2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: B > A,A4: B,A5: set @ A] :
% 0.30/0.46 ( ( member @ A @ ( F @ A4 ) @ A5 )
% 0.30/0.46 => ( member @ B @ A4 @ ( vimage @ B @ A @ F @ A5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % vimageI2
% 0.30/0.46 thf(fact_164_vimage__Collect,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: B > $o,F: A > B,Q: A > $o] :
% 0.30/0.46 ( ! [X4: A] :
% 0.30/0.46 ( ( P @ ( F @ X4 ) )
% 0.30/0.46 = ( Q @ X4 ) )
% 0.30/0.46 => ( ( vimage @ A @ B @ F @ ( collect @ B @ P ) )
% 0.30/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % vimage_Collect
% 0.30/0.46 thf(fact_165_set_Ocomp,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,F: C > B,G: B > A] :
% 0.30/0.46 ( ( comp @ ( set @ B ) @ ( set @ C ) @ ( set @ A ) @ ( vimage @ C @ B @ F ) @ ( vimage @ B @ A @ G ) )
% 0.30/0.46 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % set.comp
% 0.30/0.46 thf(fact_166_vimage__comp,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,F: A > B,G: B > C,X5: set @ C] :
% 0.30/0.46 ( ( vimage @ A @ B @ F @ ( vimage @ B @ C @ G @ X5 ) )
% 0.30/0.46 = ( vimage @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ X5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % vimage_comp
% 0.30/0.46 thf(fact_167_set_Ocompositionality,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,F: C > B,G: B > A,Set: set @ A] :
% 0.30/0.46 ( ( vimage @ C @ B @ F @ ( vimage @ B @ A @ G @ Set ) )
% 0.30/0.46 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ Set ) ) ).
% 0.30/0.46
% 0.30/0.46 % set.compositionality
% 0.30/0.46 thf(fact_168_not__arg__cong__Inr,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X5: A,Y: A] :
% 0.30/0.46 ( ( X5 != Y )
% 0.30/0.46 => ( ( sum_Inr @ A @ B @ X5 )
% 0.30/0.46 != ( sum_Inr @ A @ B @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_arg_cong_Inr
% 0.30/0.46 thf(fact_169_Inl__Inr__image__cong,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A5: set @ ( sum_sum @ A @ B ),B4: set @ ( sum_sum @ A @ B )] :
% 0.30/0.46 ( ( ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ A5 )
% 0.30/0.46 = ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ B4 ) )
% 0.30/0.46 => ( ( ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ A5 )
% 0.30/0.46 = ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ B4 ) )
% 0.30/0.46 => ( A5 = B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Inl_Inr_image_cong
% 0.30/0.46 thf(fact_170_inFr__self__hsubst,axiom,
% 0.30/0.46 ! [Tr0: dtree,Ns: set @ n,T2: t] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr0 ) @ Ns )
% 0.30/0.46 => ( ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr0 ) @ T2 )
% 0.30/0.46 = ( ( member @ t @ T2 @ ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) )
% 0.30/0.46 | ( gram_L805317505_inFrr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr0 @ T2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr_self_hsubst
% 0.30/0.46 thf(fact_171_inFr__hsubst__imp,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr0: dtree,Tr: dtree,T2: t] :
% 0.30/0.46 ( ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T2 )
% 0.30/0.46 => ( ( member @ t @ T2 @ ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) )
% 0.30/0.46 | ( gram_L805317505_inFrr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr0 @ T2 )
% 0.30/0.46 | ( gram_L1333338417e_inFr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr_hsubst_imp
% 0.30/0.46 thf(fact_172_bot__apply,axiom,
% 0.30/0.46 ! [C: $tType,D: $tType] :
% 0.30/0.46 ( ( bot @ C @ ( type2 @ C ) )
% 0.30/0.46 => ( ( bot_bot @ ( D > C ) )
% 0.30/0.46 = ( ^ [X: D] : ( bot_bot @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_apply
% 0.30/0.46 thf(fact_173_empty__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ( ( ( bot_bot @ ( set @ A ) )
% 0.30/0.46 = ( collect @ A @ P ) )
% 0.30/0.46 = ( ! [X: A] :
% 0.30/0.46 ~ ( P @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_Collect_eq
% 0.30/0.46 thf(fact_174_Collect__empty__eq,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ( ( ( collect @ A @ P )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( ! [X: A] :
% 0.30/0.46 ~ ( P @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_empty_eq
% 0.30/0.46 thf(fact_175_all__not__in__conv,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( ! [X: A] :
% 0.30/0.46 ~ ( member @ A @ X @ A5 ) )
% 0.30/0.46 = ( A5
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % all_not_in_conv
% 0.30/0.46 thf(fact_176_empty__iff,axiom,
% 0.30/0.46 ! [A: $tType,C2: A] :
% 0.30/0.46 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_iff
% 0.30/0.46 thf(fact_177_Diff__idemp,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) @ B4 )
% 0.30/0.46 = ( minus_minus @ ( set @ A ) @ A5 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Diff_idemp
% 0.30/0.46 thf(fact_178_Diff__iff,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) )
% 0.30/0.46 = ( ( member @ A @ C2 @ A5 )
% 0.30/0.46 & ~ ( member @ A @ C2 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Diff_iff
% 0.30/0.46 thf(fact_179_DiffI,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ A5 )
% 0.30/0.46 => ( ~ ( member @ A @ C2 @ B4 )
% 0.30/0.46 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % DiffI
% 0.30/0.46 thf(fact_180_singletonI,axiom,
% 0.30/0.46 ! [A: $tType,A4: A] : ( member @ A @ A4 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonI
% 0.30/0.46 thf(fact_181_Diff__cancel,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( minus_minus @ ( set @ A ) @ A5 @ A5 )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Diff_cancel
% 0.30/0.46 thf(fact_182_empty__Diff,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A5 )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_Diff
% 0.30/0.46 thf(fact_183_Diff__empty,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( minus_minus @ ( set @ A ) @ A5 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = A5 ) ).
% 0.30/0.46
% 0.30/0.46 % Diff_empty
% 0.30/0.46 thf(fact_184_Diff__insert0,axiom,
% 0.30/0.46 ! [A: $tType,X5: A,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ~ ( member @ A @ X5 @ A5 )
% 0.30/0.46 => ( ( minus_minus @ ( set @ A ) @ A5 @ ( insert @ A @ X5 @ B4 ) )
% 0.30/0.46 = ( minus_minus @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Diff_insert0
% 0.30/0.46 thf(fact_185_insert__Diff1,axiom,
% 0.30/0.46 ! [A: $tType,X5: A,B4: set @ A,A5: set @ A] :
% 0.30/0.46 ( ( member @ A @ X5 @ B4 )
% 0.30/0.46 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X5 @ A5 ) @ B4 )
% 0.30/0.46 = ( minus_minus @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_Diff1
% 0.30/0.46 thf(fact_186_vimage__empty,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: A > B] :
% 0.30/0.46 ( ( vimage @ A @ B @ F @ ( bot_bot @ ( set @ B ) ) )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % vimage_empty
% 0.30/0.46 thf(fact_187_insert__Diff__single,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,A5: set @ A] :
% 0.30/0.46 ( ( insert @ A @ A4 @ ( minus_minus @ ( set @ A ) @ A5 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.46 = ( insert @ A @ A4 @ A5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_Diff_single
% 0.30/0.46 thf(fact_188_Diff__UNIV,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( minus_minus @ ( set @ A ) @ A5 @ ( top_top @ ( set @ A ) ) )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Diff_UNIV
% 0.30/0.46 thf(fact_189_vimage__Diff,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: A > B,A5: set @ B,B4: set @ B] :
% 0.30/0.46 ( ( vimage @ A @ B @ F @ ( minus_minus @ ( set @ B ) @ A5 @ B4 ) )
% 0.30/0.46 = ( minus_minus @ ( set @ A ) @ ( vimage @ A @ B @ F @ A5 ) @ ( vimage @ A @ B @ F @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % vimage_Diff
% 0.30/0.46 thf(fact_190_bot__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( bot @ B @ ( type2 @ B ) )
% 0.30/0.46 => ( ( bot_bot @ ( A > B ) )
% 0.30/0.46 = ( ^ [X: A] : ( bot_bot @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_fun_def
% 0.30/0.46 thf(fact_191_ex__in__conv,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( ? [X: A] : ( member @ A @ X @ A5 ) )
% 0.30/0.46 = ( A5
% 0.30/0.46 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_in_conv
% 0.30/0.46 thf(fact_192_equals0I,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ! [Y3: A] :
% 0.30/0.46 ~ ( member @ A @ Y3 @ A5 )
% 0.30/0.46 => ( A5
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0I
% 0.30/0.46 thf(fact_193_equals0D,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,A4: A] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 => ~ ( member @ A @ A4 @ A5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0D
% 0.30/0.46 thf(fact_194_emptyE,axiom,
% 0.30/0.46 ! [A: $tType,A4: A] :
% 0.30/0.46 ~ ( member @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % emptyE
% 0.30/0.46 thf(fact_195_DiffD2,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) )
% 0.30/0.46 => ~ ( member @ A @ C2 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % DiffD2
% 0.30/0.46 thf(fact_196_DiffD1,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) )
% 0.30/0.46 => ( member @ A @ C2 @ A5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % DiffD1
% 0.30/0.46 thf(fact_197_DiffE,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) )
% 0.30/0.46 => ~ ( ( member @ A @ C2 @ A5 )
% 0.30/0.46 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % DiffE
% 0.30/0.46 thf(fact_198_empty__not__UNIV,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bot_bot @ ( set @ A ) )
% 0.30/0.46 != ( top_top @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_not_UNIV
% 0.30/0.46 thf(fact_199_singletonD,axiom,
% 0.30/0.46 ! [A: $tType,B2: A,A4: A] :
% 0.30/0.46 ( ( member @ A @ B2 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 => ( B2 = A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonD
% 0.30/0.46 thf(fact_200_singleton__iff,axiom,
% 0.30/0.46 ! [A: $tType,B2: A,A4: A] :
% 0.30/0.46 ( ( member @ A @ B2 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = ( B2 = A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_iff
% 0.30/0.46 thf(fact_201_doubleton__eq__iff,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,B2: A,C2: A,D2: A] :
% 0.30/0.46 ( ( ( insert @ A @ A4 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = ( insert @ A @ C2 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.46 = ( ( ( A4 = C2 )
% 0.30/0.46 & ( B2 = D2 ) )
% 0.30/0.46 | ( ( A4 = D2 )
% 0.30/0.46 & ( B2 = C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % doubleton_eq_iff
% 0.30/0.46 thf(fact_202_insert__not__empty,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,A5: set @ A] :
% 0.30/0.46 ( ( insert @ A @ A4 @ A5 )
% 0.30/0.46 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_not_empty
% 0.30/0.46 thf(fact_203_singleton__inject,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,B2: A] :
% 0.30/0.46 ( ( ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 => ( A4 = B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_inject
% 0.30/0.46 thf(fact_204_insert__Diff__if,axiom,
% 0.30/0.46 ! [A: $tType,X5: A,B4: set @ A,A5: set @ A] :
% 0.30/0.46 ( ( ( member @ A @ X5 @ B4 )
% 0.30/0.46 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X5 @ A5 ) @ B4 )
% 0.30/0.46 = ( minus_minus @ ( set @ A ) @ A5 @ B4 ) ) )
% 0.30/0.46 & ( ~ ( member @ A @ X5 @ B4 )
% 0.30/0.46 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X5 @ A5 ) @ B4 )
% 0.30/0.46 = ( insert @ A @ X5 @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_Diff_if
% 0.30/0.46 thf(fact_205_Diff__insert__absorb,axiom,
% 0.30/0.46 ! [A: $tType,X5: A,A5: set @ A] :
% 0.30/0.46 ( ~ ( member @ A @ X5 @ A5 )
% 0.30/0.46 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X5 @ A5 ) @ ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = A5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Diff_insert_absorb
% 0.30/0.46 thf(fact_206_Diff__insert2,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,A4: A,B4: set @ A] :
% 0.30/0.46 ( ( minus_minus @ ( set @ A ) @ A5 @ ( insert @ A @ A4 @ B4 ) )
% 0.30/0.46 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A5 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Diff_insert2
% 0.30/0.46 thf(fact_207_insert__Diff,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,A5: set @ A] :
% 0.30/0.46 ( ( member @ A @ A4 @ A5 )
% 0.30/0.46 => ( ( insert @ A @ A4 @ ( minus_minus @ ( set @ A ) @ A5 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.46 = A5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_Diff
% 0.30/0.46 thf(fact_208_Diff__insert,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,A4: A,B4: set @ A] :
% 0.30/0.46 ( ( minus_minus @ ( set @ A ) @ A5 @ ( insert @ A @ A4 @ B4 ) )
% 0.30/0.46 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Diff_insert
% 0.30/0.46 thf(fact_209_vimage__singleton__eq,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A4: A,F: A > B,B2: B] :
% 0.30/0.46 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ ( insert @ B @ B2 @ ( bot_bot @ ( set @ B ) ) ) ) )
% 0.30/0.46 = ( ( F @ A4 )
% 0.30/0.46 = B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % vimage_singleton_eq
% 0.30/0.46 thf(fact_210_inFr__hsubst__minus,axiom,
% 0.30/0.46 ! [Ns: set @ n,Tr0: dtree,Tr: dtree,T2: t] :
% 0.30/0.46 ( ( gram_L1333338417e_inFr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr @ T2 )
% 0.30/0.46 => ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % inFr_hsubst_minus
% 0.30/0.46 thf(fact_211_regular__inFr,axiom,
% 0.30/0.46 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 0.30/0.46 ( ( gram_L646766332egular @ Tr )
% 0.30/0.46 => ( ( member @ n @ ( root @ Tr ) @ Ns )
% 0.30/0.46 => ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 0.30/0.46 => ( ( member @ t @ T2 @ ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr ) ) )
% 0.30/0.46 | ? [Tr5: dtree] :
% 0.30/0.46 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr5 ) @ ( cont @ Tr ) )
% 0.30/0.46 & ( gram_L1333338417e_inFr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr5 @ T2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % regular_inFr
% 0.30/0.46 thf(fact_212_is__singletonI,axiom,
% 0.30/0.46 ! [A: $tType,X5: A] : ( is_singleton @ A @ ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonI
% 0.30/0.46 thf(fact_213__092_060open_062_092_060And_062n_H_O_AInr_An_H_A_092_060in_062_Atns_A_092_060Longrightarrow_062_A_092_060exists_062tr_H_O_AK_An_H_A_061_AFr_A_Ins_A_N_A_123n_125_J_Atr_H_A_092_060and_062_Awf_Atr_H_A_092_060and_062_Aroot_Atr_H_A_061_An_H_092_060close_062,axiom,
% 0.30/0.46 ! [N4: n] :
% 0.30/0.46 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N4 ) @ tns )
% 0.30/0.46 => ? [Tr5: dtree] :
% 0.30/0.46 ( ( ( k @ N4 )
% 0.30/0.46 = ( gram_L861583724lle_Fr @ ( minus_minus @ ( set @ n ) @ ns @ ( insert @ n @ n2 @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr5 ) )
% 0.30/0.46 & ( gram_L864798063lle_wf @ Tr5 )
% 0.30/0.46 & ( ( root @ Tr5 )
% 0.30/0.46 = N4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<And>n'. Inr n' \<in> tns \<Longrightarrow> \<exists>tr'. K n' = Fr (ns - {n}) tr' \<and> wf tr' \<and> root tr' = n'\<close>
% 0.30/0.46 thf(fact_214__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ftr_O_A_I_092_060And_062n_H_O_AInr_An_H_A_092_060in_062_Atns_A_092_060Longrightarrow_062_AK_An_H_A_061_AFr_A_Ins_A_N_A_123n_125_J_A_Iftr_An_H_J_A_092_060and_062_Awf_A_Iftr_An_H_J_A_092_060and_062_Aroot_A_Iftr_An_H_J_A_061_An_H_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.30/0.46 ~ ! [Ftr: n > dtree] :
% 0.30/0.46 ~ ! [N5: n] :
% 0.30/0.46 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N5 ) @ tns )
% 0.30/0.46 => ( ( ( k @ N5 )
% 0.30/0.46 = ( gram_L861583724lle_Fr @ ( minus_minus @ ( set @ n ) @ ns @ ( insert @ n @ n2 @ ( bot_bot @ ( set @ n ) ) ) ) @ ( Ftr @ N5 ) ) )
% 0.30/0.46 & ( gram_L864798063lle_wf @ ( Ftr @ N5 ) )
% 0.30/0.46 & ( ( root @ ( Ftr @ N5 ) )
% 0.30/0.46 = N5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<And>thesis. (\<And>ftr. (\<And>n'. Inr n' \<in> tns \<Longrightarrow> K n' = Fr (ns - {n}) (ftr n') \<and> wf (ftr n') \<and> root (ftr n') = n') \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.30/0.46 thf(fact_215_bot__empty__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bot_bot @ ( A > $o ) )
% 0.30/0.46 = ( ^ [X: A] : ( member @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_empty_eq
% 0.30/0.46 thf(fact_216_bot__set__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bot_bot @ ( set @ A ) )
% 0.30/0.46 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_set_def
% 0.30/0.46 thf(fact_217_not__root__Fr,axiom,
% 0.30/0.46 ! [Tr: dtree,Ns: set @ n] :
% 0.30/0.46 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 0.30/0.46 => ( ( gram_L861583724lle_Fr @ Ns @ Tr )
% 0.30/0.46 = ( bot_bot @ ( set @ t ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_root_Fr
% 0.30/0.46 thf(fact_218_is__singletonI_H,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 != ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 => ( ! [X4: A,Y3: A] :
% 0.30/0.46 ( ( member @ A @ X4 @ A5 )
% 0.30/0.46 => ( ( member @ A @ Y3 @ A5 )
% 0.30/0.46 => ( X4 = Y3 ) ) )
% 0.30/0.46 => ( is_singleton @ A @ A5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonI'
% 0.30/0.46 thf(fact_219_is__singletonE,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( is_singleton @ A @ A5 )
% 0.30/0.46 => ~ ! [X4: A] :
% 0.30/0.46 ( A5
% 0.30/0.46 != ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonE
% 0.30/0.46 thf(fact_220_is__singleton__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( is_singleton @ A )
% 0.30/0.46 = ( ^ [A10: set @ A] :
% 0.30/0.46 ? [X: A] :
% 0.30/0.46 ( A10
% 0.30/0.46 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singleton_def
% 0.30/0.46 thf(fact_221__C0_C,axiom,
% 0.30/0.46 ! [N6: n] :
% 0.30/0.46 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N6 ) @ tns )
% 0.30/0.46 => ( ( ( k @ N6 )
% 0.30/0.46 = ( gram_L861583724lle_Fr @ ( minus_minus @ ( set @ n ) @ ns @ ( insert @ n @ n2 @ ( bot_bot @ ( set @ n ) ) ) ) @ ( ftr @ N6 ) ) )
% 0.30/0.46 & ( gram_L864798063lle_wf @ ( ftr @ N6 ) )
% 0.30/0.46 & ( ( root @ ( ftr @ N6 ) )
% 0.30/0.46 = N6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % "0"
% 0.30/0.46 thf(fact_222_P,axiom,
% 0.30/0.46 member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ n2 @ tns ) @ gram_L1451583632elle_P ).
% 0.30/0.46
% 0.30/0.46 % P
% 0.30/0.46 thf(fact_223_used,axiom,
% 0.30/0.46 ! [N: n] :
% 0.30/0.46 ? [Tns: set @ ( sum_sum @ t @ n )] : ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ N @ Tns ) @ gram_L1451583632elle_P ) ).
% 0.30/0.46
% 0.30/0.46 % used
% 0.30/0.46 thf(fact_224_Fr__self__hsubst,axiom,
% 0.30/0.46 ! [Tr0: dtree,Ns: set @ n] :
% 0.30/0.46 ( ( member @ n @ ( root @ Tr0 ) @ Ns )
% 0.30/0.46 => ( ( gram_L861583724lle_Fr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr0 ) )
% 0.30/0.46 = ( sup_sup @ ( set @ t ) @ ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) @ ( gram_L1556062726le_Frr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr0 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Fr_self_hsubst
% 0.30/0.46 thf(fact_225_L__rec__notin,axiom,
% 0.30/0.46 ! [N: n,Ns: set @ n] :
% 0.30/0.46 ( ~ ( member @ n @ N @ Ns )
% 0.30/0.46 => ( ( gram_L1451583628elle_L @ Ns @ N )
% 0.30/0.46 = ( insert @ ( set @ t ) @ ( bot_bot @ ( set @ t ) ) @ ( bot_bot @ ( set @ ( set @ t ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % L_rec_notin
% 0.30/0.46 thf(fact_226_UnCI,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,B4: set @ A,A5: set @ A] :
% 0.30/0.46 ( ( ~ ( member @ A @ C2 @ B4 )
% 0.30/0.46 => ( member @ A @ C2 @ A5 ) )
% 0.30/0.46 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnCI
% 0.30/0.46 thf(fact_227_Un__iff,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 0.30/0.46 = ( ( member @ A @ C2 @ A5 )
% 0.30/0.46 | ( member @ A @ C2 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_iff
% 0.30/0.46 thf(fact_228_Un__empty,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( ( sup_sup @ ( set @ A ) @ A5 @ B4 )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( ( A5
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 & ( B4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty
% 0.30/0.46 thf(fact_229_Un__insert__right,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,A4: A,B4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A5 @ ( insert @ A @ A4 @ B4 ) )
% 0.30/0.46 = ( insert @ A @ A4 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_insert_right
% 0.30/0.46 thf(fact_230_Un__insert__left,axiom,
% 0.30/0.46 ! [A: $tType,A4: A,B4: set @ A,C4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A4 @ B4 ) @ C4 )
% 0.30/0.46 = ( insert @ A @ A4 @ ( sup_sup @ ( set @ A ) @ B4 @ C4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_insert_left
% 0.30/0.46 thf(fact_231_Un__Diff__cancel,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A5 @ ( minus_minus @ ( set @ A ) @ B4 @ A5 ) )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_Diff_cancel
% 0.30/0.46 thf(fact_232_Un__Diff__cancel2,axiom,
% 0.30/0.46 ! [A: $tType,B4: set @ A,A5: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ B4 @ A5 ) @ A5 )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ B4 @ A5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_Diff_cancel2
% 0.30/0.46 thf(fact_233_vimage__Un,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: A > B,A5: set @ B,B4: set @ B] :
% 0.30/0.46 ( ( vimage @ A @ B @ F @ ( sup_sup @ ( set @ B ) @ A5 @ B4 ) )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ ( vimage @ A @ B @ F @ A5 ) @ ( vimage @ A @ B @ F @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % vimage_Un
% 0.30/0.46 thf(fact_234_Un__empty__right,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A5 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = A5 ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty_right
% 0.30/0.46 thf(fact_235_Un__empty__left,axiom,
% 0.30/0.46 ! [A: $tType,B4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B4 )
% 0.30/0.46 = B4 ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty_left
% 0.30/0.46 thf(fact_236_insert__is__Un,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( insert @ A )
% 0.30/0.46 = ( ^ [A11: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A11 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_is_Un
% 0.30/0.46 thf(fact_237_Un__singleton__iff,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B4: set @ A,X5: A] :
% 0.30/0.46 ( ( ( sup_sup @ ( set @ A ) @ A5 @ B4 )
% 0.30/0.46 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = ( ( ( A5
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 & ( B4
% 0.30/0.46 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.46 | ( ( A5
% 0.30/0.46 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 & ( B4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 | ( ( A5
% 0.30/0.46 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 & ( B4
% 0.30/0.46 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_singleton_iff
% 0.30/0.46 thf(fact_238_singleton__Un__iff,axiom,
% 0.30/0.46 ! [A: $tType,X5: A,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 0.30/0.46 = ( ( ( A5
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 & ( B4
% 0.30/0.46 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.46 | ( ( A5
% 0.30/0.46 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 & ( B4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 | ( ( A5
% 0.30/0.46 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 & ( B4
% 0.30/0.46 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_Un_iff
% 0.30/0.46 thf(fact_239_Un__UNIV__left,axiom,
% 0.30/0.46 ! [A: $tType,B4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B4 )
% 0.30/0.46 = ( top_top @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_UNIV_left
% 0.30/0.46 thf(fact_240_Un__UNIV__right,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A5 @ ( top_top @ ( set @ A ) ) )
% 0.30/0.46 = ( top_top @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_UNIV_right
% 0.30/0.46 thf(fact_241_UnE,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 0.30/0.46 => ( ~ ( member @ A @ C2 @ A5 )
% 0.30/0.46 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnE
% 0.30/0.46 thf(fact_242_UnI1,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ A5 )
% 0.30/0.46 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI1
% 0.30/0.46 thf(fact_243_UnI2,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,B4: set @ A,A5: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ B4 )
% 0.30/0.46 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI2
% 0.30/0.46 thf(fact_244_bex__Un,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B4: set @ A,P: A > $o] :
% 0.30/0.46 ( ( ? [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 0.30/0.46 & ( P @ X ) ) )
% 0.30/0.46 = ( ? [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ A5 )
% 0.30/0.46 & ( P @ X ) )
% 0.30/0.46 | ? [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ B4 )
% 0.30/0.46 & ( P @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bex_Un
% 0.30/0.46 thf(fact_245_ball__Un,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B4: set @ A,P: A > $o] :
% 0.30/0.46 ( ( ! [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 0.30/0.46 => ( P @ X ) ) )
% 0.30/0.46 = ( ! [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ A5 )
% 0.30/0.46 => ( P @ X ) )
% 0.30/0.46 & ! [X: A] :
% 0.30/0.46 ( ( member @ A @ X @ B4 )
% 0.30/0.46 => ( P @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ball_Un
% 0.30/0.46 thf(fact_246_Un__assoc,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B4: set @ A,C4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) @ C4 )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ A5 @ ( sup_sup @ ( set @ A ) @ B4 @ C4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_assoc
% 0.30/0.46 thf(fact_247_Un__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A5 @ A5 )
% 0.30/0.46 = A5 ) ).
% 0.30/0.46
% 0.30/0.46 % Un_absorb
% 0.30/0.46 thf(fact_248_Un__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A10: set @ A,B9: set @ A] : ( sup_sup @ ( set @ A ) @ B9 @ A10 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_commute
% 0.30/0.46 thf(fact_249_Un__left__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A5 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_left_absorb
% 0.30/0.46 thf(fact_250_Un__left__commute,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B4: set @ A,C4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A5 @ ( sup_sup @ ( set @ A ) @ B4 @ C4 ) )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ B4 @ ( sup_sup @ ( set @ A ) @ A5 @ C4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_left_commute
% 0.30/0.46 thf(fact_251_Un__Diff,axiom,
% 0.30/0.46 ! [A: $tType,A5: set @ A,B4: set @ A,C4: set @ A] :
% 0.30/0.46 ( ( minus_minus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) @ C4 )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A5 @ C4 ) @ ( minus_minus @ ( set @ A ) @ B4 @ C4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_Diff
% 0.30/0.46 thf(fact_252_vimage__insert,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: A > B,A4: B,B4: set @ B] :
% 0.30/0.46 ( ( vimage @ A @ B @ F @ ( insert @ B @ A4 @ B4 ) )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ ( vimage @ A @ B @ F @ ( insert @ B @ A4 @ ( bot_bot @ ( set @ B ) ) ) ) @ ( vimage @ A @ B @ F @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % vimage_insert
% 0.30/0.46 thf(fact_253_sup__top__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X5: A] :
% 0.30/0.46 ( ( sup_sup @ A @ X5 @ ( top_top @ A ) )
% 0.30/0.46 = ( top_top @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_top_right
% 0.30/0.46 thf(fact_254_sup__top__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X5: A] :
% 0.30/0.46 ( ( sup_sup @ A @ ( top_top @ A ) @ X5 )
% 0.30/0.46 = ( top_top @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_top_left
% 0.30/0.46 thf(fact_255_subtr2__trans__Un,axiom,
% 0.30/0.46 ! [Ns122: set @ n,Tr1: dtree,Tr22: dtree,Ns23: set @ n,Tr3: dtree] :
% 0.30/0.46 ( ( gram_L1283001940subtr2 @ Ns122 @ Tr1 @ Tr22 )
% 0.30/0.46 => ( ( gram_L1283001940subtr2 @ Ns23 @ Tr22 @ Tr3 )
% 0.30/0.46 => ( gram_L1283001940subtr2 @ ( sup_sup @ ( set @ n ) @ Ns122 @ Ns23 ) @ Tr1 @ Tr3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subtr2_trans_Un
% 0.30/0.46
% 0.30/0.46 %----Type constructors (12)
% 0.30/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.30/0.46 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.30/0.46 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.30/0.46 ! [A8: $tType,A13: $tType] :
% 0.30/0.46 ( ( bounded_lattice @ A13 @ ( type2 @ A13 ) )
% 0.30/0.46 => ( bounded_lattice @ ( A8 > A13 ) @ ( type2 @ ( A8 > A13 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 0.30/0.46 ! [A8: $tType,A13: $tType] :
% 0.30/0.46 ( ( bounded_lattice @ A13 @ ( type2 @ A13 ) )
% 0.30/0.46 => ( bounded_lattice_top @ ( A8 > A13 ) @ ( type2 @ ( A8 > A13 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Otop,axiom,
% 0.30/0.46 ! [A8: $tType,A13: $tType] :
% 0.30/0.46 ( ( top @ A13 @ ( type2 @ A13 ) )
% 0.30/0.46 => ( top @ ( A8 > A13 ) @ ( type2 @ ( A8 > A13 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Obot,axiom,
% 0.30/0.46 ! [A8: $tType,A13: $tType] :
% 0.30/0.46 ( ( bot @ A13 @ ( type2 @ A13 ) )
% 0.30/0.46 => ( bot @ ( A8 > A13 ) @ ( type2 @ ( A8 > A13 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_3,axiom,
% 0.30/0.46 ! [A8: $tType] : ( bounded_lattice_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Otop_4,axiom,
% 0.30/0.46 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Obot_5,axiom,
% 0.30/0.46 ! [A8: $tType] : ( bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_6,axiom,
% 0.30/0.46 bounded_lattice_top @ $o @ ( type2 @ $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Otop_7,axiom,
% 0.30/0.46 top @ $o @ ( type2 @ $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Obot_8,axiom,
% 0.30/0.46 bot @ $o @ ( type2 @ $o ) ).
% 0.30/0.46
% 0.30/0.46 %----Helper facts (3)
% 0.30/0.46 thf(help_If_3_1_T,axiom,
% 0.30/0.46 ! [P: $o] :
% 0.30/0.46 ( ( P = $true )
% 0.30/0.46 | ( P = $false ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(help_If_2_1_T,axiom,
% 0.30/0.46 ! [A: $tType,X5: A,Y: A] :
% 0.30/0.46 ( ( if @ A @ $false @ X5 @ Y )
% 0.30/0.46 = Y ) ).
% 0.30/0.46
% 0.30/0.46 thf(help_If_1_1_T,axiom,
% 0.30/0.46 ! [A: $tType,X5: A,Y: A] :
% 0.30/0.46 ( ( if @ A @ $true @ X5 @ Y )
% 0.30/0.46 = X5 ) ).
% 0.30/0.46
% 0.30/0.46 %----Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 gram_L864798063lle_wf @ ( gram_L1004374585hsubst @ tr2 @ tr2 ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.59/1.47 ---- Embedded in THF ---
% 2.59/1.47 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.59/1.47 %%% Generated on Tue Feb 24 04:17:28 EST 2026
% 2.59/1.47 %%% using '$$dhol' embedding, version 1.3.0.
% 2.59/1.47 %%% Logic specification used:
% 2.59/1.47 %%% thf(spec, logic, $$dhol).
% 2.59/1.47
% 2.59/1.47 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.6ce4rUdsE3/DTF2DTF24932.p
% 2.59/1.47 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.59/1.47 thf(ty_t_Sum__Type_Osum, type, sum_sum: ($tType > ($tType > $tType))).
% 2.59/1.47 thf(ty_t_DTree_Odtree, type, dtree: $tType).
% 2.59/1.47 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.59/1.47 thf(ty_t_DTree_OT, type, t: $tType).
% 2.59/1.47 thf(ty_t_DTree_ON, type, n: $tType).
% 2.59/1.47 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.59/1.47 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.59/1.47 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.59/1.47 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.59/1.47 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.59/1.47 thf(sy_cl_Lattices_Obounded__lattice__top, type, bounded_lattice_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.59/1.47 thf(sy_c_DTree_ONode, type, node: (n > ((set @ ((sum_sum @ t) @ dtree)) > dtree))).
% 2.59/1.47 thf(sy_c_DTree_Ocont, type, cont: (dtree > (set @ ((sum_sum @ t) @ dtree)))).
% 2.59/1.47 thf(sy_c_DTree_Odtree_Oroot, type, root: (dtree > n)).
% 2.59/1.47 thf(sy_c_DTree_Ounfold, type, unfold: (!> [A:$tType]: (((A > n) > ((A > (set @ ((sum_sum @ t) @ A))) > (A > dtree)))))).
% 2.59/1.47 thf(sy_c_Fun_Ocomp, type, comp: (!> [B:$tType,C:$tType,A:$tType]: (((B > C) > ((A > B) > (A > C)))))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OFr, type, gram_L861583724lle_Fr: ((set @ n) > (dtree > (set @ t)))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OFrr, type, gram_L1556062726le_Frr: ((set @ n) > (dtree > (set @ t)))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH, type, gram_L1451583624elle_H: (dtree > (n > dtree))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__c, type, gram_L1221482011le_H_c: (dtree > (n > (set @ ((sum_sum @ t) @ n))))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__r, type, gram_L1221482026le_H_r: (dtree > (n > n))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OL, type, gram_L1451583628elle_L: ((set @ n) > (n > (set @ (set @ t))))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OP, type, gram_L1451583632elle_P: (set @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n))))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr, type, gram_L1231612515_deftr: (n > dtree)).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst, type, gram_L1004374585hsubst: (dtree > (dtree > dtree))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c, type, gram_L1905609002ubst_c: (dtree > (dtree > (set @ ((sum_sum @ t) @ dtree))))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r, type, gram_L1905609017ubst_r: (dtree > n)).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr, type, gram_L1333338417e_inFr: ((set @ n) > (dtree > (t > $o)))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2, type, gram_L805317441_inFr2: ((set @ n) > (dtree > (t > $o)))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFrr, type, gram_L805317505_inFrr: ((set @ n) > (dtree > (t > $o)))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr, type, gram_L830233218_inItr: ((set @ n) > (dtree > (n > $o)))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Opick, type, gram_L315592705e_pick: (dtree > (n > dtree))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Orcut, type, gram_L1828378864e_rcut: (dtree > dtree)).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oreg, type, gram_L1918716148le_reg: ((n > dtree) > (dtree > $o))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oregular, type, gram_L646766332egular: (dtree > $o)).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr, type, gram_L716654942_subtr: ((set @ n) > (dtree > (dtree > $o)))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr2, type, gram_L1283001940subtr2: ((set @ n) > (dtree > (dtree > $o)))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OsubtrOf, type, gram_L1614515765ubtrOf: (dtree > (n > dtree))).
% 2.59/1.47 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf, type, gram_L864798063lle_wf: (dtree > $o)).
% 2.59/1.47 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.59/1.47 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.59/1.47 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.59/1.47 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.59/1.47 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.59/1.47 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.59/1.47 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.59/1.47 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.59/1.47 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.59/1.47 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.59/1.47 thf(sy_c_Set_Ovimage, type, vimage: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ B) > (set @ A)))))).
% 2.59/1.47 thf(sy_c_Sum__Type_OInl, type, sum_Inl: (!> [A:$tType,B:$tType]: ((A > ((sum_sum @ A) @ B))))).
% 2.59/1.47 thf(sy_c_Sum__Type_OInr, type, sum_Inr: (!> [B:$tType,A:$tType]: ((B > ((sum_sum @ A) @ B))))).
% 2.59/1.47 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum, type, sum_rec_sum: (!> [A:$tType,T:$tType,B:$tType]: (((A > T) > ((B > T) > (((sum_sum @ A) @ B) > T)))))).
% 2.59/1.47 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.59/1.47 thf(sy_v_K____, type, k: (n > (set @ t))).
% 2.59/1.47 thf(sy_v_ftr____, type, ftr: (n > dtree)).
% 2.59/1.47 thf(sy_v_n, type, n2: n).
% 2.59/1.47 thf(sy_v_ns, type, ns: (set @ n)).
% 2.59/1.47 thf(sy_v_tns____, type, tns: (set @ ((sum_sum @ t) @ n))).
% 2.59/1.47 thf(sy_v_tr_H____, type, tr: dtree).
% 2.59/1.47 thf(sy_v_tr____, type, tr2: dtree).
% 2.59/1.47 thf(fact_0_dtr, axiom, (gram_L864798063lle_wf @ tr2)).
% 2.59/1.47 thf(fact_1_tr_H__def, axiom, (tr = ((gram_L1004374585hsubst @ tr2) @ tr2))).
% 2.59/1.47 thf(fact_2_wf__hsubst, axiom, (! [Tr0:dtree,Tr:dtree]: (((gram_L864798063lle_wf @ Tr0) => ((gram_L864798063lle_wf @ Tr) => (gram_L864798063lle_wf @ ((gram_L1004374585hsubst @ Tr0) @ Tr))))))).
% 2.59/1.47 thf(fact_3_wf__rcut, axiom, (! [Tr0:dtree]: (((gram_L864798063lle_wf @ Tr0) => (gram_L864798063lle_wf @ (gram_L1828378864e_rcut @ Tr0)))))).
% 2.59/1.47 thf(fact_4_wf__deftr, axiom, (! [N:n]: ((gram_L864798063lle_wf @ (gram_L1231612515_deftr @ N))))).
% 2.59/1.47 thf(fact_5_rtr, axiom, ((root @ tr2) = n2)).
% 2.59/1.47 thf(fact_6_n, axiom, (((member @ n) @ n2) @ ns)).
% 2.59/1.47 thf(fact_7_root__hsubst, axiom, (! [Tr0:dtree,Tr:dtree]: (((root @ ((gram_L1004374585hsubst @ Tr0) @ Tr)) = (root @ Tr))))).
% 2.59/1.47 thf(fact_8_wf__subtr, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr:dtree]: (((gram_L864798063lle_wf @ Tr1) => ((((gram_L716654942_subtr @ Ns) @ Tr) @ Tr1) => (gram_L864798063lle_wf @ Tr)))))).
% 2.59/1.47 thf(fact_9_hsubst__def, axiom, (gram_L1004374585hsubst = (^ [Tr02:dtree]: ((((unfold @ dtree) @ gram_L1905609017ubst_r) @ (gram_L1905609002ubst_c @ Tr02)))))).
% 2.59/1.47 thf(fact_10_hsubst__eq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) = (root @ Tr0)) => (((gram_L1004374585hsubst @ Tr0) @ Tr) = ((gram_L1004374585hsubst @ Tr0) @ Tr0)))))).
% 2.59/1.47 thf(fact_11_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)))))).
% 2.59/1.47 thf(fact_12_root__o__subst, axiom, (! [Tr0:dtree]: (((((((comp @ dtree) @ n) @ dtree) @ root) @ (gram_L1004374585hsubst @ Tr0)) = root)))).
% 2.59/1.47 thf(fact_13_wf__cont, axiom, (! [Tr:dtree,Tr2:dtree]: (((gram_L864798063lle_wf @ Tr) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr2)) @ (cont @ Tr)) => (gram_L864798063lle_wf @ Tr2)))))).
% 2.59/1.47 thf(fact_14_wf__pick, axiom, (! [Tr0:dtree,N:n]: (((gram_L864798063lle_wf @ Tr0) => ((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N) => (gram_L864798063lle_wf @ ((gram_L315592705e_pick @ Tr0) @ N))))))).
% 2.59/1.47 thf(fact_15_root__deftr, axiom, (! [N:n]: (((root @ (gram_L1231612515_deftr @ N)) = N)))).
% 2.59/1.47 thf(fact_16_root__rcut, axiom, (! [Tr0:dtree]: (((root @ (gram_L1828378864e_rcut @ Tr0)) = (root @ Tr0))))).
% 2.59/1.47 thf(fact_17_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)))))))).
% 2.59/1.47 thf(fact_18_pick, axiom, (! [Tr0:dtree,N:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N) => ((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ ((gram_L315592705e_pick @ Tr0) @ N)) @ Tr0) & ((root @ ((gram_L315592705e_pick @ Tr0) @ N)) = N)))))).
% 2.59/1.47 thf(fact_19_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))))))).
% 2.59/1.47 thf(fact_20_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))))))).
% 2.59/1.47 thf(fact_21_root__pick, axiom, (! [Tr0:dtree,N:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N) => ((root @ ((gram_L315592705e_pick @ Tr0) @ N)) = N))))).
% 2.59/1.47 thf(fact_22_inItr_OBase, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L830233218_inItr @ Ns) @ Tr) @ (root @ Tr)))))).
% 2.59/1.47 thf(fact_23_subtr_ORefl, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L716654942_subtr @ Ns) @ Tr) @ Tr))))).
% 2.59/1.47 thf(fact_24_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))))))).
% 2.59/1.47 thf(fact_25_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)))))).
% 2.59/1.47 thf(fact_26_subtr__pick, axiom, (! [Tr0:dtree,N:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N) => (((gram_L716654942_subtr @ (top_top @ (set @ n))) @ ((gram_L315592705e_pick @ Tr0) @ N)) @ Tr0))))).
% 2.59/1.47 thf(fact_27_inItr_Ocases, axiom, (! [A1:(set @ n),A2:dtree,A3:n]: (((((gram_L830233218_inItr @ A1) @ A2) @ A3) => (((A3 = (root @ A2)) => (~ ((((member @ n) @ (root @ A2)) @ A1)))) => (~ (((((member @ n) @ (root @ A2)) @ A1) => (! [Tr12:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ A2)) => (~ ((((gram_L830233218_inItr @ A1) @ Tr12) @ A3)))))))))))))).
% 2.59/1.47 thf(fact_28_inItr_Osimps, axiom, (gram_L830233218_inItr = (^ [A12:(set @ n),A22:dtree,A32:n]: (((? [Tr4:dtree,Ns2:(set @ n)]: (((A12 = Ns2) & ((A22 = Tr4) & ((A32 = (root @ Tr4)) & (((member @ n) @ (root @ Tr4)) @ Ns2)))))) | (? [Tr4:dtree,Ns2:(set @ n),Tr13:dtree,N2:n]: (((A12 = Ns2) & ((A22 = Tr4) & ((A32 = N2) & ((((member @ n) @ (root @ Tr4)) @ Ns2) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr4)) & (((gram_L830233218_inItr @ Ns2) @ Tr13) @ N2))))))))))))).
% 2.59/1.47 thf(fact_29_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)))))))).
% 2.59/1.47 thf(fact_30_subtr_Ocases, axiom, (! [A1:(set @ n),A2:dtree,A3:dtree]: (((((gram_L716654942_subtr @ A1) @ A2) @ A3) => (((A3 = A2) => (~ ((((member @ n) @ (root @ A2)) @ A1)))) => (~ (((((member @ n) @ (root @ A3)) @ A1) => (! [Tr23:dtree]: (((((gram_L716654942_subtr @ A1) @ A2) @ Tr23) => (~ ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr23)) @ (cont @ A3))))))))))))))).
% 2.59/1.47 thf(fact_31_subtr_Osimps, axiom, (gram_L716654942_subtr = (^ [A12:(set @ n),A22:dtree,A32:dtree]: (((? [Tr4:dtree,Ns2:(set @ n)]: (((A12 = Ns2) & ((A22 = Tr4) & ((A32 = Tr4) & (((member @ n) @ (root @ Tr4)) @ Ns2)))))) | (? [Tr32:dtree,Ns2:(set @ n),Tr13:dtree,Tr24:dtree]: (((A12 = Ns2) & ((A22 = Tr13) & ((A32 = Tr32) & ((((member @ n) @ (root @ Tr32)) @ Ns2) & ((((gram_L716654942_subtr @ Ns2) @ Tr13) @ Tr24) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr24)) @ (cont @ Tr32)))))))))))))).
% 2.59/1.47 thf(fact_32_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))))))).
% 2.59/1.47 thf(fact_33_subtr__deftr, axiom, (! [Ns:(set @ n),Tr2:dtree,N:n]: (((((gram_L716654942_subtr @ Ns) @ Tr2) @ (gram_L1231612515_deftr @ N)) => (Tr2 = (gram_L1231612515_deftr @ (root @ Tr2))))))).
% 2.59/1.47 thf(fact_34_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)))))).
% 2.59/1.47 thf(fact_35_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)))))).
% 2.59/1.47 thf(fact_36_hsubst__c__def, axiom, (gram_L1905609002ubst_c = (^ [Tr02:dtree,Tr4:dtree]: (((((if @ (set @ ((sum_sum @ t) @ dtree))) @ ((root @ Tr4) = (root @ Tr02))) @ (cont @ Tr02)) @ (cont @ Tr4)))))).
% 2.59/1.47 thf(fact_37_hsubst__r__def, axiom, (gram_L1905609017ubst_r = root)).
% 2.59/1.47 thf(fact_38_inFr__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t]: (((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 2.59/1.47 thf(fact_39_inItr_Oinducts, axiom, (! [X1:(set @ n),X2:dtree,X3:n,P:((set @ n) > (dtree > (n > $o)))]: (((((gram_L830233218_inItr @ X1) @ X2) @ X3) => ((! [Tr6:dtree,Ns3:(set @ n)]: (((((member @ n) @ (root @ Tr6)) @ Ns3) => (((P @ Ns3) @ Tr6) @ (root @ Tr6))))) => ((! [Tr6:dtree,Ns3:(set @ n),Tr12:dtree,N3:n]: (((((member @ n) @ (root @ Tr6)) @ Ns3) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr6)) => ((((gram_L830233218_inItr @ Ns3) @ Tr12) @ N3) => ((((P @ Ns3) @ Tr12) @ N3) => (((P @ Ns3) @ Tr6) @ N3))))))) => (((P @ X1) @ X2) @ X3))))))).
% 2.59/1.47 thf(fact_40_inItr__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,N:n]: (((((gram_L830233218_inItr @ Ns) @ Tr) @ N) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 2.59/1.47 thf(fact_41_not__root__inFr, axiom, (! [Tr:dtree,Ns:(set @ n),T2:t]: (((~ ((((member @ n) @ (root @ Tr)) @ Ns))) => (~ ((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2))))))).
% 2.59/1.47 thf(fact_42_subtr_Oinducts, axiom, (! [X1:(set @ n),X2:dtree,X3:dtree,P:((set @ n) > (dtree > (dtree > $o)))]: (((((gram_L716654942_subtr @ X1) @ X2) @ X3) => ((! [Tr6:dtree,Ns3:(set @ n)]: (((((member @ n) @ (root @ Tr6)) @ Ns3) => (((P @ Ns3) @ Tr6) @ Tr6)))) => ((! [Tr33:dtree,Ns3:(set @ n),Tr12:dtree,Tr23:dtree]: (((((member @ n) @ (root @ Tr33)) @ Ns3) => ((((gram_L716654942_subtr @ Ns3) @ Tr12) @ Tr23) => ((((P @ Ns3) @ Tr12) @ Tr23) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr23)) @ (cont @ Tr33)) => (((P @ Ns3) @ Tr12) @ Tr33))))))) => (((P @ X1) @ X2) @ X3))))))).
% 2.59/1.47 thf(fact_43_subtr__inductL, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree,Phi:((set @ n) > (dtree > (dtree > $o)))]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => ((! [Ns3:(set @ n),Tr6:dtree]: ((((Phi @ Ns3) @ Tr6) @ Tr6))) => ((! [Ns3:(set @ n),Tr12:dtree,Tr23:dtree,Tr33:dtree]: (((((member @ n) @ (root @ Tr12)) @ Ns3) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr23)) => ((((gram_L716654942_subtr @ Ns3) @ Tr23) @ Tr33) => ((((Phi @ Ns3) @ Tr23) @ Tr33) => (((Phi @ Ns3) @ Tr12) @ Tr33))))))) => (((Phi @ Ns) @ Tr1) @ Tr22))))))).
% 2.59/1.47 thf(fact_44_subtr__rootL__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr1)) @ Ns))))).
% 2.59/1.47 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A4:A,P:(A > $o)]: (((((member @ A) @ A4) @ ((collect @ A) @ P)) = (P @ A4))))).
% 2.59/1.47 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A5)))) = A5)))).
% 2.59/1.47 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.59/1.47 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 2.59/1.47 thf(fact_49_subtr__rootR__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L716654942_subtr @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr22)) @ Ns))))).
% 2.59/1.47 thf(fact_50_subtr__UNIV__inductL, axiom, (! [Tr1:dtree,Tr22:dtree,Phi:(dtree > (dtree > $o))]: (((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ Tr1) @ Tr22) => ((! [Tr6:dtree]: (((Phi @ Tr6) @ Tr6))) => ((! [Tr12:dtree,Tr23:dtree,Tr33:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr23)) => ((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ Tr23) @ Tr33) => (((Phi @ Tr23) @ Tr33) => ((Phi @ Tr12) @ Tr33)))))) => ((Phi @ Tr1) @ Tr22))))))).
% 2.59/1.47 thf(fact_51_subtrOf__root, axiom, (! [Tr:dtree,Tr2:dtree]: (((gram_L864798063lle_wf @ Tr) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr2)) @ (cont @ Tr)) => (((gram_L1614515765ubtrOf @ Tr) @ (root @ Tr2)) = Tr2)))))).
% 2.59/1.47 thf(fact_52_H__r__def, axiom, (gram_L1221482026le_H_r = (^ [Tr02:dtree,N2:n]: ((root @ ((gram_L315592705e_pick @ Tr02) @ N2)))))).
% 2.59/1.47 thf(fact_53_inFrr__def, axiom, (gram_L805317505_inFrr = (^ [Ns2:(set @ n),Tr4:dtree,T3:t]: ((? [Tr7:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr7)) @ (cont @ Tr4)) & (((gram_L1333338417e_inFr @ Ns2) @ Tr7) @ T3)))))))).
% 2.59/1.47 thf(fact_54_sum_Oinject_I2_J, axiom, (! [A:$tType,B:$tType,X2:B,Y2:B]: ((((((sum_Inr @ B) @ A) @ X2) = (((sum_Inr @ B) @ A) @ Y2)) = (X2 = Y2))))).
% 2.59/1.47 thf(fact_55_old_Osum_Oinject_I2_J, axiom, (! [A:$tType,B:$tType,B2:B,B3:B]: ((((((sum_Inr @ B) @ A) @ B2) = (((sum_Inr @ B) @ A) @ B3)) = (B2 = B3))))).
% 2.59/1.47 thf(fact_56_unfold_I1_J, axiom, (! [A:$tType,Rt:(A > n),Ct:(A > (set @ ((sum_sum @ t) @ A))),B2:A]: (((root @ ((((unfold @ A) @ Rt) @ Ct) @ B2)) = (Rt @ B2))))).
% 2.59/1.47 thf(fact_57_comp__apply, axiom, (! [C:$tType,A:$tType,B:$tType]: (((((comp @ B) @ A) @ C) = (^ [F2:(B > A),G2:(C > B),X:C]: ((F2 @ (G2 @ X)))))))).
% 2.59/1.47 thf(fact_58_UNIV__I, axiom, (! [A:$tType,X5:A]: ((((member @ A) @ X5) @ (top_top @ (set @ A)))))).
% 2.59/1.47 thf(fact_59_iso__tuple__UNIV__I, axiom, (! [A:$tType,X5:A]: ((((member @ A) @ X5) @ (top_top @ (set @ A)))))).
% 2.59/1.47 thf(fact_60_top__apply, axiom, (! [C:$tType,D:$tType]: ((((top @ C) @ (type2 @ C)) => ((top_top @ (D > C)) = (^ [X:D]: ((top_top @ C)))))))).
% 2.59/1.47 thf(fact_61_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 2.59/1.47 thf(fact_62_UNIV__witness, axiom, (! [A:$tType]: ((? [X4:A]: ((((member @ A) @ X4) @ (top_top @ (set @ A)))))))).
% 2.59/1.47 thf(fact_63_UNIV__eq__I, axiom, (! [A:$tType,A5:(set @ A)]: (((! [X4:A]: ((((member @ A) @ X4) @ A5))) => ((top_top @ (set @ A)) = A5))))).
% 2.59/1.47 thf(fact_64_comp__eq__dest__lhs, axiom, (! [C:$tType,B:$tType,A:$tType,A4:(C > B),B2:(A > C),C2:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A4) @ B2) = C2) => ((A4 @ (B2 @ V)) = (C2 @ V)))))).
% 2.59/1.47 thf(fact_65_comp__eq__elim, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A4:(C > B),B2:(A > C),C2:(D > B),D2:(A > D)]: ((((((((comp @ C) @ B) @ A) @ A4) @ B2) = (((((comp @ D) @ B) @ A) @ C2) @ D2)) => (! [V2:A]: (((A4 @ (B2 @ V2)) = (C2 @ (D2 @ V2))))))))).
% 2.59/1.47 thf(fact_66_comp__eq__dest, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A4:(C > B),B2:(A > C),C2:(D > B),D2:(A > D),V:A]: ((((((((comp @ C) @ B) @ A) @ A4) @ B2) = (((((comp @ D) @ B) @ A) @ C2) @ D2)) => ((A4 @ (B2 @ V)) = (C2 @ (D2 @ V))))))).
% 2.59/1.47 thf(fact_67_comp__assoc, axiom, (! [B:$tType,D:$tType,C:$tType,A:$tType,F:(D > B),G:(C > D),H:(A > C)]: (((((((comp @ C) @ B) @ A) @ (((((comp @ D) @ B) @ C) @ F) @ G)) @ H) = (((((comp @ D) @ B) @ A) @ F) @ (((((comp @ C) @ D) @ A) @ G) @ H)))))).
% 2.59/1.47 thf(fact_68_comp__def, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((comp @ B) @ C) @ A) = (^ [F2:(B > C),G2:(A > B),X:A]: ((F2 @ (G2 @ X)))))))).
% 2.59/1.47 thf(fact_69_Inr__inject, axiom, (! [A:$tType,B:$tType,X5:B,Y:B]: ((((((sum_Inr @ B) @ A) @ X5) = (((sum_Inr @ B) @ A) @ Y)) => (X5 = Y))))).
% 2.59/1.47 thf(fact_70_dtree__cong, axiom, (! [Tr:dtree,Tr2:dtree]: ((((root @ Tr) = (root @ Tr2)) => (((cont @ Tr) = (cont @ Tr2)) => (Tr = Tr2)))))).
% 2.59/1.47 thf(fact_71_old_Osum_Osimps_I8_J, axiom, (! [A:$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))))).
% 2.59/1.47 thf(fact_72_root__H, axiom, (! [Tr0:dtree,N:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N) => ((root @ ((gram_L1451583624elle_H @ Tr0) @ N)) = N))))).
% 2.59/1.47 thf(fact_73_Node__root__cont, axiom, (! [Tr:dtree]: ((((node @ (root @ Tr)) @ (cont @ Tr)) = Tr)))).
% 2.59/1.47 thf(fact_74_wf__H, axiom, (! [Tr0:dtree,N:n]: (((gram_L864798063lle_wf @ Tr0) => ((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N) => (gram_L864798063lle_wf @ ((gram_L1451583624elle_H @ Tr0) @ N))))))).
% 2.59/1.47 thf(fact_75_subtr__H, axiom, (! [Tr0:dtree,N:n,Tr1:dtree]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N) => ((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ Tr1) @ ((gram_L1451583624elle_H @ Tr0) @ N)) => (? [N1:n]: (((((gram_L830233218_inItr @ (top_top @ (set @ n))) @ Tr0) @ N1) & (Tr1 = ((gram_L1451583624elle_H @ Tr0) @ N1)))))))))).
% 2.59/1.47 thf(fact_76_inFr2__Ind, axiom, (! [Ns:(set @ n),Tr1:dtree,T2:t,Tr:dtree]: (((((gram_L805317441_inFr2 @ Ns) @ Tr1) @ T2) => ((((member @ n) @ (root @ Tr)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => (((gram_L805317441_inFr2 @ Ns) @ Tr) @ T2))))))).
% 2.59/1.47 thf(fact_77_reg__def, axiom, (gram_L1918716148le_reg = (^ [F2:(n > dtree),Tr4:dtree]: ((! [Tr7:dtree]: (((((gram_L716654942_subtr @ (top_top @ (set @ n))) @ Tr7) @ Tr4) => (Tr7 = (F2 @ (root @ Tr7)))))))))).
% 2.59/1.47 thf(fact_78_top1I, axiom, (! [A:$tType,X5:A]: (((top_top @ (A > $o)) @ X5)))).
% 2.59/1.47 thf(fact_79_root__Node, axiom, (! [N:n,As:(set @ ((sum_sum @ t) @ dtree))]: (((root @ ((node @ N) @ As)) = N)))).
% 2.59/1.47 thf(fact_80_rcut__eq, axiom, (! [Tr0:dtree]: ((((gram_L1828378864e_rcut @ Tr0) = Tr0) = ((gram_L1918716148le_reg @ (gram_L1451583624elle_H @ Tr0)) @ Tr0))))).
% 2.59/1.47 thf(fact_81_rcut__reg, axiom, (! [Tr0:dtree]: ((((gram_L1918716148le_reg @ (gram_L1451583624elle_H @ Tr0)) @ Tr0) => ((gram_L1828378864e_rcut @ Tr0) = Tr0))))).
% 2.59/1.47 thf(fact_82_reg__rcut, axiom, (! [Tr0:dtree]: (((gram_L1918716148le_reg @ (gram_L1451583624elle_H @ Tr0)) @ (gram_L1828378864e_rcut @ Tr0))))).
% 2.59/1.47 thf(fact_83_reg__root, axiom, (! [F:(n > dtree),Tr:dtree]: ((((gram_L1918716148le_reg @ F) @ Tr) => ((F @ (root @ Tr)) = Tr))))).
% 2.59/1.47 thf(fact_84_reg__subtr, axiom, (! [F:(n > dtree),Tr:dtree,Ns:(set @ n),Tr2:dtree]: ((((gram_L1918716148le_reg @ F) @ Tr) => ((((gram_L716654942_subtr @ Ns) @ Tr2) @ Tr) => ((gram_L1918716148le_reg @ F) @ Tr2)))))).
% 2.59/1.47 thf(fact_85_inFr2__root__in, axiom, (! [Ns:(set @ n),Tr:dtree,T2:t]: (((((gram_L805317441_inFr2 @ Ns) @ Tr) @ T2) => (((member @ n) @ (root @ Tr)) @ Ns))))).
% 2.59/1.47 thf(fact_86_inFr__inFr2, axiom, (gram_L1333338417e_inFr = gram_L805317441_inFr2)).
% 2.59/1.47 thf(fact_87_reg__deftr, axiom, (! [N:n]: (((gram_L1918716148le_reg @ gram_L1231612515_deftr) @ (gram_L1231612515_deftr @ N))))).
% 2.59/1.47 thf(fact_88_reg__Inr__cont, axiom, (! [F:(n > dtree),Tr:dtree,Tr2:dtree]: ((((gram_L1918716148le_reg @ F) @ Tr) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr2)) @ (cont @ Tr)) => ((gram_L1918716148le_reg @ F) @ Tr2)))))).
% 2.59/1.47 thf(fact_89_reg__def2, axiom, (gram_L1918716148le_reg = (^ [F2:(n > dtree),Tr4:dtree]: ((! [Ns2:(set @ n),Tr7:dtree]: (((((gram_L716654942_subtr @ Ns2) @ Tr7) @ Tr4) => (Tr7 = (F2 @ (root @ Tr7)))))))))).
% 2.59/1.47 thf(fact_90_root__H__pick, axiom, (! [Tr0:dtree,N:n]: (((root @ ((gram_L1451583624elle_H @ Tr0) @ N)) = (root @ ((gram_L315592705e_pick @ Tr0) @ N)))))).
% 2.59/1.47 thf(fact_91_rcut__def, axiom, (gram_L1828378864e_rcut = (^ [Tr02:dtree]: (((gram_L1451583624elle_H @ Tr02) @ (root @ Tr02)))))).
% 2.59/1.47 thf(fact_92_H__def, axiom, (gram_L1451583624elle_H = (^ [Tr02:dtree]: ((((unfold @ n) @ (gram_L1221482026le_H_r @ Tr02)) @ (gram_L1221482011le_H_c @ Tr02)))))).
% 2.59/1.47 thf(fact_93_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A))))))))).
% 2.59/1.47 thf(fact_94_regular__def2, axiom, (gram_L646766332egular = (^ [Tr4:dtree]: ((? [F2:(n > dtree)]: ((((gram_L1918716148le_reg @ F2) @ Tr4) & (! [N2:n]: (((root @ (F2 @ N2)) = N2)))))))))).
% 2.59/1.47 thf(fact_95_top__conj_I2_J, axiom, (! [A:$tType,P:$o,X5:A]: (((P & ((top_top @ (A > $o)) @ X5)) = P)))).
% 2.59/1.47 thf(fact_96_top__conj_I1_J, axiom, (! [A:$tType,X5:A,P:$o]: (((((top_top @ (A > $o)) @ X5) & P) = P)))).
% 2.59/1.47 thf(fact_97_inFr2_OInd, axiom, (! [Tr1:dtree,Tr:dtree,Ns1:(set @ n),T2:t]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr)) => ((((gram_L805317441_inFr2 @ Ns1) @ Tr1) @ T2) => (((gram_L805317441_inFr2 @ (((insert @ n) @ (root @ Tr)) @ Ns1)) @ Tr) @ T2)))))).
% 2.59/1.47 thf(fact_98_insertCI, axiom, (! [A:$tType,A4:A,B4:(set @ A),B2:A]: ((((~ ((((member @ A) @ A4) @ B4))) => (A4 = B2)) => (((member @ A) @ A4) @ (((insert @ A) @ B2) @ B4)))))).
% 2.59/1.47 thf(fact_99_insert__iff, axiom, (! [A:$tType,A4:A,B2:A,A5:(set @ A)]: (((((member @ A) @ A4) @ (((insert @ A) @ B2) @ A5)) = ((A4 = B2) | (((member @ A) @ A4) @ A5)))))).
% 2.59/1.47 thf(fact_100_insert__absorb2, axiom, (! [A:$tType,X5:A,A5:(set @ A)]: (((((insert @ A) @ X5) @ (((insert @ A) @ X5) @ A5)) = (((insert @ A) @ X5) @ A5))))).
% 2.59/1.47 thf(fact_101_insertE, axiom, (! [A:$tType,A4:A,B2:A,A5:(set @ A)]: (((((member @ A) @ A4) @ (((insert @ A) @ B2) @ A5)) => ((A4 != B2) => (((member @ A) @ A4) @ A5)))))).
% 2.59/1.47 thf(fact_102_insertI1, axiom, (! [A:$tType,A4:A,B4:(set @ A)]: ((((member @ A) @ A4) @ (((insert @ A) @ A4) @ B4))))).
% 2.59/1.47 thf(fact_103_insertI2, axiom, (! [A:$tType,A4:A,B4:(set @ A),B2:A]: (((((member @ A) @ A4) @ B4) => (((member @ A) @ A4) @ (((insert @ A) @ B2) @ B4)))))).
% 2.59/1.47 thf(fact_104_Set_Oset__insert, axiom, (! [A:$tType,X5:A,A5:(set @ A)]: (((((member @ A) @ X5) @ A5) => (~ ((! [B5:(set @ A)]: (((A5 = (((insert @ A) @ X5) @ B5)) => (((member @ A) @ X5) @ B5)))))))))).
% 2.59/1.47 thf(fact_105_insert__ident, axiom, (! [A:$tType,X5:A,A5:(set @ A),B4:(set @ A)]: (((~ ((((member @ A) @ X5) @ A5))) => ((~ ((((member @ A) @ X5) @ B4))) => (((((insert @ A) @ X5) @ A5) = (((insert @ A) @ X5) @ B4)) = (A5 = B4))))))).
% 2.59/1.47 thf(fact_106_insert__absorb, axiom, (! [A:$tType,A4:A,A5:(set @ A)]: (((((member @ A) @ A4) @ A5) => ((((insert @ A) @ A4) @ A5) = A5))))).
% 2.59/1.47 thf(fact_107_insert__eq__iff, axiom, (! [A:$tType,A4:A,A5:(set @ A),B2:A,B4:(set @ A)]: (((~ ((((member @ A) @ A4) @ A5))) => ((~ ((((member @ A) @ B2) @ B4))) => (((((insert @ A) @ A4) @ A5) = (((insert @ A) @ B2) @ B4)) = (((A4 = B2) => (A5 = B4)) & ((A4 != B2) => (? [C3:(set @ A)]: (((A5 = (((insert @ A) @ B2) @ C3)) & ((~ ((((member @ A) @ B2) @ C3))) & ((B4 = (((insert @ A) @ A4) @ C3)) & (~ ((((member @ A) @ A4) @ C3)))))))))))))))).
% 2.59/1.47 thf(fact_108_insert__commute, axiom, (! [A:$tType,X5:A,Y:A,A5:(set @ A)]: (((((insert @ A) @ X5) @ (((insert @ A) @ Y) @ A5)) = (((insert @ A) @ Y) @ (((insert @ A) @ X5) @ A5)))))).
% 2.59/1.47 thf(fact_109_mk__disjoint__insert, axiom, (! [A:$tType,A4:A,A5:(set @ A)]: (((((member @ A) @ A4) @ A5) => (? [B5:(set @ A)]: (((A5 = (((insert @ A) @ A4) @ B5)) & (~ ((((member @ A) @ A4) @ B5)))))))))).
% 2.59/1.47 thf(fact_110_insert__UNIV, axiom, (! [A:$tType,X5:A]: (((((insert @ A) @ X5) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))).
% 2.59/1.47 thf(fact_111_regular__subtr, axiom, (! [Tr:dtree,Ns:(set @ n),Tr2:dtree]: (((gram_L646766332egular @ Tr) => ((((gram_L716654942_subtr @ Ns) @ Tr2) @ Tr) => (gram_L646766332egular @ Tr2)))))).
% 2.59/1.47 thf(fact_112_regular__def, axiom, (gram_L646766332egular = (^ [Tr4:dtree]: ((? [F2:(n > dtree)]: (((gram_L1918716148le_reg @ F2) @ Tr4))))))).
% 2.59/1.47 thf(fact_113_regular__rcut, axiom, (! [Tr0:dtree]: ((gram_L646766332egular @ (gram_L1828378864e_rcut @ Tr0))))).
% 2.59/1.47 thf(fact_114_rewriteR__comp__comp2, axiom, (! [C:$tType,B:$tType,E:$tType,D:$tType,A:$tType,G:(C > B),H:(A > C),R1:(D > B),R2:(A > D),F:(B > E),L:(D > E)]: ((((((((comp @ C) @ B) @ A) @ G) @ H) = (((((comp @ D) @ B) @ A) @ R1) @ R2)) => (((((((comp @ B) @ E) @ D) @ F) @ R1) = L) => ((((((comp @ C) @ E) @ A) @ (((((comp @ B) @ E) @ C) @ F) @ G)) @ H) = (((((comp @ D) @ E) @ A) @ L) @ R2))))))).
% 2.59/1.47 thf(fact_115_rewriteL__comp__comp2, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,E:$tType,F:(C > B),G:(A > C),L1:(D > B),L2:(A > D),H:(E > A),R:(E > D)]: ((((((((comp @ C) @ B) @ A) @ F) @ G) = (((((comp @ D) @ B) @ A) @ L1) @ L2)) => (((((((comp @ A) @ D) @ E) @ L2) @ H) = R) => ((((((comp @ C) @ B) @ E) @ F) @ (((((comp @ A) @ C) @ E) @ G) @ H)) = (((((comp @ D) @ B) @ E) @ L1) @ R))))))).
% 2.59/1.47 thf(fact_116_rewriteR__comp__comp, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,G:(C > B),H:(A > C),R:(A > B),F:(B > D)]: ((((((((comp @ C) @ B) @ A) @ G) @ H) = R) => ((((((comp @ C) @ D) @ A) @ (((((comp @ B) @ D) @ C) @ F) @ G)) @ H) = (((((comp @ B) @ D) @ A) @ F) @ R)))))).
% 2.59/1.47 thf(fact_117_rewriteL__comp__comp, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,F:(C > B),G:(A > C),L:(A > B),H:(D > A)]: ((((((((comp @ C) @ B) @ A) @ F) @ G) = L) => ((((((comp @ C) @ B) @ D) @ F) @ (((((comp @ A) @ C) @ D) @ G) @ H)) = (((((comp @ A) @ B) @ D) @ L) @ H)))))).
% 2.59/1.47 thf(fact_118_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)))))).
% 2.59/1.47 thf(fact_119_inFr2_Oinducts, axiom, (! [X1:(set @ n),X2:dtree,X3:t,P:((set @ n) > (dtree > (t > $o)))]: (((((gram_L805317441_inFr2 @ X1) @ X2) @ X3) => ((! [Tr6:dtree,Ns3:(set @ n),T4:t]: (((((member @ n) @ (root @ Tr6)) @ Ns3) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T4)) @ (cont @ Tr6)) => (((P @ Ns3) @ Tr6) @ T4))))) => ((! [Tr12:dtree,Tr6:dtree,Ns12:(set @ n),T4:t]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr6)) => ((((gram_L805317441_inFr2 @ Ns12) @ Tr12) @ T4) => ((((P @ Ns12) @ Tr12) @ T4) => (((P @ (((insert @ n) @ (root @ Tr6)) @ Ns12)) @ Tr6) @ T4)))))) => (((P @ X1) @ X2) @ X3))))))).
% 2.59/1.47 thf(fact_120_inFr2_Osimps, axiom, (gram_L805317441_inFr2 = (^ [A12:(set @ n),A22:dtree,A32:t]: (((? [Tr4:dtree,Ns2:(set @ n),T3:t]: (((A12 = Ns2) & ((A22 = Tr4) & ((A32 = T3) & ((((member @ n) @ (root @ Tr4)) @ Ns2) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T3)) @ (cont @ Tr4)))))))) | (? [Tr13:dtree,Tr4:dtree,Ns13:(set @ n),T3:t]: (((A12 = (((insert @ n) @ (root @ Tr4)) @ Ns13)) & ((A22 = Tr4) & ((A32 = T3) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr4)) & (((gram_L805317441_inFr2 @ Ns13) @ Tr13) @ T3)))))))))))).
% 2.59/1.47 thf(fact_121_inFr2_Ocases, axiom, (! [A1:(set @ n),A2:dtree,A3:t]: (((((gram_L805317441_inFr2 @ A1) @ A2) @ A3) => (((((member @ n) @ (root @ A2)) @ A1) => (~ ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ A3)) @ (cont @ A2))))) => (~ ((! [Tr12:dtree,Tr6:dtree,Ns12:(set @ n)]: (((A1 = (((insert @ n) @ (root @ Tr6)) @ Ns12)) => ((A2 = Tr6) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr6)) => (~ ((((gram_L805317441_inFr2 @ Ns12) @ Tr12) @ A3))))))))))))))).
% 2.59/1.47 thf(fact_122_subtr2_Oinducts, axiom, (! [X1:(set @ n),X2:dtree,X3:dtree,P:((set @ n) > (dtree > (dtree > $o)))]: (((((gram_L1283001940subtr2 @ X1) @ X2) @ X3) => ((! [Tr6:dtree,Ns3:(set @ n)]: (((((member @ n) @ (root @ Tr6)) @ Ns3) => (((P @ Ns3) @ Tr6) @ Tr6)))) => ((! [Tr12:dtree,Ns3:(set @ n),Tr23:dtree,Tr33:dtree]: (((((member @ n) @ (root @ Tr12)) @ Ns3) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr23)) => ((((gram_L1283001940subtr2 @ Ns3) @ Tr23) @ Tr33) => ((((P @ Ns3) @ Tr23) @ Tr33) => (((P @ Ns3) @ Tr12) @ Tr33))))))) => (((P @ X1) @ X2) @ X3))))))).
% 2.59/1.47 thf(fact_123_subtr2__StepR, axiom, (! [Tr3:dtree,Ns:(set @ n),Tr22:dtree,Tr1:dtree]: (((((member @ n) @ (root @ Tr3)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr22)) @ (cont @ Tr3)) => ((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => (((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr3))))))).
% 2.59/1.47 thf(fact_124_old_Osum_Oinject_I1_J, axiom, (! [B:$tType,A:$tType,A4:A,A6:A]: ((((((sum_Inl @ A) @ B) @ A4) = (((sum_Inl @ A) @ B) @ A6)) = (A4 = A6))))).
% 2.59/1.47 thf(fact_125_sum_Oinject_I1_J, axiom, (! [B:$tType,A:$tType,X1:A,Y1:A]: ((((((sum_Inl @ A) @ B) @ X1) = (((sum_Inl @ A) @ B) @ Y1)) = (X1 = Y1))))).
% 2.59/1.47 thf(fact_126_Inr__Inl__False, axiom, (! [B:$tType,A:$tType,X5:B,Y:A]: (((((sum_Inr @ B) @ A) @ X5) != (((sum_Inl @ A) @ B) @ Y))))).
% 2.59/1.47 thf(fact_127_Inl__Inr__False, axiom, (! [A:$tType,B:$tType,X5:A,Y:B]: (((((sum_Inl @ A) @ B) @ X5) != (((sum_Inr @ B) @ A) @ Y))))).
% 2.59/1.47 thf(fact_128_old_Osum_Osimps_I7_J, axiom, (! [B:$tType,T:$tType,A:$tType,F1:(A > T),F22:(B > T),A4:A]: ((((((((sum_rec_sum @ A) @ T) @ B) @ F1) @ F22) @ (((sum_Inl @ A) @ B) @ A4)) = (F1 @ A4))))).
% 2.59/1.47 thf(fact_129_obj__sumE__f, axiom, (! [A:$tType,C:$tType,B:$tType,S:B,F:(((sum_sum @ A) @ C) > B),P:$o]: (((! [X4:A]: (((S = (F @ (((sum_Inl @ A) @ C) @ X4))) => P))) => ((! [X4:C]: (((S = (F @ (((sum_Inr @ C) @ A) @ X4))) => P))) => (! [X6:((sum_sum @ A) @ C)]: (((S = (F @ X6)) => P)))))))).
% 2.59/1.47 thf(fact_130_old_Osum_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((sum_sum @ A) @ B) > $o),Sum:((sum_sum @ A) @ B)]: (((! [A7:A]: ((P @ (((sum_Inl @ A) @ B) @ A7)))) => ((! [B6:B]: ((P @ (((sum_Inr @ B) @ A) @ B6)))) => (P @ Sum)))))).
% 2.59/1.47 thf(fact_131_old_Osum_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((sum_sum @ A) @ B)]: (((! [A7:A]: ((Y != (((sum_Inl @ A) @ B) @ A7)))) => (~ ((! [B6:B]: ((Y != (((sum_Inr @ B) @ A) @ B6)))))))))).
% 2.59/1.47 thf(fact_132_split__sum__all, axiom, (! [B:$tType,A:$tType]: (((^ [P2:(((sum_sum @ A) @ B) > $o)]: ((! [X7:((sum_sum @ A) @ B)]: ((P2 @ X7))))) = (^ [P3:(((sum_sum @ A) @ B) > $o)]: (((! [X:A]: ((P3 @ (((sum_Inl @ A) @ B) @ X)))) & (! [X:B]: ((P3 @ (((sum_Inr @ B) @ A) @ X))))))))))).
% 2.59/1.47 thf(fact_133_split__sum__ex, axiom, (! [B:$tType,A:$tType]: (((^ [P2:(((sum_sum @ A) @ B) > $o)]: ((? [X7:((sum_sum @ A) @ B)]: ((P2 @ X7))))) = (^ [P3:(((sum_sum @ A) @ B) > $o)]: (((? [X:A]: ((P3 @ (((sum_Inl @ A) @ B) @ X)))) | (? [X:B]: ((P3 @ (((sum_Inr @ B) @ A) @ X))))))))))).
% 2.59/1.47 thf(fact_134_Inr__not__Inl, axiom, (! [B:$tType,A:$tType,B2:B,A4:A]: (((((sum_Inr @ B) @ A) @ B2) != (((sum_Inl @ A) @ B) @ A4))))).
% 2.59/1.47 thf(fact_135_sumE, axiom, (! [A:$tType,B:$tType,S:((sum_sum @ A) @ B)]: (((! [X4:A]: ((S != (((sum_Inl @ A) @ B) @ X4)))) => (~ ((! [Y3:B]: ((S != (((sum_Inr @ B) @ A) @ Y3)))))))))).
% 2.59/1.47 thf(fact_136_old_Osum_Odistinct_I1_J, axiom, (! [A:$tType,B:$tType,A4:A,B3:B]: (((((sum_Inl @ A) @ B) @ A4) != (((sum_Inr @ B) @ A) @ B3))))).
% 2.59/1.47 thf(fact_137_old_Osum_Odistinct_I2_J, axiom, (! [B7:$tType,A8:$tType,B8:B7,A9:A8]: (((((sum_Inr @ B7) @ A8) @ B8) != (((sum_Inl @ A8) @ B7) @ A9))))).
% 2.59/1.47 thf(fact_138_sum_Odistinct_I1_J, axiom, (! [A:$tType,B:$tType,X1:A,X2:B]: (((((sum_Inl @ A) @ B) @ X1) != (((sum_Inr @ B) @ A) @ X2))))).
% 2.59/1.47 thf(fact_139_Inl__inject, axiom, (! [B:$tType,A:$tType,X5:A,Y:A]: ((((((sum_Inl @ A) @ B) @ X5) = (((sum_Inl @ A) @ B) @ Y)) => (X5 = Y))))).
% 2.59/1.47 thf(fact_140_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)))))).
% 2.59/1.47 thf(fact_141_subtr2_ORefl, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr)) @ Ns) => (((gram_L1283001940subtr2 @ Ns) @ Tr) @ Tr))))).
% 2.59/1.47 thf(fact_142_subtr2__rootL__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr1)) @ Ns))))).
% 2.59/1.47 thf(fact_143_subtr2__rootR__in, axiom, (! [Ns:(set @ n),Tr1:dtree,Tr22:dtree]: (((((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr22) => (((member @ n) @ (root @ Tr22)) @ Ns))))).
% 2.59/1.47 thf(fact_144_subtr__subtr2, axiom, (gram_L716654942_subtr = gram_L1283001940subtr2)).
% 2.59/1.47 thf(fact_145_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)))))).
% 2.59/1.47 thf(fact_146_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))))))))).
% 2.59/1.47 thf(fact_147_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)))))).
% 2.59/1.47 thf(fact_148_inFr_Ocases, axiom, (! [A1:(set @ n),A2:dtree,A3:t]: (((((gram_L1333338417e_inFr @ A1) @ A2) @ A3) => (((((member @ n) @ (root @ A2)) @ A1) => (~ ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ A3)) @ (cont @ A2))))) => (~ (((((member @ n) @ (root @ A2)) @ A1) => (! [Tr12:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ A2)) => (~ ((((gram_L1333338417e_inFr @ A1) @ Tr12) @ A3)))))))))))))).
% 2.59/1.47 thf(fact_149_inFr_Osimps, axiom, (gram_L1333338417e_inFr = (^ [A12:(set @ n),A22:dtree,A32:t]: (((? [Tr4:dtree,Ns2:(set @ n),T3:t]: (((A12 = Ns2) & ((A22 = Tr4) & ((A32 = T3) & ((((member @ n) @ (root @ Tr4)) @ Ns2) & (((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T3)) @ (cont @ Tr4)))))))) | (? [Tr4:dtree,Ns2:(set @ n),Tr13:dtree,T3:t]: (((A12 = Ns2) & ((A22 = Tr4) & ((A32 = T3) & ((((member @ n) @ (root @ Tr4)) @ Ns2) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr4)) & (((gram_L1333338417e_inFr @ Ns2) @ Tr13) @ T3))))))))))))).
% 2.59/1.47 thf(fact_150_inFr_Oinducts, axiom, (! [X1:(set @ n),X2:dtree,X3:t,P:((set @ n) > (dtree > (t > $o)))]: (((((gram_L1333338417e_inFr @ X1) @ X2) @ X3) => ((! [Tr6:dtree,Ns3:(set @ n),T4:t]: (((((member @ n) @ (root @ Tr6)) @ Ns3) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inl @ t) @ dtree) @ T4)) @ (cont @ Tr6)) => (((P @ Ns3) @ Tr6) @ T4))))) => ((! [Tr6:dtree,Ns3:(set @ n),Tr12:dtree,T4:t]: (((((member @ n) @ (root @ Tr6)) @ Ns3) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr12)) @ (cont @ Tr6)) => ((((gram_L1333338417e_inFr @ Ns3) @ Tr12) @ T4) => ((((P @ Ns3) @ Tr12) @ T4) => (((P @ Ns3) @ Tr6) @ T4))))))) => (((P @ X1) @ X2) @ X3))))))).
% 2.59/1.47 thf(fact_151_subtr2_OStep, axiom, (! [Tr1:dtree,Ns:(set @ n),Tr22:dtree,Tr3:dtree]: (((((member @ n) @ (root @ Tr1)) @ Ns) => ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr1)) @ (cont @ Tr22)) => ((((gram_L1283001940subtr2 @ Ns) @ Tr22) @ Tr3) => (((gram_L1283001940subtr2 @ Ns) @ Tr1) @ Tr3))))))).
% 2.59/1.47 thf(fact_152_subtr2_Ocases, axiom, (! [A1:(set @ n),A2:dtree,A3:dtree]: (((((gram_L1283001940subtr2 @ A1) @ A2) @ A3) => (((A3 = A2) => (~ ((((member @ n) @ (root @ A2)) @ A1)))) => (~ (((((member @ n) @ (root @ A2)) @ A1) => (! [Tr23:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ A2)) @ (cont @ Tr23)) => (~ ((((gram_L1283001940subtr2 @ A1) @ Tr23) @ A3)))))))))))))).
% 2.59/1.47 thf(fact_153_subtr2_Osimps, axiom, (gram_L1283001940subtr2 = (^ [A12:(set @ n),A22:dtree,A32:dtree]: (((? [Tr4:dtree,Ns2:(set @ n)]: (((A12 = Ns2) & ((A22 = Tr4) & ((A32 = Tr4) & (((member @ n) @ (root @ Tr4)) @ Ns2)))))) | (? [Tr13:dtree,Ns2:(set @ n),Tr24:dtree,Tr32:dtree]: (((A12 = Ns2) & ((A22 = Tr13) & ((A32 = Tr32) & ((((member @ n) @ (root @ Tr13)) @ Ns2) & ((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr13)) @ (cont @ Tr24)) & (((gram_L1283001940subtr2 @ Ns2) @ Tr24) @ Tr32))))))))))))).
% 2.59/1.47 thf(fact_154_obj__sumE, axiom, (! [A:$tType,B:$tType,S:((sum_sum @ A) @ B)]: (((! [X4:A]: ((S != (((sum_Inl @ A) @ B) @ X4)))) => (~ ((! [X4:B]: ((S != (((sum_Inr @ B) @ A) @ X4)))))))))).
% 2.59/1.47 thf(fact_155_Inl__cont__H, axiom, (! [Tr0:dtree,N:n]: ((((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ ((gram_L1451583624elle_H @ Tr0) @ N))) = ((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ ((gram_L315592705e_pick @ Tr0) @ N))))))).
% 2.59/1.47 thf(fact_156_Inl__cont__hsubst__eq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) = (root @ Tr0)) => (((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ ((gram_L1004374585hsubst @ Tr0) @ Tr))) = ((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ Tr0))))))).
% 2.59/1.47 thf(fact_157_Inl__cont__hsubst__neq, axiom, (! [Tr:dtree,Tr0:dtree]: ((((root @ Tr) != (root @ Tr0)) => (((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ ((gram_L1004374585hsubst @ Tr0) @ Tr))) = ((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ Tr))))))).
% 2.59/1.47 thf(fact_158_vimageI, axiom, (! [B:$tType,A:$tType,F:(B > A),A4:B,B2:A,B4:(set @ A)]: ((((F @ A4) = B2) => ((((member @ A) @ B2) @ B4) => (((member @ B) @ A4) @ ((((vimage @ B) @ A) @ F) @ B4))))))).
% 2.59/1.47 thf(fact_159_vimage__eq, axiom, (! [A:$tType,B:$tType,A4:A,F:(A > B),B4:(set @ B)]: (((((member @ A) @ A4) @ ((((vimage @ A) @ B) @ F) @ B4)) = (((member @ B) @ (F @ A4)) @ B4))))).
% 2.59/1.47 thf(fact_160_vimage__UNIV, axiom, (! [B:$tType,A:$tType,F:(A > B)]: ((((((vimage @ A) @ B) @ F) @ (top_top @ (set @ B))) = (top_top @ (set @ A)))))).
% 2.59/1.47 thf(fact_161_vimageD, axiom, (! [A:$tType,B:$tType,A4:A,F:(A > B),A5:(set @ B)]: (((((member @ A) @ A4) @ ((((vimage @ A) @ B) @ F) @ A5)) => (((member @ B) @ (F @ A4)) @ A5))))).
% 2.59/1.47 thf(fact_162_vimageE, axiom, (! [A:$tType,B:$tType,A4:A,F:(A > B),B4:(set @ B)]: (((((member @ A) @ A4) @ ((((vimage @ A) @ B) @ F) @ B4)) => (((member @ B) @ (F @ A4)) @ B4))))).
% 2.59/1.47 thf(fact_163_vimageI2, axiom, (! [B:$tType,A:$tType,F:(B > A),A4:B,A5:(set @ A)]: (((((member @ A) @ (F @ A4)) @ A5) => (((member @ B) @ A4) @ ((((vimage @ B) @ A) @ F) @ A5)))))).
% 2.59/1.47 thf(fact_164_vimage__Collect, axiom, (! [B:$tType,A:$tType,P:(B > $o),F:(A > B),Q:(A > $o)]: (((! [X4:A]: (((P @ (F @ X4)) = (Q @ X4)))) => (((((vimage @ A) @ B) @ F) @ ((collect @ B) @ P)) = ((collect @ A) @ Q)))))).
% 2.59/1.47 thf(fact_165_set_Ocomp, axiom, (! [A:$tType,B:$tType,C:$tType,F:(C > B),G:(B > A)]: (((((((comp @ (set @ B)) @ (set @ C)) @ (set @ A)) @ (((vimage @ C) @ B) @ F)) @ (((vimage @ B) @ A) @ G)) = (((vimage @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)))))).
% 2.59/1.47 thf(fact_166_vimage__comp, axiom, (! [A:$tType,B:$tType,C:$tType,F:(A > B),G:(B > C),X5:(set @ C)]: ((((((vimage @ A) @ B) @ F) @ ((((vimage @ B) @ C) @ G) @ X5)) = ((((vimage @ A) @ C) @ (((((comp @ B) @ C) @ A) @ G) @ F)) @ X5))))).
% 2.59/1.47 thf(fact_167_set_Ocompositionality, axiom, (! [C:$tType,B:$tType,A:$tType,F:(C > B),G:(B > A),Set:(set @ A)]: ((((((vimage @ C) @ B) @ F) @ ((((vimage @ B) @ A) @ G) @ Set)) = ((((vimage @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)) @ Set))))).
% 2.59/1.47 thf(fact_168_not__arg__cong__Inr, axiom, (! [B:$tType,A:$tType,X5:A,Y:A]: (((X5 != Y) => ((((sum_Inr @ A) @ B) @ X5) != (((sum_Inr @ A) @ B) @ Y)))))).
% 2.59/1.47 thf(fact_169_Inl__Inr__image__cong, axiom, (! [B:$tType,A:$tType,A5:(set @ ((sum_sum @ A) @ B)),B4:(set @ ((sum_sum @ A) @ B))]: (((((((vimage @ A) @ ((sum_sum @ A) @ B)) @ ((sum_Inl @ A) @ B)) @ A5) = ((((vimage @ A) @ ((sum_sum @ A) @ B)) @ ((sum_Inl @ A) @ B)) @ B4)) => ((((((vimage @ B) @ ((sum_sum @ A) @ B)) @ ((sum_Inr @ B) @ A)) @ A5) = ((((vimage @ B) @ ((sum_sum @ A) @ B)) @ ((sum_Inr @ B) @ A)) @ B4)) => (A5 = B4)))))).
% 2.59/1.47 thf(fact_170_inFr__self__hsubst, axiom, (! [Tr0:dtree,Ns:(set @ n),T2:t]: (((((member @ n) @ (root @ Tr0)) @ Ns) => ((((gram_L1333338417e_inFr @ Ns) @ ((gram_L1004374585hsubst @ Tr0) @ Tr0)) @ 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))))))).
% 2.59/1.47 thf(fact_171_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))))))).
% 2.59/1.47 thf(fact_172_bot__apply, axiom, (! [C:$tType,D:$tType]: ((((bot @ C) @ (type2 @ C)) => ((bot_bot @ (D > C)) = (^ [X:D]: ((bot_bot @ C)))))))).
% 2.59/1.47 thf(fact_173_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X:A]: ((~ ((P @ X))))))))).
% 2.59/1.47 thf(fact_174_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X:A]: ((~ ((P @ X))))))))).
% 2.59/1.47 thf(fact_175_all__not__in__conv, axiom, (! [A:$tType,A5:(set @ A)]: (((! [X:A]: ((~ ((((member @ A) @ X) @ A5))))) = (A5 = (bot_bot @ (set @ A))))))).
% 2.59/1.47 thf(fact_176_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 2.59/1.47 thf(fact_177_Diff__idemp, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A5) @ B4)) @ B4) = (((minus_minus @ (set @ A)) @ A5) @ B4))))).
% 2.59/1.47 thf(fact_178_Diff__iff, axiom, (! [A:$tType,C2:A,A5:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A5) @ B4)) = ((((member @ A) @ C2) @ A5) & (~ ((((member @ A) @ C2) @ B4)))))))).
% 2.59/1.47 thf(fact_179_DiffI, axiom, (! [A:$tType,C2:A,A5:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ A5) => ((~ ((((member @ A) @ C2) @ B4))) => (((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A5) @ B4))))))).
% 2.59/1.47 thf(fact_180_singletonI, axiom, (! [A:$tType,A4:A]: ((((member @ A) @ A4) @ (((insert @ A) @ A4) @ (bot_bot @ (set @ A))))))).
% 2.59/1.47 thf(fact_181_Diff__cancel, axiom, (! [A:$tType,A5:(set @ A)]: (((((minus_minus @ (set @ A)) @ A5) @ A5) = (bot_bot @ (set @ A)))))).
% 2.59/1.47 thf(fact_182_empty__Diff, axiom, (! [A:$tType,A5:(set @ A)]: (((((minus_minus @ (set @ A)) @ (bot_bot @ (set @ A))) @ A5) = (bot_bot @ (set @ A)))))).
% 2.59/1.47 thf(fact_183_Diff__empty, axiom, (! [A:$tType,A5:(set @ A)]: (((((minus_minus @ (set @ A)) @ A5) @ (bot_bot @ (set @ A))) = A5)))).
% 2.59/1.47 thf(fact_184_Diff__insert0, axiom, (! [A:$tType,X5:A,A5:(set @ A),B4:(set @ A)]: (((~ ((((member @ A) @ X5) @ A5))) => ((((minus_minus @ (set @ A)) @ A5) @ (((insert @ A) @ X5) @ B4)) = (((minus_minus @ (set @ A)) @ A5) @ B4)))))).
% 2.59/1.47 thf(fact_185_insert__Diff1, axiom, (! [A:$tType,X5:A,B4:(set @ A),A5:(set @ A)]: (((((member @ A) @ X5) @ B4) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X5) @ A5)) @ B4) = (((minus_minus @ (set @ A)) @ A5) @ B4)))))).
% 2.59/1.47 thf(fact_186_vimage__empty, axiom, (! [B:$tType,A:$tType,F:(A > B)]: ((((((vimage @ A) @ B) @ F) @ (bot_bot @ (set @ B))) = (bot_bot @ (set @ A)))))).
% 2.59/1.47 thf(fact_187_insert__Diff__single, axiom, (! [A:$tType,A4:A,A5:(set @ A)]: (((((insert @ A) @ A4) @ (((minus_minus @ (set @ A)) @ A5) @ (((insert @ A) @ A4) @ (bot_bot @ (set @ A))))) = (((insert @ A) @ A4) @ A5))))).
% 2.59/1.47 thf(fact_188_Diff__UNIV, axiom, (! [A:$tType,A5:(set @ A)]: (((((minus_minus @ (set @ A)) @ A5) @ (top_top @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 2.59/1.47 thf(fact_189_vimage__Diff, axiom, (! [A:$tType,B:$tType,F:(A > B),A5:(set @ B),B4:(set @ B)]: ((((((vimage @ A) @ B) @ F) @ (((minus_minus @ (set @ B)) @ A5) @ B4)) = (((minus_minus @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ A5)) @ ((((vimage @ A) @ B) @ F) @ B4)))))).
% 2.59/1.47 thf(fact_190_bot__fun__def, axiom, (! [B:$tType,A:$tType]: ((((bot @ B) @ (type2 @ B)) => ((bot_bot @ (A > B)) = (^ [X:A]: ((bot_bot @ B)))))))).
% 2.59/1.47 thf(fact_191_ex__in__conv, axiom, (! [A:$tType,A5:(set @ A)]: (((? [X:A]: ((((member @ A) @ X) @ A5))) = (A5 != (bot_bot @ (set @ A))))))).
% 2.59/1.47 thf(fact_192_equals0I, axiom, (! [A:$tType,A5:(set @ A)]: (((! [Y3:A]: ((~ ((((member @ A) @ Y3) @ A5))))) => (A5 = (bot_bot @ (set @ A))))))).
% 2.59/1.47 thf(fact_193_equals0D, axiom, (! [A:$tType,A5:(set @ A),A4:A]: (((A5 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A4) @ A5))))))).
% 2.59/1.47 thf(fact_194_emptyE, axiom, (! [A:$tType,A4:A]: ((~ ((((member @ A) @ A4) @ (bot_bot @ (set @ A)))))))).
% 2.59/1.47 thf(fact_195_DiffD2, axiom, (! [A:$tType,C2:A,A5:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A5) @ B4)) => (~ ((((member @ A) @ C2) @ B4))))))).
% 2.59/1.47 thf(fact_196_DiffD1, axiom, (! [A:$tType,C2:A,A5:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A5) @ B4)) => (((member @ A) @ C2) @ A5))))).
% 2.59/1.47 thf(fact_197_DiffE, axiom, (! [A:$tType,C2:A,A5:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A5) @ B4)) => (~ (((((member @ A) @ C2) @ A5) => (((member @ A) @ C2) @ B4)))))))).
% 2.59/1.47 thf(fact_198_empty__not__UNIV, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) != (top_top @ (set @ A)))))).
% 2.59/1.47 thf(fact_199_singletonD, axiom, (! [A:$tType,B2:A,A4:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A4) @ (bot_bot @ (set @ A)))) => (B2 = A4))))).
% 2.59/1.47 thf(fact_200_singleton__iff, axiom, (! [A:$tType,B2:A,A4:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A4) @ (bot_bot @ (set @ A)))) = (B2 = A4))))).
% 2.59/1.47 thf(fact_201_doubleton__eq__iff, axiom, (! [A:$tType,A4:A,B2:A,C2:A,D2:A]: ((((((insert @ A) @ A4) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C2) @ (((insert @ A) @ D2) @ (bot_bot @ (set @ A))))) = (((A4 = C2) & (B2 = D2)) | ((A4 = D2) & (B2 = C2))))))).
% 2.59/1.47 thf(fact_202_insert__not__empty, axiom, (! [A:$tType,A4:A,A5:(set @ A)]: (((((insert @ A) @ A4) @ A5) != (bot_bot @ (set @ A)))))).
% 2.59/1.47 thf(fact_203_singleton__inject, axiom, (! [A:$tType,A4:A,B2:A]: ((((((insert @ A) @ A4) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) => (A4 = B2))))).
% 2.59/1.47 thf(fact_204_insert__Diff__if, axiom, (! [A:$tType,X5:A,B4:(set @ A),A5:(set @ A)]: ((((((member @ A) @ X5) @ B4) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X5) @ A5)) @ B4) = (((minus_minus @ (set @ A)) @ A5) @ B4))) & ((~ ((((member @ A) @ X5) @ B4))) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X5) @ A5)) @ B4) = (((insert @ A) @ X5) @ (((minus_minus @ (set @ A)) @ A5) @ B4)))))))).
% 2.59/1.47 thf(fact_205_Diff__insert__absorb, axiom, (! [A:$tType,X5:A,A5:(set @ A)]: (((~ ((((member @ A) @ X5) @ A5))) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X5) @ A5)) @ (((insert @ A) @ X5) @ (bot_bot @ (set @ A)))) = A5))))).
% 2.59/1.47 thf(fact_206_Diff__insert2, axiom, (! [A:$tType,A5:(set @ A),A4:A,B4:(set @ A)]: (((((minus_minus @ (set @ A)) @ A5) @ (((insert @ A) @ A4) @ B4)) = (((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A5) @ (((insert @ A) @ A4) @ (bot_bot @ (set @ A))))) @ B4))))).
% 2.59/1.47 thf(fact_207_insert__Diff, axiom, (! [A:$tType,A4:A,A5:(set @ A)]: (((((member @ A) @ A4) @ A5) => ((((insert @ A) @ A4) @ (((minus_minus @ (set @ A)) @ A5) @ (((insert @ A) @ A4) @ (bot_bot @ (set @ A))))) = A5))))).
% 2.59/1.47 thf(fact_208_Diff__insert, axiom, (! [A:$tType,A5:(set @ A),A4:A,B4:(set @ A)]: (((((minus_minus @ (set @ A)) @ A5) @ (((insert @ A) @ A4) @ B4)) = (((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A5) @ B4)) @ (((insert @ A) @ A4) @ (bot_bot @ (set @ A)))))))).
% 2.59/1.47 thf(fact_209_vimage__singleton__eq, axiom, (! [A:$tType,B:$tType,A4:A,F:(A > B),B2:B]: (((((member @ A) @ A4) @ ((((vimage @ A) @ B) @ F) @ (((insert @ B) @ B2) @ (bot_bot @ (set @ B))))) = ((F @ A4) = B2))))).
% 2.59/1.47 thf(fact_210_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))))).
% 2.59/1.47 thf(fact_211_regular__inFr, axiom, (! [Tr:dtree,Ns:(set @ n),T2:t]: (((gram_L646766332egular @ Tr) => ((((member @ n) @ (root @ Tr)) @ Ns) => ((((gram_L1333338417e_inFr @ Ns) @ Tr) @ T2) => ((((member @ t) @ T2) @ ((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ Tr))) | (? [Tr5:dtree]: (((((member @ ((sum_sum @ t) @ dtree)) @ (((sum_Inr @ dtree) @ t) @ Tr5)) @ (cont @ Tr)) & (((gram_L1333338417e_inFr @ (((minus_minus @ (set @ n)) @ Ns) @ (((insert @ n) @ (root @ Tr)) @ (bot_bot @ (set @ n))))) @ Tr5) @ T2))))))))))).
% 2.59/1.47 thf(fact_212_is__singletonI, axiom, (! [A:$tType,X5:A]: (((is_singleton @ A) @ (((insert @ A) @ X5) @ (bot_bot @ (set @ A))))))).
% 2.59/1.47 thf(fact_213__092_060open_062_092_060And_062n_H_O_AInr_An_H_A_092_060in_062_Atns_A_092_060Longrightarrow_062_A_092_060exists_062tr_H_O_AK_An_H_A_061_AFr_A_Ins_A_N_A_123n_125_J_Atr_H_A_092_060and_062_Awf_Atr_H_A_092_060and_062_Aroot_Atr_H_A_061_An_H_092_060close_062, axiom, (! [N4:n]: (((((member @ ((sum_sum @ t) @ n)) @ (((sum_Inr @ n) @ t) @ N4)) @ tns) => (? [Tr5:dtree]: ((((k @ N4) = ((gram_L861583724lle_Fr @ (((minus_minus @ (set @ n)) @ ns) @ (((insert @ n) @ n2) @ (bot_bot @ (set @ n))))) @ Tr5)) & ((gram_L864798063lle_wf @ Tr5) & ((root @ Tr5) = N4))))))))).
% 2.59/1.47 thf(fact_214__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ftr_O_A_I_092_060And_062n_H_O_AInr_An_H_A_092_060in_062_Atns_A_092_060Longrightarrow_062_AK_An_H_A_061_AFr_A_Ins_A_N_A_123n_125_J_A_Iftr_An_H_J_A_092_060and_062_Awf_A_Iftr_An_H_J_A_092_060and_062_Aroot_A_Iftr_An_H_J_A_061_An_H_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Ftr:(n > dtree)]: ((~ ((! [N5:n]: (((((member @ ((sum_sum @ t) @ n)) @ (((sum_Inr @ n) @ t) @ N5)) @ tns) => (((k @ N5) = ((gram_L861583724lle_Fr @ (((minus_minus @ (set @ n)) @ ns) @ (((insert @ n) @ n2) @ (bot_bot @ (set @ n))))) @ (Ftr @ N5))) & ((gram_L864798063lle_wf @ (Ftr @ N5)) & ((root @ (Ftr @ N5)) = N5))))))))))))).
% 2.59/1.47 thf(fact_215_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X:A]: ((((member @ A) @ X) @ (bot_bot @ (set @ A))))))))).
% 2.59/1.47 thf(fact_216_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.59/1.47 thf(fact_217_not__root__Fr, axiom, (! [Tr:dtree,Ns:(set @ n)]: (((~ ((((member @ n) @ (root @ Tr)) @ Ns))) => (((gram_L861583724lle_Fr @ Ns) @ Tr) = (bot_bot @ (set @ t))))))).
% 2.59/1.47 thf(fact_218_is__singletonI_H, axiom, (! [A:$tType,A5:(set @ A)]: (((A5 != (bot_bot @ (set @ A))) => ((! [X4:A,Y3:A]: (((((member @ A) @ X4) @ A5) => ((((member @ A) @ Y3) @ A5) => (X4 = Y3))))) => ((is_singleton @ A) @ A5)))))).
% 2.59/1.47 thf(fact_219_is__singletonE, axiom, (! [A:$tType,A5:(set @ A)]: ((((is_singleton @ A) @ A5) => (~ ((! [X4:A]: ((A5 != (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))))))))))).
% 2.59/1.47 thf(fact_220_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A10:(set @ A)]: ((? [X:A]: ((A10 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))))))))))).
% 2.59/1.47 thf(fact_221__C0_C, axiom, (! [N6:n]: (((((member @ ((sum_sum @ t) @ n)) @ (((sum_Inr @ n) @ t) @ N6)) @ tns) => (((k @ N6) = ((gram_L861583724lle_Fr @ (((minus_minus @ (set @ n)) @ ns) @ (((insert @ n) @ n2) @ (bot_bot @ (set @ n))))) @ (ftr @ N6))) & ((gram_L864798063lle_wf @ (ftr @ N6)) & ((root @ (ftr @ N6)) = N6))))))).
% 2.59/1.47 thf(fact_222_P, axiom, (((member @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n)))) @ ((((product_Pair @ n) @ (set @ ((sum_sum @ t) @ n))) @ n2) @ tns)) @ gram_L1451583632elle_P)).
% 2.59/1.47 thf(fact_223_used, axiom, (! [N:n]: ((? [Tns:(set @ ((sum_sum @ t) @ n))]: ((((member @ ((product_prod @ n) @ (set @ ((sum_sum @ t) @ n)))) @ ((((product_Pair @ n) @ (set @ ((sum_sum @ t) @ n))) @ N) @ Tns)) @ gram_L1451583632elle_P)))))).
% 2.59/1.47 thf(fact_224_Fr__self__hsubst, axiom, (! [Tr0:dtree,Ns:(set @ n)]: (((((member @ n) @ (root @ Tr0)) @ Ns) => (((gram_L861583724lle_Fr @ Ns) @ ((gram_L1004374585hsubst @ Tr0) @ Tr0)) = (((sup_sup @ (set @ t)) @ ((((vimage @ t) @ ((sum_sum @ t) @ dtree)) @ ((sum_Inl @ t) @ dtree)) @ (cont @ Tr0))) @ ((gram_L1556062726le_Frr @ (((minus_minus @ (set @ n)) @ Ns) @ (((insert @ n) @ (root @ Tr0)) @ (bot_bot @ (set @ n))))) @ Tr0))))))).
% 2.59/1.47 thf(fact_225_L__rec__notin, axiom, (! [N:n,Ns:(set @ n)]: (((~ ((((member @ n) @ N) @ Ns))) => (((gram_L1451583628elle_L @ Ns) @ N) = (((insert @ (set @ t)) @ (bot_bot @ (set @ t))) @ (bot_bot @ (set @ (set @ t))))))))).
% 2.59/1.47 thf(fact_226_UnCI, axiom, (! [A:$tType,C2:A,B4:(set @ A),A5:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B4))) => (((member @ A) @ C2) @ A5)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A5) @ B4)))))).
% 2.59/1.47 thf(fact_227_Un__iff, axiom, (! [A:$tType,C2:A,A5:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A5) @ B4)) = ((((member @ A) @ C2) @ A5) | (((member @ A) @ C2) @ B4)))))).
% 2.59/1.47 thf(fact_228_Un__empty, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A5) @ B4) = (bot_bot @ (set @ A))) = ((A5 = (bot_bot @ (set @ A))) & (B4 = (bot_bot @ (set @ A)))))))).
% 2.59/1.47 thf(fact_229_Un__insert__right, axiom, (! [A:$tType,A5:(set @ A),A4:A,B4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ (((insert @ A) @ A4) @ B4)) = (((insert @ A) @ A4) @ (((sup_sup @ (set @ A)) @ A5) @ B4)))))).
% 2.59/1.47 thf(fact_230_Un__insert__left, axiom, (! [A:$tType,A4:A,B4:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((insert @ A) @ A4) @ B4)) @ C4) = (((insert @ A) @ A4) @ (((sup_sup @ (set @ A)) @ B4) @ C4)))))).
% 2.59/1.47 thf(fact_231_Un__Diff__cancel, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ (((minus_minus @ (set @ A)) @ B4) @ A5)) = (((sup_sup @ (set @ A)) @ A5) @ B4))))).
% 2.59/1.47 thf(fact_232_Un__Diff__cancel2, axiom, (! [A:$tType,B4:(set @ A),A5:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ B4) @ A5)) @ A5) = (((sup_sup @ (set @ A)) @ B4) @ A5))))).
% 2.59/1.47 thf(fact_233_vimage__Un, axiom, (! [A:$tType,B:$tType,F:(A > B),A5:(set @ B),B4:(set @ B)]: ((((((vimage @ A) @ B) @ F) @ (((sup_sup @ (set @ B)) @ A5) @ B4)) = (((sup_sup @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ A5)) @ ((((vimage @ A) @ B) @ F) @ B4)))))).
% 2.59/1.47 thf(fact_234_Un__empty__right, axiom, (! [A:$tType,A5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ (bot_bot @ (set @ A))) = A5)))).
% 2.59/1.47 thf(fact_235_Un__empty__left, axiom, (! [A:$tType,B4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B4) = B4)))).
% 2.59/1.47 thf(fact_236_insert__is__Un, axiom, (! [A:$tType]: (((insert @ A) = (^ [A11:A]: (((sup_sup @ (set @ A)) @ (((insert @ A) @ A11) @ (bot_bot @ (set @ A)))))))))).
% 2.59/1.47 thf(fact_237_Un__singleton__iff, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A),X5:A]: ((((((sup_sup @ (set @ A)) @ A5) @ B4) = (((insert @ A) @ X5) @ (bot_bot @ (set @ A)))) = (((A5 = (bot_bot @ (set @ A))) & (B4 = (((insert @ A) @ X5) @ (bot_bot @ (set @ A))))) | (((A5 = (((insert @ A) @ X5) @ (bot_bot @ (set @ A)))) & (B4 = (bot_bot @ (set @ A)))) | ((A5 = (((insert @ A) @ X5) @ (bot_bot @ (set @ A)))) & (B4 = (((insert @ A) @ X5) @ (bot_bot @ (set @ A))))))))))).
% 2.59/1.47 thf(fact_238_singleton__Un__iff, axiom, (! [A:$tType,X5:A,A5:(set @ A),B4:(set @ A)]: ((((((insert @ A) @ X5) @ (bot_bot @ (set @ A))) = (((sup_sup @ (set @ A)) @ A5) @ B4)) = (((A5 = (bot_bot @ (set @ A))) & (B4 = (((insert @ A) @ X5) @ (bot_bot @ (set @ A))))) | (((A5 = (((insert @ A) @ X5) @ (bot_bot @ (set @ A)))) & (B4 = (bot_bot @ (set @ A)))) | ((A5 = (((insert @ A) @ X5) @ (bot_bot @ (set @ A)))) & (B4 = (((insert @ A) @ X5) @ (bot_bot @ (set @ A))))))))))).
% 2.59/1.47 thf(fact_239_Un__UNIV__left, axiom, (! [A:$tType,B4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (top_top @ (set @ A))) @ B4) = (top_top @ (set @ A)))))).
% 2.59/1.47 thf(fact_240_Un__UNIV__right, axiom, (! [A:$tType,A5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))).
% 2.59/1.47 thf(fact_241_UnE, axiom, (! [A:$tType,C2:A,A5:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A5) @ B4)) => ((~ ((((member @ A) @ C2) @ A5))) => (((member @ A) @ C2) @ B4)))))).
% 2.59/1.47 thf(fact_242_UnI1, axiom, (! [A:$tType,C2:A,A5:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ A5) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A5) @ B4)))))).
% 2.59/1.47 thf(fact_243_UnI2, axiom, (! [A:$tType,C2:A,B4:(set @ A),A5:(set @ A)]: (((((member @ A) @ C2) @ B4) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A5) @ B4)))))).
% 2.59/1.47 thf(fact_244_bex__Un, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A),P:(A > $o)]: (((? [X:A]: (((((member @ A) @ X) @ (((sup_sup @ (set @ A)) @ A5) @ B4)) & (P @ X)))) = ((? [X:A]: (((((member @ A) @ X) @ A5) & (P @ X)))) | (? [X:A]: (((((member @ A) @ X) @ B4) & (P @ X))))))))).
% 2.59/1.47 thf(fact_245_ball__Un, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A),P:(A > $o)]: (((! [X:A]: (((((member @ A) @ X) @ (((sup_sup @ (set @ A)) @ A5) @ B4)) => (P @ X)))) = ((! [X:A]: (((((member @ A) @ X) @ A5) => (P @ X)))) & (! [X:A]: (((((member @ A) @ X) @ B4) => (P @ X))))))))).
% 2.59/1.47 thf(fact_246_Un__assoc, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A5) @ B4)) @ C4) = (((sup_sup @ (set @ A)) @ A5) @ (((sup_sup @ (set @ A)) @ B4) @ C4)))))).
% 2.59/1.47 thf(fact_247_Un__absorb, axiom, (! [A:$tType,A5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ A5) = A5)))).
% 2.59/1.47 thf(fact_248_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A10:(set @ A),B9:(set @ A)]: ((((sup_sup @ (set @ A)) @ B9) @ A10))))))).
% 2.59/1.47 thf(fact_249_Un__left__absorb, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ (((sup_sup @ (set @ A)) @ A5) @ B4)) = (((sup_sup @ (set @ A)) @ A5) @ B4))))).
% 2.59/1.47 thf(fact_250_Un__left__commute, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ (((sup_sup @ (set @ A)) @ B4) @ C4)) = (((sup_sup @ (set @ A)) @ B4) @ (((sup_sup @ (set @ A)) @ A5) @ C4)))))).
% 2.59/1.47 thf(fact_251_Un__Diff, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A),C4:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A5) @ B4)) @ C4) = (((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A5) @ C4)) @ (((minus_minus @ (set @ A)) @ B4) @ C4)))))).
% 2.59/1.47 thf(fact_252_vimage__insert, axiom, (! [A:$tType,B:$tType,F:(A > B),A4:B,B4:(set @ B)]: ((((((vimage @ A) @ B) @ F) @ (((insert @ B) @ A4) @ B4)) = (((sup_sup @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ (((insert @ B) @ A4) @ (bot_bot @ (set @ B))))) @ ((((vimage @ A) @ B) @ F) @ B4)))))).
% 2.59/1.47 thf(fact_253_sup__top__right, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X5:A]: (((((sup_sup @ A) @ X5) @ (top_top @ A)) = (top_top @ A)))))))).
% 2.59/1.47 thf(fact_254_sup__top__left, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X5:A]: (((((sup_sup @ A) @ (top_top @ A)) @ X5) = (top_top @ A)))))))).
% 2.59/1.47 thf(fact_255_subtr2__trans__Un, axiom, (! [Ns122:(set @ n),Tr1:dtree,Tr22:dtree,Ns23:(set @ n),Tr3:dtree]: (((((gram_L1283001940subtr2 @ Ns122) @ Tr1) @ Tr22) => ((((gram_L1283001940subtr2 @ Ns23) @ Tr22) @ Tr3) => (((gram_L1283001940subtr2 @ (((sup_sup @ (set @ n)) @ Ns122) @ Ns23)) @ Tr1) @ Tr3)))))).
% 2.59/1.47 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, ((bounded_lattice @ $o) @ (type2 @ $o))).
% 2.59/1.47 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: (((bounded_lattice @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.59/1.47 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A13:$tType]: ((((bounded_lattice @ A13) @ (type2 @ A13)) => ((bounded_lattice @ (A8 > A13)) @ (type2 @ (A8 > A13))))))).
% 2.59/1.47 thf(tcon_fun___Lattices_Obounded__lattice__top, axiom, (! [A8:$tType,A13:$tType]: ((((bounded_lattice @ A13) @ (type2 @ A13)) => ((bounded_lattice_top @ (A8 > A13)) @ (type2 @ (A8 > A13))))))).
% 2.59/1.47 thf(tcon_fun___Orderings_Otop, axiom, (! [A8:$tType,A13:$tType]: ((((top @ A13) @ (type2 @ A13)) => ((top @ (A8 > A13)) @ (type2 @ (A8 > A13))))))).
% 2.59/1.47 thf(tcon_fun___Orderings_Obot, axiom, (! [A8:$tType,A13:$tType]: ((((bot @ A13) @ (type2 @ A13)) => ((bot @ (A8 > A13)) @ (type2 @ (A8 > A13))))))).
% 2.59/1.47 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_3, axiom, (! [A8:$tType]: (((bounded_lattice_top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.59/1.47 thf(tcon_Set_Oset___Orderings_Otop_4, axiom, (! [A8:$tType]: (((top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.59/1.47 thf(tcon_Set_Oset___Orderings_Obot_5, axiom, (! [A8:$tType]: (((bot @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.59/1.47 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_6, axiom, ((bounded_lattice_top @ $o) @ (type2 @ $o))).
% 2.59/1.47 thf(tcon_HOL_Obool___Orderings_Otop_7, axiom, ((top @ $o) @ (type2 @ $o))).
% 2.59/1.47 thf(tcon_HOL_Obool___Orderings_Obot_8, axiom, ((bot @ $o) @ (type2 @ $o))).
% 2.59/1.47 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.59/1.47 thf(help_If_2_1_T, axiom, (! [A:$tType,X5:A,Y:A]: ((((((if @ A) @ $false) @ X5) @ Y) = Y)))).
% 2.59/1.47 thf(help_If_1_1_T, axiom, (! [A:$tType,X5:A,Y:A]: ((((((if @ A) @ $true) @ X5) @ Y) = X5)))).
% 2.59/1.47 thf(conj_0, conjecture, (gram_L864798063lle_wf @ ((gram_L1004374585hsubst @ tr2) @ tr2))).
% 2.59/1.47 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.6ce4rUdsE3/DTF2DTF24932.p
% 2.59/1.47 ------------------------
% 2.85/1.51 ---- Cleaned THF ---
% 2.85/1.52 thf(ty_t_Product__Type_Oprod,type,
% 2.85/1.52 product_prod: $tType > $tType > $tType ).
% 2.85/1.52
% 2.85/1.52 thf(ty_t_Sum__Type_Osum,type,
% 2.85/1.52 sum_sum: $tType > $tType > $tType ).
% 2.85/1.52
% 2.85/1.52 thf(ty_t_DTree_Odtree,type,
% 2.85/1.52 dtree: $tType ).
% 2.85/1.52
% 2.85/1.52 thf(ty_t_Set_Oset,type,
% 2.85/1.52 set: $tType > $tType ).
% 2.85/1.52
% 2.85/1.52 thf(ty_t_DTree_OT,type,
% 2.85/1.52 t: $tType ).
% 2.85/1.52
% 2.85/1.52 thf(ty_t_DTree_ON,type,
% 2.85/1.52 n: $tType ).
% 2.85/1.52
% 2.85/1.52 thf(ty_t_itself,type,
% 2.85/1.52 itself: $tType > $tType ).
% 2.85/1.52
% 2.85/1.52 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.85/1.52 bounded_lattice:
% 2.85/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_cl_HOL_Otype,type,
% 2.85/1.52 type:
% 2.85/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_cl_Orderings_Obot,type,
% 2.85/1.52 bot:
% 2.85/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_cl_Orderings_Otop,type,
% 2.85/1.52 top:
% 2.85/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 2.85/1.52 bounded_lattice_top:
% 2.85/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_DTree_ONode,type,
% 2.85/1.52 node: n > ( set @ ( sum_sum @ t @ dtree ) ) > dtree ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_DTree_Ocont,type,
% 2.85/1.52 cont: dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_DTree_Odtree_Oroot,type,
% 2.85/1.52 root: dtree > n ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_DTree_Ounfold,type,
% 2.85/1.52 unfold:
% 2.85/1.52 !>[A: $tType] : ( ( A > n ) > ( A > ( set @ ( sum_sum @ t @ A ) ) ) > A > dtree ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Fun_Ocomp,type,
% 2.85/1.52 comp:
% 2.85/1.52 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OFr,type,
% 2.85/1.52 gram_L861583724lle_Fr: ( set @ n ) > dtree > ( set @ t ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OFrr,type,
% 2.85/1.52 gram_L1556062726le_Frr: ( set @ n ) > dtree > ( set @ t ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH,type,
% 2.85/1.52 gram_L1451583624elle_H: dtree > n > dtree ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__c,type,
% 2.85/1.52 gram_L1221482011le_H_c: dtree > n > ( set @ ( sum_sum @ t @ n ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OH__r,type,
% 2.85/1.52 gram_L1221482026le_H_r: dtree > n > n ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OL,type,
% 2.85/1.52 gram_L1451583628elle_L: ( set @ n ) > n > ( set @ ( set @ t ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OP,type,
% 2.85/1.52 gram_L1451583632elle_P: set @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Odeftr,type,
% 2.85/1.52 gram_L1231612515_deftr: n > dtree ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst,type,
% 2.85/1.52 gram_L1004374585hsubst: dtree > dtree > dtree ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__c,type,
% 2.85/1.52 gram_L1905609002ubst_c: dtree > dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Ohsubst__r,type,
% 2.85/1.52 gram_L1905609017ubst_r: dtree > n ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr,type,
% 2.85/1.52 gram_L1333338417e_inFr: ( set @ n ) > dtree > t > $o ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFr2,type,
% 2.85/1.52 gram_L805317441_inFr2: ( set @ n ) > dtree > t > $o ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinFrr,type,
% 2.85/1.52 gram_L805317505_inFrr: ( set @ n ) > dtree > t > $o ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OinItr,type,
% 2.85/1.52 gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Opick,type,
% 2.85/1.52 gram_L315592705e_pick: dtree > n > dtree ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Orcut,type,
% 2.85/1.52 gram_L1828378864e_rcut: dtree > dtree ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oreg,type,
% 2.85/1.52 gram_L1918716148le_reg: ( n > dtree ) > dtree > $o ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Oregular,type,
% 2.85/1.52 gram_L646766332egular: dtree > $o ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr,type,
% 2.85/1.52 gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr2,type,
% 2.85/1.52 gram_L1283001940subtr2: ( set @ n ) > dtree > dtree > $o ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_OsubtrOf,type,
% 2.85/1.52 gram_L1614515765ubtrOf: dtree > n > dtree ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Gram__Lang__Mirabelle__ojxrtuoybn_Owf,type,
% 2.85/1.52 gram_L864798063lle_wf: dtree > $o ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.85/1.52 minus_minus:
% 2.85/1.52 !>[A: $tType] : ( A > A > A ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_If,type,
% 2.85/1.52 if:
% 2.85/1.52 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.85/1.52 sup_sup:
% 2.85/1.52 !>[A: $tType] : ( A > A > A ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.85/1.52 bot_bot:
% 2.85/1.52 !>[A: $tType] : A ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Orderings_Otop__class_Otop,type,
% 2.85/1.52 top_top:
% 2.85/1.52 !>[A: $tType] : A ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Product__Type_OPair,type,
% 2.85/1.52 product_Pair:
% 2.85/1.52 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Pure_Otype,type,
% 2.85/1.52 type2:
% 2.85/1.52 !>[A: $tType] : ( itself @ A ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Set_OCollect,type,
% 2.85/1.52 collect:
% 2.85/1.52 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Set_Oinsert,type,
% 2.85/1.52 insert:
% 2.85/1.52 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Set_Ois__singleton,type,
% 2.85/1.52 is_singleton:
% 2.85/1.52 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Set_Ovimage,type,
% 2.85/1.52 vimage:
% 2.85/1.52 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Sum__Type_OInl,type,
% 2.85/1.52 sum_Inl:
% 2.85/1.52 !>[A: $tType,B: $tType] : ( A > ( sum_sum @ A @ B ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Sum__Type_OInr,type,
% 2.85/1.52 sum_Inr:
% 2.85/1.52 !>[B: $tType,A: $tType] : ( B > ( sum_sum @ A @ B ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_Sum__Type_Oold_Osum_Orec__sum,type,
% 2.85/1.52 sum_rec_sum:
% 2.85/1.52 !>[A: $tType,T: $tType,B: $tType] : ( ( A > T ) > ( B > T ) > ( sum_sum @ A @ B ) > T ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_c_member,type,
% 2.85/1.52 member:
% 2.85/1.52 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_v_K____,type,
% 2.85/1.52 k: n > ( set @ t ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_v_ftr____,type,
% 2.85/1.52 ftr: n > dtree ).
% 2.85/1.52
% 2.85/1.52 thf(sy_v_n,type,
% 2.85/1.52 n2: n ).
% 2.85/1.52
% 2.85/1.52 thf(sy_v_ns,type,
% 2.85/1.52 ns: set @ n ).
% 2.85/1.52
% 2.85/1.52 thf(sy_v_tns____,type,
% 2.85/1.52 tns: set @ ( sum_sum @ t @ n ) ).
% 2.85/1.52
% 2.85/1.52 thf(sy_v_tr_H____,type,
% 2.85/1.52 tr: dtree ).
% 2.85/1.52
% 2.85/1.52 thf(sy_v_tr____,type,
% 2.85/1.52 tr2: dtree ).
% 2.85/1.52
% 2.85/1.52 thf(fact_0_dtr,axiom,
% 2.85/1.52 gram_L864798063lle_wf @ tr2 ).
% 2.85/1.52
% 2.85/1.52 thf(fact_1_tr_H__def,axiom,
% 2.85/1.52 ( tr
% 2.85/1.52 = ( gram_L1004374585hsubst @ tr2 @ tr2 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_2_wf__hsubst,axiom,
% 2.85/1.52 ! [Tr0: dtree,Tr: dtree] :
% 2.85/1.52 ( ( gram_L864798063lle_wf @ Tr0 )
% 2.85/1.52 => ( ( gram_L864798063lle_wf @ Tr )
% 2.85/1.52 => ( gram_L864798063lle_wf @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_3_wf__rcut,axiom,
% 2.85/1.52 ! [Tr0: dtree] :
% 2.85/1.52 ( ( gram_L864798063lle_wf @ Tr0 )
% 2.85/1.52 => ( gram_L864798063lle_wf @ ( gram_L1828378864e_rcut @ Tr0 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_4_wf__deftr,axiom,
% 2.85/1.52 ! [N: n] : ( gram_L864798063lle_wf @ ( gram_L1231612515_deftr @ N ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_5_rtr,axiom,
% 2.85/1.52 ( ( root @ tr2 )
% 2.85/1.52 = n2 ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_6_n,axiom,
% 2.85/1.52 member @ n @ n2 @ ns ).
% 2.85/1.52
% 2.85/1.52 thf(fact_7_root__hsubst,axiom,
% 2.85/1.52 ! [Tr0: dtree,Tr: dtree] :
% 2.85/1.52 ( ( root @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) )
% 2.85/1.52 = ( root @ Tr ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_8_wf__subtr,axiom,
% 2.85/1.52 ! [Tr1: dtree,Ns: set @ n,Tr: dtree] :
% 2.85/1.52 ( ( gram_L864798063lle_wf @ Tr1 )
% 2.85/1.52 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 2.85/1.52 => ( gram_L864798063lle_wf @ Tr ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_9_hsubst__def,axiom,
% 2.85/1.52 ( gram_L1004374585hsubst
% 2.85/1.52 = ( ^ [Tr02: dtree] : ( unfold @ dtree @ gram_L1905609017ubst_r @ ( gram_L1905609002ubst_c @ Tr02 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_10_hsubst__eq,axiom,
% 2.85/1.52 ! [Tr: dtree,Tr0: dtree] :
% 2.85/1.52 ( ( ( root @ Tr )
% 2.85/1.52 = ( root @ Tr0 ) )
% 2.85/1.52 => ( ( gram_L1004374585hsubst @ Tr0 @ Tr )
% 2.85/1.52 = ( gram_L1004374585hsubst @ Tr0 @ Tr0 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_11_inFr__hsubst__notin,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr: dtree,T2: t,Tr0: dtree] :
% 2.85/1.52 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 2.85/1.52 => ( ~ ( member @ n @ ( root @ Tr0 ) @ Ns )
% 2.85/1.52 => ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T2 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_12_root__o__subst,axiom,
% 2.85/1.52 ! [Tr0: dtree] :
% 2.85/1.52 ( ( comp @ dtree @ n @ dtree @ root @ ( gram_L1004374585hsubst @ Tr0 ) )
% 2.85/1.52 = root ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_13_wf__cont,axiom,
% 2.85/1.52 ! [Tr: dtree,Tr2: dtree] :
% 2.85/1.52 ( ( gram_L864798063lle_wf @ Tr )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 2.85/1.52 => ( gram_L864798063lle_wf @ Tr2 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_14_wf__pick,axiom,
% 2.85/1.52 ! [Tr0: dtree,N: n] :
% 2.85/1.52 ( ( gram_L864798063lle_wf @ Tr0 )
% 2.85/1.52 => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 2.85/1.52 => ( gram_L864798063lle_wf @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_15_root__deftr,axiom,
% 2.85/1.52 ! [N: n] :
% 2.85/1.52 ( ( root @ ( gram_L1231612515_deftr @ N ) )
% 2.85/1.52 = N ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_16_root__rcut,axiom,
% 2.85/1.52 ! [Tr0: dtree] :
% 2.85/1.52 ( ( root @ ( gram_L1828378864e_rcut @ Tr0 ) )
% 2.85/1.52 = ( root @ Tr0 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_17_wf__inj,axiom,
% 2.85/1.52 ! [Tr: dtree,Tr1: dtree,Tr22: dtree] :
% 2.85/1.52 ( ( gram_L864798063lle_wf @ Tr )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr ) )
% 2.85/1.52 => ( ( ( root @ Tr1 )
% 2.85/1.52 = ( root @ Tr22 ) )
% 2.85/1.52 = ( Tr1 = Tr22 ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_18_pick,axiom,
% 2.85/1.52 ! [Tr0: dtree,N: n] :
% 2.85/1.52 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 2.85/1.52 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ Tr0 @ N ) @ Tr0 )
% 2.85/1.52 & ( ( root @ ( gram_L315592705e_pick @ Tr0 @ N ) )
% 2.85/1.52 = N ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_19_inFr_OInd,axiom,
% 2.85/1.52 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,T2: t] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 2.85/1.52 => ( ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 )
% 2.85/1.52 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_20_inItr_OInd,axiom,
% 2.85/1.52 ! [Tr: dtree,Ns: set @ n,Tr1: dtree,N: n] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 2.85/1.52 => ( ( gram_L830233218_inItr @ Ns @ Tr1 @ N )
% 2.85/1.52 => ( gram_L830233218_inItr @ Ns @ Tr @ N ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_21_root__pick,axiom,
% 2.85/1.52 ! [Tr0: dtree,N: n] :
% 2.85/1.52 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 2.85/1.52 => ( ( root @ ( gram_L315592705e_pick @ Tr0 @ N ) )
% 2.85/1.52 = N ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_22_inItr_OBase,axiom,
% 2.85/1.52 ! [Tr: dtree,Ns: set @ n] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 2.85/1.52 => ( gram_L830233218_inItr @ Ns @ Tr @ ( root @ Tr ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_23_subtr_ORefl,axiom,
% 2.85/1.52 ! [Tr: dtree,Ns: set @ n] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 2.85/1.52 => ( gram_L716654942_subtr @ Ns @ Tr @ Tr ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_24_subtr_OStep,axiom,
% 2.85/1.52 ! [Tr3: dtree,Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr3 ) @ Ns )
% 2.85/1.52 => ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr3 ) )
% 2.85/1.52 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_25_subtr__inFr,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr: dtree,T2: t,Tr1: dtree] :
% 2.85/1.52 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 2.85/1.52 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 2.85/1.52 => ( gram_L1333338417e_inFr @ Ns @ Tr1 @ T2 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_26_subtr__pick,axiom,
% 2.85/1.52 ! [Tr0: dtree,N: n] :
% 2.85/1.52 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 2.85/1.52 => ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ Tr0 @ N ) @ Tr0 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_27_inItr_Ocases,axiom,
% 2.85/1.52 ! [A1: set @ n,A2: dtree,A3: n] :
% 2.85/1.52 ( ( gram_L830233218_inItr @ A1 @ A2 @ A3 )
% 2.85/1.52 => ( ( ( A3
% 2.85/1.52 = ( root @ A2 ) )
% 2.85/1.52 => ~ ( member @ n @ ( root @ A2 ) @ A1 ) )
% 2.85/1.52 => ~ ( ( member @ n @ ( root @ A2 ) @ A1 )
% 2.85/1.52 => ! [Tr12: dtree] :
% 2.85/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A2 ) )
% 2.85/1.52 => ~ ( gram_L830233218_inItr @ A1 @ Tr12 @ A3 ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_28_inItr_Osimps,axiom,
% 2.85/1.52 ( gram_L830233218_inItr
% 2.85/1.52 = ( ^ [A12: set @ n,A22: dtree,A32: n] :
% 2.85/1.52 ( ? [Tr4: dtree,Ns2: set @ n] :
% 2.85/1.52 ( ( A12 = Ns2 )
% 2.85/1.52 & ( A22 = Tr4 )
% 2.85/1.52 & ( A32
% 2.85/1.52 = ( root @ Tr4 ) )
% 2.85/1.52 & ( member @ n @ ( root @ Tr4 ) @ Ns2 ) )
% 2.85/1.52 | ? [Tr4: dtree,Ns2: set @ n,Tr13: dtree,N2: n] :
% 2.85/1.52 ( ( A12 = Ns2 )
% 2.85/1.52 & ( A22 = Tr4 )
% 2.85/1.52 & ( A32 = N2 )
% 2.85/1.52 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 2.85/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr4 ) )
% 2.85/1.52 & ( gram_L830233218_inItr @ Ns2 @ Tr13 @ N2 ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_29_inItr__subtr,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr: dtree,N: n] :
% 2.85/1.52 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 2.85/1.52 => ? [Tr5: dtree] :
% 2.85/1.52 ( ( gram_L716654942_subtr @ Ns @ Tr5 @ Tr )
% 2.85/1.52 & ( ( root @ Tr5 )
% 2.85/1.52 = N ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_30_subtr_Ocases,axiom,
% 2.85/1.52 ! [A1: set @ n,A2: dtree,A3: dtree] :
% 2.85/1.52 ( ( gram_L716654942_subtr @ A1 @ A2 @ A3 )
% 2.85/1.52 => ( ( ( A3 = A2 )
% 2.85/1.52 => ~ ( member @ n @ ( root @ A2 ) @ A1 ) )
% 2.85/1.52 => ~ ( ( member @ n @ ( root @ A3 ) @ A1 )
% 2.85/1.52 => ! [Tr23: dtree] :
% 2.85/1.52 ( ( gram_L716654942_subtr @ A1 @ A2 @ Tr23 )
% 2.85/1.52 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ A3 ) ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_31_subtr_Osimps,axiom,
% 2.85/1.52 ( gram_L716654942_subtr
% 2.85/1.52 = ( ^ [A12: set @ n,A22: dtree,A32: dtree] :
% 2.85/1.52 ( ? [Tr4: dtree,Ns2: set @ n] :
% 2.85/1.52 ( ( A12 = Ns2 )
% 2.85/1.52 & ( A22 = Tr4 )
% 2.85/1.52 & ( A32 = Tr4 )
% 2.85/1.52 & ( member @ n @ ( root @ Tr4 ) @ Ns2 ) )
% 2.85/1.52 | ? [Tr32: dtree,Ns2: set @ n,Tr13: dtree,Tr24: dtree] :
% 2.85/1.52 ( ( A12 = Ns2 )
% 2.85/1.52 & ( A22 = Tr13 )
% 2.85/1.52 & ( A32 = Tr32 )
% 2.85/1.52 & ( member @ n @ ( root @ Tr32 ) @ Ns2 )
% 2.85/1.52 & ( gram_L716654942_subtr @ Ns2 @ Tr13 @ Tr24 )
% 2.85/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr24 ) @ ( cont @ Tr32 ) ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_32_subtr__StepL,axiom,
% 2.85/1.52 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr3: dtree] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 2.85/1.52 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr3 )
% 2.85/1.52 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_33_subtr__deftr,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr2: dtree,N: n] :
% 2.85/1.52 ( ( gram_L716654942_subtr @ Ns @ Tr2 @ ( gram_L1231612515_deftr @ N ) )
% 2.85/1.52 => ( Tr2
% 2.85/1.52 = ( gram_L1231612515_deftr @ ( root @ Tr2 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_34_subtr__inItr,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr: dtree,N: n,Tr1: dtree] :
% 2.85/1.52 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 2.85/1.52 => ( ( gram_L716654942_subtr @ Ns @ Tr @ Tr1 )
% 2.85/1.52 => ( gram_L830233218_inItr @ Ns @ Tr1 @ N ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_35_subtr__trans,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr3: dtree] :
% 2.85/1.52 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 2.85/1.52 => ( ( gram_L716654942_subtr @ Ns @ Tr22 @ Tr3 )
% 2.85/1.52 => ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr3 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_36_hsubst__c__def,axiom,
% 2.85/1.52 ( gram_L1905609002ubst_c
% 2.85/1.52 = ( ^ [Tr02: dtree,Tr4: dtree] :
% 2.85/1.52 ( if @ ( set @ ( sum_sum @ t @ dtree ) )
% 2.85/1.52 @ ( ( root @ Tr4 )
% 2.85/1.52 = ( root @ Tr02 ) )
% 2.85/1.52 @ ( cont @ Tr02 )
% 2.85/1.52 @ ( cont @ Tr4 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_37_hsubst__r__def,axiom,
% 2.85/1.52 gram_L1905609017ubst_r = root ).
% 2.85/1.52
% 2.85/1.52 thf(fact_38_inFr__root__in,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 2.85/1.52 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 2.85/1.52 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_39_inItr_Oinducts,axiom,
% 2.85/1.52 ! [X1: set @ n,X2: dtree,X3: n,P: ( set @ n ) > dtree > n > $o] :
% 2.85/1.52 ( ( gram_L830233218_inItr @ X1 @ X2 @ X3 )
% 2.85/1.52 => ( ! [Tr6: dtree,Ns3: set @ n] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr6 ) @ Ns3 )
% 2.85/1.52 => ( P @ Ns3 @ Tr6 @ ( root @ Tr6 ) ) )
% 2.85/1.52 => ( ! [Tr6: dtree,Ns3: set @ n,Tr12: dtree,N3: n] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr6 ) @ Ns3 )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr6 ) )
% 2.85/1.52 => ( ( gram_L830233218_inItr @ Ns3 @ Tr12 @ N3 )
% 2.85/1.52 => ( ( P @ Ns3 @ Tr12 @ N3 )
% 2.85/1.52 => ( P @ Ns3 @ Tr6 @ N3 ) ) ) ) )
% 2.85/1.52 => ( P @ X1 @ X2 @ X3 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_40_inItr__root__in,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr: dtree,N: n] :
% 2.85/1.52 ( ( gram_L830233218_inItr @ Ns @ Tr @ N )
% 2.85/1.52 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_41_not__root__inFr,axiom,
% 2.85/1.52 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 2.85/1.52 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 2.85/1.52 => ~ ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_42_subtr_Oinducts,axiom,
% 2.85/1.52 ! [X1: set @ n,X2: dtree,X3: dtree,P: ( set @ n ) > dtree > dtree > $o] :
% 2.85/1.52 ( ( gram_L716654942_subtr @ X1 @ X2 @ X3 )
% 2.85/1.52 => ( ! [Tr6: dtree,Ns3: set @ n] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr6 ) @ Ns3 )
% 2.85/1.52 => ( P @ Ns3 @ Tr6 @ Tr6 ) )
% 2.85/1.52 => ( ! [Tr33: dtree,Ns3: set @ n,Tr12: dtree,Tr23: dtree] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr33 ) @ Ns3 )
% 2.85/1.52 => ( ( gram_L716654942_subtr @ Ns3 @ Tr12 @ Tr23 )
% 2.85/1.52 => ( ( P @ Ns3 @ Tr12 @ Tr23 )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr23 ) @ ( cont @ Tr33 ) )
% 2.85/1.52 => ( P @ Ns3 @ Tr12 @ Tr33 ) ) ) ) )
% 2.85/1.52 => ( P @ X1 @ X2 @ X3 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_43_subtr__inductL,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Phi: ( set @ n ) > dtree > dtree > $o] :
% 2.85/1.52 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 2.85/1.52 => ( ! [Ns3: set @ n,Tr6: dtree] : ( Phi @ Ns3 @ Tr6 @ Tr6 )
% 2.85/1.52 => ( ! [Ns3: set @ n,Tr12: dtree,Tr23: dtree,Tr33: dtree] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr12 ) @ Ns3 )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 2.85/1.52 => ( ( gram_L716654942_subtr @ Ns3 @ Tr23 @ Tr33 )
% 2.85/1.52 => ( ( Phi @ Ns3 @ Tr23 @ Tr33 )
% 2.85/1.52 => ( Phi @ Ns3 @ Tr12 @ Tr33 ) ) ) ) )
% 2.85/1.52 => ( Phi @ Ns @ Tr1 @ Tr22 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_44_subtr__rootL__in,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 2.85/1.52 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 2.85/1.52 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_45_mem__Collect__eq,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,P: A > $o] :
% 2.85/1.52 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 2.85/1.52 = ( P @ A4 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_46_Collect__mem__eq,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A] :
% 2.85/1.52 ( ( collect @ A
% 2.85/1.52 @ ^ [X: A] : ( member @ A @ X @ A5 ) )
% 2.85/1.52 = A5 ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_47_Collect__cong,axiom,
% 2.85/1.52 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.85/1.52 ( ! [X4: A] :
% 2.85/1.52 ( ( P @ X4 )
% 2.85/1.52 = ( Q @ X4 ) )
% 2.85/1.52 => ( ( collect @ A @ P )
% 2.85/1.52 = ( collect @ A @ Q ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_48_ext,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.85/1.52 ( ! [X4: A] :
% 2.85/1.52 ( ( F @ X4 )
% 2.85/1.52 = ( G @ X4 ) )
% 2.85/1.52 => ( F = G ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_49_subtr__rootR__in,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 2.85/1.52 ( ( gram_L716654942_subtr @ Ns @ Tr1 @ Tr22 )
% 2.85/1.52 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_50_subtr__UNIV__inductL,axiom,
% 2.85/1.52 ! [Tr1: dtree,Tr22: dtree,Phi: dtree > dtree > $o] :
% 2.85/1.52 ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr1 @ Tr22 )
% 2.85/1.52 => ( ! [Tr6: dtree] : ( Phi @ Tr6 @ Tr6 )
% 2.85/1.52 => ( ! [Tr12: dtree,Tr23: dtree,Tr33: dtree] :
% 2.85/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 2.85/1.52 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr23 @ Tr33 )
% 2.85/1.52 => ( ( Phi @ Tr23 @ Tr33 )
% 2.85/1.52 => ( Phi @ Tr12 @ Tr33 ) ) ) )
% 2.85/1.52 => ( Phi @ Tr1 @ Tr22 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_51_subtrOf__root,axiom,
% 2.85/1.52 ! [Tr: dtree,Tr2: dtree] :
% 2.85/1.52 ( ( gram_L864798063lle_wf @ Tr )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 2.85/1.52 => ( ( gram_L1614515765ubtrOf @ Tr @ ( root @ Tr2 ) )
% 2.85/1.52 = Tr2 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_52_H__r__def,axiom,
% 2.85/1.52 ( gram_L1221482026le_H_r
% 2.85/1.52 = ( ^ [Tr02: dtree,N2: n] : ( root @ ( gram_L315592705e_pick @ Tr02 @ N2 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_53_inFrr__def,axiom,
% 2.85/1.52 ( gram_L805317505_inFrr
% 2.85/1.52 = ( ^ [Ns2: set @ n,Tr4: dtree,T3: t] :
% 2.85/1.52 ? [Tr7: dtree] :
% 2.85/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr7 ) @ ( cont @ Tr4 ) )
% 2.85/1.52 & ( gram_L1333338417e_inFr @ Ns2 @ Tr7 @ T3 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_54_sum_Oinject_I2_J,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,X2: B,Y2: B] :
% 2.85/1.52 ( ( ( sum_Inr @ B @ A @ X2 )
% 2.85/1.52 = ( sum_Inr @ B @ A @ Y2 ) )
% 2.85/1.52 = ( X2 = Y2 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_55_old_Osum_Oinject_I2_J,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,B2: B,B3: B] :
% 2.85/1.52 ( ( ( sum_Inr @ B @ A @ B2 )
% 2.85/1.52 = ( sum_Inr @ B @ A @ B3 ) )
% 2.85/1.52 = ( B2 = B3 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_56_unfold_I1_J,axiom,
% 2.85/1.52 ! [A: $tType,Rt: A > n,Ct: A > ( set @ ( sum_sum @ t @ A ) ),B2: A] :
% 2.85/1.52 ( ( root @ ( unfold @ A @ Rt @ Ct @ B2 ) )
% 2.85/1.52 = ( Rt @ B2 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_57_comp__apply,axiom,
% 2.85/1.52 ! [C: $tType,A: $tType,B: $tType] :
% 2.85/1.52 ( ( comp @ B @ A @ C )
% 2.85/1.52 = ( ^ [F2: B > A,G2: C > B,X: C] : ( F2 @ ( G2 @ X ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_58_UNIV__I,axiom,
% 2.85/1.52 ! [A: $tType,X5: A] : ( member @ A @ X5 @ ( top_top @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_59_iso__tuple__UNIV__I,axiom,
% 2.85/1.52 ! [A: $tType,X5: A] : ( member @ A @ X5 @ ( top_top @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_60_top__apply,axiom,
% 2.85/1.52 ! [C: $tType,D: $tType] :
% 2.85/1.52 ( ( top @ C @ ( type2 @ C ) )
% 2.85/1.52 => ( ( top_top @ ( D > C ) )
% 2.85/1.52 = ( ^ [X: D] : ( top_top @ C ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_61_top__set__def,axiom,
% 2.85/1.52 ! [A: $tType] :
% 2.85/1.52 ( ( top_top @ ( set @ A ) )
% 2.85/1.52 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_62_UNIV__witness,axiom,
% 2.85/1.52 ! [A: $tType] :
% 2.85/1.52 ? [X4: A] : ( member @ A @ X4 @ ( top_top @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_63_UNIV__eq__I,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A] :
% 2.85/1.52 ( ! [X4: A] : ( member @ A @ X4 @ A5 )
% 2.85/1.52 => ( ( top_top @ ( set @ A ) )
% 2.85/1.52 = A5 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_64_comp__eq__dest__lhs,axiom,
% 2.85/1.52 ! [C: $tType,B: $tType,A: $tType,A4: C > B,B2: A > C,C2: A > B,V: A] :
% 2.85/1.52 ( ( ( comp @ C @ B @ A @ A4 @ B2 )
% 2.85/1.52 = C2 )
% 2.85/1.52 => ( ( A4 @ ( B2 @ V ) )
% 2.85/1.52 = ( C2 @ V ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_65_comp__eq__elim,axiom,
% 2.85/1.52 ! [C: $tType,B: $tType,D: $tType,A: $tType,A4: C > B,B2: A > C,C2: D > B,D2: A > D] :
% 2.85/1.52 ( ( ( comp @ C @ B @ A @ A4 @ B2 )
% 2.85/1.52 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 2.85/1.52 => ! [V2: A] :
% 2.85/1.52 ( ( A4 @ ( B2 @ V2 ) )
% 2.85/1.52 = ( C2 @ ( D2 @ V2 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_66_comp__eq__dest,axiom,
% 2.85/1.52 ! [C: $tType,B: $tType,D: $tType,A: $tType,A4: C > B,B2: A > C,C2: D > B,D2: A > D,V: A] :
% 2.85/1.52 ( ( ( comp @ C @ B @ A @ A4 @ B2 )
% 2.85/1.52 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 2.85/1.52 => ( ( A4 @ ( B2 @ V ) )
% 2.85/1.52 = ( C2 @ ( D2 @ V ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_67_comp__assoc,axiom,
% 2.85/1.52 ! [B: $tType,D: $tType,C: $tType,A: $tType,F: D > B,G: C > D,H: A > C] :
% 2.85/1.52 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F @ G ) @ H )
% 2.85/1.52 = ( comp @ D @ B @ A @ F @ ( comp @ C @ D @ A @ G @ H ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_68_comp__def,axiom,
% 2.85/1.52 ! [A: $tType,C: $tType,B: $tType] :
% 2.85/1.52 ( ( comp @ B @ C @ A )
% 2.85/1.52 = ( ^ [F2: B > C,G2: A > B,X: A] : ( F2 @ ( G2 @ X ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_69_Inr__inject,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,X5: B,Y: B] :
% 2.85/1.52 ( ( ( sum_Inr @ B @ A @ X5 )
% 2.85/1.52 = ( sum_Inr @ B @ A @ Y ) )
% 2.85/1.52 => ( X5 = Y ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_70_dtree__cong,axiom,
% 2.85/1.52 ! [Tr: dtree,Tr2: dtree] :
% 2.85/1.52 ( ( ( root @ Tr )
% 2.85/1.52 = ( root @ Tr2 ) )
% 2.85/1.52 => ( ( ( cont @ Tr )
% 2.85/1.52 = ( cont @ Tr2 ) )
% 2.85/1.52 => ( Tr = Tr2 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_71_old_Osum_Osimps_I8_J,axiom,
% 2.85/1.52 ! [A: $tType,T: $tType,B: $tType,F1: A > T,F22: B > T,B2: B] :
% 2.85/1.52 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inr @ B @ A @ B2 ) )
% 2.85/1.52 = ( F22 @ B2 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_72_root__H,axiom,
% 2.85/1.52 ! [Tr0: dtree,N: n] :
% 2.85/1.52 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 2.85/1.52 => ( ( root @ ( gram_L1451583624elle_H @ Tr0 @ N ) )
% 2.85/1.52 = N ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_73_Node__root__cont,axiom,
% 2.85/1.52 ! [Tr: dtree] :
% 2.85/1.52 ( ( node @ ( root @ Tr ) @ ( cont @ Tr ) )
% 2.85/1.52 = Tr ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_74_wf__H,axiom,
% 2.85/1.52 ! [Tr0: dtree,N: n] :
% 2.85/1.52 ( ( gram_L864798063lle_wf @ Tr0 )
% 2.85/1.52 => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 2.85/1.52 => ( gram_L864798063lle_wf @ ( gram_L1451583624elle_H @ Tr0 @ N ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_75_subtr__H,axiom,
% 2.85/1.52 ! [Tr0: dtree,N: n,Tr1: dtree] :
% 2.85/1.52 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N )
% 2.85/1.52 => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr1 @ ( gram_L1451583624elle_H @ Tr0 @ N ) )
% 2.85/1.52 => ? [N1: n] :
% 2.85/1.52 ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ Tr0 @ N1 )
% 2.85/1.52 & ( Tr1
% 2.85/1.52 = ( gram_L1451583624elle_H @ Tr0 @ N1 ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_76_inFr2__Ind,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 2.85/1.52 ( ( gram_L805317441_inFr2 @ Ns @ Tr1 @ T2 )
% 2.85/1.52 => ( ( member @ n @ ( root @ Tr ) @ Ns )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 2.85/1.52 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_77_reg__def,axiom,
% 2.85/1.52 ( gram_L1918716148le_reg
% 2.85/1.52 = ( ^ [F2: n > dtree,Tr4: dtree] :
% 2.85/1.52 ! [Tr7: dtree] :
% 2.85/1.52 ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ Tr7 @ Tr4 )
% 2.85/1.52 => ( Tr7
% 2.85/1.52 = ( F2 @ ( root @ Tr7 ) ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_78_top1I,axiom,
% 2.85/1.52 ! [A: $tType,X5: A] : ( top_top @ ( A > $o ) @ X5 ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_79_root__Node,axiom,
% 2.85/1.52 ! [N: n,As: set @ ( sum_sum @ t @ dtree )] :
% 2.85/1.52 ( ( root @ ( node @ N @ As ) )
% 2.85/1.52 = N ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_80_rcut__eq,axiom,
% 2.85/1.52 ! [Tr0: dtree] :
% 2.85/1.52 ( ( ( gram_L1828378864e_rcut @ Tr0 )
% 2.85/1.52 = Tr0 )
% 2.85/1.52 = ( gram_L1918716148le_reg @ ( gram_L1451583624elle_H @ Tr0 ) @ Tr0 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_81_rcut__reg,axiom,
% 2.85/1.52 ! [Tr0: dtree] :
% 2.85/1.52 ( ( gram_L1918716148le_reg @ ( gram_L1451583624elle_H @ Tr0 ) @ Tr0 )
% 2.85/1.52 => ( ( gram_L1828378864e_rcut @ Tr0 )
% 2.85/1.52 = Tr0 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_82_reg__rcut,axiom,
% 2.85/1.52 ! [Tr0: dtree] : ( gram_L1918716148le_reg @ ( gram_L1451583624elle_H @ Tr0 ) @ ( gram_L1828378864e_rcut @ Tr0 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_83_reg__root,axiom,
% 2.85/1.52 ! [F: n > dtree,Tr: dtree] :
% 2.85/1.52 ( ( gram_L1918716148le_reg @ F @ Tr )
% 2.85/1.52 => ( ( F @ ( root @ Tr ) )
% 2.85/1.52 = Tr ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_84_reg__subtr,axiom,
% 2.85/1.52 ! [F: n > dtree,Tr: dtree,Ns: set @ n,Tr2: dtree] :
% 2.85/1.52 ( ( gram_L1918716148le_reg @ F @ Tr )
% 2.85/1.52 => ( ( gram_L716654942_subtr @ Ns @ Tr2 @ Tr )
% 2.85/1.52 => ( gram_L1918716148le_reg @ F @ Tr2 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_85_inFr2__root__in,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 2.85/1.52 ( ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 )
% 2.85/1.52 => ( member @ n @ ( root @ Tr ) @ Ns ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_86_inFr__inFr2,axiom,
% 2.85/1.52 gram_L1333338417e_inFr = gram_L805317441_inFr2 ).
% 2.85/1.52
% 2.85/1.52 thf(fact_87_reg__deftr,axiom,
% 2.85/1.52 ! [N: n] : ( gram_L1918716148le_reg @ gram_L1231612515_deftr @ ( gram_L1231612515_deftr @ N ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_88_reg__Inr__cont,axiom,
% 2.85/1.52 ! [F: n > dtree,Tr: dtree,Tr2: dtree] :
% 2.85/1.52 ( ( gram_L1918716148le_reg @ F @ Tr )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr2 ) @ ( cont @ Tr ) )
% 2.85/1.52 => ( gram_L1918716148le_reg @ F @ Tr2 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_89_reg__def2,axiom,
% 2.85/1.52 ( gram_L1918716148le_reg
% 2.85/1.52 = ( ^ [F2: n > dtree,Tr4: dtree] :
% 2.85/1.52 ! [Ns2: set @ n,Tr7: dtree] :
% 2.85/1.52 ( ( gram_L716654942_subtr @ Ns2 @ Tr7 @ Tr4 )
% 2.85/1.52 => ( Tr7
% 2.85/1.52 = ( F2 @ ( root @ Tr7 ) ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_90_root__H__pick,axiom,
% 2.85/1.52 ! [Tr0: dtree,N: n] :
% 2.85/1.52 ( ( root @ ( gram_L1451583624elle_H @ Tr0 @ N ) )
% 2.85/1.52 = ( root @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_91_rcut__def,axiom,
% 2.85/1.52 ( gram_L1828378864e_rcut
% 2.85/1.52 = ( ^ [Tr02: dtree] : ( gram_L1451583624elle_H @ Tr02 @ ( root @ Tr02 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_92_H__def,axiom,
% 2.85/1.52 ( gram_L1451583624elle_H
% 2.85/1.52 = ( ^ [Tr02: dtree] : ( unfold @ n @ ( gram_L1221482026le_H_r @ Tr02 ) @ ( gram_L1221482011le_H_c @ Tr02 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_93_top__empty__eq,axiom,
% 2.85/1.52 ! [A: $tType] :
% 2.85/1.52 ( ( top_top @ ( A > $o ) )
% 2.85/1.52 = ( ^ [X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_94_regular__def2,axiom,
% 2.85/1.52 ( gram_L646766332egular
% 2.85/1.52 = ( ^ [Tr4: dtree] :
% 2.85/1.52 ? [F2: n > dtree] :
% 2.85/1.52 ( ( gram_L1918716148le_reg @ F2 @ Tr4 )
% 2.85/1.52 & ! [N2: n] :
% 2.85/1.52 ( ( root @ ( F2 @ N2 ) )
% 2.85/1.52 = N2 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_95_top__conj_I2_J,axiom,
% 2.85/1.52 ! [A: $tType,P: $o,X5: A] :
% 2.85/1.52 ( ( P
% 2.85/1.52 & ( top_top @ ( A > $o ) @ X5 ) )
% 2.85/1.52 = P ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_96_top__conj_I1_J,axiom,
% 2.85/1.52 ! [A: $tType,X5: A,P: $o] :
% 2.85/1.52 ( ( ( top_top @ ( A > $o ) @ X5 )
% 2.85/1.52 & P )
% 2.85/1.52 = P ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_97_inFr2_OInd,axiom,
% 2.85/1.52 ! [Tr1: dtree,Tr: dtree,Ns1: set @ n,T2: t] :
% 2.85/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 2.85/1.52 => ( ( gram_L805317441_inFr2 @ Ns1 @ Tr1 @ T2 )
% 2.85/1.52 => ( gram_L805317441_inFr2 @ ( insert @ n @ ( root @ Tr ) @ Ns1 ) @ Tr @ T2 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_98_insertCI,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,B4: set @ A,B2: A] :
% 2.85/1.52 ( ( ~ ( member @ A @ A4 @ B4 )
% 2.85/1.52 => ( A4 = B2 ) )
% 2.85/1.52 => ( member @ A @ A4 @ ( insert @ A @ B2 @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_99_insert__iff,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,B2: A,A5: set @ A] :
% 2.85/1.52 ( ( member @ A @ A4 @ ( insert @ A @ B2 @ A5 ) )
% 2.85/1.52 = ( ( A4 = B2 )
% 2.85/1.52 | ( member @ A @ A4 @ A5 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_100_insert__absorb2,axiom,
% 2.85/1.52 ! [A: $tType,X5: A,A5: set @ A] :
% 2.85/1.52 ( ( insert @ A @ X5 @ ( insert @ A @ X5 @ A5 ) )
% 2.85/1.52 = ( insert @ A @ X5 @ A5 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_101_insertE,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,B2: A,A5: set @ A] :
% 2.85/1.52 ( ( member @ A @ A4 @ ( insert @ A @ B2 @ A5 ) )
% 2.85/1.52 => ( ( A4 != B2 )
% 2.85/1.52 => ( member @ A @ A4 @ A5 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_102_insertI1,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,B4: set @ A] : ( member @ A @ A4 @ ( insert @ A @ A4 @ B4 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_103_insertI2,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,B4: set @ A,B2: A] :
% 2.85/1.52 ( ( member @ A @ A4 @ B4 )
% 2.85/1.52 => ( member @ A @ A4 @ ( insert @ A @ B2 @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_104_Set_Oset__insert,axiom,
% 2.85/1.52 ! [A: $tType,X5: A,A5: set @ A] :
% 2.85/1.52 ( ( member @ A @ X5 @ A5 )
% 2.85/1.52 => ~ ! [B5: set @ A] :
% 2.85/1.52 ( ( A5
% 2.85/1.52 = ( insert @ A @ X5 @ B5 ) )
% 2.85/1.52 => ( member @ A @ X5 @ B5 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_105_insert__ident,axiom,
% 2.85/1.52 ! [A: $tType,X5: A,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ~ ( member @ A @ X5 @ A5 )
% 2.85/1.52 => ( ~ ( member @ A @ X5 @ B4 )
% 2.85/1.52 => ( ( ( insert @ A @ X5 @ A5 )
% 2.85/1.52 = ( insert @ A @ X5 @ B4 ) )
% 2.85/1.52 = ( A5 = B4 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_106_insert__absorb,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,A5: set @ A] :
% 2.85/1.52 ( ( member @ A @ A4 @ A5 )
% 2.85/1.52 => ( ( insert @ A @ A4 @ A5 )
% 2.85/1.52 = A5 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_107_insert__eq__iff,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,A5: set @ A,B2: A,B4: set @ A] :
% 2.85/1.52 ( ~ ( member @ A @ A4 @ A5 )
% 2.85/1.52 => ( ~ ( member @ A @ B2 @ B4 )
% 2.85/1.52 => ( ( ( insert @ A @ A4 @ A5 )
% 2.85/1.52 = ( insert @ A @ B2 @ B4 ) )
% 2.85/1.52 = ( ( ( A4 = B2 )
% 2.85/1.52 => ( A5 = B4 ) )
% 2.85/1.52 & ( ( A4 != B2 )
% 2.85/1.52 => ? [C3: set @ A] :
% 2.85/1.52 ( ( A5
% 2.85/1.52 = ( insert @ A @ B2 @ C3 ) )
% 2.85/1.52 & ~ ( member @ A @ B2 @ C3 )
% 2.85/1.52 & ( B4
% 2.85/1.52 = ( insert @ A @ A4 @ C3 ) )
% 2.85/1.52 & ~ ( member @ A @ A4 @ C3 ) ) ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_108_insert__commute,axiom,
% 2.85/1.52 ! [A: $tType,X5: A,Y: A,A5: set @ A] :
% 2.85/1.52 ( ( insert @ A @ X5 @ ( insert @ A @ Y @ A5 ) )
% 2.85/1.52 = ( insert @ A @ Y @ ( insert @ A @ X5 @ A5 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_109_mk__disjoint__insert,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,A5: set @ A] :
% 2.85/1.52 ( ( member @ A @ A4 @ A5 )
% 2.85/1.52 => ? [B5: set @ A] :
% 2.85/1.52 ( ( A5
% 2.85/1.52 = ( insert @ A @ A4 @ B5 ) )
% 2.85/1.52 & ~ ( member @ A @ A4 @ B5 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_110_insert__UNIV,axiom,
% 2.85/1.52 ! [A: $tType,X5: A] :
% 2.85/1.52 ( ( insert @ A @ X5 @ ( top_top @ ( set @ A ) ) )
% 2.85/1.52 = ( top_top @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_111_regular__subtr,axiom,
% 2.85/1.52 ! [Tr: dtree,Ns: set @ n,Tr2: dtree] :
% 2.85/1.52 ( ( gram_L646766332egular @ Tr )
% 2.85/1.52 => ( ( gram_L716654942_subtr @ Ns @ Tr2 @ Tr )
% 2.85/1.52 => ( gram_L646766332egular @ Tr2 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_112_regular__def,axiom,
% 2.85/1.52 ( gram_L646766332egular
% 2.85/1.52 = ( ^ [Tr4: dtree] :
% 2.85/1.52 ? [F2: n > dtree] : ( gram_L1918716148le_reg @ F2 @ Tr4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_113_regular__rcut,axiom,
% 2.85/1.52 ! [Tr0: dtree] : ( gram_L646766332egular @ ( gram_L1828378864e_rcut @ Tr0 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_114_rewriteR__comp__comp2,axiom,
% 2.85/1.52 ! [C: $tType,B: $tType,E: $tType,D: $tType,A: $tType,G: C > B,H: A > C,R1: D > B,R2: A > D,F: B > E,L: D > E] :
% 2.85/1.52 ( ( ( comp @ C @ B @ A @ G @ H )
% 2.85/1.52 = ( comp @ D @ B @ A @ R1 @ R2 ) )
% 2.85/1.52 => ( ( ( comp @ B @ E @ D @ F @ R1 )
% 2.85/1.52 = L )
% 2.85/1.52 => ( ( comp @ C @ E @ A @ ( comp @ B @ E @ C @ F @ G ) @ H )
% 2.85/1.52 = ( comp @ D @ E @ A @ L @ R2 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_115_rewriteL__comp__comp2,axiom,
% 2.85/1.52 ! [A: $tType,C: $tType,B: $tType,D: $tType,E: $tType,F: C > B,G: A > C,L1: D > B,L2: A > D,H: E > A,R: E > D] :
% 2.85/1.52 ( ( ( comp @ C @ B @ A @ F @ G )
% 2.85/1.52 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 2.85/1.52 => ( ( ( comp @ A @ D @ E @ L2 @ H )
% 2.85/1.52 = R )
% 2.85/1.52 => ( ( comp @ C @ B @ E @ F @ ( comp @ A @ C @ E @ G @ H ) )
% 2.85/1.52 = ( comp @ D @ B @ E @ L1 @ R ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_116_rewriteR__comp__comp,axiom,
% 2.85/1.52 ! [C: $tType,D: $tType,B: $tType,A: $tType,G: C > B,H: A > C,R: A > B,F: B > D] :
% 2.85/1.52 ( ( ( comp @ C @ B @ A @ G @ H )
% 2.85/1.52 = R )
% 2.85/1.52 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F @ G ) @ H )
% 2.85/1.52 = ( comp @ B @ D @ A @ F @ R ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_117_rewriteL__comp__comp,axiom,
% 2.85/1.52 ! [C: $tType,B: $tType,A: $tType,D: $tType,F: C > B,G: A > C,L: A > B,H: D > A] :
% 2.85/1.52 ( ( ( comp @ C @ B @ A @ F @ G )
% 2.85/1.52 = L )
% 2.85/1.52 => ( ( comp @ C @ B @ D @ F @ ( comp @ A @ C @ D @ G @ H ) )
% 2.85/1.52 = ( comp @ A @ B @ D @ L @ H ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_118_inFr__Ind__minus,axiom,
% 2.85/1.52 ! [Ns1: set @ n,Tr1: dtree,T2: t,Tr: dtree] :
% 2.85/1.52 ( ( gram_L1333338417e_inFr @ Ns1 @ Tr1 @ T2 )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr ) )
% 2.85/1.52 => ( gram_L1333338417e_inFr @ ( insert @ n @ ( root @ Tr ) @ Ns1 ) @ Tr @ T2 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_119_inFr2_Oinducts,axiom,
% 2.85/1.52 ! [X1: set @ n,X2: dtree,X3: t,P: ( set @ n ) > dtree > t > $o] :
% 2.85/1.52 ( ( gram_L805317441_inFr2 @ X1 @ X2 @ X3 )
% 2.85/1.52 => ( ! [Tr6: dtree,Ns3: set @ n,T4: t] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr6 ) @ Ns3 )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr6 ) )
% 2.85/1.52 => ( P @ Ns3 @ Tr6 @ T4 ) ) )
% 2.85/1.52 => ( ! [Tr12: dtree,Tr6: dtree,Ns12: set @ n,T4: t] :
% 2.85/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr6 ) )
% 2.85/1.52 => ( ( gram_L805317441_inFr2 @ Ns12 @ Tr12 @ T4 )
% 2.85/1.52 => ( ( P @ Ns12 @ Tr12 @ T4 )
% 2.85/1.52 => ( P @ ( insert @ n @ ( root @ Tr6 ) @ Ns12 ) @ Tr6 @ T4 ) ) ) )
% 2.85/1.52 => ( P @ X1 @ X2 @ X3 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_120_inFr2_Osimps,axiom,
% 2.85/1.52 ( gram_L805317441_inFr2
% 2.85/1.52 = ( ^ [A12: set @ n,A22: dtree,A32: t] :
% 2.85/1.52 ( ? [Tr4: dtree,Ns2: set @ n,T3: t] :
% 2.85/1.52 ( ( A12 = Ns2 )
% 2.85/1.52 & ( A22 = Tr4 )
% 2.85/1.52 & ( A32 = T3 )
% 2.85/1.52 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 2.85/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr4 ) ) )
% 2.85/1.52 | ? [Tr13: dtree,Tr4: dtree,Ns13: set @ n,T3: t] :
% 2.85/1.52 ( ( A12
% 2.85/1.52 = ( insert @ n @ ( root @ Tr4 ) @ Ns13 ) )
% 2.85/1.52 & ( A22 = Tr4 )
% 2.85/1.52 & ( A32 = T3 )
% 2.85/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr4 ) )
% 2.85/1.52 & ( gram_L805317441_inFr2 @ Ns13 @ Tr13 @ T3 ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_121_inFr2_Ocases,axiom,
% 2.85/1.52 ! [A1: set @ n,A2: dtree,A3: t] :
% 2.85/1.52 ( ( gram_L805317441_inFr2 @ A1 @ A2 @ A3 )
% 2.85/1.52 => ( ( ( member @ n @ ( root @ A2 ) @ A1 )
% 2.85/1.52 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A3 ) @ ( cont @ A2 ) ) )
% 2.85/1.52 => ~ ! [Tr12: dtree,Tr6: dtree,Ns12: set @ n] :
% 2.85/1.52 ( ( A1
% 2.85/1.52 = ( insert @ n @ ( root @ Tr6 ) @ Ns12 ) )
% 2.85/1.52 => ( ( A2 = Tr6 )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr6 ) )
% 2.85/1.52 => ~ ( gram_L805317441_inFr2 @ Ns12 @ Tr12 @ A3 ) ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_122_subtr2_Oinducts,axiom,
% 2.85/1.52 ! [X1: set @ n,X2: dtree,X3: dtree,P: ( set @ n ) > dtree > dtree > $o] :
% 2.85/1.52 ( ( gram_L1283001940subtr2 @ X1 @ X2 @ X3 )
% 2.85/1.52 => ( ! [Tr6: dtree,Ns3: set @ n] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr6 ) @ Ns3 )
% 2.85/1.52 => ( P @ Ns3 @ Tr6 @ Tr6 ) )
% 2.85/1.52 => ( ! [Tr12: dtree,Ns3: set @ n,Tr23: dtree,Tr33: dtree] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr12 ) @ Ns3 )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr23 ) )
% 2.85/1.52 => ( ( gram_L1283001940subtr2 @ Ns3 @ Tr23 @ Tr33 )
% 2.85/1.52 => ( ( P @ Ns3 @ Tr23 @ Tr33 )
% 2.85/1.52 => ( P @ Ns3 @ Tr12 @ Tr33 ) ) ) ) )
% 2.85/1.52 => ( P @ X1 @ X2 @ X3 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_123_subtr2__StepR,axiom,
% 2.85/1.52 ! [Tr3: dtree,Ns: set @ n,Tr22: dtree,Tr1: dtree] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr3 ) @ Ns )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr22 ) @ ( cont @ Tr3 ) )
% 2.85/1.52 => ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 2.85/1.52 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_124_old_Osum_Oinject_I1_J,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType,A4: A,A6: A] :
% 2.85/1.52 ( ( ( sum_Inl @ A @ B @ A4 )
% 2.85/1.52 = ( sum_Inl @ A @ B @ A6 ) )
% 2.85/1.52 = ( A4 = A6 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_125_sum_Oinject_I1_J,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType,X1: A,Y1: A] :
% 2.85/1.52 ( ( ( sum_Inl @ A @ B @ X1 )
% 2.85/1.52 = ( sum_Inl @ A @ B @ Y1 ) )
% 2.85/1.52 = ( X1 = Y1 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_126_Inr__Inl__False,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType,X5: B,Y: A] :
% 2.85/1.52 ( ( sum_Inr @ B @ A @ X5 )
% 2.85/1.52 != ( sum_Inl @ A @ B @ Y ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_127_Inl__Inr__False,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,X5: A,Y: B] :
% 2.85/1.52 ( ( sum_Inl @ A @ B @ X5 )
% 2.85/1.52 != ( sum_Inr @ B @ A @ Y ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_128_old_Osum_Osimps_I7_J,axiom,
% 2.85/1.52 ! [B: $tType,T: $tType,A: $tType,F1: A > T,F22: B > T,A4: A] :
% 2.85/1.52 ( ( sum_rec_sum @ A @ T @ B @ F1 @ F22 @ ( sum_Inl @ A @ B @ A4 ) )
% 2.85/1.52 = ( F1 @ A4 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_129_obj__sumE__f,axiom,
% 2.85/1.52 ! [A: $tType,C: $tType,B: $tType,S: B,F: ( sum_sum @ A @ C ) > B,P: $o] :
% 2.85/1.52 ( ! [X4: A] :
% 2.85/1.52 ( ( S
% 2.85/1.52 = ( F @ ( sum_Inl @ A @ C @ X4 ) ) )
% 2.85/1.52 => P )
% 2.85/1.52 => ( ! [X4: C] :
% 2.85/1.52 ( ( S
% 2.85/1.52 = ( F @ ( sum_Inr @ C @ A @ X4 ) ) )
% 2.85/1.52 => P )
% 2.85/1.52 => ! [X6: sum_sum @ A @ C] :
% 2.85/1.52 ( ( S
% 2.85/1.52 = ( F @ X6 ) )
% 2.85/1.52 => P ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_130_old_Osum_Oinducts,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType,P: ( sum_sum @ A @ B ) > $o,Sum: sum_sum @ A @ B] :
% 2.85/1.52 ( ! [A7: A] : ( P @ ( sum_Inl @ A @ B @ A7 ) )
% 2.85/1.52 => ( ! [B6: B] : ( P @ ( sum_Inr @ B @ A @ B6 ) )
% 2.85/1.52 => ( P @ Sum ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_131_old_Osum_Oexhaust,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,Y: sum_sum @ A @ B] :
% 2.85/1.52 ( ! [A7: A] :
% 2.85/1.52 ( Y
% 2.85/1.52 != ( sum_Inl @ A @ B @ A7 ) )
% 2.85/1.52 => ~ ! [B6: B] :
% 2.85/1.52 ( Y
% 2.85/1.52 != ( sum_Inr @ B @ A @ B6 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_132_split__sum__all,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType] :
% 2.85/1.52 ( ( ^ [P2: ( sum_sum @ A @ B ) > $o] :
% 2.85/1.52 ! [X7: sum_sum @ A @ B] : ( P2 @ X7 ) )
% 2.85/1.52 = ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 2.85/1.52 ( ! [X: A] : ( P3 @ ( sum_Inl @ A @ B @ X ) )
% 2.85/1.52 & ! [X: B] : ( P3 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_133_split__sum__ex,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType] :
% 2.85/1.52 ( ( ^ [P2: ( sum_sum @ A @ B ) > $o] :
% 2.85/1.52 ? [X7: sum_sum @ A @ B] : ( P2 @ X7 ) )
% 2.85/1.52 = ( ^ [P3: ( sum_sum @ A @ B ) > $o] :
% 2.85/1.52 ( ? [X: A] : ( P3 @ ( sum_Inl @ A @ B @ X ) )
% 2.85/1.52 | ? [X: B] : ( P3 @ ( sum_Inr @ B @ A @ X ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_134_Inr__not__Inl,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType,B2: B,A4: A] :
% 2.85/1.52 ( ( sum_Inr @ B @ A @ B2 )
% 2.85/1.52 != ( sum_Inl @ A @ B @ A4 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_135_sumE,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 2.85/1.52 ( ! [X4: A] :
% 2.85/1.52 ( S
% 2.85/1.52 != ( sum_Inl @ A @ B @ X4 ) )
% 2.85/1.52 => ~ ! [Y3: B] :
% 2.85/1.52 ( S
% 2.85/1.52 != ( sum_Inr @ B @ A @ Y3 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_136_old_Osum_Odistinct_I1_J,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,A4: A,B3: B] :
% 2.85/1.52 ( ( sum_Inl @ A @ B @ A4 )
% 2.85/1.52 != ( sum_Inr @ B @ A @ B3 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_137_old_Osum_Odistinct_I2_J,axiom,
% 2.85/1.52 ! [B7: $tType,A8: $tType,B8: B7,A9: A8] :
% 2.85/1.52 ( ( sum_Inr @ B7 @ A8 @ B8 )
% 2.85/1.52 != ( sum_Inl @ A8 @ B7 @ A9 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_138_sum_Odistinct_I1_J,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,X1: A,X2: B] :
% 2.85/1.52 ( ( sum_Inl @ A @ B @ X1 )
% 2.85/1.52 != ( sum_Inr @ B @ A @ X2 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_139_Inl__inject,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType,X5: A,Y: A] :
% 2.85/1.52 ( ( ( sum_Inl @ A @ B @ X5 )
% 2.85/1.52 = ( sum_Inl @ A @ B @ Y ) )
% 2.85/1.52 => ( X5 = Y ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_140_subtr2__trans,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree,Tr3: dtree] :
% 2.85/1.52 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 2.85/1.52 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr3 )
% 2.85/1.52 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_141_subtr2_ORefl,axiom,
% 2.85/1.52 ! [Tr: dtree,Ns: set @ n] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 2.85/1.52 => ( gram_L1283001940subtr2 @ Ns @ Tr @ Tr ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_142_subtr2__rootL__in,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 2.85/1.52 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 2.85/1.52 => ( member @ n @ ( root @ Tr1 ) @ Ns ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_143_subtr2__rootR__in,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr1: dtree,Tr22: dtree] :
% 2.85/1.52 ( ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr22 )
% 2.85/1.52 => ( member @ n @ ( root @ Tr22 ) @ Ns ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_144_subtr__subtr2,axiom,
% 2.85/1.52 gram_L716654942_subtr = gram_L1283001940subtr2 ).
% 2.85/1.52
% 2.85/1.52 thf(fact_145_inFr_OBase,axiom,
% 2.85/1.52 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 2.85/1.52 => ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_146_inFr__subtr,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr: dtree,T2: t] :
% 2.85/1.52 ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 2.85/1.52 => ? [Tr5: dtree] :
% 2.85/1.52 ( ( gram_L716654942_subtr @ Ns @ Tr5 @ Tr )
% 2.85/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr5 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_147_inFr2_OBase,axiom,
% 2.85/1.52 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr ) @ Ns )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T2 ) @ ( cont @ Tr ) )
% 2.85/1.52 => ( gram_L805317441_inFr2 @ Ns @ Tr @ T2 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_148_inFr_Ocases,axiom,
% 2.85/1.52 ! [A1: set @ n,A2: dtree,A3: t] :
% 2.85/1.52 ( ( gram_L1333338417e_inFr @ A1 @ A2 @ A3 )
% 2.85/1.52 => ( ( ( member @ n @ ( root @ A2 ) @ A1 )
% 2.85/1.52 => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ A3 ) @ ( cont @ A2 ) ) )
% 2.85/1.52 => ~ ( ( member @ n @ ( root @ A2 ) @ A1 )
% 2.85/1.52 => ! [Tr12: dtree] :
% 2.85/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ A2 ) )
% 2.85/1.52 => ~ ( gram_L1333338417e_inFr @ A1 @ Tr12 @ A3 ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_149_inFr_Osimps,axiom,
% 2.85/1.52 ( gram_L1333338417e_inFr
% 2.85/1.52 = ( ^ [A12: set @ n,A22: dtree,A32: t] :
% 2.85/1.52 ( ? [Tr4: dtree,Ns2: set @ n,T3: t] :
% 2.85/1.52 ( ( A12 = Ns2 )
% 2.85/1.52 & ( A22 = Tr4 )
% 2.85/1.52 & ( A32 = T3 )
% 2.85/1.52 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 2.85/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T3 ) @ ( cont @ Tr4 ) ) )
% 2.85/1.52 | ? [Tr4: dtree,Ns2: set @ n,Tr13: dtree,T3: t] :
% 2.85/1.52 ( ( A12 = Ns2 )
% 2.85/1.52 & ( A22 = Tr4 )
% 2.85/1.52 & ( A32 = T3 )
% 2.85/1.52 & ( member @ n @ ( root @ Tr4 ) @ Ns2 )
% 2.85/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr4 ) )
% 2.85/1.52 & ( gram_L1333338417e_inFr @ Ns2 @ Tr13 @ T3 ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_150_inFr_Oinducts,axiom,
% 2.85/1.52 ! [X1: set @ n,X2: dtree,X3: t,P: ( set @ n ) > dtree > t > $o] :
% 2.85/1.52 ( ( gram_L1333338417e_inFr @ X1 @ X2 @ X3 )
% 2.85/1.52 => ( ! [Tr6: dtree,Ns3: set @ n,T4: t] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr6 ) @ Ns3 )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ T4 ) @ ( cont @ Tr6 ) )
% 2.85/1.52 => ( P @ Ns3 @ Tr6 @ T4 ) ) )
% 2.85/1.52 => ( ! [Tr6: dtree,Ns3: set @ n,Tr12: dtree,T4: t] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr6 ) @ Ns3 )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr12 ) @ ( cont @ Tr6 ) )
% 2.85/1.52 => ( ( gram_L1333338417e_inFr @ Ns3 @ Tr12 @ T4 )
% 2.85/1.52 => ( ( P @ Ns3 @ Tr12 @ T4 )
% 2.85/1.52 => ( P @ Ns3 @ Tr6 @ T4 ) ) ) ) )
% 2.85/1.52 => ( P @ X1 @ X2 @ X3 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_151_subtr2_OStep,axiom,
% 2.85/1.52 ! [Tr1: dtree,Ns: set @ n,Tr22: dtree,Tr3: dtree] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr1 ) @ Ns )
% 2.85/1.52 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr1 ) @ ( cont @ Tr22 ) )
% 2.85/1.52 => ( ( gram_L1283001940subtr2 @ Ns @ Tr22 @ Tr3 )
% 2.85/1.52 => ( gram_L1283001940subtr2 @ Ns @ Tr1 @ Tr3 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_152_subtr2_Ocases,axiom,
% 2.85/1.52 ! [A1: set @ n,A2: dtree,A3: dtree] :
% 2.85/1.52 ( ( gram_L1283001940subtr2 @ A1 @ A2 @ A3 )
% 2.85/1.52 => ( ( ( A3 = A2 )
% 2.85/1.52 => ~ ( member @ n @ ( root @ A2 ) @ A1 ) )
% 2.85/1.52 => ~ ( ( member @ n @ ( root @ A2 ) @ A1 )
% 2.85/1.52 => ! [Tr23: dtree] :
% 2.85/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A2 ) @ ( cont @ Tr23 ) )
% 2.85/1.52 => ~ ( gram_L1283001940subtr2 @ A1 @ Tr23 @ A3 ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_153_subtr2_Osimps,axiom,
% 2.85/1.52 ( gram_L1283001940subtr2
% 2.85/1.52 = ( ^ [A12: set @ n,A22: dtree,A32: dtree] :
% 2.85/1.52 ( ? [Tr4: dtree,Ns2: set @ n] :
% 2.85/1.52 ( ( A12 = Ns2 )
% 2.85/1.52 & ( A22 = Tr4 )
% 2.85/1.52 & ( A32 = Tr4 )
% 2.85/1.52 & ( member @ n @ ( root @ Tr4 ) @ Ns2 ) )
% 2.85/1.52 | ? [Tr13: dtree,Ns2: set @ n,Tr24: dtree,Tr32: dtree] :
% 2.85/1.52 ( ( A12 = Ns2 )
% 2.85/1.52 & ( A22 = Tr13 )
% 2.85/1.52 & ( A32 = Tr32 )
% 2.85/1.52 & ( member @ n @ ( root @ Tr13 ) @ Ns2 )
% 2.85/1.52 & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr13 ) @ ( cont @ Tr24 ) )
% 2.85/1.52 & ( gram_L1283001940subtr2 @ Ns2 @ Tr24 @ Tr32 ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_154_obj__sumE,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,S: sum_sum @ A @ B] :
% 2.85/1.52 ( ! [X4: A] :
% 2.85/1.52 ( S
% 2.85/1.52 != ( sum_Inl @ A @ B @ X4 ) )
% 2.85/1.52 => ~ ! [X4: B] :
% 2.85/1.52 ( S
% 2.85/1.52 != ( sum_Inr @ B @ A @ X4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_155_Inl__cont__H,axiom,
% 2.85/1.52 ! [Tr0: dtree,N: n] :
% 2.85/1.52 ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1451583624elle_H @ Tr0 @ N ) ) )
% 2.85/1.52 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L315592705e_pick @ Tr0 @ N ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_156_Inl__cont__hsubst__eq,axiom,
% 2.85/1.52 ! [Tr: dtree,Tr0: dtree] :
% 2.85/1.52 ( ( ( root @ Tr )
% 2.85/1.52 = ( root @ Tr0 ) )
% 2.85/1.52 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 2.85/1.52 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_157_Inl__cont__hsubst__neq,axiom,
% 2.85/1.52 ! [Tr: dtree,Tr0: dtree] :
% 2.85/1.52 ( ( ( root @ Tr )
% 2.85/1.52 != ( root @ Tr0 ) )
% 2.85/1.52 => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) ) )
% 2.85/1.52 = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_158_vimageI,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType,F: B > A,A4: B,B2: A,B4: set @ A] :
% 2.85/1.52 ( ( ( F @ A4 )
% 2.85/1.52 = B2 )
% 2.85/1.52 => ( ( member @ A @ B2 @ B4 )
% 2.85/1.52 => ( member @ B @ A4 @ ( vimage @ B @ A @ F @ B4 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_159_vimage__eq,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,A4: A,F: A > B,B4: set @ B] :
% 2.85/1.52 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ B4 ) )
% 2.85/1.52 = ( member @ B @ ( F @ A4 ) @ B4 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_160_vimage__UNIV,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType,F: A > B] :
% 2.85/1.52 ( ( vimage @ A @ B @ F @ ( top_top @ ( set @ B ) ) )
% 2.85/1.52 = ( top_top @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_161_vimageD,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,A4: A,F: A > B,A5: set @ B] :
% 2.85/1.52 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ A5 ) )
% 2.85/1.52 => ( member @ B @ ( F @ A4 ) @ A5 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_162_vimageE,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,A4: A,F: A > B,B4: set @ B] :
% 2.85/1.52 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ B4 ) )
% 2.85/1.52 => ( member @ B @ ( F @ A4 ) @ B4 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_163_vimageI2,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType,F: B > A,A4: B,A5: set @ A] :
% 2.85/1.52 ( ( member @ A @ ( F @ A4 ) @ A5 )
% 2.85/1.52 => ( member @ B @ A4 @ ( vimage @ B @ A @ F @ A5 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_164_vimage__Collect,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType,P: B > $o,F: A > B,Q: A > $o] :
% 2.85/1.52 ( ! [X4: A] :
% 2.85/1.52 ( ( P @ ( F @ X4 ) )
% 2.85/1.52 = ( Q @ X4 ) )
% 2.85/1.52 => ( ( vimage @ A @ B @ F @ ( collect @ B @ P ) )
% 2.85/1.52 = ( collect @ A @ Q ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_165_set_Ocomp,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,C: $tType,F: C > B,G: B > A] :
% 2.85/1.52 ( ( comp @ ( set @ B ) @ ( set @ C ) @ ( set @ A ) @ ( vimage @ C @ B @ F ) @ ( vimage @ B @ A @ G ) )
% 2.85/1.52 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_166_vimage__comp,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,C: $tType,F: A > B,G: B > C,X5: set @ C] :
% 2.85/1.52 ( ( vimage @ A @ B @ F @ ( vimage @ B @ C @ G @ X5 ) )
% 2.85/1.52 = ( vimage @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ X5 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_167_set_Ocompositionality,axiom,
% 2.85/1.52 ! [C: $tType,B: $tType,A: $tType,F: C > B,G: B > A,Set: set @ A] :
% 2.85/1.52 ( ( vimage @ C @ B @ F @ ( vimage @ B @ A @ G @ Set ) )
% 2.85/1.52 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ Set ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_168_not__arg__cong__Inr,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType,X5: A,Y: A] :
% 2.85/1.52 ( ( X5 != Y )
% 2.85/1.52 => ( ( sum_Inr @ A @ B @ X5 )
% 2.85/1.52 != ( sum_Inr @ A @ B @ Y ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_169_Inl__Inr__image__cong,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType,A5: set @ ( sum_sum @ A @ B ),B4: set @ ( sum_sum @ A @ B )] :
% 2.85/1.52 ( ( ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ A5 )
% 2.85/1.52 = ( vimage @ A @ ( sum_sum @ A @ B ) @ ( sum_Inl @ A @ B ) @ B4 ) )
% 2.85/1.52 => ( ( ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ A5 )
% 2.85/1.52 = ( vimage @ B @ ( sum_sum @ A @ B ) @ ( sum_Inr @ B @ A ) @ B4 ) )
% 2.85/1.52 => ( A5 = B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_170_inFr__self__hsubst,axiom,
% 2.85/1.52 ! [Tr0: dtree,Ns: set @ n,T2: t] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr0 ) @ Ns )
% 2.85/1.52 => ( ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr0 ) @ T2 )
% 2.85/1.52 = ( ( member @ t @ T2 @ ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) )
% 2.85/1.52 | ( gram_L805317505_inFrr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr0 @ T2 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_171_inFr__hsubst__imp,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr0: dtree,Tr: dtree,T2: t] :
% 2.85/1.52 ( ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T2 )
% 2.85/1.52 => ( ( member @ t @ T2 @ ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) )
% 2.85/1.52 | ( gram_L805317505_inFrr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr0 @ T2 )
% 2.85/1.52 | ( gram_L1333338417e_inFr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr @ T2 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_172_bot__apply,axiom,
% 2.85/1.52 ! [C: $tType,D: $tType] :
% 2.85/1.52 ( ( bot @ C @ ( type2 @ C ) )
% 2.85/1.52 => ( ( bot_bot @ ( D > C ) )
% 2.85/1.52 = ( ^ [X: D] : ( bot_bot @ C ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_173_empty__Collect__eq,axiom,
% 2.85/1.52 ! [A: $tType,P: A > $o] :
% 2.85/1.52 ( ( ( bot_bot @ ( set @ A ) )
% 2.85/1.52 = ( collect @ A @ P ) )
% 2.85/1.52 = ( ! [X: A] :
% 2.85/1.52 ~ ( P @ X ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_174_Collect__empty__eq,axiom,
% 2.85/1.52 ! [A: $tType,P: A > $o] :
% 2.85/1.52 ( ( ( collect @ A @ P )
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.52 = ( ! [X: A] :
% 2.85/1.52 ~ ( P @ X ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_175_all__not__in__conv,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A] :
% 2.85/1.52 ( ( ! [X: A] :
% 2.85/1.52 ~ ( member @ A @ X @ A5 ) )
% 2.85/1.52 = ( A5
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_176_empty__iff,axiom,
% 2.85/1.52 ! [A: $tType,C2: A] :
% 2.85/1.52 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_177_Diff__idemp,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) @ B4 )
% 2.85/1.52 = ( minus_minus @ ( set @ A ) @ A5 @ B4 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_178_Diff__iff,axiom,
% 2.85/1.52 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) )
% 2.85/1.52 = ( ( member @ A @ C2 @ A5 )
% 2.85/1.52 & ~ ( member @ A @ C2 @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_179_DiffI,axiom,
% 2.85/1.52 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ( member @ A @ C2 @ A5 )
% 2.85/1.52 => ( ~ ( member @ A @ C2 @ B4 )
% 2.85/1.52 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_180_singletonI,axiom,
% 2.85/1.52 ! [A: $tType,A4: A] : ( member @ A @ A4 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_181_Diff__cancel,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A] :
% 2.85/1.52 ( ( minus_minus @ ( set @ A ) @ A5 @ A5 )
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_182_empty__Diff,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A] :
% 2.85/1.52 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A5 )
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_183_Diff__empty,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A] :
% 2.85/1.52 ( ( minus_minus @ ( set @ A ) @ A5 @ ( bot_bot @ ( set @ A ) ) )
% 2.85/1.52 = A5 ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_184_Diff__insert0,axiom,
% 2.85/1.52 ! [A: $tType,X5: A,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ~ ( member @ A @ X5 @ A5 )
% 2.85/1.52 => ( ( minus_minus @ ( set @ A ) @ A5 @ ( insert @ A @ X5 @ B4 ) )
% 2.85/1.52 = ( minus_minus @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_185_insert__Diff1,axiom,
% 2.85/1.52 ! [A: $tType,X5: A,B4: set @ A,A5: set @ A] :
% 2.85/1.52 ( ( member @ A @ X5 @ B4 )
% 2.85/1.52 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X5 @ A5 ) @ B4 )
% 2.85/1.52 = ( minus_minus @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_186_vimage__empty,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType,F: A > B] :
% 2.85/1.52 ( ( vimage @ A @ B @ F @ ( bot_bot @ ( set @ B ) ) )
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_187_insert__Diff__single,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,A5: set @ A] :
% 2.85/1.52 ( ( insert @ A @ A4 @ ( minus_minus @ ( set @ A ) @ A5 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.85/1.52 = ( insert @ A @ A4 @ A5 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_188_Diff__UNIV,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A] :
% 2.85/1.52 ( ( minus_minus @ ( set @ A ) @ A5 @ ( top_top @ ( set @ A ) ) )
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_189_vimage__Diff,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,F: A > B,A5: set @ B,B4: set @ B] :
% 2.85/1.52 ( ( vimage @ A @ B @ F @ ( minus_minus @ ( set @ B ) @ A5 @ B4 ) )
% 2.85/1.52 = ( minus_minus @ ( set @ A ) @ ( vimage @ A @ B @ F @ A5 ) @ ( vimage @ A @ B @ F @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_190_bot__fun__def,axiom,
% 2.85/1.52 ! [B: $tType,A: $tType] :
% 2.85/1.52 ( ( bot @ B @ ( type2 @ B ) )
% 2.85/1.52 => ( ( bot_bot @ ( A > B ) )
% 2.85/1.52 = ( ^ [X: A] : ( bot_bot @ B ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_191_ex__in__conv,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A] :
% 2.85/1.52 ( ( ? [X: A] : ( member @ A @ X @ A5 ) )
% 2.85/1.52 = ( A5
% 2.85/1.52 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_192_equals0I,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A] :
% 2.85/1.52 ( ! [Y3: A] :
% 2.85/1.52 ~ ( member @ A @ Y3 @ A5 )
% 2.85/1.52 => ( A5
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_193_equals0D,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A,A4: A] :
% 2.85/1.52 ( ( A5
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.52 => ~ ( member @ A @ A4 @ A5 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_194_emptyE,axiom,
% 2.85/1.52 ! [A: $tType,A4: A] :
% 2.85/1.52 ~ ( member @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_195_DiffD2,axiom,
% 2.85/1.52 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) )
% 2.85/1.52 => ~ ( member @ A @ C2 @ B4 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_196_DiffD1,axiom,
% 2.85/1.52 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) )
% 2.85/1.52 => ( member @ A @ C2 @ A5 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_197_DiffE,axiom,
% 2.85/1.52 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) )
% 2.85/1.52 => ~ ( ( member @ A @ C2 @ A5 )
% 2.85/1.52 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_198_empty__not__UNIV,axiom,
% 2.85/1.52 ! [A: $tType] :
% 2.85/1.52 ( ( bot_bot @ ( set @ A ) )
% 2.85/1.52 != ( top_top @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_199_singletonD,axiom,
% 2.85/1.52 ! [A: $tType,B2: A,A4: A] :
% 2.85/1.52 ( ( member @ A @ B2 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.52 => ( B2 = A4 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_200_singleton__iff,axiom,
% 2.85/1.52 ! [A: $tType,B2: A,A4: A] :
% 2.85/1.52 ( ( member @ A @ B2 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.52 = ( B2 = A4 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_201_doubleton__eq__iff,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,B2: A,C2: A,D2: A] :
% 2.85/1.52 ( ( ( insert @ A @ A4 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.52 = ( insert @ A @ C2 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.85/1.52 = ( ( ( A4 = C2 )
% 2.85/1.52 & ( B2 = D2 ) )
% 2.85/1.52 | ( ( A4 = D2 )
% 2.85/1.52 & ( B2 = C2 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_202_insert__not__empty,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,A5: set @ A] :
% 2.85/1.52 ( ( insert @ A @ A4 @ A5 )
% 2.85/1.52 != ( bot_bot @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_203_singleton__inject,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,B2: A] :
% 2.85/1.52 ( ( ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 2.85/1.52 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.52 => ( A4 = B2 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_204_insert__Diff__if,axiom,
% 2.85/1.52 ! [A: $tType,X5: A,B4: set @ A,A5: set @ A] :
% 2.85/1.52 ( ( ( member @ A @ X5 @ B4 )
% 2.85/1.52 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X5 @ A5 ) @ B4 )
% 2.85/1.52 = ( minus_minus @ ( set @ A ) @ A5 @ B4 ) ) )
% 2.85/1.52 & ( ~ ( member @ A @ X5 @ B4 )
% 2.85/1.52 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X5 @ A5 ) @ B4 )
% 2.85/1.52 = ( insert @ A @ X5 @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_205_Diff__insert__absorb,axiom,
% 2.85/1.52 ! [A: $tType,X5: A,A5: set @ A] :
% 2.85/1.52 ( ~ ( member @ A @ X5 @ A5 )
% 2.85/1.52 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X5 @ A5 ) @ ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.52 = A5 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_206_Diff__insert2,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A,A4: A,B4: set @ A] :
% 2.85/1.52 ( ( minus_minus @ ( set @ A ) @ A5 @ ( insert @ A @ A4 @ B4 ) )
% 2.85/1.52 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A5 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) @ B4 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_207_insert__Diff,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,A5: set @ A] :
% 2.85/1.52 ( ( member @ A @ A4 @ A5 )
% 2.85/1.52 => ( ( insert @ A @ A4 @ ( minus_minus @ ( set @ A ) @ A5 @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.85/1.52 = A5 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_208_Diff__insert,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A,A4: A,B4: set @ A] :
% 2.85/1.52 ( ( minus_minus @ ( set @ A ) @ A5 @ ( insert @ A @ A4 @ B4 ) )
% 2.85/1.52 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A5 @ B4 ) @ ( insert @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_209_vimage__singleton__eq,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,A4: A,F: A > B,B2: B] :
% 2.85/1.52 ( ( member @ A @ A4 @ ( vimage @ A @ B @ F @ ( insert @ B @ B2 @ ( bot_bot @ ( set @ B ) ) ) ) )
% 2.85/1.52 = ( ( F @ A4 )
% 2.85/1.52 = B2 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_210_inFr__hsubst__minus,axiom,
% 2.85/1.52 ! [Ns: set @ n,Tr0: dtree,Tr: dtree,T2: t] :
% 2.85/1.52 ( ( gram_L1333338417e_inFr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr @ T2 )
% 2.85/1.52 => ( gram_L1333338417e_inFr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr ) @ T2 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_211_regular__inFr,axiom,
% 2.85/1.52 ! [Tr: dtree,Ns: set @ n,T2: t] :
% 2.85/1.52 ( ( gram_L646766332egular @ Tr )
% 2.85/1.52 => ( ( member @ n @ ( root @ Tr ) @ Ns )
% 2.85/1.52 => ( ( gram_L1333338417e_inFr @ Ns @ Tr @ T2 )
% 2.85/1.52 => ( ( member @ t @ T2 @ ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr ) ) )
% 2.85/1.52 | ? [Tr5: dtree] :
% 2.85/1.52 ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ Tr5 ) @ ( cont @ Tr ) )
% 2.85/1.52 & ( gram_L1333338417e_inFr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr5 @ T2 ) ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_212_is__singletonI,axiom,
% 2.85/1.52 ! [A: $tType,X5: A] : ( is_singleton @ A @ ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_213__092_060open_062_092_060And_062n_H_O_AInr_An_H_A_092_060in_062_Atns_A_092_060Longrightarrow_062_A_092_060exists_062tr_H_O_AK_An_H_A_061_AFr_A_Ins_A_N_A_123n_125_J_Atr_H_A_092_060and_062_Awf_Atr_H_A_092_060and_062_Aroot_Atr_H_A_061_An_H_092_060close_062,axiom,
% 2.85/1.52 ! [N4: n] :
% 2.85/1.52 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N4 ) @ tns )
% 2.85/1.52 => ? [Tr5: dtree] :
% 2.85/1.52 ( ( ( k @ N4 )
% 2.85/1.52 = ( gram_L861583724lle_Fr @ ( minus_minus @ ( set @ n ) @ ns @ ( insert @ n @ n2 @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr5 ) )
% 2.85/1.52 & ( gram_L864798063lle_wf @ Tr5 )
% 2.85/1.52 & ( ( root @ Tr5 )
% 2.85/1.52 = N4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_214__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ftr_O_A_I_092_060And_062n_H_O_AInr_An_H_A_092_060in_062_Atns_A_092_060Longrightarrow_062_AK_An_H_A_061_AFr_A_Ins_A_N_A_123n_125_J_A_Iftr_An_H_J_A_092_060and_062_Awf_A_Iftr_An_H_J_A_092_060and_062_Aroot_A_Iftr_An_H_J_A_061_An_H_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.85/1.52 ~ ! [Ftr: n > dtree] :
% 2.85/1.52 ~ ! [N5: n] :
% 2.85/1.52 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N5 ) @ tns )
% 2.85/1.52 => ( ( ( k @ N5 )
% 2.85/1.52 = ( gram_L861583724lle_Fr @ ( minus_minus @ ( set @ n ) @ ns @ ( insert @ n @ n2 @ ( bot_bot @ ( set @ n ) ) ) ) @ ( Ftr @ N5 ) ) )
% 2.85/1.52 & ( gram_L864798063lle_wf @ ( Ftr @ N5 ) )
% 2.85/1.52 & ( ( root @ ( Ftr @ N5 ) )
% 2.85/1.52 = N5 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_215_bot__empty__eq,axiom,
% 2.85/1.52 ! [A: $tType] :
% 2.85/1.52 ( ( bot_bot @ ( A > $o ) )
% 2.85/1.52 = ( ^ [X: A] : ( member @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_216_bot__set__def,axiom,
% 2.85/1.52 ! [A: $tType] :
% 2.85/1.52 ( ( bot_bot @ ( set @ A ) )
% 2.85/1.52 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_217_not__root__Fr,axiom,
% 2.85/1.52 ! [Tr: dtree,Ns: set @ n] :
% 2.85/1.52 ( ~ ( member @ n @ ( root @ Tr ) @ Ns )
% 2.85/1.52 => ( ( gram_L861583724lle_Fr @ Ns @ Tr )
% 2.85/1.52 = ( bot_bot @ ( set @ t ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_218_is__singletonI_H,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A] :
% 2.85/1.52 ( ( A5
% 2.85/1.52 != ( bot_bot @ ( set @ A ) ) )
% 2.85/1.52 => ( ! [X4: A,Y3: A] :
% 2.85/1.52 ( ( member @ A @ X4 @ A5 )
% 2.85/1.52 => ( ( member @ A @ Y3 @ A5 )
% 2.85/1.52 => ( X4 = Y3 ) ) )
% 2.85/1.52 => ( is_singleton @ A @ A5 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_219_is__singletonE,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A] :
% 2.85/1.52 ( ( is_singleton @ A @ A5 )
% 2.85/1.52 => ~ ! [X4: A] :
% 2.85/1.52 ( A5
% 2.85/1.52 != ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_220_is__singleton__def,axiom,
% 2.85/1.52 ! [A: $tType] :
% 2.85/1.52 ( ( is_singleton @ A )
% 2.85/1.52 = ( ^ [A10: set @ A] :
% 2.85/1.52 ? [X: A] :
% 2.85/1.52 ( A10
% 2.85/1.52 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_221__C0_C,axiom,
% 2.85/1.52 ! [N6: n] :
% 2.85/1.52 ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ N6 ) @ tns )
% 2.85/1.52 => ( ( ( k @ N6 )
% 2.85/1.52 = ( gram_L861583724lle_Fr @ ( minus_minus @ ( set @ n ) @ ns @ ( insert @ n @ n2 @ ( bot_bot @ ( set @ n ) ) ) ) @ ( ftr @ N6 ) ) )
% 2.85/1.52 & ( gram_L864798063lle_wf @ ( ftr @ N6 ) )
% 2.85/1.52 & ( ( root @ ( ftr @ N6 ) )
% 2.85/1.52 = N6 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_222_P,axiom,
% 2.85/1.52 member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ n2 @ tns ) @ gram_L1451583632elle_P ).
% 2.85/1.52
% 2.85/1.52 thf(fact_223_used,axiom,
% 2.85/1.52 ! [N: n] :
% 2.85/1.52 ? [Tns: set @ ( sum_sum @ t @ n )] : ( member @ ( product_prod @ n @ ( set @ ( sum_sum @ t @ n ) ) ) @ ( product_Pair @ n @ ( set @ ( sum_sum @ t @ n ) ) @ N @ Tns ) @ gram_L1451583632elle_P ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_224_Fr__self__hsubst,axiom,
% 2.85/1.52 ! [Tr0: dtree,Ns: set @ n] :
% 2.85/1.52 ( ( member @ n @ ( root @ Tr0 ) @ Ns )
% 2.85/1.52 => ( ( gram_L861583724lle_Fr @ Ns @ ( gram_L1004374585hsubst @ Tr0 @ Tr0 ) )
% 2.85/1.52 = ( sup_sup @ ( set @ t ) @ ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ Tr0 ) ) @ ( gram_L1556062726le_Frr @ ( minus_minus @ ( set @ n ) @ Ns @ ( insert @ n @ ( root @ Tr0 ) @ ( bot_bot @ ( set @ n ) ) ) ) @ Tr0 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_225_L__rec__notin,axiom,
% 2.85/1.52 ! [N: n,Ns: set @ n] :
% 2.85/1.52 ( ~ ( member @ n @ N @ Ns )
% 2.85/1.52 => ( ( gram_L1451583628elle_L @ Ns @ N )
% 2.85/1.52 = ( insert @ ( set @ t ) @ ( bot_bot @ ( set @ t ) ) @ ( bot_bot @ ( set @ ( set @ t ) ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_226_UnCI,axiom,
% 2.85/1.52 ! [A: $tType,C2: A,B4: set @ A,A5: set @ A] :
% 2.85/1.52 ( ( ~ ( member @ A @ C2 @ B4 )
% 2.85/1.52 => ( member @ A @ C2 @ A5 ) )
% 2.85/1.52 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_227_Un__iff,axiom,
% 2.85/1.52 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 2.85/1.52 = ( ( member @ A @ C2 @ A5 )
% 2.85/1.52 | ( member @ A @ C2 @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_228_Un__empty,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ( ( sup_sup @ ( set @ A ) @ A5 @ B4 )
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.52 = ( ( A5
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.52 & ( B4
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_229_Un__insert__right,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A,A4: A,B4: set @ A] :
% 2.85/1.52 ( ( sup_sup @ ( set @ A ) @ A5 @ ( insert @ A @ A4 @ B4 ) )
% 2.85/1.52 = ( insert @ A @ A4 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_230_Un__insert__left,axiom,
% 2.85/1.52 ! [A: $tType,A4: A,B4: set @ A,C4: set @ A] :
% 2.85/1.52 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A4 @ B4 ) @ C4 )
% 2.85/1.52 = ( insert @ A @ A4 @ ( sup_sup @ ( set @ A ) @ B4 @ C4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_231_Un__Diff__cancel,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ( sup_sup @ ( set @ A ) @ A5 @ ( minus_minus @ ( set @ A ) @ B4 @ A5 ) )
% 2.85/1.52 = ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_232_Un__Diff__cancel2,axiom,
% 2.85/1.52 ! [A: $tType,B4: set @ A,A5: set @ A] :
% 2.85/1.52 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ B4 @ A5 ) @ A5 )
% 2.85/1.52 = ( sup_sup @ ( set @ A ) @ B4 @ A5 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_233_vimage__Un,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,F: A > B,A5: set @ B,B4: set @ B] :
% 2.85/1.52 ( ( vimage @ A @ B @ F @ ( sup_sup @ ( set @ B ) @ A5 @ B4 ) )
% 2.85/1.52 = ( sup_sup @ ( set @ A ) @ ( vimage @ A @ B @ F @ A5 ) @ ( vimage @ A @ B @ F @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_234_Un__empty__right,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A] :
% 2.85/1.52 ( ( sup_sup @ ( set @ A ) @ A5 @ ( bot_bot @ ( set @ A ) ) )
% 2.85/1.52 = A5 ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_235_Un__empty__left,axiom,
% 2.85/1.52 ! [A: $tType,B4: set @ A] :
% 2.85/1.52 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B4 )
% 2.85/1.52 = B4 ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_236_insert__is__Un,axiom,
% 2.85/1.52 ! [A: $tType] :
% 2.85/1.52 ( ( insert @ A )
% 2.85/1.52 = ( ^ [A11: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A11 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_237_Un__singleton__iff,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A,B4: set @ A,X5: A] :
% 2.85/1.52 ( ( ( sup_sup @ ( set @ A ) @ A5 @ B4 )
% 2.85/1.52 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.52 = ( ( ( A5
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.52 & ( B4
% 2.85/1.52 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.85/1.52 | ( ( A5
% 2.85/1.52 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.52 & ( B4
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.52 | ( ( A5
% 2.85/1.52 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.52 & ( B4
% 2.85/1.52 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_238_singleton__Un__iff,axiom,
% 2.85/1.52 ! [A: $tType,X5: A,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ( ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) )
% 2.85/1.52 = ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 2.85/1.52 = ( ( ( A5
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) )
% 2.85/1.52 & ( B4
% 2.85/1.52 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.85/1.52 | ( ( A5
% 2.85/1.52 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.52 & ( B4
% 2.85/1.52 = ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.52 | ( ( A5
% 2.85/1.52 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.85/1.52 & ( B4
% 2.85/1.52 = ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_239_Un__UNIV__left,axiom,
% 2.85/1.52 ! [A: $tType,B4: set @ A] :
% 2.85/1.52 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B4 )
% 2.85/1.52 = ( top_top @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_240_Un__UNIV__right,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A] :
% 2.85/1.52 ( ( sup_sup @ ( set @ A ) @ A5 @ ( top_top @ ( set @ A ) ) )
% 2.85/1.52 = ( top_top @ ( set @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_241_UnE,axiom,
% 2.85/1.52 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 2.85/1.52 => ( ~ ( member @ A @ C2 @ A5 )
% 2.85/1.52 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_242_UnI1,axiom,
% 2.85/1.52 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ( member @ A @ C2 @ A5 )
% 2.85/1.52 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_243_UnI2,axiom,
% 2.85/1.52 ! [A: $tType,C2: A,B4: set @ A,A5: set @ A] :
% 2.85/1.52 ( ( member @ A @ C2 @ B4 )
% 2.85/1.52 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_244_bex__Un,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A,B4: set @ A,P: A > $o] :
% 2.85/1.52 ( ( ? [X: A] :
% 2.85/1.52 ( ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 2.85/1.52 & ( P @ X ) ) )
% 2.85/1.52 = ( ? [X: A] :
% 2.85/1.52 ( ( member @ A @ X @ A5 )
% 2.85/1.52 & ( P @ X ) )
% 2.85/1.52 | ? [X: A] :
% 2.85/1.52 ( ( member @ A @ X @ B4 )
% 2.85/1.52 & ( P @ X ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_245_ball__Un,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A,B4: set @ A,P: A > $o] :
% 2.85/1.52 ( ( ! [X: A] :
% 2.85/1.52 ( ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 2.85/1.52 => ( P @ X ) ) )
% 2.85/1.52 = ( ! [X: A] :
% 2.85/1.52 ( ( member @ A @ X @ A5 )
% 2.85/1.52 => ( P @ X ) )
% 2.85/1.52 & ! [X: A] :
% 2.85/1.52 ( ( member @ A @ X @ B4 )
% 2.85/1.52 => ( P @ X ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_246_Un__assoc,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A,B4: set @ A,C4: set @ A] :
% 2.85/1.52 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) @ C4 )
% 2.85/1.52 = ( sup_sup @ ( set @ A ) @ A5 @ ( sup_sup @ ( set @ A ) @ B4 @ C4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_247_Un__absorb,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A] :
% 2.85/1.52 ( ( sup_sup @ ( set @ A ) @ A5 @ A5 )
% 2.85/1.52 = A5 ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_248_Un__commute,axiom,
% 2.85/1.52 ! [A: $tType] :
% 2.85/1.52 ( ( sup_sup @ ( set @ A ) )
% 2.85/1.52 = ( ^ [A10: set @ A,B9: set @ A] : ( sup_sup @ ( set @ A ) @ B9 @ A10 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_249_Un__left__absorb,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A,B4: set @ A] :
% 2.85/1.52 ( ( sup_sup @ ( set @ A ) @ A5 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 2.85/1.52 = ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_250_Un__left__commute,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A,B4: set @ A,C4: set @ A] :
% 2.85/1.52 ( ( sup_sup @ ( set @ A ) @ A5 @ ( sup_sup @ ( set @ A ) @ B4 @ C4 ) )
% 2.85/1.52 = ( sup_sup @ ( set @ A ) @ B4 @ ( sup_sup @ ( set @ A ) @ A5 @ C4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_251_Un__Diff,axiom,
% 2.85/1.52 ! [A: $tType,A5: set @ A,B4: set @ A,C4: set @ A] :
% 2.85/1.52 ( ( minus_minus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) @ C4 )
% 2.85/1.52 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A5 @ C4 ) @ ( minus_minus @ ( set @ A ) @ B4 @ C4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_252_vimage__insert,axiom,
% 2.85/1.52 ! [A: $tType,B: $tType,F: A > B,A4: B,B4: set @ B] :
% 2.85/1.52 ( ( vimage @ A @ B @ F @ ( insert @ B @ A4 @ B4 ) )
% 2.85/1.52 = ( sup_sup @ ( set @ A ) @ ( vimage @ A @ B @ F @ ( insert @ B @ A4 @ ( bot_bot @ ( set @ B ) ) ) ) @ ( vimage @ A @ B @ F @ B4 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_253_sup__top__right,axiom,
% 2.85/1.52 ! [A: $tType] :
% 2.85/1.52 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 2.85/1.52 => ! [X5: A] :
% 2.85/1.52 ( ( sup_sup @ A @ X5 @ ( top_top @ A ) )
% 2.85/1.52 = ( top_top @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_254_sup__top__left,axiom,
% 2.85/1.52 ! [A: $tType] :
% 2.85/1.52 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 2.85/1.52 => ! [X5: A] :
% 2.85/1.52 ( ( sup_sup @ A @ ( top_top @ A ) @ X5 )
% 2.85/1.52 = ( top_top @ A ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(fact_255_subtr2__trans__Un,axiom,
% 2.85/1.52 ! [Ns122: set @ n,Tr1: dtree,Tr22: dtree,Ns23: set @ n,Tr3: dtree] :
% 2.85/1.52 ( ( gram_L1283001940subtr2 @ Ns122 @ Tr1 @ Tr22 )
% 2.85/1.52 => ( ( gram_L1283001940subtr2 @ Ns23 @ Tr22 @ Tr3 )
% 2.85/1.52 => ( gram_L1283001940subtr2 @ ( sup_sup @ ( set @ n ) @ Ns122 @ Ns23 ) @ Tr1 @ Tr3 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.85/1.52 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 2.85/1.52
% 2.85/1.52 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.85/1.52 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.85/1.52 ! [A8: $tType,A13: $tType] :
% 2.85/1.52 ( ( bounded_lattice @ A13 @ ( type2 @ A13 ) )
% 2.85/1.52 => ( bounded_lattice @ ( A8 > A13 ) @ ( type2 @ ( A8 > A13 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 2.85/1.52 ! [A8: $tType,A13: $tType] :
% 2.85/1.52 ( ( bounded_lattice @ A13 @ ( type2 @ A13 ) )
% 2.85/1.52 => ( bounded_lattice_top @ ( A8 > A13 ) @ ( type2 @ ( A8 > A13 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(tcon_fun___Orderings_Otop,axiom,
% 2.85/1.52 ! [A8: $tType,A13: $tType] :
% 2.85/1.52 ( ( top @ A13 @ ( type2 @ A13 ) )
% 2.85/1.52 => ( top @ ( A8 > A13 ) @ ( type2 @ ( A8 > A13 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(tcon_fun___Orderings_Obot,axiom,
% 2.85/1.52 ! [A8: $tType,A13: $tType] :
% 2.85/1.52 ( ( bot @ A13 @ ( type2 @ A13 ) )
% 2.85/1.52 => ( bot @ ( A8 > A13 ) @ ( type2 @ ( A8 > A13 ) ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_3,axiom,
% 2.85/1.52 ! [A8: $tType] : ( bounded_lattice_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(tcon_Set_Oset___Orderings_Otop_4,axiom,
% 2.85/1.52 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(tcon_Set_Oset___Orderings_Obot_5,axiom,
% 2.85/1.52 ! [A8: $tType] : ( bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_6,axiom,
% 2.85/1.52 bounded_lattice_top @ $o @ ( type2 @ $o ) ).
% 2.85/1.52
% 2.85/1.52 thf(tcon_HOL_Obool___Orderings_Otop_7,axiom,
% 2.85/1.52 top @ $o @ ( type2 @ $o ) ).
% 2.85/1.52
% 2.85/1.52 thf(tcon_HOL_Obool___Orderings_Obot_8,axiom,
% 2.85/1.52 bot @ $o @ ( type2 @ $o ) ).
% 2.85/1.52
% 2.85/1.52 thf(help_If_3_1_T,axiom,
% 2.85/1.52 ! [P: $o] :
% 2.85/1.52 ( ( P = $true )
% 2.85/1.52 | ( P = $false ) ) ).
% 2.85/1.52
% 2.85/1.52 thf(help_If_2_1_T,axiom,
% 2.85/1.52 ! [A: $tType,X5: A,Y: A] :
% 2.85/1.52 ( ( if @ A @ $false @ X5 @ Y )
% 2.85/1.52 = Y ) ).
% 2.85/1.52
% 2.85/1.52 thf(help_If_1_1_T,axiom,
% 2.85/1.52 ! [A: $tType,X5: A,Y: A] :
% 2.85/1.52 ( ( if @ A @ $true @ X5 @ Y )
% 2.85/1.52 = X5 ) ).
% 2.85/1.52
% 2.85/1.52 thf(conj_0,conjecture,
% 2.85/1.52 gram_L864798063lle_wf @ ( gram_L1004374585hsubst @ tr2 @ tr2 ) ).
% 2.85/1.52 ------------------------
% 2.85/1.55 % (25219)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_24932 for (2999ds/4Mi)
% 2.85/1.55 % (25220)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_24932 for (2999ds/27Mi)
% 2.85/1.55 % (25222)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_24932 for (2999ds/2Mi)
% 2.85/1.55 % (25222)Instruction limit reached!
% 2.85/1.55 % (25222)------------------------------
% 2.85/1.55 % (25222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.55 % (25222)Termination reason: Unknown
% 2.85/1.55 % (25222)Termination phase: shuffling
% 2.85/1.55
% 2.85/1.55 % (25222)Memory used [KB]: 1407
% 2.85/1.55 % (25222)Time elapsed: 0.002 s
% 2.85/1.55 % (25222)Instructions burned: 3 (million)
% 2.85/1.55 % (25222)------------------------------
% 2.85/1.55 % (25222)------------------------------
% 2.85/1.55 % (25219)Instruction limit reached!
% 2.85/1.55 % (25219)------------------------------
% 2.85/1.55 % (25219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.55 % (25219)Termination reason: Unknown
% 2.85/1.55 % (25219)Termination phase: shuffling
% 2.85/1.55
% 2.85/1.55 % (25219)Memory used [KB]: 1535
% 2.85/1.55 % (25219)Time elapsed: 0.003 s
% 2.85/1.55 % (25219)Instructions burned: 6 (million)
% 2.85/1.55 % (25219)------------------------------
% 2.85/1.55 % (25219)------------------------------
% 2.85/1.55 % (25221)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24932 for (2999ds/2Mi)
% 2.85/1.55 % (25221)Instruction limit reached!
% 2.85/1.55 % (25221)------------------------------
% 2.85/1.55 % (25221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.55 % (25221)Termination reason: Unknown
% 2.85/1.55 % (25221)Termination phase: shuffling
% 2.85/1.55
% 2.85/1.55 % (25221)Memory used [KB]: 1279
% 2.85/1.55 % (25221)Time elapsed: 0.003 s
% 2.85/1.55 % (25221)Instructions burned: 2 (million)
% 2.85/1.55 % (25221)------------------------------
% 2.85/1.55 % (25221)------------------------------
% 2.85/1.56 % (25218)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24932 for (2999ds/183Mi)
% 2.85/1.56 % (25223)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_24932 for (2999ds/275Mi)
% 2.85/1.56 % (25224)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24932 for (2999ds/18Mi)
% 2.85/1.56 % (25220)Instruction limit reached!
% 2.85/1.56 % (25220)------------------------------
% 2.85/1.56 % (25220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.56 % (25220)Termination reason: Unknown
% 2.85/1.56 % (25220)Termination phase: Property scanning
% 2.85/1.56
% 2.85/1.56 % (25220)Memory used [KB]: 1791
% 2.85/1.56 % (25220)Time elapsed: 0.011 s
% 2.85/1.56 % (25220)Instructions burned: 30 (million)
% 2.85/1.56 % (25220)------------------------------
% 2.85/1.56 % (25220)------------------------------
% 2.85/1.56 % (25225)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24932 for (2999ds/3Mi)
% 2.85/1.56 % (25226)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_24932 for (2999ds/37Mi)
% 2.85/1.56 % (25225)Instruction limit reached!
% 2.85/1.56 % (25225)------------------------------
% 2.85/1.56 % (25225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.56 % (25225)Termination reason: Unknown
% 2.85/1.56 % (25225)Termination phase: shuffling
% 2.85/1.56
% 2.85/1.56 % (25225)Memory used [KB]: 1407
% 2.85/1.56 % (25225)Time elapsed: 0.003 s
% 2.85/1.56 % (25225)Instructions burned: 3 (million)
% 2.85/1.56 % (25225)------------------------------
% 2.85/1.56 % (25225)------------------------------
% 2.85/1.57 % (25227)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_24932 for (2999ds/15Mi)
% 2.85/1.57 % (25224)Instruction limit reached!
% 2.85/1.57 % (25224)------------------------------
% 2.85/1.57 % (25224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.57 % (25224)Termination reason: Unknown
% 2.85/1.57 % (25224)Termination phase: shuffling
% 2.85/1.57
% 2.85/1.57 % (25224)Memory used [KB]: 1663
% 2.85/1.57 % (25224)Time elapsed: 0.013 s
% 2.85/1.57 % (25224)Instructions burned: 18 (million)
% 2.85/1.57 % (25224)------------------------------
% 2.85/1.57 % (25224)------------------------------
% 2.85/1.57 % (25228)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_24932 for (2999ds/3Mi)
% 2.85/1.57 % (25228)Instruction limit reached!
% 2.85/1.57 % (25228)------------------------------
% 2.85/1.57 % (25228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.57 % (25228)Termination reason: Unknown
% 2.85/1.57 % (25228)Termination phase: shuffling
% 2.85/1.57
% 2.85/1.57 % (25228)Memory used [KB]: 1407
% 2.85/1.57 % (25228)Time elapsed: 0.003 s
% 2.85/1.57 % (25228)Instructions burned: 4 (million)
% 2.85/1.57 % (25228)------------------------------
% 2.85/1.57 % (25228)------------------------------
% 2.85/1.57 % (25229)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_24932 for (2999ds/1041Mi)
% 2.85/1.57 % (25226)Instruction limit reached!
% 2.85/1.57 % (25226)------------------------------
% 2.85/1.57 % (25226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.57 % (25226)Termination reason: Unknown
% 2.85/1.57 % (25226)Termination phase: shuffling
% 2.85/1.57
% 2.85/1.57 % (25226)Memory used [KB]: 2174
% 2.85/1.57 % (25226)Time elapsed: 0.013 s
% 2.85/1.57 % (25226)Instructions burned: 38 (million)
% 2.85/1.57 % (25226)------------------------------
% 2.85/1.57 % (25226)------------------------------
% 2.85/1.57 % (25227)Instruction limit reached!
% 2.85/1.57 % (25227)------------------------------
% 2.85/1.57 % (25227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.57 % (25227)Termination reason: Unknown
% 2.85/1.57 % (25227)Termination phase: shuffling
% 2.85/1.57
% 2.85/1.57 % (25227)Memory used [KB]: 1663
% 2.85/1.57 % (25227)Time elapsed: 0.008 s
% 2.85/1.57 % (25227)Instructions burned: 16 (million)
% 2.85/1.57 % (25227)------------------------------
% 2.85/1.57 % (25227)------------------------------
% 2.85/1.58 % (25231)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_24932 for (2999ds/16Mi)
% 2.85/1.58 % (25232)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_24932 for (2999ds/3Mi)
% 2.85/1.58 % (25233)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_24932 for (2999ds/3Mi)
% 2.85/1.59 % (25232)Instruction limit reached!
% 2.85/1.59 % (25232)------------------------------
% 2.85/1.59 % (25232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.59 % (25232)Termination reason: Unknown
% 2.85/1.59 % (25232)Termination phase: shuffling
% 2.85/1.59
% 2.85/1.59 % (25232)Memory used [KB]: 1407
% 2.85/1.59 % (25232)Time elapsed: 0.003 s
% 2.85/1.59 % (25232)Instructions burned: 4 (million)
% 2.85/1.59 % (25232)------------------------------
% 2.85/1.59 % (25232)------------------------------
% 2.85/1.59 % (25233)Instruction limit reached!
% 2.85/1.59 % (25233)------------------------------
% 2.85/1.59 % (25233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.59 % (25233)Termination reason: Unknown
% 2.85/1.59 % (25233)Termination phase: shuffling
% 2.85/1.59
% 2.85/1.59 % (25233)Memory used [KB]: 1407
% 2.85/1.59 % (25233)Time elapsed: 0.003 s
% 2.85/1.59 % (25233)Instructions burned: 4 (million)
% 2.85/1.59 % (25233)------------------------------
% 2.85/1.59 % (25233)------------------------------
% 2.85/1.59 % (25230)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_24932 for (2999ds/7Mi)
% 2.85/1.59 % (25231)Instruction limit reached!
% 2.85/1.59 % (25231)------------------------------
% 2.85/1.59 % (25231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.59 % (25231)Termination reason: Unknown
% 2.85/1.59 % (25231)Termination phase: shuffling
% 2.85/1.59
% 2.85/1.59 % (25231)Memory used [KB]: 1663
% 2.85/1.59 % (25231)Time elapsed: 0.007 s
% 2.85/1.59 % (25231)Instructions burned: 16 (million)
% 2.85/1.59 % (25231)------------------------------
% 2.85/1.59 % (25231)------------------------------
% 2.85/1.59 % (25230)Instruction limit reached!
% 2.85/1.59 % (25230)------------------------------
% 2.85/1.59 % (25230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.85/1.59 % (25230)Termination reason: Unknown
% 2.85/1.59 % (25230)Termination phase: shuffling
% 2.85/1.59
% 2.85/1.59 % (25230)Memory used [KB]: 1407
% 2.85/1.59 % (25230)Time elapsed: 0.006 s
% 2.85/1.59 % (25230)Instructions burned: 7 (million)
% 2.85/1.59 % (25230)------------------------------
% 2.85/1.59 % (25230)------------------------------
% 2.85/1.60 % (25235)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_24932 for (2999ds/3Mi)
% 2.89/1.60 % (25235)Instruction limit reached!
% 2.89/1.60 % (25235)------------------------------
% 2.89/1.60 % (25235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.60 % (25235)Termination reason: Unknown
% 2.89/1.60 % (25235)Termination phase: shuffling
% 2.89/1.60
% 2.89/1.60 % (25235)Memory used [KB]: 1407
% 2.89/1.60 % (25235)Time elapsed: 0.003 s
% 2.89/1.60 % (25235)Instructions burned: 4 (million)
% 2.89/1.60 % (25235)------------------------------
% 2.89/1.60 % (25235)------------------------------
% 2.89/1.60 % (25236)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_24932 for (2999ds/4Mi)
% 2.89/1.60 % (25236)Instruction limit reached!
% 2.89/1.60 % (25236)------------------------------
% 2.89/1.60 % (25236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.60 % (25236)Termination reason: Unknown
% 2.89/1.60 % (25236)Termination phase: shuffling
% 2.89/1.60
% 2.89/1.60 % (25236)Memory used [KB]: 1407
% 2.89/1.60 % (25236)Time elapsed: 0.003 s
% 2.89/1.60 % (25236)Instructions burned: 4 (million)
% 2.89/1.60 % (25236)------------------------------
% 2.89/1.60 % (25236)------------------------------
% 2.89/1.60 % (25234)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_24932 for (2999ds/7Mi)
% 2.89/1.61 % (25238)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_24932 for (2999ds/710Mi)
% 2.89/1.61 % (25234)Instruction limit reached!
% 2.89/1.61 % (25234)------------------------------
% 2.89/1.61 % (25234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.61 % (25234)Termination reason: Unknown
% 2.89/1.61 % (25234)Termination phase: shuffling
% 2.89/1.61
% 2.89/1.61 % (25234)Memory used [KB]: 1407
% 2.89/1.61 % (25234)Time elapsed: 0.007 s
% 2.89/1.61 % (25234)Instructions burned: 8 (million)
% 2.89/1.61 % (25234)------------------------------
% 2.89/1.61 % (25234)------------------------------
% 2.89/1.61 % (25223)First to succeed.
% 2.89/1.61 % (25237)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_24932 for (2999ds/18Mi)
% 2.89/1.61 % (25239)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_24932 for (2999ds/6Mi)
% 2.89/1.61 % (25223)Refutation found. Thanks to Tanya!
% 2.89/1.61 % SZS status Theorem for DTF2THF_24932
% 2.89/1.61 % SZS output start Proof for DTF2THF_24932
% 2.89/1.61 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.89/1.61 thf(type_def_7, type, n: $tType).
% 2.89/1.61 thf(type_def_8, type, t: $tType).
% 2.89/1.61 thf(type_def_9, type, dtree: $tType).
% 2.89/1.61 thf(type_def_10, type, sum_sum: ($tType * $tType) > $tType).
% 2.89/1.61 thf(type_def_11, type, set: ($tType) > $tType).
% 2.89/1.61 thf(type_def_12, type, product_prod: ($tType * $tType) > $tType).
% 2.89/1.61 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 2.89/1.61 thf(func_def_1, type, sum_sum: ($tType * $tType) > $tType).
% 2.89/1.61 thf(func_def_2, type, dtree: $tType).
% 2.89/1.61 thf(func_def_3, type, set: ($tType) > $tType).
% 2.89/1.61 thf(func_def_4, type, t: $tType).
% 2.89/1.61 thf(func_def_5, type, n: $tType).
% 2.89/1.61 thf(func_def_6, type, itself: ($tType) > $tType).
% 2.89/1.61 thf(func_def_7, type, bounded_lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.61 thf(func_def_8, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.61 thf(func_def_9, type, bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.61 thf(func_def_10, type, top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.61 thf(func_def_11, type, bounded_lattice_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.61 thf(func_def_12, type, node: n > set @ sum_sum @ t @ dtree > dtree).
% 2.89/1.61 thf(func_def_13, type, cont: dtree > set @ sum_sum @ t @ dtree).
% 2.89/1.61 thf(func_def_14, type, root: dtree > n).
% 2.89/1.61 thf(func_def_15, type, unfold: !>[X0: $tType]:((X0 > n) > (X0 > set @ sum_sum @ t @ X0) > X0 > dtree)).
% 2.89/1.61 thf(func_def_16, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X0) > X2 > X1)).
% 2.89/1.61 thf(func_def_17, type, gram_L861583724lle_Fr: set @ n > dtree > set @ t).
% 2.89/1.61 thf(func_def_18, type, gram_L1556062726le_Frr: set @ n > dtree > set @ t).
% 2.89/1.61 thf(func_def_19, type, gram_L1451583624elle_H: dtree > n > dtree).
% 2.89/1.61 thf(func_def_20, type, gram_L1221482011le_H_c: dtree > n > set @ sum_sum @ t @ n).
% 2.89/1.61 thf(func_def_21, type, gram_L1221482026le_H_r: dtree > n > n).
% 2.89/1.61 thf(func_def_22, type, gram_L1451583628elle_L: set @ n > n > set @ set @ t).
% 2.89/1.61 thf(func_def_23, type, gram_L1451583632elle_P: set @ product_prod @ n @ set @ sum_sum @ t @ n).
% 2.89/1.61 thf(func_def_24, type, gram_L1231612515_deftr: n > dtree).
% 2.89/1.61 thf(func_def_25, type, gram_L1004374585hsubst: dtree > dtree > dtree).
% 2.89/1.61 thf(func_def_26, type, gram_L1905609002ubst_c: dtree > dtree > set @ sum_sum @ t @ dtree).
% 2.89/1.61 thf(func_def_27, type, gram_L1905609017ubst_r: dtree > n).
% 2.89/1.61 thf(func_def_28, type, gram_L1333338417e_inFr: set @ n > dtree > t > $o).
% 2.89/1.61 thf(func_def_29, type, gram_L805317441_inFr2: set @ n > dtree > t > $o).
% 2.89/1.61 thf(func_def_30, type, gram_L805317505_inFrr: set @ n > dtree > t > $o).
% 2.89/1.61 thf(func_def_31, type, gram_L830233218_inItr: set @ n > dtree > n > $o).
% 2.89/1.61 thf(func_def_32, type, gram_L315592705e_pick: dtree > n > dtree).
% 2.89/1.61 thf(func_def_33, type, gram_L1828378864e_rcut: dtree > dtree).
% 2.89/1.61 thf(func_def_34, type, gram_L1918716148le_reg: (n > dtree) > dtree > $o).
% 2.89/1.61 thf(func_def_35, type, gram_L646766332egular: dtree > $o).
% 2.89/1.61 thf(func_def_36, type, gram_L716654942_subtr: set @ n > dtree > dtree > $o).
% 2.89/1.61 thf(func_def_37, type, gram_L1283001940subtr2: set @ n > dtree > dtree > $o).
% 2.89/1.61 thf(func_def_38, type, gram_L1614515765ubtrOf: dtree > n > dtree).
% 2.89/1.61 thf(func_def_39, type, gram_L864798063lle_wf: dtree > $o).
% 2.89/1.61 thf(func_def_40, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.89/1.61 thf(func_def_41, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.89/1.61 thf(func_def_42, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.89/1.61 thf(func_def_43, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.89/1.61 thf(func_def_44, type, top_top: !>[X0: $tType]:(X0)).
% 2.89/1.61 thf(func_def_45, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 2.89/1.61 thf(func_def_46, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.89/1.61 thf(func_def_47, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.89/1.61 thf(func_def_48, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 2.89/1.61 thf(func_def_49, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 2.89/1.61 thf(func_def_50, type, vimage: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X1 > set @ X0)).
% 2.89/1.61 thf(func_def_51, type, sum_Inl: !>[X0: $tType, X1: $tType]:(X0 > sum_sum @ X0 @ X1)).
% 2.89/1.61 thf(func_def_52, type, sum_Inr: !>[X0: $tType, X1: $tType]:(X0 > sum_sum @ X1 @ X0)).
% 2.89/1.61 thf(func_def_53, type, sum_rec_sum: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1)).
% 2.89/1.61 thf(func_def_54, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.89/1.61 thf(func_def_55, type, k: n > set @ t).
% 2.89/1.61 thf(func_def_56, type, ftr: n > dtree).
% 2.89/1.61 thf(func_def_57, type, n2: n).
% 2.89/1.61 thf(func_def_58, type, ns: set @ n).
% 2.89/1.61 thf(func_def_59, type, tns: set @ sum_sum @ t @ n).
% 2.89/1.61 thf(func_def_60, type, tr: dtree).
% 2.89/1.61 thf(func_def_61, type, tr2: dtree).
% 2.89/1.61 thf(func_def_79, type, sP0: !>[X0: $tType]:(X0 > set @ X0 > X0 > set @ X0 > $o)).
% 2.89/1.61 thf(func_def_80, type, sP1: !>[X0: $tType]:(X0 > set @ X0 > X0 > set @ X0 > $o)).
% 2.89/1.61 thf(func_def_81, type, sP2: (set @ n > dtree > t > $o) > $o).
% 2.89/1.61 thf(func_def_82, type, sP3: (set @ n > dtree > dtree > $o) > $o).
% 2.89/1.61 thf(func_def_83, type, sK4: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 2.89/1.61 thf(func_def_84, type, sK5: !>[X0: $tType]:(X0 > set @ X0 > X0 > set @ X0 > set @ X0)).
% 2.89/1.61 thf(func_def_85, type, sK6: (dtree > dtree > $o) > dtree).
% 2.89/1.61 thf(func_def_86, type, sK7: (dtree > dtree > $o) > dtree).
% 2.89/1.61 thf(func_def_87, type, sK8: (dtree > dtree > $o) > dtree).
% 2.89/1.61 thf(func_def_88, type, sK9: (dtree > dtree > $o) > dtree).
% 2.89/1.61 thf(func_def_89, type, sK10: !>[X0: $tType]:(set @ X0 > X0)).
% 2.89/1.61 thf(func_def_90, type, sK11: t > dtree > set @ n > dtree).
% 2.89/1.61 thf(func_def_91, type, sK12: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X0)).
% 2.89/1.61 thf(func_def_92, type, sK13: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X1)).
% 2.89/1.61 thf(func_def_93, type, sK14: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.89/1.61 thf(func_def_94, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:($o > (sum_sum @ X0 @ X1 > X2) > X2 > X0)).
% 2.89/1.61 thf(func_def_95, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType]:($o > (sum_sum @ X0 @ X1 > X2) > X2 > X1)).
% 2.89/1.61 thf(func_def_96, type, sK17: (set @ n > dtree > dtree > $o) > set @ n).
% 2.89/1.61 thf(func_def_97, type, sK18: (set @ n > dtree > dtree > $o) > dtree).
% 2.89/1.61 thf(func_def_98, type, sK19: (set @ n > dtree > dtree > $o) > dtree).
% 2.89/1.61 thf(func_def_99, type, sK20: (set @ n > dtree > dtree > $o) > dtree).
% 2.89/1.61 thf(func_def_100, type, sK21: (set @ n > dtree > dtree > $o) > set @ n).
% 2.89/1.61 thf(func_def_101, type, sK22: (set @ n > dtree > dtree > $o) > dtree).
% 2.89/1.61 thf(func_def_102, type, sK23: (set @ n > dtree > t > $o) > dtree).
% 2.89/1.61 thf(func_def_103, type, sK24: (set @ n > dtree > t > $o) > set @ n).
% 2.89/1.61 thf(func_def_104, type, sK25: (set @ n > dtree > t > $o) > dtree).
% 2.89/1.61 thf(func_def_105, type, sK26: (set @ n > dtree > t > $o) > t).
% 2.89/1.61 thf(func_def_106, type, sK27: (set @ n > dtree > t > $o) > dtree).
% 2.89/1.61 thf(func_def_107, type, sK28: (set @ n > dtree > t > $o) > set @ n).
% 2.89/1.61 thf(func_def_108, type, sK29: (set @ n > dtree > t > $o) > t).
% 2.89/1.61 thf(func_def_109, type, sK30: t > dtree > set @ n > dtree).
% 2.89/1.61 thf(func_def_110, type, sK31: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > $o) > X1)).
% 2.89/1.61 thf(func_def_111, type, sK32: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > $o) > X0)).
% 2.89/1.61 thf(func_def_112, type, sK33: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X1)).
% 2.89/1.61 thf(func_def_113, type, sK34: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X0)).
% 2.89/1.61 thf(func_def_114, type, sK35: (set @ n > dtree > dtree > $o) > dtree).
% 2.89/1.61 thf(func_def_115, type, sK36: (set @ n > dtree > dtree > $o) > set @ n).
% 2.89/1.61 thf(func_def_116, type, sK37: (set @ n > dtree > dtree > $o) > dtree).
% 2.89/1.61 thf(func_def_117, type, sK38: (set @ n > dtree > dtree > $o) > dtree).
% 2.89/1.61 thf(func_def_118, type, sK39: (set @ n > dtree > dtree > $o) > dtree).
% 2.89/1.61 thf(func_def_119, type, sK40: (set @ n > dtree > dtree > $o) > set @ n).
% 2.89/1.61 thf(func_def_120, type, sK41: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 2.89/1.61 thf(func_def_121, type, sK42: !>[X0: $tType]:(set @ X0 > X0)).
% 2.89/1.61 thf(func_def_122, type, sK43: !>[X0: $tType]:(set @ X0 > X0)).
% 2.89/1.61 thf(func_def_123, type, sK44: dtree > dtree > set @ n > dtree).
% 2.89/1.61 thf(func_def_124, type, sK45: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X0)).
% 2.89/1.61 thf(func_def_125, type, sK46: !>[X0: $tType, X1: $tType]:(sum_sum @ X0 @ X1 > X1)).
% 2.89/1.61 thf(func_def_127, type, ph48: !>[X0: $tType]:(X0)).
% 2.89/1.61 thf(f1148,plain,(
% 2.89/1.61 $false),
% 2.89/1.61 inference(subsumption_resolution,[status(thm)],[f1147,f956])).
% 2.89/1.61 thf(f956,plain,(
% 2.89/1.61 ((gram_L864798063lle_wf @ tr2) = $true)),
% 2.89/1.61 inference(cnf_transformation,[status(thm)],[f570])).
% 2.89/1.61 thf(f570,plain,(
% 2.89/1.61 ((gram_L864798063lle_wf @ tr2) = $true)),
% 2.89/1.61 inference(fool_elimination,[status(thm)],[f569])).
% 2.89/1.61 thf(f569,plain,(
% 2.89/1.61 (gram_L864798063lle_wf @ tr2)),
% 2.89/1.61 inference(rectify,[status(thm)],[f1])).
% 2.89/1.61 thf(f1,axiom,(
% 2.89/1.61 (gram_L864798063lle_wf @ tr2)),
% 2.89/1.61 file('/export/starexec/sandbox/tmp/tmp.6ce4rUdsE3/DTF2THF_24932.p',fact_0_dtr)).
% 2.89/1.61 thf(f1147,plain,(
% 2.89/1.61 ((gram_L864798063lle_wf @ tr2) != $true)),
% 2.89/1.61 inference(trivial_inequality_removal,[status(thm)],[f1146])).
% 2.89/1.61 thf(f1146,plain,(
% 2.89/1.61 ($true != $true) | ((gram_L864798063lle_wf @ tr2) != $true)),
% 2.89/1.61 inference(duplicate_literal_removal,[status(thm)],[f1145])).
% 2.89/1.61 thf(f1145,plain,(
% 2.89/1.61 ((gram_L864798063lle_wf @ tr2) != $true) | ((gram_L864798063lle_wf @ tr2) != $true) | ($true != $true)),
% 2.89/1.61 inference(superposition,[status(thm)],[f990,f1059])).
% 2.89/1.61 thf(f1059,plain,(
% 2.89/1.61 ( ! [X0 : dtree,X1 : dtree] : (((gram_L864798063lle_wf @ (gram_L1004374585hsubst @ X0 @ X1)) = $true) | ((gram_L864798063lle_wf @ X1) != $true) | ((gram_L864798063lle_wf @ X0) != $true)) )),
% 2.89/1.61 inference(cnf_transformation,[status(thm)],[f808])).
% 2.89/1.61 thf(f808,plain,(
% 2.89/1.61 ! [X0 : dtree,X1 : dtree] : (((gram_L864798063lle_wf @ X0) != $true) | ((gram_L864798063lle_wf @ X1) != $true) | ((gram_L864798063lle_wf @ (gram_L1004374585hsubst @ X0 @ X1)) = $true))),
% 2.89/1.61 inference(flattening,[status(thm)],[f807])).
% 2.89/1.61 thf(f807,plain,(
% 2.89/1.61 ! [X0 : dtree,X1 : dtree] : ((((gram_L864798063lle_wf @ (gram_L1004374585hsubst @ X0 @ X1)) = $true) | ((gram_L864798063lle_wf @ X1) != $true)) | ((gram_L864798063lle_wf @ X0) != $true))),
% 2.89/1.61 inference(ennf_transformation,[status(thm)],[f506])).
% 2.89/1.61 thf(f506,plain,(
% 2.89/1.61 ! [X0 : dtree,X1 : dtree] : (((gram_L864798063lle_wf @ X0) = $true) => (((gram_L864798063lle_wf @ X1) = $true) => ((gram_L864798063lle_wf @ (gram_L1004374585hsubst @ X0 @ X1)) = $true)))),
% 2.89/1.61 inference(fool_elimination,[status(thm)],[f505])).
% 2.89/1.61 thf(f505,plain,(
% 2.89/1.61 ! [X0 : dtree,X1 : dtree] : ((gram_L864798063lle_wf @ X0) => ((gram_L864798063lle_wf @ X1) => (gram_L864798063lle_wf @ (gram_L1004374585hsubst @ X0 @ X1))))),
% 2.89/1.61 inference(rectify,[status(thm)],[f3])).
% 2.89/1.61 thf(f3,axiom,(
% 2.89/1.61 ! [X4 : dtree,X5 : dtree] : ((gram_L864798063lle_wf @ X4) => ((gram_L864798063lle_wf @ X5) => (gram_L864798063lle_wf @ (gram_L1004374585hsubst @ X4 @ X5))))),
% 2.89/1.61 file('/export/starexec/sandbox/tmp/tmp.6ce4rUdsE3/DTF2THF_24932.p',fact_2_wf__hsubst)).
% 2.89/1.61 thf(f990,plain,(
% 2.89/1.61 ((gram_L864798063lle_wf @ (gram_L1004374585hsubst @ tr2 @ tr2)) != $true)),
% 2.89/1.61 inference(cnf_transformation,[status(thm)],[f653])).
% 2.89/1.61 thf(f653,plain,(
% 2.89/1.61 ((gram_L864798063lle_wf @ (gram_L1004374585hsubst @ tr2 @ tr2)) != $true)),
% 2.89/1.61 inference(flattening,[status(thm)],[f574])).
% 2.89/1.61 thf(f574,plain,(
% 2.89/1.61 ~((gram_L864798063lle_wf @ (gram_L1004374585hsubst @ tr2 @ tr2)) = $true)),
% 2.89/1.61 inference(fool_elimination,[status(thm)],[f573])).
% 2.89/1.61 thf(f573,plain,(
% 2.89/1.61 ~(gram_L864798063lle_wf @ (gram_L1004374585hsubst @ tr2 @ tr2))),
% 2.89/1.61 inference(rectify,[status(thm)],[f273])).
% 2.89/1.61 thf(f273,negated_conjecture,(
% 2.89/1.61 ~(gram_L864798063lle_wf @ (gram_L1004374585hsubst @ tr2 @ tr2))),
% 2.89/1.61 inference(negated_conjecture,[status(cth)],[f272])).
% 2.89/1.61 thf(f272,conjecture,(
% 2.89/1.61 (gram_L864798063lle_wf @ (gram_L1004374585hsubst @ tr2 @ tr2))),
% 2.89/1.61 file('/export/starexec/sandbox/tmp/tmp.6ce4rUdsE3/DTF2THF_24932.p',conj_0)).
% 2.89/1.61 % SZS output end Proof for DTF2THF_24932
% 2.89/1.61 % (25223)------------------------------
% 2.89/1.61 % (25223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.61 % (25223)Termination reason: Refutation
% 2.89/1.61
% 2.89/1.61 % (25223)Memory used [KB]: 6780
% 2.89/1.61 % (25223)Time elapsed: 0.053 s
% 2.89/1.61 % (25223)Instructions burned: 87 (million)
% 2.89/1.61 % (25223)------------------------------
% 2.89/1.61 % (25223)------------------------------
% 2.89/1.61 % (25217)Success in time 0.081 s
%------------------------------------------------------------------------------