TPTP Problem File: SLH0460^1.p
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%------------------------------------------------------------------------------
% File : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain : Archive of Formal Proofs
% Problem :
% Version : Especial.
% English :
% Refs : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source : [Des23]
% Names : Stalnaker_Logic/0000_Stalnaker_Logic/prob_00194_006123__6361372_1 [Des23]
% Status : Theorem
% Rating : ? v8.2.0
% Syntax : Number of formulae : 1665 ( 592 unt; 383 typ; 0 def)
% Number of atoms : 4068 (1508 equ; 0 cnn)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 13540 ( 379 ~; 82 |; 339 &;10828 @)
% ( 0 <=>;1912 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Number of types : 41 ( 40 usr)
% Number of type conns : 1966 (1966 >; 0 *; 0 +; 0 <<)
% Number of symbols : 346 ( 343 usr; 17 con; 0-3 aty)
% Number of variables : 4471 ( 444 ^;3846 !; 181 ?;4471 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2023-01-19 16:11:57.313
%------------------------------------------------------------------------------
% Could-be-implicit typings (40)
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% Explicit typings (343)
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thf(sy_c_Set_Oinsert_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
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thf(sy_c_Set_Oremove_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_Set_Othe__elem_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
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thf(sy_c_Stalnaker__Logic_Oconjunct_001tf__a,type,
stalnaker_conjunct_a: list_Epistemic_fm_a > epistemic_fm_a ).
thf(sy_c_Wellfounded_Oaccp_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
accp_Epistemic_fm_a: ( epistemic_fm_a > epistemic_fm_a > $o ) > epistemic_fm_a > $o ).
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thf(sy_c_member_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_member_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
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thf(sy_c_member_001t__Set__Oset_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J,type,
member2517045796615263401c_fm_a: set_li769143395467472256c_fm_a > set_se4933744490392479200c_fm_a > $o ).
thf(sy_v_A,type,
a2: epistemic_fm_a > $o ).
thf(sy_v_i,type,
i: a ).
% Relevant facts (1270)
thf(fact_0_K__imp__trans,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,R: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ Q ) )
=> ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ Q @ R ) )
=> ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ R ) ) ) ) ).
% K_imp_trans
thf(fact_1_K__imp__trans_H,axiom,
! [A: epistemic_fm_a > $o,Q: epistemic_fm_a,R: epistemic_fm_a,P: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ Q @ R ) )
=> ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ Q ) @ ( epistemic_Imp_a @ P @ R ) ) ) ) ).
% K_imp_trans'
thf(fact_2_K__conjunction__in__mult,axiom,
! [A: epistemic_fm_a > $o,I: a,G: list_Epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( stalnaker_conjunct_a @ G ) ) @ ( stalnaker_conjunct_a @ ( map_Ep7084560364594560580c_fm_a @ ( epistemic_K_a @ I ) @ G ) ) ) ) ).
% K_conjunction_in_mult
thf(fact_3_list_Omap__disc__iff,axiom,
! [F: set_Epistemic_fm_a > epistemic_fm_a,A2: list_s580375451141968640c_fm_a] :
( ( ( map_se8248101584983471204c_fm_a @ F @ A2 )
= nil_Epistemic_fm_a )
= ( A2 = nil_se102576565402781184c_fm_a ) ) ).
% list.map_disc_iff
thf(fact_4_list_Omap__disc__iff,axiom,
! [F: set_Epistemic_fm_a > list_Epistemic_fm_a,A2: list_s580375451141968640c_fm_a] :
( ( ( map_se6909769656262425450c_fm_a @ F @ A2 )
= nil_li2451196919128234278c_fm_a )
= ( A2 = nil_se102576565402781184c_fm_a ) ) ).
% list.map_disc_iff
thf(fact_5_list_Omap__disc__iff,axiom,
! [F: epistemic_fm_a > set_Epistemic_fm_a,A2: list_Epistemic_fm_a] :
( ( ( map_Ep6135353274472911908c_fm_a @ F @ A2 )
= nil_se102576565402781184c_fm_a )
= ( A2 = nil_Epistemic_fm_a ) ) ).
% list.map_disc_iff
thf(fact_6_list_Omap__disc__iff,axiom,
! [F: list_Epistemic_fm_a > set_Epistemic_fm_a,A2: list_l6083326122719238310c_fm_a] :
( ( ( map_li6596013992111160350c_fm_a @ F @ A2 )
= nil_se102576565402781184c_fm_a )
= ( A2 = nil_li2451196919128234278c_fm_a ) ) ).
% list.map_disc_iff
thf(fact_7_list_Omap__disc__iff,axiom,
! [F: set_Epistemic_fm_a > set_Epistemic_fm_a,A2: list_s580375451141968640c_fm_a] :
( ( ( map_se7333198834109155908c_fm_a @ F @ A2 )
= nil_se102576565402781184c_fm_a )
= ( A2 = nil_se102576565402781184c_fm_a ) ) ).
% list.map_disc_iff
thf(fact_8_list_Omap__disc__iff,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,A2: list_Epistemic_fm_a] :
( ( ( map_Ep1988204514693272906c_fm_a @ F @ A2 )
= nil_li2451196919128234278c_fm_a )
= ( A2 = nil_Epistemic_fm_a ) ) ).
% list.map_disc_iff
thf(fact_9_list_Omap__disc__iff,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,A2: list_l6083326122719238310c_fm_a] :
( ( ( map_li3080774272885743684c_fm_a @ F @ A2 )
= nil_li2451196919128234278c_fm_a )
= ( A2 = nil_li2451196919128234278c_fm_a ) ) ).
% list.map_disc_iff
thf(fact_10_list_Omap__disc__iff,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,A2: list_l6083326122719238310c_fm_a] :
( ( ( map_li3858915945532548554c_fm_a @ F @ A2 )
= nil_li5178944226519631276c_fm_a )
= ( A2 = nil_li2451196919128234278c_fm_a ) ) ).
% list.map_disc_iff
thf(fact_11_list_Omap__disc__iff,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,A2: list_l6083326122719238310c_fm_a] :
( ( ( map_li5516866612190465598c_fm_a @ F @ A2 )
= nil_Epistemic_fm_a )
= ( A2 = nil_li2451196919128234278c_fm_a ) ) ).
% list.map_disc_iff
thf(fact_12_list_Omap__disc__iff,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,A2: list_Epistemic_fm_a] :
( ( ( map_Ep7084560364594560580c_fm_a @ F @ A2 )
= nil_Epistemic_fm_a )
= ( A2 = nil_Epistemic_fm_a ) ) ).
% list.map_disc_iff
thf(fact_13_Nil__is__map__conv,axiom,
! [F: set_Epistemic_fm_a > epistemic_fm_a,Xs: list_s580375451141968640c_fm_a] :
( ( nil_Epistemic_fm_a
= ( map_se8248101584983471204c_fm_a @ F @ Xs ) )
= ( Xs = nil_se102576565402781184c_fm_a ) ) ).
% Nil_is_map_conv
thf(fact_14_Nil__is__map__conv,axiom,
! [F: set_Epistemic_fm_a > list_Epistemic_fm_a,Xs: list_s580375451141968640c_fm_a] :
( ( nil_li2451196919128234278c_fm_a
= ( map_se6909769656262425450c_fm_a @ F @ Xs ) )
= ( Xs = nil_se102576565402781184c_fm_a ) ) ).
% Nil_is_map_conv
thf(fact_15_Nil__is__map__conv,axiom,
! [F: epistemic_fm_a > set_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( nil_se102576565402781184c_fm_a
= ( map_Ep6135353274472911908c_fm_a @ F @ Xs ) )
= ( Xs = nil_Epistemic_fm_a ) ) ).
% Nil_is_map_conv
thf(fact_16_Nil__is__map__conv,axiom,
! [F: list_Epistemic_fm_a > set_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( nil_se102576565402781184c_fm_a
= ( map_li6596013992111160350c_fm_a @ F @ Xs ) )
= ( Xs = nil_li2451196919128234278c_fm_a ) ) ).
% Nil_is_map_conv
thf(fact_17_Nil__is__map__conv,axiom,
! [F: set_Epistemic_fm_a > set_Epistemic_fm_a,Xs: list_s580375451141968640c_fm_a] :
( ( nil_se102576565402781184c_fm_a
= ( map_se7333198834109155908c_fm_a @ F @ Xs ) )
= ( Xs = nil_se102576565402781184c_fm_a ) ) ).
% Nil_is_map_conv
thf(fact_18_Nil__is__map__conv,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( nil_li2451196919128234278c_fm_a
= ( map_Ep1988204514693272906c_fm_a @ F @ Xs ) )
= ( Xs = nil_Epistemic_fm_a ) ) ).
% Nil_is_map_conv
thf(fact_19_Nil__is__map__conv,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( nil_li2451196919128234278c_fm_a
= ( map_li3080774272885743684c_fm_a @ F @ Xs ) )
= ( Xs = nil_li2451196919128234278c_fm_a ) ) ).
% Nil_is_map_conv
thf(fact_20_Nil__is__map__conv,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( nil_li5178944226519631276c_fm_a
= ( map_li3858915945532548554c_fm_a @ F @ Xs ) )
= ( Xs = nil_li2451196919128234278c_fm_a ) ) ).
% Nil_is_map_conv
thf(fact_21_Nil__is__map__conv,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( nil_Epistemic_fm_a
= ( map_li5516866612190465598c_fm_a @ F @ Xs ) )
= ( Xs = nil_li2451196919128234278c_fm_a ) ) ).
% Nil_is_map_conv
thf(fact_22_Nil__is__map__conv,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( nil_Epistemic_fm_a
= ( map_Ep7084560364594560580c_fm_a @ F @ Xs ) )
= ( Xs = nil_Epistemic_fm_a ) ) ).
% Nil_is_map_conv
thf(fact_23_map__is__Nil__conv,axiom,
! [F: set_Epistemic_fm_a > epistemic_fm_a,Xs: list_s580375451141968640c_fm_a] :
( ( ( map_se8248101584983471204c_fm_a @ F @ Xs )
= nil_Epistemic_fm_a )
= ( Xs = nil_se102576565402781184c_fm_a ) ) ).
% map_is_Nil_conv
thf(fact_24_map__is__Nil__conv,axiom,
! [F: set_Epistemic_fm_a > list_Epistemic_fm_a,Xs: list_s580375451141968640c_fm_a] :
( ( ( map_se6909769656262425450c_fm_a @ F @ Xs )
= nil_li2451196919128234278c_fm_a )
= ( Xs = nil_se102576565402781184c_fm_a ) ) ).
% map_is_Nil_conv
thf(fact_25_map__is__Nil__conv,axiom,
! [F: epistemic_fm_a > set_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( ( map_Ep6135353274472911908c_fm_a @ F @ Xs )
= nil_se102576565402781184c_fm_a )
= ( Xs = nil_Epistemic_fm_a ) ) ).
% map_is_Nil_conv
thf(fact_26_map__is__Nil__conv,axiom,
! [F: list_Epistemic_fm_a > set_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( ( map_li6596013992111160350c_fm_a @ F @ Xs )
= nil_se102576565402781184c_fm_a )
= ( Xs = nil_li2451196919128234278c_fm_a ) ) ).
% map_is_Nil_conv
thf(fact_27_map__is__Nil__conv,axiom,
! [F: set_Epistemic_fm_a > set_Epistemic_fm_a,Xs: list_s580375451141968640c_fm_a] :
( ( ( map_se7333198834109155908c_fm_a @ F @ Xs )
= nil_se102576565402781184c_fm_a )
= ( Xs = nil_se102576565402781184c_fm_a ) ) ).
% map_is_Nil_conv
thf(fact_28_map__is__Nil__conv,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( ( map_Ep1988204514693272906c_fm_a @ F @ Xs )
= nil_li2451196919128234278c_fm_a )
= ( Xs = nil_Epistemic_fm_a ) ) ).
% map_is_Nil_conv
thf(fact_29_map__is__Nil__conv,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( ( map_li3080774272885743684c_fm_a @ F @ Xs )
= nil_li2451196919128234278c_fm_a )
= ( Xs = nil_li2451196919128234278c_fm_a ) ) ).
% map_is_Nil_conv
thf(fact_30_map__is__Nil__conv,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( ( map_li3858915945532548554c_fm_a @ F @ Xs )
= nil_li5178944226519631276c_fm_a )
= ( Xs = nil_li2451196919128234278c_fm_a ) ) ).
% map_is_Nil_conv
thf(fact_31_map__is__Nil__conv,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( ( map_li5516866612190465598c_fm_a @ F @ Xs )
= nil_Epistemic_fm_a )
= ( Xs = nil_li2451196919128234278c_fm_a ) ) ).
% map_is_Nil_conv
thf(fact_32_map__is__Nil__conv,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs )
= nil_Epistemic_fm_a )
= ( Xs = nil_Epistemic_fm_a ) ) ).
% map_is_Nil_conv
thf(fact_33_map__ident,axiom,
( ( map_li3080774272885743684c_fm_a
@ ^ [X: list_Epistemic_fm_a] : X )
= ( ^ [Xs2: list_l6083326122719238310c_fm_a] : Xs2 ) ) ).
% map_ident
thf(fact_34_map__ident,axiom,
( ( map_Ep7084560364594560580c_fm_a
@ ^ [X: epistemic_fm_a] : X )
= ( ^ [Xs2: list_Epistemic_fm_a] : Xs2 ) ) ).
% map_ident
thf(fact_35_K__A2_H,axiom,
! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ Q ) ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ Q ) ) ) ) ).
% K_A2'
thf(fact_36_K__map,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,I: a] :
( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ Q ) )
=> ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ Q ) ) ) ) ).
% K_map
thf(fact_37_fm_Oinject_I5_J,axiom,
! [X61: a,X62: epistemic_fm_a,Y61: a,Y62: epistemic_fm_a] :
( ( ( epistemic_K_a @ X61 @ X62 )
= ( epistemic_K_a @ Y61 @ Y62 ) )
= ( ( X61 = Y61 )
& ( X62 = Y62 ) ) ) ).
% fm.inject(5)
thf(fact_38_fm_Oinject_I4_J,axiom,
! [X51: epistemic_fm_a,X52: epistemic_fm_a,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
( ( ( epistemic_Imp_a @ X51 @ X52 )
= ( epistemic_Imp_a @ Y51 @ Y52 ) )
= ( ( X51 = Y51 )
& ( X52 = Y52 ) ) ) ).
% fm.inject(4)
thf(fact_39_R2,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,I: a] :
( ( epistemic_AK_a @ A @ P )
=> ( epistemic_AK_a @ A @ ( epistemic_K_a @ I @ P ) ) ) ).
% R2
thf(fact_40_R1,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ P )
=> ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ Q ) )
=> ( epistemic_AK_a @ A @ Q ) ) ) ).
% R1
thf(fact_41_K__trans,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,R: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ Q ) @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ Q @ R ) @ ( epistemic_Imp_a @ P @ R ) ) ) ) ).
% K_trans
thf(fact_42_fm_Odistinct_I29_J,axiom,
! [X51: epistemic_fm_a,X52: epistemic_fm_a,X61: a,X62: epistemic_fm_a] :
( ( epistemic_Imp_a @ X51 @ X52 )
!= ( epistemic_K_a @ X61 @ X62 ) ) ).
% fm.distinct(29)
thf(fact_43_Ax,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a] :
( ( A @ P )
=> ( epistemic_AK_a @ A @ P ) ) ).
% Ax
thf(fact_44_list_Omap__ident,axiom,
! [T: list_l6083326122719238310c_fm_a] :
( ( map_li3080774272885743684c_fm_a
@ ^ [X: list_Epistemic_fm_a] : X
@ T )
= T ) ).
% list.map_ident
thf(fact_45_list_Omap__ident,axiom,
! [T: list_Epistemic_fm_a] :
( ( map_Ep7084560364594560580c_fm_a
@ ^ [X: epistemic_fm_a] : X
@ T )
= T ) ).
% list.map_ident
thf(fact_46_list_Osimps_I8_J,axiom,
! [F: epistemic_fm_a > set_Epistemic_fm_a] :
( ( map_Ep6135353274472911908c_fm_a @ F @ nil_Epistemic_fm_a )
= nil_se102576565402781184c_fm_a ) ).
% list.simps(8)
thf(fact_47_list_Osimps_I8_J,axiom,
! [F: list_Epistemic_fm_a > set_Epistemic_fm_a] :
( ( map_li6596013992111160350c_fm_a @ F @ nil_li2451196919128234278c_fm_a )
= nil_se102576565402781184c_fm_a ) ).
% list.simps(8)
thf(fact_48_list_Osimps_I8_J,axiom,
! [F: set_Epistemic_fm_a > epistemic_fm_a] :
( ( map_se8248101584983471204c_fm_a @ F @ nil_se102576565402781184c_fm_a )
= nil_Epistemic_fm_a ) ).
% list.simps(8)
thf(fact_49_list_Osimps_I8_J,axiom,
! [F: set_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( map_se6909769656262425450c_fm_a @ F @ nil_se102576565402781184c_fm_a )
= nil_li2451196919128234278c_fm_a ) ).
% list.simps(8)
thf(fact_50_list_Osimps_I8_J,axiom,
! [F: set_Epistemic_fm_a > set_Epistemic_fm_a] :
( ( map_se7333198834109155908c_fm_a @ F @ nil_se102576565402781184c_fm_a )
= nil_se102576565402781184c_fm_a ) ).
% list.simps(8)
thf(fact_51_list_Osimps_I8_J,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a] :
( ( map_Ep1988204514693272906c_fm_a @ F @ nil_Epistemic_fm_a )
= nil_li2451196919128234278c_fm_a ) ).
% list.simps(8)
thf(fact_52_list_Osimps_I8_J,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( map_li3080774272885743684c_fm_a @ F @ nil_li2451196919128234278c_fm_a )
= nil_li2451196919128234278c_fm_a ) ).
% list.simps(8)
thf(fact_53_list_Osimps_I8_J,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( map_li3858915945532548554c_fm_a @ F @ nil_li2451196919128234278c_fm_a )
= nil_li5178944226519631276c_fm_a ) ).
% list.simps(8)
thf(fact_54_list_Osimps_I8_J,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a] :
( ( map_li5516866612190465598c_fm_a @ F @ nil_li2451196919128234278c_fm_a )
= nil_Epistemic_fm_a ) ).
% list.simps(8)
thf(fact_55_list_Osimps_I8_J,axiom,
! [F: epistemic_fm_a > epistemic_fm_a] :
( ( map_Ep7084560364594560580c_fm_a @ F @ nil_Epistemic_fm_a )
= nil_Epistemic_fm_a ) ).
% list.simps(8)
thf(fact_56_map__eq__map__tailrec,axiom,
map_Ep1988204514693272906c_fm_a = map_ta2019361550626295956c_fm_a ).
% map_eq_map_tailrec
thf(fact_57_map__eq__map__tailrec,axiom,
map_li3080774272885743684c_fm_a = map_ta7821446597547650702c_fm_a ).
% map_eq_map_tailrec
thf(fact_58_map__eq__map__tailrec,axiom,
map_li3858915945532548554c_fm_a = map_ta6463483919923529492c_fm_a ).
% map_eq_map_tailrec
thf(fact_59_map__eq__map__tailrec,axiom,
map_li5516866612190465598c_fm_a = map_ta5548023648123488648c_fm_a ).
% map_eq_map_tailrec
thf(fact_60_map__eq__map__tailrec,axiom,
map_Ep7084560364594560580c_fm_a = map_ta875960198429730446c_fm_a ).
% map_eq_map_tailrec
thf(fact_61_list__ex1__simps_I1_J,axiom,
! [P2: list_Epistemic_fm_a > $o] :
~ ( list_e1371837923195959913c_fm_a @ P2 @ nil_li2451196919128234278c_fm_a ) ).
% list_ex1_simps(1)
thf(fact_62_list__ex1__simps_I1_J,axiom,
! [P2: set_Epistemic_fm_a > $o] :
~ ( list_e3415556844334454979c_fm_a @ P2 @ nil_se102576565402781184c_fm_a ) ).
% list_ex1_simps(1)
thf(fact_63_list__ex1__simps_I1_J,axiom,
! [P2: epistemic_fm_a > $o] :
~ ( list_e2031426293596896995c_fm_a @ P2 @ nil_Epistemic_fm_a ) ).
% list_ex1_simps(1)
thf(fact_64_conjunct_Osimps_I1_J,axiom,
( ( stalnaker_conjunct_a @ nil_Epistemic_fm_a )
= ( epistemic_Imp_a @ epistemic_FF_a @ epistemic_FF_a ) ) ).
% conjunct.simps(1)
thf(fact_65_K__distrib__K__imp,axiom,
! [A: epistemic_fm_a > $o,I: a,G: list_Epistemic_fm_a,Q: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_K_a @ I @ ( epistemic_imply_a @ G @ Q ) ) )
=> ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( map_Ep7084560364594560580c_fm_a @ ( epistemic_K_a @ I ) @ G ) @ ( epistemic_K_a @ I @ Q ) ) ) ) ).
% K_distrib_K_imp
thf(fact_66_K__imply__conjunct,axiom,
! [A: epistemic_fm_a > $o,G: list_Epistemic_fm_a,P: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G @ P ) )
=> ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G ) @ P ) ) ) ).
% K_imply_conjunct
thf(fact_67_K__conjunct__imply,axiom,
! [A: epistemic_fm_a > $o,G: list_Epistemic_fm_a,P: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G ) @ P ) )
=> ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G @ P ) ) ) ).
% K_conjunct_imply
thf(fact_68_bind__simps_I1_J,axiom,
! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( bind_E5557050373637598221c_fm_a @ nil_Epistemic_fm_a @ F )
= nil_li2451196919128234278c_fm_a ) ).
% bind_simps(1)
thf(fact_69_bind__simps_I1_J,axiom,
! [F: epistemic_fm_a > list_s580375451141968640c_fm_a] :
( ( bind_E2618557688023538791c_fm_a @ nil_Epistemic_fm_a @ F )
= nil_se102576565402781184c_fm_a ) ).
% bind_simps(1)
thf(fact_70_bind__simps_I1_J,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( bind_l9085712471134790913c_fm_a @ nil_li2451196919128234278c_fm_a @ F )
= nil_Epistemic_fm_a ) ).
% bind_simps(1)
thf(fact_71_bind__simps_I1_J,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( bind_l6536575428307499399c_fm_a @ nil_li2451196919128234278c_fm_a @ F )
= nil_li2451196919128234278c_fm_a ) ).
% bind_simps(1)
thf(fact_72_bind__simps_I1_J,axiom,
! [F: list_Epistemic_fm_a > list_s580375451141968640c_fm_a] :
( ( bind_l1363406430957618913c_fm_a @ nil_li2451196919128234278c_fm_a @ F )
= nil_se102576565402781184c_fm_a ) ).
% bind_simps(1)
thf(fact_73_bind__simps_I1_J,axiom,
! [F: set_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( bind_s4731305998534098087c_fm_a @ nil_se102576565402781184c_fm_a @ F )
= nil_Epistemic_fm_a ) ).
% bind_simps(1)
thf(fact_74_bind__simps_I1_J,axiom,
! [F: set_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( bind_s1677162095108884013c_fm_a @ nil_se102576565402781184c_fm_a @ F )
= nil_li2451196919128234278c_fm_a ) ).
% bind_simps(1)
thf(fact_75_bind__simps_I1_J,axiom,
! [F: set_Epistemic_fm_a > list_s580375451141968640c_fm_a] :
( ( bind_s3527534645263337095c_fm_a @ nil_se102576565402781184c_fm_a @ F )
= nil_se102576565402781184c_fm_a ) ).
% bind_simps(1)
thf(fact_76_bind__simps_I1_J,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a] :
( ( bind_E8451893407412458119c_fm_a @ nil_Epistemic_fm_a @ F )
= nil_Epistemic_fm_a ) ).
% bind_simps(1)
thf(fact_77_A2,axiom,
! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ Q ) ) ) @ ( epistemic_K_a @ I @ Q ) ) ) ).
% A2
thf(fact_78_K__conj__imply__factor,axiom,
! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a,R: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ Q ) ) @ R ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Con_a @ P @ Q ) ) @ R ) ) ) ).
% K_conj_imply_factor
thf(fact_79_K__conjunction__out,axiom,
! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ Q ) ) @ ( epistemic_K_a @ I @ ( epistemic_Con_a @ P @ Q ) ) ) ) ).
% K_conjunction_out
thf(fact_80_K__conjunction__in,axiom,
! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Con_a @ P @ Q ) ) @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ Q ) ) ) ) ).
% K_conjunction_in
thf(fact_81_member__rec_I2_J,axiom,
! [Y: list_Epistemic_fm_a] :
~ ( member594239076476917947c_fm_a @ nil_li2451196919128234278c_fm_a @ Y ) ).
% member_rec(2)
thf(fact_82_member__rec_I2_J,axiom,
! [Y: set_Epistemic_fm_a] :
~ ( member378061430901374997c_fm_a @ nil_se102576565402781184c_fm_a @ Y ) ).
% member_rec(2)
thf(fact_83_member__rec_I2_J,axiom,
! [Y: epistemic_fm_a] :
~ ( member6038508265109909045c_fm_a @ nil_Epistemic_fm_a @ Y ) ).
% member_rec(2)
thf(fact_84_fm_Oinject_I3_J,axiom,
! [X41: epistemic_fm_a,X42: epistemic_fm_a,Y41: epistemic_fm_a,Y42: epistemic_fm_a] :
( ( ( epistemic_Con_a @ X41 @ X42 )
= ( epistemic_Con_a @ Y41 @ Y42 ) )
= ( ( X41 = Y41 )
& ( X42 = Y42 ) ) ) ).
% fm.inject(3)
thf(fact_85_fm_Odistinct_I5_J,axiom,
! [X41: epistemic_fm_a,X42: epistemic_fm_a] :
( epistemic_FF_a
!= ( epistemic_Con_a @ X41 @ X42 ) ) ).
% fm.distinct(5)
thf(fact_86_fm_Odistinct_I7_J,axiom,
! [X51: epistemic_fm_a,X52: epistemic_fm_a] :
( epistemic_FF_a
!= ( epistemic_Imp_a @ X51 @ X52 ) ) ).
% fm.distinct(7)
thf(fact_87_fm_Odistinct_I9_J,axiom,
! [X61: a,X62: epistemic_fm_a] :
( epistemic_FF_a
!= ( epistemic_K_a @ X61 @ X62 ) ) ).
% fm.distinct(9)
thf(fact_88_fm_Odistinct_I25_J,axiom,
! [X41: epistemic_fm_a,X42: epistemic_fm_a,X51: epistemic_fm_a,X52: epistemic_fm_a] :
( ( epistemic_Con_a @ X41 @ X42 )
!= ( epistemic_Imp_a @ X51 @ X52 ) ) ).
% fm.distinct(25)
thf(fact_89_fm_Odistinct_I27_J,axiom,
! [X41: epistemic_fm_a,X42: epistemic_fm_a,X61: a,X62: epistemic_fm_a] :
( ( epistemic_Con_a @ X41 @ X42 )
!= ( epistemic_K_a @ X61 @ X62 ) ) ).
% fm.distinct(27)
thf(fact_90_K__thm,axiom,
! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ Q @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_Con_a @ P @ Q ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ).
% K_thm
thf(fact_91_K__right__mp,axiom,
! [A: epistemic_fm_a > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
=> ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ ( epistemic_Imp_a @ P @ Q ) ) )
=> ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ Q ) ) ) ) ).
% K_right_mp
thf(fact_92_imply_Osimps_I1_J,axiom,
! [Q: epistemic_fm_a] :
( ( epistemic_imply_a @ nil_Epistemic_fm_a @ Q )
= Q ) ).
% imply.simps(1)
thf(fact_93_K__imply__multi,axiom,
! [A: epistemic_fm_a > $o,A2: epistemic_fm_a,B: epistemic_fm_a,C: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ A2 @ B ) )
=> ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ A2 @ C ) )
=> ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ A2 @ ( epistemic_Con_a @ B @ C ) ) ) ) ) ).
% K_imply_multi
thf(fact_94_K__multi__imply,axiom,
! [A: epistemic_fm_a > $o,A2: epistemic_fm_a,B: epistemic_fm_a,C: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ A2 @ ( epistemic_Imp_a @ B @ C ) ) )
=> ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Con_a @ A2 @ B ) @ C ) ) ) ).
% K_multi_imply
thf(fact_95_K__LK,axiom,
! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ).
% K_LK
thf(fact_96_K__L__dual,axiom,
! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ P ) ) ) ).
% K_L_dual
thf(fact_97_AK_Ocases,axiom,
! [A: epistemic_fm_a > $o,A2: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ A2 )
=> ( ~ ! [G2: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H @ A2 )
=> ( ! [I2: a,P3: epistemic_fm_a,Q2: epistemic_fm_a] :
( A2
!= ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I2 @ P3 ) @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P3 @ Q2 ) ) ) @ ( epistemic_K_a @ I2 @ Q2 ) ) )
=> ( ~ ( A @ A2 )
=> ( ! [P3: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ P3 )
=> ~ ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P3 @ A2 ) ) )
=> ~ ! [P3: epistemic_fm_a] :
( ? [I2: a] :
( A2
= ( epistemic_K_a @ I2 @ P3 ) )
=> ~ ( epistemic_AK_a @ A @ P3 ) ) ) ) ) ) ) ).
% AK.cases
thf(fact_98_mem__Collect__eq,axiom,
! [A2: list_Epistemic_fm_a,P2: list_Epistemic_fm_a > $o] :
( ( member5906877432388582473c_fm_a @ A2 @ ( collec5191077796991884427c_fm_a @ P2 ) )
= ( P2 @ A2 ) ) ).
% mem_Collect_eq
thf(fact_99_mem__Collect__eq,axiom,
! [A2: produc5756089960658898087c_fm_a,P2: produc5756089960658898087c_fm_a > $o] :
( ( member3265983909902097104c_fm_a @ A2 @ ( collec6124610372686893330c_fm_a @ P2 ) )
= ( P2 @ A2 ) ) ).
% mem_Collect_eq
thf(fact_100_mem__Collect__eq,axiom,
! [A2: produc2203834439629243303c_fm_a,P2: produc2203834439629243303c_fm_a > $o] :
( ( member5029746173879296720c_fm_a @ A2 @ ( collec7391038856303340306c_fm_a @ P2 ) )
= ( P2 @ A2 ) ) ).
% mem_Collect_eq
thf(fact_101_mem__Collect__eq,axiom,
! [A2: set_Epistemic_fm_a,P2: set_Epistemic_fm_a > $o] :
( ( member536094252920883875c_fm_a @ A2 @ ( collec2519470961442302949c_fm_a @ P2 ) )
= ( P2 @ A2 ) ) ).
% mem_Collect_eq
thf(fact_102_mem__Collect__eq,axiom,
! [A2: epistemic_fm_a,P2: epistemic_fm_a > $o] :
( ( member6642669571620171971c_fm_a @ A2 @ ( collec4904205152690461189c_fm_a @ P2 ) )
= ( P2 @ A2 ) ) ).
% mem_Collect_eq
thf(fact_103_Collect__mem__eq,axiom,
! [A: set_li769143395467472256c_fm_a] :
( ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ X @ A ) )
= A ) ).
% Collect_mem_eq
thf(fact_104_Collect__mem__eq,axiom,
! [A: set_Pr3219225162411408519c_fm_a] :
( ( collec6124610372686893330c_fm_a
@ ^ [X: produc5756089960658898087c_fm_a] : ( member3265983909902097104c_fm_a @ X @ A ) )
= A ) ).
% Collect_mem_eq
thf(fact_105_Collect__mem__eq,axiom,
! [A: set_Pr8948481099588399239c_fm_a] :
( ( collec7391038856303340306c_fm_a
@ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ A ) )
= A ) ).
% Collect_mem_eq
thf(fact_106_Collect__mem__eq,axiom,
! [A: set_se5208064806568342746c_fm_a] :
( ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ A ) )
= A ) ).
% Collect_mem_eq
thf(fact_107_Collect__mem__eq,axiom,
! [A: set_Epistemic_fm_a] :
( ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ A ) )
= A ) ).
% Collect_mem_eq
thf(fact_108_Collect__cong,axiom,
! [P2: set_Epistemic_fm_a > $o,Q3: set_Epistemic_fm_a > $o] :
( ! [X2: set_Epistemic_fm_a] :
( ( P2 @ X2 )
= ( Q3 @ X2 ) )
=> ( ( collec2519470961442302949c_fm_a @ P2 )
= ( collec2519470961442302949c_fm_a @ Q3 ) ) ) ).
% Collect_cong
thf(fact_109_Collect__cong,axiom,
! [P2: epistemic_fm_a > $o,Q3: epistemic_fm_a > $o] :
( ! [X2: epistemic_fm_a] :
( ( P2 @ X2 )
= ( Q3 @ X2 ) )
=> ( ( collec4904205152690461189c_fm_a @ P2 )
= ( collec4904205152690461189c_fm_a @ Q3 ) ) ) ).
% Collect_cong
thf(fact_110_AK_Osimps,axiom,
( epistemic_AK_a
= ( ^ [A3: epistemic_fm_a > $o,A4: epistemic_fm_a] :
( ? [P4: epistemic_fm_a] :
( ( A4 = P4 )
& ! [G3: list_char > $o,H2: epistemic_fm_a > $o] : ( epistemic_eval_a @ G3 @ H2 @ P4 ) )
| ? [I3: a,P4: epistemic_fm_a,Q4: epistemic_fm_a] :
( A4
= ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I3 @ P4 ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P4 @ Q4 ) ) ) @ ( epistemic_K_a @ I3 @ Q4 ) ) )
| ? [P4: epistemic_fm_a] :
( ( A4 = P4 )
& ( A3 @ P4 ) )
| ? [P4: epistemic_fm_a,Q4: epistemic_fm_a] :
( ( A4 = Q4 )
& ( epistemic_AK_a @ A3 @ P4 )
& ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ P4 @ Q4 ) ) )
| ? [P4: epistemic_fm_a,I3: a] :
( ( A4
= ( epistemic_K_a @ I3 @ P4 ) )
& ( epistemic_AK_a @ A3 @ P4 ) ) ) ) ) ).
% AK.simps
thf(fact_111_AxB_Ocases,axiom,
! [A2: epistemic_fm_a] :
( ( epistemic_AxB_a @ A2 )
=> ~ ! [P3: epistemic_fm_a,I2: a] :
( A2
!= ( epistemic_Imp_a @ P3 @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P3 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ).
% AxB.cases
thf(fact_112_AxB_Osimps,axiom,
( epistemic_AxB_a
= ( ^ [A4: epistemic_fm_a] :
? [P4: epistemic_fm_a,I3: a] :
( A4
= ( epistemic_Imp_a @ P4 @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P4 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).
% AxB.simps
thf(fact_113_AxB_Ointros,axiom,
! [P: epistemic_fm_a,I: a] : ( epistemic_AxB_a @ ( epistemic_Imp_a @ P @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).
% AxB.intros
thf(fact_114_conjunct__imply,axiom,
! [G: list_Epistemic_fm_a,P: epistemic_fm_a,G2: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G ) @ P ) @ ( epistemic_imply_a @ G @ P ) ) ) ).
% conjunct_imply
thf(fact_115_imply__conjunct,axiom,
! [G: list_Epistemic_fm_a,P: epistemic_fm_a,G2: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H @ ( epistemic_Imp_a @ ( epistemic_imply_a @ G @ P ) @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G ) @ P ) ) ) ).
% imply_conjunct
thf(fact_116_Ax5_Ocases,axiom,
! [A2: epistemic_fm_a] :
( ( epistemic_Ax5_a @ A2 )
=> ~ ! [I2: a,P3: epistemic_fm_a] :
( A2
!= ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P3 @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P3 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ).
% Ax5.cases
thf(fact_117_Ax5_Osimps,axiom,
( epistemic_Ax5_a
= ( ^ [A4: epistemic_fm_a] :
? [I3: a,P4: epistemic_fm_a] :
( A4
= ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P4 @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P4 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).
% Ax5.simps
thf(fact_118_eval_Osimps_I5_J,axiom,
! [G4: list_char > $o,H3: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
( ( epistemic_eval_a @ G4 @ H3 @ ( epistemic_Imp_a @ P @ Q ) )
= ( ( epistemic_eval_a @ G4 @ H3 @ P )
=> ( epistemic_eval_a @ G4 @ H3 @ Q ) ) ) ).
% eval.simps(5)
thf(fact_119_eval_Osimps_I6_J,axiom,
! [Ux: list_char > $o,H3: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
( ( epistemic_eval_a @ Ux @ H3 @ ( epistemic_K_a @ I @ P ) )
= ( H3 @ ( epistemic_K_a @ I @ P ) ) ) ).
% eval.simps(6)
thf(fact_120_A1,axiom,
! [P: epistemic_fm_a,A: epistemic_fm_a > $o] :
( ! [G5: list_char > $o,H4: epistemic_fm_a > $o] : ( epistemic_eval_a @ G5 @ H4 @ P )
=> ( epistemic_AK_a @ A @ P ) ) ).
% A1
thf(fact_121_eval_Osimps_I1_J,axiom,
! [Uu: list_char > $o,Uv: epistemic_fm_a > $o] :
~ ( epistemic_eval_a @ Uu @ Uv @ epistemic_FF_a ) ).
% eval.simps(1)
thf(fact_122_eval_Osimps_I4_J,axiom,
! [G4: list_char > $o,H3: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
( ( epistemic_eval_a @ G4 @ H3 @ ( epistemic_Con_a @ P @ Q ) )
= ( ( epistemic_eval_a @ G4 @ H3 @ P )
& ( epistemic_eval_a @ G4 @ H3 @ Q ) ) ) ).
% eval.simps(4)
thf(fact_123_duality__taut,axiom,
! [I: a,P: epistemic_fm_a,Q: epistemic_fm_a,G2: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ Q @ epistemic_FF_a ) ) ) @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ Q @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ) ).
% duality_taut
thf(fact_124_Ax5_Ointros,axiom,
! [I: a,P: epistemic_fm_a] : ( epistemic_Ax5_a @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).
% Ax5.intros
thf(fact_125_K5__L,axiom,
! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A )
=> ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ P ) ) ) ) ).
% K5_L
thf(fact_126_K__Boole,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,G: list_Epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ G ) @ epistemic_FF_a ) )
=> ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G @ P ) ) ) ).
% K_Boole
thf(fact_127_distribution,axiom,
! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ Q ) ) ) @ ( epistemic_K_a @ I @ Q ) ) ) ).
% distribution
thf(fact_128_K__ImpI,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,G: list_Epistemic_fm_a,Q: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ G ) @ Q ) )
=> ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G @ ( epistemic_Imp_a @ P @ Q ) ) ) ) ).
% K_ImpI
thf(fact_129_K__mp,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,G: list_Epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ ( cons_Epistemic_fm_a @ ( epistemic_Imp_a @ P @ Q ) @ G ) ) @ Q ) ) ).
% K_mp
thf(fact_130_KB4__5,axiom,
! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
( ( ord_le4043730696559282883fm_a_o @ epistemic_AxB_a @ A )
=> ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax4_a @ A )
=> ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).
% KB4_5
thf(fact_131_Ax4_Ointros,axiom,
! [I: a,P: epistemic_fm_a] : ( epistemic_Ax4_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ).
% Ax4.intros
thf(fact_132_Ax4_Osimps,axiom,
( epistemic_Ax4_a
= ( ^ [A4: epistemic_fm_a] :
? [I3: a,P4: epistemic_fm_a] :
( A4
= ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P4 ) @ ( epistemic_K_a @ I3 @ ( epistemic_K_a @ I3 @ P4 ) ) ) ) ) ) ).
% Ax4.simps
thf(fact_133_Ax4_Ocases,axiom,
! [A2: epistemic_fm_a] :
( ( epistemic_Ax4_a @ A2 )
=> ~ ! [I2: a,P3: epistemic_fm_a] :
( A2
!= ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ P3 ) @ ( epistemic_K_a @ I2 @ ( epistemic_K_a @ I2 @ P3 ) ) ) ) ) ).
% Ax4.cases
thf(fact_134_gen__length__code_I1_J,axiom,
! [N: nat] :
( ( gen_le594266534207918899c_fm_a @ N @ nil_li2451196919128234278c_fm_a )
= N ) ).
% gen_length_code(1)
thf(fact_135_gen__length__code_I1_J,axiom,
! [N: nat] :
( ( gen_le8786096720482678413c_fm_a @ N @ nil_se102576565402781184c_fm_a )
= N ) ).
% gen_length_code(1)
thf(fact_136_gen__length__code_I1_J,axiom,
! [N: nat] :
( ( gen_le2174843865799460013c_fm_a @ N @ nil_Epistemic_fm_a )
= N ) ).
% gen_length_code(1)
thf(fact_137_list_Oinject,axiom,
! [X21: epistemic_fm_a,X22: list_Epistemic_fm_a,Y21: epistemic_fm_a,Y22: list_Epistemic_fm_a] :
( ( ( cons_Epistemic_fm_a @ X21 @ X22 )
= ( cons_Epistemic_fm_a @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% list.inject
thf(fact_138_list_Oinject,axiom,
! [X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a,Y21: list_Epistemic_fm_a,Y22: list_l6083326122719238310c_fm_a] :
( ( ( cons_l8134865115577406678c_fm_a @ X21 @ X22 )
= ( cons_l8134865115577406678c_fm_a @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% list.inject
thf(fact_139_Imp__intro,axiom,
! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
( ( ( episte7081087998767065248c_fm_a @ M @ W @ P )
=> ( episte7081087998767065248c_fm_a @ M @ W @ Q ) )
=> ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Imp_a @ P @ Q ) ) ) ).
% Imp_intro
thf(fact_140_not__Cons__self2,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( cons_Epistemic_fm_a @ X3 @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_141_not__Cons__self2,axiom,
! [X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( cons_l8134865115577406678c_fm_a @ X3 @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_142_transpose_Ocases,axiom,
! [X3: list_l985973790606564998c_fm_a] :
( ( X3 != nil_li5433889876484989702c_fm_a )
=> ( ! [Xss: list_l985973790606564998c_fm_a] :
( X3
!= ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ Xss ) )
=> ~ ! [X2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a,Xss: list_l985973790606564998c_fm_a] :
( X3
!= ( cons_l1626872963913326262c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs3 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_143_transpose_Ocases,axiom,
! [X3: list_l3671048651222332332c_fm_a] :
( ( X3 != nil_li5178944226519631276c_fm_a )
=> ( ! [Xss: list_l3671048651222332332c_fm_a] :
( X3
!= ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ Xss ) )
=> ~ ! [X2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a,Xss: list_l3671048651222332332c_fm_a] :
( X3
!= ( cons_l2479501935080859996c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs3 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_144_transpose_Ocases,axiom,
! [X3: list_l6083326122719238310c_fm_a] :
( ( X3 != nil_li2451196919128234278c_fm_a )
=> ( ! [Xss: list_l6083326122719238310c_fm_a] :
( X3
!= ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ Xss ) )
=> ~ ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Xss: list_l6083326122719238310c_fm_a] :
( X3
!= ( cons_l8134865115577406678c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_145_list_Odistinct_I1_J,axiom,
! [X21: set_Epistemic_fm_a,X22: list_s580375451141968640c_fm_a] :
( nil_se102576565402781184c_fm_a
!= ( cons_s4394448069393209776c_fm_a @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_146_list_Odistinct_I1_J,axiom,
! [X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] :
( nil_li2451196919128234278c_fm_a
!= ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_147_list_Odistinct_I1_J,axiom,
! [X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
( nil_Epistemic_fm_a
!= ( cons_Epistemic_fm_a @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_148_list_OdiscI,axiom,
! [List: list_s580375451141968640c_fm_a,X21: set_Epistemic_fm_a,X22: list_s580375451141968640c_fm_a] :
( ( List
= ( cons_s4394448069393209776c_fm_a @ X21 @ X22 ) )
=> ( List != nil_se102576565402781184c_fm_a ) ) ).
% list.discI
thf(fact_149_list_OdiscI,axiom,
! [List: list_l6083326122719238310c_fm_a,X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] :
( ( List
= ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) )
=> ( List != nil_li2451196919128234278c_fm_a ) ) ).
% list.discI
thf(fact_150_list_OdiscI,axiom,
! [List: list_Epistemic_fm_a,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
( ( List
= ( cons_Epistemic_fm_a @ X21 @ X22 ) )
=> ( List != nil_Epistemic_fm_a ) ) ).
% list.discI
thf(fact_151_list_Oexhaust,axiom,
! [Y: list_s580375451141968640c_fm_a] :
( ( Y != nil_se102576565402781184c_fm_a )
=> ~ ! [X212: set_Epistemic_fm_a,X222: list_s580375451141968640c_fm_a] :
( Y
!= ( cons_s4394448069393209776c_fm_a @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_152_list_Oexhaust,axiom,
! [Y: list_l6083326122719238310c_fm_a] :
( ( Y != nil_li2451196919128234278c_fm_a )
=> ~ ! [X212: list_Epistemic_fm_a,X222: list_l6083326122719238310c_fm_a] :
( Y
!= ( cons_l8134865115577406678c_fm_a @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_153_list_Oexhaust,axiom,
! [Y: list_Epistemic_fm_a] :
( ( Y != nil_Epistemic_fm_a )
=> ~ ! [X212: epistemic_fm_a,X222: list_Epistemic_fm_a] :
( Y
!= ( cons_Epistemic_fm_a @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_154_min__list_Ocases,axiom,
! [X3: list_s580375451141968640c_fm_a] :
( ! [X2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] :
( X3
!= ( cons_s4394448069393209776c_fm_a @ X2 @ Xs3 ) )
=> ( X3 = nil_se102576565402781184c_fm_a ) ) ).
% min_list.cases
thf(fact_155_remdups__adj_Ocases,axiom,
! [X3: list_s580375451141968640c_fm_a] :
( ( X3 != nil_se102576565402781184c_fm_a )
=> ( ! [X2: set_Epistemic_fm_a] :
( X3
!= ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a ) )
=> ~ ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] :
( X3
!= ( cons_s4394448069393209776c_fm_a @ X2 @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Xs3 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_156_remdups__adj_Ocases,axiom,
! [X3: list_l6083326122719238310c_fm_a] :
( ( X3 != nil_li2451196919128234278c_fm_a )
=> ( ! [X2: list_Epistemic_fm_a] :
( X3
!= ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a ) )
=> ~ ! [X2: list_Epistemic_fm_a,Y2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] :
( X3
!= ( cons_l8134865115577406678c_fm_a @ X2 @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Xs3 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_157_remdups__adj_Ocases,axiom,
! [X3: list_Epistemic_fm_a] :
( ( X3 != nil_Epistemic_fm_a )
=> ( ! [X2: epistemic_fm_a] :
( X3
!= ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) )
=> ~ ! [X2: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( X3
!= ( cons_Epistemic_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_158_neq__Nil__conv,axiom,
! [Xs: list_s580375451141968640c_fm_a] :
( ( Xs != nil_se102576565402781184c_fm_a )
= ( ? [Y3: set_Epistemic_fm_a,Ys: list_s580375451141968640c_fm_a] :
( Xs
= ( cons_s4394448069393209776c_fm_a @ Y3 @ Ys ) ) ) ) ).
% neq_Nil_conv
thf(fact_159_neq__Nil__conv,axiom,
! [Xs: list_l6083326122719238310c_fm_a] :
( ( Xs != nil_li2451196919128234278c_fm_a )
= ( ? [Y3: list_Epistemic_fm_a,Ys: list_l6083326122719238310c_fm_a] :
( Xs
= ( cons_l8134865115577406678c_fm_a @ Y3 @ Ys ) ) ) ) ).
% neq_Nil_conv
thf(fact_160_neq__Nil__conv,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( Xs != nil_Epistemic_fm_a )
= ( ? [Y3: epistemic_fm_a,Ys: list_Epistemic_fm_a] :
( Xs
= ( cons_Epistemic_fm_a @ Y3 @ Ys ) ) ) ) ).
% neq_Nil_conv
thf(fact_161_list__induct2_H,axiom,
! [P2: list_s580375451141968640c_fm_a > list_s580375451141968640c_fm_a > $o,Xs: list_s580375451141968640c_fm_a,Ys2: list_s580375451141968640c_fm_a] :
( ( P2 @ nil_se102576565402781184c_fm_a @ nil_se102576565402781184c_fm_a )
=> ( ! [X2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] : ( P2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs3 ) @ nil_se102576565402781184c_fm_a )
=> ( ! [Y2: set_Epistemic_fm_a,Ys3: list_s580375451141968640c_fm_a] : ( P2 @ nil_se102576565402781184c_fm_a @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Ys3 ) )
=> ( ! [X2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a,Y2: set_Epistemic_fm_a,Ys3: list_s580375451141968640c_fm_a] :
( ( P2 @ Xs3 @ Ys3 )
=> ( P2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs3 ) @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Ys3 ) ) )
=> ( P2 @ Xs @ Ys2 ) ) ) ) ) ).
% list_induct2'
thf(fact_162_list__induct2_H,axiom,
! [P2: list_s580375451141968640c_fm_a > list_Epistemic_fm_a > $o,Xs: list_s580375451141968640c_fm_a,Ys2: list_Epistemic_fm_a] :
( ( P2 @ nil_se102576565402781184c_fm_a @ nil_Epistemic_fm_a )
=> ( ! [X2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] : ( P2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs3 ) @ nil_Epistemic_fm_a )
=> ( ! [Y2: epistemic_fm_a,Ys3: list_Epistemic_fm_a] : ( P2 @ nil_se102576565402781184c_fm_a @ ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) )
=> ( ! [X2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a,Y2: epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
( ( P2 @ Xs3 @ Ys3 )
=> ( P2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs3 ) @ ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) ) )
=> ( P2 @ Xs @ Ys2 ) ) ) ) ) ).
% list_induct2'
thf(fact_163_list__induct2_H,axiom,
! [P2: list_s580375451141968640c_fm_a > list_l6083326122719238310c_fm_a > $o,Xs: list_s580375451141968640c_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
( ( P2 @ nil_se102576565402781184c_fm_a @ nil_li2451196919128234278c_fm_a )
=> ( ! [X2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] : ( P2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs3 ) @ nil_li2451196919128234278c_fm_a )
=> ( ! [Y2: list_Epistemic_fm_a,Ys3: list_l6083326122719238310c_fm_a] : ( P2 @ nil_se102576565402781184c_fm_a @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Ys3 ) )
=> ( ! [X2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a,Y2: list_Epistemic_fm_a,Ys3: list_l6083326122719238310c_fm_a] :
( ( P2 @ Xs3 @ Ys3 )
=> ( P2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs3 ) @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Ys3 ) ) )
=> ( P2 @ Xs @ Ys2 ) ) ) ) ) ).
% list_induct2'
thf(fact_164_list__induct2_H,axiom,
! [P2: list_Epistemic_fm_a > list_s580375451141968640c_fm_a > $o,Xs: list_Epistemic_fm_a,Ys2: list_s580375451141968640c_fm_a] :
( ( P2 @ nil_Epistemic_fm_a @ nil_se102576565402781184c_fm_a )
=> ( ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] : ( P2 @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ nil_se102576565402781184c_fm_a )
=> ( ! [Y2: set_Epistemic_fm_a,Ys3: list_s580375451141968640c_fm_a] : ( P2 @ nil_Epistemic_fm_a @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Ys3 ) )
=> ( ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Y2: set_Epistemic_fm_a,Ys3: list_s580375451141968640c_fm_a] :
( ( P2 @ Xs3 @ Ys3 )
=> ( P2 @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Ys3 ) ) )
=> ( P2 @ Xs @ Ys2 ) ) ) ) ) ).
% list_induct2'
thf(fact_165_list__induct2_H,axiom,
! [P2: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a > $o,Xs: list_Epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
( ( P2 @ nil_Epistemic_fm_a @ nil_li2451196919128234278c_fm_a )
=> ( ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] : ( P2 @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ nil_li2451196919128234278c_fm_a )
=> ( ! [Y2: list_Epistemic_fm_a,Ys3: list_l6083326122719238310c_fm_a] : ( P2 @ nil_Epistemic_fm_a @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Ys3 ) )
=> ( ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Y2: list_Epistemic_fm_a,Ys3: list_l6083326122719238310c_fm_a] :
( ( P2 @ Xs3 @ Ys3 )
=> ( P2 @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Ys3 ) ) )
=> ( P2 @ Xs @ Ys2 ) ) ) ) ) ).
% list_induct2'
thf(fact_166_list__induct2_H,axiom,
! [P2: list_l6083326122719238310c_fm_a > list_s580375451141968640c_fm_a > $o,Xs: list_l6083326122719238310c_fm_a,Ys2: list_s580375451141968640c_fm_a] :
( ( P2 @ nil_li2451196919128234278c_fm_a @ nil_se102576565402781184c_fm_a )
=> ( ! [X2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] : ( P2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs3 ) @ nil_se102576565402781184c_fm_a )
=> ( ! [Y2: set_Epistemic_fm_a,Ys3: list_s580375451141968640c_fm_a] : ( P2 @ nil_li2451196919128234278c_fm_a @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Ys3 ) )
=> ( ! [X2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a,Y2: set_Epistemic_fm_a,Ys3: list_s580375451141968640c_fm_a] :
( ( P2 @ Xs3 @ Ys3 )
=> ( P2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs3 ) @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Ys3 ) ) )
=> ( P2 @ Xs @ Ys2 ) ) ) ) ) ).
% list_induct2'
thf(fact_167_list__induct2_H,axiom,
! [P2: list_l6083326122719238310c_fm_a > list_Epistemic_fm_a > $o,Xs: list_l6083326122719238310c_fm_a,Ys2: list_Epistemic_fm_a] :
( ( P2 @ nil_li2451196919128234278c_fm_a @ nil_Epistemic_fm_a )
=> ( ! [X2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] : ( P2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs3 ) @ nil_Epistemic_fm_a )
=> ( ! [Y2: epistemic_fm_a,Ys3: list_Epistemic_fm_a] : ( P2 @ nil_li2451196919128234278c_fm_a @ ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) )
=> ( ! [X2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a,Y2: epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
( ( P2 @ Xs3 @ Ys3 )
=> ( P2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs3 ) @ ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) ) )
=> ( P2 @ Xs @ Ys2 ) ) ) ) ) ).
% list_induct2'
thf(fact_168_list__induct2_H,axiom,
! [P2: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o,Xs: list_l6083326122719238310c_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
( ( P2 @ nil_li2451196919128234278c_fm_a @ nil_li2451196919128234278c_fm_a )
=> ( ! [X2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] : ( P2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs3 ) @ nil_li2451196919128234278c_fm_a )
=> ( ! [Y2: list_Epistemic_fm_a,Ys3: list_l6083326122719238310c_fm_a] : ( P2 @ nil_li2451196919128234278c_fm_a @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Ys3 ) )
=> ( ! [X2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a,Y2: list_Epistemic_fm_a,Ys3: list_l6083326122719238310c_fm_a] :
( ( P2 @ Xs3 @ Ys3 )
=> ( P2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs3 ) @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Ys3 ) ) )
=> ( P2 @ Xs @ Ys2 ) ) ) ) ) ).
% list_induct2'
thf(fact_169_list__induct2_H,axiom,
! [P2: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( P2 @ nil_Epistemic_fm_a @ nil_Epistemic_fm_a )
=> ( ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] : ( P2 @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ nil_Epistemic_fm_a )
=> ( ! [Y2: epistemic_fm_a,Ys3: list_Epistemic_fm_a] : ( P2 @ nil_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) )
=> ( ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Y2: epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
( ( P2 @ Xs3 @ Ys3 )
=> ( P2 @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) ) )
=> ( P2 @ Xs @ Ys2 ) ) ) ) ) ).
% list_induct2'
thf(fact_170_list__nonempty__induct,axiom,
! [Xs: list_s580375451141968640c_fm_a,P2: list_s580375451141968640c_fm_a > $o] :
( ( Xs != nil_se102576565402781184c_fm_a )
=> ( ! [X2: set_Epistemic_fm_a] : ( P2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a ) )
=> ( ! [X2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] :
( ( Xs3 != nil_se102576565402781184c_fm_a )
=> ( ( P2 @ Xs3 )
=> ( P2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs3 ) ) ) )
=> ( P2 @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_171_list__nonempty__induct,axiom,
! [Xs: list_l6083326122719238310c_fm_a,P2: list_l6083326122719238310c_fm_a > $o] :
( ( Xs != nil_li2451196919128234278c_fm_a )
=> ( ! [X2: list_Epistemic_fm_a] : ( P2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a ) )
=> ( ! [X2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] :
( ( Xs3 != nil_li2451196919128234278c_fm_a )
=> ( ( P2 @ Xs3 )
=> ( P2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs3 ) ) ) )
=> ( P2 @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_172_list__nonempty__induct,axiom,
! [Xs: list_Epistemic_fm_a,P2: list_Epistemic_fm_a > $o] :
( ( Xs != nil_Epistemic_fm_a )
=> ( ! [X2: epistemic_fm_a] : ( P2 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) )
=> ( ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( ( Xs3 != nil_Epistemic_fm_a )
=> ( ( P2 @ Xs3 )
=> ( P2 @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) ) ) )
=> ( P2 @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_173_list_Osimps_I9_J,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
( ( map_Ep1988204514693272906c_fm_a @ F @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
= ( cons_l8134865115577406678c_fm_a @ ( F @ X21 ) @ ( map_Ep1988204514693272906c_fm_a @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_174_list_Osimps_I9_J,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] :
( ( map_li3858915945532548554c_fm_a @ F @ ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) )
= ( cons_l2479501935080859996c_fm_a @ ( F @ X21 ) @ ( map_li3858915945532548554c_fm_a @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_175_list_Osimps_I9_J,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] :
( ( map_li5516866612190465598c_fm_a @ F @ ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) )
= ( cons_Epistemic_fm_a @ ( F @ X21 ) @ ( map_li5516866612190465598c_fm_a @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_176_list_Osimps_I9_J,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] :
( ( map_li3080774272885743684c_fm_a @ F @ ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) )
= ( cons_l8134865115577406678c_fm_a @ ( F @ X21 ) @ ( map_li3080774272885743684c_fm_a @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_177_list_Osimps_I9_J,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
( ( map_Ep7084560364594560580c_fm_a @ F @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
= ( cons_Epistemic_fm_a @ ( F @ X21 ) @ ( map_Ep7084560364594560580c_fm_a @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_178_Cons__eq__map__D,axiom,
! [X3: list_l6083326122719238310c_fm_a,Xs: list_l3671048651222332332c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
( ( ( cons_l2479501935080859996c_fm_a @ X3 @ Xs )
= ( map_li3858915945532548554c_fm_a @ F @ Ys2 ) )
=> ? [Z: list_Epistemic_fm_a,Zs: list_l6083326122719238310c_fm_a] :
( ( Ys2
= ( cons_l8134865115577406678c_fm_a @ Z @ Zs ) )
& ( X3
= ( F @ Z ) )
& ( Xs
= ( map_li3858915945532548554c_fm_a @ F @ Zs ) ) ) ) ).
% Cons_eq_map_D
thf(fact_179_Cons__eq__map__D,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
( ( ( cons_Epistemic_fm_a @ X3 @ Xs )
= ( map_li5516866612190465598c_fm_a @ F @ Ys2 ) )
=> ? [Z: list_Epistemic_fm_a,Zs: list_l6083326122719238310c_fm_a] :
( ( Ys2
= ( cons_l8134865115577406678c_fm_a @ Z @ Zs ) )
& ( X3
= ( F @ Z ) )
& ( Xs
= ( map_li5516866612190465598c_fm_a @ F @ Zs ) ) ) ) ).
% Cons_eq_map_D
thf(fact_180_Cons__eq__map__D,axiom,
! [X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( cons_l8134865115577406678c_fm_a @ X3 @ Xs )
= ( map_Ep1988204514693272906c_fm_a @ F @ Ys2 ) )
=> ? [Z: epistemic_fm_a,Zs: list_Epistemic_fm_a] :
( ( Ys2
= ( cons_Epistemic_fm_a @ Z @ Zs ) )
& ( X3
= ( F @ Z ) )
& ( Xs
= ( map_Ep1988204514693272906c_fm_a @ F @ Zs ) ) ) ) ).
% Cons_eq_map_D
thf(fact_181_Cons__eq__map__D,axiom,
! [X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
( ( ( cons_l8134865115577406678c_fm_a @ X3 @ Xs )
= ( map_li3080774272885743684c_fm_a @ F @ Ys2 ) )
=> ? [Z: list_Epistemic_fm_a,Zs: list_l6083326122719238310c_fm_a] :
( ( Ys2
= ( cons_l8134865115577406678c_fm_a @ Z @ Zs ) )
& ( X3
= ( F @ Z ) )
& ( Xs
= ( map_li3080774272885743684c_fm_a @ F @ Zs ) ) ) ) ).
% Cons_eq_map_D
thf(fact_182_Cons__eq__map__D,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( cons_Epistemic_fm_a @ X3 @ Xs )
= ( map_Ep7084560364594560580c_fm_a @ F @ Ys2 ) )
=> ? [Z: epistemic_fm_a,Zs: list_Epistemic_fm_a] :
( ( Ys2
= ( cons_Epistemic_fm_a @ Z @ Zs ) )
& ( X3
= ( F @ Z ) )
& ( Xs
= ( map_Ep7084560364594560580c_fm_a @ F @ Zs ) ) ) ) ).
% Cons_eq_map_D
thf(fact_183_map__eq__Cons__D,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a,Ys2: list_l3671048651222332332c_fm_a] :
( ( ( map_li3858915945532548554c_fm_a @ F @ Xs )
= ( cons_l2479501935080859996c_fm_a @ Y @ Ys2 ) )
=> ? [Z: list_Epistemic_fm_a,Zs: list_l6083326122719238310c_fm_a] :
( ( Xs
= ( cons_l8134865115577406678c_fm_a @ Z @ Zs ) )
& ( ( F @ Z )
= Y )
& ( ( map_li3858915945532548554c_fm_a @ F @ Zs )
= Ys2 ) ) ) ).
% map_eq_Cons_D
thf(fact_184_map__eq__Cons__D,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,Y: epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( map_li5516866612190465598c_fm_a @ F @ Xs )
= ( cons_Epistemic_fm_a @ Y @ Ys2 ) )
=> ? [Z: list_Epistemic_fm_a,Zs: list_l6083326122719238310c_fm_a] :
( ( Xs
= ( cons_l8134865115577406678c_fm_a @ Z @ Zs ) )
& ( ( F @ Z )
= Y )
& ( ( map_li5516866612190465598c_fm_a @ F @ Zs )
= Ys2 ) ) ) ).
% map_eq_Cons_D
thf(fact_185_map__eq__Cons__D,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs: list_Epistemic_fm_a,Y: list_Epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
( ( ( map_Ep1988204514693272906c_fm_a @ F @ Xs )
= ( cons_l8134865115577406678c_fm_a @ Y @ Ys2 ) )
=> ? [Z: epistemic_fm_a,Zs: list_Epistemic_fm_a] :
( ( Xs
= ( cons_Epistemic_fm_a @ Z @ Zs ) )
& ( ( F @ Z )
= Y )
& ( ( map_Ep1988204514693272906c_fm_a @ F @ Zs )
= Ys2 ) ) ) ).
% map_eq_Cons_D
thf(fact_186_map__eq__Cons__D,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,Y: list_Epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
( ( ( map_li3080774272885743684c_fm_a @ F @ Xs )
= ( cons_l8134865115577406678c_fm_a @ Y @ Ys2 ) )
=> ? [Z: list_Epistemic_fm_a,Zs: list_l6083326122719238310c_fm_a] :
( ( Xs
= ( cons_l8134865115577406678c_fm_a @ Z @ Zs ) )
& ( ( F @ Z )
= Y )
& ( ( map_li3080774272885743684c_fm_a @ F @ Zs )
= Ys2 ) ) ) ).
% map_eq_Cons_D
thf(fact_187_map__eq__Cons__D,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a,Y: epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs )
= ( cons_Epistemic_fm_a @ Y @ Ys2 ) )
=> ? [Z: epistemic_fm_a,Zs: list_Epistemic_fm_a] :
( ( Xs
= ( cons_Epistemic_fm_a @ Z @ Zs ) )
& ( ( F @ Z )
= Y )
& ( ( map_Ep7084560364594560580c_fm_a @ F @ Zs )
= Ys2 ) ) ) ).
% map_eq_Cons_D
thf(fact_188_Cons__eq__map__conv,axiom,
! [X3: list_l6083326122719238310c_fm_a,Xs: list_l3671048651222332332c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
( ( ( cons_l2479501935080859996c_fm_a @ X3 @ Xs )
= ( map_li3858915945532548554c_fm_a @ F @ Ys2 ) )
= ( ? [Z2: list_Epistemic_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
( ( Ys2
= ( cons_l8134865115577406678c_fm_a @ Z2 @ Zs2 ) )
& ( X3
= ( F @ Z2 ) )
& ( Xs
= ( map_li3858915945532548554c_fm_a @ F @ Zs2 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_189_Cons__eq__map__conv,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
( ( ( cons_Epistemic_fm_a @ X3 @ Xs )
= ( map_li5516866612190465598c_fm_a @ F @ Ys2 ) )
= ( ? [Z2: list_Epistemic_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
( ( Ys2
= ( cons_l8134865115577406678c_fm_a @ Z2 @ Zs2 ) )
& ( X3
= ( F @ Z2 ) )
& ( Xs
= ( map_li5516866612190465598c_fm_a @ F @ Zs2 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_190_Cons__eq__map__conv,axiom,
! [X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( cons_l8134865115577406678c_fm_a @ X3 @ Xs )
= ( map_Ep1988204514693272906c_fm_a @ F @ Ys2 ) )
= ( ? [Z2: epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
( ( Ys2
= ( cons_Epistemic_fm_a @ Z2 @ Zs2 ) )
& ( X3
= ( F @ Z2 ) )
& ( Xs
= ( map_Ep1988204514693272906c_fm_a @ F @ Zs2 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_191_Cons__eq__map__conv,axiom,
! [X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
( ( ( cons_l8134865115577406678c_fm_a @ X3 @ Xs )
= ( map_li3080774272885743684c_fm_a @ F @ Ys2 ) )
= ( ? [Z2: list_Epistemic_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
( ( Ys2
= ( cons_l8134865115577406678c_fm_a @ Z2 @ Zs2 ) )
& ( X3
= ( F @ Z2 ) )
& ( Xs
= ( map_li3080774272885743684c_fm_a @ F @ Zs2 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_192_Cons__eq__map__conv,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( cons_Epistemic_fm_a @ X3 @ Xs )
= ( map_Ep7084560364594560580c_fm_a @ F @ Ys2 ) )
= ( ? [Z2: epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
( ( Ys2
= ( cons_Epistemic_fm_a @ Z2 @ Zs2 ) )
& ( X3
= ( F @ Z2 ) )
& ( Xs
= ( map_Ep7084560364594560580c_fm_a @ F @ Zs2 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_193_map__eq__Cons__conv,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a,Ys2: list_l3671048651222332332c_fm_a] :
( ( ( map_li3858915945532548554c_fm_a @ F @ Xs )
= ( cons_l2479501935080859996c_fm_a @ Y @ Ys2 ) )
= ( ? [Z2: list_Epistemic_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
( ( Xs
= ( cons_l8134865115577406678c_fm_a @ Z2 @ Zs2 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_li3858915945532548554c_fm_a @ F @ Zs2 )
= Ys2 ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_194_map__eq__Cons__conv,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,Y: epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( map_li5516866612190465598c_fm_a @ F @ Xs )
= ( cons_Epistemic_fm_a @ Y @ Ys2 ) )
= ( ? [Z2: list_Epistemic_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
( ( Xs
= ( cons_l8134865115577406678c_fm_a @ Z2 @ Zs2 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_li5516866612190465598c_fm_a @ F @ Zs2 )
= Ys2 ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_195_map__eq__Cons__conv,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs: list_Epistemic_fm_a,Y: list_Epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
( ( ( map_Ep1988204514693272906c_fm_a @ F @ Xs )
= ( cons_l8134865115577406678c_fm_a @ Y @ Ys2 ) )
= ( ? [Z2: epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
( ( Xs
= ( cons_Epistemic_fm_a @ Z2 @ Zs2 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_Ep1988204514693272906c_fm_a @ F @ Zs2 )
= Ys2 ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_196_map__eq__Cons__conv,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,Y: list_Epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
( ( ( map_li3080774272885743684c_fm_a @ F @ Xs )
= ( cons_l8134865115577406678c_fm_a @ Y @ Ys2 ) )
= ( ? [Z2: list_Epistemic_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
( ( Xs
= ( cons_l8134865115577406678c_fm_a @ Z2 @ Zs2 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_li3080774272885743684c_fm_a @ F @ Zs2 )
= Ys2 ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_197_map__eq__Cons__conv,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a,Y: epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs )
= ( cons_Epistemic_fm_a @ Y @ Ys2 ) )
= ( ? [Z2: epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
( ( Xs
= ( cons_Epistemic_fm_a @ Z2 @ Zs2 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_Ep7084560364594560580c_fm_a @ F @ Zs2 )
= Ys2 ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_198_semantics_Osimps_I5_J,axiom,
! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
( ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Imp_a @ P @ Q ) )
= ( ( episte7081087998767065248c_fm_a @ M @ W @ P )
=> ( episte7081087998767065248c_fm_a @ M @ W @ Q ) ) ) ).
% semantics.simps(5)
thf(fact_199_semantics_Osimps_I1_J,axiom,
! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
~ ( episte7081087998767065248c_fm_a @ M @ W @ epistemic_FF_a ) ).
% semantics.simps(1)
thf(fact_200_semantics_Osimps_I4_J,axiom,
! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
( ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Con_a @ P @ Q ) )
= ( ( episte7081087998767065248c_fm_a @ M @ W @ P )
& ( episte7081087998767065248c_fm_a @ M @ W @ Q ) ) ) ).
% semantics.simps(4)
thf(fact_201_tautology,axiom,
! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
( ! [G5: list_char > $o,H4: epistemic_fm_a > $o] : ( epistemic_eval_a @ G5 @ H4 @ P )
=> ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ).
% tautology
thf(fact_202_member__rec_I1_J,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a,Y: epistemic_fm_a] :
( ( member6038508265109909045c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs ) @ Y )
= ( ( X3 = Y )
| ( member6038508265109909045c_fm_a @ Xs @ Y ) ) ) ).
% member_rec(1)
thf(fact_203_member__rec_I1_J,axiom,
! [X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,Y: list_Epistemic_fm_a] :
( ( member594239076476917947c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs ) @ Y )
= ( ( X3 = Y )
| ( member594239076476917947c_fm_a @ Xs @ Y ) ) ) ).
% member_rec(1)
thf(fact_204_imply_Osimps_I2_J,axiom,
! [P: epistemic_fm_a,Ps: list_Epistemic_fm_a,Q: epistemic_fm_a] :
( ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ Ps ) @ Q )
= ( epistemic_Imp_a @ P @ ( epistemic_imply_a @ Ps @ Q ) ) ) ).
% imply.simps(2)
thf(fact_205_K__imply__head,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Ps: list_Epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ Ps ) @ P ) ) ).
% K_imply_head
thf(fact_206_K__imply__Cons,axiom,
! [A: epistemic_fm_a > $o,Ps: list_Epistemic_fm_a,Q: epistemic_fm_a,P: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ Q ) )
=> ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ Ps ) @ Q ) ) ) ).
% K_imply_Cons
thf(fact_207_K__swap,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,G: list_Epistemic_fm_a,R: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ ( cons_Epistemic_fm_a @ Q @ G ) ) @ R ) )
=> ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ Q @ ( cons_Epistemic_fm_a @ P @ G ) ) @ R ) ) ) ).
% K_swap
thf(fact_208_K4__L,axiom,
! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax4_a @ A )
=> ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).
% K4_L
thf(fact_209_conjunct_Osimps_I2_J,axiom,
! [P: epistemic_fm_a,Ps: list_Epistemic_fm_a] :
( ( stalnaker_conjunct_a @ ( cons_Epistemic_fm_a @ P @ Ps ) )
= ( epistemic_Con_a @ P @ ( stalnaker_conjunct_a @ Ps ) ) ) ).
% conjunct.simps(2)
thf(fact_210_predicate1I,axiom,
! [P2: epistemic_fm_a > $o,Q3: epistemic_fm_a > $o] :
( ! [X2: epistemic_fm_a] :
( ( P2 @ X2 )
=> ( Q3 @ X2 ) )
=> ( ord_le4043730696559282883fm_a_o @ P2 @ Q3 ) ) ).
% predicate1I
thf(fact_211_S5_H__B,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,I: a] :
( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A )
=> ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A )
=> ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).
% S5'_B
thf(fact_212_dual__order_Orefl,axiom,
! [A2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ A2 @ A2 ) ).
% dual_order.refl
thf(fact_213_dual__order_Orefl,axiom,
! [A2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A2 @ A2 ) ).
% dual_order.refl
thf(fact_214_dual__order_Orefl,axiom,
! [A2: set_li769143395467472256c_fm_a] : ( ord_le2931979837777675552c_fm_a @ A2 @ A2 ) ).
% dual_order.refl
thf(fact_215_order__refl,axiom,
! [X3: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ X3 @ X3 ) ).
% order_refl
thf(fact_216_order__refl,axiom,
! [X3: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ X3 @ X3 ) ).
% order_refl
thf(fact_217_order__refl,axiom,
! [X3: set_li769143395467472256c_fm_a] : ( ord_le2931979837777675552c_fm_a @ X3 @ X3 ) ).
% order_refl
thf(fact_218_S5_H__4,axiom,
! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A )
=> ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A )
=> ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ) ) ).
% S5'_4
thf(fact_219_le__fun__def,axiom,
( ord_le4043730696559282883fm_a_o
= ( ^ [F2: epistemic_fm_a > $o,G3: epistemic_fm_a > $o] :
! [X: epistemic_fm_a] : ( ord_less_eq_o @ ( F2 @ X ) @ ( G3 @ X ) ) ) ) ).
% le_fun_def
thf(fact_220_le__funI,axiom,
! [F: epistemic_fm_a > $o,G4: epistemic_fm_a > $o] :
( ! [X2: epistemic_fm_a] : ( ord_less_eq_o @ ( F @ X2 ) @ ( G4 @ X2 ) )
=> ( ord_le4043730696559282883fm_a_o @ F @ G4 ) ) ).
% le_funI
thf(fact_221_le__funE,axiom,
! [F: epistemic_fm_a > $o,G4: epistemic_fm_a > $o,X3: epistemic_fm_a] :
( ( ord_le4043730696559282883fm_a_o @ F @ G4 )
=> ( ord_less_eq_o @ ( F @ X3 ) @ ( G4 @ X3 ) ) ) ).
% le_funE
thf(fact_222_le__funD,axiom,
! [F: epistemic_fm_a > $o,G4: epistemic_fm_a > $o,X3: epistemic_fm_a] :
( ( ord_le4043730696559282883fm_a_o @ F @ G4 )
=> ( ord_less_eq_o @ ( F @ X3 ) @ ( G4 @ X3 ) ) ) ).
% le_funD
thf(fact_223_T__L,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,I: a] :
( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A )
=> ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).
% T_L
thf(fact_224_AxT_Ointros,axiom,
! [I: a,P: epistemic_fm_a] : ( epistemic_AxT_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ P ) ) ).
% AxT.intros
thf(fact_225_AxT_Osimps,axiom,
( epistemic_AxT_a
= ( ^ [A4: epistemic_fm_a] :
? [I3: a,P4: epistemic_fm_a] :
( A4
= ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P4 ) @ P4 ) ) ) ) ).
% AxT.simps
thf(fact_226_AxT_Ocases,axiom,
! [A2: epistemic_fm_a] :
( ( epistemic_AxT_a @ A2 )
=> ~ ! [I2: a,P3: epistemic_fm_a] :
( A2
!= ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ P3 ) @ P3 ) ) ) ).
% AxT.cases
thf(fact_227_order__class_Oorder__eq__iff,axiom,
( ( ^ [Y4: epistemic_fm_a > $o,Z3: epistemic_fm_a > $o] : ( Y4 = Z3 ) )
= ( ^ [X: epistemic_fm_a > $o,Y3: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X @ Y3 )
& ( ord_le4043730696559282883fm_a_o @ Y3 @ X ) ) ) ) ).
% order_class.order_eq_iff
thf(fact_228_order__class_Oorder__eq__iff,axiom,
( ( ^ [Y4: set_Epistemic_fm_a,Z3: set_Epistemic_fm_a] : ( Y4 = Z3 ) )
= ( ^ [X: set_Epistemic_fm_a,Y3: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X @ Y3 )
& ( ord_le3275665582123262618c_fm_a @ Y3 @ X ) ) ) ) ).
% order_class.order_eq_iff
thf(fact_229_order__class_Oorder__eq__iff,axiom,
( ( ^ [Y4: set_li769143395467472256c_fm_a,Z3: set_li769143395467472256c_fm_a] : ( Y4 = Z3 ) )
= ( ^ [X: set_li769143395467472256c_fm_a,Y3: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X @ Y3 )
& ( ord_le2931979837777675552c_fm_a @ Y3 @ X ) ) ) ) ).
% order_class.order_eq_iff
thf(fact_230_ord__eq__le__trans,axiom,
! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( A2 = B )
=> ( ( ord_le4043730696559282883fm_a_o @ B @ C )
=> ( ord_le4043730696559282883fm_a_o @ A2 @ C ) ) ) ).
% ord_eq_le_trans
thf(fact_231_ord__eq__le__trans,axiom,
! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( A2 = B )
=> ( ( ord_le3275665582123262618c_fm_a @ B @ C )
=> ( ord_le3275665582123262618c_fm_a @ A2 @ C ) ) ) ).
% ord_eq_le_trans
thf(fact_232_ord__eq__le__trans,axiom,
! [A2: set_li769143395467472256c_fm_a,B: set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( A2 = B )
=> ( ( ord_le2931979837777675552c_fm_a @ B @ C )
=> ( ord_le2931979837777675552c_fm_a @ A2 @ C ) ) ) ).
% ord_eq_le_trans
thf(fact_233_ord__le__eq__trans,axiom,
! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
=> ( ( B = C )
=> ( ord_le4043730696559282883fm_a_o @ A2 @ C ) ) ) ).
% ord_le_eq_trans
thf(fact_234_ord__le__eq__trans,axiom,
! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
=> ( ( B = C )
=> ( ord_le3275665582123262618c_fm_a @ A2 @ C ) ) ) ).
% ord_le_eq_trans
thf(fact_235_ord__le__eq__trans,axiom,
! [A2: set_li769143395467472256c_fm_a,B: set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A2 @ B )
=> ( ( B = C )
=> ( ord_le2931979837777675552c_fm_a @ A2 @ C ) ) ) ).
% ord_le_eq_trans
thf(fact_236_order__antisym,axiom,
! [X3: epistemic_fm_a > $o,Y: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X3 @ Y )
=> ( ( ord_le4043730696559282883fm_a_o @ Y @ X3 )
=> ( X3 = Y ) ) ) ).
% order_antisym
thf(fact_237_order__antisym,axiom,
! [X3: set_Epistemic_fm_a,Y: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X3 @ Y )
=> ( ( ord_le3275665582123262618c_fm_a @ Y @ X3 )
=> ( X3 = Y ) ) ) ).
% order_antisym
thf(fact_238_order__antisym,axiom,
! [X3: set_li769143395467472256c_fm_a,Y: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X3 @ Y )
=> ( ( ord_le2931979837777675552c_fm_a @ Y @ X3 )
=> ( X3 = Y ) ) ) ).
% order_antisym
thf(fact_239_order_Otrans,axiom,
! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
=> ( ( ord_le4043730696559282883fm_a_o @ B @ C )
=> ( ord_le4043730696559282883fm_a_o @ A2 @ C ) ) ) ).
% order.trans
thf(fact_240_order_Otrans,axiom,
! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
=> ( ( ord_le3275665582123262618c_fm_a @ B @ C )
=> ( ord_le3275665582123262618c_fm_a @ A2 @ C ) ) ) ).
% order.trans
thf(fact_241_order_Otrans,axiom,
! [A2: set_li769143395467472256c_fm_a,B: set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A2 @ B )
=> ( ( ord_le2931979837777675552c_fm_a @ B @ C )
=> ( ord_le2931979837777675552c_fm_a @ A2 @ C ) ) ) ).
% order.trans
thf(fact_242_order__trans,axiom,
! [X3: epistemic_fm_a > $o,Y: epistemic_fm_a > $o,Z4: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X3 @ Y )
=> ( ( ord_le4043730696559282883fm_a_o @ Y @ Z4 )
=> ( ord_le4043730696559282883fm_a_o @ X3 @ Z4 ) ) ) ).
% order_trans
thf(fact_243_order__trans,axiom,
! [X3: set_Epistemic_fm_a,Y: set_Epistemic_fm_a,Z4: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X3 @ Y )
=> ( ( ord_le3275665582123262618c_fm_a @ Y @ Z4 )
=> ( ord_le3275665582123262618c_fm_a @ X3 @ Z4 ) ) ) ).
% order_trans
thf(fact_244_order__trans,axiom,
! [X3: set_li769143395467472256c_fm_a,Y: set_li769143395467472256c_fm_a,Z4: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X3 @ Y )
=> ( ( ord_le2931979837777675552c_fm_a @ Y @ Z4 )
=> ( ord_le2931979837777675552c_fm_a @ X3 @ Z4 ) ) ) ).
% order_trans
thf(fact_245_dual__order_Oeq__iff,axiom,
( ( ^ [Y4: epistemic_fm_a > $o,Z3: epistemic_fm_a > $o] : ( Y4 = Z3 ) )
= ( ^ [A4: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ B2 @ A4 )
& ( ord_le4043730696559282883fm_a_o @ A4 @ B2 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_246_dual__order_Oeq__iff,axiom,
( ( ^ [Y4: set_Epistemic_fm_a,Z3: set_Epistemic_fm_a] : ( Y4 = Z3 ) )
= ( ^ [A4: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ B2 @ A4 )
& ( ord_le3275665582123262618c_fm_a @ A4 @ B2 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_247_dual__order_Oeq__iff,axiom,
( ( ^ [Y4: set_li769143395467472256c_fm_a,Z3: set_li769143395467472256c_fm_a] : ( Y4 = Z3 ) )
= ( ^ [A4: set_li769143395467472256c_fm_a,B2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ B2 @ A4 )
& ( ord_le2931979837777675552c_fm_a @ A4 @ B2 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_248_dual__order_Oantisym,axiom,
! [B: epistemic_fm_a > $o,A2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ B @ A2 )
=> ( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
=> ( A2 = B ) ) ) ).
% dual_order.antisym
thf(fact_249_dual__order_Oantisym,axiom,
! [B: set_Epistemic_fm_a,A2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ B @ A2 )
=> ( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
=> ( A2 = B ) ) ) ).
% dual_order.antisym
thf(fact_250_dual__order_Oantisym,axiom,
! [B: set_li769143395467472256c_fm_a,A2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ B @ A2 )
=> ( ( ord_le2931979837777675552c_fm_a @ A2 @ B )
=> ( A2 = B ) ) ) ).
% dual_order.antisym
thf(fact_251_dual__order_Otrans,axiom,
! [B: epistemic_fm_a > $o,A2: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ B @ A2 )
=> ( ( ord_le4043730696559282883fm_a_o @ C @ B )
=> ( ord_le4043730696559282883fm_a_o @ C @ A2 ) ) ) ).
% dual_order.trans
thf(fact_252_dual__order_Otrans,axiom,
! [B: set_Epistemic_fm_a,A2: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ B @ A2 )
=> ( ( ord_le3275665582123262618c_fm_a @ C @ B )
=> ( ord_le3275665582123262618c_fm_a @ C @ A2 ) ) ) ).
% dual_order.trans
thf(fact_253_dual__order_Otrans,axiom,
! [B: set_li769143395467472256c_fm_a,A2: set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ B @ A2 )
=> ( ( ord_le2931979837777675552c_fm_a @ C @ B )
=> ( ord_le2931979837777675552c_fm_a @ C @ A2 ) ) ) ).
% dual_order.trans
thf(fact_254_antisym,axiom,
! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
=> ( ( ord_le4043730696559282883fm_a_o @ B @ A2 )
=> ( A2 = B ) ) ) ).
% antisym
thf(fact_255_antisym,axiom,
! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
=> ( ( ord_le3275665582123262618c_fm_a @ B @ A2 )
=> ( A2 = B ) ) ) ).
% antisym
thf(fact_256_antisym,axiom,
! [A2: set_li769143395467472256c_fm_a,B: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A2 @ B )
=> ( ( ord_le2931979837777675552c_fm_a @ B @ A2 )
=> ( A2 = B ) ) ) ).
% antisym
thf(fact_257_Orderings_Oorder__eq__iff,axiom,
( ( ^ [Y4: epistemic_fm_a > $o,Z3: epistemic_fm_a > $o] : ( Y4 = Z3 ) )
= ( ^ [A4: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ A4 @ B2 )
& ( ord_le4043730696559282883fm_a_o @ B2 @ A4 ) ) ) ) ).
% Orderings.order_eq_iff
thf(fact_258_Orderings_Oorder__eq__iff,axiom,
( ( ^ [Y4: set_Epistemic_fm_a,Z3: set_Epistemic_fm_a] : ( Y4 = Z3 ) )
= ( ^ [A4: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A4 @ B2 )
& ( ord_le3275665582123262618c_fm_a @ B2 @ A4 ) ) ) ) ).
% Orderings.order_eq_iff
thf(fact_259_Orderings_Oorder__eq__iff,axiom,
( ( ^ [Y4: set_li769143395467472256c_fm_a,Z3: set_li769143395467472256c_fm_a] : ( Y4 = Z3 ) )
= ( ^ [A4: set_li769143395467472256c_fm_a,B2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A4 @ B2 )
& ( ord_le2931979837777675552c_fm_a @ B2 @ A4 ) ) ) ) ).
% Orderings.order_eq_iff
thf(fact_260_order__subst1,axiom,
! [A2: epistemic_fm_a > $o,F: ( epistemic_fm_a > $o ) > epistemic_fm_a > $o,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ B ) )
=> ( ( ord_le4043730696559282883fm_a_o @ B @ C )
=> ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_261_order__subst1,axiom,
! [A2: epistemic_fm_a > $o,F: set_Epistemic_fm_a > epistemic_fm_a > $o,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ B ) )
=> ( ( ord_le3275665582123262618c_fm_a @ B @ C )
=> ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_262_order__subst1,axiom,
! [A2: epistemic_fm_a > $o,F: set_li769143395467472256c_fm_a > epistemic_fm_a > $o,B: set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ B ) )
=> ( ( ord_le2931979837777675552c_fm_a @ B @ C )
=> ( ! [X2: set_li769143395467472256c_fm_a,Y2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X2 @ Y2 )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_263_order__subst1,axiom,
! [A2: set_Epistemic_fm_a,F: ( epistemic_fm_a > $o ) > set_Epistemic_fm_a,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ B ) )
=> ( ( ord_le4043730696559282883fm_a_o @ B @ C )
=> ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_264_order__subst1,axiom,
! [A2: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ B ) )
=> ( ( ord_le3275665582123262618c_fm_a @ B @ C )
=> ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_265_order__subst1,axiom,
! [A2: set_Epistemic_fm_a,F: set_li769143395467472256c_fm_a > set_Epistemic_fm_a,B: set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ B ) )
=> ( ( ord_le2931979837777675552c_fm_a @ B @ C )
=> ( ! [X2: set_li769143395467472256c_fm_a,Y2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X2 @ Y2 )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_266_order__subst1,axiom,
! [A2: set_li769143395467472256c_fm_a,F: ( epistemic_fm_a > $o ) > set_li769143395467472256c_fm_a,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( ord_le2931979837777675552c_fm_a @ A2 @ ( F @ B ) )
=> ( ( ord_le4043730696559282883fm_a_o @ B @ C )
=> ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_267_order__subst1,axiom,
! [A2: set_li769143395467472256c_fm_a,F: set_Epistemic_fm_a > set_li769143395467472256c_fm_a,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A2 @ ( F @ B ) )
=> ( ( ord_le3275665582123262618c_fm_a @ B @ C )
=> ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_268_order__subst1,axiom,
! [A2: set_li769143395467472256c_fm_a,F: set_li769143395467472256c_fm_a > set_li769143395467472256c_fm_a,B: set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A2 @ ( F @ B ) )
=> ( ( ord_le2931979837777675552c_fm_a @ B @ C )
=> ( ! [X2: set_li769143395467472256c_fm_a,Y2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X2 @ Y2 )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_269_order__subst2,axiom,
! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,F: ( epistemic_fm_a > $o ) > epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
=> ( ( ord_le4043730696559282883fm_a_o @ ( F @ B ) @ C )
=> ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_270_order__subst2,axiom,
! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,F: ( epistemic_fm_a > $o ) > set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
=> ( ( ord_le3275665582123262618c_fm_a @ ( F @ B ) @ C )
=> ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_271_order__subst2,axiom,
! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,F: ( epistemic_fm_a > $o ) > set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
=> ( ( ord_le2931979837777675552c_fm_a @ ( F @ B ) @ C )
=> ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_272_order__subst2,axiom,
! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
=> ( ( ord_le4043730696559282883fm_a_o @ ( F @ B ) @ C )
=> ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_273_order__subst2,axiom,
! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
=> ( ( ord_le3275665582123262618c_fm_a @ ( F @ B ) @ C )
=> ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_274_order__subst2,axiom,
! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
=> ( ( ord_le2931979837777675552c_fm_a @ ( F @ B ) @ C )
=> ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_275_order__subst2,axiom,
! [A2: set_li769143395467472256c_fm_a,B: set_li769143395467472256c_fm_a,F: set_li769143395467472256c_fm_a > epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( ord_le2931979837777675552c_fm_a @ A2 @ B )
=> ( ( ord_le4043730696559282883fm_a_o @ ( F @ B ) @ C )
=> ( ! [X2: set_li769143395467472256c_fm_a,Y2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X2 @ Y2 )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_276_order__subst2,axiom,
! [A2: set_li769143395467472256c_fm_a,B: set_li769143395467472256c_fm_a,F: set_li769143395467472256c_fm_a > set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A2 @ B )
=> ( ( ord_le3275665582123262618c_fm_a @ ( F @ B ) @ C )
=> ( ! [X2: set_li769143395467472256c_fm_a,Y2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X2 @ Y2 )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_277_order__subst2,axiom,
! [A2: set_li769143395467472256c_fm_a,B: set_li769143395467472256c_fm_a,F: set_li769143395467472256c_fm_a > set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A2 @ B )
=> ( ( ord_le2931979837777675552c_fm_a @ ( F @ B ) @ C )
=> ( ! [X2: set_li769143395467472256c_fm_a,Y2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X2 @ Y2 )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).
% order_subst2
thf(fact_278_order__eq__refl,axiom,
! [X3: epistemic_fm_a > $o,Y: epistemic_fm_a > $o] :
( ( X3 = Y )
=> ( ord_le4043730696559282883fm_a_o @ X3 @ Y ) ) ).
% order_eq_refl
thf(fact_279_order__eq__refl,axiom,
! [X3: set_Epistemic_fm_a,Y: set_Epistemic_fm_a] :
( ( X3 = Y )
=> ( ord_le3275665582123262618c_fm_a @ X3 @ Y ) ) ).
% order_eq_refl
thf(fact_280_order__eq__refl,axiom,
! [X3: set_li769143395467472256c_fm_a,Y: set_li769143395467472256c_fm_a] :
( ( X3 = Y )
=> ( ord_le2931979837777675552c_fm_a @ X3 @ Y ) ) ).
% order_eq_refl
thf(fact_281_ord__eq__le__subst,axiom,
! [A2: epistemic_fm_a > $o,F: ( epistemic_fm_a > $o ) > epistemic_fm_a > $o,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( A2
= ( F @ B ) )
=> ( ( ord_le4043730696559282883fm_a_o @ B @ C )
=> ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_282_ord__eq__le__subst,axiom,
! [A2: set_Epistemic_fm_a,F: ( epistemic_fm_a > $o ) > set_Epistemic_fm_a,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( A2
= ( F @ B ) )
=> ( ( ord_le4043730696559282883fm_a_o @ B @ C )
=> ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_283_ord__eq__le__subst,axiom,
! [A2: set_li769143395467472256c_fm_a,F: ( epistemic_fm_a > $o ) > set_li769143395467472256c_fm_a,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( A2
= ( F @ B ) )
=> ( ( ord_le4043730696559282883fm_a_o @ B @ C )
=> ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_284_ord__eq__le__subst,axiom,
! [A2: epistemic_fm_a > $o,F: set_Epistemic_fm_a > epistemic_fm_a > $o,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( A2
= ( F @ B ) )
=> ( ( ord_le3275665582123262618c_fm_a @ B @ C )
=> ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_285_ord__eq__le__subst,axiom,
! [A2: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( A2
= ( F @ B ) )
=> ( ( ord_le3275665582123262618c_fm_a @ B @ C )
=> ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_286_ord__eq__le__subst,axiom,
! [A2: set_li769143395467472256c_fm_a,F: set_Epistemic_fm_a > set_li769143395467472256c_fm_a,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( A2
= ( F @ B ) )
=> ( ( ord_le3275665582123262618c_fm_a @ B @ C )
=> ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_287_ord__eq__le__subst,axiom,
! [A2: epistemic_fm_a > $o,F: set_li769143395467472256c_fm_a > epistemic_fm_a > $o,B: set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( A2
= ( F @ B ) )
=> ( ( ord_le2931979837777675552c_fm_a @ B @ C )
=> ( ! [X2: set_li769143395467472256c_fm_a,Y2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X2 @ Y2 )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_288_ord__eq__le__subst,axiom,
! [A2: set_Epistemic_fm_a,F: set_li769143395467472256c_fm_a > set_Epistemic_fm_a,B: set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( A2
= ( F @ B ) )
=> ( ( ord_le2931979837777675552c_fm_a @ B @ C )
=> ( ! [X2: set_li769143395467472256c_fm_a,Y2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X2 @ Y2 )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_289_ord__eq__le__subst,axiom,
! [A2: set_li769143395467472256c_fm_a,F: set_li769143395467472256c_fm_a > set_li769143395467472256c_fm_a,B: set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( A2
= ( F @ B ) )
=> ( ( ord_le2931979837777675552c_fm_a @ B @ C )
=> ( ! [X2: set_li769143395467472256c_fm_a,Y2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X2 @ Y2 )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_290_ord__le__eq__subst,axiom,
! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,F: ( epistemic_fm_a > $o ) > epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_291_ord__le__eq__subst,axiom,
! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,F: ( epistemic_fm_a > $o ) > set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_292_ord__le__eq__subst,axiom,
! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,F: ( epistemic_fm_a > $o ) > set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_293_ord__le__eq__subst,axiom,
! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_294_ord__le__eq__subst,axiom,
! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_295_ord__le__eq__subst,axiom,
! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_296_ord__le__eq__subst,axiom,
! [A2: set_li769143395467472256c_fm_a,B: set_li769143395467472256c_fm_a,F: set_li769143395467472256c_fm_a > epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
( ( ord_le2931979837777675552c_fm_a @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: set_li769143395467472256c_fm_a,Y2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X2 @ Y2 )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_297_ord__le__eq__subst,axiom,
! [A2: set_li769143395467472256c_fm_a,B: set_li769143395467472256c_fm_a,F: set_li769143395467472256c_fm_a > set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: set_li769143395467472256c_fm_a,Y2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X2 @ Y2 )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_298_ord__le__eq__subst,axiom,
! [A2: set_li769143395467472256c_fm_a,B: set_li769143395467472256c_fm_a,F: set_li769143395467472256c_fm_a > set_li769143395467472256c_fm_a,C: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: set_li769143395467472256c_fm_a,Y2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X2 @ Y2 )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_299_order__antisym__conv,axiom,
! [Y: epistemic_fm_a > $o,X3: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ Y @ X3 )
=> ( ( ord_le4043730696559282883fm_a_o @ X3 @ Y )
= ( X3 = Y ) ) ) ).
% order_antisym_conv
thf(fact_300_order__antisym__conv,axiom,
! [Y: set_Epistemic_fm_a,X3: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ Y @ X3 )
=> ( ( ord_le3275665582123262618c_fm_a @ X3 @ Y )
= ( X3 = Y ) ) ) ).
% order_antisym_conv
thf(fact_301_order__antisym__conv,axiom,
! [Y: set_li769143395467472256c_fm_a,X3: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ Y @ X3 )
=> ( ( ord_le2931979837777675552c_fm_a @ X3 @ Y )
= ( X3 = Y ) ) ) ).
% order_antisym_conv
thf(fact_302_predicate1D,axiom,
! [P2: epistemic_fm_a > $o,Q3: epistemic_fm_a > $o,X3: epistemic_fm_a] :
( ( ord_le4043730696559282883fm_a_o @ P2 @ Q3 )
=> ( ( P2 @ X3 )
=> ( Q3 @ X3 ) ) ) ).
% predicate1D
thf(fact_303_rev__predicate1D,axiom,
! [P2: epistemic_fm_a > $o,X3: epistemic_fm_a,Q3: epistemic_fm_a > $o] :
( ( P2 @ X3 )
=> ( ( ord_le4043730696559282883fm_a_o @ P2 @ Q3 )
=> ( Q3 @ X3 ) ) ) ).
% rev_predicate1D
thf(fact_304_S5__S5_H,axiom,
! [P: epistemic_fm_a] :
( ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_AxB_a @ P4 )
| ( epistemic_Ax4_a @ P4 ) )
@ P )
=> ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_Ax5_a @ P4 ) )
@ P ) ) ).
% S5_S5'
thf(fact_305_S5_H__S5,axiom,
! [P: epistemic_fm_a] :
( ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_Ax5_a @ P4 ) )
@ P )
=> ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_AxB_a @ P4 )
| ( epistemic_Ax4_a @ P4 ) )
@ P ) ) ).
% S5'_S5
thf(fact_306_S5__S5_H__assms,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ( ? [Qs: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G )
& ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_AxB_a @ P4 )
| ( epistemic_Ax4_a @ P4 ) )
@ ( epistemic_imply_a @ Qs @ P ) ) ) )
= ( ? [Qs: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G )
& ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_Ax5_a @ P4 ) )
@ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).
% S5_S5'_assms
thf(fact_307_product__lists_Osimps_I1_J,axiom,
( ( produc4433783857981728015c_fm_a @ nil_li5178944226519631276c_fm_a )
= ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ nil_li5178944226519631276c_fm_a ) ) ).
% product_lists.simps(1)
thf(fact_308_product__lists_Osimps_I1_J,axiom,
( ( produc3894803040673298025c_fm_a @ nil_li5433889876484989702c_fm_a )
= ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ nil_li5433889876484989702c_fm_a ) ) ).
% product_lists.simps(1)
thf(fact_309_product__lists_Osimps_I1_J,axiom,
( ( produc1391074687832863881c_fm_a @ nil_li2451196919128234278c_fm_a )
= ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ nil_li2451196919128234278c_fm_a ) ) ).
% product_lists.simps(1)
thf(fact_310_map__rec,axiom,
( map_li3858915945532548554c_fm_a
= ( ^ [F2: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( rec_li4767119888041796650c_fm_a @ nil_li5178944226519631276c_fm_a
@ ^ [X: list_Epistemic_fm_a,Uu2: list_l6083326122719238310c_fm_a] : ( cons_l2479501935080859996c_fm_a @ ( F2 @ X ) ) ) ) ) ).
% map_rec
thf(fact_311_map__rec,axiom,
( map_li5516866612190465598c_fm_a
= ( ^ [F2: list_Epistemic_fm_a > epistemic_fm_a] :
( rec_li2845402903074671286c_fm_a @ nil_Epistemic_fm_a
@ ^ [X: list_Epistemic_fm_a,Uu2: list_l6083326122719238310c_fm_a] : ( cons_Epistemic_fm_a @ ( F2 @ X ) ) ) ) ) ).
% map_rec
thf(fact_312_map__rec,axiom,
( map_Ep1988204514693272906c_fm_a
= ( ^ [F2: epistemic_fm_a > list_Epistemic_fm_a] :
( rec_li2622076421192168746c_fm_a @ nil_li2451196919128234278c_fm_a
@ ^ [X: epistemic_fm_a,Uu2: list_Epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ ( F2 @ X ) ) ) ) ) ).
% map_rec
thf(fact_313_map__rec,axiom,
( map_li3080774272885743684c_fm_a
= ( ^ [F2: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( rec_li5579148116651729200c_fm_a @ nil_li2451196919128234278c_fm_a
@ ^ [X: list_Epistemic_fm_a,Uu2: list_l6083326122719238310c_fm_a] : ( cons_l8134865115577406678c_fm_a @ ( F2 @ X ) ) ) ) ) ).
% map_rec
thf(fact_314_map__rec,axiom,
( map_Ep7084560364594560580c_fm_a
= ( ^ [F2: epistemic_fm_a > epistemic_fm_a] :
( rec_li4360243526537435568c_fm_a @ nil_Epistemic_fm_a
@ ^ [X: epistemic_fm_a,Uu2: list_Epistemic_fm_a] : ( cons_Epistemic_fm_a @ ( F2 @ X ) ) ) ) ) ).
% map_rec
thf(fact_315_subseqs_Osimps_I1_J,axiom,
( ( subseq3170398737635186805c_fm_a @ nil_li2451196919128234278c_fm_a )
= ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ nil_li5178944226519631276c_fm_a ) ) ).
% subseqs.simps(1)
thf(fact_316_subseqs_Osimps_I1_J,axiom,
( ( subseq7171631445414591695c_fm_a @ nil_se102576565402781184c_fm_a )
= ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ nil_li5433889876484989702c_fm_a ) ) ).
% subseqs.simps(1)
thf(fact_317_subseqs_Osimps_I1_J,axiom,
( ( subseq859285839621985007c_fm_a @ nil_Epistemic_fm_a )
= ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ nil_li2451196919128234278c_fm_a ) ) ).
% subseqs.simps(1)
thf(fact_318_less__eq__set__def,axiom,
( ord_le7112219575281605754c_fm_a
= ( ^ [A3: set_se5208064806568342746c_fm_a,B3: set_se5208064806568342746c_fm_a] :
( ord_le1568123225352354019fm_a_o
@ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ A3 )
@ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ B3 ) ) ) ) ).
% less_eq_set_def
thf(fact_319_less__eq__set__def,axiom,
( ord_le8873477448617899047c_fm_a
= ( ^ [A3: set_Pr3219225162411408519c_fm_a,B3: set_Pr3219225162411408519c_fm_a] :
( ord_le3724781943004833654fm_a_o
@ ^ [X: produc5756089960658898087c_fm_a] : ( member3265983909902097104c_fm_a @ X @ A3 )
@ ^ [X: produc5756089960658898087c_fm_a] : ( member3265983909902097104c_fm_a @ X @ B3 ) ) ) ) ).
% less_eq_set_def
thf(fact_320_less__eq__set__def,axiom,
( ord_le8222437384497874983c_fm_a
= ( ^ [A3: set_Pr8948481099588399239c_fm_a,B3: set_Pr8948481099588399239c_fm_a] :
( ord_le4942933042592423798fm_a_o
@ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ A3 )
@ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ B3 ) ) ) ) ).
% less_eq_set_def
thf(fact_321_less__eq__set__def,axiom,
( ord_le3275665582123262618c_fm_a
= ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
( ord_le4043730696559282883fm_a_o
@ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ A3 )
@ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ B3 ) ) ) ) ).
% less_eq_set_def
thf(fact_322_less__eq__set__def,axiom,
( ord_le2931979837777675552c_fm_a
= ( ^ [A3: set_li769143395467472256c_fm_a,B3: set_li769143395467472256c_fm_a] :
( ord_le5289359451089373629fm_a_o
@ ^ [X: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ X @ A3 )
@ ^ [X: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ X @ B3 ) ) ) ) ).
% less_eq_set_def
thf(fact_323_pred__subset__eq,axiom,
! [R2: set_se5208064806568342746c_fm_a,S: set_se5208064806568342746c_fm_a] :
( ( ord_le1568123225352354019fm_a_o
@ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ R2 )
@ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ S ) )
= ( ord_le7112219575281605754c_fm_a @ R2 @ S ) ) ).
% pred_subset_eq
thf(fact_324_pred__subset__eq,axiom,
! [R2: set_Pr3219225162411408519c_fm_a,S: set_Pr3219225162411408519c_fm_a] :
( ( ord_le3724781943004833654fm_a_o
@ ^ [X: produc5756089960658898087c_fm_a] : ( member3265983909902097104c_fm_a @ X @ R2 )
@ ^ [X: produc5756089960658898087c_fm_a] : ( member3265983909902097104c_fm_a @ X @ S ) )
= ( ord_le8873477448617899047c_fm_a @ R2 @ S ) ) ).
% pred_subset_eq
thf(fact_325_pred__subset__eq,axiom,
! [R2: set_Pr8948481099588399239c_fm_a,S: set_Pr8948481099588399239c_fm_a] :
( ( ord_le4942933042592423798fm_a_o
@ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ R2 )
@ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ S ) )
= ( ord_le8222437384497874983c_fm_a @ R2 @ S ) ) ).
% pred_subset_eq
thf(fact_326_pred__subset__eq,axiom,
! [R2: set_li769143395467472256c_fm_a,S: set_li769143395467472256c_fm_a] :
( ( ord_le5289359451089373629fm_a_o
@ ^ [X: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ X @ R2 )
@ ^ [X: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ X @ S ) )
= ( ord_le2931979837777675552c_fm_a @ R2 @ S ) ) ).
% pred_subset_eq
thf(fact_327_pred__subset__eq,axiom,
! [R2: set_Epistemic_fm_a,S: set_Epistemic_fm_a] :
( ( ord_le4043730696559282883fm_a_o
@ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ R2 )
@ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ S ) )
= ( ord_le3275665582123262618c_fm_a @ R2 @ S ) ) ).
% pred_subset_eq
thf(fact_328_insert__Nil,axiom,
! [X3: set_Epistemic_fm_a] :
( ( insert1868103382419917334c_fm_a @ X3 @ nil_se102576565402781184c_fm_a )
= ( cons_s4394448069393209776c_fm_a @ X3 @ nil_se102576565402781184c_fm_a ) ) ).
% insert_Nil
thf(fact_329_insert__Nil,axiom,
! [X3: list_Epistemic_fm_a] :
( ( insert335162795743670844c_fm_a @ X3 @ nil_li2451196919128234278c_fm_a )
= ( cons_l8134865115577406678c_fm_a @ X3 @ nil_li2451196919128234278c_fm_a ) ) ).
% insert_Nil
thf(fact_330_insert__Nil,axiom,
! [X3: epistemic_fm_a] :
( ( insert177310161492556854c_fm_a @ X3 @ nil_Epistemic_fm_a )
= ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) ).
% insert_Nil
thf(fact_331_concat__map__singleton,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( concat5652308878773863783c_fm_a
@ ( map_li5567427098789011152c_fm_a
@ ^ [X: list_Epistemic_fm_a] : ( cons_l2479501935080859996c_fm_a @ ( F @ X ) @ nil_li5178944226519631276c_fm_a )
@ Xs ) )
= ( map_li3858915945532548554c_fm_a @ F @ Xs ) ) ).
% concat_map_singleton
thf(fact_332_concat__map__singleton,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( concat2780896542826320603c_fm_a
@ ( map_li3080774272885743684c_fm_a
@ ^ [X: list_Epistemic_fm_a] : ( cons_Epistemic_fm_a @ ( F @ X ) @ nil_Epistemic_fm_a )
@ Xs ) )
= ( map_li5516866612190465598c_fm_a @ F @ Xs ) ) ).
% concat_map_singleton
thf(fact_333_concat__map__singleton,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( concat6109960377493484129c_fm_a
@ ( map_Ep4939040189629079504c_fm_a
@ ^ [X: epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ ( F @ X ) @ nil_li2451196919128234278c_fm_a )
@ Xs ) )
= ( map_Ep1988204514693272906c_fm_a @ F @ Xs ) ) ).
% concat_map_singleton
thf(fact_334_concat__map__singleton,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( concat6109960377493484129c_fm_a
@ ( map_li3858915945532548554c_fm_a
@ ^ [X: list_Epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ ( F @ X ) @ nil_li2451196919128234278c_fm_a )
@ Xs ) )
= ( map_li3080774272885743684c_fm_a @ F @ Xs ) ) ).
% concat_map_singleton
thf(fact_335_concat__map__singleton,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( concat2780896542826320603c_fm_a
@ ( map_Ep1988204514693272906c_fm_a
@ ^ [X: epistemic_fm_a] : ( cons_Epistemic_fm_a @ ( F @ X ) @ nil_Epistemic_fm_a )
@ Xs ) )
= ( map_Ep7084560364594560580c_fm_a @ F @ Xs ) ) ).
% concat_map_singleton
thf(fact_336_list__ex1__simps_I2_J,axiom,
! [P2: list_Epistemic_fm_a > $o,X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( list_e1371837923195959913c_fm_a @ P2 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs ) )
= ( ( ( P2 @ X3 )
=> ( list_a5890043570083025364c_fm_a
@ ^ [Y3: list_Epistemic_fm_a] :
( ~ ( P2 @ Y3 )
| ( X3 = Y3 ) )
@ Xs ) )
& ( ~ ( P2 @ X3 )
=> ( list_e1371837923195959913c_fm_a @ P2 @ Xs ) ) ) ) ).
% list_ex1_simps(2)
thf(fact_337_list__ex1__simps_I2_J,axiom,
! [P2: epistemic_fm_a > $o,X3: epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( list_e2031426293596896995c_fm_a @ P2 @ ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= ( ( ( P2 @ X3 )
=> ( list_a5841931967666341838c_fm_a
@ ^ [Y3: epistemic_fm_a] :
( ~ ( P2 @ Y3 )
| ( X3 = Y3 ) )
@ Xs ) )
& ( ~ ( P2 @ X3 )
=> ( list_e2031426293596896995c_fm_a @ P2 @ Xs ) ) ) ) ).
% list_ex1_simps(2)
thf(fact_338_subset__antisym,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
=> ( ( ord_le3275665582123262618c_fm_a @ B4 @ A )
=> ( A = B4 ) ) ) ).
% subset_antisym
thf(fact_339_subset__antisym,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A @ B4 )
=> ( ( ord_le2931979837777675552c_fm_a @ B4 @ A )
=> ( A = B4 ) ) ) ).
% subset_antisym
thf(fact_340_subsetI,axiom,
! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
( ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ A )
=> ( member536094252920883875c_fm_a @ X2 @ B4 ) )
=> ( ord_le7112219575281605754c_fm_a @ A @ B4 ) ) ).
% subsetI
thf(fact_341_subsetI,axiom,
! [A: set_Pr3219225162411408519c_fm_a,B4: set_Pr3219225162411408519c_fm_a] :
( ! [X2: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X2 @ A )
=> ( member3265983909902097104c_fm_a @ X2 @ B4 ) )
=> ( ord_le8873477448617899047c_fm_a @ A @ B4 ) ) ).
% subsetI
thf(fact_342_subsetI,axiom,
! [A: set_Pr8948481099588399239c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
( ! [X2: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X2 @ A )
=> ( member5029746173879296720c_fm_a @ X2 @ B4 ) )
=> ( ord_le8222437384497874983c_fm_a @ A @ B4 ) ) ).
% subsetI
thf(fact_343_subsetI,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ A )
=> ( member6642669571620171971c_fm_a @ X2 @ B4 ) )
=> ( ord_le3275665582123262618c_fm_a @ A @ B4 ) ) ).
% subsetI
thf(fact_344_subsetI,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a] :
( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ A )
=> ( member5906877432388582473c_fm_a @ X2 @ B4 ) )
=> ( ord_le2931979837777675552c_fm_a @ A @ B4 ) ) ).
% subsetI
thf(fact_345_map__eq__conv,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs: list_Epistemic_fm_a,G4: epistemic_fm_a > list_Epistemic_fm_a] :
( ( ( map_Ep1988204514693272906c_fm_a @ F @ Xs )
= ( map_Ep1988204514693272906c_fm_a @ G4 @ Xs ) )
= ( ! [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ( ( F @ X )
= ( G4 @ X ) ) ) ) ) ).
% map_eq_conv
thf(fact_346_map__eq__conv,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,G4: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( ( map_li3080774272885743684c_fm_a @ F @ Xs )
= ( map_li3080774272885743684c_fm_a @ G4 @ Xs ) )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ( ( F @ X )
= ( G4 @ X ) ) ) ) ) ).
% map_eq_conv
thf(fact_347_map__eq__conv,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs: list_l6083326122719238310c_fm_a,G4: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( ( map_li3858915945532548554c_fm_a @ F @ Xs )
= ( map_li3858915945532548554c_fm_a @ G4 @ Xs ) )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ( ( F @ X )
= ( G4 @ X ) ) ) ) ) ).
% map_eq_conv
thf(fact_348_map__eq__conv,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,G4: list_Epistemic_fm_a > epistemic_fm_a] :
( ( ( map_li5516866612190465598c_fm_a @ F @ Xs )
= ( map_li5516866612190465598c_fm_a @ G4 @ Xs ) )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ( ( F @ X )
= ( G4 @ X ) ) ) ) ) ).
% map_eq_conv
thf(fact_349_map__eq__conv,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a,G4: epistemic_fm_a > epistemic_fm_a] :
( ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs )
= ( map_Ep7084560364594560580c_fm_a @ G4 @ Xs ) )
= ( ! [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ( ( F @ X )
= ( G4 @ X ) ) ) ) ) ).
% map_eq_conv
thf(fact_350_list__all__simps_I1_J,axiom,
! [P2: list_Epistemic_fm_a > $o,X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( list_a5890043570083025364c_fm_a @ P2 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs ) )
= ( ( P2 @ X3 )
& ( list_a5890043570083025364c_fm_a @ P2 @ Xs ) ) ) ).
% list_all_simps(1)
thf(fact_351_list__all__simps_I1_J,axiom,
! [P2: epistemic_fm_a > $o,X3: epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( list_a5841931967666341838c_fm_a @ P2 @ ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= ( ( P2 @ X3 )
& ( list_a5841931967666341838c_fm_a @ P2 @ Xs ) ) ) ).
% list_all_simps(1)
thf(fact_352_list_Opred__inject_I2_J,axiom,
! [P2: list_Epistemic_fm_a > $o,A2: list_Epistemic_fm_a,Aa: list_l6083326122719238310c_fm_a] :
( ( list_a5890043570083025364c_fm_a @ P2 @ ( cons_l8134865115577406678c_fm_a @ A2 @ Aa ) )
= ( ( P2 @ A2 )
& ( list_a5890043570083025364c_fm_a @ P2 @ Aa ) ) ) ).
% list.pred_inject(2)
thf(fact_353_list_Opred__inject_I2_J,axiom,
! [P2: epistemic_fm_a > $o,A2: epistemic_fm_a,Aa: list_Epistemic_fm_a] :
( ( list_a5841931967666341838c_fm_a @ P2 @ ( cons_Epistemic_fm_a @ A2 @ Aa ) )
= ( ( P2 @ A2 )
& ( list_a5841931967666341838c_fm_a @ P2 @ Aa ) ) ) ).
% list.pred_inject(2)
thf(fact_354_list__all__simps_I2_J,axiom,
! [P2: list_Epistemic_fm_a > $o] : ( list_a5890043570083025364c_fm_a @ P2 @ nil_li2451196919128234278c_fm_a ) ).
% list_all_simps(2)
thf(fact_355_list__all__simps_I2_J,axiom,
! [P2: set_Epistemic_fm_a > $o] : ( list_a5130230249644717486c_fm_a @ P2 @ nil_se102576565402781184c_fm_a ) ).
% list_all_simps(2)
thf(fact_356_list__all__simps_I2_J,axiom,
! [P2: epistemic_fm_a > $o] : ( list_a5841931967666341838c_fm_a @ P2 @ nil_Epistemic_fm_a ) ).
% list_all_simps(2)
thf(fact_357_in__set__insert,axiom,
! [X3: set_Epistemic_fm_a,Xs: list_s580375451141968640c_fm_a] :
( ( member536094252920883875c_fm_a @ X3 @ ( set_se8855941934996405007c_fm_a @ Xs ) )
=> ( ( insert1868103382419917334c_fm_a @ X3 @ Xs )
= Xs ) ) ).
% in_set_insert
thf(fact_358_in__set__insert,axiom,
! [X3: produc5756089960658898087c_fm_a,Xs: list_P7917480606449584557c_fm_a] :
( ( member3265983909902097104c_fm_a @ X3 @ ( set_Pr5015285182815091004c_fm_a @ Xs ) )
=> ( ( insert7000960152310464963c_fm_a @ X3 @ Xs )
= Xs ) ) ).
% in_set_insert
thf(fact_359_in__set__insert,axiom,
! [X3: produc2203834439629243303c_fm_a,Xs: list_P3099032918374241197c_fm_a] :
( ( member5029746173879296720c_fm_a @ X3 @ ( set_Pr6083076219314900284c_fm_a @ Xs ) )
=> ( ( insert423680279517344963c_fm_a @ X3 @ Xs )
= Xs ) ) ).
% in_set_insert
thf(fact_360_in__set__insert,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ( ( insert177310161492556854c_fm_a @ X3 @ Xs )
= Xs ) ) ).
% in_set_insert
thf(fact_361_in__set__insert,axiom,
! [X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ( ( insert335162795743670844c_fm_a @ X3 @ Xs )
= Xs ) ) ).
% in_set_insert
thf(fact_362_not__in__set__insert,axiom,
! [X3: set_Epistemic_fm_a,Xs: list_s580375451141968640c_fm_a] :
( ~ ( member536094252920883875c_fm_a @ X3 @ ( set_se8855941934996405007c_fm_a @ Xs ) )
=> ( ( insert1868103382419917334c_fm_a @ X3 @ Xs )
= ( cons_s4394448069393209776c_fm_a @ X3 @ Xs ) ) ) ).
% not_in_set_insert
thf(fact_363_not__in__set__insert,axiom,
! [X3: produc5756089960658898087c_fm_a,Xs: list_P7917480606449584557c_fm_a] :
( ~ ( member3265983909902097104c_fm_a @ X3 @ ( set_Pr5015285182815091004c_fm_a @ Xs ) )
=> ( ( insert7000960152310464963c_fm_a @ X3 @ Xs )
= ( cons_P7190808671141380701c_fm_a @ X3 @ Xs ) ) ) ).
% not_in_set_insert
thf(fact_364_not__in__set__insert,axiom,
! [X3: produc2203834439629243303c_fm_a,Xs: list_P3099032918374241197c_fm_a] :
( ~ ( member5029746173879296720c_fm_a @ X3 @ ( set_Pr6083076219314900284c_fm_a @ Xs ) )
=> ( ( insert423680279517344963c_fm_a @ X3 @ Xs )
= ( cons_P6232728021713608541c_fm_a @ X3 @ Xs ) ) ) ).
% not_in_set_insert
thf(fact_365_not__in__set__insert,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ~ ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ( ( insert177310161492556854c_fm_a @ X3 @ Xs )
= ( cons_Epistemic_fm_a @ X3 @ Xs ) ) ) ).
% not_in_set_insert
thf(fact_366_not__in__set__insert,axiom,
! [X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ~ ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ( ( insert335162795743670844c_fm_a @ X3 @ Xs )
= ( cons_l8134865115577406678c_fm_a @ X3 @ Xs ) ) ) ).
% not_in_set_insert
thf(fact_367_subset__code_I1_J,axiom,
! [Xs: list_s580375451141968640c_fm_a,B4: set_se5208064806568342746c_fm_a] :
( ( ord_le7112219575281605754c_fm_a @ ( set_se8855941934996405007c_fm_a @ Xs ) @ B4 )
= ( ! [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( set_se8855941934996405007c_fm_a @ Xs ) )
=> ( member536094252920883875c_fm_a @ X @ B4 ) ) ) ) ).
% subset_code(1)
thf(fact_368_subset__code_I1_J,axiom,
! [Xs: list_P7917480606449584557c_fm_a,B4: set_Pr3219225162411408519c_fm_a] :
( ( ord_le8873477448617899047c_fm_a @ ( set_Pr5015285182815091004c_fm_a @ Xs ) @ B4 )
= ( ! [X: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X @ ( set_Pr5015285182815091004c_fm_a @ Xs ) )
=> ( member3265983909902097104c_fm_a @ X @ B4 ) ) ) ) ).
% subset_code(1)
thf(fact_369_subset__code_I1_J,axiom,
! [Xs: list_P3099032918374241197c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
( ( ord_le8222437384497874983c_fm_a @ ( set_Pr6083076219314900284c_fm_a @ Xs ) @ B4 )
= ( ! [X: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X @ ( set_Pr6083076219314900284c_fm_a @ Xs ) )
=> ( member5029746173879296720c_fm_a @ X @ B4 ) ) ) ) ).
% subset_code(1)
thf(fact_370_subset__code_I1_J,axiom,
! [Xs: list_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Xs ) @ B4 )
= ( ! [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ( member6642669571620171971c_fm_a @ X @ B4 ) ) ) ) ).
% subset_code(1)
thf(fact_371_subset__code_I1_J,axiom,
! [Xs: list_l6083326122719238310c_fm_a,B4: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ ( set_li8442223810127165109c_fm_a @ Xs ) @ B4 )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ( member5906877432388582473c_fm_a @ X @ B4 ) ) ) ) ).
% subset_code(1)
thf(fact_372_Collect__mono__iff,axiom,
! [P2: set_Epistemic_fm_a > $o,Q3: set_Epistemic_fm_a > $o] :
( ( ord_le7112219575281605754c_fm_a @ ( collec2519470961442302949c_fm_a @ P2 ) @ ( collec2519470961442302949c_fm_a @ Q3 ) )
= ( ! [X: set_Epistemic_fm_a] :
( ( P2 @ X )
=> ( Q3 @ X ) ) ) ) ).
% Collect_mono_iff
thf(fact_373_Collect__mono__iff,axiom,
! [P2: epistemic_fm_a > $o,Q3: epistemic_fm_a > $o] :
( ( ord_le3275665582123262618c_fm_a @ ( collec4904205152690461189c_fm_a @ P2 ) @ ( collec4904205152690461189c_fm_a @ Q3 ) )
= ( ! [X: epistemic_fm_a] :
( ( P2 @ X )
=> ( Q3 @ X ) ) ) ) ).
% Collect_mono_iff
thf(fact_374_Collect__mono__iff,axiom,
! [P2: list_Epistemic_fm_a > $o,Q3: list_Epistemic_fm_a > $o] :
( ( ord_le2931979837777675552c_fm_a @ ( collec5191077796991884427c_fm_a @ P2 ) @ ( collec5191077796991884427c_fm_a @ Q3 ) )
= ( ! [X: list_Epistemic_fm_a] :
( ( P2 @ X )
=> ( Q3 @ X ) ) ) ) ).
% Collect_mono_iff
thf(fact_375_Collect__subset,axiom,
! [A: set_Pr3219225162411408519c_fm_a,P2: produc5756089960658898087c_fm_a > $o] :
( ord_le8873477448617899047c_fm_a
@ ( collec6124610372686893330c_fm_a
@ ^ [X: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X @ A )
& ( P2 @ X ) ) )
@ A ) ).
% Collect_subset
thf(fact_376_Collect__subset,axiom,
! [A: set_Pr8948481099588399239c_fm_a,P2: produc2203834439629243303c_fm_a > $o] :
( ord_le8222437384497874983c_fm_a
@ ( collec7391038856303340306c_fm_a
@ ^ [X: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X @ A )
& ( P2 @ X ) ) )
@ A ) ).
% Collect_subset
thf(fact_377_Collect__subset,axiom,
! [A: set_se5208064806568342746c_fm_a,P2: set_Epistemic_fm_a > $o] :
( ord_le7112219575281605754c_fm_a
@ ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ A )
& ( P2 @ X ) ) )
@ A ) ).
% Collect_subset
thf(fact_378_Collect__subset,axiom,
! [A: set_Epistemic_fm_a,P2: epistemic_fm_a > $o] :
( ord_le3275665582123262618c_fm_a
@ ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ A )
& ( P2 @ X ) ) )
@ A ) ).
% Collect_subset
thf(fact_379_Collect__subset,axiom,
! [A: set_li769143395467472256c_fm_a,P2: list_Epistemic_fm_a > $o] :
( ord_le2931979837777675552c_fm_a
@ ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ A )
& ( P2 @ X ) ) )
@ A ) ).
% Collect_subset
thf(fact_380_set__eq__subset,axiom,
( ( ^ [Y4: set_Epistemic_fm_a,Z3: set_Epistemic_fm_a] : ( Y4 = Z3 ) )
= ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A3 @ B3 )
& ( ord_le3275665582123262618c_fm_a @ B3 @ A3 ) ) ) ) ).
% set_eq_subset
thf(fact_381_set__eq__subset,axiom,
( ( ^ [Y4: set_li769143395467472256c_fm_a,Z3: set_li769143395467472256c_fm_a] : ( Y4 = Z3 ) )
= ( ^ [A3: set_li769143395467472256c_fm_a,B3: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A3 @ B3 )
& ( ord_le2931979837777675552c_fm_a @ B3 @ A3 ) ) ) ) ).
% set_eq_subset
thf(fact_382_subset__trans,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,C2: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
=> ( ( ord_le3275665582123262618c_fm_a @ B4 @ C2 )
=> ( ord_le3275665582123262618c_fm_a @ A @ C2 ) ) ) ).
% subset_trans
thf(fact_383_subset__trans,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a,C2: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A @ B4 )
=> ( ( ord_le2931979837777675552c_fm_a @ B4 @ C2 )
=> ( ord_le2931979837777675552c_fm_a @ A @ C2 ) ) ) ).
% subset_trans
thf(fact_384_Collect__mono,axiom,
! [P2: set_Epistemic_fm_a > $o,Q3: set_Epistemic_fm_a > $o] :
( ! [X2: set_Epistemic_fm_a] :
( ( P2 @ X2 )
=> ( Q3 @ X2 ) )
=> ( ord_le7112219575281605754c_fm_a @ ( collec2519470961442302949c_fm_a @ P2 ) @ ( collec2519470961442302949c_fm_a @ Q3 ) ) ) ).
% Collect_mono
thf(fact_385_Collect__mono,axiom,
! [P2: epistemic_fm_a > $o,Q3: epistemic_fm_a > $o] :
( ! [X2: epistemic_fm_a] :
( ( P2 @ X2 )
=> ( Q3 @ X2 ) )
=> ( ord_le3275665582123262618c_fm_a @ ( collec4904205152690461189c_fm_a @ P2 ) @ ( collec4904205152690461189c_fm_a @ Q3 ) ) ) ).
% Collect_mono
thf(fact_386_Collect__mono,axiom,
! [P2: list_Epistemic_fm_a > $o,Q3: list_Epistemic_fm_a > $o] :
( ! [X2: list_Epistemic_fm_a] :
( ( P2 @ X2 )
=> ( Q3 @ X2 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( collec5191077796991884427c_fm_a @ P2 ) @ ( collec5191077796991884427c_fm_a @ Q3 ) ) ) ).
% Collect_mono
thf(fact_387_subset__refl,axiom,
! [A: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A @ A ) ).
% subset_refl
thf(fact_388_subset__refl,axiom,
! [A: set_li769143395467472256c_fm_a] : ( ord_le2931979837777675552c_fm_a @ A @ A ) ).
% subset_refl
thf(fact_389_subset__iff,axiom,
( ord_le7112219575281605754c_fm_a
= ( ^ [A3: set_se5208064806568342746c_fm_a,B3: set_se5208064806568342746c_fm_a] :
! [T2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ T2 @ A3 )
=> ( member536094252920883875c_fm_a @ T2 @ B3 ) ) ) ) ).
% subset_iff
thf(fact_390_subset__iff,axiom,
( ord_le8873477448617899047c_fm_a
= ( ^ [A3: set_Pr3219225162411408519c_fm_a,B3: set_Pr3219225162411408519c_fm_a] :
! [T2: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ T2 @ A3 )
=> ( member3265983909902097104c_fm_a @ T2 @ B3 ) ) ) ) ).
% subset_iff
thf(fact_391_subset__iff,axiom,
( ord_le8222437384497874983c_fm_a
= ( ^ [A3: set_Pr8948481099588399239c_fm_a,B3: set_Pr8948481099588399239c_fm_a] :
! [T2: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ T2 @ A3 )
=> ( member5029746173879296720c_fm_a @ T2 @ B3 ) ) ) ) ).
% subset_iff
thf(fact_392_subset__iff,axiom,
( ord_le3275665582123262618c_fm_a
= ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
! [T2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ T2 @ A3 )
=> ( member6642669571620171971c_fm_a @ T2 @ B3 ) ) ) ) ).
% subset_iff
thf(fact_393_subset__iff,axiom,
( ord_le2931979837777675552c_fm_a
= ( ^ [A3: set_li769143395467472256c_fm_a,B3: set_li769143395467472256c_fm_a] :
! [T2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ T2 @ A3 )
=> ( member5906877432388582473c_fm_a @ T2 @ B3 ) ) ) ) ).
% subset_iff
thf(fact_394_equalityD2,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ( A = B4 )
=> ( ord_le3275665582123262618c_fm_a @ B4 @ A ) ) ).
% equalityD2
thf(fact_395_equalityD2,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a] :
( ( A = B4 )
=> ( ord_le2931979837777675552c_fm_a @ B4 @ A ) ) ).
% equalityD2
thf(fact_396_equalityD1,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ( A = B4 )
=> ( ord_le3275665582123262618c_fm_a @ A @ B4 ) ) ).
% equalityD1
thf(fact_397_equalityD1,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a] :
( ( A = B4 )
=> ( ord_le2931979837777675552c_fm_a @ A @ B4 ) ) ).
% equalityD1
thf(fact_398_subset__eq,axiom,
( ord_le7112219575281605754c_fm_a
= ( ^ [A3: set_se5208064806568342746c_fm_a,B3: set_se5208064806568342746c_fm_a] :
! [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ A3 )
=> ( member536094252920883875c_fm_a @ X @ B3 ) ) ) ) ).
% subset_eq
thf(fact_399_subset__eq,axiom,
( ord_le8873477448617899047c_fm_a
= ( ^ [A3: set_Pr3219225162411408519c_fm_a,B3: set_Pr3219225162411408519c_fm_a] :
! [X: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X @ A3 )
=> ( member3265983909902097104c_fm_a @ X @ B3 ) ) ) ) ).
% subset_eq
thf(fact_400_subset__eq,axiom,
( ord_le8222437384497874983c_fm_a
= ( ^ [A3: set_Pr8948481099588399239c_fm_a,B3: set_Pr8948481099588399239c_fm_a] :
! [X: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X @ A3 )
=> ( member5029746173879296720c_fm_a @ X @ B3 ) ) ) ) ).
% subset_eq
thf(fact_401_subset__eq,axiom,
( ord_le3275665582123262618c_fm_a
= ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
! [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ A3 )
=> ( member6642669571620171971c_fm_a @ X @ B3 ) ) ) ) ).
% subset_eq
thf(fact_402_subset__eq,axiom,
( ord_le2931979837777675552c_fm_a
= ( ^ [A3: set_li769143395467472256c_fm_a,B3: set_li769143395467472256c_fm_a] :
! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ A3 )
=> ( member5906877432388582473c_fm_a @ X @ B3 ) ) ) ) ).
% subset_eq
thf(fact_403_equalityE,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ( A = B4 )
=> ~ ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
=> ~ ( ord_le3275665582123262618c_fm_a @ B4 @ A ) ) ) ).
% equalityE
thf(fact_404_equalityE,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a] :
( ( A = B4 )
=> ~ ( ( ord_le2931979837777675552c_fm_a @ A @ B4 )
=> ~ ( ord_le2931979837777675552c_fm_a @ B4 @ A ) ) ) ).
% equalityE
thf(fact_405_subsetD,axiom,
! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a,C: set_Epistemic_fm_a] :
( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
=> ( ( member536094252920883875c_fm_a @ C @ A )
=> ( member536094252920883875c_fm_a @ C @ B4 ) ) ) ).
% subsetD
thf(fact_406_subsetD,axiom,
! [A: set_Pr3219225162411408519c_fm_a,B4: set_Pr3219225162411408519c_fm_a,C: produc5756089960658898087c_fm_a] :
( ( ord_le8873477448617899047c_fm_a @ A @ B4 )
=> ( ( member3265983909902097104c_fm_a @ C @ A )
=> ( member3265983909902097104c_fm_a @ C @ B4 ) ) ) ).
% subsetD
thf(fact_407_subsetD,axiom,
! [A: set_Pr8948481099588399239c_fm_a,B4: set_Pr8948481099588399239c_fm_a,C: produc2203834439629243303c_fm_a] :
( ( ord_le8222437384497874983c_fm_a @ A @ B4 )
=> ( ( member5029746173879296720c_fm_a @ C @ A )
=> ( member5029746173879296720c_fm_a @ C @ B4 ) ) ) ).
% subsetD
thf(fact_408_subsetD,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,C: epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
=> ( ( member6642669571620171971c_fm_a @ C @ A )
=> ( member6642669571620171971c_fm_a @ C @ B4 ) ) ) ).
% subsetD
thf(fact_409_subsetD,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a,C: list_Epistemic_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A @ B4 )
=> ( ( member5906877432388582473c_fm_a @ C @ A )
=> ( member5906877432388582473c_fm_a @ C @ B4 ) ) ) ).
% subsetD
thf(fact_410_in__mono,axiom,
! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a,X3: set_Epistemic_fm_a] :
( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
=> ( ( member536094252920883875c_fm_a @ X3 @ A )
=> ( member536094252920883875c_fm_a @ X3 @ B4 ) ) ) ).
% in_mono
thf(fact_411_in__mono,axiom,
! [A: set_Pr3219225162411408519c_fm_a,B4: set_Pr3219225162411408519c_fm_a,X3: produc5756089960658898087c_fm_a] :
( ( ord_le8873477448617899047c_fm_a @ A @ B4 )
=> ( ( member3265983909902097104c_fm_a @ X3 @ A )
=> ( member3265983909902097104c_fm_a @ X3 @ B4 ) ) ) ).
% in_mono
thf(fact_412_in__mono,axiom,
! [A: set_Pr8948481099588399239c_fm_a,B4: set_Pr8948481099588399239c_fm_a,X3: produc2203834439629243303c_fm_a] :
( ( ord_le8222437384497874983c_fm_a @ A @ B4 )
=> ( ( member5029746173879296720c_fm_a @ X3 @ A )
=> ( member5029746173879296720c_fm_a @ X3 @ B4 ) ) ) ).
% in_mono
thf(fact_413_in__mono,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,X3: epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
=> ( ( member6642669571620171971c_fm_a @ X3 @ A )
=> ( member6642669571620171971c_fm_a @ X3 @ B4 ) ) ) ).
% in_mono
thf(fact_414_in__mono,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a,X3: list_Epistemic_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A @ B4 )
=> ( ( member5906877432388582473c_fm_a @ X3 @ A )
=> ( member5906877432388582473c_fm_a @ X3 @ B4 ) ) ) ).
% in_mono
thf(fact_415_list_Opred__mono__strong,axiom,
! [P2: set_Epistemic_fm_a > $o,X3: list_s580375451141968640c_fm_a,Pa: set_Epistemic_fm_a > $o] :
( ( list_a5130230249644717486c_fm_a @ P2 @ X3 )
=> ( ! [Z: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ Z @ ( set_se8855941934996405007c_fm_a @ X3 ) )
=> ( ( P2 @ Z )
=> ( Pa @ Z ) ) )
=> ( list_a5130230249644717486c_fm_a @ Pa @ X3 ) ) ) ).
% list.pred_mono_strong
thf(fact_416_list_Opred__mono__strong,axiom,
! [P2: produc5756089960658898087c_fm_a > $o,X3: list_P7917480606449584557c_fm_a,Pa: produc5756089960658898087c_fm_a > $o] :
( ( list_a4957036963921897819c_fm_a @ P2 @ X3 )
=> ( ! [Z: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ Z @ ( set_Pr5015285182815091004c_fm_a @ X3 ) )
=> ( ( P2 @ Z )
=> ( Pa @ Z ) ) )
=> ( list_a4957036963921897819c_fm_a @ Pa @ X3 ) ) ) ).
% list.pred_mono_strong
thf(fact_417_list_Opred__mono__strong,axiom,
! [P2: produc2203834439629243303c_fm_a > $o,X3: list_P3099032918374241197c_fm_a,Pa: produc2203834439629243303c_fm_a > $o] :
( ( list_a7787577967835477083c_fm_a @ P2 @ X3 )
=> ( ! [Z: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ Z @ ( set_Pr6083076219314900284c_fm_a @ X3 ) )
=> ( ( P2 @ Z )
=> ( Pa @ Z ) ) )
=> ( list_a7787577967835477083c_fm_a @ Pa @ X3 ) ) ) ).
% list.pred_mono_strong
thf(fact_418_list_Opred__mono__strong,axiom,
! [P2: list_Epistemic_fm_a > $o,X3: list_l6083326122719238310c_fm_a,Pa: list_Epistemic_fm_a > $o] :
( ( list_a5890043570083025364c_fm_a @ P2 @ X3 )
=> ( ! [Z: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ Z @ ( set_li8442223810127165109c_fm_a @ X3 ) )
=> ( ( P2 @ Z )
=> ( Pa @ Z ) ) )
=> ( list_a5890043570083025364c_fm_a @ Pa @ X3 ) ) ) ).
% list.pred_mono_strong
thf(fact_419_list_Opred__mono__strong,axiom,
! [P2: epistemic_fm_a > $o,X3: list_Epistemic_fm_a,Pa: epistemic_fm_a > $o] :
( ( list_a5841931967666341838c_fm_a @ P2 @ X3 )
=> ( ! [Z: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Z @ ( set_Epistemic_fm_a2 @ X3 ) )
=> ( ( P2 @ Z )
=> ( Pa @ Z ) ) )
=> ( list_a5841931967666341838c_fm_a @ Pa @ X3 ) ) ) ).
% list.pred_mono_strong
thf(fact_420_list__all__cong,axiom,
! [X3: list_s580375451141968640c_fm_a,Ya: list_s580375451141968640c_fm_a,P2: set_Epistemic_fm_a > $o,Pa: set_Epistemic_fm_a > $o] :
( ( X3 = Ya )
=> ( ! [Z: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ Z @ ( set_se8855941934996405007c_fm_a @ Ya ) )
=> ( ( P2 @ Z )
= ( Pa @ Z ) ) )
=> ( ( list_a5130230249644717486c_fm_a @ P2 @ X3 )
= ( list_a5130230249644717486c_fm_a @ Pa @ Ya ) ) ) ) ).
% list_all_cong
thf(fact_421_list__all__cong,axiom,
! [X3: list_P7917480606449584557c_fm_a,Ya: list_P7917480606449584557c_fm_a,P2: produc5756089960658898087c_fm_a > $o,Pa: produc5756089960658898087c_fm_a > $o] :
( ( X3 = Ya )
=> ( ! [Z: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ Z @ ( set_Pr5015285182815091004c_fm_a @ Ya ) )
=> ( ( P2 @ Z )
= ( Pa @ Z ) ) )
=> ( ( list_a4957036963921897819c_fm_a @ P2 @ X3 )
= ( list_a4957036963921897819c_fm_a @ Pa @ Ya ) ) ) ) ).
% list_all_cong
thf(fact_422_list__all__cong,axiom,
! [X3: list_P3099032918374241197c_fm_a,Ya: list_P3099032918374241197c_fm_a,P2: produc2203834439629243303c_fm_a > $o,Pa: produc2203834439629243303c_fm_a > $o] :
( ( X3 = Ya )
=> ( ! [Z: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ Z @ ( set_Pr6083076219314900284c_fm_a @ Ya ) )
=> ( ( P2 @ Z )
= ( Pa @ Z ) ) )
=> ( ( list_a7787577967835477083c_fm_a @ P2 @ X3 )
= ( list_a7787577967835477083c_fm_a @ Pa @ Ya ) ) ) ) ).
% list_all_cong
thf(fact_423_list__all__cong,axiom,
! [X3: list_l6083326122719238310c_fm_a,Ya: list_l6083326122719238310c_fm_a,P2: list_Epistemic_fm_a > $o,Pa: list_Epistemic_fm_a > $o] :
( ( X3 = Ya )
=> ( ! [Z: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ Z @ ( set_li8442223810127165109c_fm_a @ Ya ) )
=> ( ( P2 @ Z )
= ( Pa @ Z ) ) )
=> ( ( list_a5890043570083025364c_fm_a @ P2 @ X3 )
= ( list_a5890043570083025364c_fm_a @ Pa @ Ya ) ) ) ) ).
% list_all_cong
thf(fact_424_list__all__cong,axiom,
! [X3: list_Epistemic_fm_a,Ya: list_Epistemic_fm_a,P2: epistemic_fm_a > $o,Pa: epistemic_fm_a > $o] :
( ( X3 = Ya )
=> ( ! [Z: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Z @ ( set_Epistemic_fm_a2 @ Ya ) )
=> ( ( P2 @ Z )
= ( Pa @ Z ) ) )
=> ( ( list_a5841931967666341838c_fm_a @ P2 @ X3 )
= ( list_a5841931967666341838c_fm_a @ Pa @ Ya ) ) ) ) ).
% list_all_cong
thf(fact_425_List_Oinsert__def,axiom,
( insert1868103382419917334c_fm_a
= ( ^ [X: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] : ( if_lis3811715425919989702c_fm_a @ ( member536094252920883875c_fm_a @ X @ ( set_se8855941934996405007c_fm_a @ Xs2 ) ) @ Xs2 @ ( cons_s4394448069393209776c_fm_a @ X @ Xs2 ) ) ) ) ).
% List.insert_def
thf(fact_426_List_Oinsert__def,axiom,
( insert7000960152310464963c_fm_a
= ( ^ [X: produc5756089960658898087c_fm_a,Xs2: list_P7917480606449584557c_fm_a] : ( if_lis974313005191179635c_fm_a @ ( member3265983909902097104c_fm_a @ X @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) ) @ Xs2 @ ( cons_P7190808671141380701c_fm_a @ X @ Xs2 ) ) ) ) ).
% List.insert_def
thf(fact_427_List_Oinsert__def,axiom,
( insert423680279517344963c_fm_a
= ( ^ [X: produc2203834439629243303c_fm_a,Xs2: list_P3099032918374241197c_fm_a] : ( if_lis4277834422595218803c_fm_a @ ( member5029746173879296720c_fm_a @ X @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) ) @ Xs2 @ ( cons_P6232728021713608541c_fm_a @ X @ Xs2 ) ) ) ) ).
% List.insert_def
thf(fact_428_List_Oinsert__def,axiom,
( insert177310161492556854c_fm_a
= ( ^ [X: epistemic_fm_a,Xs2: list_Epistemic_fm_a] : ( if_lis2878681784746929638c_fm_a @ ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs2 ) ) @ Xs2 @ ( cons_Epistemic_fm_a @ X @ Xs2 ) ) ) ) ).
% List.insert_def
thf(fact_429_List_Oinsert__def,axiom,
( insert335162795743670844c_fm_a
= ( ^ [X: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] : ( if_lis342421823373228652c_fm_a @ ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs2 ) ) @ Xs2 @ ( cons_l8134865115577406678c_fm_a @ X @ Xs2 ) ) ) ) ).
% List.insert_def
thf(fact_430_list_Opred__True,axiom,
( ( list_a5841931967666341838c_fm_a
@ ^ [Uu2: epistemic_fm_a] : $true )
= ( ^ [Uu2: list_Epistemic_fm_a] : $true ) ) ).
% list.pred_True
thf(fact_431_list_Oset__intros_I2_J,axiom,
! [Y: set_Epistemic_fm_a,X22: list_s580375451141968640c_fm_a,X21: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ Y @ ( set_se8855941934996405007c_fm_a @ X22 ) )
=> ( member536094252920883875c_fm_a @ Y @ ( set_se8855941934996405007c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X21 @ X22 ) ) ) ) ).
% list.set_intros(2)
thf(fact_432_list_Oset__intros_I2_J,axiom,
! [Y: produc5756089960658898087c_fm_a,X22: list_P7917480606449584557c_fm_a,X21: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ Y @ ( set_Pr5015285182815091004c_fm_a @ X22 ) )
=> ( member3265983909902097104c_fm_a @ Y @ ( set_Pr5015285182815091004c_fm_a @ ( cons_P7190808671141380701c_fm_a @ X21 @ X22 ) ) ) ) ).
% list.set_intros(2)
thf(fact_433_list_Oset__intros_I2_J,axiom,
! [Y: produc2203834439629243303c_fm_a,X22: list_P3099032918374241197c_fm_a,X21: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ Y @ ( set_Pr6083076219314900284c_fm_a @ X22 ) )
=> ( member5029746173879296720c_fm_a @ Y @ ( set_Pr6083076219314900284c_fm_a @ ( cons_P6232728021713608541c_fm_a @ X21 @ X22 ) ) ) ) ).
% list.set_intros(2)
thf(fact_434_list_Oset__intros_I2_J,axiom,
! [Y: epistemic_fm_a,X22: list_Epistemic_fm_a,X21: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Y @ ( set_Epistemic_fm_a2 @ X22 ) )
=> ( member6642669571620171971c_fm_a @ Y @ ( set_Epistemic_fm_a2 @ ( cons_Epistemic_fm_a @ X21 @ X22 ) ) ) ) ).
% list.set_intros(2)
thf(fact_435_list_Oset__intros_I2_J,axiom,
! [Y: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a,X21: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ Y @ ( set_li8442223810127165109c_fm_a @ X22 ) )
=> ( member5906877432388582473c_fm_a @ Y @ ( set_li8442223810127165109c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) ) ) ) ).
% list.set_intros(2)
thf(fact_436_list_Oset__intros_I1_J,axiom,
! [X21: set_Epistemic_fm_a,X22: list_s580375451141968640c_fm_a] : ( member536094252920883875c_fm_a @ X21 @ ( set_se8855941934996405007c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X21 @ X22 ) ) ) ).
% list.set_intros(1)
thf(fact_437_list_Oset__intros_I1_J,axiom,
! [X21: produc5756089960658898087c_fm_a,X22: list_P7917480606449584557c_fm_a] : ( member3265983909902097104c_fm_a @ X21 @ ( set_Pr5015285182815091004c_fm_a @ ( cons_P7190808671141380701c_fm_a @ X21 @ X22 ) ) ) ).
% list.set_intros(1)
thf(fact_438_list_Oset__intros_I1_J,axiom,
! [X21: produc2203834439629243303c_fm_a,X22: list_P3099032918374241197c_fm_a] : ( member5029746173879296720c_fm_a @ X21 @ ( set_Pr6083076219314900284c_fm_a @ ( cons_P6232728021713608541c_fm_a @ X21 @ X22 ) ) ) ).
% list.set_intros(1)
thf(fact_439_list_Oset__intros_I1_J,axiom,
! [X21: epistemic_fm_a,X22: list_Epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X21 @ ( set_Epistemic_fm_a2 @ ( cons_Epistemic_fm_a @ X21 @ X22 ) ) ) ).
% list.set_intros(1)
thf(fact_440_list_Oset__intros_I1_J,axiom,
! [X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] : ( member5906877432388582473c_fm_a @ X21 @ ( set_li8442223810127165109c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) ) ) ).
% list.set_intros(1)
thf(fact_441_list_Oset__cases,axiom,
! [E: set_Epistemic_fm_a,A2: list_s580375451141968640c_fm_a] :
( ( member536094252920883875c_fm_a @ E @ ( set_se8855941934996405007c_fm_a @ A2 ) )
=> ( ! [Z22: list_s580375451141968640c_fm_a] :
( A2
!= ( cons_s4394448069393209776c_fm_a @ E @ Z22 ) )
=> ~ ! [Z1: set_Epistemic_fm_a,Z22: list_s580375451141968640c_fm_a] :
( ( A2
= ( cons_s4394448069393209776c_fm_a @ Z1 @ Z22 ) )
=> ~ ( member536094252920883875c_fm_a @ E @ ( set_se8855941934996405007c_fm_a @ Z22 ) ) ) ) ) ).
% list.set_cases
thf(fact_442_list_Oset__cases,axiom,
! [E: produc5756089960658898087c_fm_a,A2: list_P7917480606449584557c_fm_a] :
( ( member3265983909902097104c_fm_a @ E @ ( set_Pr5015285182815091004c_fm_a @ A2 ) )
=> ( ! [Z22: list_P7917480606449584557c_fm_a] :
( A2
!= ( cons_P7190808671141380701c_fm_a @ E @ Z22 ) )
=> ~ ! [Z1: produc5756089960658898087c_fm_a,Z22: list_P7917480606449584557c_fm_a] :
( ( A2
= ( cons_P7190808671141380701c_fm_a @ Z1 @ Z22 ) )
=> ~ ( member3265983909902097104c_fm_a @ E @ ( set_Pr5015285182815091004c_fm_a @ Z22 ) ) ) ) ) ).
% list.set_cases
thf(fact_443_list_Oset__cases,axiom,
! [E: produc2203834439629243303c_fm_a,A2: list_P3099032918374241197c_fm_a] :
( ( member5029746173879296720c_fm_a @ E @ ( set_Pr6083076219314900284c_fm_a @ A2 ) )
=> ( ! [Z22: list_P3099032918374241197c_fm_a] :
( A2
!= ( cons_P6232728021713608541c_fm_a @ E @ Z22 ) )
=> ~ ! [Z1: produc2203834439629243303c_fm_a,Z22: list_P3099032918374241197c_fm_a] :
( ( A2
= ( cons_P6232728021713608541c_fm_a @ Z1 @ Z22 ) )
=> ~ ( member5029746173879296720c_fm_a @ E @ ( set_Pr6083076219314900284c_fm_a @ Z22 ) ) ) ) ) ).
% list.set_cases
thf(fact_444_list_Oset__cases,axiom,
! [E: epistemic_fm_a,A2: list_Epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ E @ ( set_Epistemic_fm_a2 @ A2 ) )
=> ( ! [Z22: list_Epistemic_fm_a] :
( A2
!= ( cons_Epistemic_fm_a @ E @ Z22 ) )
=> ~ ! [Z1: epistemic_fm_a,Z22: list_Epistemic_fm_a] :
( ( A2
= ( cons_Epistemic_fm_a @ Z1 @ Z22 ) )
=> ~ ( member6642669571620171971c_fm_a @ E @ ( set_Epistemic_fm_a2 @ Z22 ) ) ) ) ) ).
% list.set_cases
thf(fact_445_list_Oset__cases,axiom,
! [E: list_Epistemic_fm_a,A2: list_l6083326122719238310c_fm_a] :
( ( member5906877432388582473c_fm_a @ E @ ( set_li8442223810127165109c_fm_a @ A2 ) )
=> ( ! [Z22: list_l6083326122719238310c_fm_a] :
( A2
!= ( cons_l8134865115577406678c_fm_a @ E @ Z22 ) )
=> ~ ! [Z1: list_Epistemic_fm_a,Z22: list_l6083326122719238310c_fm_a] :
( ( A2
= ( cons_l8134865115577406678c_fm_a @ Z1 @ Z22 ) )
=> ~ ( member5906877432388582473c_fm_a @ E @ ( set_li8442223810127165109c_fm_a @ Z22 ) ) ) ) ) ).
% list.set_cases
thf(fact_446_set__ConsD,axiom,
! [Y: set_Epistemic_fm_a,X3: set_Epistemic_fm_a,Xs: list_s580375451141968640c_fm_a] :
( ( member536094252920883875c_fm_a @ Y @ ( set_se8855941934996405007c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs ) ) )
=> ( ( Y = X3 )
| ( member536094252920883875c_fm_a @ Y @ ( set_se8855941934996405007c_fm_a @ Xs ) ) ) ) ).
% set_ConsD
thf(fact_447_set__ConsD,axiom,
! [Y: produc5756089960658898087c_fm_a,X3: produc5756089960658898087c_fm_a,Xs: list_P7917480606449584557c_fm_a] :
( ( member3265983909902097104c_fm_a @ Y @ ( set_Pr5015285182815091004c_fm_a @ ( cons_P7190808671141380701c_fm_a @ X3 @ Xs ) ) )
=> ( ( Y = X3 )
| ( member3265983909902097104c_fm_a @ Y @ ( set_Pr5015285182815091004c_fm_a @ Xs ) ) ) ) ).
% set_ConsD
thf(fact_448_set__ConsD,axiom,
! [Y: produc2203834439629243303c_fm_a,X3: produc2203834439629243303c_fm_a,Xs: list_P3099032918374241197c_fm_a] :
( ( member5029746173879296720c_fm_a @ Y @ ( set_Pr6083076219314900284c_fm_a @ ( cons_P6232728021713608541c_fm_a @ X3 @ Xs ) ) )
=> ( ( Y = X3 )
| ( member5029746173879296720c_fm_a @ Y @ ( set_Pr6083076219314900284c_fm_a @ Xs ) ) ) ) ).
% set_ConsD
thf(fact_449_set__ConsD,axiom,
! [Y: epistemic_fm_a,X3: epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Y @ ( set_Epistemic_fm_a2 @ ( cons_Epistemic_fm_a @ X3 @ Xs ) ) )
=> ( ( Y = X3 )
| ( member6642669571620171971c_fm_a @ Y @ ( set_Epistemic_fm_a2 @ Xs ) ) ) ) ).
% set_ConsD
thf(fact_450_set__ConsD,axiom,
! [Y: list_Epistemic_fm_a,X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( member5906877432388582473c_fm_a @ Y @ ( set_li8442223810127165109c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs ) ) )
=> ( ( Y = X3 )
| ( member5906877432388582473c_fm_a @ Y @ ( set_li8442223810127165109c_fm_a @ Xs ) ) ) ) ).
% set_ConsD
thf(fact_451_set__subset__Cons,axiom,
! [Xs: list_Epistemic_fm_a,X3: epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Xs ) @ ( set_Epistemic_fm_a2 @ ( cons_Epistemic_fm_a @ X3 @ Xs ) ) ) ).
% set_subset_Cons
thf(fact_452_set__subset__Cons,axiom,
! [Xs: list_l6083326122719238310c_fm_a,X3: list_Epistemic_fm_a] : ( ord_le2931979837777675552c_fm_a @ ( set_li8442223810127165109c_fm_a @ Xs ) @ ( set_li8442223810127165109c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs ) ) ) ).
% set_subset_Cons
thf(fact_453_list_Omap__cong,axiom,
! [X3: list_Epistemic_fm_a,Ya: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,G4: epistemic_fm_a > list_Epistemic_fm_a] :
( ( X3 = Ya )
=> ( ! [Z: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Z @ ( set_Epistemic_fm_a2 @ Ya ) )
=> ( ( F @ Z )
= ( G4 @ Z ) ) )
=> ( ( map_Ep1988204514693272906c_fm_a @ F @ X3 )
= ( map_Ep1988204514693272906c_fm_a @ G4 @ Ya ) ) ) ) ).
% list.map_cong
thf(fact_454_list_Omap__cong,axiom,
! [X3: list_l6083326122719238310c_fm_a,Ya: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,G4: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( X3 = Ya )
=> ( ! [Z: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ Z @ ( set_li8442223810127165109c_fm_a @ Ya ) )
=> ( ( F @ Z )
= ( G4 @ Z ) ) )
=> ( ( map_li3080774272885743684c_fm_a @ F @ X3 )
= ( map_li3080774272885743684c_fm_a @ G4 @ Ya ) ) ) ) ).
% list.map_cong
thf(fact_455_list_Omap__cong,axiom,
! [X3: list_l6083326122719238310c_fm_a,Ya: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,G4: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( X3 = Ya )
=> ( ! [Z: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ Z @ ( set_li8442223810127165109c_fm_a @ Ya ) )
=> ( ( F @ Z )
= ( G4 @ Z ) ) )
=> ( ( map_li3858915945532548554c_fm_a @ F @ X3 )
= ( map_li3858915945532548554c_fm_a @ G4 @ Ya ) ) ) ) ).
% list.map_cong
thf(fact_456_list_Omap__cong,axiom,
! [X3: list_l6083326122719238310c_fm_a,Ya: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,G4: list_Epistemic_fm_a > epistemic_fm_a] :
( ( X3 = Ya )
=> ( ! [Z: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ Z @ ( set_li8442223810127165109c_fm_a @ Ya ) )
=> ( ( F @ Z )
= ( G4 @ Z ) ) )
=> ( ( map_li5516866612190465598c_fm_a @ F @ X3 )
= ( map_li5516866612190465598c_fm_a @ G4 @ Ya ) ) ) ) ).
% list.map_cong
thf(fact_457_list_Omap__cong,axiom,
! [X3: list_Epistemic_fm_a,Ya: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,G4: epistemic_fm_a > epistemic_fm_a] :
( ( X3 = Ya )
=> ( ! [Z: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Z @ ( set_Epistemic_fm_a2 @ Ya ) )
=> ( ( F @ Z )
= ( G4 @ Z ) ) )
=> ( ( map_Ep7084560364594560580c_fm_a @ F @ X3 )
= ( map_Ep7084560364594560580c_fm_a @ G4 @ Ya ) ) ) ) ).
% list.map_cong
thf(fact_458_list_Omap__cong0,axiom,
! [X3: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,G4: epistemic_fm_a > list_Epistemic_fm_a] :
( ! [Z: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Z @ ( set_Epistemic_fm_a2 @ X3 ) )
=> ( ( F @ Z )
= ( G4 @ Z ) ) )
=> ( ( map_Ep1988204514693272906c_fm_a @ F @ X3 )
= ( map_Ep1988204514693272906c_fm_a @ G4 @ X3 ) ) ) ).
% list.map_cong0
thf(fact_459_list_Omap__cong0,axiom,
! [X3: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,G4: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ! [Z: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ Z @ ( set_li8442223810127165109c_fm_a @ X3 ) )
=> ( ( F @ Z )
= ( G4 @ Z ) ) )
=> ( ( map_li3080774272885743684c_fm_a @ F @ X3 )
= ( map_li3080774272885743684c_fm_a @ G4 @ X3 ) ) ) ).
% list.map_cong0
thf(fact_460_list_Omap__cong0,axiom,
! [X3: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,G4: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ! [Z: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ Z @ ( set_li8442223810127165109c_fm_a @ X3 ) )
=> ( ( F @ Z )
= ( G4 @ Z ) ) )
=> ( ( map_li3858915945532548554c_fm_a @ F @ X3 )
= ( map_li3858915945532548554c_fm_a @ G4 @ X3 ) ) ) ).
% list.map_cong0
thf(fact_461_list_Omap__cong0,axiom,
! [X3: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,G4: list_Epistemic_fm_a > epistemic_fm_a] :
( ! [Z: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ Z @ ( set_li8442223810127165109c_fm_a @ X3 ) )
=> ( ( F @ Z )
= ( G4 @ Z ) ) )
=> ( ( map_li5516866612190465598c_fm_a @ F @ X3 )
= ( map_li5516866612190465598c_fm_a @ G4 @ X3 ) ) ) ).
% list.map_cong0
thf(fact_462_list_Omap__cong0,axiom,
! [X3: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,G4: epistemic_fm_a > epistemic_fm_a] :
( ! [Z: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Z @ ( set_Epistemic_fm_a2 @ X3 ) )
=> ( ( F @ Z )
= ( G4 @ Z ) ) )
=> ( ( map_Ep7084560364594560580c_fm_a @ F @ X3 )
= ( map_Ep7084560364594560580c_fm_a @ G4 @ X3 ) ) ) ).
% list.map_cong0
thf(fact_463_list_Oinj__map__strong,axiom,
! [X3: list_Epistemic_fm_a,Xa: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,Fa: epistemic_fm_a > list_Epistemic_fm_a] :
( ! [Z: epistemic_fm_a,Za: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Z @ ( set_Epistemic_fm_a2 @ X3 ) )
=> ( ( member6642669571620171971c_fm_a @ Za @ ( set_Epistemic_fm_a2 @ Xa ) )
=> ( ( ( F @ Z )
= ( Fa @ Za ) )
=> ( Z = Za ) ) ) )
=> ( ( ( map_Ep1988204514693272906c_fm_a @ F @ X3 )
= ( map_Ep1988204514693272906c_fm_a @ Fa @ Xa ) )
=> ( X3 = Xa ) ) ) ).
% list.inj_map_strong
thf(fact_464_list_Oinj__map__strong,axiom,
! [X3: list_l6083326122719238310c_fm_a,Xa: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,Fa: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ! [Z: list_Epistemic_fm_a,Za: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ Z @ ( set_li8442223810127165109c_fm_a @ X3 ) )
=> ( ( member5906877432388582473c_fm_a @ Za @ ( set_li8442223810127165109c_fm_a @ Xa ) )
=> ( ( ( F @ Z )
= ( Fa @ Za ) )
=> ( Z = Za ) ) ) )
=> ( ( ( map_li3080774272885743684c_fm_a @ F @ X3 )
= ( map_li3080774272885743684c_fm_a @ Fa @ Xa ) )
=> ( X3 = Xa ) ) ) ).
% list.inj_map_strong
thf(fact_465_list_Oinj__map__strong,axiom,
! [X3: list_l6083326122719238310c_fm_a,Xa: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Fa: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ! [Z: list_Epistemic_fm_a,Za: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ Z @ ( set_li8442223810127165109c_fm_a @ X3 ) )
=> ( ( member5906877432388582473c_fm_a @ Za @ ( set_li8442223810127165109c_fm_a @ Xa ) )
=> ( ( ( F @ Z )
= ( Fa @ Za ) )
=> ( Z = Za ) ) ) )
=> ( ( ( map_li3858915945532548554c_fm_a @ F @ X3 )
= ( map_li3858915945532548554c_fm_a @ Fa @ Xa ) )
=> ( X3 = Xa ) ) ) ).
% list.inj_map_strong
thf(fact_466_list_Oinj__map__strong,axiom,
! [X3: list_l6083326122719238310c_fm_a,Xa: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,Fa: list_Epistemic_fm_a > epistemic_fm_a] :
( ! [Z: list_Epistemic_fm_a,Za: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ Z @ ( set_li8442223810127165109c_fm_a @ X3 ) )
=> ( ( member5906877432388582473c_fm_a @ Za @ ( set_li8442223810127165109c_fm_a @ Xa ) )
=> ( ( ( F @ Z )
= ( Fa @ Za ) )
=> ( Z = Za ) ) ) )
=> ( ( ( map_li5516866612190465598c_fm_a @ F @ X3 )
= ( map_li5516866612190465598c_fm_a @ Fa @ Xa ) )
=> ( X3 = Xa ) ) ) ).
% list.inj_map_strong
thf(fact_467_list_Oinj__map__strong,axiom,
! [X3: list_Epistemic_fm_a,Xa: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,Fa: epistemic_fm_a > epistemic_fm_a] :
( ! [Z: epistemic_fm_a,Za: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Z @ ( set_Epistemic_fm_a2 @ X3 ) )
=> ( ( member6642669571620171971c_fm_a @ Za @ ( set_Epistemic_fm_a2 @ Xa ) )
=> ( ( ( F @ Z )
= ( Fa @ Za ) )
=> ( Z = Za ) ) ) )
=> ( ( ( map_Ep7084560364594560580c_fm_a @ F @ X3 )
= ( map_Ep7084560364594560580c_fm_a @ Fa @ Xa ) )
=> ( X3 = Xa ) ) ) ).
% list.inj_map_strong
thf(fact_468_list_Omap__ident__strong,axiom,
! [T: list_s580375451141968640c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a] :
( ! [Z: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ Z @ ( set_se8855941934996405007c_fm_a @ T ) )
=> ( ( F @ Z )
= Z ) )
=> ( ( map_se7333198834109155908c_fm_a @ F @ T )
= T ) ) ).
% list.map_ident_strong
thf(fact_469_list_Omap__ident__strong,axiom,
! [T: list_P7917480606449584557c_fm_a,F: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a] :
( ! [Z: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ Z @ ( set_Pr5015285182815091004c_fm_a @ T ) )
=> ( ( F @ Z )
= Z ) )
=> ( ( map_Pr5661761254319454724c_fm_a @ F @ T )
= T ) ) ).
% list.map_ident_strong
thf(fact_470_list_Omap__ident__strong,axiom,
! [T: list_P3099032918374241197c_fm_a,F: produc2203834439629243303c_fm_a > produc2203834439629243303c_fm_a] :
( ! [Z: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ Z @ ( set_Pr6083076219314900284c_fm_a @ T ) )
=> ( ( F @ Z )
= Z ) )
=> ( ( map_Pr2297397278705060868c_fm_a @ F @ T )
= T ) ) ).
% list.map_ident_strong
thf(fact_471_list_Omap__ident__strong,axiom,
! [T: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ! [Z: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ Z @ ( set_li8442223810127165109c_fm_a @ T ) )
=> ( ( F @ Z )
= Z ) )
=> ( ( map_li3080774272885743684c_fm_a @ F @ T )
= T ) ) ).
% list.map_ident_strong
thf(fact_472_list_Omap__ident__strong,axiom,
! [T: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
( ! [Z: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Z @ ( set_Epistemic_fm_a2 @ T ) )
=> ( ( F @ Z )
= Z ) )
=> ( ( map_Ep7084560364594560580c_fm_a @ F @ T )
= T ) ) ).
% list.map_ident_strong
thf(fact_473_map__ext,axiom,
! [Xs: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,G4: epistemic_fm_a > list_Epistemic_fm_a] :
( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ( ( F @ X2 )
= ( G4 @ X2 ) ) )
=> ( ( map_Ep1988204514693272906c_fm_a @ F @ Xs )
= ( map_Ep1988204514693272906c_fm_a @ G4 @ Xs ) ) ) ).
% map_ext
thf(fact_474_map__ext,axiom,
! [Xs: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,G4: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ( ( F @ X2 )
= ( G4 @ X2 ) ) )
=> ( ( map_li3080774272885743684c_fm_a @ F @ Xs )
= ( map_li3080774272885743684c_fm_a @ G4 @ Xs ) ) ) ).
% map_ext
thf(fact_475_map__ext,axiom,
! [Xs: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,G4: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ( ( F @ X2 )
= ( G4 @ X2 ) ) )
=> ( ( map_li3858915945532548554c_fm_a @ F @ Xs )
= ( map_li3858915945532548554c_fm_a @ G4 @ Xs ) ) ) ).
% map_ext
thf(fact_476_map__ext,axiom,
! [Xs: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,G4: list_Epistemic_fm_a > epistemic_fm_a] :
( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ( ( F @ X2 )
= ( G4 @ X2 ) ) )
=> ( ( map_li5516866612190465598c_fm_a @ F @ Xs )
= ( map_li5516866612190465598c_fm_a @ G4 @ Xs ) ) ) ).
% map_ext
thf(fact_477_map__ext,axiom,
! [Xs: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,G4: epistemic_fm_a > epistemic_fm_a] :
( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ( ( F @ X2 )
= ( G4 @ X2 ) ) )
=> ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs )
= ( map_Ep7084560364594560580c_fm_a @ G4 @ Xs ) ) ) ).
% map_ext
thf(fact_478_map__idI,axiom,
! [Xs: list_s580375451141968640c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a] :
( ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Xs ) )
=> ( ( F @ X2 )
= X2 ) )
=> ( ( map_se7333198834109155908c_fm_a @ F @ Xs )
= Xs ) ) ).
% map_idI
thf(fact_479_map__idI,axiom,
! [Xs: list_P7917480606449584557c_fm_a,F: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a] :
( ! [X2: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Xs ) )
=> ( ( F @ X2 )
= X2 ) )
=> ( ( map_Pr5661761254319454724c_fm_a @ F @ Xs )
= Xs ) ) ).
% map_idI
thf(fact_480_map__idI,axiom,
! [Xs: list_P3099032918374241197c_fm_a,F: produc2203834439629243303c_fm_a > produc2203834439629243303c_fm_a] :
( ! [X2: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Xs ) )
=> ( ( F @ X2 )
= X2 ) )
=> ( ( map_Pr2297397278705060868c_fm_a @ F @ Xs )
= Xs ) ) ).
% map_idI
thf(fact_481_map__idI,axiom,
! [Xs: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ( ( F @ X2 )
= X2 ) )
=> ( ( map_li3080774272885743684c_fm_a @ F @ Xs )
= Xs ) ) ).
% map_idI
thf(fact_482_map__idI,axiom,
! [Xs: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ( ( F @ X2 )
= X2 ) )
=> ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs )
= Xs ) ) ).
% map_idI
thf(fact_483_map__cong,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,G4: epistemic_fm_a > list_Epistemic_fm_a] :
( ( Xs = Ys2 )
=> ( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Ys2 ) )
=> ( ( F @ X2 )
= ( G4 @ X2 ) ) )
=> ( ( map_Ep1988204514693272906c_fm_a @ F @ Xs )
= ( map_Ep1988204514693272906c_fm_a @ G4 @ Ys2 ) ) ) ) ).
% map_cong
thf(fact_484_map__cong,axiom,
! [Xs: list_l6083326122719238310c_fm_a,Ys2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,G4: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( Xs = Ys2 )
=> ( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Ys2 ) )
=> ( ( F @ X2 )
= ( G4 @ X2 ) ) )
=> ( ( map_li3080774272885743684c_fm_a @ F @ Xs )
= ( map_li3080774272885743684c_fm_a @ G4 @ Ys2 ) ) ) ) ).
% map_cong
thf(fact_485_map__cong,axiom,
! [Xs: list_l6083326122719238310c_fm_a,Ys2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,G4: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( Xs = Ys2 )
=> ( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Ys2 ) )
=> ( ( F @ X2 )
= ( G4 @ X2 ) ) )
=> ( ( map_li3858915945532548554c_fm_a @ F @ Xs )
= ( map_li3858915945532548554c_fm_a @ G4 @ Ys2 ) ) ) ) ).
% map_cong
thf(fact_486_map__cong,axiom,
! [Xs: list_l6083326122719238310c_fm_a,Ys2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,G4: list_Epistemic_fm_a > epistemic_fm_a] :
( ( Xs = Ys2 )
=> ( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Ys2 ) )
=> ( ( F @ X2 )
= ( G4 @ X2 ) ) )
=> ( ( map_li5516866612190465598c_fm_a @ F @ Xs )
= ( map_li5516866612190465598c_fm_a @ G4 @ Ys2 ) ) ) ) ).
% map_cong
thf(fact_487_map__cong,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,G4: epistemic_fm_a > epistemic_fm_a] :
( ( Xs = Ys2 )
=> ( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Ys2 ) )
=> ( ( F @ X2 )
= ( G4 @ X2 ) ) )
=> ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs )
= ( map_Ep7084560364594560580c_fm_a @ G4 @ Ys2 ) ) ) ) ).
% map_cong
thf(fact_488_ex__map__conv,axiom,
! [Ys2: list_l3671048651222332332c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( ? [Xs2: list_l6083326122719238310c_fm_a] :
( Ys2
= ( map_li3858915945532548554c_fm_a @ F @ Xs2 ) ) )
= ( ! [X: list_l6083326122719238310c_fm_a] :
( ( member7465314387053329231c_fm_a @ X @ ( set_li647609056391172027c_fm_a @ Ys2 ) )
=> ? [Y3: list_Epistemic_fm_a] :
( X
= ( F @ Y3 ) ) ) ) ) ).
% ex_map_conv
thf(fact_489_ex__map__conv,axiom,
! [Ys2: list_Epistemic_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a] :
( ( ? [Xs2: list_l6083326122719238310c_fm_a] :
( Ys2
= ( map_li5516866612190465598c_fm_a @ F @ Xs2 ) ) )
= ( ! [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Ys2 ) )
=> ? [Y3: list_Epistemic_fm_a] :
( X
= ( F @ Y3 ) ) ) ) ) ).
% ex_map_conv
thf(fact_490_ex__map__conv,axiom,
! [Ys2: list_l6083326122719238310c_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a] :
( ( ? [Xs2: list_Epistemic_fm_a] :
( Ys2
= ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 ) ) )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Ys2 ) )
=> ? [Y3: epistemic_fm_a] :
( X
= ( F @ Y3 ) ) ) ) ) ).
% ex_map_conv
thf(fact_491_ex__map__conv,axiom,
! [Ys2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( ? [Xs2: list_l6083326122719238310c_fm_a] :
( Ys2
= ( map_li3080774272885743684c_fm_a @ F @ Xs2 ) ) )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Ys2 ) )
=> ? [Y3: list_Epistemic_fm_a] :
( X
= ( F @ Y3 ) ) ) ) ) ).
% ex_map_conv
thf(fact_492_ex__map__conv,axiom,
! [Ys2: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
( ( ? [Xs2: list_Epistemic_fm_a] :
( Ys2
= ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) ) )
= ( ! [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Ys2 ) )
=> ? [Y3: epistemic_fm_a] :
( X
= ( F @ Y3 ) ) ) ) ) ).
% ex_map_conv
thf(fact_493_map__concat,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( map_Ep1988204514693272906c_fm_a @ F @ ( concat2780896542826320603c_fm_a @ Xs ) )
= ( concat6109960377493484129c_fm_a @ ( map_li3858915945532548554c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F ) @ Xs ) ) ) ).
% map_concat
thf(fact_494_map__concat,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs: list_l3671048651222332332c_fm_a] :
( ( map_li3080774272885743684c_fm_a @ F @ ( concat6109960377493484129c_fm_a @ Xs ) )
= ( concat6109960377493484129c_fm_a @ ( map_li8347733892191492164c_fm_a @ ( map_li3080774272885743684c_fm_a @ F ) @ Xs ) ) ) ).
% map_concat
thf(fact_495_map__concat,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs: list_l3671048651222332332c_fm_a] :
( ( map_li3858915945532548554c_fm_a @ F @ ( concat6109960377493484129c_fm_a @ Xs ) )
= ( concat5652308878773863783c_fm_a @ ( map_li3568483382057536586c_fm_a @ ( map_li3858915945532548554c_fm_a @ F ) @ Xs ) ) ) ).
% map_concat
thf(fact_496_map__concat,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs: list_l3671048651222332332c_fm_a] :
( ( map_li5516866612190465598c_fm_a @ F @ ( concat6109960377493484129c_fm_a @ Xs ) )
= ( concat2780896542826320603c_fm_a @ ( map_li8743910666895923134c_fm_a @ ( map_li5516866612190465598c_fm_a @ F ) @ Xs ) ) ) ).
% map_concat
thf(fact_497_map__concat,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( map_Ep7084560364594560580c_fm_a @ F @ ( concat2780896542826320603c_fm_a @ Xs ) )
= ( concat2780896542826320603c_fm_a @ ( map_li3080774272885743684c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ Xs ) ) ) ).
% map_concat
thf(fact_498_list_Opred__inject_I1_J,axiom,
! [P2: list_Epistemic_fm_a > $o] : ( list_a5890043570083025364c_fm_a @ P2 @ nil_li2451196919128234278c_fm_a ) ).
% list.pred_inject(1)
thf(fact_499_list_Opred__inject_I1_J,axiom,
! [P2: set_Epistemic_fm_a > $o] : ( list_a5130230249644717486c_fm_a @ P2 @ nil_se102576565402781184c_fm_a ) ).
% list.pred_inject(1)
thf(fact_500_list_Opred__inject_I1_J,axiom,
! [P2: epistemic_fm_a > $o] : ( list_a5841931967666341838c_fm_a @ P2 @ nil_Epistemic_fm_a ) ).
% list.pred_inject(1)
thf(fact_501_list_Opred__mono,axiom,
! [P2: epistemic_fm_a > $o,Pa: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ P2 @ Pa )
=> ( ord_le5289359451089373629fm_a_o @ ( list_a5841931967666341838c_fm_a @ P2 ) @ ( list_a5841931967666341838c_fm_a @ Pa ) ) ) ).
% list.pred_mono
thf(fact_502_list__bind__cong,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,G4: epistemic_fm_a > list_Epistemic_fm_a] :
( ( Xs = Ys2 )
=> ( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ( ( F @ X2 )
= ( G4 @ X2 ) ) )
=> ( ( bind_E8451893407412458119c_fm_a @ Xs @ F )
= ( bind_E8451893407412458119c_fm_a @ Ys2 @ G4 ) ) ) ) ).
% list_bind_cong
thf(fact_503_product__lists_Osimps_I2_J,axiom,
! [Xs: list_l6083326122719238310c_fm_a,Xss2: list_l3671048651222332332c_fm_a] :
( ( produc4433783857981728015c_fm_a @ ( cons_l2479501935080859996c_fm_a @ Xs @ Xss2 ) )
= ( concat5652308878773863783c_fm_a
@ ( map_li5567427098789011152c_fm_a
@ ^ [X: list_Epistemic_fm_a] : ( map_li8347733892191492164c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X ) @ ( produc4433783857981728015c_fm_a @ Xss2 ) )
@ Xs ) ) ) ).
% product_lists.simps(2)
thf(fact_504_product__lists_Osimps_I2_J,axiom,
! [Xs: list_Epistemic_fm_a,Xss2: list_l6083326122719238310c_fm_a] :
( ( produc1391074687832863881c_fm_a @ ( cons_l8134865115577406678c_fm_a @ Xs @ Xss2 ) )
= ( concat6109960377493484129c_fm_a
@ ( map_Ep4939040189629079504c_fm_a
@ ^ [X: epistemic_fm_a] : ( map_li3080774272885743684c_fm_a @ ( cons_Epistemic_fm_a @ X ) @ ( produc1391074687832863881c_fm_a @ Xss2 ) )
@ Xs ) ) ) ).
% product_lists.simps(2)
thf(fact_505_list__ex1__iff,axiom,
( list_e3415556844334454979c_fm_a
= ( ^ [P5: set_Epistemic_fm_a > $o,Xs2: list_s580375451141968640c_fm_a] :
? [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
& ( P5 @ X )
& ! [Y3: set_Epistemic_fm_a] :
( ( ( member536094252920883875c_fm_a @ Y3 @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
& ( P5 @ Y3 ) )
=> ( Y3 = X ) ) ) ) ) ).
% list_ex1_iff
thf(fact_506_list__ex1__iff,axiom,
( list_e8094467569734695152c_fm_a
= ( ^ [P5: produc5756089960658898087c_fm_a > $o,Xs2: list_P7917480606449584557c_fm_a] :
? [X: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) )
& ( P5 @ X )
& ! [Y3: produc5756089960658898087c_fm_a] :
( ( ( member3265983909902097104c_fm_a @ Y3 @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) )
& ( P5 @ Y3 ) )
=> ( Y3 = X ) ) ) ) ) ).
% list_ex1_iff
thf(fact_507_list__ex1__iff,axiom,
( list_e6284074732749938928c_fm_a
= ( ^ [P5: produc2203834439629243303c_fm_a > $o,Xs2: list_P3099032918374241197c_fm_a] :
? [X: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) )
& ( P5 @ X )
& ! [Y3: produc2203834439629243303c_fm_a] :
( ( ( member5029746173879296720c_fm_a @ Y3 @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) )
& ( P5 @ Y3 ) )
=> ( Y3 = X ) ) ) ) ) ).
% list_ex1_iff
thf(fact_508_list__ex1__iff,axiom,
( list_e1371837923195959913c_fm_a
= ( ^ [P5: list_Epistemic_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a] :
? [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
& ( P5 @ X )
& ! [Y3: list_Epistemic_fm_a] :
( ( ( member5906877432388582473c_fm_a @ Y3 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
& ( P5 @ Y3 ) )
=> ( Y3 = X ) ) ) ) ) ).
% list_ex1_iff
thf(fact_509_list__ex1__iff,axiom,
( list_e2031426293596896995c_fm_a
= ( ^ [P5: epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] :
? [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs2 ) )
& ( P5 @ X )
& ! [Y3: epistemic_fm_a] :
( ( ( member6642669571620171971c_fm_a @ Y3 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
& ( P5 @ Y3 ) )
=> ( Y3 = X ) ) ) ) ) ).
% list_ex1_iff
thf(fact_510_list_Omap__cong__pred,axiom,
! [X3: list_l6083326122719238310c_fm_a,Ya: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,G4: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( X3 = Ya )
=> ( ( list_a5890043570083025364c_fm_a
@ ^ [Z2: list_Epistemic_fm_a] :
( ( F @ Z2 )
= ( G4 @ Z2 ) )
@ Ya )
=> ( ( map_li3080774272885743684c_fm_a @ F @ X3 )
= ( map_li3080774272885743684c_fm_a @ G4 @ Ya ) ) ) ) ).
% list.map_cong_pred
thf(fact_511_list_Omap__cong__pred,axiom,
! [X3: list_l6083326122719238310c_fm_a,Ya: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,G4: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( X3 = Ya )
=> ( ( list_a5890043570083025364c_fm_a
@ ^ [Z2: list_Epistemic_fm_a] :
( ( F @ Z2 )
= ( G4 @ Z2 ) )
@ Ya )
=> ( ( map_li3858915945532548554c_fm_a @ F @ X3 )
= ( map_li3858915945532548554c_fm_a @ G4 @ Ya ) ) ) ) ).
% list.map_cong_pred
thf(fact_512_list_Omap__cong__pred,axiom,
! [X3: list_l6083326122719238310c_fm_a,Ya: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,G4: list_Epistemic_fm_a > epistemic_fm_a] :
( ( X3 = Ya )
=> ( ( list_a5890043570083025364c_fm_a
@ ^ [Z2: list_Epistemic_fm_a] :
( ( F @ Z2 )
= ( G4 @ Z2 ) )
@ Ya )
=> ( ( map_li5516866612190465598c_fm_a @ F @ X3 )
= ( map_li5516866612190465598c_fm_a @ G4 @ Ya ) ) ) ) ).
% list.map_cong_pred
thf(fact_513_list_Omap__cong__pred,axiom,
! [X3: list_Epistemic_fm_a,Ya: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,G4: epistemic_fm_a > list_Epistemic_fm_a] :
( ( X3 = Ya )
=> ( ( list_a5841931967666341838c_fm_a
@ ^ [Z2: epistemic_fm_a] :
( ( F @ Z2 )
= ( G4 @ Z2 ) )
@ Ya )
=> ( ( map_Ep1988204514693272906c_fm_a @ F @ X3 )
= ( map_Ep1988204514693272906c_fm_a @ G4 @ Ya ) ) ) ) ).
% list.map_cong_pred
thf(fact_514_list_Omap__cong__pred,axiom,
! [X3: list_Epistemic_fm_a,Ya: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,G4: epistemic_fm_a > epistemic_fm_a] :
( ( X3 = Ya )
=> ( ( list_a5841931967666341838c_fm_a
@ ^ [Z2: epistemic_fm_a] :
( ( F @ Z2 )
= ( G4 @ Z2 ) )
@ Ya )
=> ( ( map_Ep7084560364594560580c_fm_a @ F @ X3 )
= ( map_Ep7084560364594560580c_fm_a @ G4 @ Ya ) ) ) ) ).
% list.map_cong_pred
thf(fact_515_List_Obind__def,axiom,
( bind_E8451893407412458119c_fm_a
= ( ^ [Xs2: list_Epistemic_fm_a,F2: epistemic_fm_a > list_Epistemic_fm_a] : ( concat2780896542826320603c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F2 @ Xs2 ) ) ) ) ).
% List.bind_def
thf(fact_516_List_Obind__def,axiom,
( bind_l9085712471134790913c_fm_a
= ( ^ [Xs2: list_l6083326122719238310c_fm_a,F2: list_Epistemic_fm_a > list_Epistemic_fm_a] : ( concat2780896542826320603c_fm_a @ ( map_li3080774272885743684c_fm_a @ F2 @ Xs2 ) ) ) ) ).
% List.bind_def
thf(fact_517_List_Obind__def,axiom,
( bind_l6536575428307499399c_fm_a
= ( ^ [Xs2: list_l6083326122719238310c_fm_a,F2: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] : ( concat6109960377493484129c_fm_a @ ( map_li3858915945532548554c_fm_a @ F2 @ Xs2 ) ) ) ) ).
% List.bind_def
thf(fact_518_in__set__member,axiom,
! [X3: set_Epistemic_fm_a,Xs: list_s580375451141968640c_fm_a] :
( ( member536094252920883875c_fm_a @ X3 @ ( set_se8855941934996405007c_fm_a @ Xs ) )
= ( member378061430901374997c_fm_a @ Xs @ X3 ) ) ).
% in_set_member
thf(fact_519_in__set__member,axiom,
! [X3: produc5756089960658898087c_fm_a,Xs: list_P7917480606449584557c_fm_a] :
( ( member3265983909902097104c_fm_a @ X3 @ ( set_Pr5015285182815091004c_fm_a @ Xs ) )
= ( member9135556340679744834c_fm_a @ Xs @ X3 ) ) ).
% in_set_member
thf(fact_520_in__set__member,axiom,
! [X3: produc2203834439629243303c_fm_a,Xs: list_P3099032918374241197c_fm_a] :
( ( member5029746173879296720c_fm_a @ X3 @ ( set_Pr6083076219314900284c_fm_a @ Xs ) )
= ( member7699131040134686530c_fm_a @ Xs @ X3 ) ) ).
% in_set_member
thf(fact_521_in__set__member,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ Xs ) )
= ( member6038508265109909045c_fm_a @ Xs @ X3 ) ) ).
% in_set_member
thf(fact_522_in__set__member,axiom,
! [X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ Xs ) )
= ( member594239076476917947c_fm_a @ Xs @ X3 ) ) ).
% in_set_member
thf(fact_523_list_Osimps_I7_J,axiom,
! [F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
( ( rec_li4360243526537435568c_fm_a @ F1 @ F22 @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
= ( F22 @ X21 @ X22 @ ( rec_li4360243526537435568c_fm_a @ F1 @ F22 @ X22 ) ) ) ).
% list.simps(7)
thf(fact_524_list_Osimps_I6_J,axiom,
! [F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( rec_li4360243526537435568c_fm_a @ F1 @ F22 @ nil_Epistemic_fm_a )
= F1 ) ).
% list.simps(6)
thf(fact_525_K__imply__weaken,axiom,
! [A: epistemic_fm_a > $o,Ps: list_Epistemic_fm_a,Q: epistemic_fm_a,Ps2: list_Epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ Q ) )
=> ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Ps ) @ ( set_Epistemic_fm_a2 @ Ps2 ) )
=> ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps2 @ Q ) ) ) ) ).
% K_imply_weaken
thf(fact_526_concat_Osimps_I1_J,axiom,
( ( concat6109960377493484129c_fm_a @ nil_li5178944226519631276c_fm_a )
= nil_li2451196919128234278c_fm_a ) ).
% concat.simps(1)
thf(fact_527_concat_Osimps_I1_J,axiom,
( ( concat2941956077894552763c_fm_a @ nil_li5433889876484989702c_fm_a )
= nil_se102576565402781184c_fm_a ) ).
% concat.simps(1)
thf(fact_528_concat_Osimps_I1_J,axiom,
( ( concat2780896542826320603c_fm_a @ nil_li2451196919128234278c_fm_a )
= nil_Epistemic_fm_a ) ).
% concat.simps(1)
thf(fact_529_tautology__imply__superset,axiom,
! [Ps: list_Epistemic_fm_a,Qs2: list_Epistemic_fm_a,R: epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Ps ) @ ( set_Epistemic_fm_a2 @ Qs2 ) )
=> ! [G2: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H @ ( epistemic_Imp_a @ ( epistemic_imply_a @ Ps @ R ) @ ( epistemic_imply_a @ Qs2 @ R ) ) ) ) ).
% tautology_imply_superset
thf(fact_530_can__select__set__list__ex1,axiom,
! [P2: list_Epistemic_fm_a > $o,A: list_l6083326122719238310c_fm_a] :
( ( can_se7491264451046533021c_fm_a @ P2 @ ( set_li8442223810127165109c_fm_a @ A ) )
= ( list_e1371837923195959913c_fm_a @ P2 @ A ) ) ).
% can_select_set_list_ex1
thf(fact_531_can__select__set__list__ex1,axiom,
! [P2: epistemic_fm_a > $o,A: list_Epistemic_fm_a] :
( ( can_se5173380710277125655c_fm_a @ P2 @ ( set_Epistemic_fm_a2 @ A ) )
= ( list_e2031426293596896995c_fm_a @ P2 @ A ) ) ).
% can_select_set_list_ex1
thf(fact_532_rec__list__Nil__imp,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( F
= ( rec_li4360243526537435568c_fm_a @ F1 @ F22 ) )
=> ( ( F @ nil_Epistemic_fm_a )
= F1 ) ) ).
% rec_list_Nil_imp
thf(fact_533_rec__list__Cons__imp,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,X3: epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( F
= ( rec_li4360243526537435568c_fm_a @ F1 @ F22 ) )
=> ( ( F @ ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= ( F22 @ X3 @ Xs @ ( F @ Xs ) ) ) ) ).
% rec_list_Cons_imp
thf(fact_534_the__elem__set,axiom,
! [X3: set_Epistemic_fm_a] :
( ( the_el1285646365920873327c_fm_a @ ( set_se8855941934996405007c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X3 @ nil_se102576565402781184c_fm_a ) ) )
= X3 ) ).
% the_elem_set
thf(fact_535_the__elem__set,axiom,
! [X3: list_Epistemic_fm_a] :
( ( the_el8584007648813340437c_fm_a @ ( set_li8442223810127165109c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ nil_li2451196919128234278c_fm_a ) ) )
= X3 ) ).
% the_elem_set
thf(fact_536_the__elem__set,axiom,
! [X3: epistemic_fm_a] :
( ( the_el2173195877760541071c_fm_a @ ( set_Epistemic_fm_a2 @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) )
= X3 ) ).
% the_elem_set
thf(fact_537_strong__soundness_092_060_094sub_062K,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a,P2: episte1560738328020401952t_unit > $o] :
( ? [Qs3: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G )
& ( epistemic_AK_a
@ ^ [Uu2: epistemic_fm_a] : $false
@ ( epistemic_imply_a @ Qs3 @ P ) ) )
=> ! [M2: episte1560738328020401952t_unit] :
( ( P2 @ M2 )
=> ! [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ ( episte8072386903178013299t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ G )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ).
% strong_soundness\<^sub>K
thf(fact_538_strong__soundness,axiom,
! [A: epistemic_fm_a > $o,P2: episte94448284482925344t_unit > $o,G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte94448284482925344t_unit,W2: epistemic_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member6642669571620171971c_fm_a @ W2 @ ( episte6390737319716712051t_unit @ M3 ) )
=> ( episte5333283044364550848c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ? [Qs3: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G )
& ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs3 @ P ) ) )
=> ! [M2: episte94448284482925344t_unit] :
( ( P2 @ M2 )
=> ! [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ ( episte6390737319716712051t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ G )
=> ( episte5333283044364550848c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte5333283044364550848c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ) ).
% strong_soundness
thf(fact_539_strong__soundness,axiom,
! [A: epistemic_fm_a > $o,P2: episte1905851639235817760t_unit > $o,G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte1905851639235817760t_unit,W2: list_Epistemic_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member5906877432388582473c_fm_a @ W2 @ ( episte3604461938431221107t_unit @ M3 ) )
=> ( episte3437425354345704390c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ? [Qs3: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G )
& ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs3 @ P ) ) )
=> ! [M2: episte1905851639235817760t_unit] :
( ( P2 @ M2 )
=> ! [X4: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X4 @ ( episte3604461938431221107t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ G )
=> ( episte3437425354345704390c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte3437425354345704390c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ) ).
% strong_soundness
thf(fact_540_strong__soundness,axiom,
! [A: epistemic_fm_a > $o,P2: episte1613917330360936672t_unit > $o,G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte1613917330360936672t_unit,W2: produc5756089960658898087c_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member3265983909902097104c_fm_a @ W2 @ ( episte795400727954352563t_unit @ M3 ) )
=> ( episte3243793293402417485c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ? [Qs3: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G )
& ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs3 @ P ) ) )
=> ! [M2: episte1613917330360936672t_unit] :
( ( P2 @ M2 )
=> ! [X4: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X4 @ ( episte795400727954352563t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ G )
=> ( episte3243793293402417485c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte3243793293402417485c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ) ).
% strong_soundness
thf(fact_541_strong__soundness,axiom,
! [A: epistemic_fm_a > $o,P2: episte9194023259896155360t_unit > $o,G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte9194023259896155360t_unit,W2: produc2203834439629243303c_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member5029746173879296720c_fm_a @ W2 @ ( episte5714722596736476595t_unit @ M3 ) )
=> ( episte7505603015783396941c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ? [Qs3: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G )
& ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs3 @ P ) ) )
=> ! [M2: episte9194023259896155360t_unit] :
( ( P2 @ M2 )
=> ! [X4: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X4 @ ( episte5714722596736476595t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ G )
=> ( episte7505603015783396941c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte7505603015783396941c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ) ).
% strong_soundness
thf(fact_542_strong__soundness,axiom,
! [A: epistemic_fm_a > $o,P2: episte1560738328020401952t_unit > $o,G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte1560738328020401952t_unit,W2: set_Epistemic_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member536094252920883875c_fm_a @ W2 @ ( episte8072386903178013299t_unit @ M3 ) )
=> ( episte7081087998767065248c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ? [Qs3: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G )
& ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs3 @ P ) ) )
=> ! [M2: episte1560738328020401952t_unit] :
( ( P2 @ M2 )
=> ! [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ ( episte8072386903178013299t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ G )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ) ).
% strong_soundness
thf(fact_543_maps__def,axiom,
( maps_E6072454603808916545c_fm_a
= ( ^ [F2: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] : ( concat2780896542826320603c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F2 @ Xs2 ) ) ) ) ).
% maps_def
thf(fact_544_maps__def,axiom,
( maps_l2078986973461115323c_fm_a
= ( ^ [F2: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] : ( concat2780896542826320603c_fm_a @ ( map_li3080774272885743684c_fm_a @ F2 @ Xs2 ) ) ) ) ).
% maps_def
thf(fact_545_maps__def,axiom,
( maps_l3685687229838205249c_fm_a
= ( ^ [F2: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a] : ( concat6109960377493484129c_fm_a @ ( map_li3858915945532548554c_fm_a @ F2 @ Xs2 ) ) ) ) ).
% maps_def
thf(fact_546_Nil__eq__concat__conv,axiom,
! [Xss2: list_l3671048651222332332c_fm_a] :
( ( nil_li2451196919128234278c_fm_a
= ( concat6109960377493484129c_fm_a @ Xss2 ) )
= ( ! [X: list_l6083326122719238310c_fm_a] :
( ( member7465314387053329231c_fm_a @ X @ ( set_li647609056391172027c_fm_a @ Xss2 ) )
=> ( X = nil_li2451196919128234278c_fm_a ) ) ) ) ).
% Nil_eq_concat_conv
thf(fact_547_Nil__eq__concat__conv,axiom,
! [Xss2: list_l985973790606564998c_fm_a] :
( ( nil_se102576565402781184c_fm_a
= ( concat2941956077894552763c_fm_a @ Xss2 ) )
= ( ! [X: list_s580375451141968640c_fm_a] :
( ( member2328277852289759785c_fm_a @ X @ ( set_li3422124509070804117c_fm_a @ Xss2 ) )
=> ( X = nil_se102576565402781184c_fm_a ) ) ) ) ).
% Nil_eq_concat_conv
thf(fact_548_Nil__eq__concat__conv,axiom,
! [Xss2: list_l6083326122719238310c_fm_a] :
( ( nil_Epistemic_fm_a
= ( concat2780896542826320603c_fm_a @ Xss2 ) )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xss2 ) )
=> ( X = nil_Epistemic_fm_a ) ) ) ) ).
% Nil_eq_concat_conv
thf(fact_549_concat__eq__Nil__conv,axiom,
! [Xss2: list_l3671048651222332332c_fm_a] :
( ( ( concat6109960377493484129c_fm_a @ Xss2 )
= nil_li2451196919128234278c_fm_a )
= ( ! [X: list_l6083326122719238310c_fm_a] :
( ( member7465314387053329231c_fm_a @ X @ ( set_li647609056391172027c_fm_a @ Xss2 ) )
=> ( X = nil_li2451196919128234278c_fm_a ) ) ) ) ).
% concat_eq_Nil_conv
thf(fact_550_concat__eq__Nil__conv,axiom,
! [Xss2: list_l985973790606564998c_fm_a] :
( ( ( concat2941956077894552763c_fm_a @ Xss2 )
= nil_se102576565402781184c_fm_a )
= ( ! [X: list_s580375451141968640c_fm_a] :
( ( member2328277852289759785c_fm_a @ X @ ( set_li3422124509070804117c_fm_a @ Xss2 ) )
=> ( X = nil_se102576565402781184c_fm_a ) ) ) ) ).
% concat_eq_Nil_conv
thf(fact_551_concat__eq__Nil__conv,axiom,
! [Xss2: list_l6083326122719238310c_fm_a] :
( ( ( concat2780896542826320603c_fm_a @ Xss2 )
= nil_Epistemic_fm_a )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xss2 ) )
=> ( X = nil_Epistemic_fm_a ) ) ) ) ).
% concat_eq_Nil_conv
thf(fact_552_list_Ocase__distrib,axiom,
! [H3: list_Epistemic_fm_a > list_Epistemic_fm_a,F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,List: list_Epistemic_fm_a] :
( ( H3 @ ( case_l8442927312758267104c_fm_a @ F1 @ F22 @ List ) )
= ( case_l8442927312758267104c_fm_a @ ( H3 @ F1 )
@ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
@ List ) ) ).
% list.case_distrib
thf(fact_553_list_Ocase__distrib,axiom,
! [H3: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,List: list_Epistemic_fm_a] :
( ( H3 @ ( case_l8442927312758267104c_fm_a @ F1 @ F22 @ List ) )
= ( case_l5707353781634818138c_fm_a @ ( H3 @ F1 )
@ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
@ List ) ) ).
% list.case_distrib
thf(fact_554_list_Ocase__distrib,axiom,
! [H3: list_Epistemic_fm_a > $o,F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,List: list_Epistemic_fm_a] :
( ( H3 @ ( case_l8442927312758267104c_fm_a @ F1 @ F22 @ List ) )
= ( case_l2021589626981272552c_fm_a @ ( H3 @ F1 )
@ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
@ List ) ) ).
% list.case_distrib
thf(fact_555_list_Ocase__distrib,axiom,
! [H3: list_l6083326122719238310c_fm_a > list_Epistemic_fm_a,F1: list_l6083326122719238310c_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,List: list_Epistemic_fm_a] :
( ( H3 @ ( case_l5707353781634818138c_fm_a @ F1 @ F22 @ List ) )
= ( case_l8442927312758267104c_fm_a @ ( H3 @ F1 )
@ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
@ List ) ) ).
% list.case_distrib
thf(fact_556_list_Ocase__distrib,axiom,
! [H3: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a,F1: list_l6083326122719238310c_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,List: list_Epistemic_fm_a] :
( ( H3 @ ( case_l5707353781634818138c_fm_a @ F1 @ F22 @ List ) )
= ( case_l5707353781634818138c_fm_a @ ( H3 @ F1 )
@ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
@ List ) ) ).
% list.case_distrib
thf(fact_557_list_Ocase__distrib,axiom,
! [H3: list_l6083326122719238310c_fm_a > $o,F1: list_l6083326122719238310c_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,List: list_Epistemic_fm_a] :
( ( H3 @ ( case_l5707353781634818138c_fm_a @ F1 @ F22 @ List ) )
= ( case_l2021589626981272552c_fm_a @ ( H3 @ F1 )
@ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
@ List ) ) ).
% list.case_distrib
thf(fact_558_list_Ocase__distrib,axiom,
! [H3: $o > list_Epistemic_fm_a,F1: $o,F22: epistemic_fm_a > list_Epistemic_fm_a > $o,List: list_Epistemic_fm_a] :
( ( H3 @ ( case_l2021589626981272552c_fm_a @ F1 @ F22 @ List ) )
= ( case_l8442927312758267104c_fm_a @ ( H3 @ F1 )
@ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
@ List ) ) ).
% list.case_distrib
thf(fact_559_list_Ocase__distrib,axiom,
! [H3: $o > list_l6083326122719238310c_fm_a,F1: $o,F22: epistemic_fm_a > list_Epistemic_fm_a > $o,List: list_Epistemic_fm_a] :
( ( H3 @ ( case_l2021589626981272552c_fm_a @ F1 @ F22 @ List ) )
= ( case_l5707353781634818138c_fm_a @ ( H3 @ F1 )
@ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
@ List ) ) ).
% list.case_distrib
thf(fact_560_list_Ocase__distrib,axiom,
! [H3: $o > $o,F1: $o,F22: epistemic_fm_a > list_Epistemic_fm_a > $o,List: list_Epistemic_fm_a] :
( ( H3 @ ( case_l2021589626981272552c_fm_a @ F1 @ F22 @ List ) )
= ( case_l2021589626981272552c_fm_a @ ( H3 @ F1 )
@ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
@ List ) ) ).
% list.case_distrib
thf(fact_561_can__select__def,axiom,
( can_se5173380710277125655c_fm_a
= ( ^ [P5: epistemic_fm_a > $o,A3: set_Epistemic_fm_a] :
? [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ A3 )
& ( P5 @ X )
& ! [Y3: epistemic_fm_a] :
( ( ( member6642669571620171971c_fm_a @ Y3 @ A3 )
& ( P5 @ Y3 ) )
=> ( Y3 = X ) ) ) ) ) ).
% can_select_def
thf(fact_562_can__select__def,axiom,
( can_se8336582597686632439c_fm_a
= ( ^ [P5: set_Epistemic_fm_a > $o,A3: set_se5208064806568342746c_fm_a] :
? [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ A3 )
& ( P5 @ X )
& ! [Y3: set_Epistemic_fm_a] :
( ( ( member536094252920883875c_fm_a @ Y3 @ A3 )
& ( P5 @ Y3 ) )
=> ( Y3 = X ) ) ) ) ) ).
% can_select_def
thf(fact_563_can__select__def,axiom,
( can_se7491264451046533021c_fm_a
= ( ^ [P5: list_Epistemic_fm_a > $o,A3: set_li769143395467472256c_fm_a] :
? [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ A3 )
& ( P5 @ X )
& ! [Y3: list_Epistemic_fm_a] :
( ( ( member5906877432388582473c_fm_a @ Y3 @ A3 )
& ( P5 @ Y3 ) )
=> ( Y3 = X ) ) ) ) ) ).
% can_select_def
thf(fact_564_can__select__def,axiom,
( can_se5687140424174772772c_fm_a
= ( ^ [P5: produc5756089960658898087c_fm_a > $o,A3: set_Pr3219225162411408519c_fm_a] :
? [X: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X @ A3 )
& ( P5 @ X )
& ! [Y3: produc5756089960658898087c_fm_a] :
( ( ( member3265983909902097104c_fm_a @ Y3 @ A3 )
& ( P5 @ Y3 ) )
=> ( Y3 = X ) ) ) ) ) ).
% can_select_def
thf(fact_565_can__select__def,axiom,
( can_se4087753133389225508c_fm_a
= ( ^ [P5: produc2203834439629243303c_fm_a > $o,A3: set_Pr8948481099588399239c_fm_a] :
? [X: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X @ A3 )
& ( P5 @ X )
& ! [Y3: produc2203834439629243303c_fm_a] :
( ( ( member5029746173879296720c_fm_a @ Y3 @ A3 )
& ( P5 @ Y3 ) )
=> ( Y3 = X ) ) ) ) ) ).
% can_select_def
thf(fact_566_subseqs__refl,axiom,
! [Xs: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ Xs @ ( set_li8442223810127165109c_fm_a @ ( subseq859285839621985007c_fm_a @ Xs ) ) ) ).
% subseqs_refl
thf(fact_567_list_Osimps_I5_J,axiom,
! [F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
( ( case_l8442927312758267104c_fm_a @ F1 @ F22 @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
= ( F22 @ X21 @ X22 ) ) ).
% list.simps(5)
thf(fact_568_list_Osimps_I5_J,axiom,
! [F1: list_l6083326122719238310c_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
( ( case_l5707353781634818138c_fm_a @ F1 @ F22 @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
= ( F22 @ X21 @ X22 ) ) ).
% list.simps(5)
thf(fact_569_list_Osimps_I5_J,axiom,
! [F1: $o,F22: epistemic_fm_a > list_Epistemic_fm_a > $o,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
( ( case_l2021589626981272552c_fm_a @ F1 @ F22 @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
= ( F22 @ X21 @ X22 ) ) ).
% list.simps(5)
thf(fact_570_list_Osimps_I4_J,axiom,
! [F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( case_l8442927312758267104c_fm_a @ F1 @ F22 @ nil_Epistemic_fm_a )
= F1 ) ).
% list.simps(4)
thf(fact_571_list_Osimps_I4_J,axiom,
! [F1: list_l6083326122719238310c_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( case_l5707353781634818138c_fm_a @ F1 @ F22 @ nil_Epistemic_fm_a )
= F1 ) ).
% list.simps(4)
thf(fact_572_list_Osimps_I4_J,axiom,
! [F1: $o,F22: epistemic_fm_a > list_Epistemic_fm_a > $o] :
( ( case_l2021589626981272552c_fm_a @ F1 @ F22 @ nil_Epistemic_fm_a )
= F1 ) ).
% list.simps(4)
thf(fact_573_Cons__in__subseqsD,axiom,
! [Y: epistemic_fm_a,Ys2: list_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ ( cons_Epistemic_fm_a @ Y @ Ys2 ) @ ( set_li8442223810127165109c_fm_a @ ( subseq859285839621985007c_fm_a @ Xs ) ) )
=> ( member5906877432388582473c_fm_a @ Ys2 @ ( set_li8442223810127165109c_fm_a @ ( subseq859285839621985007c_fm_a @ Xs ) ) ) ) ).
% Cons_in_subseqsD
thf(fact_574_Cons__in__subseqsD,axiom,
! [Y: list_Epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( member7465314387053329231c_fm_a @ ( cons_l8134865115577406678c_fm_a @ Y @ Ys2 ) @ ( set_li647609056391172027c_fm_a @ ( subseq3170398737635186805c_fm_a @ Xs ) ) )
=> ( member7465314387053329231c_fm_a @ Ys2 @ ( set_li647609056391172027c_fm_a @ ( subseq3170398737635186805c_fm_a @ Xs ) ) ) ) ).
% Cons_in_subseqsD
thf(fact_575_generalization,axiom,
! [P: epistemic_fm_a,W: epistemic_fm_a,M: episte94448284482925344t_unit,I: a] :
( ! [M3: episte94448284482925344t_unit,X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ ( episte6390737319716712051t_unit @ M3 ) )
=> ( episte5333283044364550848c_fm_a @ M3 @ X2 @ P ) )
=> ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
=> ( episte5333283044364550848c_fm_a @ M @ W @ ( epistemic_K_a @ I @ P ) ) ) ) ).
% generalization
thf(fact_576_generalization,axiom,
! [P: epistemic_fm_a,W: list_Epistemic_fm_a,M: episte1905851639235817760t_unit,I: a] :
( ! [M3: episte1905851639235817760t_unit,X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ ( episte3604461938431221107t_unit @ M3 ) )
=> ( episte3437425354345704390c_fm_a @ M3 @ X2 @ P ) )
=> ( ( member5906877432388582473c_fm_a @ W @ ( episte3604461938431221107t_unit @ M ) )
=> ( episte3437425354345704390c_fm_a @ M @ W @ ( epistemic_K_a @ I @ P ) ) ) ) ).
% generalization
thf(fact_577_generalization,axiom,
! [P: epistemic_fm_a,W: produc5756089960658898087c_fm_a,M: episte1613917330360936672t_unit,I: a] :
( ! [M3: episte1613917330360936672t_unit,X2: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X2 @ ( episte795400727954352563t_unit @ M3 ) )
=> ( episte3243793293402417485c_fm_a @ M3 @ X2 @ P ) )
=> ( ( member3265983909902097104c_fm_a @ W @ ( episte795400727954352563t_unit @ M ) )
=> ( episte3243793293402417485c_fm_a @ M @ W @ ( epistemic_K_a @ I @ P ) ) ) ) ).
% generalization
thf(fact_578_generalization,axiom,
! [P: epistemic_fm_a,W: produc2203834439629243303c_fm_a,M: episte9194023259896155360t_unit,I: a] :
( ! [M3: episte9194023259896155360t_unit,X2: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X2 @ ( episte5714722596736476595t_unit @ M3 ) )
=> ( episte7505603015783396941c_fm_a @ M3 @ X2 @ P ) )
=> ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
=> ( episte7505603015783396941c_fm_a @ M @ W @ ( epistemic_K_a @ I @ P ) ) ) ) ).
% generalization
thf(fact_579_generalization,axiom,
! [P: epistemic_fm_a,W: set_Epistemic_fm_a,M: episte1560738328020401952t_unit,I: a] :
( ! [M3: episte1560738328020401952t_unit,X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ P ) )
=> ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
=> ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_K_a @ I @ P ) ) ) ) ).
% generalization
thf(fact_580_soundness,axiom,
! [A: epistemic_fm_a > $o,P2: episte94448284482925344t_unit > $o,P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
( ! [M3: episte94448284482925344t_unit,W2: epistemic_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member6642669571620171971c_fm_a @ W2 @ ( episte6390737319716712051t_unit @ M3 ) )
=> ( episte5333283044364550848c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ( epistemic_AK_a @ A @ P )
=> ( ( P2 @ M )
=> ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
=> ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ) ).
% soundness
thf(fact_581_soundness,axiom,
! [A: epistemic_fm_a > $o,P2: episte1905851639235817760t_unit > $o,P: epistemic_fm_a,M: episte1905851639235817760t_unit,W: list_Epistemic_fm_a] :
( ! [M3: episte1905851639235817760t_unit,W2: list_Epistemic_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member5906877432388582473c_fm_a @ W2 @ ( episte3604461938431221107t_unit @ M3 ) )
=> ( episte3437425354345704390c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ( epistemic_AK_a @ A @ P )
=> ( ( P2 @ M )
=> ( ( member5906877432388582473c_fm_a @ W @ ( episte3604461938431221107t_unit @ M ) )
=> ( episte3437425354345704390c_fm_a @ M @ W @ P ) ) ) ) ) ).
% soundness
thf(fact_582_soundness,axiom,
! [A: epistemic_fm_a > $o,P2: episte1613917330360936672t_unit > $o,P: epistemic_fm_a,M: episte1613917330360936672t_unit,W: produc5756089960658898087c_fm_a] :
( ! [M3: episte1613917330360936672t_unit,W2: produc5756089960658898087c_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member3265983909902097104c_fm_a @ W2 @ ( episte795400727954352563t_unit @ M3 ) )
=> ( episte3243793293402417485c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ( epistemic_AK_a @ A @ P )
=> ( ( P2 @ M )
=> ( ( member3265983909902097104c_fm_a @ W @ ( episte795400727954352563t_unit @ M ) )
=> ( episte3243793293402417485c_fm_a @ M @ W @ P ) ) ) ) ) ).
% soundness
thf(fact_583_soundness,axiom,
! [A: epistemic_fm_a > $o,P2: episte9194023259896155360t_unit > $o,P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
( ! [M3: episte9194023259896155360t_unit,W2: produc2203834439629243303c_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member5029746173879296720c_fm_a @ W2 @ ( episte5714722596736476595t_unit @ M3 ) )
=> ( episte7505603015783396941c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ( epistemic_AK_a @ A @ P )
=> ( ( P2 @ M )
=> ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
=> ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ) ).
% soundness
thf(fact_584_soundness,axiom,
! [A: epistemic_fm_a > $o,P2: episte1560738328020401952t_unit > $o,P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
( ! [M3: episte1560738328020401952t_unit,W2: set_Epistemic_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member536094252920883875c_fm_a @ W2 @ ( episte8072386903178013299t_unit @ M3 ) )
=> ( episte7081087998767065248c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ( epistemic_AK_a @ A @ P )
=> ( ( P2 @ M )
=> ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
=> ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ) ).
% soundness
thf(fact_585_maps__simps_I2_J,axiom,
! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( maps_E7773696912818698439c_fm_a @ F @ nil_Epistemic_fm_a )
= nil_li2451196919128234278c_fm_a ) ).
% maps_simps(2)
thf(fact_586_maps__simps_I2_J,axiom,
! [F: epistemic_fm_a > list_s580375451141968640c_fm_a] :
( ( maps_E2162433029970929185c_fm_a @ F @ nil_Epistemic_fm_a )
= nil_se102576565402781184c_fm_a ) ).
% maps_simps(2)
thf(fact_587_maps__simps_I2_J,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( maps_l2078986973461115323c_fm_a @ F @ nil_li2451196919128234278c_fm_a )
= nil_Epistemic_fm_a ) ).
% maps_simps(2)
thf(fact_588_maps__simps_I2_J,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( maps_l3685687229838205249c_fm_a @ F @ nil_li2451196919128234278c_fm_a )
= nil_li2451196919128234278c_fm_a ) ).
% maps_simps(2)
thf(fact_589_maps__simps_I2_J,axiom,
! [F: list_Epistemic_fm_a > list_s580375451141968640c_fm_a] :
( ( maps_l5051011768039730075c_fm_a @ F @ nil_li2451196919128234278c_fm_a )
= nil_se102576565402781184c_fm_a ) ).
% maps_simps(2)
thf(fact_590_maps__simps_I2_J,axiom,
! [F: set_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( maps_s4275181340481488481c_fm_a @ F @ nil_se102576565402781184c_fm_a )
= nil_Epistemic_fm_a ) ).
% maps_simps(2)
thf(fact_591_maps__simps_I2_J,axiom,
! [F: set_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( maps_s5364767432190995175c_fm_a @ F @ nil_se102576565402781184c_fm_a )
= nil_li2451196919128234278c_fm_a ) ).
% maps_simps(2)
thf(fact_592_maps__simps_I2_J,axiom,
! [F: set_Epistemic_fm_a > list_s580375451141968640c_fm_a] :
( ( maps_s148483366175664193c_fm_a @ F @ nil_se102576565402781184c_fm_a )
= nil_se102576565402781184c_fm_a ) ).
% maps_simps(2)
thf(fact_593_maps__simps_I2_J,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a] :
( ( maps_E6072454603808916545c_fm_a @ F @ nil_Epistemic_fm_a )
= nil_Epistemic_fm_a ) ).
% maps_simps(2)
thf(fact_594_subset__CollectI,axiom,
! [B4: set_Pr3219225162411408519c_fm_a,A: set_Pr3219225162411408519c_fm_a,Q3: produc5756089960658898087c_fm_a > $o,P2: produc5756089960658898087c_fm_a > $o] :
( ( ord_le8873477448617899047c_fm_a @ B4 @ A )
=> ( ! [X2: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X2 @ B4 )
=> ( ( Q3 @ X2 )
=> ( P2 @ X2 ) ) )
=> ( ord_le8873477448617899047c_fm_a
@ ( collec6124610372686893330c_fm_a
@ ^ [X: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X @ B4 )
& ( Q3 @ X ) ) )
@ ( collec6124610372686893330c_fm_a
@ ^ [X: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X @ A )
& ( P2 @ X ) ) ) ) ) ) ).
% subset_CollectI
thf(fact_595_subset__CollectI,axiom,
! [B4: set_Pr8948481099588399239c_fm_a,A: set_Pr8948481099588399239c_fm_a,Q3: produc2203834439629243303c_fm_a > $o,P2: produc2203834439629243303c_fm_a > $o] :
( ( ord_le8222437384497874983c_fm_a @ B4 @ A )
=> ( ! [X2: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X2 @ B4 )
=> ( ( Q3 @ X2 )
=> ( P2 @ X2 ) ) )
=> ( ord_le8222437384497874983c_fm_a
@ ( collec7391038856303340306c_fm_a
@ ^ [X: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X @ B4 )
& ( Q3 @ X ) ) )
@ ( collec7391038856303340306c_fm_a
@ ^ [X: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X @ A )
& ( P2 @ X ) ) ) ) ) ) ).
% subset_CollectI
thf(fact_596_subset__CollectI,axiom,
! [B4: set_se5208064806568342746c_fm_a,A: set_se5208064806568342746c_fm_a,Q3: set_Epistemic_fm_a > $o,P2: set_Epistemic_fm_a > $o] :
( ( ord_le7112219575281605754c_fm_a @ B4 @ A )
=> ( ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ B4 )
=> ( ( Q3 @ X2 )
=> ( P2 @ X2 ) ) )
=> ( ord_le7112219575281605754c_fm_a
@ ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ B4 )
& ( Q3 @ X ) ) )
@ ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ A )
& ( P2 @ X ) ) ) ) ) ) ).
% subset_CollectI
thf(fact_597_subset__CollectI,axiom,
! [B4: set_Epistemic_fm_a,A: set_Epistemic_fm_a,Q3: epistemic_fm_a > $o,P2: epistemic_fm_a > $o] :
( ( ord_le3275665582123262618c_fm_a @ B4 @ A )
=> ( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ B4 )
=> ( ( Q3 @ X2 )
=> ( P2 @ X2 ) ) )
=> ( ord_le3275665582123262618c_fm_a
@ ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ B4 )
& ( Q3 @ X ) ) )
@ ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ A )
& ( P2 @ X ) ) ) ) ) ) ).
% subset_CollectI
thf(fact_598_subset__CollectI,axiom,
! [B4: set_li769143395467472256c_fm_a,A: set_li769143395467472256c_fm_a,Q3: list_Epistemic_fm_a > $o,P2: list_Epistemic_fm_a > $o] :
( ( ord_le2931979837777675552c_fm_a @ B4 @ A )
=> ( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ B4 )
=> ( ( Q3 @ X2 )
=> ( P2 @ X2 ) ) )
=> ( ord_le2931979837777675552c_fm_a
@ ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ B4 )
& ( Q3 @ X ) ) )
@ ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ A )
& ( P2 @ X ) ) ) ) ) ) ).
% subset_CollectI
thf(fact_599_subset__Collect__iff,axiom,
! [B4: set_Pr3219225162411408519c_fm_a,A: set_Pr3219225162411408519c_fm_a,P2: produc5756089960658898087c_fm_a > $o] :
( ( ord_le8873477448617899047c_fm_a @ B4 @ A )
=> ( ( ord_le8873477448617899047c_fm_a @ B4
@ ( collec6124610372686893330c_fm_a
@ ^ [X: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X @ A )
& ( P2 @ X ) ) ) )
= ( ! [X: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X @ B4 )
=> ( P2 @ X ) ) ) ) ) ).
% subset_Collect_iff
thf(fact_600_subset__Collect__iff,axiom,
! [B4: set_Pr8948481099588399239c_fm_a,A: set_Pr8948481099588399239c_fm_a,P2: produc2203834439629243303c_fm_a > $o] :
( ( ord_le8222437384497874983c_fm_a @ B4 @ A )
=> ( ( ord_le8222437384497874983c_fm_a @ B4
@ ( collec7391038856303340306c_fm_a
@ ^ [X: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X @ A )
& ( P2 @ X ) ) ) )
= ( ! [X: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X @ B4 )
=> ( P2 @ X ) ) ) ) ) ).
% subset_Collect_iff
thf(fact_601_subset__Collect__iff,axiom,
! [B4: set_se5208064806568342746c_fm_a,A: set_se5208064806568342746c_fm_a,P2: set_Epistemic_fm_a > $o] :
( ( ord_le7112219575281605754c_fm_a @ B4 @ A )
=> ( ( ord_le7112219575281605754c_fm_a @ B4
@ ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ A )
& ( P2 @ X ) ) ) )
= ( ! [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ B4 )
=> ( P2 @ X ) ) ) ) ) ).
% subset_Collect_iff
thf(fact_602_subset__Collect__iff,axiom,
! [B4: set_Epistemic_fm_a,A: set_Epistemic_fm_a,P2: epistemic_fm_a > $o] :
( ( ord_le3275665582123262618c_fm_a @ B4 @ A )
=> ( ( ord_le3275665582123262618c_fm_a @ B4
@ ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ A )
& ( P2 @ X ) ) ) )
= ( ! [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ B4 )
=> ( P2 @ X ) ) ) ) ) ).
% subset_Collect_iff
thf(fact_603_subset__Collect__iff,axiom,
! [B4: set_li769143395467472256c_fm_a,A: set_li769143395467472256c_fm_a,P2: list_Epistemic_fm_a > $o] :
( ( ord_le2931979837777675552c_fm_a @ B4 @ A )
=> ( ( ord_le2931979837777675552c_fm_a @ B4
@ ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ A )
& ( P2 @ X ) ) ) )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ B4 )
=> ( P2 @ X ) ) ) ) ) ).
% subset_Collect_iff
thf(fact_604_strong__completeness_092_060_094sub_062K,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte1560738328020401952t_unit,X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
=> ( ! [Xa3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa3 @ G )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Xa3 ) )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ P ) ) )
=> ? [Qs4: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs4 ) @ G )
& ( epistemic_AK_a
@ ^ [Uu2: epistemic_fm_a] : $false
@ ( epistemic_imply_a @ Qs4 @ P ) ) ) ) ).
% strong_completeness\<^sub>K
thf(fact_605_main_092_060_094sub_062K,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ( ! [M4: episte1560738328020401952t_unit,X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
=> ( ! [Y3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Y3 @ G )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ Y3 ) )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) )
= ( ? [Qs: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G )
& ( epistemic_AK_a
@ ^ [Uu2: epistemic_fm_a] : $false
@ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).
% main\<^sub>K
thf(fact_606_soundness__imply,axiom,
! [A: epistemic_fm_a > $o,P2: episte94448284482925344t_unit > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte94448284482925344t_unit,W2: epistemic_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member6642669571620171971c_fm_a @ W2 @ ( episte6390737319716712051t_unit @ M3 ) )
=> ( episte5333283044364550848c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
=> ! [M2: episte94448284482925344t_unit] :
( ( P2 @ M2 )
=> ! [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ ( episte6390737319716712051t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ ( set_Epistemic_fm_a2 @ Ps ) )
=> ( episte5333283044364550848c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte5333283044364550848c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ) ).
% soundness_imply
thf(fact_607_soundness__imply,axiom,
! [A: epistemic_fm_a > $o,P2: episte1905851639235817760t_unit > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte1905851639235817760t_unit,W2: list_Epistemic_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member5906877432388582473c_fm_a @ W2 @ ( episte3604461938431221107t_unit @ M3 ) )
=> ( episte3437425354345704390c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
=> ! [M2: episte1905851639235817760t_unit] :
( ( P2 @ M2 )
=> ! [X4: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X4 @ ( episte3604461938431221107t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ ( set_Epistemic_fm_a2 @ Ps ) )
=> ( episte3437425354345704390c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte3437425354345704390c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ) ).
% soundness_imply
thf(fact_608_soundness__imply,axiom,
! [A: epistemic_fm_a > $o,P2: episte1613917330360936672t_unit > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte1613917330360936672t_unit,W2: produc5756089960658898087c_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member3265983909902097104c_fm_a @ W2 @ ( episte795400727954352563t_unit @ M3 ) )
=> ( episte3243793293402417485c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
=> ! [M2: episte1613917330360936672t_unit] :
( ( P2 @ M2 )
=> ! [X4: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X4 @ ( episte795400727954352563t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ ( set_Epistemic_fm_a2 @ Ps ) )
=> ( episte3243793293402417485c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte3243793293402417485c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ) ).
% soundness_imply
thf(fact_609_soundness__imply,axiom,
! [A: epistemic_fm_a > $o,P2: episte9194023259896155360t_unit > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte9194023259896155360t_unit,W2: produc2203834439629243303c_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member5029746173879296720c_fm_a @ W2 @ ( episte5714722596736476595t_unit @ M3 ) )
=> ( episte7505603015783396941c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
=> ! [M2: episte9194023259896155360t_unit] :
( ( P2 @ M2 )
=> ! [X4: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X4 @ ( episte5714722596736476595t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ ( set_Epistemic_fm_a2 @ Ps ) )
=> ( episte7505603015783396941c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte7505603015783396941c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ) ).
% soundness_imply
thf(fact_610_soundness__imply,axiom,
! [A: epistemic_fm_a > $o,P2: episte1560738328020401952t_unit > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte1560738328020401952t_unit,W2: set_Epistemic_fm_a,P3: epistemic_fm_a] :
( ( A @ P3 )
=> ( ( P2 @ M3 )
=> ( ( member536094252920883875c_fm_a @ W2 @ ( episte8072386903178013299t_unit @ M3 ) )
=> ( episte7081087998767065248c_fm_a @ M3 @ W2 @ P3 ) ) ) )
=> ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
=> ! [M2: episte1560738328020401952t_unit] :
( ( P2 @ M2 )
=> ! [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ ( episte8072386903178013299t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ ( set_Epistemic_fm_a2 @ Ps ) )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ) ).
% soundness_imply
thf(fact_611_concat__map__maps,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( concat2780896542826320603c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ Xs ) )
= ( maps_E6072454603808916545c_fm_a @ F @ Xs ) ) ).
% concat_map_maps
thf(fact_612_concat__map__maps,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( concat2780896542826320603c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ Xs ) )
= ( maps_l2078986973461115323c_fm_a @ F @ Xs ) ) ).
% concat_map_maps
thf(fact_613_concat__map__maps,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( concat6109960377493484129c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ Xs ) )
= ( maps_l3685687229838205249c_fm_a @ F @ Xs ) ) ).
% concat_map_maps
thf(fact_614_strong__soundness_092_060_094sub_062K_092_060_094sub_0625,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ? [Qs3: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G )
& ( epistemic_AK_a @ epistemic_Ax5_a @ ( epistemic_imply_a @ Qs3 @ P ) ) )
=> ! [M2: episte1560738328020401952t_unit] :
( ( episte2449151000174023629t_unit @ M2 )
=> ! [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ ( episte8072386903178013299t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ G )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ).
% strong_soundness\<^sub>K\<^sub>5
thf(fact_615_transpose_Oelims,axiom,
! [X3: list_l985973790606564998c_fm_a,Y: list_l985973790606564998c_fm_a] :
( ( ( transp493887097527820938c_fm_a @ X3 )
= Y )
=> ( ( ( X3 = nil_li5433889876484989702c_fm_a )
=> ( Y != nil_li5433889876484989702c_fm_a ) )
=> ( ! [Xss: list_l985973790606564998c_fm_a] :
( ( X3
= ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ Xss ) )
=> ( Y
!= ( transp493887097527820938c_fm_a @ Xss ) ) )
=> ~ ! [X2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a,Xss: list_l985973790606564998c_fm_a] :
( ( X3
= ( cons_l1626872963913326262c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs3 ) @ Xss ) )
=> ( Y
!= ( cons_l1626872963913326262c_fm_a
@ ( cons_s4394448069393209776c_fm_a @ X2
@ ( concat2941956077894552763c_fm_a
@ ( map_li1341364954853471300c_fm_a
@ ( case_l6572946392233364704c_fm_a @ nil_se102576565402781184c_fm_a
@ ^ [H2: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_s4394448069393209776c_fm_a @ H2 @ nil_se102576565402781184c_fm_a ) )
@ Xss ) ) )
@ ( transp493887097527820938c_fm_a
@ ( cons_l1626872963913326262c_fm_a @ Xs3
@ ( concat4130251116320034881c_fm_a
@ ( map_li7441020096712412618c_fm_a
@ ( case_l4953383812495590490c_fm_a @ nil_li5433889876484989702c_fm_a
@ ^ [H2: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_l1626872963913326262c_fm_a @ T2 @ nil_li5433889876484989702c_fm_a ) )
@ Xss ) ) ) ) ) ) ) ) ) ) ).
% transpose.elims
thf(fact_616_transpose_Oelims,axiom,
! [X3: list_l3671048651222332332c_fm_a,Y: list_l3671048651222332332c_fm_a] :
( ( ( transp7189280393105805488c_fm_a @ X3 )
= Y )
=> ( ( ( X3 = nil_li5178944226519631276c_fm_a )
=> ( Y != nil_li5178944226519631276c_fm_a ) )
=> ( ! [Xss: list_l3671048651222332332c_fm_a] :
( ( X3
= ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ Xss ) )
=> ( Y
!= ( transp7189280393105805488c_fm_a @ Xss ) ) )
=> ~ ! [X2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a,Xss: list_l3671048651222332332c_fm_a] :
( ( X3
= ( cons_l2479501935080859996c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs3 ) @ Xss ) )
=> ( Y
!= ( cons_l2479501935080859996c_fm_a
@ ( cons_l8134865115577406678c_fm_a @ X2
@ ( concat6109960377493484129c_fm_a
@ ( map_li8347733892191492164c_fm_a
@ ( case_l116314299590685792c_fm_a @ nil_li2451196919128234278c_fm_a
@ ^ [H2: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l8134865115577406678c_fm_a @ H2 @ nil_li2451196919128234278c_fm_a ) )
@ Xss ) ) )
@ ( transp7189280393105805488c_fm_a
@ ( cons_l2479501935080859996c_fm_a @ Xs3
@ ( concat5652308878773863783c_fm_a
@ ( map_li3568483382057536586c_fm_a
@ ( case_l7601246044141707098c_fm_a @ nil_li5178944226519631276c_fm_a
@ ^ [H2: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l2479501935080859996c_fm_a @ T2 @ nil_li5178944226519631276c_fm_a ) )
@ Xss ) ) ) ) ) ) ) ) ) ) ).
% transpose.elims
thf(fact_617_transpose_Oelims,axiom,
! [X3: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a] :
( ( ( transp2882070860200649898c_fm_a @ X3 )
= Y )
=> ( ( ( X3 = nil_li2451196919128234278c_fm_a )
=> ( Y != nil_li2451196919128234278c_fm_a ) )
=> ( ! [Xss: list_l6083326122719238310c_fm_a] :
( ( X3
= ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ Xss ) )
=> ( Y
!= ( transp2882070860200649898c_fm_a @ Xss ) ) )
=> ~ ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Xss: list_l6083326122719238310c_fm_a] :
( ( X3
= ( cons_l8134865115577406678c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ Xss ) )
=> ( Y
!= ( cons_l8134865115577406678c_fm_a
@ ( cons_Epistemic_fm_a @ X2
@ ( concat2780896542826320603c_fm_a
@ ( map_li3080774272885743684c_fm_a
@ ( case_l8442927312758267104c_fm_a @ nil_Epistemic_fm_a
@ ^ [H2: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_Epistemic_fm_a @ H2 @ nil_Epistemic_fm_a ) )
@ Xss ) ) )
@ ( transp2882070860200649898c_fm_a
@ ( cons_l8134865115577406678c_fm_a @ Xs3
@ ( concat6109960377493484129c_fm_a
@ ( map_li3858915945532548554c_fm_a
@ ( case_l5707353781634818138c_fm_a @ nil_li2451196919128234278c_fm_a
@ ^ [H2: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ T2 @ nil_li2451196919128234278c_fm_a ) )
@ Xss ) ) ) ) ) ) ) ) ) ) ).
% transpose.elims
thf(fact_618_transpose_Osimps_I3_J,axiom,
! [X3: set_Epistemic_fm_a,Xs: list_s580375451141968640c_fm_a,Xss2: list_l985973790606564998c_fm_a] :
( ( transp493887097527820938c_fm_a @ ( cons_l1626872963913326262c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs ) @ Xss2 ) )
= ( cons_l1626872963913326262c_fm_a
@ ( cons_s4394448069393209776c_fm_a @ X3
@ ( concat2941956077894552763c_fm_a
@ ( map_li1341364954853471300c_fm_a
@ ( case_l6572946392233364704c_fm_a @ nil_se102576565402781184c_fm_a
@ ^ [H2: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_s4394448069393209776c_fm_a @ H2 @ nil_se102576565402781184c_fm_a ) )
@ Xss2 ) ) )
@ ( transp493887097527820938c_fm_a
@ ( cons_l1626872963913326262c_fm_a @ Xs
@ ( concat4130251116320034881c_fm_a
@ ( map_li7441020096712412618c_fm_a
@ ( case_l4953383812495590490c_fm_a @ nil_li5433889876484989702c_fm_a
@ ^ [H2: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_l1626872963913326262c_fm_a @ T2 @ nil_li5433889876484989702c_fm_a ) )
@ Xss2 ) ) ) ) ) ) ).
% transpose.simps(3)
thf(fact_619_transpose_Osimps_I3_J,axiom,
! [X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,Xss2: list_l3671048651222332332c_fm_a] :
( ( transp7189280393105805488c_fm_a @ ( cons_l2479501935080859996c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs ) @ Xss2 ) )
= ( cons_l2479501935080859996c_fm_a
@ ( cons_l8134865115577406678c_fm_a @ X3
@ ( concat6109960377493484129c_fm_a
@ ( map_li8347733892191492164c_fm_a
@ ( case_l116314299590685792c_fm_a @ nil_li2451196919128234278c_fm_a
@ ^ [H2: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l8134865115577406678c_fm_a @ H2 @ nil_li2451196919128234278c_fm_a ) )
@ Xss2 ) ) )
@ ( transp7189280393105805488c_fm_a
@ ( cons_l2479501935080859996c_fm_a @ Xs
@ ( concat5652308878773863783c_fm_a
@ ( map_li3568483382057536586c_fm_a
@ ( case_l7601246044141707098c_fm_a @ nil_li5178944226519631276c_fm_a
@ ^ [H2: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l2479501935080859996c_fm_a @ T2 @ nil_li5178944226519631276c_fm_a ) )
@ Xss2 ) ) ) ) ) ) ).
% transpose.simps(3)
thf(fact_620_transpose_Osimps_I3_J,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a,Xss2: list_l6083326122719238310c_fm_a] :
( ( transp2882070860200649898c_fm_a @ ( cons_l8134865115577406678c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs ) @ Xss2 ) )
= ( cons_l8134865115577406678c_fm_a
@ ( cons_Epistemic_fm_a @ X3
@ ( concat2780896542826320603c_fm_a
@ ( map_li3080774272885743684c_fm_a
@ ( case_l8442927312758267104c_fm_a @ nil_Epistemic_fm_a
@ ^ [H2: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_Epistemic_fm_a @ H2 @ nil_Epistemic_fm_a ) )
@ Xss2 ) ) )
@ ( transp2882070860200649898c_fm_a
@ ( cons_l8134865115577406678c_fm_a @ Xs
@ ( concat6109960377493484129c_fm_a
@ ( map_li3858915945532548554c_fm_a
@ ( case_l5707353781634818138c_fm_a @ nil_li2451196919128234278c_fm_a
@ ^ [H2: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ T2 @ nil_li2451196919128234278c_fm_a ) )
@ Xss2 ) ) ) ) ) ) ).
% transpose.simps(3)
thf(fact_621_strong__soundness_092_060_094sub_062K_092_060_094sub_062B,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ? [Qs3: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G )
& ( epistemic_AK_a @ epistemic_AxB_a @ ( epistemic_imply_a @ Qs3 @ P ) ) )
=> ! [M2: episte1560738328020401952t_unit] :
( ( episte5478016696552465318t_unit @ M2 )
=> ! [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ ( episte8072386903178013299t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ G )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ).
% strong_soundness\<^sub>K\<^sub>B
thf(fact_622_strong__soundness_092_060_094sub_062T,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ? [Qs3: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G )
& ( epistemic_AK_a @ epistemic_AxT_a @ ( epistemic_imply_a @ Qs3 @ P ) ) )
=> ! [M2: episte1560738328020401952t_unit] :
( ( episte5648423998891577755t_unit @ M2 )
=> ! [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ ( episte8072386903178013299t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ G )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ).
% strong_soundness\<^sub>T
thf(fact_623_strong__soundness_092_060_094sub_062K_092_060_094sub_0624,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ? [Qs3: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G )
& ( epistemic_AK_a @ epistemic_Ax4_a @ ( epistemic_imply_a @ Qs3 @ P ) ) )
=> ! [M2: episte1560738328020401952t_unit] :
( ( episte8364071018013720454t_unit @ M2 )
=> ! [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ ( episte8072386903178013299t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ G )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ).
% strong_soundness\<^sub>K\<^sub>4
thf(fact_624_main_092_060_094sub_062K_092_060_094sub_0625,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ( ! [M4: episte1560738328020401952t_unit] :
( ( episte2449151000174023629t_unit @ M4 )
=> ! [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
=> ( ! [Y3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Y3 @ G )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ Y3 ) )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) ) )
= ( ? [Qs: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G )
& ( epistemic_AK_a @ epistemic_Ax5_a @ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).
% main\<^sub>K\<^sub>5
thf(fact_625_refl__Euclid__equiv,axiom,
! [M: episte1560738328020401952t_unit] :
( ( episte5648423998891577755t_unit @ M )
=> ( ( episte2449151000174023629t_unit @ M )
=> ( ( episte5648423998891577755t_unit @ M )
& ( episte5478016696552465318t_unit @ M )
& ( episte8364071018013720454t_unit @ M ) ) ) ) ).
% refl_Euclid_equiv
thf(fact_626_symm__trans__Euclid,axiom,
! [M: episte1560738328020401952t_unit] :
( ( episte5478016696552465318t_unit @ M )
=> ( ( episte8364071018013720454t_unit @ M )
=> ( episte2449151000174023629t_unit @ M ) ) ) ).
% symm_trans_Euclid
thf(fact_627_transpose_Osimps_I1_J,axiom,
( ( transp2882070860200649898c_fm_a @ nil_li2451196919128234278c_fm_a )
= nil_li2451196919128234278c_fm_a ) ).
% transpose.simps(1)
thf(fact_628_list_Odisc__eq__case_I2_J,axiom,
! [List: list_l6083326122719238310c_fm_a] :
( ( List != nil_li2451196919128234278c_fm_a )
= ( case_l3589819172248781038c_fm_a @ $false
@ ^ [Uu2: list_Epistemic_fm_a,Uv2: list_l6083326122719238310c_fm_a] : $true
@ List ) ) ).
% list.disc_eq_case(2)
thf(fact_629_list_Odisc__eq__case_I2_J,axiom,
! [List: list_s580375451141968640c_fm_a] :
( ( List != nil_se102576565402781184c_fm_a )
= ( case_l4166027460215902664c_fm_a @ $false
@ ^ [Uu2: set_Epistemic_fm_a,Uv2: list_s580375451141968640c_fm_a] : $true
@ List ) ) ).
% list.disc_eq_case(2)
thf(fact_630_list_Odisc__eq__case_I2_J,axiom,
! [List: list_Epistemic_fm_a] :
( ( List != nil_Epistemic_fm_a )
= ( case_l2021589626981272552c_fm_a @ $false
@ ^ [Uu2: epistemic_fm_a,Uv2: list_Epistemic_fm_a] : $true
@ List ) ) ).
% list.disc_eq_case(2)
thf(fact_631_list_Odisc__eq__case_I1_J,axiom,
! [List: list_l6083326122719238310c_fm_a] :
( ( List = nil_li2451196919128234278c_fm_a )
= ( case_l3589819172248781038c_fm_a @ $true
@ ^ [Uu2: list_Epistemic_fm_a,Uv2: list_l6083326122719238310c_fm_a] : $false
@ List ) ) ).
% list.disc_eq_case(1)
thf(fact_632_list_Odisc__eq__case_I1_J,axiom,
! [List: list_s580375451141968640c_fm_a] :
( ( List = nil_se102576565402781184c_fm_a )
= ( case_l4166027460215902664c_fm_a @ $true
@ ^ [Uu2: set_Epistemic_fm_a,Uv2: list_s580375451141968640c_fm_a] : $false
@ List ) ) ).
% list.disc_eq_case(1)
thf(fact_633_list_Odisc__eq__case_I1_J,axiom,
! [List: list_Epistemic_fm_a] :
( ( List = nil_Epistemic_fm_a )
= ( case_l2021589626981272552c_fm_a @ $true
@ ^ [Uu2: epistemic_fm_a,Uv2: list_Epistemic_fm_a] : $false
@ List ) ) ).
% list.disc_eq_case(1)
thf(fact_634_soundness__AxT5,axiom,
! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_Ax5_a @ P ) )
=> ( ( ( episte5633553332388074907t_unit @ M )
& ( episte2438601301504999334t_unit @ M )
& ( episte2264091934940175238t_unit @ M ) )
=> ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
=> ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT5
thf(fact_635_soundness__AxT5,axiom,
! [P: epistemic_fm_a,M: episte1905851639235817760t_unit,W: list_Epistemic_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_Ax5_a @ P ) )
=> ( ( ( episte8696558436685192347t_unit @ M )
& ( episte5977966464841548710t_unit @ M )
& ( episte5775042212120887174t_unit @ M ) )
=> ( ( member5906877432388582473c_fm_a @ W @ ( episte3604461938431221107t_unit @ M ) )
=> ( episte3437425354345704390c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT5
thf(fact_636_soundness__AxT5,axiom,
! [P: epistemic_fm_a,M: episte1613917330360936672t_unit,W: produc5756089960658898087c_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_Ax5_a @ P ) )
=> ( ( ( episte4530333484083845339t_unit @ M )
& ( episte4316142217893016038t_unit @ M )
& ( episte3840578366024428998t_unit @ M ) )
=> ( ( member3265983909902097104c_fm_a @ W @ ( episte795400727954352563t_unit @ M ) )
=> ( episte3243793293402417485c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT5
thf(fact_637_soundness__AxT5,axiom,
! [P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_Ax5_a @ P ) )
=> ( ( ( episte3030712104470226139t_unit @ M )
& ( episte2922248646238569446t_unit @ M )
& ( episte9001638012126461894t_unit @ M ) )
=> ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
=> ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT5
thf(fact_638_soundness__AxT5,axiom,
! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_Ax5_a @ P ) )
=> ( ( ( episte5648423998891577755t_unit @ M )
& ( episte5478016696552465318t_unit @ M )
& ( episte8364071018013720454t_unit @ M ) )
=> ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
=> ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT5
thf(fact_639_transpose_Osimps_I2_J,axiom,
! [Xss2: list_l3671048651222332332c_fm_a] :
( ( transp7189280393105805488c_fm_a @ ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ Xss2 ) )
= ( transp7189280393105805488c_fm_a @ Xss2 ) ) ).
% transpose.simps(2)
thf(fact_640_transpose_Osimps_I2_J,axiom,
! [Xss2: list_l985973790606564998c_fm_a] :
( ( transp493887097527820938c_fm_a @ ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ Xss2 ) )
= ( transp493887097527820938c_fm_a @ Xss2 ) ) ).
% transpose.simps(2)
thf(fact_641_transpose_Osimps_I2_J,axiom,
! [Xss2: list_l6083326122719238310c_fm_a] :
( ( transp2882070860200649898c_fm_a @ ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ Xss2 ) )
= ( transp2882070860200649898c_fm_a @ Xss2 ) ) ).
% transpose.simps(2)
thf(fact_642_transpose__empty,axiom,
! [Xs: list_l3671048651222332332c_fm_a] :
( ( ( transp7189280393105805488c_fm_a @ Xs )
= nil_li5178944226519631276c_fm_a )
= ( ! [X: list_l6083326122719238310c_fm_a] :
( ( member7465314387053329231c_fm_a @ X @ ( set_li647609056391172027c_fm_a @ Xs ) )
=> ( X = nil_li2451196919128234278c_fm_a ) ) ) ) ).
% transpose_empty
thf(fact_643_transpose__empty,axiom,
! [Xs: list_l985973790606564998c_fm_a] :
( ( ( transp493887097527820938c_fm_a @ Xs )
= nil_li5433889876484989702c_fm_a )
= ( ! [X: list_s580375451141968640c_fm_a] :
( ( member2328277852289759785c_fm_a @ X @ ( set_li3422124509070804117c_fm_a @ Xs ) )
=> ( X = nil_se102576565402781184c_fm_a ) ) ) ) ).
% transpose_empty
thf(fact_644_transpose__empty,axiom,
! [Xs: list_l6083326122719238310c_fm_a] :
( ( ( transp2882070860200649898c_fm_a @ Xs )
= nil_li2451196919128234278c_fm_a )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ( X = nil_Epistemic_fm_a ) ) ) ) ).
% transpose_empty
thf(fact_645_transpose__map__map,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs: list_l3671048651222332332c_fm_a] :
( ( transp7189280393105805488c_fm_a @ ( map_li8347733892191492164c_fm_a @ ( map_li3080774272885743684c_fm_a @ F ) @ Xs ) )
= ( map_li8347733892191492164c_fm_a @ ( map_li3080774272885743684c_fm_a @ F ) @ ( transp7189280393105805488c_fm_a @ Xs ) ) ) ).
% transpose_map_map
thf(fact_646_transpose__map__map,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs: list_l3671048651222332332c_fm_a] :
( ( transp9220707655006416950c_fm_a @ ( map_li3568483382057536586c_fm_a @ ( map_li3858915945532548554c_fm_a @ F ) @ Xs ) )
= ( map_li3568483382057536586c_fm_a @ ( map_li3858915945532548554c_fm_a @ F ) @ ( transp7189280393105805488c_fm_a @ Xs ) ) ) ).
% transpose_map_map
thf(fact_647_transpose__map__map,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( transp7189280393105805488c_fm_a @ ( map_li3858915945532548554c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F ) @ Xs ) )
= ( map_li3858915945532548554c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F ) @ ( transp2882070860200649898c_fm_a @ Xs ) ) ) ).
% transpose_map_map
thf(fact_648_transpose__map__map,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs: list_l3671048651222332332c_fm_a] :
( ( transp2882070860200649898c_fm_a @ ( map_li8743910666895923134c_fm_a @ ( map_li5516866612190465598c_fm_a @ F ) @ Xs ) )
= ( map_li8743910666895923134c_fm_a @ ( map_li5516866612190465598c_fm_a @ F ) @ ( transp7189280393105805488c_fm_a @ Xs ) ) ) ).
% transpose_map_map
thf(fact_649_transpose__map__map,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( transp2882070860200649898c_fm_a @ ( map_li3080774272885743684c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ Xs ) )
= ( map_li3080774272885743684c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ ( transp2882070860200649898c_fm_a @ Xs ) ) ) ).
% transpose_map_map
thf(fact_650_soundness__AxTB4,axiom,
! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_AxB_a @ P )
| ( epistemic_Ax4_a @ P ) )
=> ( ( ( episte5633553332388074907t_unit @ M )
& ( episte2438601301504999334t_unit @ M )
& ( episte2264091934940175238t_unit @ M ) )
=> ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
=> ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxTB4
thf(fact_651_soundness__AxTB4,axiom,
! [P: epistemic_fm_a,M: episte1905851639235817760t_unit,W: list_Epistemic_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_AxB_a @ P )
| ( epistemic_Ax4_a @ P ) )
=> ( ( ( episte8696558436685192347t_unit @ M )
& ( episte5977966464841548710t_unit @ M )
& ( episte5775042212120887174t_unit @ M ) )
=> ( ( member5906877432388582473c_fm_a @ W @ ( episte3604461938431221107t_unit @ M ) )
=> ( episte3437425354345704390c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxTB4
thf(fact_652_soundness__AxTB4,axiom,
! [P: epistemic_fm_a,M: episte1613917330360936672t_unit,W: produc5756089960658898087c_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_AxB_a @ P )
| ( epistemic_Ax4_a @ P ) )
=> ( ( ( episte4530333484083845339t_unit @ M )
& ( episte4316142217893016038t_unit @ M )
& ( episte3840578366024428998t_unit @ M ) )
=> ( ( member3265983909902097104c_fm_a @ W @ ( episte795400727954352563t_unit @ M ) )
=> ( episte3243793293402417485c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxTB4
thf(fact_653_soundness__AxTB4,axiom,
! [P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_AxB_a @ P )
| ( epistemic_Ax4_a @ P ) )
=> ( ( ( episte3030712104470226139t_unit @ M )
& ( episte2922248646238569446t_unit @ M )
& ( episte9001638012126461894t_unit @ M ) )
=> ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
=> ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxTB4
thf(fact_654_soundness__AxTB4,axiom,
! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_AxB_a @ P )
| ( epistemic_Ax4_a @ P ) )
=> ( ( ( episte5648423998891577755t_unit @ M )
& ( episte5478016696552465318t_unit @ M )
& ( episte8364071018013720454t_unit @ M ) )
=> ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
=> ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxTB4
thf(fact_655_main_092_060_094sub_062S_092_060_094sub_0625_H,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ( ! [M4: episte1560738328020401952t_unit] :
( ( ( episte5648423998891577755t_unit @ M4 )
& ( episte5478016696552465318t_unit @ M4 )
& ( episte8364071018013720454t_unit @ M4 ) )
=> ! [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
=> ( ! [Y3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Y3 @ G )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ Y3 ) )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) ) )
= ( ? [Qs: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G )
& ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_Ax5_a @ P4 ) )
@ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).
% main\<^sub>S\<^sub>5'
thf(fact_656_strong__completeness_092_060_094sub_062S_092_060_094sub_0625_H,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte1560738328020401952t_unit] :
( ( ( episte5648423998891577755t_unit @ M3 )
& ( episte5478016696552465318t_unit @ M3 )
& ( episte8364071018013720454t_unit @ M3 ) )
=> ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
=> ( ! [Xa3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa3 @ G )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Xa3 ) )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ P ) ) ) )
=> ? [Qs4: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs4 ) @ G )
& ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_Ax5_a @ P4 ) )
@ ( epistemic_imply_a @ Qs4 @ P ) ) ) ) ).
% strong_completeness\<^sub>S\<^sub>5'
thf(fact_657_soundness__AxT4,axiom,
! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_Ax4_a @ P ) )
=> ( ( ( episte5633553332388074907t_unit @ M )
& ( episte2264091934940175238t_unit @ M ) )
=> ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
=> ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT4
thf(fact_658_soundness__AxT4,axiom,
! [P: epistemic_fm_a,M: episte1905851639235817760t_unit,W: list_Epistemic_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_Ax4_a @ P ) )
=> ( ( ( episte8696558436685192347t_unit @ M )
& ( episte5775042212120887174t_unit @ M ) )
=> ( ( member5906877432388582473c_fm_a @ W @ ( episte3604461938431221107t_unit @ M ) )
=> ( episte3437425354345704390c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT4
thf(fact_659_soundness__AxT4,axiom,
! [P: epistemic_fm_a,M: episte1613917330360936672t_unit,W: produc5756089960658898087c_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_Ax4_a @ P ) )
=> ( ( ( episte4530333484083845339t_unit @ M )
& ( episte3840578366024428998t_unit @ M ) )
=> ( ( member3265983909902097104c_fm_a @ W @ ( episte795400727954352563t_unit @ M ) )
=> ( episte3243793293402417485c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT4
thf(fact_660_soundness__AxT4,axiom,
! [P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_Ax4_a @ P ) )
=> ( ( ( episte3030712104470226139t_unit @ M )
& ( episte9001638012126461894t_unit @ M ) )
=> ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
=> ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT4
thf(fact_661_soundness__AxT4,axiom,
! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
( ( ( epistemic_AxT_a @ P )
| ( epistemic_Ax4_a @ P ) )
=> ( ( ( episte5648423998891577755t_unit @ M )
& ( episte8364071018013720454t_unit @ M ) )
=> ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
=> ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT4
thf(fact_662_main_092_060_094sub_062S_092_060_094sub_0625,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ( ! [M4: episte1560738328020401952t_unit] :
( ( ( episte5648423998891577755t_unit @ M4 )
& ( episte5478016696552465318t_unit @ M4 )
& ( episte8364071018013720454t_unit @ M4 ) )
=> ! [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
=> ( ! [Y3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Y3 @ G )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ Y3 ) )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) ) )
= ( ? [Qs: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G )
& ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_AxB_a @ P4 )
| ( epistemic_Ax4_a @ P4 ) )
@ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).
% main\<^sub>S\<^sub>5
thf(fact_663_strong__completeness_092_060_094sub_062S_092_060_094sub_0625,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte1560738328020401952t_unit] :
( ( ( episte5648423998891577755t_unit @ M3 )
& ( episte5478016696552465318t_unit @ M3 )
& ( episte8364071018013720454t_unit @ M3 ) )
=> ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
=> ( ! [Xa3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa3 @ G )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Xa3 ) )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ P ) ) ) )
=> ? [Qs4: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs4 ) @ G )
& ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_AxB_a @ P4 )
| ( epistemic_Ax4_a @ P4 ) )
@ ( epistemic_imply_a @ Qs4 @ P ) ) ) ) ).
% strong_completeness\<^sub>S\<^sub>5
thf(fact_664_neg__introspection,axiom,
! [M: episte94448284482925344t_unit,W: epistemic_fm_a,I: a,P: epistemic_fm_a] :
( ( episte2438601301504999334t_unit @ M )
=> ( ( episte2264091934940175238t_unit @ M )
=> ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
=> ( episte5333283044364550848c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ) ) ) ) ).
% neg_introspection
thf(fact_665_neg__introspection,axiom,
! [M: episte1905851639235817760t_unit,W: list_Epistemic_fm_a,I: a,P: epistemic_fm_a] :
( ( episte5977966464841548710t_unit @ M )
=> ( ( episte5775042212120887174t_unit @ M )
=> ( ( member5906877432388582473c_fm_a @ W @ ( episte3604461938431221107t_unit @ M ) )
=> ( episte3437425354345704390c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ) ) ) ) ).
% neg_introspection
thf(fact_666_neg__introspection,axiom,
! [M: episte1613917330360936672t_unit,W: produc5756089960658898087c_fm_a,I: a,P: epistemic_fm_a] :
( ( episte4316142217893016038t_unit @ M )
=> ( ( episte3840578366024428998t_unit @ M )
=> ( ( member3265983909902097104c_fm_a @ W @ ( episte795400727954352563t_unit @ M ) )
=> ( episte3243793293402417485c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ) ) ) ) ).
% neg_introspection
thf(fact_667_neg__introspection,axiom,
! [M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a,I: a,P: epistemic_fm_a] :
( ( episte2922248646238569446t_unit @ M )
=> ( ( episte9001638012126461894t_unit @ M )
=> ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
=> ( episte7505603015783396941c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ) ) ) ) ).
% neg_introspection
thf(fact_668_neg__introspection,axiom,
! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,I: a,P: epistemic_fm_a] :
( ( episte5478016696552465318t_unit @ M )
=> ( ( episte8364071018013720454t_unit @ M )
=> ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
=> ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ) ) ) ) ).
% neg_introspection
thf(fact_669_strong__completeness_092_060_094sub_062S_092_060_094sub_0624,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte1560738328020401952t_unit] :
( ( ( episte5648423998891577755t_unit @ M3 )
& ( episte8364071018013720454t_unit @ M3 ) )
=> ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
=> ( ! [Xa3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa3 @ G )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Xa3 ) )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ P ) ) ) )
=> ? [Qs4: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs4 ) @ G )
& ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_Ax4_a @ P4 ) )
@ ( epistemic_imply_a @ Qs4 @ P ) ) ) ) ).
% strong_completeness\<^sub>S\<^sub>4
thf(fact_670_main_092_060_094sub_062S_092_060_094sub_0624,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ( ! [M4: episte1560738328020401952t_unit] :
( ( ( episte5648423998891577755t_unit @ M4 )
& ( episte8364071018013720454t_unit @ M4 ) )
=> ! [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
=> ( ! [Y3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Y3 @ G )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ Y3 ) )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) ) )
= ( ? [Qs: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G )
& ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_Ax4_a @ P4 ) )
@ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).
% main\<^sub>S\<^sub>4
thf(fact_671_strong__soundness_092_060_094sub_062S_092_060_094sub_0625_H,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ? [Qs3: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G )
& ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_Ax5_a @ P4 ) )
@ ( epistemic_imply_a @ Qs3 @ P ) ) )
=> ! [M2: episte1560738328020401952t_unit] :
( ( ( episte5648423998891577755t_unit @ M2 )
& ( episte5478016696552465318t_unit @ M2 )
& ( episte8364071018013720454t_unit @ M2 ) )
=> ! [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ ( episte8072386903178013299t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ G )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ).
% strong_soundness\<^sub>S\<^sub>5'
thf(fact_672_soundness__Ax4,axiom,
! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
( ( epistemic_Ax4_a @ P )
=> ( ( episte2264091934940175238t_unit @ M )
=> ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
=> ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_Ax4
thf(fact_673_soundness__Ax4,axiom,
! [P: epistemic_fm_a,M: episte1905851639235817760t_unit,W: list_Epistemic_fm_a] :
( ( epistemic_Ax4_a @ P )
=> ( ( episte5775042212120887174t_unit @ M )
=> ( ( member5906877432388582473c_fm_a @ W @ ( episte3604461938431221107t_unit @ M ) )
=> ( episte3437425354345704390c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_Ax4
thf(fact_674_soundness__Ax4,axiom,
! [P: epistemic_fm_a,M: episte1613917330360936672t_unit,W: produc5756089960658898087c_fm_a] :
( ( epistemic_Ax4_a @ P )
=> ( ( episte3840578366024428998t_unit @ M )
=> ( ( member3265983909902097104c_fm_a @ W @ ( episte795400727954352563t_unit @ M ) )
=> ( episte3243793293402417485c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_Ax4
thf(fact_675_soundness__Ax4,axiom,
! [P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
( ( epistemic_Ax4_a @ P )
=> ( ( episte9001638012126461894t_unit @ M )
=> ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
=> ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_Ax4
thf(fact_676_soundness__Ax4,axiom,
! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
( ( epistemic_Ax4_a @ P )
=> ( ( episte8364071018013720454t_unit @ M )
=> ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
=> ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_Ax4
thf(fact_677_strong__soundness_092_060_094sub_062S_092_060_094sub_0625,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ? [Qs3: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G )
& ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_AxB_a @ P4 )
| ( epistemic_Ax4_a @ P4 ) )
@ ( epistemic_imply_a @ Qs3 @ P ) ) )
=> ! [M2: episte1560738328020401952t_unit] :
( ( ( episte5648423998891577755t_unit @ M2 )
& ( episte5478016696552465318t_unit @ M2 )
& ( episte8364071018013720454t_unit @ M2 ) )
=> ! [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ ( episte8072386903178013299t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ G )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ).
% strong_soundness\<^sub>S\<^sub>5
thf(fact_678_soundness__AxT,axiom,
! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
( ( epistemic_AxT_a @ P )
=> ( ( episte5633553332388074907t_unit @ M )
=> ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
=> ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT
thf(fact_679_soundness__AxT,axiom,
! [P: epistemic_fm_a,M: episte1905851639235817760t_unit,W: list_Epistemic_fm_a] :
( ( epistemic_AxT_a @ P )
=> ( ( episte8696558436685192347t_unit @ M )
=> ( ( member5906877432388582473c_fm_a @ W @ ( episte3604461938431221107t_unit @ M ) )
=> ( episte3437425354345704390c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT
thf(fact_680_soundness__AxT,axiom,
! [P: epistemic_fm_a,M: episte1613917330360936672t_unit,W: produc5756089960658898087c_fm_a] :
( ( epistemic_AxT_a @ P )
=> ( ( episte4530333484083845339t_unit @ M )
=> ( ( member3265983909902097104c_fm_a @ W @ ( episte795400727954352563t_unit @ M ) )
=> ( episte3243793293402417485c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT
thf(fact_681_soundness__AxT,axiom,
! [P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
( ( epistemic_AxT_a @ P )
=> ( ( episte3030712104470226139t_unit @ M )
=> ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
=> ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT
thf(fact_682_soundness__AxT,axiom,
! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
( ( epistemic_AxT_a @ P )
=> ( ( episte5648423998891577755t_unit @ M )
=> ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
=> ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxT
thf(fact_683_soundness__AxB,axiom,
! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
( ( epistemic_AxB_a @ P )
=> ( ( episte2438601301504999334t_unit @ M )
=> ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
=> ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxB
thf(fact_684_soundness__AxB,axiom,
! [P: epistemic_fm_a,M: episte1905851639235817760t_unit,W: list_Epistemic_fm_a] :
( ( epistemic_AxB_a @ P )
=> ( ( episte5977966464841548710t_unit @ M )
=> ( ( member5906877432388582473c_fm_a @ W @ ( episte3604461938431221107t_unit @ M ) )
=> ( episte3437425354345704390c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxB
thf(fact_685_soundness__AxB,axiom,
! [P: epistemic_fm_a,M: episte1613917330360936672t_unit,W: produc5756089960658898087c_fm_a] :
( ( epistemic_AxB_a @ P )
=> ( ( episte4316142217893016038t_unit @ M )
=> ( ( member3265983909902097104c_fm_a @ W @ ( episte795400727954352563t_unit @ M ) )
=> ( episte3243793293402417485c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxB
thf(fact_686_soundness__AxB,axiom,
! [P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
( ( epistemic_AxB_a @ P )
=> ( ( episte2922248646238569446t_unit @ M )
=> ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
=> ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxB
thf(fact_687_soundness__AxB,axiom,
! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
( ( epistemic_AxB_a @ P )
=> ( ( episte5478016696552465318t_unit @ M )
=> ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
=> ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_AxB
thf(fact_688_pos__introspection,axiom,
! [M: episte94448284482925344t_unit,W: epistemic_fm_a,I: a,P: epistemic_fm_a] :
( ( episte2264091934940175238t_unit @ M )
=> ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
=> ( episte5333283044364550848c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ) ) ).
% pos_introspection
thf(fact_689_pos__introspection,axiom,
! [M: episte1905851639235817760t_unit,W: list_Epistemic_fm_a,I: a,P: epistemic_fm_a] :
( ( episte5775042212120887174t_unit @ M )
=> ( ( member5906877432388582473c_fm_a @ W @ ( episte3604461938431221107t_unit @ M ) )
=> ( episte3437425354345704390c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ) ) ).
% pos_introspection
thf(fact_690_pos__introspection,axiom,
! [M: episte1613917330360936672t_unit,W: produc5756089960658898087c_fm_a,I: a,P: epistemic_fm_a] :
( ( episte3840578366024428998t_unit @ M )
=> ( ( member3265983909902097104c_fm_a @ W @ ( episte795400727954352563t_unit @ M ) )
=> ( episte3243793293402417485c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ) ) ).
% pos_introspection
thf(fact_691_pos__introspection,axiom,
! [M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a,I: a,P: epistemic_fm_a] :
( ( episte9001638012126461894t_unit @ M )
=> ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
=> ( episte7505603015783396941c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ) ) ).
% pos_introspection
thf(fact_692_pos__introspection,axiom,
! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,I: a,P: epistemic_fm_a] :
( ( episte8364071018013720454t_unit @ M )
=> ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
=> ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ) ) ).
% pos_introspection
thf(fact_693_truth,axiom,
! [M: episte94448284482925344t_unit,W: epistemic_fm_a,I: a,P: epistemic_fm_a] :
( ( episte5633553332388074907t_unit @ M )
=> ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
=> ( episte5333283044364550848c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ P ) ) ) ) ).
% truth
thf(fact_694_truth,axiom,
! [M: episte1905851639235817760t_unit,W: list_Epistemic_fm_a,I: a,P: epistemic_fm_a] :
( ( episte8696558436685192347t_unit @ M )
=> ( ( member5906877432388582473c_fm_a @ W @ ( episte3604461938431221107t_unit @ M ) )
=> ( episte3437425354345704390c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ P ) ) ) ) ).
% truth
thf(fact_695_truth,axiom,
! [M: episte1613917330360936672t_unit,W: produc5756089960658898087c_fm_a,I: a,P: epistemic_fm_a] :
( ( episte4530333484083845339t_unit @ M )
=> ( ( member3265983909902097104c_fm_a @ W @ ( episte795400727954352563t_unit @ M ) )
=> ( episte3243793293402417485c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ P ) ) ) ) ).
% truth
thf(fact_696_truth,axiom,
! [M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a,I: a,P: epistemic_fm_a] :
( ( episte3030712104470226139t_unit @ M )
=> ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
=> ( episte7505603015783396941c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ P ) ) ) ) ).
% truth
thf(fact_697_truth,axiom,
! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,I: a,P: epistemic_fm_a] :
( ( episte5648423998891577755t_unit @ M )
=> ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
=> ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ P ) ) ) ) ).
% truth
thf(fact_698_strong__soundness_092_060_094sub_062S_092_060_094sub_0624,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ? [Qs3: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G )
& ( epistemic_AK_a
@ ^ [P4: epistemic_fm_a] :
( ( epistemic_AxT_a @ P4 )
| ( epistemic_Ax4_a @ P4 ) )
@ ( epistemic_imply_a @ Qs3 @ P ) ) )
=> ! [M2: episte1560738328020401952t_unit] :
( ( ( episte5648423998891577755t_unit @ M2 )
& ( episte8364071018013720454t_unit @ M2 ) )
=> ! [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ ( episte8072386903178013299t_unit @ M2 ) )
=> ( ! [Xa2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa2 @ G )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ Xa2 ) )
=> ( episte7081087998767065248c_fm_a @ M2 @ X4 @ P ) ) ) ) ) ).
% strong_soundness\<^sub>S\<^sub>4
thf(fact_699_strong__completeness_092_060_094sub_062K_092_060_094sub_0624,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte1560738328020401952t_unit] :
( ( episte8364071018013720454t_unit @ M3 )
=> ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
=> ( ! [Xa3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa3 @ G )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Xa3 ) )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ P ) ) ) )
=> ? [Qs4: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs4 ) @ G )
& ( epistemic_AK_a @ epistemic_Ax4_a @ ( epistemic_imply_a @ Qs4 @ P ) ) ) ) ).
% strong_completeness\<^sub>K\<^sub>4
thf(fact_700_main_092_060_094sub_062K_092_060_094sub_0624,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ( ! [M4: episte1560738328020401952t_unit] :
( ( episte8364071018013720454t_unit @ M4 )
=> ! [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
=> ( ! [Y3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Y3 @ G )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ Y3 ) )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) ) )
= ( ? [Qs: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G )
& ( epistemic_AK_a @ epistemic_Ax4_a @ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).
% main\<^sub>K\<^sub>4
thf(fact_701_main_092_060_094sub_062T,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ( ! [M4: episte1560738328020401952t_unit] :
( ( episte5648423998891577755t_unit @ M4 )
=> ! [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
=> ( ! [Y3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Y3 @ G )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ Y3 ) )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) ) )
= ( ? [Qs: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G )
& ( epistemic_AK_a @ epistemic_AxT_a @ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).
% main\<^sub>T
thf(fact_702_strong__completeness_092_060_094sub_062T,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte1560738328020401952t_unit] :
( ( episte5648423998891577755t_unit @ M3 )
=> ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
=> ( ! [Xa3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa3 @ G )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Xa3 ) )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ P ) ) ) )
=> ? [Qs4: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs4 ) @ G )
& ( epistemic_AK_a @ epistemic_AxT_a @ ( epistemic_imply_a @ Qs4 @ P ) ) ) ) ).
% strong_completeness\<^sub>T
thf(fact_703_strong__completeness_092_060_094sub_062K_092_060_094sub_062B,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte1560738328020401952t_unit] :
( ( episte5478016696552465318t_unit @ M3 )
=> ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
=> ( ! [Xa3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa3 @ G )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Xa3 ) )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ P ) ) ) )
=> ? [Qs4: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs4 ) @ G )
& ( epistemic_AK_a @ epistemic_AxB_a @ ( epistemic_imply_a @ Qs4 @ P ) ) ) ) ).
% strong_completeness\<^sub>K\<^sub>B
thf(fact_704_main_092_060_094sub_062K_092_060_094sub_062B,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ( ! [M4: episte1560738328020401952t_unit] :
( ( episte5478016696552465318t_unit @ M4 )
=> ! [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
=> ( ! [Y3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Y3 @ G )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ Y3 ) )
=> ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) ) )
= ( ? [Qs: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G )
& ( epistemic_AK_a @ epistemic_AxB_a @ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).
% main\<^sub>K\<^sub>B
thf(fact_705_soundness__Ax5,axiom,
! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
( ( epistemic_Ax5_a @ P )
=> ( ( episte4583239219080210381t_unit @ M )
=> ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
=> ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_Ax5
thf(fact_706_soundness__Ax5,axiom,
! [P: epistemic_fm_a,M: episte1905851639235817760t_unit,W: list_Epistemic_fm_a] :
( ( epistemic_Ax5_a @ P )
=> ( ( episte1170649842907983053t_unit @ M )
=> ( ( member5906877432388582473c_fm_a @ W @ ( episte3604461938431221107t_unit @ M ) )
=> ( episte3437425354345704390c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_Ax5
thf(fact_707_soundness__Ax5,axiom,
! [P: epistemic_fm_a,M: episte1613917330360936672t_unit,W: produc5756089960658898087c_fm_a] :
( ( epistemic_Ax5_a @ P )
=> ( ( episte7679778137286046989t_unit @ M )
=> ( ( member3265983909902097104c_fm_a @ W @ ( episte795400727954352563t_unit @ M ) )
=> ( episte3243793293402417485c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_Ax5
thf(fact_708_soundness__Ax5,axiom,
! [P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
( ( epistemic_Ax5_a @ P )
=> ( ( episte2443128549434688781t_unit @ M )
=> ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
=> ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_Ax5
thf(fact_709_soundness__Ax5,axiom,
! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
( ( epistemic_Ax5_a @ P )
=> ( ( episte2449151000174023629t_unit @ M )
=> ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
=> ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ).
% soundness_Ax5
thf(fact_710_strong__completeness_092_060_094sub_062K_092_060_094sub_0625,axiom,
! [G: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ! [M3: episte1560738328020401952t_unit] :
( ( episte2449151000174023629t_unit @ M3 )
=> ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
=> ( ! [Xa3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa3 @ G )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Xa3 ) )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ P ) ) ) )
=> ? [Qs4: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs4 ) @ G )
& ( epistemic_AK_a @ epistemic_Ax5_a @ ( epistemic_imply_a @ Qs4 @ P ) ) ) ) ).
% strong_completeness\<^sub>K\<^sub>5
thf(fact_711_transpose_Opsimps_I3_J,axiom,
! [X3: set_Epistemic_fm_a,Xs: list_s580375451141968640c_fm_a,Xss2: list_l985973790606564998c_fm_a] :
( ( accp_l1289336314643896847c_fm_a @ transp578517656548729263c_fm_a @ ( cons_l1626872963913326262c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs ) @ Xss2 ) )
=> ( ( transp493887097527820938c_fm_a @ ( cons_l1626872963913326262c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs ) @ Xss2 ) )
= ( cons_l1626872963913326262c_fm_a
@ ( cons_s4394448069393209776c_fm_a @ X3
@ ( concat2941956077894552763c_fm_a
@ ( map_li1341364954853471300c_fm_a
@ ( case_l6572946392233364704c_fm_a @ nil_se102576565402781184c_fm_a
@ ^ [H2: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_s4394448069393209776c_fm_a @ H2 @ nil_se102576565402781184c_fm_a ) )
@ Xss2 ) ) )
@ ( transp493887097527820938c_fm_a
@ ( cons_l1626872963913326262c_fm_a @ Xs
@ ( concat4130251116320034881c_fm_a
@ ( map_li7441020096712412618c_fm_a
@ ( case_l4953383812495590490c_fm_a @ nil_li5433889876484989702c_fm_a
@ ^ [H2: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_l1626872963913326262c_fm_a @ T2 @ nil_li5433889876484989702c_fm_a ) )
@ Xss2 ) ) ) ) ) ) ) ).
% transpose.psimps(3)
thf(fact_712_transpose_Opsimps_I3_J,axiom,
! [X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,Xss2: list_l3671048651222332332c_fm_a] :
( ( accp_l8971127668057225909c_fm_a @ transp5805013372743109973c_fm_a @ ( cons_l2479501935080859996c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs ) @ Xss2 ) )
=> ( ( transp7189280393105805488c_fm_a @ ( cons_l2479501935080859996c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs ) @ Xss2 ) )
= ( cons_l2479501935080859996c_fm_a
@ ( cons_l8134865115577406678c_fm_a @ X3
@ ( concat6109960377493484129c_fm_a
@ ( map_li8347733892191492164c_fm_a
@ ( case_l116314299590685792c_fm_a @ nil_li2451196919128234278c_fm_a
@ ^ [H2: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l8134865115577406678c_fm_a @ H2 @ nil_li2451196919128234278c_fm_a ) )
@ Xss2 ) ) )
@ ( transp7189280393105805488c_fm_a
@ ( cons_l2479501935080859996c_fm_a @ Xs
@ ( concat5652308878773863783c_fm_a
@ ( map_li3568483382057536586c_fm_a
@ ( case_l7601246044141707098c_fm_a @ nil_li5178944226519631276c_fm_a
@ ^ [H2: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l2479501935080859996c_fm_a @ T2 @ nil_li5178944226519631276c_fm_a ) )
@ Xss2 ) ) ) ) ) ) ) ).
% transpose.psimps(3)
thf(fact_713_transpose_Opsimps_I3_J,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a,Xss2: list_l6083326122719238310c_fm_a] :
( ( accp_l7472382826029824047c_fm_a @ transp597054356388329423c_fm_a @ ( cons_l8134865115577406678c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs ) @ Xss2 ) )
=> ( ( transp2882070860200649898c_fm_a @ ( cons_l8134865115577406678c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs ) @ Xss2 ) )
= ( cons_l8134865115577406678c_fm_a
@ ( cons_Epistemic_fm_a @ X3
@ ( concat2780896542826320603c_fm_a
@ ( map_li3080774272885743684c_fm_a
@ ( case_l8442927312758267104c_fm_a @ nil_Epistemic_fm_a
@ ^ [H2: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_Epistemic_fm_a @ H2 @ nil_Epistemic_fm_a ) )
@ Xss2 ) ) )
@ ( transp2882070860200649898c_fm_a
@ ( cons_l8134865115577406678c_fm_a @ Xs
@ ( concat6109960377493484129c_fm_a
@ ( map_li3858915945532548554c_fm_a
@ ( case_l5707353781634818138c_fm_a @ nil_li2451196919128234278c_fm_a
@ ^ [H2: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ T2 @ nil_li2451196919128234278c_fm_a ) )
@ Xss2 ) ) ) ) ) ) ) ).
% transpose.psimps(3)
thf(fact_714_transpose_Opinduct,axiom,
! [A0: list_l985973790606564998c_fm_a,P2: list_l985973790606564998c_fm_a > $o] :
( ( accp_l1289336314643896847c_fm_a @ transp578517656548729263c_fm_a @ A0 )
=> ( ( ( accp_l1289336314643896847c_fm_a @ transp578517656548729263c_fm_a @ nil_li5433889876484989702c_fm_a )
=> ( P2 @ nil_li5433889876484989702c_fm_a ) )
=> ( ! [Xss: list_l985973790606564998c_fm_a] :
( ( accp_l1289336314643896847c_fm_a @ transp578517656548729263c_fm_a @ ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ Xss ) )
=> ( ( P2 @ Xss )
=> ( P2 @ ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ Xss ) ) ) )
=> ( ! [X2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a,Xss: list_l985973790606564998c_fm_a] :
( ( accp_l1289336314643896847c_fm_a @ transp578517656548729263c_fm_a @ ( cons_l1626872963913326262c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs3 ) @ Xss ) )
=> ( ( P2
@ ( cons_l1626872963913326262c_fm_a @ Xs3
@ ( concat4130251116320034881c_fm_a
@ ( map_li7441020096712412618c_fm_a
@ ( case_l4953383812495590490c_fm_a @ nil_li5433889876484989702c_fm_a
@ ^ [H2: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_l1626872963913326262c_fm_a @ T2 @ nil_li5433889876484989702c_fm_a ) )
@ Xss ) ) ) )
=> ( P2 @ ( cons_l1626872963913326262c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs3 ) @ Xss ) ) ) )
=> ( P2 @ A0 ) ) ) ) ) ).
% transpose.pinduct
thf(fact_715_transpose_Opinduct,axiom,
! [A0: list_l3671048651222332332c_fm_a,P2: list_l3671048651222332332c_fm_a > $o] :
( ( accp_l8971127668057225909c_fm_a @ transp5805013372743109973c_fm_a @ A0 )
=> ( ( ( accp_l8971127668057225909c_fm_a @ transp5805013372743109973c_fm_a @ nil_li5178944226519631276c_fm_a )
=> ( P2 @ nil_li5178944226519631276c_fm_a ) )
=> ( ! [Xss: list_l3671048651222332332c_fm_a] :
( ( accp_l8971127668057225909c_fm_a @ transp5805013372743109973c_fm_a @ ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ Xss ) )
=> ( ( P2 @ Xss )
=> ( P2 @ ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ Xss ) ) ) )
=> ( ! [X2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a,Xss: list_l3671048651222332332c_fm_a] :
( ( accp_l8971127668057225909c_fm_a @ transp5805013372743109973c_fm_a @ ( cons_l2479501935080859996c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs3 ) @ Xss ) )
=> ( ( P2
@ ( cons_l2479501935080859996c_fm_a @ Xs3
@ ( concat5652308878773863783c_fm_a
@ ( map_li3568483382057536586c_fm_a
@ ( case_l7601246044141707098c_fm_a @ nil_li5178944226519631276c_fm_a
@ ^ [H2: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l2479501935080859996c_fm_a @ T2 @ nil_li5178944226519631276c_fm_a ) )
@ Xss ) ) ) )
=> ( P2 @ ( cons_l2479501935080859996c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs3 ) @ Xss ) ) ) )
=> ( P2 @ A0 ) ) ) ) ) ).
% transpose.pinduct
thf(fact_716_transpose_Opinduct,axiom,
! [A0: list_l6083326122719238310c_fm_a,P2: list_l6083326122719238310c_fm_a > $o] :
( ( accp_l7472382826029824047c_fm_a @ transp597054356388329423c_fm_a @ A0 )
=> ( ( ( accp_l7472382826029824047c_fm_a @ transp597054356388329423c_fm_a @ nil_li2451196919128234278c_fm_a )
=> ( P2 @ nil_li2451196919128234278c_fm_a ) )
=> ( ! [Xss: list_l6083326122719238310c_fm_a] :
( ( accp_l7472382826029824047c_fm_a @ transp597054356388329423c_fm_a @ ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ Xss ) )
=> ( ( P2 @ Xss )
=> ( P2 @ ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ Xss ) ) ) )
=> ( ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Xss: list_l6083326122719238310c_fm_a] :
( ( accp_l7472382826029824047c_fm_a @ transp597054356388329423c_fm_a @ ( cons_l8134865115577406678c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ Xss ) )
=> ( ( P2
@ ( cons_l8134865115577406678c_fm_a @ Xs3
@ ( concat6109960377493484129c_fm_a
@ ( map_li3858915945532548554c_fm_a
@ ( case_l5707353781634818138c_fm_a @ nil_li2451196919128234278c_fm_a
@ ^ [H2: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ T2 @ nil_li2451196919128234278c_fm_a ) )
@ Xss ) ) ) )
=> ( P2 @ ( cons_l8134865115577406678c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ Xss ) ) ) )
=> ( P2 @ A0 ) ) ) ) ) ).
% transpose.pinduct
thf(fact_717_subset__code_I3_J,axiom,
~ ( ord_le7112219575281605754c_fm_a @ ( coset_774667214334347501c_fm_a @ nil_se102576565402781184c_fm_a ) @ ( set_se8855941934996405007c_fm_a @ nil_se102576565402781184c_fm_a ) ) ).
% subset_code(3)
thf(fact_718_subset__code_I3_J,axiom,
~ ( ord_le2931979837777675552c_fm_a @ ( coset_1387336592765253011c_fm_a @ nil_li2451196919128234278c_fm_a ) @ ( set_li8442223810127165109c_fm_a @ nil_li2451196919128234278c_fm_a ) ) ).
% subset_code(3)
thf(fact_719_subset__code_I3_J,axiom,
~ ( ord_le3275665582123262618c_fm_a @ ( coset_Epistemic_fm_a @ nil_Epistemic_fm_a ) @ ( set_Epistemic_fm_a2 @ nil_Epistemic_fm_a ) ) ).
% subset_code(3)
thf(fact_720_consistent__def,axiom,
( episte2285483198712856226tent_a
= ( ^ [A3: epistemic_fm_a > $o,S2: set_Epistemic_fm_a] :
~ ? [Qs: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ S2 )
& ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Qs @ epistemic_FF_a ) ) ) ) ) ).
% consistent_def
thf(fact_721_Collect__restrict,axiom,
! [X5: set_Pr3219225162411408519c_fm_a,P2: produc5756089960658898087c_fm_a > $o] :
( ord_le8873477448617899047c_fm_a
@ ( collec6124610372686893330c_fm_a
@ ^ [X: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X @ X5 )
& ( P2 @ X ) ) )
@ X5 ) ).
% Collect_restrict
thf(fact_722_Collect__restrict,axiom,
! [X5: set_Pr8948481099588399239c_fm_a,P2: produc2203834439629243303c_fm_a > $o] :
( ord_le8222437384497874983c_fm_a
@ ( collec7391038856303340306c_fm_a
@ ^ [X: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X @ X5 )
& ( P2 @ X ) ) )
@ X5 ) ).
% Collect_restrict
thf(fact_723_Collect__restrict,axiom,
! [X5: set_se5208064806568342746c_fm_a,P2: set_Epistemic_fm_a > $o] :
( ord_le7112219575281605754c_fm_a
@ ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ X5 )
& ( P2 @ X ) ) )
@ X5 ) ).
% Collect_restrict
thf(fact_724_Collect__restrict,axiom,
! [X5: set_Epistemic_fm_a,P2: epistemic_fm_a > $o] :
( ord_le3275665582123262618c_fm_a
@ ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ X5 )
& ( P2 @ X ) ) )
@ X5 ) ).
% Collect_restrict
thf(fact_725_Collect__restrict,axiom,
! [X5: set_li769143395467472256c_fm_a,P2: list_Epistemic_fm_a > $o] :
( ord_le2931979837777675552c_fm_a
@ ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ X5 )
& ( P2 @ X ) ) )
@ X5 ) ).
% Collect_restrict
thf(fact_726_prop__restrict,axiom,
! [X3: produc5756089960658898087c_fm_a,Z5: set_Pr3219225162411408519c_fm_a,X5: set_Pr3219225162411408519c_fm_a,P2: produc5756089960658898087c_fm_a > $o] :
( ( member3265983909902097104c_fm_a @ X3 @ Z5 )
=> ( ( ord_le8873477448617899047c_fm_a @ Z5
@ ( collec6124610372686893330c_fm_a
@ ^ [X: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X @ X5 )
& ( P2 @ X ) ) ) )
=> ( P2 @ X3 ) ) ) ).
% prop_restrict
thf(fact_727_prop__restrict,axiom,
! [X3: produc2203834439629243303c_fm_a,Z5: set_Pr8948481099588399239c_fm_a,X5: set_Pr8948481099588399239c_fm_a,P2: produc2203834439629243303c_fm_a > $o] :
( ( member5029746173879296720c_fm_a @ X3 @ Z5 )
=> ( ( ord_le8222437384497874983c_fm_a @ Z5
@ ( collec7391038856303340306c_fm_a
@ ^ [X: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X @ X5 )
& ( P2 @ X ) ) ) )
=> ( P2 @ X3 ) ) ) ).
% prop_restrict
thf(fact_728_prop__restrict,axiom,
! [X3: set_Epistemic_fm_a,Z5: set_se5208064806568342746c_fm_a,X5: set_se5208064806568342746c_fm_a,P2: set_Epistemic_fm_a > $o] :
( ( member536094252920883875c_fm_a @ X3 @ Z5 )
=> ( ( ord_le7112219575281605754c_fm_a @ Z5
@ ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ X5 )
& ( P2 @ X ) ) ) )
=> ( P2 @ X3 ) ) ) ).
% prop_restrict
thf(fact_729_prop__restrict,axiom,
! [X3: epistemic_fm_a,Z5: set_Epistemic_fm_a,X5: set_Epistemic_fm_a,P2: epistemic_fm_a > $o] :
( ( member6642669571620171971c_fm_a @ X3 @ Z5 )
=> ( ( ord_le3275665582123262618c_fm_a @ Z5
@ ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ X5 )
& ( P2 @ X ) ) ) )
=> ( P2 @ X3 ) ) ) ).
% prop_restrict
thf(fact_730_prop__restrict,axiom,
! [X3: list_Epistemic_fm_a,Z5: set_li769143395467472256c_fm_a,X5: set_li769143395467472256c_fm_a,P2: list_Epistemic_fm_a > $o] :
( ( member5906877432388582473c_fm_a @ X3 @ Z5 )
=> ( ( ord_le2931979837777675552c_fm_a @ Z5
@ ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ X5 )
& ( P2 @ X ) ) ) )
=> ( P2 @ X3 ) ) ) ).
% prop_restrict
thf(fact_731_consistent__hereditary,axiom,
! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a,S3: set_Epistemic_fm_a] :
( ( episte2285483198712856226tent_a @ A @ S )
=> ( ( ord_le3275665582123262618c_fm_a @ S3 @ S )
=> ( episte2285483198712856226tent_a @ A @ S3 ) ) ) ).
% consistent_hereditary
thf(fact_732_transpose_Opsimps_I1_J,axiom,
( ( accp_l7472382826029824047c_fm_a @ transp597054356388329423c_fm_a @ nil_li2451196919128234278c_fm_a )
=> ( ( transp2882070860200649898c_fm_a @ nil_li2451196919128234278c_fm_a )
= nil_li2451196919128234278c_fm_a ) ) ).
% transpose.psimps(1)
thf(fact_733_transpose_Opsimps_I2_J,axiom,
! [Xss2: list_l3671048651222332332c_fm_a] :
( ( accp_l8971127668057225909c_fm_a @ transp5805013372743109973c_fm_a @ ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ Xss2 ) )
=> ( ( transp7189280393105805488c_fm_a @ ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ Xss2 ) )
= ( transp7189280393105805488c_fm_a @ Xss2 ) ) ) ).
% transpose.psimps(2)
thf(fact_734_transpose_Opsimps_I2_J,axiom,
! [Xss2: list_l985973790606564998c_fm_a] :
( ( accp_l1289336314643896847c_fm_a @ transp578517656548729263c_fm_a @ ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ Xss2 ) )
=> ( ( transp493887097527820938c_fm_a @ ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ Xss2 ) )
= ( transp493887097527820938c_fm_a @ Xss2 ) ) ) ).
% transpose.psimps(2)
thf(fact_735_transpose_Opsimps_I2_J,axiom,
! [Xss2: list_l6083326122719238310c_fm_a] :
( ( accp_l7472382826029824047c_fm_a @ transp597054356388329423c_fm_a @ ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ Xss2 ) )
=> ( ( transp2882070860200649898c_fm_a @ ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ Xss2 ) )
= ( transp2882070860200649898c_fm_a @ Xss2 ) ) ) ).
% transpose.psimps(2)
thf(fact_736_subset__code_I2_J,axiom,
! [A: set_se5208064806568342746c_fm_a,Ys2: list_s580375451141968640c_fm_a] :
( ( ord_le7112219575281605754c_fm_a @ A @ ( coset_774667214334347501c_fm_a @ Ys2 ) )
= ( ! [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( set_se8855941934996405007c_fm_a @ Ys2 ) )
=> ~ ( member536094252920883875c_fm_a @ X @ A ) ) ) ) ).
% subset_code(2)
thf(fact_737_subset__code_I2_J,axiom,
! [A: set_Pr3219225162411408519c_fm_a,Ys2: list_P7917480606449584557c_fm_a] :
( ( ord_le8873477448617899047c_fm_a @ A @ ( coset_6168105701261197850c_fm_a @ Ys2 ) )
= ( ! [X: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X @ ( set_Pr5015285182815091004c_fm_a @ Ys2 ) )
=> ~ ( member3265983909902097104c_fm_a @ X @ A ) ) ) ) ).
% subset_code(2)
thf(fact_738_subset__code_I2_J,axiom,
! [A: set_Pr8948481099588399239c_fm_a,Ys2: list_P3099032918374241197c_fm_a] :
( ( ord_le8222437384497874983c_fm_a @ A @ ( coset_804875090598011930c_fm_a @ Ys2 ) )
= ( ! [X: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X @ ( set_Pr6083076219314900284c_fm_a @ Ys2 ) )
=> ~ ( member5029746173879296720c_fm_a @ X @ A ) ) ) ) ).
% subset_code(2)
thf(fact_739_subset__code_I2_J,axiom,
! [A: set_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A @ ( coset_Epistemic_fm_a @ Ys2 ) )
= ( ! [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Ys2 ) )
=> ~ ( member6642669571620171971c_fm_a @ X @ A ) ) ) ) ).
% subset_code(2)
thf(fact_740_subset__code_I2_J,axiom,
! [A: set_li769143395467472256c_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A @ ( coset_1387336592765253011c_fm_a @ Ys2 ) )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Ys2 ) )
=> ~ ( member5906877432388582473c_fm_a @ X @ A ) ) ) ) ).
% subset_code(2)
thf(fact_741_accp__subset,axiom,
! [R1: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o,R22: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o] :
( ( ord_le7821966774285193230fm_a_o @ R1 @ R22 )
=> ( ord_le2363486873338524983fm_a_o @ ( accp_l7472382826029824047c_fm_a @ R22 ) @ ( accp_l7472382826029824047c_fm_a @ R1 ) ) ) ).
% accp_subset
thf(fact_742_accp__subset,axiom,
! [R1: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a > $o,R22: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a > $o] :
( ( ord_le2311501905961223630fm_a_o @ R1 @ R22 )
=> ( ord_le3724781943004833654fm_a_o @ ( accp_P1207204058359408560c_fm_a @ R22 ) @ ( accp_P1207204058359408560c_fm_a @ R1 ) ) ) ).
% accp_subset
thf(fact_743_accp__subset,axiom,
! [R1: produc7493720319326827993c_fm_a > produc7493720319326827993c_fm_a > $o,R22: produc7493720319326827993c_fm_a > produc7493720319326827993c_fm_a > $o] :
( ( ord_le8486165426724920142fm_a_o @ R1 @ R22 )
=> ( ord_le7091422540096163780fm_a_o @ ( accp_P8153917284782618338c_fm_a @ R22 ) @ ( accp_P8153917284782618338c_fm_a @ R1 ) ) ) ).
% accp_subset
thf(fact_744_accp__subset,axiom,
! [R1: epistemic_fm_a > epistemic_fm_a > $o,R22: epistemic_fm_a > epistemic_fm_a > $o] :
( ( ord_le3934200179093585166fm_a_o @ R1 @ R22 )
=> ( ord_le4043730696559282883fm_a_o @ ( accp_Epistemic_fm_a @ R22 ) @ ( accp_Epistemic_fm_a @ R1 ) ) ) ).
% accp_subset
thf(fact_745_accp__subset__induct,axiom,
! [D: list_l6083326122719238310c_fm_a > $o,R2: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o,X3: list_l6083326122719238310c_fm_a,P2: list_l6083326122719238310c_fm_a > $o] :
( ( ord_le2363486873338524983fm_a_o @ D @ ( accp_l7472382826029824047c_fm_a @ R2 ) )
=> ( ! [X2: list_l6083326122719238310c_fm_a,Z: list_l6083326122719238310c_fm_a] :
( ( D @ X2 )
=> ( ( R2 @ Z @ X2 )
=> ( D @ Z ) ) )
=> ( ( D @ X3 )
=> ( ! [X2: list_l6083326122719238310c_fm_a] :
( ( D @ X2 )
=> ( ! [Z6: list_l6083326122719238310c_fm_a] :
( ( R2 @ Z6 @ X2 )
=> ( P2 @ Z6 ) )
=> ( P2 @ X2 ) ) )
=> ( P2 @ X3 ) ) ) ) ) ).
% accp_subset_induct
thf(fact_746_accp__subset__induct,axiom,
! [D: produc5756089960658898087c_fm_a > $o,R2: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a > $o,X3: produc5756089960658898087c_fm_a,P2: produc5756089960658898087c_fm_a > $o] :
( ( ord_le3724781943004833654fm_a_o @ D @ ( accp_P1207204058359408560c_fm_a @ R2 ) )
=> ( ! [X2: produc5756089960658898087c_fm_a,Z: produc5756089960658898087c_fm_a] :
( ( D @ X2 )
=> ( ( R2 @ Z @ X2 )
=> ( D @ Z ) ) )
=> ( ( D @ X3 )
=> ( ! [X2: produc5756089960658898087c_fm_a] :
( ( D @ X2 )
=> ( ! [Z6: produc5756089960658898087c_fm_a] :
( ( R2 @ Z6 @ X2 )
=> ( P2 @ Z6 ) )
=> ( P2 @ X2 ) ) )
=> ( P2 @ X3 ) ) ) ) ) ).
% accp_subset_induct
thf(fact_747_accp__subset__induct,axiom,
! [D: produc7493720319326827993c_fm_a > $o,R2: produc7493720319326827993c_fm_a > produc7493720319326827993c_fm_a > $o,X3: produc7493720319326827993c_fm_a,P2: produc7493720319326827993c_fm_a > $o] :
( ( ord_le7091422540096163780fm_a_o @ D @ ( accp_P8153917284782618338c_fm_a @ R2 ) )
=> ( ! [X2: produc7493720319326827993c_fm_a,Z: produc7493720319326827993c_fm_a] :
( ( D @ X2 )
=> ( ( R2 @ Z @ X2 )
=> ( D @ Z ) ) )
=> ( ( D @ X3 )
=> ( ! [X2: produc7493720319326827993c_fm_a] :
( ( D @ X2 )
=> ( ! [Z6: produc7493720319326827993c_fm_a] :
( ( R2 @ Z6 @ X2 )
=> ( P2 @ Z6 ) )
=> ( P2 @ X2 ) ) )
=> ( P2 @ X3 ) ) ) ) ) ).
% accp_subset_induct
thf(fact_748_accp__subset__induct,axiom,
! [D: epistemic_fm_a > $o,R2: epistemic_fm_a > epistemic_fm_a > $o,X3: epistemic_fm_a,P2: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ D @ ( accp_Epistemic_fm_a @ R2 ) )
=> ( ! [X2: epistemic_fm_a,Z: epistemic_fm_a] :
( ( D @ X2 )
=> ( ( R2 @ Z @ X2 )
=> ( D @ Z ) ) )
=> ( ( D @ X3 )
=> ( ! [X2: epistemic_fm_a] :
( ( D @ X2 )
=> ( ! [Z6: epistemic_fm_a] :
( ( R2 @ Z6 @ X2 )
=> ( P2 @ Z6 ) )
=> ( P2 @ X2 ) ) )
=> ( P2 @ X3 ) ) ) ) ) ).
% accp_subset_induct
thf(fact_749_AxB__symmetric_H,axiom,
! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,W3: set_Epistemic_fm_a,I: a] :
( ( ord_le4043730696559282883fm_a_o @ epistemic_AxB_a @ A )
=> ( ( episte2285483198712856226tent_a @ A @ V )
=> ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
=> ( ( episte2285483198712856226tent_a @ A @ W3 )
=> ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W3 )
=> ( ( member536094252920883875c_fm_a @ W3
@ ( collec2519470961442302949c_fm_a
@ ( ord_le3275665582123262618c_fm_a
@ ( collec4904205152690461189c_fm_a
@ ^ [P4: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P4 ) @ V ) ) ) ) )
=> ( member536094252920883875c_fm_a @ V
@ ( collec2519470961442302949c_fm_a
@ ( ord_le3275665582123262618c_fm_a
@ ( collec4904205152690461189c_fm_a
@ ^ [P4: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P4 ) @ W3 ) ) ) ) ) ) ) ) ) ) ) ).
% AxB_symmetric'
thf(fact_750_Ax5__Euclidean,axiom,
! [A: epistemic_fm_a > $o,U: set_Epistemic_fm_a,V: set_Epistemic_fm_a,W3: set_Epistemic_fm_a,I: a] :
( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A )
=> ( ( episte2285483198712856226tent_a @ A @ U )
=> ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ U )
=> ( ( episte2285483198712856226tent_a @ A @ V )
=> ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
=> ( ( episte2285483198712856226tent_a @ A @ W3 )
=> ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W3 )
=> ( ( member536094252920883875c_fm_a @ V
@ ( collec2519470961442302949c_fm_a
@ ( ord_le3275665582123262618c_fm_a
@ ( collec4904205152690461189c_fm_a
@ ^ [P4: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P4 ) @ U ) ) ) ) )
=> ( ( member536094252920883875c_fm_a @ W3
@ ( collec2519470961442302949c_fm_a
@ ( ord_le3275665582123262618c_fm_a
@ ( collec4904205152690461189c_fm_a
@ ^ [P4: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P4 ) @ U ) ) ) ) )
=> ( member536094252920883875c_fm_a @ W3
@ ( collec2519470961442302949c_fm_a
@ ( ord_le3275665582123262618c_fm_a
@ ( collec4904205152690461189c_fm_a
@ ^ [P4: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P4 ) @ V ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% Ax5_Euclidean
thf(fact_751_Ax4__transitive,axiom,
! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,W3: set_Epistemic_fm_a,I: a,U: set_Epistemic_fm_a] :
( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax4_a @ A )
=> ( ( episte2285483198712856226tent_a @ A @ V )
=> ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
=> ( ( member536094252920883875c_fm_a @ W3
@ ( collec2519470961442302949c_fm_a
@ ( ord_le3275665582123262618c_fm_a
@ ( collec4904205152690461189c_fm_a
@ ^ [P4: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P4 ) @ V ) ) ) ) )
=> ( ( member536094252920883875c_fm_a @ U
@ ( collec2519470961442302949c_fm_a
@ ( ord_le3275665582123262618c_fm_a
@ ( collec4904205152690461189c_fm_a
@ ^ [P4: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P4 ) @ W3 ) ) ) ) )
=> ( member536094252920883875c_fm_a @ U
@ ( collec2519470961442302949c_fm_a
@ ( ord_le3275665582123262618c_fm_a
@ ( collec4904205152690461189c_fm_a
@ ^ [P4: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P4 ) @ V ) ) ) ) ) ) ) ) ) ) ).
% Ax4_transitive
thf(fact_752_AxT__reflexive,axiom,
! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,I: a] :
( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A )
=> ( ( episte2285483198712856226tent_a @ A @ V )
=> ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
=> ( member536094252920883875c_fm_a @ V
@ ( collec2519470961442302949c_fm_a
@ ( ord_le3275665582123262618c_fm_a
@ ( collec4904205152690461189c_fm_a
@ ^ [P4: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P4 ) @ V ) ) ) ) ) ) ) ) ).
% AxT_reflexive
thf(fact_753_ax__in__maximal,axiom,
! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ( episte2285483198712856226tent_a @ A @ V )
=> ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
=> ( ( A @ P )
=> ( member6642669571620171971c_fm_a @ P @ V ) ) ) ) ).
% ax_in_maximal
thf(fact_754_consequent__in__maximal,axiom,
! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
( ( episte2285483198712856226tent_a @ A @ V )
=> ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
=> ( ( member6642669571620171971c_fm_a @ P @ V )
=> ( ( member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ P @ Q ) @ V )
=> ( member6642669571620171971c_fm_a @ Q @ V ) ) ) ) ) ).
% consequent_in_maximal
thf(fact_755_deriv__in__maximal,axiom,
! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ( episte2285483198712856226tent_a @ A @ V )
=> ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
=> ( ( epistemic_AK_a @ A @ P )
=> ( member6642669571620171971c_fm_a @ P @ V ) ) ) ) ).
% deriv_in_maximal
thf(fact_756_maximal__extension,axiom,
! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a] :
( ( episte2285483198712856226tent_a @ A @ V )
=> ~ ! [W4: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ V @ W4 )
=> ( ( episte2285483198712856226tent_a @ A @ W4 )
=> ~ ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W4 ) ) ) ) ).
% maximal_extension
thf(fact_757_exactly__one__in__maximal,axiom,
! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ( episte2285483198712856226tent_a @ A @ V )
=> ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
=> ( ( member6642669571620171971c_fm_a @ P @ V )
= ( ~ ( member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ V ) ) ) ) ) ).
% exactly_one_in_maximal
thf(fact_758_remove__code_I2_J,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( remove5552923366785645183c_fm_a @ X3 @ ( coset_Epistemic_fm_a @ Xs ) )
= ( coset_Epistemic_fm_a @ ( insert177310161492556854c_fm_a @ X3 @ Xs ) ) ) ).
% remove_code(2)
thf(fact_759_conj__subset__def,axiom,
! [A: set_se5208064806568342746c_fm_a,P2: set_Epistemic_fm_a > $o,Q3: set_Epistemic_fm_a > $o] :
( ( ord_le7112219575281605754c_fm_a @ A
@ ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] :
( ( P2 @ X )
& ( Q3 @ X ) ) ) )
= ( ( ord_le7112219575281605754c_fm_a @ A @ ( collec2519470961442302949c_fm_a @ P2 ) )
& ( ord_le7112219575281605754c_fm_a @ A @ ( collec2519470961442302949c_fm_a @ Q3 ) ) ) ) ).
% conj_subset_def
thf(fact_760_conj__subset__def,axiom,
! [A: set_Epistemic_fm_a,P2: epistemic_fm_a > $o,Q3: epistemic_fm_a > $o] :
( ( ord_le3275665582123262618c_fm_a @ A
@ ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( P2 @ X )
& ( Q3 @ X ) ) ) )
= ( ( ord_le3275665582123262618c_fm_a @ A @ ( collec4904205152690461189c_fm_a @ P2 ) )
& ( ord_le3275665582123262618c_fm_a @ A @ ( collec4904205152690461189c_fm_a @ Q3 ) ) ) ) ).
% conj_subset_def
thf(fact_761_conj__subset__def,axiom,
! [A: set_li769143395467472256c_fm_a,P2: list_Epistemic_fm_a > $o,Q3: list_Epistemic_fm_a > $o] :
( ( ord_le2931979837777675552c_fm_a @ A
@ ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( P2 @ X )
& ( Q3 @ X ) ) ) )
= ( ( ord_le2931979837777675552c_fm_a @ A @ ( collec5191077796991884427c_fm_a @ P2 ) )
& ( ord_le2931979837777675552c_fm_a @ A @ ( collec5191077796991884427c_fm_a @ Q3 ) ) ) ) ).
% conj_subset_def
thf(fact_762_subset__subseqs,axiom,
! [X5: set_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ X5 @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ( member536094252920883875c_fm_a @ X5 @ ( image_971165786557580383c_fm_a @ set_Epistemic_fm_a2 @ ( set_li8442223810127165109c_fm_a @ ( subseq859285839621985007c_fm_a @ Xs ) ) ) ) ) ).
% subset_subseqs
thf(fact_763_subset__subseqs,axiom,
! [X5: set_li769143395467472256c_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ X5 @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ( member2517045796615263401c_fm_a @ X5 @ ( image_7951968421222759263c_fm_a @ set_li8442223810127165109c_fm_a @ ( set_li647609056391172027c_fm_a @ ( subseq3170398737635186805c_fm_a @ Xs ) ) ) ) ) ).
% subset_subseqs
thf(fact_764_transpose__aux__filter__tail,axiom,
! [Xss2: list_l3671048651222332332c_fm_a] :
( ( concat5652308878773863783c_fm_a
@ ( map_li3568483382057536586c_fm_a
@ ( case_l7601246044141707098c_fm_a @ nil_li5178944226519631276c_fm_a
@ ^ [H2: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l2479501935080859996c_fm_a @ T2 @ nil_li5178944226519631276c_fm_a ) )
@ Xss2 ) )
= ( map_li8347733892191492164c_fm_a @ tl_lis3363300823944467983c_fm_a
@ ( filter389827114350055331c_fm_a
@ ^ [Ys: list_l6083326122719238310c_fm_a] : ( Ys != nil_li2451196919128234278c_fm_a )
@ Xss2 ) ) ) ).
% transpose_aux_filter_tail
thf(fact_765_transpose__aux__filter__tail,axiom,
! [Xss2: list_l985973790606564998c_fm_a] :
( ( concat4130251116320034881c_fm_a
@ ( map_li7441020096712412618c_fm_a
@ ( case_l4953383812495590490c_fm_a @ nil_li5433889876484989702c_fm_a
@ ^ [H2: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_l1626872963913326262c_fm_a @ T2 @ nil_li5433889876484989702c_fm_a ) )
@ Xss2 ) )
= ( map_li1341364954853471300c_fm_a @ tl_set2007602089164433257c_fm_a
@ ( filter1974008165531859069c_fm_a
@ ^ [Ys: list_s580375451141968640c_fm_a] : ( Ys != nil_se102576565402781184c_fm_a )
@ Xss2 ) ) ) ).
% transpose_aux_filter_tail
thf(fact_766_transpose__aux__filter__tail,axiom,
! [Xss2: list_l6083326122719238310c_fm_a] :
( ( concat6109960377493484129c_fm_a
@ ( map_li3858915945532548554c_fm_a
@ ( case_l5707353781634818138c_fm_a @ nil_li2451196919128234278c_fm_a
@ ^ [H2: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ T2 @ nil_li2451196919128234278c_fm_a ) )
@ Xss2 ) )
= ( map_li3080774272885743684c_fm_a @ tl_Epistemic_fm_a
@ ( filter441479637125139101c_fm_a
@ ^ [Ys: list_Epistemic_fm_a] : ( Ys != nil_Epistemic_fm_a )
@ Xss2 ) ) ) ).
% transpose_aux_filter_tail
thf(fact_767_image__ident,axiom,
! [Y5: set_Epistemic_fm_a] :
( ( image_4449434806354059013c_fm_a
@ ^ [X: epistemic_fm_a] : X
@ Y5 )
= Y5 ) ).
% image_ident
thf(fact_768_image__ident,axiom,
! [Y5: set_li769143395467472256c_fm_a] :
( ( image_7387318756023638021c_fm_a
@ ^ [X: list_Epistemic_fm_a] : X
@ Y5 )
= Y5 ) ).
% image_ident
thf(fact_769_filter__filter,axiom,
! [P2: list_Epistemic_fm_a > $o,Q3: list_Epistemic_fm_a > $o,Xs: list_l6083326122719238310c_fm_a] :
( ( filter441479637125139101c_fm_a @ P2 @ ( filter441479637125139101c_fm_a @ Q3 @ Xs ) )
= ( filter441479637125139101c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( Q3 @ X )
& ( P2 @ X ) )
@ Xs ) ) ).
% filter_filter
thf(fact_770_filter__filter,axiom,
! [P2: epistemic_fm_a > $o,Q3: epistemic_fm_a > $o,Xs: list_Epistemic_fm_a] :
( ( filter7636273809395300631c_fm_a @ P2 @ ( filter7636273809395300631c_fm_a @ Q3 @ Xs ) )
= ( filter7636273809395300631c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( Q3 @ X )
& ( P2 @ X ) )
@ Xs ) ) ).
% filter_filter
thf(fact_771_filter__True,axiom,
! [Xs: list_Epistemic_fm_a,P2: epistemic_fm_a > $o] :
( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ( P2 @ X2 ) )
=> ( ( filter7636273809395300631c_fm_a @ P2 @ Xs )
= Xs ) ) ).
% filter_True
thf(fact_772_filter__True,axiom,
! [Xs: list_l6083326122719238310c_fm_a,P2: list_Epistemic_fm_a > $o] :
( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ( P2 @ X2 ) )
=> ( ( filter441479637125139101c_fm_a @ P2 @ Xs )
= Xs ) ) ).
% filter_True
thf(fact_773_set__filter,axiom,
! [P2: produc5756089960658898087c_fm_a > $o,Xs: list_P7917480606449584557c_fm_a] :
( ( set_Pr5015285182815091004c_fm_a @ ( filter8648851334721324324c_fm_a @ P2 @ Xs ) )
= ( collec6124610372686893330c_fm_a
@ ^ [X: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X @ ( set_Pr5015285182815091004c_fm_a @ Xs ) )
& ( P2 @ X ) ) ) ) ).
% set_filter
thf(fact_774_set__filter,axiom,
! [P2: produc2203834439629243303c_fm_a > $o,Xs: list_P3099032918374241197c_fm_a] :
( ( set_Pr6083076219314900284c_fm_a @ ( filter326375931097202980c_fm_a @ P2 @ Xs ) )
= ( collec7391038856303340306c_fm_a
@ ^ [X: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X @ ( set_Pr6083076219314900284c_fm_a @ Xs ) )
& ( P2 @ X ) ) ) ) ).
% set_filter
thf(fact_775_set__filter,axiom,
! [P2: set_Epistemic_fm_a > $o,Xs: list_s580375451141968640c_fm_a] :
( ( set_se8855941934996405007c_fm_a @ ( filter2620125754611450615c_fm_a @ P2 @ Xs ) )
= ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( set_se8855941934996405007c_fm_a @ Xs ) )
& ( P2 @ X ) ) ) ) ).
% set_filter
thf(fact_776_set__filter,axiom,
! [P2: epistemic_fm_a > $o,Xs: list_Epistemic_fm_a] :
( ( set_Epistemic_fm_a2 @ ( filter7636273809395300631c_fm_a @ P2 @ Xs ) )
= ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs ) )
& ( P2 @ X ) ) ) ) ).
% set_filter
thf(fact_777_set__filter,axiom,
! [P2: list_Epistemic_fm_a > $o,Xs: list_l6083326122719238310c_fm_a] :
( ( set_li8442223810127165109c_fm_a @ ( filter441479637125139101c_fm_a @ P2 @ Xs ) )
= ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs ) )
& ( P2 @ X ) ) ) ) ).
% set_filter
thf(fact_778_list_Oset__map,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,V2: list_l6083326122719238310c_fm_a] :
( ( set_li647609056391172027c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ V2 ) )
= ( image_6931812158510582027c_fm_a @ F @ ( set_li8442223810127165109c_fm_a @ V2 ) ) ) ).
% list.set_map
thf(fact_779_list_Oset__map,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,V2: list_l6083326122719238310c_fm_a] :
( ( set_Epistemic_fm_a2 @ ( map_li5516866612190465598c_fm_a @ F @ V2 ) )
= ( image_7959425827855735423c_fm_a @ F @ ( set_li8442223810127165109c_fm_a @ V2 ) ) ) ).
% list.set_map
thf(fact_780_list_Oset__map,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,V2: list_Epistemic_fm_a] :
( ( set_li8442223810127165109c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ V2 ) )
= ( image_4430763730358542731c_fm_a @ F @ ( set_Epistemic_fm_a2 @ V2 ) ) ) ).
% list.set_map
thf(fact_781_list_Oset__map,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,V2: list_l6083326122719238310c_fm_a] :
( ( set_li8442223810127165109c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ V2 ) )
= ( image_7387318756023638021c_fm_a @ F @ ( set_li8442223810127165109c_fm_a @ V2 ) ) ) ).
% list.set_map
thf(fact_782_list_Oset__map,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,V2: list_Epistemic_fm_a] :
( ( set_Epistemic_fm_a2 @ ( map_Ep7084560364594560580c_fm_a @ F @ V2 ) )
= ( image_4449434806354059013c_fm_a @ F @ ( set_Epistemic_fm_a2 @ V2 ) ) ) ).
% list.set_map
thf(fact_783_filter__False,axiom,
! [Xs: list_s580375451141968640c_fm_a,P2: set_Epistemic_fm_a > $o] :
( ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Xs ) )
=> ~ ( P2 @ X2 ) )
=> ( ( filter2620125754611450615c_fm_a @ P2 @ Xs )
= nil_se102576565402781184c_fm_a ) ) ).
% filter_False
thf(fact_784_filter__False,axiom,
! [Xs: list_l6083326122719238310c_fm_a,P2: list_Epistemic_fm_a > $o] :
( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ~ ( P2 @ X2 ) )
=> ( ( filter441479637125139101c_fm_a @ P2 @ Xs )
= nil_li2451196919128234278c_fm_a ) ) ).
% filter_False
thf(fact_785_filter__False,axiom,
! [Xs: list_Epistemic_fm_a,P2: epistemic_fm_a > $o] :
( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ~ ( P2 @ X2 ) )
=> ( ( filter7636273809395300631c_fm_a @ P2 @ Xs )
= nil_Epistemic_fm_a ) ) ).
% filter_False
thf(fact_786_Compr__image__eq,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a,P2: epistemic_fm_a > $o] :
( ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ ( image_4449434806354059013c_fm_a @ F @ A ) )
& ( P2 @ X ) ) )
= ( image_4449434806354059013c_fm_a @ F
@ ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ A )
& ( P2 @ ( F @ X ) ) ) ) ) ) ).
% Compr_image_eq
thf(fact_787_Compr__image__eq,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,A: set_Epistemic_fm_a,P2: list_Epistemic_fm_a > $o] :
( ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( image_4430763730358542731c_fm_a @ F @ A ) )
& ( P2 @ X ) ) )
= ( image_4430763730358542731c_fm_a @ F
@ ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ A )
& ( P2 @ ( F @ X ) ) ) ) ) ) ).
% Compr_image_eq
thf(fact_788_Compr__image__eq,axiom,
! [F: epistemic_fm_a > set_Epistemic_fm_a,A: set_Epistemic_fm_a,P2: set_Epistemic_fm_a > $o] :
( ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( image_1263732536703906021c_fm_a @ F @ A ) )
& ( P2 @ X ) ) )
= ( image_1263732536703906021c_fm_a @ F
@ ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ A )
& ( P2 @ ( F @ X ) ) ) ) ) ) ).
% Compr_image_eq
thf(fact_789_Compr__image__eq,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,A: set_li769143395467472256c_fm_a,P2: epistemic_fm_a > $o] :
( ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ ( image_7959425827855735423c_fm_a @ F @ A ) )
& ( P2 @ X ) ) )
= ( image_7959425827855735423c_fm_a @ F
@ ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ A )
& ( P2 @ ( F @ X ) ) ) ) ) ) ).
% Compr_image_eq
thf(fact_790_Compr__image__eq,axiom,
! [F: set_Epistemic_fm_a > epistemic_fm_a,A: set_se5208064806568342746c_fm_a,P2: epistemic_fm_a > $o] :
( ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ ( image_3376480847214465317c_fm_a @ F @ A ) )
& ( P2 @ X ) ) )
= ( image_3376480847214465317c_fm_a @ F
@ ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ A )
& ( P2 @ ( F @ X ) ) ) ) ) ) ).
% Compr_image_eq
thf(fact_791_Compr__image__eq,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,P2: list_Epistemic_fm_a > $o] :
( ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( image_7387318756023638021c_fm_a @ F @ A ) )
& ( P2 @ X ) ) )
= ( image_7387318756023638021c_fm_a @ F
@ ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ A )
& ( P2 @ ( F @ X ) ) ) ) ) ) ).
% Compr_image_eq
thf(fact_792_Compr__image__eq,axiom,
! [F: set_Epistemic_fm_a > list_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,P2: list_Epistemic_fm_a > $o] :
( ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( image_1284921450708845483c_fm_a @ F @ A ) )
& ( P2 @ X ) ) )
= ( image_1284921450708845483c_fm_a @ F
@ ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ A )
& ( P2 @ ( F @ X ) ) ) ) ) ) ).
% Compr_image_eq
thf(fact_793_Compr__image__eq,axiom,
! [F: list_Epistemic_fm_a > set_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,P2: set_Epistemic_fm_a > $o] :
( ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( image_971165786557580383c_fm_a @ F @ A ) )
& ( P2 @ X ) ) )
= ( image_971165786557580383c_fm_a @ F
@ ( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ A )
& ( P2 @ ( F @ X ) ) ) ) ) ) ).
% Compr_image_eq
thf(fact_794_Compr__image__eq,axiom,
! [F: set_Epistemic_fm_a > set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,P2: set_Epistemic_fm_a > $o] :
( ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( image_8582343580727714565c_fm_a @ F @ A ) )
& ( P2 @ X ) ) )
= ( image_8582343580727714565c_fm_a @ F
@ ( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ A )
& ( P2 @ ( F @ X ) ) ) ) ) ) ).
% Compr_image_eq
thf(fact_795_Compr__image__eq,axiom,
! [F: epistemic_fm_a > produc2203834439629243303c_fm_a,A: set_Epistemic_fm_a,P2: produc2203834439629243303c_fm_a > $o] :
( ( collec7391038856303340306c_fm_a
@ ^ [X: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X @ ( image_6012374219615907858c_fm_a @ F @ A ) )
& ( P2 @ X ) ) )
= ( image_6012374219615907858c_fm_a @ F
@ ( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ A )
& ( P2 @ ( F @ X ) ) ) ) ) ) ).
% Compr_image_eq
thf(fact_796_image__image,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,G4: epistemic_fm_a > list_Epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( image_7959425827855735423c_fm_a @ F @ ( image_4430763730358542731c_fm_a @ G4 @ A ) )
= ( image_4449434806354059013c_fm_a
@ ^ [X: epistemic_fm_a] : ( F @ ( G4 @ X ) )
@ A ) ) ).
% image_image
thf(fact_797_image__image,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,G4: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( image_4449434806354059013c_fm_a @ F @ ( image_4449434806354059013c_fm_a @ G4 @ A ) )
= ( image_4449434806354059013c_fm_a
@ ^ [X: epistemic_fm_a] : ( F @ ( G4 @ X ) )
@ A ) ) ).
% image_image
thf(fact_798_image__image,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,G4: list_Epistemic_fm_a > list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a] :
( ( image_7387318756023638021c_fm_a @ F @ ( image_7387318756023638021c_fm_a @ G4 @ A ) )
= ( image_7387318756023638021c_fm_a
@ ^ [X: list_Epistemic_fm_a] : ( F @ ( G4 @ X ) )
@ A ) ) ).
% image_image
thf(fact_799_image__image,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,G4: epistemic_fm_a > list_Epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( image_7387318756023638021c_fm_a @ F @ ( image_4430763730358542731c_fm_a @ G4 @ A ) )
= ( image_4430763730358542731c_fm_a
@ ^ [X: epistemic_fm_a] : ( F @ ( G4 @ X ) )
@ A ) ) ).
% image_image
thf(fact_800_image__image,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,G4: list_Epistemic_fm_a > epistemic_fm_a,A: set_li769143395467472256c_fm_a] :
( ( image_4430763730358542731c_fm_a @ F @ ( image_7959425827855735423c_fm_a @ G4 @ A ) )
= ( image_7387318756023638021c_fm_a
@ ^ [X: list_Epistemic_fm_a] : ( F @ ( G4 @ X ) )
@ A ) ) ).
% image_image
thf(fact_801_image__image,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,G4: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( image_4430763730358542731c_fm_a @ F @ ( image_4449434806354059013c_fm_a @ G4 @ A ) )
= ( image_4430763730358542731c_fm_a
@ ^ [X: epistemic_fm_a] : ( F @ ( G4 @ X ) )
@ A ) ) ).
% image_image
thf(fact_802_imageE,axiom,
! [B: epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ B @ ( image_4449434806354059013c_fm_a @ F @ A ) )
=> ~ ! [X2: epistemic_fm_a] :
( ( B
= ( F @ X2 ) )
=> ~ ( member6642669571620171971c_fm_a @ X2 @ A ) ) ) ).
% imageE
thf(fact_803_imageE,axiom,
! [B: epistemic_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
( ( member6642669571620171971c_fm_a @ B @ ( image_3376480847214465317c_fm_a @ F @ A ) )
=> ~ ! [X2: set_Epistemic_fm_a] :
( ( B
= ( F @ X2 ) )
=> ~ ( member536094252920883875c_fm_a @ X2 @ A ) ) ) ).
% imageE
thf(fact_804_imageE,axiom,
! [B: epistemic_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,A: set_li769143395467472256c_fm_a] :
( ( member6642669571620171971c_fm_a @ B @ ( image_7959425827855735423c_fm_a @ F @ A ) )
=> ~ ! [X2: list_Epistemic_fm_a] :
( ( B
= ( F @ X2 ) )
=> ~ ( member5906877432388582473c_fm_a @ X2 @ A ) ) ) ).
% imageE
thf(fact_805_imageE,axiom,
! [B: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ B @ ( image_1263732536703906021c_fm_a @ F @ A ) )
=> ~ ! [X2: epistemic_fm_a] :
( ( B
= ( F @ X2 ) )
=> ~ ( member6642669571620171971c_fm_a @ X2 @ A ) ) ) ).
% imageE
thf(fact_806_imageE,axiom,
! [B: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ B @ ( image_4430763730358542731c_fm_a @ F @ A ) )
=> ~ ! [X2: epistemic_fm_a] :
( ( B
= ( F @ X2 ) )
=> ~ ( member6642669571620171971c_fm_a @ X2 @ A ) ) ) ).
% imageE
thf(fact_807_imageE,axiom,
! [B: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
( ( member536094252920883875c_fm_a @ B @ ( image_8582343580727714565c_fm_a @ F @ A ) )
=> ~ ! [X2: set_Epistemic_fm_a] :
( ( B
= ( F @ X2 ) )
=> ~ ( member536094252920883875c_fm_a @ X2 @ A ) ) ) ).
% imageE
thf(fact_808_imageE,axiom,
! [B: set_Epistemic_fm_a,F: list_Epistemic_fm_a > set_Epistemic_fm_a,A: set_li769143395467472256c_fm_a] :
( ( member536094252920883875c_fm_a @ B @ ( image_971165786557580383c_fm_a @ F @ A ) )
=> ~ ! [X2: list_Epistemic_fm_a] :
( ( B
= ( F @ X2 ) )
=> ~ ( member5906877432388582473c_fm_a @ X2 @ A ) ) ) ).
% imageE
thf(fact_809_imageE,axiom,
! [B: list_Epistemic_fm_a,F: set_Epistemic_fm_a > list_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
( ( member5906877432388582473c_fm_a @ B @ ( image_1284921450708845483c_fm_a @ F @ A ) )
=> ~ ! [X2: set_Epistemic_fm_a] :
( ( B
= ( F @ X2 ) )
=> ~ ( member536094252920883875c_fm_a @ X2 @ A ) ) ) ).
% imageE
thf(fact_810_imageE,axiom,
! [B: list_Epistemic_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a] :
( ( member5906877432388582473c_fm_a @ B @ ( image_7387318756023638021c_fm_a @ F @ A ) )
=> ~ ! [X2: list_Epistemic_fm_a] :
( ( B
= ( F @ X2 ) )
=> ~ ( member5906877432388582473c_fm_a @ X2 @ A ) ) ) ).
% imageE
thf(fact_811_imageE,axiom,
! [B: epistemic_fm_a,F: produc2203834439629243303c_fm_a > epistemic_fm_a,A: set_Pr8948481099588399239c_fm_a] :
( ( member6642669571620171971c_fm_a @ B @ ( image_2228126887729148984c_fm_a @ F @ A ) )
=> ~ ! [X2: produc2203834439629243303c_fm_a] :
( ( B
= ( F @ X2 ) )
=> ~ ( member5029746173879296720c_fm_a @ X2 @ A ) ) ) ).
% imageE
thf(fact_812_filter_Osimps_I2_J,axiom,
! [P2: epistemic_fm_a > $o,X3: epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( ( P2 @ X3 )
=> ( ( filter7636273809395300631c_fm_a @ P2 @ ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= ( cons_Epistemic_fm_a @ X3 @ ( filter7636273809395300631c_fm_a @ P2 @ Xs ) ) ) )
& ( ~ ( P2 @ X3 )
=> ( ( filter7636273809395300631c_fm_a @ P2 @ ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= ( filter7636273809395300631c_fm_a @ P2 @ Xs ) ) ) ) ).
% filter.simps(2)
thf(fact_813_filter_Osimps_I2_J,axiom,
! [P2: list_Epistemic_fm_a > $o,X3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( ( P2 @ X3 )
=> ( ( filter441479637125139101c_fm_a @ P2 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs ) )
= ( cons_l8134865115577406678c_fm_a @ X3 @ ( filter441479637125139101c_fm_a @ P2 @ Xs ) ) ) )
& ( ~ ( P2 @ X3 )
=> ( ( filter441479637125139101c_fm_a @ P2 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs ) )
= ( filter441479637125139101c_fm_a @ P2 @ Xs ) ) ) ) ).
% filter.simps(2)
thf(fact_814_filter_Osimps_I1_J,axiom,
! [P2: list_Epistemic_fm_a > $o] :
( ( filter441479637125139101c_fm_a @ P2 @ nil_li2451196919128234278c_fm_a )
= nil_li2451196919128234278c_fm_a ) ).
% filter.simps(1)
thf(fact_815_filter_Osimps_I1_J,axiom,
! [P2: set_Epistemic_fm_a > $o] :
( ( filter2620125754611450615c_fm_a @ P2 @ nil_se102576565402781184c_fm_a )
= nil_se102576565402781184c_fm_a ) ).
% filter.simps(1)
thf(fact_816_filter_Osimps_I1_J,axiom,
! [P2: epistemic_fm_a > $o] :
( ( filter7636273809395300631c_fm_a @ P2 @ nil_Epistemic_fm_a )
= nil_Epistemic_fm_a ) ).
% filter.simps(1)
thf(fact_817_filter__id__conv,axiom,
! [P2: epistemic_fm_a > $o,Xs: list_Epistemic_fm_a] :
( ( ( filter7636273809395300631c_fm_a @ P2 @ Xs )
= Xs )
= ( ! [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ( P2 @ X ) ) ) ) ).
% filter_id_conv
thf(fact_818_filter__id__conv,axiom,
! [P2: list_Epistemic_fm_a > $o,Xs: list_l6083326122719238310c_fm_a] :
( ( ( filter441479637125139101c_fm_a @ P2 @ Xs )
= Xs )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ( P2 @ X ) ) ) ) ).
% filter_id_conv
thf(fact_819_filter__cong,axiom,
! [Xs: list_s580375451141968640c_fm_a,Ys2: list_s580375451141968640c_fm_a,P2: set_Epistemic_fm_a > $o,Q3: set_Epistemic_fm_a > $o] :
( ( Xs = Ys2 )
=> ( ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Ys2 ) )
=> ( ( P2 @ X2 )
= ( Q3 @ X2 ) ) )
=> ( ( filter2620125754611450615c_fm_a @ P2 @ Xs )
= ( filter2620125754611450615c_fm_a @ Q3 @ Ys2 ) ) ) ) ).
% filter_cong
thf(fact_820_filter__cong,axiom,
! [Xs: list_P7917480606449584557c_fm_a,Ys2: list_P7917480606449584557c_fm_a,P2: produc5756089960658898087c_fm_a > $o,Q3: produc5756089960658898087c_fm_a > $o] :
( ( Xs = Ys2 )
=> ( ! [X2: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Ys2 ) )
=> ( ( P2 @ X2 )
= ( Q3 @ X2 ) ) )
=> ( ( filter8648851334721324324c_fm_a @ P2 @ Xs )
= ( filter8648851334721324324c_fm_a @ Q3 @ Ys2 ) ) ) ) ).
% filter_cong
thf(fact_821_filter__cong,axiom,
! [Xs: list_P3099032918374241197c_fm_a,Ys2: list_P3099032918374241197c_fm_a,P2: produc2203834439629243303c_fm_a > $o,Q3: produc2203834439629243303c_fm_a > $o] :
( ( Xs = Ys2 )
=> ( ! [X2: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Ys2 ) )
=> ( ( P2 @ X2 )
= ( Q3 @ X2 ) ) )
=> ( ( filter326375931097202980c_fm_a @ P2 @ Xs )
= ( filter326375931097202980c_fm_a @ Q3 @ Ys2 ) ) ) ) ).
% filter_cong
thf(fact_822_filter__cong,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a,P2: epistemic_fm_a > $o,Q3: epistemic_fm_a > $o] :
( ( Xs = Ys2 )
=> ( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Ys2 ) )
=> ( ( P2 @ X2 )
= ( Q3 @ X2 ) ) )
=> ( ( filter7636273809395300631c_fm_a @ P2 @ Xs )
= ( filter7636273809395300631c_fm_a @ Q3 @ Ys2 ) ) ) ) ).
% filter_cong
thf(fact_823_filter__cong,axiom,
! [Xs: list_l6083326122719238310c_fm_a,Ys2: list_l6083326122719238310c_fm_a,P2: list_Epistemic_fm_a > $o,Q3: list_Epistemic_fm_a > $o] :
( ( Xs = Ys2 )
=> ( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Ys2 ) )
=> ( ( P2 @ X2 )
= ( Q3 @ X2 ) ) )
=> ( ( filter441479637125139101c_fm_a @ P2 @ Xs )
= ( filter441479637125139101c_fm_a @ Q3 @ Ys2 ) ) ) ) ).
% filter_cong
thf(fact_824_image__mono,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
=> ( ord_le3275665582123262618c_fm_a @ ( image_4449434806354059013c_fm_a @ F @ A ) @ ( image_4449434806354059013c_fm_a @ F @ B4 ) ) ) ).
% image_mono
thf(fact_825_image__mono,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
=> ( ord_le2931979837777675552c_fm_a @ ( image_4430763730358542731c_fm_a @ F @ A ) @ ( image_4430763730358542731c_fm_a @ F @ B4 ) ) ) ).
% image_mono
thf(fact_826_image__mono,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A @ B4 )
=> ( ord_le3275665582123262618c_fm_a @ ( image_7959425827855735423c_fm_a @ F @ A ) @ ( image_7959425827855735423c_fm_a @ F @ B4 ) ) ) ).
% image_mono
thf(fact_827_image__mono,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A @ B4 )
=> ( ord_le2931979837777675552c_fm_a @ ( image_7387318756023638021c_fm_a @ F @ A ) @ ( image_7387318756023638021c_fm_a @ F @ B4 ) ) ) ).
% image_mono
thf(fact_828_image__subsetI,axiom,
! [A: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ A )
=> ( member6642669571620171971c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le3275665582123262618c_fm_a @ ( image_4449434806354059013c_fm_a @ F @ A ) @ B4 ) ) ).
% image_subsetI
thf(fact_829_image__subsetI,axiom,
! [A: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,B4: set_se5208064806568342746c_fm_a] :
( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ A )
=> ( member536094252920883875c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le7112219575281605754c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) @ B4 ) ) ).
% image_subsetI
thf(fact_830_image__subsetI,axiom,
! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ A )
=> ( member6642669571620171971c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le3275665582123262618c_fm_a @ ( image_3376480847214465317c_fm_a @ F @ A ) @ B4 ) ) ).
% image_subsetI
thf(fact_831_image__subsetI,axiom,
! [A: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ A )
=> ( member6642669571620171971c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le3275665582123262618c_fm_a @ ( image_7959425827855735423c_fm_a @ F @ A ) @ B4 ) ) ).
% image_subsetI
thf(fact_832_image__subsetI,axiom,
! [A: set_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,B4: set_li769143395467472256c_fm_a] :
( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ A )
=> ( member5906877432388582473c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( image_4430763730358542731c_fm_a @ F @ A ) @ B4 ) ) ).
% image_subsetI
thf(fact_833_image__subsetI,axiom,
! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,B4: set_se5208064806568342746c_fm_a] :
( ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ A )
=> ( member536094252920883875c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le7112219575281605754c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) @ B4 ) ) ).
% image_subsetI
thf(fact_834_image__subsetI,axiom,
! [A: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > set_Epistemic_fm_a,B4: set_se5208064806568342746c_fm_a] :
( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ A )
=> ( member536094252920883875c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le7112219575281605754c_fm_a @ ( image_971165786557580383c_fm_a @ F @ A ) @ B4 ) ) ).
% image_subsetI
thf(fact_835_image__subsetI,axiom,
! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > list_Epistemic_fm_a,B4: set_li769143395467472256c_fm_a] :
( ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ A )
=> ( member5906877432388582473c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( image_1284921450708845483c_fm_a @ F @ A ) @ B4 ) ) ).
% image_subsetI
thf(fact_836_image__subsetI,axiom,
! [A: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,B4: set_li769143395467472256c_fm_a] :
( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ A )
=> ( member5906877432388582473c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( image_7387318756023638021c_fm_a @ F @ A ) @ B4 ) ) ).
% image_subsetI
thf(fact_837_image__subsetI,axiom,
! [A: set_Epistemic_fm_a,F: epistemic_fm_a > produc2203834439629243303c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ A )
=> ( member5029746173879296720c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le8222437384497874983c_fm_a @ ( image_6012374219615907858c_fm_a @ F @ A ) @ B4 ) ) ).
% image_subsetI
thf(fact_838_subset__imageE,axiom,
! [B4: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ B4 @ ( image_4449434806354059013c_fm_a @ F @ A ) )
=> ~ ! [C3: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ C3 @ A )
=> ( B4
!= ( image_4449434806354059013c_fm_a @ F @ C3 ) ) ) ) ).
% subset_imageE
thf(fact_839_subset__imageE,axiom,
! [B4: set_Epistemic_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,A: set_li769143395467472256c_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ B4 @ ( image_7959425827855735423c_fm_a @ F @ A ) )
=> ~ ! [C3: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ C3 @ A )
=> ( B4
!= ( image_7959425827855735423c_fm_a @ F @ C3 ) ) ) ) ).
% subset_imageE
thf(fact_840_subset__imageE,axiom,
! [B4: set_li769143395467472256c_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ B4 @ ( image_4430763730358542731c_fm_a @ F @ A ) )
=> ~ ! [C3: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ C3 @ A )
=> ( B4
!= ( image_4430763730358542731c_fm_a @ F @ C3 ) ) ) ) ).
% subset_imageE
thf(fact_841_subset__imageE,axiom,
! [B4: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ B4 @ ( image_7387318756023638021c_fm_a @ F @ A ) )
=> ~ ! [C3: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ C3 @ A )
=> ( B4
!= ( image_7387318756023638021c_fm_a @ F @ C3 ) ) ) ) ).
% subset_imageE
thf(fact_842_image__subset__iff,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( image_4449434806354059013c_fm_a @ F @ A ) @ B4 )
= ( ! [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ A )
=> ( member6642669571620171971c_fm_a @ ( F @ X ) @ B4 ) ) ) ) ).
% image_subset_iff
thf(fact_843_image__subset__iff,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ ( image_7387318756023638021c_fm_a @ F @ A ) @ B4 )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ A )
=> ( member5906877432388582473c_fm_a @ ( F @ X ) @ B4 ) ) ) ) ).
% image_subset_iff
thf(fact_844_image__subset__iff,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,A: set_Epistemic_fm_a,B4: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ ( image_4430763730358542731c_fm_a @ F @ A ) @ B4 )
= ( ! [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ A )
=> ( member5906877432388582473c_fm_a @ ( F @ X ) @ B4 ) ) ) ) ).
% image_subset_iff
thf(fact_845_subset__image__iff,axiom,
! [B4: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ B4 @ ( image_4449434806354059013c_fm_a @ F @ A ) )
= ( ? [AA: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ AA @ A )
& ( B4
= ( image_4449434806354059013c_fm_a @ F @ AA ) ) ) ) ) ).
% subset_image_iff
thf(fact_846_subset__image__iff,axiom,
! [B4: set_Epistemic_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,A: set_li769143395467472256c_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ B4 @ ( image_7959425827855735423c_fm_a @ F @ A ) )
= ( ? [AA: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ AA @ A )
& ( B4
= ( image_7959425827855735423c_fm_a @ F @ AA ) ) ) ) ) ).
% subset_image_iff
thf(fact_847_subset__image__iff,axiom,
! [B4: set_li769143395467472256c_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ B4 @ ( image_4430763730358542731c_fm_a @ F @ A ) )
= ( ? [AA: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ AA @ A )
& ( B4
= ( image_4430763730358542731c_fm_a @ F @ AA ) ) ) ) ) ).
% subset_image_iff
thf(fact_848_subset__image__iff,axiom,
! [B4: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ B4 @ ( image_7387318756023638021c_fm_a @ F @ A ) )
= ( ? [AA: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ AA @ A )
& ( B4
= ( image_7387318756023638021c_fm_a @ F @ AA ) ) ) ) ) ).
% subset_image_iff
thf(fact_849_list_Osel_I3_J,axiom,
! [X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
( ( tl_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
= X22 ) ).
% list.sel(3)
thf(fact_850_list_Osel_I3_J,axiom,
! [X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] :
( ( tl_lis3363300823944467983c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) )
= X22 ) ).
% list.sel(3)
thf(fact_851_list_Osel_I2_J,axiom,
( ( tl_lis3363300823944467983c_fm_a @ nil_li2451196919128234278c_fm_a )
= nil_li2451196919128234278c_fm_a ) ).
% list.sel(2)
thf(fact_852_list_Osel_I2_J,axiom,
( ( tl_set2007602089164433257c_fm_a @ nil_se102576565402781184c_fm_a )
= nil_se102576565402781184c_fm_a ) ).
% list.sel(2)
thf(fact_853_list_Osel_I2_J,axiom,
( ( tl_Epistemic_fm_a @ nil_Epistemic_fm_a )
= nil_Epistemic_fm_a ) ).
% list.sel(2)
thf(fact_854_map__tl,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( map_Ep1988204514693272906c_fm_a @ F @ ( tl_Epistemic_fm_a @ Xs ) )
= ( tl_lis3363300823944467983c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ Xs ) ) ) ).
% map_tl
thf(fact_855_map__tl,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( map_li3080774272885743684c_fm_a @ F @ ( tl_lis3363300823944467983c_fm_a @ Xs ) )
= ( tl_lis3363300823944467983c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ Xs ) ) ) ).
% map_tl
thf(fact_856_map__tl,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( map_li3858915945532548554c_fm_a @ F @ ( tl_lis3363300823944467983c_fm_a @ Xs ) )
= ( tl_lis547664705162099221c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ Xs ) ) ) ).
% map_tl
thf(fact_857_map__tl,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( map_li5516866612190465598c_fm_a @ F @ ( tl_lis3363300823944467983c_fm_a @ Xs ) )
= ( tl_Epistemic_fm_a @ ( map_li5516866612190465598c_fm_a @ F @ Xs ) ) ) ).
% map_tl
thf(fact_858_map__tl,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( map_Ep7084560364594560580c_fm_a @ F @ ( tl_Epistemic_fm_a @ Xs ) )
= ( tl_Epistemic_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs ) ) ) ).
% map_tl
thf(fact_859_image__Collect__subsetI,axiom,
! [P2: epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ! [X2: epistemic_fm_a] :
( ( P2 @ X2 )
=> ( member6642669571620171971c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le3275665582123262618c_fm_a @ ( image_4449434806354059013c_fm_a @ F @ ( collec4904205152690461189c_fm_a @ P2 ) ) @ B4 ) ) ).
% image_Collect_subsetI
thf(fact_860_image__Collect__subsetI,axiom,
! [P2: epistemic_fm_a > $o,F: epistemic_fm_a > set_Epistemic_fm_a,B4: set_se5208064806568342746c_fm_a] :
( ! [X2: epistemic_fm_a] :
( ( P2 @ X2 )
=> ( member536094252920883875c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le7112219575281605754c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ ( collec4904205152690461189c_fm_a @ P2 ) ) @ B4 ) ) ).
% image_Collect_subsetI
thf(fact_861_image__Collect__subsetI,axiom,
! [P2: set_Epistemic_fm_a > $o,F: set_Epistemic_fm_a > epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ! [X2: set_Epistemic_fm_a] :
( ( P2 @ X2 )
=> ( member6642669571620171971c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le3275665582123262618c_fm_a @ ( image_3376480847214465317c_fm_a @ F @ ( collec2519470961442302949c_fm_a @ P2 ) ) @ B4 ) ) ).
% image_Collect_subsetI
thf(fact_862_image__Collect__subsetI,axiom,
! [P2: epistemic_fm_a > $o,F: epistemic_fm_a > list_Epistemic_fm_a,B4: set_li769143395467472256c_fm_a] :
( ! [X2: epistemic_fm_a] :
( ( P2 @ X2 )
=> ( member5906877432388582473c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( image_4430763730358542731c_fm_a @ F @ ( collec4904205152690461189c_fm_a @ P2 ) ) @ B4 ) ) ).
% image_Collect_subsetI
thf(fact_863_image__Collect__subsetI,axiom,
! [P2: set_Epistemic_fm_a > $o,F: set_Epistemic_fm_a > set_Epistemic_fm_a,B4: set_se5208064806568342746c_fm_a] :
( ! [X2: set_Epistemic_fm_a] :
( ( P2 @ X2 )
=> ( member536094252920883875c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le7112219575281605754c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ ( collec2519470961442302949c_fm_a @ P2 ) ) @ B4 ) ) ).
% image_Collect_subsetI
thf(fact_864_image__Collect__subsetI,axiom,
! [P2: list_Epistemic_fm_a > $o,F: list_Epistemic_fm_a > list_Epistemic_fm_a,B4: set_li769143395467472256c_fm_a] :
( ! [X2: list_Epistemic_fm_a] :
( ( P2 @ X2 )
=> ( member5906877432388582473c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( image_7387318756023638021c_fm_a @ F @ ( collec5191077796991884427c_fm_a @ P2 ) ) @ B4 ) ) ).
% image_Collect_subsetI
thf(fact_865_image__Collect__subsetI,axiom,
! [P2: set_Epistemic_fm_a > $o,F: set_Epistemic_fm_a > list_Epistemic_fm_a,B4: set_li769143395467472256c_fm_a] :
( ! [X2: set_Epistemic_fm_a] :
( ( P2 @ X2 )
=> ( member5906877432388582473c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( image_1284921450708845483c_fm_a @ F @ ( collec2519470961442302949c_fm_a @ P2 ) ) @ B4 ) ) ).
% image_Collect_subsetI
thf(fact_866_image__Collect__subsetI,axiom,
! [P2: epistemic_fm_a > $o,F: epistemic_fm_a > produc2203834439629243303c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
( ! [X2: epistemic_fm_a] :
( ( P2 @ X2 )
=> ( member5029746173879296720c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le8222437384497874983c_fm_a @ ( image_6012374219615907858c_fm_a @ F @ ( collec4904205152690461189c_fm_a @ P2 ) ) @ B4 ) ) ).
% image_Collect_subsetI
thf(fact_867_image__Collect__subsetI,axiom,
! [P2: set_Epistemic_fm_a > $o,F: set_Epistemic_fm_a > produc2203834439629243303c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
( ! [X2: set_Epistemic_fm_a] :
( ( P2 @ X2 )
=> ( member5029746173879296720c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le8222437384497874983c_fm_a @ ( image_2216701362236150322c_fm_a @ F @ ( collec2519470961442302949c_fm_a @ P2 ) ) @ B4 ) ) ).
% image_Collect_subsetI
thf(fact_868_image__Collect__subsetI,axiom,
! [P2: epistemic_fm_a > $o,F: epistemic_fm_a > produc5756089960658898087c_fm_a,B4: set_Pr3219225162411408519c_fm_a] :
( ! [X2: epistemic_fm_a] :
( ( P2 @ X2 )
=> ( member3265983909902097104c_fm_a @ ( F @ X2 ) @ B4 ) )
=> ( ord_le8873477448617899047c_fm_a @ ( image_3997668846444615186c_fm_a @ F @ ( collec4904205152690461189c_fm_a @ P2 ) ) @ B4 ) ) ).
% image_Collect_subsetI
thf(fact_869_filter__is__subset,axiom,
! [P2: epistemic_fm_a > $o,Xs: list_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ ( filter7636273809395300631c_fm_a @ P2 @ Xs ) ) @ ( set_Epistemic_fm_a2 @ Xs ) ) ).
% filter_is_subset
thf(fact_870_filter__is__subset,axiom,
! [P2: list_Epistemic_fm_a > $o,Xs: list_l6083326122719238310c_fm_a] : ( ord_le2931979837777675552c_fm_a @ ( set_li8442223810127165109c_fm_a @ ( filter441479637125139101c_fm_a @ P2 @ Xs ) ) @ ( set_li8442223810127165109c_fm_a @ Xs ) ) ).
% filter_is_subset
thf(fact_871_empty__filter__conv,axiom,
! [P2: set_Epistemic_fm_a > $o,Xs: list_s580375451141968640c_fm_a] :
( ( nil_se102576565402781184c_fm_a
= ( filter2620125754611450615c_fm_a @ P2 @ Xs ) )
= ( ! [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( set_se8855941934996405007c_fm_a @ Xs ) )
=> ~ ( P2 @ X ) ) ) ) ).
% empty_filter_conv
thf(fact_872_empty__filter__conv,axiom,
! [P2: list_Epistemic_fm_a > $o,Xs: list_l6083326122719238310c_fm_a] :
( ( nil_li2451196919128234278c_fm_a
= ( filter441479637125139101c_fm_a @ P2 @ Xs ) )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ~ ( P2 @ X ) ) ) ) ).
% empty_filter_conv
thf(fact_873_empty__filter__conv,axiom,
! [P2: epistemic_fm_a > $o,Xs: list_Epistemic_fm_a] :
( ( nil_Epistemic_fm_a
= ( filter7636273809395300631c_fm_a @ P2 @ Xs ) )
= ( ! [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ~ ( P2 @ X ) ) ) ) ).
% empty_filter_conv
thf(fact_874_filter__empty__conv,axiom,
! [P2: set_Epistemic_fm_a > $o,Xs: list_s580375451141968640c_fm_a] :
( ( ( filter2620125754611450615c_fm_a @ P2 @ Xs )
= nil_se102576565402781184c_fm_a )
= ( ! [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ ( set_se8855941934996405007c_fm_a @ Xs ) )
=> ~ ( P2 @ X ) ) ) ) ).
% filter_empty_conv
thf(fact_875_filter__empty__conv,axiom,
! [P2: list_Epistemic_fm_a > $o,Xs: list_l6083326122719238310c_fm_a] :
( ( ( filter441479637125139101c_fm_a @ P2 @ Xs )
= nil_li2451196919128234278c_fm_a )
= ( ! [X: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs ) )
=> ~ ( P2 @ X ) ) ) ) ).
% filter_empty_conv
thf(fact_876_filter__empty__conv,axiom,
! [P2: epistemic_fm_a > $o,Xs: list_Epistemic_fm_a] :
( ( ( filter7636273809395300631c_fm_a @ P2 @ Xs )
= nil_Epistemic_fm_a )
= ( ! [X: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs ) )
=> ~ ( P2 @ X ) ) ) ) ).
% filter_empty_conv
thf(fact_877_image__set,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( image_4430763730358542731c_fm_a @ F @ ( set_Epistemic_fm_a2 @ Xs ) )
= ( set_li8442223810127165109c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ Xs ) ) ) ).
% image_set
thf(fact_878_image__set,axiom,
! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( image_6931812158510582027c_fm_a @ F @ ( set_li8442223810127165109c_fm_a @ Xs ) )
= ( set_li647609056391172027c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ Xs ) ) ) ).
% image_set
thf(fact_879_image__set,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( image_7959425827855735423c_fm_a @ F @ ( set_li8442223810127165109c_fm_a @ Xs ) )
= ( set_Epistemic_fm_a2 @ ( map_li5516866612190465598c_fm_a @ F @ Xs ) ) ) ).
% image_set
thf(fact_880_image__set,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] :
( ( image_7387318756023638021c_fm_a @ F @ ( set_li8442223810127165109c_fm_a @ Xs ) )
= ( set_li8442223810127165109c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ Xs ) ) ) ).
% image_set
thf(fact_881_image__set,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( image_4449434806354059013c_fm_a @ F @ ( set_Epistemic_fm_a2 @ Xs ) )
= ( set_Epistemic_fm_a2 @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs ) ) ) ).
% image_set
thf(fact_882_Nil__tl,axiom,
! [Xs: list_s580375451141968640c_fm_a] :
( ( nil_se102576565402781184c_fm_a
= ( tl_set2007602089164433257c_fm_a @ Xs ) )
= ( ( Xs = nil_se102576565402781184c_fm_a )
| ? [X: set_Epistemic_fm_a] :
( Xs
= ( cons_s4394448069393209776c_fm_a @ X @ nil_se102576565402781184c_fm_a ) ) ) ) ).
% Nil_tl
thf(fact_883_Nil__tl,axiom,
! [Xs: list_l6083326122719238310c_fm_a] :
( ( nil_li2451196919128234278c_fm_a
= ( tl_lis3363300823944467983c_fm_a @ Xs ) )
= ( ( Xs = nil_li2451196919128234278c_fm_a )
| ? [X: list_Epistemic_fm_a] :
( Xs
= ( cons_l8134865115577406678c_fm_a @ X @ nil_li2451196919128234278c_fm_a ) ) ) ) ).
% Nil_tl
thf(fact_884_Nil__tl,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( nil_Epistemic_fm_a
= ( tl_Epistemic_fm_a @ Xs ) )
= ( ( Xs = nil_Epistemic_fm_a )
| ? [X: epistemic_fm_a] :
( Xs
= ( cons_Epistemic_fm_a @ X @ nil_Epistemic_fm_a ) ) ) ) ).
% Nil_tl
thf(fact_885_tl__Nil,axiom,
! [Xs: list_s580375451141968640c_fm_a] :
( ( ( tl_set2007602089164433257c_fm_a @ Xs )
= nil_se102576565402781184c_fm_a )
= ( ( Xs = nil_se102576565402781184c_fm_a )
| ? [X: set_Epistemic_fm_a] :
( Xs
= ( cons_s4394448069393209776c_fm_a @ X @ nil_se102576565402781184c_fm_a ) ) ) ) ).
% tl_Nil
thf(fact_886_tl__Nil,axiom,
! [Xs: list_l6083326122719238310c_fm_a] :
( ( ( tl_lis3363300823944467983c_fm_a @ Xs )
= nil_li2451196919128234278c_fm_a )
= ( ( Xs = nil_li2451196919128234278c_fm_a )
| ? [X: list_Epistemic_fm_a] :
( Xs
= ( cons_l8134865115577406678c_fm_a @ X @ nil_li2451196919128234278c_fm_a ) ) ) ) ).
% tl_Nil
thf(fact_887_tl__Nil,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( ( tl_Epistemic_fm_a @ Xs )
= nil_Epistemic_fm_a )
= ( ( Xs = nil_Epistemic_fm_a )
| ? [X: epistemic_fm_a] :
( Xs
= ( cons_Epistemic_fm_a @ X @ nil_Epistemic_fm_a ) ) ) ) ).
% tl_Nil
thf(fact_888_list_Oset__sel_I2_J,axiom,
! [A2: list_P7917480606449584557c_fm_a,X3: produc5756089960658898087c_fm_a] :
( ( A2 != nil_Pr1848654487927912109c_fm_a )
=> ( ( member3265983909902097104c_fm_a @ X3 @ ( set_Pr5015285182815091004c_fm_a @ ( tl_Pro8821402481993660054c_fm_a @ A2 ) ) )
=> ( member3265983909902097104c_fm_a @ X3 @ ( set_Pr5015285182815091004c_fm_a @ A2 ) ) ) ) ).
% list.set_sel(2)
thf(fact_889_list_Oset__sel_I2_J,axiom,
! [A2: list_P3099032918374241197c_fm_a,X3: produc2203834439629243303c_fm_a] :
( ( A2 != nil_Pr2379126408512758701c_fm_a )
=> ( ( member5029746173879296720c_fm_a @ X3 @ ( set_Pr6083076219314900284c_fm_a @ ( tl_Pro4131336186639185046c_fm_a @ A2 ) ) )
=> ( member5029746173879296720c_fm_a @ X3 @ ( set_Pr6083076219314900284c_fm_a @ A2 ) ) ) ) ).
% list.set_sel(2)
thf(fact_890_list_Oset__sel_I2_J,axiom,
! [A2: list_s580375451141968640c_fm_a,X3: set_Epistemic_fm_a] :
( ( A2 != nil_se102576565402781184c_fm_a )
=> ( ( member536094252920883875c_fm_a @ X3 @ ( set_se8855941934996405007c_fm_a @ ( tl_set2007602089164433257c_fm_a @ A2 ) ) )
=> ( member536094252920883875c_fm_a @ X3 @ ( set_se8855941934996405007c_fm_a @ A2 ) ) ) ) ).
% list.set_sel(2)
thf(fact_891_list_Oset__sel_I2_J,axiom,
! [A2: list_l6083326122719238310c_fm_a,X3: list_Epistemic_fm_a] :
( ( A2 != nil_li2451196919128234278c_fm_a )
=> ( ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ ( tl_lis3363300823944467983c_fm_a @ A2 ) ) )
=> ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ A2 ) ) ) ) ).
% list.set_sel(2)
thf(fact_892_list_Oset__sel_I2_J,axiom,
! [A2: list_Epistemic_fm_a,X3: epistemic_fm_a] :
( ( A2 != nil_Epistemic_fm_a )
=> ( ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ ( tl_Epistemic_fm_a @ A2 ) ) )
=> ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ A2 ) ) ) ) ).
% list.set_sel(2)
thf(fact_893_filter__concat,axiom,
! [P: list_Epistemic_fm_a > $o,Xs: list_l3671048651222332332c_fm_a] :
( ( filter441479637125139101c_fm_a @ P @ ( concat6109960377493484129c_fm_a @ Xs ) )
= ( concat6109960377493484129c_fm_a @ ( map_li8347733892191492164c_fm_a @ ( filter441479637125139101c_fm_a @ P ) @ Xs ) ) ) ).
% filter_concat
thf(fact_894_filter__concat,axiom,
! [P: epistemic_fm_a > $o,Xs: list_l6083326122719238310c_fm_a] :
( ( filter7636273809395300631c_fm_a @ P @ ( concat2780896542826320603c_fm_a @ Xs ) )
= ( concat2780896542826320603c_fm_a @ ( map_li3080774272885743684c_fm_a @ ( filter7636273809395300631c_fm_a @ P ) @ Xs ) ) ) ).
% filter_concat
thf(fact_895_list_Omap__sel_I2_J,axiom,
! [A2: list_s580375451141968640c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a] :
( ( A2 != nil_se102576565402781184c_fm_a )
=> ( ( tl_Epistemic_fm_a @ ( map_se8248101584983471204c_fm_a @ F @ A2 ) )
= ( map_se8248101584983471204c_fm_a @ F @ ( tl_set2007602089164433257c_fm_a @ A2 ) ) ) ) ).
% list.map_sel(2)
thf(fact_896_list_Omap__sel_I2_J,axiom,
! [A2: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a] :
( ( A2 != nil_Epistemic_fm_a )
=> ( ( tl_lis3363300823944467983c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ A2 ) )
= ( map_Ep1988204514693272906c_fm_a @ F @ ( tl_Epistemic_fm_a @ A2 ) ) ) ) ).
% list.map_sel(2)
thf(fact_897_list_Omap__sel_I2_J,axiom,
! [A2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( A2 != nil_li2451196919128234278c_fm_a )
=> ( ( tl_lis3363300823944467983c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ A2 ) )
= ( map_li3080774272885743684c_fm_a @ F @ ( tl_lis3363300823944467983c_fm_a @ A2 ) ) ) ) ).
% list.map_sel(2)
thf(fact_898_list_Omap__sel_I2_J,axiom,
! [A2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( A2 != nil_li2451196919128234278c_fm_a )
=> ( ( tl_lis547664705162099221c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ A2 ) )
= ( map_li3858915945532548554c_fm_a @ F @ ( tl_lis3363300823944467983c_fm_a @ A2 ) ) ) ) ).
% list.map_sel(2)
thf(fact_899_list_Omap__sel_I2_J,axiom,
! [A2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a] :
( ( A2 != nil_li2451196919128234278c_fm_a )
=> ( ( tl_Epistemic_fm_a @ ( map_li5516866612190465598c_fm_a @ F @ A2 ) )
= ( map_li5516866612190465598c_fm_a @ F @ ( tl_lis3363300823944467983c_fm_a @ A2 ) ) ) ) ).
% list.map_sel(2)
thf(fact_900_list_Omap__sel_I2_J,axiom,
! [A2: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
( ( A2 != nil_Epistemic_fm_a )
=> ( ( tl_Epistemic_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ A2 ) )
= ( map_Ep7084560364594560580c_fm_a @ F @ ( tl_Epistemic_fm_a @ A2 ) ) ) ) ).
% list.map_sel(2)
thf(fact_901_tl__def,axiom,
( tl_lis3363300823944467983c_fm_a
= ( case_l116314299590685792c_fm_a @ nil_li2451196919128234278c_fm_a
@ ^ [X213: list_Epistemic_fm_a,X223: list_l6083326122719238310c_fm_a] : X223 ) ) ).
% tl_def
thf(fact_902_tl__def,axiom,
( tl_set2007602089164433257c_fm_a
= ( case_l6572946392233364704c_fm_a @ nil_se102576565402781184c_fm_a
@ ^ [X213: set_Epistemic_fm_a,X223: list_s580375451141968640c_fm_a] : X223 ) ) ).
% tl_def
thf(fact_903_tl__def,axiom,
( tl_Epistemic_fm_a
= ( case_l8442927312758267104c_fm_a @ nil_Epistemic_fm_a
@ ^ [X213: epistemic_fm_a,X223: list_Epistemic_fm_a] : X223 ) ) ).
% tl_def
thf(fact_904_transpose__aux__filter__head,axiom,
! [Xss2: list_l985973790606564998c_fm_a] :
( ( concat2941956077894552763c_fm_a
@ ( map_li1341364954853471300c_fm_a
@ ( case_l6572946392233364704c_fm_a @ nil_se102576565402781184c_fm_a
@ ^ [H2: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_s4394448069393209776c_fm_a @ H2 @ nil_se102576565402781184c_fm_a ) )
@ Xss2 ) )
= ( map_li3594797534415244862c_fm_a @ hd_set2739578467680395621c_fm_a
@ ( filter1974008165531859069c_fm_a
@ ^ [Ys: list_s580375451141968640c_fm_a] : ( Ys != nil_se102576565402781184c_fm_a )
@ Xss2 ) ) ) ).
% transpose_aux_filter_head
thf(fact_905_transpose__aux__filter__head,axiom,
! [Xss2: list_l3671048651222332332c_fm_a] :
( ( concat6109960377493484129c_fm_a
@ ( map_li8347733892191492164c_fm_a
@ ( case_l116314299590685792c_fm_a @ nil_li2451196919128234278c_fm_a
@ ^ [H2: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l8134865115577406678c_fm_a @ H2 @ nil_li2451196919128234278c_fm_a ) )
@ Xss2 ) )
= ( map_li8743910666895923134c_fm_a @ hd_lis6228752984540680715c_fm_a
@ ( filter389827114350055331c_fm_a
@ ^ [Ys: list_l6083326122719238310c_fm_a] : ( Ys != nil_li2451196919128234278c_fm_a )
@ Xss2 ) ) ) ).
% transpose_aux_filter_head
thf(fact_906_transpose__aux__filter__head,axiom,
! [Xss2: list_l6083326122719238310c_fm_a] :
( ( concat2780896542826320603c_fm_a
@ ( map_li3080774272885743684c_fm_a
@ ( case_l8442927312758267104c_fm_a @ nil_Epistemic_fm_a
@ ^ [H2: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_Epistemic_fm_a @ H2 @ nil_Epistemic_fm_a ) )
@ Xss2 ) )
= ( map_li5516866612190465598c_fm_a @ hd_Epistemic_fm_a
@ ( filter441479637125139101c_fm_a
@ ^ [Ys: list_Epistemic_fm_a] : ( Ys != nil_Epistemic_fm_a )
@ Xss2 ) ) ) ).
% transpose_aux_filter_head
thf(fact_907_all__subset__image,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a,P2: set_Epistemic_fm_a > $o] :
( ( ! [B3: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ B3 @ ( image_4449434806354059013c_fm_a @ F @ A ) )
=> ( P2 @ B3 ) ) )
= ( ! [B3: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ B3 @ A )
=> ( P2 @ ( image_4449434806354059013c_fm_a @ F @ B3 ) ) ) ) ) ).
% all_subset_image
thf(fact_908_all__subset__image,axiom,
! [F: list_Epistemic_fm_a > epistemic_fm_a,A: set_li769143395467472256c_fm_a,P2: set_Epistemic_fm_a > $o] :
( ( ! [B3: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ B3 @ ( image_7959425827855735423c_fm_a @ F @ A ) )
=> ( P2 @ B3 ) ) )
= ( ! [B3: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ B3 @ A )
=> ( P2 @ ( image_7959425827855735423c_fm_a @ F @ B3 ) ) ) ) ) ).
% all_subset_image
thf(fact_909_all__subset__image,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,A: set_Epistemic_fm_a,P2: set_li769143395467472256c_fm_a > $o] :
( ( ! [B3: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ B3 @ ( image_4430763730358542731c_fm_a @ F @ A ) )
=> ( P2 @ B3 ) ) )
= ( ! [B3: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ B3 @ A )
=> ( P2 @ ( image_4430763730358542731c_fm_a @ F @ B3 ) ) ) ) ) ).
% all_subset_image
thf(fact_910_all__subset__image,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,P2: set_li769143395467472256c_fm_a > $o] :
( ( ! [B3: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ B3 @ ( image_7387318756023638021c_fm_a @ F @ A ) )
=> ( P2 @ B3 ) ) )
= ( ! [B3: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ B3 @ A )
=> ( P2 @ ( image_7387318756023638021c_fm_a @ F @ B3 ) ) ) ) ) ).
% all_subset_image
thf(fact_911_set__concat,axiom,
! [Xs: list_l6083326122719238310c_fm_a] :
( ( set_Epistemic_fm_a2 @ ( concat2780896542826320603c_fm_a @ Xs ) )
= ( comple7868773486375872231c_fm_a @ ( image_971165786557580383c_fm_a @ set_Epistemic_fm_a2 @ ( set_li8442223810127165109c_fm_a @ Xs ) ) ) ) ).
% set_concat
thf(fact_912_set__concat,axiom,
! [Xs: list_l3671048651222332332c_fm_a] :
( ( set_li8442223810127165109c_fm_a @ ( concat6109960377493484129c_fm_a @ Xs ) )
= ( comple943813931376279277c_fm_a @ ( image_7951968421222759263c_fm_a @ set_li8442223810127165109c_fm_a @ ( set_li647609056391172027c_fm_a @ Xs ) ) ) ) ).
% set_concat
thf(fact_913_subseqs__powset,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( image_971165786557580383c_fm_a @ set_Epistemic_fm_a2 @ ( set_li8442223810127165109c_fm_a @ ( subseq859285839621985007c_fm_a @ Xs ) ) )
= ( pow_Epistemic_fm_a @ ( set_Epistemic_fm_a2 @ Xs ) ) ) ).
% subseqs_powset
thf(fact_914_subseqs__powset,axiom,
! [Xs: list_l6083326122719238310c_fm_a] :
( ( image_7951968421222759263c_fm_a @ set_li8442223810127165109c_fm_a @ ( set_li647609056391172027c_fm_a @ ( subseq3170398737635186805c_fm_a @ Xs ) ) )
= ( pow_li7854932614473680829c_fm_a @ ( set_li8442223810127165109c_fm_a @ Xs ) ) ) ).
% subseqs_powset
thf(fact_915_Pow__iff,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ A @ ( pow_Epistemic_fm_a @ B4 ) )
= ( ord_le3275665582123262618c_fm_a @ A @ B4 ) ) ).
% Pow_iff
thf(fact_916_Pow__iff,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a] :
( ( member2517045796615263401c_fm_a @ A @ ( pow_li7854932614473680829c_fm_a @ B4 ) )
= ( ord_le2931979837777675552c_fm_a @ A @ B4 ) ) ).
% Pow_iff
thf(fact_917_PowI,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
=> ( member536094252920883875c_fm_a @ A @ ( pow_Epistemic_fm_a @ B4 ) ) ) ).
% PowI
thf(fact_918_PowI,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A @ B4 )
=> ( member2517045796615263401c_fm_a @ A @ ( pow_li7854932614473680829c_fm_a @ B4 ) ) ) ).
% PowI
thf(fact_919_hd__Cons__tl,axiom,
! [Xs: list_s580375451141968640c_fm_a] :
( ( Xs != nil_se102576565402781184c_fm_a )
=> ( ( cons_s4394448069393209776c_fm_a @ ( hd_set2739578467680395621c_fm_a @ Xs ) @ ( tl_set2007602089164433257c_fm_a @ Xs ) )
= Xs ) ) ).
% hd_Cons_tl
thf(fact_920_hd__Cons__tl,axiom,
! [Xs: list_l6083326122719238310c_fm_a] :
( ( Xs != nil_li2451196919128234278c_fm_a )
=> ( ( cons_l8134865115577406678c_fm_a @ ( hd_lis6228752984540680715c_fm_a @ Xs ) @ ( tl_lis3363300823944467983c_fm_a @ Xs ) )
= Xs ) ) ).
% hd_Cons_tl
thf(fact_921_hd__Cons__tl,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( Xs != nil_Epistemic_fm_a )
=> ( ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ Xs ) @ ( tl_Epistemic_fm_a @ Xs ) )
= Xs ) ) ).
% hd_Cons_tl
thf(fact_922_list_Ocollapse,axiom,
! [List: list_s580375451141968640c_fm_a] :
( ( List != nil_se102576565402781184c_fm_a )
=> ( ( cons_s4394448069393209776c_fm_a @ ( hd_set2739578467680395621c_fm_a @ List ) @ ( tl_set2007602089164433257c_fm_a @ List ) )
= List ) ) ).
% list.collapse
thf(fact_923_list_Ocollapse,axiom,
! [List: list_l6083326122719238310c_fm_a] :
( ( List != nil_li2451196919128234278c_fm_a )
=> ( ( cons_l8134865115577406678c_fm_a @ ( hd_lis6228752984540680715c_fm_a @ List ) @ ( tl_lis3363300823944467983c_fm_a @ List ) )
= List ) ) ).
% list.collapse
thf(fact_924_list_Ocollapse,axiom,
! [List: list_Epistemic_fm_a] :
( ( List != nil_Epistemic_fm_a )
=> ( ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) )
= List ) ) ).
% list.collapse
thf(fact_925_hd__def,axiom,
( hd_Epistemic_fm_a
= ( case_l5911136813010175462c_fm_a @ undefi6158949259153642370c_fm_a
@ ^ [X213: epistemic_fm_a,X223: list_Epistemic_fm_a] : X213 ) ) ).
% hd_def
thf(fact_926_hd__def,axiom,
( hd_lis6228752984540680715c_fm_a
= ( case_l5930680263517320678c_fm_a @ undefi2327196743408399240c_fm_a
@ ^ [X213: list_Epistemic_fm_a,X223: list_l6083326122719238310c_fm_a] : X213 ) ) ).
% hd_def
thf(fact_927_Pow__mono,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
=> ( ord_le7112219575281605754c_fm_a @ ( pow_Epistemic_fm_a @ A ) @ ( pow_Epistemic_fm_a @ B4 ) ) ) ).
% Pow_mono
thf(fact_928_Pow__mono,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A @ B4 )
=> ( ord_le3241105215597788544c_fm_a @ ( pow_li7854932614473680829c_fm_a @ A ) @ ( pow_li7854932614473680829c_fm_a @ B4 ) ) ) ).
% Pow_mono
thf(fact_929_PowD,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ A @ ( pow_Epistemic_fm_a @ B4 ) )
=> ( ord_le3275665582123262618c_fm_a @ A @ B4 ) ) ).
% PowD
thf(fact_930_PowD,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a] :
( ( member2517045796615263401c_fm_a @ A @ ( pow_li7854932614473680829c_fm_a @ B4 ) )
=> ( ord_le2931979837777675552c_fm_a @ A @ B4 ) ) ).
% PowD
thf(fact_931_list_Osel_I1_J,axiom,
! [X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
( ( hd_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
= X21 ) ).
% list.sel(1)
thf(fact_932_list_Osel_I1_J,axiom,
! [X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] :
( ( hd_lis6228752984540680715c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) )
= X21 ) ).
% list.sel(1)
thf(fact_933_Pow__def,axiom,
( pow_Epistemic_fm_a
= ( ^ [A3: set_Epistemic_fm_a] :
( collec2519470961442302949c_fm_a
@ ^ [B3: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ B3 @ A3 ) ) ) ) ).
% Pow_def
thf(fact_934_Pow__def,axiom,
( pow_li7854932614473680829c_fm_a
= ( ^ [A3: set_li769143395467472256c_fm_a] :
( collec4111825885563579627c_fm_a
@ ^ [B3: set_li769143395467472256c_fm_a] : ( ord_le2931979837777675552c_fm_a @ B3 @ A3 ) ) ) ) ).
% Pow_def
thf(fact_935_hd__concat,axiom,
! [Xs: list_l3671048651222332332c_fm_a] :
( ( Xs != nil_li5178944226519631276c_fm_a )
=> ( ( ( hd_lis1359242352192849937c_fm_a @ Xs )
!= nil_li2451196919128234278c_fm_a )
=> ( ( hd_lis6228752984540680715c_fm_a @ ( concat6109960377493484129c_fm_a @ Xs ) )
= ( hd_lis6228752984540680715c_fm_a @ ( hd_lis1359242352192849937c_fm_a @ Xs ) ) ) ) ) ).
% hd_concat
thf(fact_936_hd__concat,axiom,
! [Xs: list_l985973790606564998c_fm_a] :
( ( Xs != nil_li5433889876484989702c_fm_a )
=> ( ( ( hd_lis8341250705491003371c_fm_a @ Xs )
!= nil_se102576565402781184c_fm_a )
=> ( ( hd_set2739578467680395621c_fm_a @ ( concat2941956077894552763c_fm_a @ Xs ) )
= ( hd_set2739578467680395621c_fm_a @ ( hd_lis8341250705491003371c_fm_a @ Xs ) ) ) ) ) ).
% hd_concat
thf(fact_937_hd__concat,axiom,
! [Xs: list_l6083326122719238310c_fm_a] :
( ( Xs != nil_li2451196919128234278c_fm_a )
=> ( ( ( hd_lis6228752984540680715c_fm_a @ Xs )
!= nil_Epistemic_fm_a )
=> ( ( hd_Epistemic_fm_a @ ( concat2780896542826320603c_fm_a @ Xs ) )
= ( hd_Epistemic_fm_a @ ( hd_lis6228752984540680715c_fm_a @ Xs ) ) ) ) ) ).
% hd_concat
thf(fact_938_image__Pow__mono,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( image_4449434806354059013c_fm_a @ F @ A ) @ B4 )
=> ( ord_le7112219575281605754c_fm_a @ ( image_8582343580727714565c_fm_a @ ( image_4449434806354059013c_fm_a @ F ) @ ( pow_Epistemic_fm_a @ A ) ) @ ( pow_Epistemic_fm_a @ B4 ) ) ) ).
% image_Pow_mono
thf(fact_939_image__Pow__mono,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ ( image_7387318756023638021c_fm_a @ F @ A ) @ B4 )
=> ( ord_le3241105215597788544c_fm_a @ ( image_8805014153957852165c_fm_a @ ( image_7387318756023638021c_fm_a @ F ) @ ( pow_li7854932614473680829c_fm_a @ A ) ) @ ( pow_li7854932614473680829c_fm_a @ B4 ) ) ) ).
% image_Pow_mono
thf(fact_940_image__Pow__mono,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,A: set_Epistemic_fm_a,B4: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ ( image_4430763730358542731c_fm_a @ F @ A ) @ B4 )
=> ( ord_le3241105215597788544c_fm_a @ ( image_4454716909333697547c_fm_a @ ( image_4430763730358542731c_fm_a @ F ) @ ( pow_Epistemic_fm_a @ A ) ) @ ( pow_li7854932614473680829c_fm_a @ B4 ) ) ) ).
% image_Pow_mono
thf(fact_941_list_Oset__sel_I1_J,axiom,
! [A2: list_P7917480606449584557c_fm_a] :
( ( A2 != nil_Pr1848654487927912109c_fm_a )
=> ( member3265983909902097104c_fm_a @ ( hd_Pro993334397642901138c_fm_a @ A2 ) @ ( set_Pr5015285182815091004c_fm_a @ A2 ) ) ) ).
% list.set_sel(1)
thf(fact_942_list_Oset__sel_I1_J,axiom,
! [A2: list_P3099032918374241197c_fm_a] :
( ( A2 != nil_Pr2379126408512758701c_fm_a )
=> ( member5029746173879296720c_fm_a @ ( hd_Pro2014797444510195858c_fm_a @ A2 ) @ ( set_Pr6083076219314900284c_fm_a @ A2 ) ) ) ).
% list.set_sel(1)
thf(fact_943_list_Oset__sel_I1_J,axiom,
! [A2: list_s580375451141968640c_fm_a] :
( ( A2 != nil_se102576565402781184c_fm_a )
=> ( member536094252920883875c_fm_a @ ( hd_set2739578467680395621c_fm_a @ A2 ) @ ( set_se8855941934996405007c_fm_a @ A2 ) ) ) ).
% list.set_sel(1)
thf(fact_944_list_Oset__sel_I1_J,axiom,
! [A2: list_l6083326122719238310c_fm_a] :
( ( A2 != nil_li2451196919128234278c_fm_a )
=> ( member5906877432388582473c_fm_a @ ( hd_lis6228752984540680715c_fm_a @ A2 ) @ ( set_li8442223810127165109c_fm_a @ A2 ) ) ) ).
% list.set_sel(1)
thf(fact_945_list_Oset__sel_I1_J,axiom,
! [A2: list_Epistemic_fm_a] :
( ( A2 != nil_Epistemic_fm_a )
=> ( member6642669571620171971c_fm_a @ ( hd_Epistemic_fm_a @ A2 ) @ ( set_Epistemic_fm_a2 @ A2 ) ) ) ).
% list.set_sel(1)
thf(fact_946_hd__in__set,axiom,
! [Xs: list_P7917480606449584557c_fm_a] :
( ( Xs != nil_Pr1848654487927912109c_fm_a )
=> ( member3265983909902097104c_fm_a @ ( hd_Pro993334397642901138c_fm_a @ Xs ) @ ( set_Pr5015285182815091004c_fm_a @ Xs ) ) ) ).
% hd_in_set
thf(fact_947_hd__in__set,axiom,
! [Xs: list_P3099032918374241197c_fm_a] :
( ( Xs != nil_Pr2379126408512758701c_fm_a )
=> ( member5029746173879296720c_fm_a @ ( hd_Pro2014797444510195858c_fm_a @ Xs ) @ ( set_Pr6083076219314900284c_fm_a @ Xs ) ) ) ).
% hd_in_set
thf(fact_948_hd__in__set,axiom,
! [Xs: list_s580375451141968640c_fm_a] :
( ( Xs != nil_se102576565402781184c_fm_a )
=> ( member536094252920883875c_fm_a @ ( hd_set2739578467680395621c_fm_a @ Xs ) @ ( set_se8855941934996405007c_fm_a @ Xs ) ) ) ).
% hd_in_set
thf(fact_949_hd__in__set,axiom,
! [Xs: list_l6083326122719238310c_fm_a] :
( ( Xs != nil_li2451196919128234278c_fm_a )
=> ( member5906877432388582473c_fm_a @ ( hd_lis6228752984540680715c_fm_a @ Xs ) @ ( set_li8442223810127165109c_fm_a @ Xs ) ) ) ).
% hd_in_set
thf(fact_950_hd__in__set,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( Xs != nil_Epistemic_fm_a )
=> ( member6642669571620171971c_fm_a @ ( hd_Epistemic_fm_a @ Xs ) @ ( set_Epistemic_fm_a2 @ Xs ) ) ) ).
% hd_in_set
thf(fact_951_list_Omap__sel_I1_J,axiom,
! [A2: list_s580375451141968640c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a] :
( ( A2 != nil_se102576565402781184c_fm_a )
=> ( ( hd_Epistemic_fm_a @ ( map_se8248101584983471204c_fm_a @ F @ A2 ) )
= ( F @ ( hd_set2739578467680395621c_fm_a @ A2 ) ) ) ) ).
% list.map_sel(1)
thf(fact_952_list_Omap__sel_I1_J,axiom,
! [A2: list_s580375451141968640c_fm_a,F: set_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( A2 != nil_se102576565402781184c_fm_a )
=> ( ( hd_lis6228752984540680715c_fm_a @ ( map_se6909769656262425450c_fm_a @ F @ A2 ) )
= ( F @ ( hd_set2739578467680395621c_fm_a @ A2 ) ) ) ) ).
% list.map_sel(1)
thf(fact_953_list_Omap__sel_I1_J,axiom,
! [A2: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a] :
( ( A2 != nil_Epistemic_fm_a )
=> ( ( hd_lis6228752984540680715c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ A2 ) )
= ( F @ ( hd_Epistemic_fm_a @ A2 ) ) ) ) ).
% list.map_sel(1)
thf(fact_954_list_Omap__sel_I1_J,axiom,
! [A2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( A2 != nil_li2451196919128234278c_fm_a )
=> ( ( hd_lis6228752984540680715c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ A2 ) )
= ( F @ ( hd_lis6228752984540680715c_fm_a @ A2 ) ) ) ) ).
% list.map_sel(1)
thf(fact_955_list_Omap__sel_I1_J,axiom,
! [A2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( A2 != nil_li2451196919128234278c_fm_a )
=> ( ( hd_lis1359242352192849937c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ A2 ) )
= ( F @ ( hd_lis6228752984540680715c_fm_a @ A2 ) ) ) ) ).
% list.map_sel(1)
thf(fact_956_list_Omap__sel_I1_J,axiom,
! [A2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a] :
( ( A2 != nil_li2451196919128234278c_fm_a )
=> ( ( hd_Epistemic_fm_a @ ( map_li5516866612190465598c_fm_a @ F @ A2 ) )
= ( F @ ( hd_lis6228752984540680715c_fm_a @ A2 ) ) ) ) ).
% list.map_sel(1)
thf(fact_957_list_Omap__sel_I1_J,axiom,
! [A2: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
( ( A2 != nil_Epistemic_fm_a )
=> ( ( hd_Epistemic_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ A2 ) )
= ( F @ ( hd_Epistemic_fm_a @ A2 ) ) ) ) ).
% list.map_sel(1)
thf(fact_958_hd__map,axiom,
! [Xs: list_s580375451141968640c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a] :
( ( Xs != nil_se102576565402781184c_fm_a )
=> ( ( hd_Epistemic_fm_a @ ( map_se8248101584983471204c_fm_a @ F @ Xs ) )
= ( F @ ( hd_set2739578467680395621c_fm_a @ Xs ) ) ) ) ).
% hd_map
thf(fact_959_hd__map,axiom,
! [Xs: list_s580375451141968640c_fm_a,F: set_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( Xs != nil_se102576565402781184c_fm_a )
=> ( ( hd_lis6228752984540680715c_fm_a @ ( map_se6909769656262425450c_fm_a @ F @ Xs ) )
= ( F @ ( hd_set2739578467680395621c_fm_a @ Xs ) ) ) ) ).
% hd_map
thf(fact_960_hd__map,axiom,
! [Xs: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a] :
( ( Xs != nil_Epistemic_fm_a )
=> ( ( hd_lis6228752984540680715c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ Xs ) )
= ( F @ ( hd_Epistemic_fm_a @ Xs ) ) ) ) ).
% hd_map
thf(fact_961_hd__map,axiom,
! [Xs: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( Xs != nil_li2451196919128234278c_fm_a )
=> ( ( hd_lis6228752984540680715c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ Xs ) )
= ( F @ ( hd_lis6228752984540680715c_fm_a @ Xs ) ) ) ) ).
% hd_map
thf(fact_962_hd__map,axiom,
! [Xs: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( Xs != nil_li2451196919128234278c_fm_a )
=> ( ( hd_lis1359242352192849937c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ Xs ) )
= ( F @ ( hd_lis6228752984540680715c_fm_a @ Xs ) ) ) ) ).
% hd_map
thf(fact_963_hd__map,axiom,
! [Xs: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a] :
( ( Xs != nil_li2451196919128234278c_fm_a )
=> ( ( hd_Epistemic_fm_a @ ( map_li5516866612190465598c_fm_a @ F @ Xs ) )
= ( F @ ( hd_lis6228752984540680715c_fm_a @ Xs ) ) ) ) ).
% hd_map
thf(fact_964_hd__map,axiom,
! [Xs: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
( ( Xs != nil_Epistemic_fm_a )
=> ( ( hd_Epistemic_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs ) )
= ( F @ ( hd_Epistemic_fm_a @ Xs ) ) ) ) ).
% hd_map
thf(fact_965_list_Oexpand,axiom,
! [List: list_l6083326122719238310c_fm_a,List2: list_l6083326122719238310c_fm_a] :
( ( ( List = nil_li2451196919128234278c_fm_a )
= ( List2 = nil_li2451196919128234278c_fm_a ) )
=> ( ( ( List != nil_li2451196919128234278c_fm_a )
=> ( ( List2 != nil_li2451196919128234278c_fm_a )
=> ( ( ( hd_lis6228752984540680715c_fm_a @ List )
= ( hd_lis6228752984540680715c_fm_a @ List2 ) )
& ( ( tl_lis3363300823944467983c_fm_a @ List )
= ( tl_lis3363300823944467983c_fm_a @ List2 ) ) ) ) )
=> ( List = List2 ) ) ) ).
% list.expand
thf(fact_966_list_Oexpand,axiom,
! [List: list_s580375451141968640c_fm_a,List2: list_s580375451141968640c_fm_a] :
( ( ( List = nil_se102576565402781184c_fm_a )
= ( List2 = nil_se102576565402781184c_fm_a ) )
=> ( ( ( List != nil_se102576565402781184c_fm_a )
=> ( ( List2 != nil_se102576565402781184c_fm_a )
=> ( ( ( hd_set2739578467680395621c_fm_a @ List )
= ( hd_set2739578467680395621c_fm_a @ List2 ) )
& ( ( tl_set2007602089164433257c_fm_a @ List )
= ( tl_set2007602089164433257c_fm_a @ List2 ) ) ) ) )
=> ( List = List2 ) ) ) ).
% list.expand
thf(fact_967_list_Oexpand,axiom,
! [List: list_Epistemic_fm_a,List2: list_Epistemic_fm_a] :
( ( ( List = nil_Epistemic_fm_a )
= ( List2 = nil_Epistemic_fm_a ) )
=> ( ( ( List != nil_Epistemic_fm_a )
=> ( ( List2 != nil_Epistemic_fm_a )
=> ( ( ( hd_Epistemic_fm_a @ List )
= ( hd_Epistemic_fm_a @ List2 ) )
& ( ( tl_Epistemic_fm_a @ List )
= ( tl_Epistemic_fm_a @ List2 ) ) ) ) )
=> ( List = List2 ) ) ) ).
% list.expand
thf(fact_968_list_Oexhaust__sel,axiom,
! [List: list_s580375451141968640c_fm_a] :
( ( List != nil_se102576565402781184c_fm_a )
=> ( List
= ( cons_s4394448069393209776c_fm_a @ ( hd_set2739578467680395621c_fm_a @ List ) @ ( tl_set2007602089164433257c_fm_a @ List ) ) ) ) ).
% list.exhaust_sel
thf(fact_969_list_Oexhaust__sel,axiom,
! [List: list_l6083326122719238310c_fm_a] :
( ( List != nil_li2451196919128234278c_fm_a )
=> ( List
= ( cons_l8134865115577406678c_fm_a @ ( hd_lis6228752984540680715c_fm_a @ List ) @ ( tl_lis3363300823944467983c_fm_a @ List ) ) ) ) ).
% list.exhaust_sel
thf(fact_970_list_Oexhaust__sel,axiom,
! [List: list_Epistemic_fm_a] :
( ( List != nil_Epistemic_fm_a )
=> ( List
= ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) ) ) ).
% list.exhaust_sel
thf(fact_971_list_Ocase__eq__if,axiom,
( case_l8442927312758267104c_fm_a
= ( ^ [F12: list_Epistemic_fm_a,F23: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,List3: list_Epistemic_fm_a] : ( if_lis2878681784746929638c_fm_a @ ( List3 = nil_Epistemic_fm_a ) @ F12 @ ( F23 @ ( hd_Epistemic_fm_a @ List3 ) @ ( tl_Epistemic_fm_a @ List3 ) ) ) ) ) ).
% list.case_eq_if
thf(fact_972_list_Ocase__eq__if,axiom,
( case_l5707353781634818138c_fm_a
= ( ^ [F12: list_l6083326122719238310c_fm_a,F23: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,List3: list_Epistemic_fm_a] : ( if_lis342421823373228652c_fm_a @ ( List3 = nil_Epistemic_fm_a ) @ F12 @ ( F23 @ ( hd_Epistemic_fm_a @ List3 ) @ ( tl_Epistemic_fm_a @ List3 ) ) ) ) ) ).
% list.case_eq_if
thf(fact_973_list_Ocase__eq__if,axiom,
( case_l2021589626981272552c_fm_a
= ( ^ [F12: $o,F23: epistemic_fm_a > list_Epistemic_fm_a > $o,List3: list_Epistemic_fm_a] :
( ( ( List3 = nil_Epistemic_fm_a )
=> F12 )
& ( ( List3 != nil_Epistemic_fm_a )
=> ( F23 @ ( hd_Epistemic_fm_a @ List3 ) @ ( tl_Epistemic_fm_a @ List3 ) ) ) ) ) ) ).
% list.case_eq_if
thf(fact_974_set__list__bind,axiom,
! [Xs: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a] :
( ( set_Epistemic_fm_a2 @ ( bind_E8451893407412458119c_fm_a @ Xs @ F ) )
= ( comple7868773486375872231c_fm_a
@ ( image_1263732536703906021c_fm_a
@ ^ [X: epistemic_fm_a] : ( set_Epistemic_fm_a2 @ ( F @ X ) )
@ ( set_Epistemic_fm_a2 @ Xs ) ) ) ) ).
% set_list_bind
thf(fact_975_set__list__bind,axiom,
! [Xs: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
( ( set_Epistemic_fm_a2 @ ( bind_l9085712471134790913c_fm_a @ Xs @ F ) )
= ( comple7868773486375872231c_fm_a
@ ( image_971165786557580383c_fm_a
@ ^ [X: list_Epistemic_fm_a] : ( set_Epistemic_fm_a2 @ ( F @ X ) )
@ ( set_li8442223810127165109c_fm_a @ Xs ) ) ) ) ).
% set_list_bind
thf(fact_976_set__list__bind,axiom,
! [Xs: list_Epistemic_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( set_li8442223810127165109c_fm_a @ ( bind_E5557050373637598221c_fm_a @ Xs @ F ) )
= ( comple943813931376279277c_fm_a
@ ( image_2304902010338030059c_fm_a
@ ^ [X: epistemic_fm_a] : ( set_li8442223810127165109c_fm_a @ ( F @ X ) )
@ ( set_Epistemic_fm_a2 @ Xs ) ) ) ) ).
% set_list_bind
thf(fact_977_set__list__bind,axiom,
! [Xs: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
( ( set_li8442223810127165109c_fm_a @ ( bind_l6536575428307499399c_fm_a @ Xs @ F ) )
= ( comple943813931376279277c_fm_a
@ ( image_1280919820078628965c_fm_a
@ ^ [X: list_Epistemic_fm_a] : ( set_li8442223810127165109c_fm_a @ ( F @ X ) )
@ ( set_li8442223810127165109c_fm_a @ Xs ) ) ) ) ).
% set_list_bind
thf(fact_978_list_Osplit__sel__asm,axiom,
! [P2: list_Epistemic_fm_a > $o,F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,List: list_Epistemic_fm_a] :
( ( P2 @ ( case_l8442927312758267104c_fm_a @ F1 @ F22 @ List ) )
= ( ~ ( ( ( List = nil_Epistemic_fm_a )
& ~ ( P2 @ F1 ) )
| ( ( List
= ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) )
& ~ ( P2 @ ( F22 @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) ) ) ) ) ) ).
% list.split_sel_asm
thf(fact_979_list_Osplit__sel__asm,axiom,
! [P2: list_l6083326122719238310c_fm_a > $o,F1: list_l6083326122719238310c_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,List: list_Epistemic_fm_a] :
( ( P2 @ ( case_l5707353781634818138c_fm_a @ F1 @ F22 @ List ) )
= ( ~ ( ( ( List = nil_Epistemic_fm_a )
& ~ ( P2 @ F1 ) )
| ( ( List
= ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) )
& ~ ( P2 @ ( F22 @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) ) ) ) ) ) ).
% list.split_sel_asm
thf(fact_980_list_Osplit__sel__asm,axiom,
! [P2: $o > $o,F1: $o,F22: epistemic_fm_a > list_Epistemic_fm_a > $o,List: list_Epistemic_fm_a] :
( ( P2 @ ( case_l2021589626981272552c_fm_a @ F1 @ F22 @ List ) )
= ( ~ ( ( ( List = nil_Epistemic_fm_a )
& ~ ( P2 @ F1 ) )
| ( ( List
= ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) )
& ~ ( P2 @ ( F22 @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) ) ) ) ) ) ).
% list.split_sel_asm
thf(fact_981_list_Osplit__sel,axiom,
! [P2: list_Epistemic_fm_a > $o,F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,List: list_Epistemic_fm_a] :
( ( P2 @ ( case_l8442927312758267104c_fm_a @ F1 @ F22 @ List ) )
= ( ( ( List = nil_Epistemic_fm_a )
=> ( P2 @ F1 ) )
& ( ( List
= ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) )
=> ( P2 @ ( F22 @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) ) ) ) ) ).
% list.split_sel
thf(fact_982_list_Osplit__sel,axiom,
! [P2: list_l6083326122719238310c_fm_a > $o,F1: list_l6083326122719238310c_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,List: list_Epistemic_fm_a] :
( ( P2 @ ( case_l5707353781634818138c_fm_a @ F1 @ F22 @ List ) )
= ( ( ( List = nil_Epistemic_fm_a )
=> ( P2 @ F1 ) )
& ( ( List
= ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) )
=> ( P2 @ ( F22 @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) ) ) ) ) ).
% list.split_sel
thf(fact_983_list_Osplit__sel,axiom,
! [P2: $o > $o,F1: $o,F22: epistemic_fm_a > list_Epistemic_fm_a > $o,List: list_Epistemic_fm_a] :
( ( P2 @ ( case_l2021589626981272552c_fm_a @ F1 @ F22 @ List ) )
= ( ( ( List = nil_Epistemic_fm_a )
=> ( P2 @ F1 ) )
& ( ( List
= ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) )
=> ( P2 @ ( F22 @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) ) ) ) ) ).
% list.split_sel
thf(fact_984_UN__I,axiom,
! [A2: epistemic_fm_a,A: set_Epistemic_fm_a,B: epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ A2 @ A )
=> ( ( member6642669571620171971c_fm_a @ B @ ( B4 @ A2 ) )
=> ( member6642669571620171971c_fm_a @ B @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ A ) ) ) ) ) ).
% UN_I
thf(fact_985_UN__I,axiom,
! [A2: epistemic_fm_a,A: set_Epistemic_fm_a,B: set_Epistemic_fm_a,B4: epistemic_fm_a > set_se5208064806568342746c_fm_a] :
( ( member6642669571620171971c_fm_a @ A2 @ A )
=> ( ( member536094252920883875c_fm_a @ B @ ( B4 @ A2 ) )
=> ( member536094252920883875c_fm_a @ B @ ( comple7261557488043011271c_fm_a @ ( image_2544827684617158341c_fm_a @ B4 @ A ) ) ) ) ) ).
% UN_I
thf(fact_986_UN__I,axiom,
! [A2: epistemic_fm_a,A: set_Epistemic_fm_a,B: list_Epistemic_fm_a,B4: epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( member6642669571620171971c_fm_a @ A2 @ A )
=> ( ( member5906877432388582473c_fm_a @ B @ ( B4 @ A2 ) )
=> ( member5906877432388582473c_fm_a @ B @ ( comple943813931376279277c_fm_a @ ( image_2304902010338030059c_fm_a @ B4 @ A ) ) ) ) ) ).
% UN_I
thf(fact_987_UN__I,axiom,
! [A2: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,B: epistemic_fm_a,B4: set_Epistemic_fm_a > set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ A2 @ A )
=> ( ( member6642669571620171971c_fm_a @ B @ ( B4 @ A2 ) )
=> ( member6642669571620171971c_fm_a @ B @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ B4 @ A ) ) ) ) ) ).
% UN_I
thf(fact_988_UN__I,axiom,
! [A2: list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,B: epistemic_fm_a,B4: list_Epistemic_fm_a > set_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ A2 @ A )
=> ( ( member6642669571620171971c_fm_a @ B @ ( B4 @ A2 ) )
=> ( member6642669571620171971c_fm_a @ B @ ( comple7868773486375872231c_fm_a @ ( image_971165786557580383c_fm_a @ B4 @ A ) ) ) ) ) ).
% UN_I
thf(fact_989_UN__I,axiom,
! [A2: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,B: set_Epistemic_fm_a,B4: set_Epistemic_fm_a > set_se5208064806568342746c_fm_a] :
( ( member536094252920883875c_fm_a @ A2 @ A )
=> ( ( member536094252920883875c_fm_a @ B @ ( B4 @ A2 ) )
=> ( member536094252920883875c_fm_a @ B @ ( comple7261557488043011271c_fm_a @ ( image_3447524139502481637c_fm_a @ B4 @ A ) ) ) ) ) ).
% UN_I
thf(fact_990_UN__I,axiom,
! [A2: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,B: list_Epistemic_fm_a,B4: set_Epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( member536094252920883875c_fm_a @ A2 @ A )
=> ( ( member5906877432388582473c_fm_a @ B @ ( B4 @ A2 ) )
=> ( member5906877432388582473c_fm_a @ B @ ( comple943813931376279277c_fm_a @ ( image_4454716909333697547c_fm_a @ B4 @ A ) ) ) ) ) ).
% UN_I
thf(fact_991_UN__I,axiom,
! [A2: list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,B: set_Epistemic_fm_a,B4: list_Epistemic_fm_a > set_se5208064806568342746c_fm_a] :
( ( member5906877432388582473c_fm_a @ A2 @ A )
=> ( ( member536094252920883875c_fm_a @ B @ ( B4 @ A2 ) )
=> ( member536094252920883875c_fm_a @ B @ ( comple7261557488043011271c_fm_a @ ( image_1788385642175310399c_fm_a @ B4 @ A ) ) ) ) ) ).
% UN_I
thf(fact_992_UN__I,axiom,
! [A2: list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,B: list_Epistemic_fm_a,B4: list_Epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( member5906877432388582473c_fm_a @ A2 @ A )
=> ( ( member5906877432388582473c_fm_a @ B @ ( B4 @ A2 ) )
=> ( member5906877432388582473c_fm_a @ B @ ( comple943813931376279277c_fm_a @ ( image_1280919820078628965c_fm_a @ B4 @ A ) ) ) ) ) ).
% UN_I
thf(fact_993_UN__I,axiom,
! [A2: epistemic_fm_a,A: set_Epistemic_fm_a,B: produc2203834439629243303c_fm_a,B4: epistemic_fm_a > set_Pr8948481099588399239c_fm_a] :
( ( member6642669571620171971c_fm_a @ A2 @ A )
=> ( ( member5029746173879296720c_fm_a @ B @ ( B4 @ A2 ) )
=> ( member5029746173879296720c_fm_a @ B @ ( comple4943171375639111156c_fm_a @ ( image_9048304998161641714c_fm_a @ B4 @ A ) ) ) ) ) ).
% UN_I
thf(fact_994_SUP__subset__mono,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,G4: epistemic_fm_a > set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
=> ( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) ) @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ G4 @ B4 ) ) ) ) ) ).
% SUP_subset_mono
thf(fact_995_SUP__subset__mono,axiom,
! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,G4: set_Epistemic_fm_a > set_Epistemic_fm_a] :
( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
=> ( ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) ) @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ G4 @ B4 ) ) ) ) ) ).
% SUP_subset_mono
thf(fact_996_SUP__subset__mono,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a > $o,G4: epistemic_fm_a > epistemic_fm_a > $o] :
( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
=> ( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) ) @ ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ G4 @ B4 ) ) ) ) ) ).
% SUP_subset_mono
thf(fact_997_SUP__subset__mono,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,F: epistemic_fm_a > set_li769143395467472256c_fm_a,G4: epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
=> ( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ ( image_2304902010338030059c_fm_a @ F @ A ) ) @ ( comple943813931376279277c_fm_a @ ( image_2304902010338030059c_fm_a @ G4 @ B4 ) ) ) ) ) ).
% SUP_subset_mono
thf(fact_998_SUP__subset__mono,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > set_Epistemic_fm_a,G4: list_Epistemic_fm_a > set_Epistemic_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A @ B4 )
=> ( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_971165786557580383c_fm_a @ F @ A ) ) @ ( comple7868773486375872231c_fm_a @ ( image_971165786557580383c_fm_a @ G4 @ B4 ) ) ) ) ) ).
% SUP_subset_mono
thf(fact_999_SUP__subset__mono,axiom,
! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a > $o,G4: set_Epistemic_fm_a > epistemic_fm_a > $o] :
( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
=> ( ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ F @ A ) ) @ ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ G4 @ B4 ) ) ) ) ) ).
% SUP_subset_mono
thf(fact_1000_SUP__subset__mono,axiom,
! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_li769143395467472256c_fm_a,G4: set_Epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
=> ( ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ ( image_4454716909333697547c_fm_a @ F @ A ) ) @ ( comple943813931376279277c_fm_a @ ( image_4454716909333697547c_fm_a @ G4 @ B4 ) ) ) ) ) ).
% SUP_subset_mono
thf(fact_1001_SUP__subset__mono,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a > $o,G4: list_Epistemic_fm_a > epistemic_fm_a > $o] :
( ( ord_le2931979837777675552c_fm_a @ A @ B4 )
=> ( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_5665756400672781630fm_a_o @ F @ A ) ) @ ( comple310706794042174646fm_a_o @ ( image_5665756400672781630fm_a_o @ G4 @ B4 ) ) ) ) ) ).
% SUP_subset_mono
thf(fact_1002_SUP__subset__mono,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > set_li769143395467472256c_fm_a,G4: list_Epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ A @ B4 )
=> ( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ ( image_1280919820078628965c_fm_a @ F @ A ) ) @ ( comple943813931376279277c_fm_a @ ( image_1280919820078628965c_fm_a @ G4 @ B4 ) ) ) ) ) ).
% SUP_subset_mono
thf(fact_1003_SUP__subset__mono,axiom,
! [A: set_Pr8948481099588399239c_fm_a,B4: set_Pr8948481099588399239c_fm_a,F: produc2203834439629243303c_fm_a > set_Epistemic_fm_a,G4: produc2203834439629243303c_fm_a > set_Epistemic_fm_a] :
( ( ord_le8222437384497874983c_fm_a @ A @ B4 )
=> ( ! [X2: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_2962633504076741144c_fm_a @ F @ A ) ) @ ( comple7868773486375872231c_fm_a @ ( image_2962633504076741144c_fm_a @ G4 @ B4 ) ) ) ) ) ).
% SUP_subset_mono
thf(fact_1004_Sup__set__def,axiom,
( comple943813931376279277c_fm_a
= ( ^ [A3: set_se4933744490392479200c_fm_a] :
( collec5191077796991884427c_fm_a
@ ^ [X: list_Epistemic_fm_a] : ( complete_Sup_Sup_o @ ( image_1196584143029417117fm_a_o @ ( member5906877432388582473c_fm_a @ X ) @ A3 ) ) ) ) ) ).
% Sup_set_def
thf(fact_1005_Sup__set__def,axiom,
( comple465936238348385524c_fm_a
= ( ^ [A3: set_se7763386188871805031c_fm_a] :
( collec6124610372686893330c_fm_a
@ ^ [X: produc5756089960658898087c_fm_a] : ( complete_Sup_Sup_o @ ( image_8674248430498571222fm_a_o @ ( member3265983909902097104c_fm_a @ X ) @ A3 ) ) ) ) ) ).
% Sup_set_def
thf(fact_1006_Sup__set__def,axiom,
( comple4943171375639111156c_fm_a
= ( ^ [A3: set_se299085161135970663c_fm_a] :
( collec7391038856303340306c_fm_a
@ ^ [X: produc2203834439629243303c_fm_a] : ( complete_Sup_Sup_o @ ( image_7450034960710452694fm_a_o @ ( member5029746173879296720c_fm_a @ X ) @ A3 ) ) ) ) ) ).
% Sup_set_def
thf(fact_1007_Sup__set__def,axiom,
( comple7261557488043011271c_fm_a
= ( ^ [A3: set_se8609989359752948410c_fm_a] :
( collec2519470961442302949c_fm_a
@ ^ [X: set_Epistemic_fm_a] : ( complete_Sup_Sup_o @ ( image_5152694684804562371fm_a_o @ ( member536094252920883875c_fm_a @ X ) @ A3 ) ) ) ) ) ).
% Sup_set_def
thf(fact_1008_Sup__set__def,axiom,
( comple7868773486375872231c_fm_a
= ( ^ [A3: set_se5208064806568342746c_fm_a] :
( collec4904205152690461189c_fm_a
@ ^ [X: epistemic_fm_a] : ( complete_Sup_Sup_o @ ( image_3094577733827872675fm_a_o @ ( member6642669571620171971c_fm_a @ X ) @ A3 ) ) ) ) ) ).
% Sup_set_def
thf(fact_1009_SUP__Sup__eq,axiom,
! [S: set_se5208064806568342746c_fm_a] :
( ( comple310706794042174646fm_a_o
@ ( image_6902499629341727256fm_a_o
@ ^ [I3: set_Epistemic_fm_a,X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ I3 )
@ S ) )
= ( ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ ( comple7868773486375872231c_fm_a @ S ) ) ) ) ).
% SUP_Sup_eq
thf(fact_1010_SUP__Sup__eq,axiom,
! [S: set_se8609989359752948410c_fm_a] :
( ( comple5897411722154495702fm_a_o
@ ( image_1826592184436450840fm_a_o
@ ^ [I3: set_se5208064806568342746c_fm_a,X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ I3 )
@ S ) )
= ( ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ ( comple7261557488043011271c_fm_a @ S ) ) ) ) ).
% SUP_Sup_eq
thf(fact_1011_SUP__Sup__eq,axiom,
! [S: set_se4933744490392479200c_fm_a] :
( ( comple1476929635979318832fm_a_o
@ ( image_4891140734946918168fm_a_o
@ ^ [I3: set_li769143395467472256c_fm_a,X: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ X @ I3 )
@ S ) )
= ( ^ [X: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ X @ ( comple943813931376279277c_fm_a @ S ) ) ) ) ).
% SUP_Sup_eq
thf(fact_1012_SUP__Sup__eq,axiom,
! [S: set_se7763386188871805031c_fm_a] :
( ( comple5814866779918804201fm_a_o
@ ( image_932562322207053144fm_a_o
@ ^ [I3: set_Pr3219225162411408519c_fm_a,X: produc5756089960658898087c_fm_a] : ( member3265983909902097104c_fm_a @ X @ I3 )
@ S ) )
= ( ^ [X: produc5756089960658898087c_fm_a] : ( member3265983909902097104c_fm_a @ X @ ( comple465936238348385524c_fm_a @ S ) ) ) ) ).
% SUP_Sup_eq
thf(fact_1013_SUP__Sup__eq,axiom,
! [S: set_se299085161135970663c_fm_a] :
( ( comple351761190663948265fm_a_o
@ ( image_2567633269180325208fm_a_o
@ ^ [I3: set_Pr8948481099588399239c_fm_a,X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ I3 )
@ S ) )
= ( ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ ( comple4943171375639111156c_fm_a @ S ) ) ) ) ).
% SUP_Sup_eq
thf(fact_1014_Inf_OINF__identity__eq,axiom,
! [Inf: set_Epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( Inf
@ ( image_4449434806354059013c_fm_a
@ ^ [X: epistemic_fm_a] : X
@ A ) )
= ( Inf @ A ) ) ).
% Inf.INF_identity_eq
thf(fact_1015_Inf_OINF__identity__eq,axiom,
! [Inf: set_li769143395467472256c_fm_a > list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a] :
( ( Inf
@ ( image_7387318756023638021c_fm_a
@ ^ [X: list_Epistemic_fm_a] : X
@ A ) )
= ( Inf @ A ) ) ).
% Inf.INF_identity_eq
thf(fact_1016_Sup_OSUP__identity__eq,axiom,
! [Sup: set_Epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( Sup
@ ( image_4449434806354059013c_fm_a
@ ^ [X: epistemic_fm_a] : X
@ A ) )
= ( Sup @ A ) ) ).
% Sup.SUP_identity_eq
thf(fact_1017_Sup_OSUP__identity__eq,axiom,
! [Sup: set_li769143395467472256c_fm_a > list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a] :
( ( Sup
@ ( image_7387318756023638021c_fm_a
@ ^ [X: list_Epistemic_fm_a] : X
@ A ) )
= ( Sup @ A ) ) ).
% Sup.SUP_identity_eq
thf(fact_1018_Sup__eqI,axiom,
! [A: set_Epistemic_fm_a_o,X3: epistemic_fm_a > $o] :
( ! [Y2: epistemic_fm_a > $o] :
( ( member4486839677911940090fm_a_o @ Y2 @ A )
=> ( ord_le4043730696559282883fm_a_o @ Y2 @ X3 ) )
=> ( ! [Y2: epistemic_fm_a > $o] :
( ! [Z6: epistemic_fm_a > $o] :
( ( member4486839677911940090fm_a_o @ Z6 @ A )
=> ( ord_le4043730696559282883fm_a_o @ Z6 @ Y2 ) )
=> ( ord_le4043730696559282883fm_a_o @ X3 @ Y2 ) )
=> ( ( comple310706794042174646fm_a_o @ A )
= X3 ) ) ) ).
% Sup_eqI
thf(fact_1019_Sup__eqI,axiom,
! [A: set_se5208064806568342746c_fm_a,X3: set_Epistemic_fm_a] :
( ! [Y2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ Y2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ Y2 @ X3 ) )
=> ( ! [Y2: set_Epistemic_fm_a] :
( ! [Z6: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ Z6 @ A )
=> ( ord_le3275665582123262618c_fm_a @ Z6 @ Y2 ) )
=> ( ord_le3275665582123262618c_fm_a @ X3 @ Y2 ) )
=> ( ( comple7868773486375872231c_fm_a @ A )
= X3 ) ) ) ).
% Sup_eqI
thf(fact_1020_Sup__eqI,axiom,
! [A: set_se4933744490392479200c_fm_a,X3: set_li769143395467472256c_fm_a] :
( ! [Y2: set_li769143395467472256c_fm_a] :
( ( member2517045796615263401c_fm_a @ Y2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ Y2 @ X3 ) )
=> ( ! [Y2: set_li769143395467472256c_fm_a] :
( ! [Z6: set_li769143395467472256c_fm_a] :
( ( member2517045796615263401c_fm_a @ Z6 @ A )
=> ( ord_le2931979837777675552c_fm_a @ Z6 @ Y2 ) )
=> ( ord_le2931979837777675552c_fm_a @ X3 @ Y2 ) )
=> ( ( comple943813931376279277c_fm_a @ A )
= X3 ) ) ) ).
% Sup_eqI
thf(fact_1021_Sup__mono,axiom,
! [A: set_Epistemic_fm_a_o,B4: set_Epistemic_fm_a_o] :
( ! [A5: epistemic_fm_a > $o] :
( ( member4486839677911940090fm_a_o @ A5 @ A )
=> ? [X4: epistemic_fm_a > $o] :
( ( member4486839677911940090fm_a_o @ X4 @ B4 )
& ( ord_le4043730696559282883fm_a_o @ A5 @ X4 ) ) )
=> ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ A ) @ ( comple310706794042174646fm_a_o @ B4 ) ) ) ).
% Sup_mono
thf(fact_1022_Sup__mono,axiom,
! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
( ! [A5: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ A5 @ A )
=> ? [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ B4 )
& ( ord_le3275665582123262618c_fm_a @ A5 @ X4 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ A ) @ ( comple7868773486375872231c_fm_a @ B4 ) ) ) ).
% Sup_mono
thf(fact_1023_Sup__mono,axiom,
! [A: set_se4933744490392479200c_fm_a,B4: set_se4933744490392479200c_fm_a] :
( ! [A5: set_li769143395467472256c_fm_a] :
( ( member2517045796615263401c_fm_a @ A5 @ A )
=> ? [X4: set_li769143395467472256c_fm_a] :
( ( member2517045796615263401c_fm_a @ X4 @ B4 )
& ( ord_le2931979837777675552c_fm_a @ A5 @ X4 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ A ) @ ( comple943813931376279277c_fm_a @ B4 ) ) ) ).
% Sup_mono
thf(fact_1024_Sup__least,axiom,
! [A: set_Epistemic_fm_a_o,Z4: epistemic_fm_a > $o] :
( ! [X2: epistemic_fm_a > $o] :
( ( member4486839677911940090fm_a_o @ X2 @ A )
=> ( ord_le4043730696559282883fm_a_o @ X2 @ Z4 ) )
=> ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ A ) @ Z4 ) ) ).
% Sup_least
thf(fact_1025_Sup__least,axiom,
! [A: set_se5208064806568342746c_fm_a,Z4: set_Epistemic_fm_a] :
( ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ X2 @ Z4 ) )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ A ) @ Z4 ) ) ).
% Sup_least
thf(fact_1026_Sup__least,axiom,
! [A: set_se4933744490392479200c_fm_a,Z4: set_li769143395467472256c_fm_a] :
( ! [X2: set_li769143395467472256c_fm_a] :
( ( member2517045796615263401c_fm_a @ X2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ X2 @ Z4 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ A ) @ Z4 ) ) ).
% Sup_least
thf(fact_1027_Sup__upper,axiom,
! [X3: epistemic_fm_a > $o,A: set_Epistemic_fm_a_o] :
( ( member4486839677911940090fm_a_o @ X3 @ A )
=> ( ord_le4043730696559282883fm_a_o @ X3 @ ( comple310706794042174646fm_a_o @ A ) ) ) ).
% Sup_upper
thf(fact_1028_Sup__upper,axiom,
! [X3: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
( ( member536094252920883875c_fm_a @ X3 @ A )
=> ( ord_le3275665582123262618c_fm_a @ X3 @ ( comple7868773486375872231c_fm_a @ A ) ) ) ).
% Sup_upper
thf(fact_1029_Sup__upper,axiom,
! [X3: set_li769143395467472256c_fm_a,A: set_se4933744490392479200c_fm_a] :
( ( member2517045796615263401c_fm_a @ X3 @ A )
=> ( ord_le2931979837777675552c_fm_a @ X3 @ ( comple943813931376279277c_fm_a @ A ) ) ) ).
% Sup_upper
thf(fact_1030_Sup__le__iff,axiom,
! [A: set_Epistemic_fm_a_o,B: epistemic_fm_a > $o] :
( ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ A ) @ B )
= ( ! [X: epistemic_fm_a > $o] :
( ( member4486839677911940090fm_a_o @ X @ A )
=> ( ord_le4043730696559282883fm_a_o @ X @ B ) ) ) ) ).
% Sup_le_iff
thf(fact_1031_Sup__le__iff,axiom,
! [A: set_se5208064806568342746c_fm_a,B: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ A ) @ B )
= ( ! [X: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X @ A )
=> ( ord_le3275665582123262618c_fm_a @ X @ B ) ) ) ) ).
% Sup_le_iff
thf(fact_1032_Sup__le__iff,axiom,
! [A: set_se4933744490392479200c_fm_a,B: set_li769143395467472256c_fm_a] :
( ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ A ) @ B )
= ( ! [X: set_li769143395467472256c_fm_a] :
( ( member2517045796615263401c_fm_a @ X @ A )
=> ( ord_le2931979837777675552c_fm_a @ X @ B ) ) ) ) ).
% Sup_le_iff
thf(fact_1033_Sup__upper2,axiom,
! [U2: epistemic_fm_a > $o,A: set_Epistemic_fm_a_o,V2: epistemic_fm_a > $o] :
( ( member4486839677911940090fm_a_o @ U2 @ A )
=> ( ( ord_le4043730696559282883fm_a_o @ V2 @ U2 )
=> ( ord_le4043730696559282883fm_a_o @ V2 @ ( comple310706794042174646fm_a_o @ A ) ) ) ) ).
% Sup_upper2
thf(fact_1034_Sup__upper2,axiom,
! [U2: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,V2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ U2 @ A )
=> ( ( ord_le3275665582123262618c_fm_a @ V2 @ U2 )
=> ( ord_le3275665582123262618c_fm_a @ V2 @ ( comple7868773486375872231c_fm_a @ A ) ) ) ) ).
% Sup_upper2
thf(fact_1035_Sup__upper2,axiom,
! [U2: set_li769143395467472256c_fm_a,A: set_se4933744490392479200c_fm_a,V2: set_li769143395467472256c_fm_a] :
( ( member2517045796615263401c_fm_a @ U2 @ A )
=> ( ( ord_le2931979837777675552c_fm_a @ V2 @ U2 )
=> ( ord_le2931979837777675552c_fm_a @ V2 @ ( comple943813931376279277c_fm_a @ A ) ) ) ) ).
% Sup_upper2
thf(fact_1036_Union__subsetI,axiom,
! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
( ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ A )
=> ? [Y6: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ Y6 @ B4 )
& ( ord_le3275665582123262618c_fm_a @ X2 @ Y6 ) ) )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ A ) @ ( comple7868773486375872231c_fm_a @ B4 ) ) ) ).
% Union_subsetI
thf(fact_1037_Union__subsetI,axiom,
! [A: set_se4933744490392479200c_fm_a,B4: set_se4933744490392479200c_fm_a] :
( ! [X2: set_li769143395467472256c_fm_a] :
( ( member2517045796615263401c_fm_a @ X2 @ A )
=> ? [Y6: set_li769143395467472256c_fm_a] :
( ( member2517045796615263401c_fm_a @ Y6 @ B4 )
& ( ord_le2931979837777675552c_fm_a @ X2 @ Y6 ) ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ A ) @ ( comple943813931376279277c_fm_a @ B4 ) ) ) ).
% Union_subsetI
thf(fact_1038_Union__upper,axiom,
! [B4: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
( ( member536094252920883875c_fm_a @ B4 @ A )
=> ( ord_le3275665582123262618c_fm_a @ B4 @ ( comple7868773486375872231c_fm_a @ A ) ) ) ).
% Union_upper
thf(fact_1039_Union__upper,axiom,
! [B4: set_li769143395467472256c_fm_a,A: set_se4933744490392479200c_fm_a] :
( ( member2517045796615263401c_fm_a @ B4 @ A )
=> ( ord_le2931979837777675552c_fm_a @ B4 @ ( comple943813931376279277c_fm_a @ A ) ) ) ).
% Union_upper
thf(fact_1040_Union__least,axiom,
! [A: set_se5208064806568342746c_fm_a,C2: set_Epistemic_fm_a] :
( ! [X6: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X6 @ A )
=> ( ord_le3275665582123262618c_fm_a @ X6 @ C2 ) )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ A ) @ C2 ) ) ).
% Union_least
thf(fact_1041_Union__least,axiom,
! [A: set_se4933744490392479200c_fm_a,C2: set_li769143395467472256c_fm_a] :
( ! [X6: set_li769143395467472256c_fm_a] :
( ( member2517045796615263401c_fm_a @ X6 @ A )
=> ( ord_le2931979837777675552c_fm_a @ X6 @ C2 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ A ) @ C2 ) ) ).
% Union_least
thf(fact_1042_Union__mono,axiom,
! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ A ) @ ( comple7868773486375872231c_fm_a @ B4 ) ) ) ).
% Union_mono
thf(fact_1043_Union__mono,axiom,
! [A: set_se4933744490392479200c_fm_a,B4: set_se4933744490392479200c_fm_a] :
( ( ord_le3241105215597788544c_fm_a @ A @ B4 )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ A ) @ ( comple943813931376279277c_fm_a @ B4 ) ) ) ).
% Union_mono
thf(fact_1044_subset__Pow__Union,axiom,
! [A: set_se5208064806568342746c_fm_a] : ( ord_le7112219575281605754c_fm_a @ A @ ( pow_Epistemic_fm_a @ ( comple7868773486375872231c_fm_a @ A ) ) ) ).
% subset_Pow_Union
thf(fact_1045_image__Union,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,S: set_se5208064806568342746c_fm_a] :
( ( image_4449434806354059013c_fm_a @ F @ ( comple7868773486375872231c_fm_a @ S ) )
= ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ ( image_4449434806354059013c_fm_a @ F ) @ S ) ) ) ).
% image_Union
thf(fact_1046_image__Union,axiom,
! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,S: set_se4933744490392479200c_fm_a] :
( ( image_7387318756023638021c_fm_a @ F @ ( comple943813931376279277c_fm_a @ S ) )
= ( comple943813931376279277c_fm_a @ ( image_8805014153957852165c_fm_a @ ( image_7387318756023638021c_fm_a @ F ) @ S ) ) ) ).
% image_Union
thf(fact_1047_image__Union,axiom,
! [F: epistemic_fm_a > list_Epistemic_fm_a,S: set_se5208064806568342746c_fm_a] :
( ( image_4430763730358542731c_fm_a @ F @ ( comple7868773486375872231c_fm_a @ S ) )
= ( comple943813931376279277c_fm_a @ ( image_4454716909333697547c_fm_a @ ( image_4430763730358542731c_fm_a @ F ) @ S ) ) ) ).
% image_Union
thf(fact_1048_UN__E,axiom,
! [B: epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ B @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ A ) ) )
=> ~ ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ A )
=> ~ ( member6642669571620171971c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).
% UN_E
thf(fact_1049_UN__E,axiom,
! [B: epistemic_fm_a,B4: set_Epistemic_fm_a > set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
( ( member6642669571620171971c_fm_a @ B @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ B4 @ A ) ) )
=> ~ ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ A )
=> ~ ( member6642669571620171971c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).
% UN_E
thf(fact_1050_UN__E,axiom,
! [B: epistemic_fm_a,B4: list_Epistemic_fm_a > set_Epistemic_fm_a,A: set_li769143395467472256c_fm_a] :
( ( member6642669571620171971c_fm_a @ B @ ( comple7868773486375872231c_fm_a @ ( image_971165786557580383c_fm_a @ B4 @ A ) ) )
=> ~ ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ A )
=> ~ ( member6642669571620171971c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).
% UN_E
thf(fact_1051_UN__E,axiom,
! [B: set_Epistemic_fm_a,B4: epistemic_fm_a > set_se5208064806568342746c_fm_a,A: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ B @ ( comple7261557488043011271c_fm_a @ ( image_2544827684617158341c_fm_a @ B4 @ A ) ) )
=> ~ ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ A )
=> ~ ( member536094252920883875c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).
% UN_E
thf(fact_1052_UN__E,axiom,
! [B: list_Epistemic_fm_a,B4: epistemic_fm_a > set_li769143395467472256c_fm_a,A: set_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ B @ ( comple943813931376279277c_fm_a @ ( image_2304902010338030059c_fm_a @ B4 @ A ) ) )
=> ~ ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ A )
=> ~ ( member5906877432388582473c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).
% UN_E
thf(fact_1053_UN__E,axiom,
! [B: set_Epistemic_fm_a,B4: set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,A: set_se5208064806568342746c_fm_a] :
( ( member536094252920883875c_fm_a @ B @ ( comple7261557488043011271c_fm_a @ ( image_3447524139502481637c_fm_a @ B4 @ A ) ) )
=> ~ ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ A )
=> ~ ( member536094252920883875c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).
% UN_E
thf(fact_1054_UN__E,axiom,
! [B: set_Epistemic_fm_a,B4: list_Epistemic_fm_a > set_se5208064806568342746c_fm_a,A: set_li769143395467472256c_fm_a] :
( ( member536094252920883875c_fm_a @ B @ ( comple7261557488043011271c_fm_a @ ( image_1788385642175310399c_fm_a @ B4 @ A ) ) )
=> ~ ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ A )
=> ~ ( member536094252920883875c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).
% UN_E
thf(fact_1055_UN__E,axiom,
! [B: list_Epistemic_fm_a,B4: set_Epistemic_fm_a > set_li769143395467472256c_fm_a,A: set_se5208064806568342746c_fm_a] :
( ( member5906877432388582473c_fm_a @ B @ ( comple943813931376279277c_fm_a @ ( image_4454716909333697547c_fm_a @ B4 @ A ) ) )
=> ~ ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ A )
=> ~ ( member5906877432388582473c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).
% UN_E
thf(fact_1056_UN__E,axiom,
! [B: list_Epistemic_fm_a,B4: list_Epistemic_fm_a > set_li769143395467472256c_fm_a,A: set_li769143395467472256c_fm_a] :
( ( member5906877432388582473c_fm_a @ B @ ( comple943813931376279277c_fm_a @ ( image_1280919820078628965c_fm_a @ B4 @ A ) ) )
=> ~ ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ A )
=> ~ ( member5906877432388582473c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).
% UN_E
thf(fact_1057_UN__E,axiom,
! [B: epistemic_fm_a,B4: produc2203834439629243303c_fm_a > set_Epistemic_fm_a,A: set_Pr8948481099588399239c_fm_a] :
( ( member6642669571620171971c_fm_a @ B @ ( comple7868773486375872231c_fm_a @ ( image_2962633504076741144c_fm_a @ B4 @ A ) ) )
=> ~ ! [X2: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X2 @ A )
=> ~ ( member6642669571620171971c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).
% UN_E
thf(fact_1058_SUP__eq,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,G4: epistemic_fm_a > set_Epistemic_fm_a] :
( ! [I2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I2 @ A )
=> ? [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ B4 )
& ( ord_le3275665582123262618c_fm_a @ ( F @ I2 ) @ ( G4 @ X4 ) ) ) )
=> ( ! [J: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ J @ B4 )
=> ? [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ A )
& ( ord_le3275665582123262618c_fm_a @ ( G4 @ J ) @ ( F @ X4 ) ) ) )
=> ( ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) )
= ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ G4 @ B4 ) ) ) ) ) ).
% SUP_eq
thf(fact_1059_SUP__eq,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a > $o,G4: epistemic_fm_a > epistemic_fm_a > $o] :
( ! [I2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I2 @ A )
=> ? [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ B4 )
& ( ord_le4043730696559282883fm_a_o @ ( F @ I2 ) @ ( G4 @ X4 ) ) ) )
=> ( ! [J: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ J @ B4 )
=> ? [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ A )
& ( ord_le4043730696559282883fm_a_o @ ( G4 @ J ) @ ( F @ X4 ) ) ) )
=> ( ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) )
= ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ G4 @ B4 ) ) ) ) ) ).
% SUP_eq
thf(fact_1060_SUP__eq,axiom,
! [A: set_Epistemic_fm_a,B4: set_se5208064806568342746c_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,G4: set_Epistemic_fm_a > set_Epistemic_fm_a] :
( ! [I2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I2 @ A )
=> ? [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ B4 )
& ( ord_le3275665582123262618c_fm_a @ ( F @ I2 ) @ ( G4 @ X4 ) ) ) )
=> ( ! [J: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ J @ B4 )
=> ? [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ A )
& ( ord_le3275665582123262618c_fm_a @ ( G4 @ J ) @ ( F @ X4 ) ) ) )
=> ( ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) )
= ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ G4 @ B4 ) ) ) ) ) ).
% SUP_eq
thf(fact_1061_SUP__eq,axiom,
! [A: set_Epistemic_fm_a,B4: set_li769143395467472256c_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,G4: list_Epistemic_fm_a > set_Epistemic_fm_a] :
( ! [I2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I2 @ A )
=> ? [X4: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X4 @ B4 )
& ( ord_le3275665582123262618c_fm_a @ ( F @ I2 ) @ ( G4 @ X4 ) ) ) )
=> ( ! [J: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ J @ B4 )
=> ? [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ A )
& ( ord_le3275665582123262618c_fm_a @ ( G4 @ J ) @ ( F @ X4 ) ) ) )
=> ( ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) )
= ( comple7868773486375872231c_fm_a @ ( image_971165786557580383c_fm_a @ G4 @ B4 ) ) ) ) ) ).
% SUP_eq
thf(fact_1062_SUP__eq,axiom,
! [A: set_se5208064806568342746c_fm_a,B4: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,G4: epistemic_fm_a > set_Epistemic_fm_a] :
( ! [I2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ I2 @ A )
=> ? [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ B4 )
& ( ord_le3275665582123262618c_fm_a @ ( F @ I2 ) @ ( G4 @ X4 ) ) ) )
=> ( ! [J: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ J @ B4 )
=> ? [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ A )
& ( ord_le3275665582123262618c_fm_a @ ( G4 @ J ) @ ( F @ X4 ) ) ) )
=> ( ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) )
= ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ G4 @ B4 ) ) ) ) ) ).
% SUP_eq
thf(fact_1063_SUP__eq,axiom,
! [A: set_li769143395467472256c_fm_a,B4: set_Epistemic_fm_a,F: list_Epistemic_fm_a > set_Epistemic_fm_a,G4: epistemic_fm_a > set_Epistemic_fm_a] :
( ! [I2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ I2 @ A )
=> ? [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ B4 )
& ( ord_le3275665582123262618c_fm_a @ ( F @ I2 ) @ ( G4 @ X4 ) ) ) )
=> ( ! [J: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ J @ B4 )
=> ? [X4: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X4 @ A )
& ( ord_le3275665582123262618c_fm_a @ ( G4 @ J ) @ ( F @ X4 ) ) ) )
=> ( ( comple7868773486375872231c_fm_a @ ( image_971165786557580383c_fm_a @ F @ A ) )
= ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ G4 @ B4 ) ) ) ) ) ).
% SUP_eq
thf(fact_1064_SUP__eq,axiom,
! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,F: epistemic_fm_a > set_li769143395467472256c_fm_a,G4: epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ! [I2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I2 @ A )
=> ? [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ B4 )
& ( ord_le2931979837777675552c_fm_a @ ( F @ I2 ) @ ( G4 @ X4 ) ) ) )
=> ( ! [J: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ J @ B4 )
=> ? [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ A )
& ( ord_le2931979837777675552c_fm_a @ ( G4 @ J ) @ ( F @ X4 ) ) ) )
=> ( ( comple943813931376279277c_fm_a @ ( image_2304902010338030059c_fm_a @ F @ A ) )
= ( comple943813931376279277c_fm_a @ ( image_2304902010338030059c_fm_a @ G4 @ B4 ) ) ) ) ) ).
% SUP_eq
thf(fact_1065_SUP__eq,axiom,
! [A: set_Epistemic_fm_a,B4: set_se5208064806568342746c_fm_a,F: epistemic_fm_a > epistemic_fm_a > $o,G4: set_Epistemic_fm_a > epistemic_fm_a > $o] :
( ! [I2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I2 @ A )
=> ? [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ B4 )
& ( ord_le4043730696559282883fm_a_o @ ( F @ I2 ) @ ( G4 @ X4 ) ) ) )
=> ( ! [J: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ J @ B4 )
=> ? [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ A )
& ( ord_le4043730696559282883fm_a_o @ ( G4 @ J ) @ ( F @ X4 ) ) ) )
=> ( ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) )
= ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ G4 @ B4 ) ) ) ) ) ).
% SUP_eq
thf(fact_1066_SUP__eq,axiom,
! [A: set_Epistemic_fm_a,B4: set_li769143395467472256c_fm_a,F: epistemic_fm_a > epistemic_fm_a > $o,G4: list_Epistemic_fm_a > epistemic_fm_a > $o] :
( ! [I2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I2 @ A )
=> ? [X4: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X4 @ B4 )
& ( ord_le4043730696559282883fm_a_o @ ( F @ I2 ) @ ( G4 @ X4 ) ) ) )
=> ( ! [J: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ J @ B4 )
=> ? [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ A )
& ( ord_le4043730696559282883fm_a_o @ ( G4 @ J ) @ ( F @ X4 ) ) ) )
=> ( ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) )
= ( comple310706794042174646fm_a_o @ ( image_5665756400672781630fm_a_o @ G4 @ B4 ) ) ) ) ) ).
% SUP_eq
thf(fact_1067_SUP__eq,axiom,
! [A: set_se5208064806568342746c_fm_a,B4: set_Epistemic_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a > $o,G4: epistemic_fm_a > epistemic_fm_a > $o] :
( ! [I2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ I2 @ A )
=> ? [X4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X4 @ B4 )
& ( ord_le4043730696559282883fm_a_o @ ( F @ I2 ) @ ( G4 @ X4 ) ) ) )
=> ( ! [J: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ J @ B4 )
=> ? [X4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X4 @ A )
& ( ord_le4043730696559282883fm_a_o @ ( G4 @ J ) @ ( F @ X4 ) ) ) )
=> ( ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ F @ A ) )
= ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ G4 @ B4 ) ) ) ) ) ).
% SUP_eq
thf(fact_1068_Sup__subset__mono,axiom,
! [A: set_Epistemic_fm_a_o,B4: set_Epistemic_fm_a_o] :
( ( ord_le4525777775358908921fm_a_o @ A @ B4 )
=> ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ A ) @ ( comple310706794042174646fm_a_o @ B4 ) ) ) ).
% Sup_subset_mono
thf(fact_1069_Sup__subset__mono,axiom,
! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ A ) @ ( comple7868773486375872231c_fm_a @ B4 ) ) ) ).
% Sup_subset_mono
thf(fact_1070_Sup__subset__mono,axiom,
! [A: set_se4933744490392479200c_fm_a,B4: set_se4933744490392479200c_fm_a] :
( ( ord_le3241105215597788544c_fm_a @ A @ B4 )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ A ) @ ( comple943813931376279277c_fm_a @ B4 ) ) ) ).
% Sup_subset_mono
thf(fact_1071_SUP__upper2,axiom,
! [I: epistemic_fm_a,A: set_Epistemic_fm_a,U2: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I @ A )
=> ( ( ord_le3275665582123262618c_fm_a @ U2 @ ( F @ I ) )
=> ( ord_le3275665582123262618c_fm_a @ U2 @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) ) ) ) ) ).
% SUP_upper2
thf(fact_1072_SUP__upper2,axiom,
! [I: epistemic_fm_a,A: set_Epistemic_fm_a,U2: epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a > $o] :
( ( member6642669571620171971c_fm_a @ I @ A )
=> ( ( ord_le4043730696559282883fm_a_o @ U2 @ ( F @ I ) )
=> ( ord_le4043730696559282883fm_a_o @ U2 @ ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) ) ) ) ) ).
% SUP_upper2
thf(fact_1073_SUP__upper2,axiom,
! [I: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,U2: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ I @ A )
=> ( ( ord_le3275665582123262618c_fm_a @ U2 @ ( F @ I ) )
=> ( ord_le3275665582123262618c_fm_a @ U2 @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) ) ) ) ) ).
% SUP_upper2
thf(fact_1074_SUP__upper2,axiom,
! [I: list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,U2: set_Epistemic_fm_a,F: list_Epistemic_fm_a > set_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ I @ A )
=> ( ( ord_le3275665582123262618c_fm_a @ U2 @ ( F @ I ) )
=> ( ord_le3275665582123262618c_fm_a @ U2 @ ( comple7868773486375872231c_fm_a @ ( image_971165786557580383c_fm_a @ F @ A ) ) ) ) ) ).
% SUP_upper2
thf(fact_1075_SUP__upper2,axiom,
! [I: epistemic_fm_a,A: set_Epistemic_fm_a,U2: set_li769143395467472256c_fm_a,F: epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( member6642669571620171971c_fm_a @ I @ A )
=> ( ( ord_le2931979837777675552c_fm_a @ U2 @ ( F @ I ) )
=> ( ord_le2931979837777675552c_fm_a @ U2 @ ( comple943813931376279277c_fm_a @ ( image_2304902010338030059c_fm_a @ F @ A ) ) ) ) ) ).
% SUP_upper2
thf(fact_1076_SUP__upper2,axiom,
! [I: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,U2: epistemic_fm_a > $o,F: set_Epistemic_fm_a > epistemic_fm_a > $o] :
( ( member536094252920883875c_fm_a @ I @ A )
=> ( ( ord_le4043730696559282883fm_a_o @ U2 @ ( F @ I ) )
=> ( ord_le4043730696559282883fm_a_o @ U2 @ ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ F @ A ) ) ) ) ) ).
% SUP_upper2
thf(fact_1077_SUP__upper2,axiom,
! [I: list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,U2: epistemic_fm_a > $o,F: list_Epistemic_fm_a > epistemic_fm_a > $o] :
( ( member5906877432388582473c_fm_a @ I @ A )
=> ( ( ord_le4043730696559282883fm_a_o @ U2 @ ( F @ I ) )
=> ( ord_le4043730696559282883fm_a_o @ U2 @ ( comple310706794042174646fm_a_o @ ( image_5665756400672781630fm_a_o @ F @ A ) ) ) ) ) ).
% SUP_upper2
thf(fact_1078_SUP__upper2,axiom,
! [I: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,U2: set_li769143395467472256c_fm_a,F: set_Epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( member536094252920883875c_fm_a @ I @ A )
=> ( ( ord_le2931979837777675552c_fm_a @ U2 @ ( F @ I ) )
=> ( ord_le2931979837777675552c_fm_a @ U2 @ ( comple943813931376279277c_fm_a @ ( image_4454716909333697547c_fm_a @ F @ A ) ) ) ) ) ).
% SUP_upper2
thf(fact_1079_SUP__upper2,axiom,
! [I: list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,U2: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( member5906877432388582473c_fm_a @ I @ A )
=> ( ( ord_le2931979837777675552c_fm_a @ U2 @ ( F @ I ) )
=> ( ord_le2931979837777675552c_fm_a @ U2 @ ( comple943813931376279277c_fm_a @ ( image_1280919820078628965c_fm_a @ F @ A ) ) ) ) ) ).
% SUP_upper2
thf(fact_1080_SUP__upper2,axiom,
! [I: produc2203834439629243303c_fm_a,A: set_Pr8948481099588399239c_fm_a,U2: set_Epistemic_fm_a,F: produc2203834439629243303c_fm_a > set_Epistemic_fm_a] :
( ( member5029746173879296720c_fm_a @ I @ A )
=> ( ( ord_le3275665582123262618c_fm_a @ U2 @ ( F @ I ) )
=> ( ord_le3275665582123262618c_fm_a @ U2 @ ( comple7868773486375872231c_fm_a @ ( image_2962633504076741144c_fm_a @ F @ A ) ) ) ) ) ).
% SUP_upper2
thf(fact_1081_SUP__upper,axiom,
! [I: epistemic_fm_a,A: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I ) @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) ) ) ) ).
% SUP_upper
thf(fact_1082_SUP__upper,axiom,
! [I: epistemic_fm_a,A: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a > $o] :
( ( member6642669571620171971c_fm_a @ I @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ I ) @ ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) ) ) ) ).
% SUP_upper
thf(fact_1083_SUP__upper,axiom,
! [I: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ I @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I ) @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) ) ) ) ).
% SUP_upper
thf(fact_1084_SUP__upper,axiom,
! [I: list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > set_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ I @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I ) @ ( comple7868773486375872231c_fm_a @ ( image_971165786557580383c_fm_a @ F @ A ) ) ) ) ).
% SUP_upper
thf(fact_1085_SUP__upper,axiom,
! [I: epistemic_fm_a,A: set_Epistemic_fm_a,F: epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( member6642669571620171971c_fm_a @ I @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ I ) @ ( comple943813931376279277c_fm_a @ ( image_2304902010338030059c_fm_a @ F @ A ) ) ) ) ).
% SUP_upper
thf(fact_1086_SUP__upper,axiom,
! [I: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a > $o] :
( ( member536094252920883875c_fm_a @ I @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ I ) @ ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ F @ A ) ) ) ) ).
% SUP_upper
thf(fact_1087_SUP__upper,axiom,
! [I: list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a > $o] :
( ( member5906877432388582473c_fm_a @ I @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ I ) @ ( comple310706794042174646fm_a_o @ ( image_5665756400672781630fm_a_o @ F @ A ) ) ) ) ).
% SUP_upper
thf(fact_1088_SUP__upper,axiom,
! [I: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( member536094252920883875c_fm_a @ I @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ I ) @ ( comple943813931376279277c_fm_a @ ( image_4454716909333697547c_fm_a @ F @ A ) ) ) ) ).
% SUP_upper
thf(fact_1089_SUP__upper,axiom,
! [I: list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( member5906877432388582473c_fm_a @ I @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ I ) @ ( comple943813931376279277c_fm_a @ ( image_1280919820078628965c_fm_a @ F @ A ) ) ) ) ).
% SUP_upper
thf(fact_1090_SUP__upper,axiom,
! [I: produc2203834439629243303c_fm_a,A: set_Pr8948481099588399239c_fm_a,F: produc2203834439629243303c_fm_a > set_Epistemic_fm_a] :
( ( member5029746173879296720c_fm_a @ I @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I ) @ ( comple7868773486375872231c_fm_a @ ( image_2962633504076741144c_fm_a @ F @ A ) ) ) ) ).
% SUP_upper
thf(fact_1091_SUP__least,axiom,
! [A: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,U2: set_Epistemic_fm_a] :
( ! [I2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I2 ) @ U2 ) )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) ) @ U2 ) ) ).
% SUP_least
thf(fact_1092_SUP__least,axiom,
! [A: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a > $o,U2: epistemic_fm_a > $o] :
( ! [I2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I2 @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ I2 ) @ U2 ) )
=> ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) ) @ U2 ) ) ).
% SUP_least
thf(fact_1093_SUP__least,axiom,
! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,U2: set_Epistemic_fm_a] :
( ! [I2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ I2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I2 ) @ U2 ) )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) ) @ U2 ) ) ).
% SUP_least
thf(fact_1094_SUP__least,axiom,
! [A: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > set_Epistemic_fm_a,U2: set_Epistemic_fm_a] :
( ! [I2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ I2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I2 ) @ U2 ) )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_971165786557580383c_fm_a @ F @ A ) ) @ U2 ) ) ).
% SUP_least
thf(fact_1095_SUP__least,axiom,
! [A: set_Epistemic_fm_a,F: epistemic_fm_a > set_li769143395467472256c_fm_a,U2: set_li769143395467472256c_fm_a] :
( ! [I2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ I2 ) @ U2 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ ( image_2304902010338030059c_fm_a @ F @ A ) ) @ U2 ) ) ).
% SUP_least
thf(fact_1096_SUP__least,axiom,
! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a > $o,U2: epistemic_fm_a > $o] :
( ! [I2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ I2 @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ I2 ) @ U2 ) )
=> ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ F @ A ) ) @ U2 ) ) ).
% SUP_least
thf(fact_1097_SUP__least,axiom,
! [A: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a > $o,U2: epistemic_fm_a > $o] :
( ! [I2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ I2 @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ I2 ) @ U2 ) )
=> ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_5665756400672781630fm_a_o @ F @ A ) ) @ U2 ) ) ).
% SUP_least
thf(fact_1098_SUP__least,axiom,
! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_li769143395467472256c_fm_a,U2: set_li769143395467472256c_fm_a] :
( ! [I2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ I2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ I2 ) @ U2 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ ( image_4454716909333697547c_fm_a @ F @ A ) ) @ U2 ) ) ).
% SUP_least
thf(fact_1099_SUP__least,axiom,
! [A: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > set_li769143395467472256c_fm_a,U2: set_li769143395467472256c_fm_a] :
( ! [I2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ I2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ I2 ) @ U2 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ ( image_1280919820078628965c_fm_a @ F @ A ) ) @ U2 ) ) ).
% SUP_least
thf(fact_1100_SUP__least,axiom,
! [A: set_Pr8948481099588399239c_fm_a,F: produc2203834439629243303c_fm_a > set_Epistemic_fm_a,U2: set_Epistemic_fm_a] :
( ! [I2: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ I2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I2 ) @ U2 ) )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_2962633504076741144c_fm_a @ F @ A ) ) @ U2 ) ) ).
% SUP_least
thf(fact_1101_SUP__eqI,axiom,
! [A: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,X3: set_Epistemic_fm_a] :
( ! [I2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I2 ) @ X3 ) )
=> ( ! [Y2: set_Epistemic_fm_a] :
( ! [I4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I4 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I4 ) @ Y2 ) )
=> ( ord_le3275665582123262618c_fm_a @ X3 @ Y2 ) )
=> ( ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) )
= X3 ) ) ) ).
% SUP_eqI
thf(fact_1102_SUP__eqI,axiom,
! [A: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a > $o,X3: epistemic_fm_a > $o] :
( ! [I2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I2 @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ I2 ) @ X3 ) )
=> ( ! [Y2: epistemic_fm_a > $o] :
( ! [I4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I4 @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ I4 ) @ Y2 ) )
=> ( ord_le4043730696559282883fm_a_o @ X3 @ Y2 ) )
=> ( ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) )
= X3 ) ) ) ).
% SUP_eqI
thf(fact_1103_SUP__eqI,axiom,
! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,X3: set_Epistemic_fm_a] :
( ! [I2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ I2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I2 ) @ X3 ) )
=> ( ! [Y2: set_Epistemic_fm_a] :
( ! [I4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ I4 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I4 ) @ Y2 ) )
=> ( ord_le3275665582123262618c_fm_a @ X3 @ Y2 ) )
=> ( ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) )
= X3 ) ) ) ).
% SUP_eqI
thf(fact_1104_SUP__eqI,axiom,
! [A: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > set_Epistemic_fm_a,X3: set_Epistemic_fm_a] :
( ! [I2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ I2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I2 ) @ X3 ) )
=> ( ! [Y2: set_Epistemic_fm_a] :
( ! [I4: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ I4 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I4 ) @ Y2 ) )
=> ( ord_le3275665582123262618c_fm_a @ X3 @ Y2 ) )
=> ( ( comple7868773486375872231c_fm_a @ ( image_971165786557580383c_fm_a @ F @ A ) )
= X3 ) ) ) ).
% SUP_eqI
thf(fact_1105_SUP__eqI,axiom,
! [A: set_Epistemic_fm_a,F: epistemic_fm_a > set_li769143395467472256c_fm_a,X3: set_li769143395467472256c_fm_a] :
( ! [I2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ I2 ) @ X3 ) )
=> ( ! [Y2: set_li769143395467472256c_fm_a] :
( ! [I4: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ I4 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ I4 ) @ Y2 ) )
=> ( ord_le2931979837777675552c_fm_a @ X3 @ Y2 ) )
=> ( ( comple943813931376279277c_fm_a @ ( image_2304902010338030059c_fm_a @ F @ A ) )
= X3 ) ) ) ).
% SUP_eqI
thf(fact_1106_SUP__eqI,axiom,
! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a > $o,X3: epistemic_fm_a > $o] :
( ! [I2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ I2 @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ I2 ) @ X3 ) )
=> ( ! [Y2: epistemic_fm_a > $o] :
( ! [I4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ I4 @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ I4 ) @ Y2 ) )
=> ( ord_le4043730696559282883fm_a_o @ X3 @ Y2 ) )
=> ( ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ F @ A ) )
= X3 ) ) ) ).
% SUP_eqI
thf(fact_1107_SUP__eqI,axiom,
! [A: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a > $o,X3: epistemic_fm_a > $o] :
( ! [I2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ I2 @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ I2 ) @ X3 ) )
=> ( ! [Y2: epistemic_fm_a > $o] :
( ! [I4: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ I4 @ A )
=> ( ord_le4043730696559282883fm_a_o @ ( F @ I4 ) @ Y2 ) )
=> ( ord_le4043730696559282883fm_a_o @ X3 @ Y2 ) )
=> ( ( comple310706794042174646fm_a_o @ ( image_5665756400672781630fm_a_o @ F @ A ) )
= X3 ) ) ) ).
% SUP_eqI
thf(fact_1108_SUP__eqI,axiom,
! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_li769143395467472256c_fm_a,X3: set_li769143395467472256c_fm_a] :
( ! [I2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ I2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ I2 ) @ X3 ) )
=> ( ! [Y2: set_li769143395467472256c_fm_a] :
( ! [I4: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ I4 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ I4 ) @ Y2 ) )
=> ( ord_le2931979837777675552c_fm_a @ X3 @ Y2 ) )
=> ( ( comple943813931376279277c_fm_a @ ( image_4454716909333697547c_fm_a @ F @ A ) )
= X3 ) ) ) ).
% SUP_eqI
thf(fact_1109_SUP__eqI,axiom,
! [A: set_li769143395467472256c_fm_a,F: list_Epistemic_fm_a > set_li769143395467472256c_fm_a,X3: set_li769143395467472256c_fm_a] :
( ! [I2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ I2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ I2 ) @ X3 ) )
=> ( ! [Y2: set_li769143395467472256c_fm_a] :
( ! [I4: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ I4 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( F @ I4 ) @ Y2 ) )
=> ( ord_le2931979837777675552c_fm_a @ X3 @ Y2 ) )
=> ( ( comple943813931376279277c_fm_a @ ( image_1280919820078628965c_fm_a @ F @ A ) )
= X3 ) ) ) ).
% SUP_eqI
thf(fact_1110_SUP__eqI,axiom,
! [A: set_Pr8948481099588399239c_fm_a,F: produc2203834439629243303c_fm_a > set_Epistemic_fm_a,X3: set_Epistemic_fm_a] :
( ! [I2: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ I2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I2 ) @ X3 ) )
=> ( ! [Y2: set_Epistemic_fm_a] :
( ! [I4: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ I4 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( F @ I4 ) @ Y2 ) )
=> ( ord_le3275665582123262618c_fm_a @ X3 @ Y2 ) )
=> ( ( comple7868773486375872231c_fm_a @ ( image_2962633504076741144c_fm_a @ F @ A ) )
= X3 ) ) ) ).
% SUP_eqI
thf(fact_1111_UN__upper,axiom,
! [A2: epistemic_fm_a,A: set_Epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ A2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( B4 @ A2 ) @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ A ) ) ) ) ).
% UN_upper
thf(fact_1112_UN__upper,axiom,
! [A2: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,B4: set_Epistemic_fm_a > set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ A2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( B4 @ A2 ) @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ B4 @ A ) ) ) ) ).
% UN_upper
thf(fact_1113_UN__upper,axiom,
! [A2: list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,B4: list_Epistemic_fm_a > set_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ A2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( B4 @ A2 ) @ ( comple7868773486375872231c_fm_a @ ( image_971165786557580383c_fm_a @ B4 @ A ) ) ) ) ).
% UN_upper
thf(fact_1114_UN__upper,axiom,
! [A2: produc5756089960658898087c_fm_a,A: set_Pr3219225162411408519c_fm_a,B4: produc5756089960658898087c_fm_a > set_Epistemic_fm_a] :
( ( member3265983909902097104c_fm_a @ A2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( B4 @ A2 ) @ ( comple7868773486375872231c_fm_a @ ( image_6064767392369154840c_fm_a @ B4 @ A ) ) ) ) ).
% UN_upper
thf(fact_1115_UN__upper,axiom,
! [A2: produc2203834439629243303c_fm_a,A: set_Pr8948481099588399239c_fm_a,B4: produc2203834439629243303c_fm_a > set_Epistemic_fm_a] :
( ( member5029746173879296720c_fm_a @ A2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( B4 @ A2 ) @ ( comple7868773486375872231c_fm_a @ ( image_2962633504076741144c_fm_a @ B4 @ A ) ) ) ) ).
% UN_upper
thf(fact_1116_UN__upper,axiom,
! [A2: epistemic_fm_a,A: set_Epistemic_fm_a,B4: epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( member6642669571620171971c_fm_a @ A2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( B4 @ A2 ) @ ( comple943813931376279277c_fm_a @ ( image_2304902010338030059c_fm_a @ B4 @ A ) ) ) ) ).
% UN_upper
thf(fact_1117_UN__upper,axiom,
! [A2: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,B4: set_Epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( member536094252920883875c_fm_a @ A2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( B4 @ A2 ) @ ( comple943813931376279277c_fm_a @ ( image_4454716909333697547c_fm_a @ B4 @ A ) ) ) ) ).
% UN_upper
thf(fact_1118_UN__upper,axiom,
! [A2: list_Epistemic_fm_a,A: set_li769143395467472256c_fm_a,B4: list_Epistemic_fm_a > set_li769143395467472256c_fm_a] :
( ( member5906877432388582473c_fm_a @ A2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( B4 @ A2 ) @ ( comple943813931376279277c_fm_a @ ( image_1280919820078628965c_fm_a @ B4 @ A ) ) ) ) ).
% UN_upper
thf(fact_1119_UN__upper,axiom,
! [A2: produc5756089960658898087c_fm_a,A: set_Pr3219225162411408519c_fm_a,B4: produc5756089960658898087c_fm_a > set_li769143395467472256c_fm_a] :
( ( member3265983909902097104c_fm_a @ A2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( B4 @ A2 ) @ ( comple943813931376279277c_fm_a @ ( image_3845426937307473566c_fm_a @ B4 @ A ) ) ) ) ).
% UN_upper
thf(fact_1120_UN__upper,axiom,
! [A2: produc2203834439629243303c_fm_a,A: set_Pr8948481099588399239c_fm_a,B4: produc2203834439629243303c_fm_a > set_li769143395467472256c_fm_a] :
( ( member5029746173879296720c_fm_a @ A2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( B4 @ A2 ) @ ( comple943813931376279277c_fm_a @ ( image_5431830184107165086c_fm_a @ B4 @ A ) ) ) ) ).
% UN_upper
thf(fact_1121_UN__least,axiom,
! [A: set_Pr8948481099588399239c_fm_a,B4: produc2203834439629243303c_fm_a > set_Epistemic_fm_a,C2: set_Epistemic_fm_a] :
( ! [X2: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X2 @ A )
=> ( ord_le3275665582123262618c_fm_a @ ( B4 @ X2 ) @ C2 ) )
=> ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_2962633504076741144c_fm_a @ B4 @ A ) ) @ C2 ) ) ).
% UN_least
thf(fact_1122_UN__least,axiom,
! [A: set_Epistemic_fm_a,B4: epistemic_fm_a > set_li769143395467472256c_fm_a,C2: set_li769143395467472256c_fm_a] :
( ! [X2: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ X2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( B4 @ X2 ) @ C2 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ ( image_2304902010338030059c_fm_a @ B4 @ A ) ) @ C2 ) ) ).
% UN_least
thf(fact_1123_UN__least,axiom,
! [A: set_se5208064806568342746c_fm_a,B4: set_Epistemic_fm_a > set_li769143395467472256c_fm_a,C2: set_li769143395467472256c_fm_a] :
( ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( B4 @ X2 ) @ C2 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ ( image_4454716909333697547c_fm_a @ B4 @ A ) ) @ C2 ) ) ).
% UN_least
thf(fact_1124_UN__least,axiom,
! [A: set_li769143395467472256c_fm_a,B4: list_Epistemic_fm_a > set_li769143395467472256c_fm_a,C2: set_li769143395467472256c_fm_a] :
( ! [X2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ X2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( B4 @ X2 ) @ C2 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ ( image_1280919820078628965c_fm_a @ B4 @ A ) ) @ C2 ) ) ).
% UN_least
thf(fact_1125_UN__least,axiom,
! [A: set_Pr3219225162411408519c_fm_a,B4: produc5756089960658898087c_fm_a > set_li769143395467472256c_fm_a,C2: set_li769143395467472256c_fm_a] :
( ! [X2: produc5756089960658898087c_fm_a] :
( ( member3265983909902097104c_fm_a @ X2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( B4 @ X2 ) @ C2 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ ( image_3845426937307473566c_fm_a @ B4 @ A ) ) @ C2 ) ) ).
% UN_least
thf(fact_1126_UN__least,axiom,
! [A: set_Pr8948481099588399239c_fm_a,B4: produc2203834439629243303c_fm_a > set_li769143395467472256c_fm_a,C2: set_li769143395467472256c_fm_a] :
( ! [X2: produc2203834439629243303c_fm_a] :
( ( member5029746173879296720c_fm_a @ X2 @ A )
=> ( ord_le2931979837777675552c_fm_a @ ( B4 @ X2 ) @ C2 ) )
=> ( ord_le2931979837777675552c_fm_a @ ( comple943813931376279277c_fm_a @ ( image_5431830184107165086c_fm_a @ B4 @ A ) ) @ C2 ) ) ).
% UN_least
thf(fact_1127_Cons__in__shuffles__iff,axiom,
! [Z4: epistemic_fm_a,Zs3: list_Epistemic_fm_a,Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ ( cons_Epistemic_fm_a @ Z4 @ Zs3 ) @ ( shuffl511019022169630517c_fm_a @ Xs @ Ys2 ) )
= ( ( ( Xs != nil_Epistemic_fm_a )
& ( ( hd_Epistemic_fm_a @ Xs )
= Z4 )
& ( member5906877432388582473c_fm_a @ Zs3 @ ( shuffl511019022169630517c_fm_a @ ( tl_Epistemic_fm_a @ Xs ) @ Ys2 ) ) )
| ( ( Ys2 != nil_Epistemic_fm_a )
& ( ( hd_Epistemic_fm_a @ Ys2 )
= Z4 )
& ( member5906877432388582473c_fm_a @ Zs3 @ ( shuffl511019022169630517c_fm_a @ Xs @ ( tl_Epistemic_fm_a @ Ys2 ) ) ) ) ) ) ).
% Cons_in_shuffles_iff
thf(fact_1128_Nil__in__shuffles,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ nil_Epistemic_fm_a @ ( shuffl511019022169630517c_fm_a @ Xs @ Ys2 ) )
= ( ( Xs = nil_Epistemic_fm_a )
& ( Ys2 = nil_Epistemic_fm_a ) ) ) ).
% Nil_in_shuffles
thf(fact_1129_Nil__in__shufflesI,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( Xs = nil_Epistemic_fm_a )
=> ( ( Ys2 = nil_Epistemic_fm_a )
=> ( member5906877432388582473c_fm_a @ nil_Epistemic_fm_a @ ( shuffl511019022169630517c_fm_a @ Xs @ Ys2 ) ) ) ) ).
% Nil_in_shufflesI
thf(fact_1130_shufflesE,axiom,
! [Zs3: list_Epistemic_fm_a,Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ Zs3 @ ( shuffl511019022169630517c_fm_a @ Xs @ Ys2 ) )
=> ( ( ( Zs3 = Xs )
=> ( Ys2 != nil_Epistemic_fm_a ) )
=> ( ( ( Zs3 = Ys2 )
=> ( Xs != nil_Epistemic_fm_a ) )
=> ( ! [X2: epistemic_fm_a,Xs4: list_Epistemic_fm_a] :
( ( Xs
= ( cons_Epistemic_fm_a @ X2 @ Xs4 ) )
=> ! [Z: epistemic_fm_a,Zs4: list_Epistemic_fm_a] :
( ( Zs3
= ( cons_Epistemic_fm_a @ Z @ Zs4 ) )
=> ( ( X2 = Z )
=> ~ ( member5906877432388582473c_fm_a @ Zs4 @ ( shuffl511019022169630517c_fm_a @ Xs4 @ Ys2 ) ) ) ) )
=> ~ ! [Y2: epistemic_fm_a,Ys4: list_Epistemic_fm_a] :
( ( Ys2
= ( cons_Epistemic_fm_a @ Y2 @ Ys4 ) )
=> ! [Z: epistemic_fm_a,Zs4: list_Epistemic_fm_a] :
( ( Zs3
= ( cons_Epistemic_fm_a @ Z @ Zs4 ) )
=> ( ( Y2 = Z )
=> ~ ( member5906877432388582473c_fm_a @ Zs4 @ ( shuffl511019022169630517c_fm_a @ Xs @ Ys4 ) ) ) ) ) ) ) ) ) ).
% shufflesE
thf(fact_1131_empty__Shift,axiom,
! [Kl: set_li769143395467472256c_fm_a,K: epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ nil_Epistemic_fm_a @ Kl )
=> ( ( member6642669571620171971c_fm_a @ K @ ( bNF_Gr1093487135560555701c_fm_a @ Kl @ nil_Epistemic_fm_a ) )
=> ( member5906877432388582473c_fm_a @ nil_Epistemic_fm_a @ ( bNF_Gr8437504134799245625c_fm_a @ Kl @ K ) ) ) ) ).
% empty_Shift
thf(fact_1132_map__lists__mono,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( image_4449434806354059013c_fm_a @ F @ A ) @ B4 )
=> ( ord_le2931979837777675552c_fm_a @ ( image_7387318756023638021c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ ( lists_Epistemic_fm_a @ A ) ) @ ( lists_Epistemic_fm_a @ B4 ) ) ) ).
% map_lists_mono
thf(fact_1133_Nil__in__lists,axiom,
! [A: set_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ nil_Epistemic_fm_a @ ( lists_Epistemic_fm_a @ A ) ) ).
% Nil_in_lists
thf(fact_1134_lists_Osimps,axiom,
! [A2: list_Epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ A2 @ ( lists_Epistemic_fm_a @ A ) )
= ( ( A2 = nil_Epistemic_fm_a )
| ? [A4: epistemic_fm_a,L: list_Epistemic_fm_a] :
( ( A2
= ( cons_Epistemic_fm_a @ A4 @ L ) )
& ( member6642669571620171971c_fm_a @ A4 @ A )
& ( member5906877432388582473c_fm_a @ L @ ( lists_Epistemic_fm_a @ A ) ) ) ) ) ).
% lists.simps
thf(fact_1135_lists_Ocases,axiom,
! [A2: list_Epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( member5906877432388582473c_fm_a @ A2 @ ( lists_Epistemic_fm_a @ A ) )
=> ( ( A2 != nil_Epistemic_fm_a )
=> ~ ! [A5: epistemic_fm_a,L2: list_Epistemic_fm_a] :
( ( A2
= ( cons_Epistemic_fm_a @ A5 @ L2 ) )
=> ( ( member6642669571620171971c_fm_a @ A5 @ A )
=> ~ ( member5906877432388582473c_fm_a @ L2 @ ( lists_Epistemic_fm_a @ A ) ) ) ) ) ) ).
% lists.cases
thf(fact_1136_map__lists__surjective,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
( ( ( image_4449434806354059013c_fm_a @ F @ A )
= B4 )
=> ( ( image_7387318756023638021c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ ( lists_Epistemic_fm_a @ A ) )
= ( lists_Epistemic_fm_a @ B4 ) ) ) ).
% map_lists_surjective
thf(fact_1137_lists__image,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
( ( lists_Epistemic_fm_a @ ( image_4449434806354059013c_fm_a @ F @ A ) )
= ( image_7387318756023638021c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ ( lists_Epistemic_fm_a @ A ) ) ) ).
% lists_image
thf(fact_1138_distinct__adj__Cons,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( distin8123941861610682872c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= ( ( Xs = nil_Epistemic_fm_a )
| ( ( X3
!= ( hd_Epistemic_fm_a @ Xs ) )
& ( distin8123941861610682872c_fm_a @ Xs ) ) ) ) ).
% distinct_adj_Cons
thf(fact_1139_distinct__adj__Nil,axiom,
distin8123941861610682872c_fm_a @ nil_Epistemic_fm_a ).
% distinct_adj_Nil
thf(fact_1140_distinct__adj__mapD,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( distin8123941861610682872c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs ) )
=> ( distin8123941861610682872c_fm_a @ Xs ) ) ).
% distinct_adj_mapD
thf(fact_1141_sorted__wrt_Ocases,axiom,
! [X3: produc7493720319326827993c_fm_a] :
( ! [P6: epistemic_fm_a > epistemic_fm_a > $o] :
( X3
!= ( produc2047528423811058377c_fm_a @ P6 @ nil_Epistemic_fm_a ) )
=> ~ ! [P6: epistemic_fm_a > epistemic_fm_a > $o,X2: epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
( X3
!= ( produc2047528423811058377c_fm_a @ P6 @ ( cons_Epistemic_fm_a @ X2 @ Ys3 ) ) ) ) ).
% sorted_wrt.cases
thf(fact_1142_successively_Ocases,axiom,
! [X3: produc7493720319326827993c_fm_a] :
( ! [P6: epistemic_fm_a > epistemic_fm_a > $o] :
( X3
!= ( produc2047528423811058377c_fm_a @ P6 @ nil_Epistemic_fm_a ) )
=> ( ! [P6: epistemic_fm_a > epistemic_fm_a > $o,X2: epistemic_fm_a] :
( X3
!= ( produc2047528423811058377c_fm_a @ P6 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) )
=> ~ ! [P6: epistemic_fm_a > epistemic_fm_a > $o,X2: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( X3
!= ( produc2047528423811058377c_fm_a @ P6 @ ( cons_Epistemic_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ).
% successively.cases
thf(fact_1143_distinct__adj__singleton,axiom,
! [X3: epistemic_fm_a] : ( distin8123941861610682872c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) ).
% distinct_adj_singleton
thf(fact_1144_append__is__Nil__conv,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( append9179727413925872949c_fm_a @ Xs @ Ys2 )
= nil_Epistemic_fm_a )
= ( ( Xs = nil_Epistemic_fm_a )
& ( Ys2 = nil_Epistemic_fm_a ) ) ) ).
% append_is_Nil_conv
thf(fact_1145_Nil__is__append__conv,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( nil_Epistemic_fm_a
= ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( ( Xs = nil_Epistemic_fm_a )
& ( Ys2 = nil_Epistemic_fm_a ) ) ) ).
% Nil_is_append_conv
thf(fact_1146_self__append__conv2,axiom,
! [Y: list_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( Y
= ( append9179727413925872949c_fm_a @ Xs @ Y ) )
= ( Xs = nil_Epistemic_fm_a ) ) ).
% self_append_conv2
thf(fact_1147_append__self__conv2,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( append9179727413925872949c_fm_a @ Xs @ Ys2 )
= Ys2 )
= ( Xs = nil_Epistemic_fm_a ) ) ).
% append_self_conv2
thf(fact_1148_self__append__conv,axiom,
! [Y: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( Y
= ( append9179727413925872949c_fm_a @ Y @ Ys2 ) )
= ( Ys2 = nil_Epistemic_fm_a ) ) ).
% self_append_conv
thf(fact_1149_append__self__conv,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( append9179727413925872949c_fm_a @ Xs @ Ys2 )
= Xs )
= ( Ys2 = nil_Epistemic_fm_a ) ) ).
% append_self_conv
thf(fact_1150_append__Nil2,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( append9179727413925872949c_fm_a @ Xs @ nil_Epistemic_fm_a )
= Xs ) ).
% append_Nil2
thf(fact_1151_append_Oright__neutral,axiom,
! [A2: list_Epistemic_fm_a] :
( ( append9179727413925872949c_fm_a @ A2 @ nil_Epistemic_fm_a )
= A2 ) ).
% append.right_neutral
thf(fact_1152_map__append,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( map_Ep7084560364594560580c_fm_a @ F @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( append9179727413925872949c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs ) @ ( map_Ep7084560364594560580c_fm_a @ F @ Ys2 ) ) ) ).
% map_append
thf(fact_1153_append1__eq__conv,axiom,
! [Xs: list_Epistemic_fm_a,X3: epistemic_fm_a,Ys2: list_Epistemic_fm_a,Y: epistemic_fm_a] :
( ( ( append9179727413925872949c_fm_a @ Xs @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) )
= ( append9179727413925872949c_fm_a @ Ys2 @ ( cons_Epistemic_fm_a @ Y @ nil_Epistemic_fm_a ) ) )
= ( ( Xs = Ys2 )
& ( X3 = Y ) ) ) ).
% append1_eq_conv
thf(fact_1154_hd__append2,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( Xs != nil_Epistemic_fm_a )
=> ( ( hd_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( hd_Epistemic_fm_a @ Xs ) ) ) ).
% hd_append2
thf(fact_1155_tl__append2,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( Xs != nil_Epistemic_fm_a )
=> ( ( tl_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( append9179727413925872949c_fm_a @ ( tl_Epistemic_fm_a @ Xs ) @ Ys2 ) ) ) ).
% tl_append2
thf(fact_1156_map__eq__append__conv,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a] :
( ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs )
= ( append9179727413925872949c_fm_a @ Ys2 @ Zs3 ) )
= ( ? [Us: list_Epistemic_fm_a,Vs: list_Epistemic_fm_a] :
( ( Xs
= ( append9179727413925872949c_fm_a @ Us @ Vs ) )
& ( Ys2
= ( map_Ep7084560364594560580c_fm_a @ F @ Us ) )
& ( Zs3
= ( map_Ep7084560364594560580c_fm_a @ F @ Vs ) ) ) ) ) ).
% map_eq_append_conv
thf(fact_1157_append__eq__map__conv,axiom,
! [Ys2: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( ( append9179727413925872949c_fm_a @ Ys2 @ Zs3 )
= ( map_Ep7084560364594560580c_fm_a @ F @ Xs ) )
= ( ? [Us: list_Epistemic_fm_a,Vs: list_Epistemic_fm_a] :
( ( Xs
= ( append9179727413925872949c_fm_a @ Us @ Vs ) )
& ( Ys2
= ( map_Ep7084560364594560580c_fm_a @ F @ Us ) )
& ( Zs3
= ( map_Ep7084560364594560580c_fm_a @ F @ Vs ) ) ) ) ) ).
% append_eq_map_conv
thf(fact_1158_eq__Nil__appendI,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( Xs = Ys2 )
=> ( Xs
= ( append9179727413925872949c_fm_a @ nil_Epistemic_fm_a @ Ys2 ) ) ) ).
% eq_Nil_appendI
thf(fact_1159_append_Oleft__neutral,axiom,
! [A2: list_Epistemic_fm_a] :
( ( append9179727413925872949c_fm_a @ nil_Epistemic_fm_a @ A2 )
= A2 ) ).
% append.left_neutral
thf(fact_1160_append__Nil,axiom,
! [Ys2: list_Epistemic_fm_a] :
( ( append9179727413925872949c_fm_a @ nil_Epistemic_fm_a @ Ys2 )
= Ys2 ) ).
% append_Nil
thf(fact_1161_rev__nonempty__induct,axiom,
! [Xs: list_Epistemic_fm_a,P2: list_Epistemic_fm_a > $o] :
( ( Xs != nil_Epistemic_fm_a )
=> ( ! [X2: epistemic_fm_a] : ( P2 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) )
=> ( ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( ( Xs3 != nil_Epistemic_fm_a )
=> ( ( P2 @ Xs3 )
=> ( P2 @ ( append9179727413925872949c_fm_a @ Xs3 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ) ) )
=> ( P2 @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_1162_append__eq__Cons__conv,axiom,
! [Ys2: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a,X3: epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( ( append9179727413925872949c_fm_a @ Ys2 @ Zs3 )
= ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= ( ( ( Ys2 = nil_Epistemic_fm_a )
& ( Zs3
= ( cons_Epistemic_fm_a @ X3 @ Xs ) ) )
| ? [Ys5: list_Epistemic_fm_a] :
( ( Ys2
= ( cons_Epistemic_fm_a @ X3 @ Ys5 ) )
& ( ( append9179727413925872949c_fm_a @ Ys5 @ Zs3 )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_1163_Cons__eq__append__conv,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a] :
( ( ( cons_Epistemic_fm_a @ X3 @ Xs )
= ( append9179727413925872949c_fm_a @ Ys2 @ Zs3 ) )
= ( ( ( Ys2 = nil_Epistemic_fm_a )
& ( ( cons_Epistemic_fm_a @ X3 @ Xs )
= Zs3 ) )
| ? [Ys5: list_Epistemic_fm_a] :
( ( ( cons_Epistemic_fm_a @ X3 @ Ys5 )
= Ys2 )
& ( Xs
= ( append9179727413925872949c_fm_a @ Ys5 @ Zs3 ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_1164_rev__exhaust,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( Xs != nil_Epistemic_fm_a )
=> ~ ! [Ys3: list_Epistemic_fm_a,Y2: epistemic_fm_a] :
( Xs
!= ( append9179727413925872949c_fm_a @ Ys3 @ ( cons_Epistemic_fm_a @ Y2 @ nil_Epistemic_fm_a ) ) ) ) ).
% rev_exhaust
thf(fact_1165_rev__induct,axiom,
! [P2: list_Epistemic_fm_a > $o,Xs: list_Epistemic_fm_a] :
( ( P2 @ nil_Epistemic_fm_a )
=> ( ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( ( P2 @ Xs3 )
=> ( P2 @ ( append9179727413925872949c_fm_a @ Xs3 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ) )
=> ( P2 @ Xs ) ) ) ).
% rev_induct
thf(fact_1166_concat__eq__append__conv,axiom,
! [Xss2: list_l6083326122719238310c_fm_a,Ys2: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a] :
( ( ( concat2780896542826320603c_fm_a @ Xss2 )
= ( append9179727413925872949c_fm_a @ Ys2 @ Zs3 ) )
= ( ( ( Xss2 = nil_li2451196919128234278c_fm_a )
=> ( ( Ys2 = nil_Epistemic_fm_a )
& ( Zs3 = nil_Epistemic_fm_a ) ) )
& ( ( Xss2 != nil_li2451196919128234278c_fm_a )
=> ? [Xss1: list_l6083326122719238310c_fm_a,Xs2: list_Epistemic_fm_a,Xs5: list_Epistemic_fm_a,Xss22: list_l6083326122719238310c_fm_a] :
( ( Xss2
= ( append1384085151619559355c_fm_a @ Xss1 @ ( cons_l8134865115577406678c_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Xs5 ) @ Xss22 ) ) )
& ( Ys2
= ( append9179727413925872949c_fm_a @ ( concat2780896542826320603c_fm_a @ Xss1 ) @ Xs2 ) )
& ( Zs3
= ( append9179727413925872949c_fm_a @ Xs5 @ ( concat2780896542826320603c_fm_a @ Xss22 ) ) ) ) ) ) ) ).
% concat_eq_append_conv
thf(fact_1167_shuffles_Ocases,axiom,
! [X3: produc5756089960658898087c_fm_a] :
( ! [Ys3: list_Epistemic_fm_a] :
( X3
!= ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Ys3 ) )
=> ( ! [Xs3: list_Epistemic_fm_a] :
( X3
!= ( produc6057521592714631063c_fm_a @ Xs3 @ nil_Epistemic_fm_a ) )
=> ~ ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Y2: epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
( X3
!= ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) ) ) ) ) ).
% shuffles.cases
thf(fact_1168_splice_Ocases,axiom,
! [X3: produc5756089960658898087c_fm_a] :
( ! [Ys3: list_Epistemic_fm_a] :
( X3
!= ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Ys3 ) )
=> ~ ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
( X3
!= ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ Ys3 ) ) ) ).
% splice.cases
thf(fact_1169_longest__common__prefix,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
? [Ps3: list_Epistemic_fm_a,Xs4: list_Epistemic_fm_a,Ys4: list_Epistemic_fm_a] :
( ( Xs
= ( append9179727413925872949c_fm_a @ Ps3 @ Xs4 ) )
& ( Ys2
= ( append9179727413925872949c_fm_a @ Ps3 @ Ys4 ) )
& ( ( Xs4 = nil_Epistemic_fm_a )
| ( Ys4 = nil_Epistemic_fm_a )
| ( ( hd_Epistemic_fm_a @ Xs4 )
!= ( hd_Epistemic_fm_a @ Ys4 ) ) ) ) ).
% longest_common_prefix
thf(fact_1170_hd__append,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( Xs = nil_Epistemic_fm_a )
=> ( ( hd_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( hd_Epistemic_fm_a @ Ys2 ) ) )
& ( ( Xs != nil_Epistemic_fm_a )
=> ( ( hd_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( hd_Epistemic_fm_a @ Xs ) ) ) ) ).
% hd_append
thf(fact_1171_tl__append__if,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( Xs = nil_Epistemic_fm_a )
=> ( ( tl_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( tl_Epistemic_fm_a @ Ys2 ) ) )
& ( ( Xs != nil_Epistemic_fm_a )
=> ( ( tl_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( append9179727413925872949c_fm_a @ ( tl_Epistemic_fm_a @ Xs ) @ Ys2 ) ) ) ) ).
% tl_append_if
thf(fact_1172_SuccI,axiom,
! [Kl2: list_Epistemic_fm_a,K: epistemic_fm_a,Kl: set_li769143395467472256c_fm_a] :
( ( member5906877432388582473c_fm_a @ ( append9179727413925872949c_fm_a @ Kl2 @ ( cons_Epistemic_fm_a @ K @ nil_Epistemic_fm_a ) ) @ Kl )
=> ( member6642669571620171971c_fm_a @ K @ ( bNF_Gr1093487135560555701c_fm_a @ Kl @ Kl2 ) ) ) ).
% SuccI
thf(fact_1173_SuccD,axiom,
! [K: epistemic_fm_a,Kl: set_li769143395467472256c_fm_a,Kl2: list_Epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ K @ ( bNF_Gr1093487135560555701c_fm_a @ Kl @ Kl2 ) )
=> ( member5906877432388582473c_fm_a @ ( append9179727413925872949c_fm_a @ Kl2 @ ( cons_Epistemic_fm_a @ K @ nil_Epistemic_fm_a ) ) @ Kl ) ) ).
% SuccD
thf(fact_1174_Succ__def,axiom,
( bNF_Gr1093487135560555701c_fm_a
= ( ^ [Kl3: set_li769143395467472256c_fm_a,Kl4: list_Epistemic_fm_a] :
( collec4904205152690461189c_fm_a
@ ^ [K2: epistemic_fm_a] : ( member5906877432388582473c_fm_a @ ( append9179727413925872949c_fm_a @ Kl4 @ ( cons_Epistemic_fm_a @ K2 @ nil_Epistemic_fm_a ) ) @ Kl3 ) ) ) ) ).
% Succ_def
thf(fact_1175_rotate1__hd__tl,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( Xs != nil_Epistemic_fm_a )
=> ( ( rotate3540958558250653293c_fm_a @ Xs )
= ( append9179727413925872949c_fm_a @ ( tl_Epistemic_fm_a @ Xs ) @ ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ Xs ) @ nil_Epistemic_fm_a ) ) ) ) ).
% rotate1_hd_tl
thf(fact_1176_distinct__adj__append__iff,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( distin8123941861610682872c_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( ( distin8123941861610682872c_fm_a @ Xs )
& ( distin8123941861610682872c_fm_a @ Ys2 )
& ( ( Xs = nil_Epistemic_fm_a )
| ( Ys2 = nil_Epistemic_fm_a )
| ( ( last_Epistemic_fm_a @ Xs )
!= ( hd_Epistemic_fm_a @ Ys2 ) ) ) ) ) ).
% distinct_adj_append_iff
thf(fact_1177_rotate1__is__Nil__conv,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( ( rotate3540958558250653293c_fm_a @ Xs )
= nil_Epistemic_fm_a )
= ( Xs = nil_Epistemic_fm_a ) ) ).
% rotate1_is_Nil_conv
thf(fact_1178_last__appendR,axiom,
! [Ys2: list_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( Ys2 != nil_Epistemic_fm_a )
=> ( ( last_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( last_Epistemic_fm_a @ Ys2 ) ) ) ).
% last_appendR
thf(fact_1179_last__appendL,axiom,
! [Ys2: list_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( Ys2 = nil_Epistemic_fm_a )
=> ( ( last_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( last_Epistemic_fm_a @ Xs ) ) ) ).
% last_appendL
thf(fact_1180_last__snoc,axiom,
! [Xs: list_Epistemic_fm_a,X3: epistemic_fm_a] :
( ( last_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) )
= X3 ) ).
% last_snoc
thf(fact_1181_rotate1_Osimps_I1_J,axiom,
( ( rotate3540958558250653293c_fm_a @ nil_Epistemic_fm_a )
= nil_Epistemic_fm_a ) ).
% rotate1.simps(1)
thf(fact_1182_rotate1__map,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( rotate3540958558250653293c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs ) )
= ( map_Ep7084560364594560580c_fm_a @ F @ ( rotate3540958558250653293c_fm_a @ Xs ) ) ) ).
% rotate1_map
thf(fact_1183_last_Osimps,axiom,
! [Xs: list_Epistemic_fm_a,X3: epistemic_fm_a] :
( ( ( Xs = nil_Epistemic_fm_a )
=> ( ( last_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= X3 ) )
& ( ( Xs != nil_Epistemic_fm_a )
=> ( ( last_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= ( last_Epistemic_fm_a @ Xs ) ) ) ) ).
% last.simps
thf(fact_1184_last__ConsL,axiom,
! [Xs: list_Epistemic_fm_a,X3: epistemic_fm_a] :
( ( Xs = nil_Epistemic_fm_a )
=> ( ( last_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= X3 ) ) ).
% last_ConsL
thf(fact_1185_last__ConsR,axiom,
! [Xs: list_Epistemic_fm_a,X3: epistemic_fm_a] :
( ( Xs != nil_Epistemic_fm_a )
=> ( ( last_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= ( last_Epistemic_fm_a @ Xs ) ) ) ).
% last_ConsR
thf(fact_1186_last__in__set,axiom,
! [As: list_Epistemic_fm_a] :
( ( As != nil_Epistemic_fm_a )
=> ( member6642669571620171971c_fm_a @ ( last_Epistemic_fm_a @ As ) @ ( set_Epistemic_fm_a2 @ As ) ) ) ).
% last_in_set
thf(fact_1187_last__map,axiom,
! [Xs: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
( ( Xs != nil_Epistemic_fm_a )
=> ( ( last_Epistemic_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs ) )
= ( F @ ( last_Epistemic_fm_a @ Xs ) ) ) ) ).
% last_map
thf(fact_1188_longest__common__suffix,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
? [Ss: list_Epistemic_fm_a,Xs4: list_Epistemic_fm_a,Ys4: list_Epistemic_fm_a] :
( ( Xs
= ( append9179727413925872949c_fm_a @ Xs4 @ Ss ) )
& ( Ys2
= ( append9179727413925872949c_fm_a @ Ys4 @ Ss ) )
& ( ( Xs4 = nil_Epistemic_fm_a )
| ( Ys4 = nil_Epistemic_fm_a )
| ( ( last_Epistemic_fm_a @ Xs4 )
!= ( last_Epistemic_fm_a @ Ys4 ) ) ) ) ).
% longest_common_suffix
thf(fact_1189_last__append,axiom,
! [Ys2: list_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( ( Ys2 = nil_Epistemic_fm_a )
=> ( ( last_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( last_Epistemic_fm_a @ Xs ) ) )
& ( ( Ys2 != nil_Epistemic_fm_a )
=> ( ( last_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( last_Epistemic_fm_a @ Ys2 ) ) ) ) ).
% last_append
thf(fact_1190_hd__Nil__eq__last,axiom,
( ( hd_Epistemic_fm_a @ nil_Epistemic_fm_a )
= ( last_Epistemic_fm_a @ nil_Epistemic_fm_a ) ) ).
% hd_Nil_eq_last
thf(fact_1191_last__tl,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( ( Xs = nil_Epistemic_fm_a )
| ( ( tl_Epistemic_fm_a @ Xs )
!= nil_Epistemic_fm_a ) )
=> ( ( last_Epistemic_fm_a @ ( tl_Epistemic_fm_a @ Xs ) )
= ( last_Epistemic_fm_a @ Xs ) ) ) ).
% last_tl
thf(fact_1192_rotate1_Osimps_I2_J,axiom,
! [X3: epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( rotate3540958558250653293c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= ( append9179727413925872949c_fm_a @ Xs @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) ) ).
% rotate1.simps(2)
thf(fact_1193_append__butlast__last__id,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( Xs != nil_Epistemic_fm_a )
=> ( ( append9179727413925872949c_fm_a @ ( butlas2200625790165101420c_fm_a @ Xs ) @ ( cons_Epistemic_fm_a @ ( last_Epistemic_fm_a @ Xs ) @ nil_Epistemic_fm_a ) )
= Xs ) ) ).
% append_butlast_last_id
thf(fact_1194_splice_Opinduct,axiom,
! [A0: list_Epistemic_fm_a,A1: list_Epistemic_fm_a,P2: list_Epistemic_fm_a > list_Epistemic_fm_a > $o] :
( ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ A0 @ A1 ) )
=> ( ! [Ys3: list_Epistemic_fm_a] :
( ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Ys3 ) )
=> ( P2 @ nil_Epistemic_fm_a @ Ys3 ) )
=> ( ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
( ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ Ys3 ) )
=> ( ( P2 @ Ys3 @ Xs3 )
=> ( P2 @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ Ys3 ) ) )
=> ( P2 @ A0 @ A1 ) ) ) ) ).
% splice.pinduct
thf(fact_1195_snoc__listrel1__snoc__iff,axiom,
! [Xs: list_Epistemic_fm_a,X3: epistemic_fm_a,Ys2: list_Epistemic_fm_a,Y: epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) @ ( append9179727413925872949c_fm_a @ Ys2 @ ( cons_Epistemic_fm_a @ Y @ nil_Epistemic_fm_a ) ) ) @ ( listre1262483926937514105c_fm_a @ R ) )
= ( ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs @ Ys2 ) @ ( listre1262483926937514105c_fm_a @ R ) )
& ( X3 = Y ) )
| ( ( Xs = Ys2 )
& ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X3 @ Y ) @ R ) ) ) ) ).
% snoc_listrel1_snoc_iff
thf(fact_1196_butlast__snoc,axiom,
! [Xs: list_Epistemic_fm_a,X3: epistemic_fm_a] :
( ( butlas2200625790165101420c_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) )
= Xs ) ).
% butlast_snoc
thf(fact_1197_butlast_Osimps_I1_J,axiom,
( ( butlas2200625790165101420c_fm_a @ nil_Epistemic_fm_a )
= nil_Epistemic_fm_a ) ).
% butlast.simps(1)
thf(fact_1198_map__butlast,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( map_Ep7084560364594560580c_fm_a @ F @ ( butlas2200625790165101420c_fm_a @ Xs ) )
= ( butlas2200625790165101420c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs ) ) ) ).
% map_butlast
thf(fact_1199_not__Nil__listrel1,axiom,
! [Xs: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
~ ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Xs ) @ ( listre1262483926937514105c_fm_a @ R ) ) ).
% not_Nil_listrel1
thf(fact_1200_not__listrel1__Nil,axiom,
! [Xs: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
~ ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs @ nil_Epistemic_fm_a ) @ ( listre1262483926937514105c_fm_a @ R ) ) ).
% not_listrel1_Nil
thf(fact_1201_butlast_Osimps_I2_J,axiom,
! [Xs: list_Epistemic_fm_a,X3: epistemic_fm_a] :
( ( ( Xs = nil_Epistemic_fm_a )
=> ( ( butlas2200625790165101420c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= nil_Epistemic_fm_a ) )
& ( ( Xs != nil_Epistemic_fm_a )
=> ( ( butlas2200625790165101420c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= ( cons_Epistemic_fm_a @ X3 @ ( butlas2200625790165101420c_fm_a @ Xs ) ) ) ) ) ).
% butlast.simps(2)
thf(fact_1202_butlast__append,axiom,
! [Ys2: list_Epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( ( Ys2 = nil_Epistemic_fm_a )
=> ( ( butlas2200625790165101420c_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( butlas2200625790165101420c_fm_a @ Xs ) ) )
& ( ( Ys2 != nil_Epistemic_fm_a )
=> ( ( butlas2200625790165101420c_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( append9179727413925872949c_fm_a @ Xs @ ( butlas2200625790165101420c_fm_a @ Ys2 ) ) ) ) ) ).
% butlast_append
thf(fact_1203_snoc__eq__iff__butlast,axiom,
! [Xs: list_Epistemic_fm_a,X3: epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( append9179727413925872949c_fm_a @ Xs @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) )
= Ys2 )
= ( ( Ys2 != nil_Epistemic_fm_a )
& ( ( butlas2200625790165101420c_fm_a @ Ys2 )
= Xs )
& ( ( last_Epistemic_fm_a @ Ys2 )
= X3 ) ) ) ).
% snoc_eq_iff_butlast
thf(fact_1204_splice_Opelims,axiom,
! [X3: list_Epistemic_fm_a,Xa: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
( ( ( splice5109564810699471347c_fm_a @ X3 @ Xa )
= Y )
=> ( ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ X3 @ Xa ) )
=> ( ( ( X3 = nil_Epistemic_fm_a )
=> ( ( Y = Xa )
=> ~ ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Xa ) ) ) )
=> ~ ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( ( X3
= ( cons_Epistemic_fm_a @ X2 @ Xs3 ) )
=> ( ( Y
= ( cons_Epistemic_fm_a @ X2 @ ( splice5109564810699471347c_fm_a @ Xa @ Xs3 ) ) )
=> ~ ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ Xa ) ) ) ) ) ) ) ).
% splice.pelims
thf(fact_1205_shuffles_Opinduct,axiom,
! [A0: list_Epistemic_fm_a,A1: list_Epistemic_fm_a,P2: list_Epistemic_fm_a > list_Epistemic_fm_a > $o] :
( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ A0 @ A1 ) )
=> ( ! [Ys3: list_Epistemic_fm_a] :
( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Ys3 ) )
=> ( P2 @ nil_Epistemic_fm_a @ Ys3 ) )
=> ( ! [Xs3: list_Epistemic_fm_a] :
( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs3 @ nil_Epistemic_fm_a ) )
=> ( P2 @ Xs3 @ nil_Epistemic_fm_a ) )
=> ( ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Y2: epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) ) )
=> ( ( P2 @ Xs3 @ ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) )
=> ( ( P2 @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ Ys3 )
=> ( P2 @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) ) ) ) )
=> ( P2 @ A0 @ A1 ) ) ) ) ) ).
% shuffles.pinduct
thf(fact_1206_splice_Opsimps_I1_J,axiom,
! [Ys2: list_Epistemic_fm_a] :
( ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Ys2 ) )
=> ( ( splice5109564810699471347c_fm_a @ nil_Epistemic_fm_a @ Ys2 )
= Ys2 ) ) ).
% splice.psimps(1)
thf(fact_1207_split__Nil__iff,axiom,
! [Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( ( splice5109564810699471347c_fm_a @ Xs @ Ys2 )
= nil_Epistemic_fm_a )
= ( ( Xs = nil_Epistemic_fm_a )
& ( Ys2 = nil_Epistemic_fm_a ) ) ) ).
% split_Nil_iff
thf(fact_1208_splice__Nil2,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( splice5109564810699471347c_fm_a @ Xs @ nil_Epistemic_fm_a )
= Xs ) ).
% splice_Nil2
thf(fact_1209_splice_Osimps_I1_J,axiom,
! [Ys2: list_Epistemic_fm_a] :
( ( splice5109564810699471347c_fm_a @ nil_Epistemic_fm_a @ Ys2 )
= Ys2 ) ).
% splice.simps(1)
thf(fact_1210_splice_Oelims,axiom,
! [X3: list_Epistemic_fm_a,Xa: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
( ( ( splice5109564810699471347c_fm_a @ X3 @ Xa )
= Y )
=> ( ( ( X3 = nil_Epistemic_fm_a )
=> ( Y != Xa ) )
=> ~ ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( ( X3
= ( cons_Epistemic_fm_a @ X2 @ Xs3 ) )
=> ( Y
!= ( cons_Epistemic_fm_a @ X2 @ ( splice5109564810699471347c_fm_a @ Xa @ Xs3 ) ) ) ) ) ) ).
% splice.elims
thf(fact_1211_lexord__Nil__left,axiom,
! [Y: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Y ) @ ( lexord7736047576645873805c_fm_a @ R ) )
= ( ? [A4: epistemic_fm_a,X: list_Epistemic_fm_a] :
( Y
= ( cons_Epistemic_fm_a @ A4 @ X ) ) ) ) ).
% lexord_Nil_left
thf(fact_1212_lexord__Nil__right,axiom,
! [X3: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
~ ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ X3 @ nil_Epistemic_fm_a ) @ ( lexord7736047576645873805c_fm_a @ R ) ) ).
% lexord_Nil_right
thf(fact_1213_shuffles_Opelims,axiom,
! [X3: list_Epistemic_fm_a,Xa: list_Epistemic_fm_a,Y: set_li769143395467472256c_fm_a] :
( ( ( shuffl511019022169630517c_fm_a @ X3 @ Xa )
= Y )
=> ( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ X3 @ Xa ) )
=> ( ( ( X3 = nil_Epistemic_fm_a )
=> ( ( Y
= ( insert6567282714061225712c_fm_a @ Xa @ bot_bo8284763806281179116c_fm_a ) )
=> ~ ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Xa ) ) ) )
=> ( ( ( Xa = nil_Epistemic_fm_a )
=> ( ( Y
= ( insert6567282714061225712c_fm_a @ X3 @ bot_bo8284763806281179116c_fm_a ) )
=> ~ ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ X3 @ nil_Epistemic_fm_a ) ) ) )
=> ~ ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( ( X3
= ( cons_Epistemic_fm_a @ X2 @ Xs3 ) )
=> ! [Y2: epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
( ( Xa
= ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) )
=> ( ( Y
= ( sup_su1755902861286427476c_fm_a @ ( image_7387318756023638021c_fm_a @ ( cons_Epistemic_fm_a @ X2 ) @ ( shuffl511019022169630517c_fm_a @ Xs3 @ ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) ) ) @ ( image_7387318756023638021c_fm_a @ ( cons_Epistemic_fm_a @ Y2 ) @ ( shuffl511019022169630517c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ Ys3 ) ) ) )
=> ~ ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) ) ) ) ) ) ) ) ) ) ).
% shuffles.pelims
thf(fact_1214_successively__append__iff,axiom,
! [P2: epistemic_fm_a > epistemic_fm_a > $o,Xs: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
( ( succes6989878846294031341c_fm_a @ P2 @ ( append9179727413925872949c_fm_a @ Xs @ Ys2 ) )
= ( ( succes6989878846294031341c_fm_a @ P2 @ Xs )
& ( succes6989878846294031341c_fm_a @ P2 @ Ys2 )
& ( ( Xs = nil_Epistemic_fm_a )
| ( Ys2 = nil_Epistemic_fm_a )
| ( P2 @ ( last_Epistemic_fm_a @ Xs ) @ ( hd_Epistemic_fm_a @ Ys2 ) ) ) ) ) ).
% successively_append_iff
thf(fact_1215_set__empty2,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( bot_bo3626323581529592678c_fm_a
= ( set_Epistemic_fm_a2 @ Xs ) )
= ( Xs = nil_Epistemic_fm_a ) ) ).
% set_empty2
thf(fact_1216_set__empty,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( ( set_Epistemic_fm_a2 @ Xs )
= bot_bo3626323581529592678c_fm_a )
= ( Xs = nil_Epistemic_fm_a ) ) ).
% set_empty
thf(fact_1217_lists__empty,axiom,
( ( lists_Epistemic_fm_a @ bot_bo3626323581529592678c_fm_a )
= ( insert6567282714061225712c_fm_a @ nil_Epistemic_fm_a @ bot_bo8284763806281179116c_fm_a ) ) ).
% lists_empty
thf(fact_1218_successively_Osimps_I1_J,axiom,
! [P2: epistemic_fm_a > epistemic_fm_a > $o] : ( succes6989878846294031341c_fm_a @ P2 @ nil_Epistemic_fm_a ) ).
% successively.simps(1)
thf(fact_1219_shuffles_Osimps_I1_J,axiom,
! [Ys2: list_Epistemic_fm_a] :
( ( shuffl511019022169630517c_fm_a @ nil_Epistemic_fm_a @ Ys2 )
= ( insert6567282714061225712c_fm_a @ Ys2 @ bot_bo8284763806281179116c_fm_a ) ) ).
% shuffles.simps(1)
thf(fact_1220_shuffles_Osimps_I2_J,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( shuffl511019022169630517c_fm_a @ Xs @ nil_Epistemic_fm_a )
= ( insert6567282714061225712c_fm_a @ Xs @ bot_bo8284763806281179116c_fm_a ) ) ).
% shuffles.simps(2)
thf(fact_1221_successively__map,axiom,
! [P2: epistemic_fm_a > epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( succes6989878846294031341c_fm_a @ P2 @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs ) )
= ( succes6989878846294031341c_fm_a
@ ^ [X: epistemic_fm_a,Y3: epistemic_fm_a] : ( P2 @ ( F @ X ) @ ( F @ Y3 ) )
@ Xs ) ) ).
% successively_map
thf(fact_1222_empty__set,axiom,
( bot_bo3626323581529592678c_fm_a
= ( set_Epistemic_fm_a2 @ nil_Epistemic_fm_a ) ) ).
% empty_set
thf(fact_1223_successively_Oelims_I2_J,axiom,
! [X3: epistemic_fm_a > epistemic_fm_a > $o,Xa: list_Epistemic_fm_a] :
( ( succes6989878846294031341c_fm_a @ X3 @ Xa )
=> ( ( Xa != nil_Epistemic_fm_a )
=> ( ! [X2: epistemic_fm_a] :
( Xa
!= ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) )
=> ~ ! [X2: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( ( Xa
= ( cons_Epistemic_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) )
=> ~ ( ( X3 @ X2 @ Y2 )
& ( succes6989878846294031341c_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ).
% successively.elims(2)
thf(fact_1224_successively_Oelims_I1_J,axiom,
! [X3: epistemic_fm_a > epistemic_fm_a > $o,Xa: list_Epistemic_fm_a,Y: $o] :
( ( ( succes6989878846294031341c_fm_a @ X3 @ Xa )
= Y )
=> ( ( ( Xa = nil_Epistemic_fm_a )
=> ~ Y )
=> ( ( ? [X2: epistemic_fm_a] :
( Xa
= ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) )
=> ~ Y )
=> ~ ! [X2: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( ( Xa
= ( cons_Epistemic_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) )
=> ( Y
= ( ~ ( ( X3 @ X2 @ Y2 )
& ( succes6989878846294031341c_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ) ) ).
% successively.elims(1)
thf(fact_1225_successively_Osimps_I2_J,axiom,
! [P2: epistemic_fm_a > epistemic_fm_a > $o,X3: epistemic_fm_a] : ( succes6989878846294031341c_fm_a @ P2 @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) ).
% successively.simps(2)
thf(fact_1226_shuffles_Opsimps_I1_J,axiom,
! [Ys2: list_Epistemic_fm_a] :
( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Ys2 ) )
=> ( ( shuffl511019022169630517c_fm_a @ nil_Epistemic_fm_a @ Ys2 )
= ( insert6567282714061225712c_fm_a @ Ys2 @ bot_bo8284763806281179116c_fm_a ) ) ) ).
% shuffles.psimps(1)
thf(fact_1227_shuffles_Opsimps_I2_J,axiom,
! [Xs: list_Epistemic_fm_a] :
( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs @ nil_Epistemic_fm_a ) )
=> ( ( shuffl511019022169630517c_fm_a @ Xs @ nil_Epistemic_fm_a )
= ( insert6567282714061225712c_fm_a @ Xs @ bot_bo8284763806281179116c_fm_a ) ) ) ).
% shuffles.psimps(2)
thf(fact_1228_shuffles_Oelims,axiom,
! [X3: list_Epistemic_fm_a,Xa: list_Epistemic_fm_a,Y: set_li769143395467472256c_fm_a] :
( ( ( shuffl511019022169630517c_fm_a @ X3 @ Xa )
= Y )
=> ( ( ( X3 = nil_Epistemic_fm_a )
=> ( Y
!= ( insert6567282714061225712c_fm_a @ Xa @ bot_bo8284763806281179116c_fm_a ) ) )
=> ( ( ( Xa = nil_Epistemic_fm_a )
=> ( Y
!= ( insert6567282714061225712c_fm_a @ X3 @ bot_bo8284763806281179116c_fm_a ) ) )
=> ~ ! [X2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( ( X3
= ( cons_Epistemic_fm_a @ X2 @ Xs3 ) )
=> ! [Y2: epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
( ( Xa
= ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) )
=> ( Y
!= ( sup_su1755902861286427476c_fm_a @ ( image_7387318756023638021c_fm_a @ ( cons_Epistemic_fm_a @ X2 ) @ ( shuffl511019022169630517c_fm_a @ Xs3 @ ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) ) ) @ ( image_7387318756023638021c_fm_a @ ( cons_Epistemic_fm_a @ Y2 ) @ ( shuffl511019022169630517c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs3 ) @ Ys3 ) ) ) ) ) ) ) ) ) ).
% shuffles.elims
thf(fact_1229_successively__Cons,axiom,
! [P2: epistemic_fm_a > epistemic_fm_a > $o,X3: epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( succes6989878846294031341c_fm_a @ P2 @ ( cons_Epistemic_fm_a @ X3 @ Xs ) )
= ( ( Xs = nil_Epistemic_fm_a )
| ( ( P2 @ X3 @ ( hd_Epistemic_fm_a @ Xs ) )
& ( succes6989878846294031341c_fm_a @ P2 @ Xs ) ) ) ) ).
% successively_Cons
thf(fact_1230_partition_Osimps_I1_J,axiom,
! [P2: epistemic_fm_a > $o] :
( ( partit1738664135152837401c_fm_a @ P2 @ nil_Epistemic_fm_a )
= ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ nil_Epistemic_fm_a ) ) ).
% partition.simps(1)
thf(fact_1231_set__Cons__sing__Nil,axiom,
! [A: set_Epistemic_fm_a] :
( ( set_Co4868574198862222544c_fm_a @ A @ ( insert6567282714061225712c_fm_a @ nil_Epistemic_fm_a @ bot_bo8284763806281179116c_fm_a ) )
= ( image_4430763730358542731c_fm_a
@ ^ [X: epistemic_fm_a] : ( cons_Epistemic_fm_a @ X @ nil_Epistemic_fm_a )
@ A ) ) ).
% set_Cons_sing_Nil
thf(fact_1232_listset_Osimps_I1_J,axiom,
( ( listse5025355581707466111c_fm_a @ nil_se102576565402781184c_fm_a )
= ( insert6567282714061225712c_fm_a @ nil_Epistemic_fm_a @ bot_bo8284763806281179116c_fm_a ) ) ).
% listset.simps(1)
thf(fact_1233_successively_Opelims_I2_J,axiom,
! [X3: epistemic_fm_a > epistemic_fm_a > $o,Xa: list_Epistemic_fm_a] :
( ( succes6989878846294031341c_fm_a @ X3 @ Xa )
=> ( ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X3 @ Xa ) )
=> ( ( ( Xa = nil_Epistemic_fm_a )
=> ~ ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X3 @ nil_Epistemic_fm_a ) ) )
=> ( ! [X2: epistemic_fm_a] :
( ( Xa
= ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) )
=> ~ ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X3 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ) )
=> ~ ! [X2: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( ( Xa
= ( cons_Epistemic_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) )
=> ( ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X3 @ ( cons_Epistemic_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) )
=> ~ ( ( X3 @ X2 @ Y2 )
& ( succes6989878846294031341c_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ) ) ).
% successively.pelims(2)
thf(fact_1234_consistent__consequent_H,axiom,
! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
( ( episte2285483198712856226tent_a @ A @ V )
=> ( ( member6642669571620171971c_fm_a @ P @ V )
=> ( ! [G5: list_char > $o,H4: epistemic_fm_a > $o] : ( epistemic_eval_a @ G5 @ H4 @ ( epistemic_Imp_a @ P @ Q ) )
=> ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ Q @ bot_bo3626323581529592678c_fm_a ) @ V ) ) ) ) ) ).
% consistent_consequent'
thf(fact_1235_consistent__consequent,axiom,
! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
( ( episte2285483198712856226tent_a @ A @ V )
=> ( ( member6642669571620171971c_fm_a @ P @ V )
=> ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ Q ) )
=> ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ Q @ bot_bo3626323581529592678c_fm_a ) @ V ) ) ) ) ) ).
% consistent_consequent
thf(fact_1236_inconsistent__imply,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,G: list_Epistemic_fm_a] :
( ~ ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ ( set_Epistemic_fm_a2 @ G ) ) )
=> ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G @ P ) ) ) ).
% inconsistent_imply
thf(fact_1237_completeness_092_060_094sub_062A,axiom,
! [P: epistemic_fm_a,A: epistemic_fm_a > $o] :
( ! [M3: episte1560738328020401952t_unit,X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
=> ( ! [Xa3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa3 @ bot_bo3626323581529592678c_fm_a )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Xa3 ) )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ P ) ) )
=> ( epistemic_AK_a @ A @ P ) ) ).
% completeness\<^sub>A
thf(fact_1238_inconsistent__subset,axiom,
! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a] :
( ( episte2285483198712856226tent_a @ A @ V )
=> ( ~ ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ P @ bot_bo3626323581529592678c_fm_a ) @ V ) )
=> ~ ! [V3: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ V3 ) @ V )
=> ~ ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ V3 ) @ epistemic_FF_a ) ) ) ) ) ).
% inconsistent_subset
thf(fact_1239_Pow__set_I1_J,axiom,
( ( pow_Epistemic_fm_a @ ( set_Epistemic_fm_a2 @ nil_Epistemic_fm_a ) )
= ( insert7129737658439086282c_fm_a @ bot_bo3626323581529592678c_fm_a @ bot_bo1868452413526482246c_fm_a ) ) ).
% Pow_set(1)
thf(fact_1240_successively_Opelims_I1_J,axiom,
! [X3: epistemic_fm_a > epistemic_fm_a > $o,Xa: list_Epistemic_fm_a,Y: $o] :
( ( ( succes6989878846294031341c_fm_a @ X3 @ Xa )
= Y )
=> ( ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X3 @ Xa ) )
=> ( ( ( Xa = nil_Epistemic_fm_a )
=> ( Y
=> ~ ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X3 @ nil_Epistemic_fm_a ) ) ) )
=> ( ! [X2: epistemic_fm_a] :
( ( Xa
= ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) )
=> ( Y
=> ~ ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X3 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ) ) )
=> ~ ! [X2: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( ( Xa
= ( cons_Epistemic_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) )
=> ( ( Y
= ( ( X3 @ X2 @ Y2 )
& ( succes6989878846294031341c_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) )
=> ~ ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X3 @ ( cons_Epistemic_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ) ) ) ).
% successively.pelims(1)
thf(fact_1241_map__comp__map,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,G4: epistemic_fm_a > epistemic_fm_a] :
( ( comp_l5131143140338395773c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ ( map_Ep7084560364594560580c_fm_a @ G4 ) )
= ( map_Ep7084560364594560580c_fm_a @ ( comp_E612253880081530103c_fm_a @ F @ G4 ) ) ) ).
% map_comp_map
thf(fact_1242_List_Omap_Ocomp,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,G4: epistemic_fm_a > epistemic_fm_a] :
( ( comp_l5131143140338395773c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ ( map_Ep7084560364594560580c_fm_a @ G4 ) )
= ( map_Ep7084560364594560580c_fm_a @ ( comp_E612253880081530103c_fm_a @ F @ G4 ) ) ) ).
% List.map.comp
thf(fact_1243_map__map,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,G4: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( map_Ep7084560364594560580c_fm_a @ F @ ( map_Ep7084560364594560580c_fm_a @ G4 @ Xs ) )
= ( map_Ep7084560364594560580c_fm_a @ ( comp_E612253880081530103c_fm_a @ F @ G4 ) @ Xs ) ) ).
% map_map
thf(fact_1244_List_Omap_Ocompositionality,axiom,
! [F: epistemic_fm_a > epistemic_fm_a,G4: epistemic_fm_a > epistemic_fm_a,List: list_Epistemic_fm_a] :
( ( map_Ep7084560364594560580c_fm_a @ F @ ( map_Ep7084560364594560580c_fm_a @ G4 @ List ) )
= ( map_Ep7084560364594560580c_fm_a @ ( comp_E612253880081530103c_fm_a @ F @ G4 ) @ List ) ) ).
% List.map.compositionality
thf(fact_1245_list_Omap__comp,axiom,
! [G4: epistemic_fm_a > epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,V2: list_Epistemic_fm_a] :
( ( map_Ep7084560364594560580c_fm_a @ G4 @ ( map_Ep7084560364594560580c_fm_a @ F @ V2 ) )
= ( map_Ep7084560364594560580c_fm_a @ ( comp_E612253880081530103c_fm_a @ G4 @ F ) @ V2 ) ) ).
% list.map_comp
thf(fact_1246_exists__finite__inconsistent,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,V: set_Epistemic_fm_a] :
( ~ ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ V ) )
=> ~ ! [W4: set_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ W4 ) @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ V ) )
=> ( ~ ( member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ W4 )
=> ( ( finite3304564945125563331c_fm_a @ W4 )
=> ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ W4 ) ) ) ) ) ) ).
% exists_finite_inconsistent
thf(fact_1247_list_Opred__map,axiom,
! [Q3: epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a,X3: list_Epistemic_fm_a] :
( ( list_a5841931967666341838c_fm_a @ Q3 @ ( map_Ep7084560364594560580c_fm_a @ F @ X3 ) )
= ( list_a5841931967666341838c_fm_a @ ( comp_E2819036835534555897c_fm_a @ Q3 @ F ) @ X3 ) ) ).
% list.pred_map
thf(fact_1248_filter__map,axiom,
! [P2: epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a,Xs: list_Epistemic_fm_a] :
( ( filter7636273809395300631c_fm_a @ P2 @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs ) )
= ( map_Ep7084560364594560580c_fm_a @ F @ ( filter7636273809395300631c_fm_a @ ( comp_E2819036835534555897c_fm_a @ P2 @ F ) @ Xs ) ) ) ).
% filter_map
thf(fact_1249_listrel_ONil,axiom,
! [R: set_Pr8948481099588399239c_fm_a] : ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ nil_Epistemic_fm_a ) @ ( listre1023041962361757425c_fm_a @ R ) ) ).
% listrel.Nil
thf(fact_1250_listrel__Nil1,axiom,
! [Xs: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Xs ) @ ( listre1023041962361757425c_fm_a @ R ) )
=> ( Xs = nil_Epistemic_fm_a ) ) ).
% listrel_Nil1
thf(fact_1251_listrel__Nil2,axiom,
! [Xs: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs @ nil_Epistemic_fm_a ) @ ( listre1023041962361757425c_fm_a @ R ) )
=> ( Xs = nil_Epistemic_fm_a ) ) ).
% listrel_Nil2
thf(fact_1252_fm_Odistinct_I23_J,axiom,
! [X31: epistemic_fm_a,X32: epistemic_fm_a,X61: a,X62: epistemic_fm_a] :
( ( epistemic_Dis_a @ X31 @ X32 )
!= ( epistemic_K_a @ X61 @ X62 ) ) ).
% fm.distinct(23)
thf(fact_1253_fm_Odistinct_I21_J,axiom,
! [X31: epistemic_fm_a,X32: epistemic_fm_a,X51: epistemic_fm_a,X52: epistemic_fm_a] :
( ( epistemic_Dis_a @ X31 @ X32 )
!= ( epistemic_Imp_a @ X51 @ X52 ) ) ).
% fm.distinct(21)
thf(fact_1254_K__DisL,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Ps: list_Epistemic_fm_a,Q: epistemic_fm_a,P7: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ Ps ) @ Q ) )
=> ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P7 @ Ps ) @ Q ) )
=> ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ ( epistemic_Dis_a @ P @ P7 ) @ Ps ) @ Q ) ) ) ) ).
% K_DisL
thf(fact_1255_K__DisE,axiom,
! [A: epistemic_fm_a > $o,P: epistemic_fm_a,G: list_Epistemic_fm_a,R: epistemic_fm_a,Q: epistemic_fm_a] :
( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ G ) @ R ) )
=> ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ Q @ G ) @ R ) )
=> ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G @ ( epistemic_Dis_a @ P @ Q ) ) )
=> ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G @ R ) ) ) ) ) ).
% K_DisE
thf(fact_1256_listrel_Osimps,axiom,
! [A1: list_Epistemic_fm_a,A22: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ A1 @ A22 ) @ ( listre1023041962361757425c_fm_a @ R ) )
= ( ( ( A1 = nil_Epistemic_fm_a )
& ( A22 = nil_Epistemic_fm_a ) )
| ? [X: epistemic_fm_a,Y3: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
( ( A1
= ( cons_Epistemic_fm_a @ X @ Xs2 ) )
& ( A22
= ( cons_Epistemic_fm_a @ Y3 @ Ys ) )
& ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y3 ) @ R )
& ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs2 @ Ys ) @ ( listre1023041962361757425c_fm_a @ R ) ) ) ) ) ).
% listrel.simps
thf(fact_1257_listrel_Ocases,axiom,
! [A1: list_Epistemic_fm_a,A22: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ A1 @ A22 ) @ ( listre1023041962361757425c_fm_a @ R ) )
=> ( ( ( A1 = nil_Epistemic_fm_a )
=> ( A22 != nil_Epistemic_fm_a ) )
=> ~ ! [X2: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( ( A1
= ( cons_Epistemic_fm_a @ X2 @ Xs3 ) )
=> ! [Ys3: list_Epistemic_fm_a] :
( ( A22
= ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) )
=> ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X2 @ Y2 ) @ R )
=> ~ ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs3 @ Ys3 ) @ ( listre1023041962361757425c_fm_a @ R ) ) ) ) ) ) ) ).
% listrel.cases
thf(fact_1258_fm_Oexhaust,axiom,
! [Y: epistemic_fm_a] :
( ( Y != epistemic_FF_a )
=> ( ! [X24: list_char] :
( Y
!= ( epistemic_Pro_a @ X24 ) )
=> ( ! [X312: epistemic_fm_a,X322: epistemic_fm_a] :
( Y
!= ( epistemic_Dis_a @ X312 @ X322 ) )
=> ( ! [X412: epistemic_fm_a,X422: epistemic_fm_a] :
( Y
!= ( epistemic_Con_a @ X412 @ X422 ) )
=> ( ! [X512: epistemic_fm_a,X522: epistemic_fm_a] :
( Y
!= ( epistemic_Imp_a @ X512 @ X522 ) )
=> ~ ! [X612: a,X622: epistemic_fm_a] :
( Y
!= ( epistemic_K_a @ X612 @ X622 ) ) ) ) ) ) ) ).
% fm.exhaust
thf(fact_1259_fm_Odistinct_I15_J,axiom,
! [X25: list_char,X51: epistemic_fm_a,X52: epistemic_fm_a] :
( ( epistemic_Pro_a @ X25 )
!= ( epistemic_Imp_a @ X51 @ X52 ) ) ).
% fm.distinct(15)
thf(fact_1260_fm_Odistinct_I17_J,axiom,
! [X25: list_char,X61: a,X62: epistemic_fm_a] :
( ( epistemic_Pro_a @ X25 )
!= ( epistemic_K_a @ X61 @ X62 ) ) ).
% fm.distinct(17)
thf(fact_1261_listrelp_ONil,axiom,
! [R: epistemic_fm_a > epistemic_fm_a > $o] : ( listre7830505053103709503c_fm_a @ R @ nil_Epistemic_fm_a @ nil_Epistemic_fm_a ) ).
% listrelp.Nil
thf(fact_1262_listrelp_Osimps,axiom,
( listre7830505053103709503c_fm_a
= ( ^ [R3: epistemic_fm_a > epistemic_fm_a > $o,A12: list_Epistemic_fm_a,A23: list_Epistemic_fm_a] :
( ( ( A12 = nil_Epistemic_fm_a )
& ( A23 = nil_Epistemic_fm_a ) )
| ? [X: epistemic_fm_a,Y3: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
( ( A12
= ( cons_Epistemic_fm_a @ X @ Xs2 ) )
& ( A23
= ( cons_Epistemic_fm_a @ Y3 @ Ys ) )
& ( R3 @ X @ Y3 )
& ( listre7830505053103709503c_fm_a @ R3 @ Xs2 @ Ys ) ) ) ) ) ).
% listrelp.simps
thf(fact_1263_listrelp_Ocases,axiom,
! [R: epistemic_fm_a > epistemic_fm_a > $o,A1: list_Epistemic_fm_a,A22: list_Epistemic_fm_a] :
( ( listre7830505053103709503c_fm_a @ R @ A1 @ A22 )
=> ( ( ( A1 = nil_Epistemic_fm_a )
=> ( A22 != nil_Epistemic_fm_a ) )
=> ~ ! [X2: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
( ( A1
= ( cons_Epistemic_fm_a @ X2 @ Xs3 ) )
=> ! [Ys3: list_Epistemic_fm_a] :
( ( A22
= ( cons_Epistemic_fm_a @ Y2 @ Ys3 ) )
=> ( ( R @ X2 @ Y2 )
=> ~ ( listre7830505053103709503c_fm_a @ R @ Xs3 @ Ys3 ) ) ) ) ) ) ).
% listrelp.cases
thf(fact_1264_strong__completeness,axiom,
! [P2: episte1560738328020401952t_unit > $o,G: set_Epistemic_fm_a,P: epistemic_fm_a,A: epistemic_fm_a > $o] :
( ! [M3: episte1560738328020401952t_unit] :
( ( P2 @ M3 )
=> ! [X2: set_Epistemic_fm_a] :
( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
=> ( ! [Xa3: epistemic_fm_a] :
( ( member6642669571620171971c_fm_a @ Xa3 @ G )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Xa3 ) )
=> ( episte7081087998767065248c_fm_a @ M3 @ X2 @ P ) ) ) )
=> ( ( P2
@ ( episte2888590659910966568t_unit
@ ( collec2519470961442302949c_fm_a
@ ^ [W5: set_Epistemic_fm_a] :
( ( episte2285483198712856226tent_a @ A @ W5 )
& ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W5 ) ) )
@ ^ [I3: a,V4: set_Epistemic_fm_a] :
( collec2519470961442302949c_fm_a
@ ( ord_le3275665582123262618c_fm_a
@ ( collec4904205152690461189c_fm_a
@ ^ [P4: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I3 @ P4 ) @ V4 ) ) ) )
@ ( episte8239586592105053771t_unit
@ ^ [V4: set_Epistemic_fm_a,X: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X ) @ V4 )
@ product_Unity ) ) )
=> ? [Qs4: list_Epistemic_fm_a] :
( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs4 ) @ G )
& ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs4 @ P ) ) ) ) ) ).
% strong_completeness
thf(fact_1265_fm_Orel__cases,axiom,
! [R2: a > a > $o,A2: epistemic_fm_a,B: epistemic_fm_a] :
( ( epistemic_rel_fm_a_a @ R2 @ A2 @ B )
=> ( ( ( A2 = epistemic_FF_a )
=> ( B != epistemic_FF_a ) )
=> ( ! [X2: list_char] :
( ( A2
= ( epistemic_Pro_a @ X2 ) )
=> ! [Y2: list_char] :
( ( B
= ( epistemic_Pro_a @ Y2 ) )
=> ( X2 != Y2 ) ) )
=> ( ! [X12: epistemic_fm_a,X2a: epistemic_fm_a] :
( ( A2
= ( epistemic_Dis_a @ X12 @ X2a ) )
=> ! [Y1: epistemic_fm_a,Y2a: epistemic_fm_a] :
( ( B
= ( epistemic_Dis_a @ Y1 @ Y2a ) )
=> ( ( epistemic_rel_fm_a_a @ R2 @ X12 @ Y1 )
=> ~ ( epistemic_rel_fm_a_a @ R2 @ X2a @ Y2a ) ) ) )
=> ( ! [X1a: epistemic_fm_a,X2b: epistemic_fm_a] :
( ( A2
= ( epistemic_Con_a @ X1a @ X2b ) )
=> ! [Y1a: epistemic_fm_a,Y2b: epistemic_fm_a] :
( ( B
= ( epistemic_Con_a @ Y1a @ Y2b ) )
=> ( ( epistemic_rel_fm_a_a @ R2 @ X1a @ Y1a )
=> ~ ( epistemic_rel_fm_a_a @ R2 @ X2b @ Y2b ) ) ) )
=> ( ! [X1b: epistemic_fm_a,X2c: epistemic_fm_a] :
( ( A2
= ( epistemic_Imp_a @ X1b @ X2c ) )
=> ! [Y1b: epistemic_fm_a,Y2c: epistemic_fm_a] :
( ( B
= ( epistemic_Imp_a @ Y1b @ Y2c ) )
=> ( ( epistemic_rel_fm_a_a @ R2 @ X1b @ Y1b )
=> ~ ( epistemic_rel_fm_a_a @ R2 @ X2c @ Y2c ) ) ) )
=> ~ ! [X1c: a,X2d: epistemic_fm_a] :
( ( A2
= ( epistemic_K_a @ X1c @ X2d ) )
=> ! [Y1c: a,Y2d: epistemic_fm_a] :
( ( B
= ( epistemic_K_a @ Y1c @ Y2d ) )
=> ( ( R2 @ X1c @ Y1c )
=> ~ ( epistemic_rel_fm_a_a @ R2 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).
% fm.rel_cases
thf(fact_1266_fm_Orel__inject_I6_J,axiom,
! [R2: a > a > $o,X61: a,X62: epistemic_fm_a,Y61: a,Y62: epistemic_fm_a] :
( ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_K_a @ X61 @ X62 ) @ ( epistemic_K_a @ Y61 @ Y62 ) )
= ( ( R2 @ X61 @ Y61 )
& ( epistemic_rel_fm_a_a @ R2 @ X62 @ Y62 ) ) ) ).
% fm.rel_inject(6)
thf(fact_1267_fm_Orel__intros_I6_J,axiom,
! [R2: a > a > $o,X61: a,Y61: a,X62: epistemic_fm_a,Y62: epistemic_fm_a] :
( ( R2 @ X61 @ Y61 )
=> ( ( epistemic_rel_fm_a_a @ R2 @ X62 @ Y62 )
=> ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_K_a @ X61 @ X62 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ) ) ).
% fm.rel_intros(6)
thf(fact_1268_fm_Orel__inject_I5_J,axiom,
! [R2: a > a > $o,X51: epistemic_fm_a,X52: epistemic_fm_a,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
( ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ X51 @ X52 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) )
= ( ( epistemic_rel_fm_a_a @ R2 @ X51 @ Y51 )
& ( epistemic_rel_fm_a_a @ R2 @ X52 @ Y52 ) ) ) ).
% fm.rel_inject(5)
thf(fact_1269_fm_Orel__intros_I5_J,axiom,
! [R2: a > a > $o,X51: epistemic_fm_a,Y51: epistemic_fm_a,X52: epistemic_fm_a,Y52: epistemic_fm_a] :
( ( epistemic_rel_fm_a_a @ R2 @ X51 @ Y51 )
=> ( ( epistemic_rel_fm_a_a @ R2 @ X52 @ Y52 )
=> ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ X51 @ X52 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ) ) ).
% fm.rel_intros(5)
% Helper facts (11)
thf(help_If_2_1_If_001t__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_T,axiom,
! [X3: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
( ( if_lis2878681784746929638c_fm_a @ $false @ X3 @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_T,axiom,
! [X3: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
( ( if_lis2878681784746929638c_fm_a @ $true @ X3 @ Y )
= X3 ) ).
thf(help_If_2_1_If_001t__List__Olist_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_T,axiom,
! [X3: list_s580375451141968640c_fm_a,Y: list_s580375451141968640c_fm_a] :
( ( if_lis3811715425919989702c_fm_a @ $false @ X3 @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__List__Olist_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_T,axiom,
! [X3: list_s580375451141968640c_fm_a,Y: list_s580375451141968640c_fm_a] :
( ( if_lis3811715425919989702c_fm_a @ $true @ X3 @ Y )
= X3 ) ).
thf(help_If_2_1_If_001t__List__Olist_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_T,axiom,
! [X3: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a] :
( ( if_lis342421823373228652c_fm_a @ $false @ X3 @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__List__Olist_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_T,axiom,
! [X3: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a] :
( ( if_lis342421823373228652c_fm_a @ $true @ X3 @ Y )
= X3 ) ).
thf(help_If_2_1_If_001t__List__Olist_It__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_J_T,axiom,
! [X3: list_P3099032918374241197c_fm_a,Y: list_P3099032918374241197c_fm_a] :
( ( if_lis4277834422595218803c_fm_a @ $false @ X3 @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__List__Olist_It__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_J_T,axiom,
! [X3: list_P3099032918374241197c_fm_a,Y: list_P3099032918374241197c_fm_a] :
( ( if_lis4277834422595218803c_fm_a @ $true @ X3 @ Y )
= X3 ) ).
thf(help_If_3_1_If_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_J_T,axiom,
! [P2: $o] :
( ( P2 = $true )
| ( P2 = $false ) ) ).
thf(help_If_2_1_If_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_J_T,axiom,
! [X3: list_P7917480606449584557c_fm_a,Y: list_P7917480606449584557c_fm_a] :
( ( if_lis974313005191179635c_fm_a @ $false @ X3 @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_J_T,axiom,
! [X3: list_P7917480606449584557c_fm_a,Y: list_P7917480606449584557c_fm_a] :
( ( if_lis974313005191179635c_fm_a @ $true @ X3 @ Y )
= X3 ) ).
% Conjectures (1)
thf(conj_0,conjecture,
epistemic_AK_a @ a2 @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ ( map_Ep7084560364594560580c_fm_a @ ( epistemic_K_a @ i ) @ nil_Epistemic_fm_a ) ) @ ( epistemic_K_a @ i @ ( stalnaker_conjunct_a @ nil_Epistemic_fm_a ) ) ) ).
%------------------------------------------------------------------------------