TPTP Problem File: SLH0830^1.p
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- Solve Problem
%------------------------------------------------------------------------------
% 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_00321_010816__6644668_1 [Des23]
% Status : Theorem
% Rating : ? v8.2.0
% Syntax : Number of formulae : 1541 ( 647 unt; 250 typ; 0 def)
% Number of atoms : 3755 (1158 equ; 0 cnn)
% Maximal formula atoms : 21 ( 2 avg)
% Number of connectives : 12123 ( 421 ~; 70 |; 309 &;9833 @)
% ( 0 <=>;1490 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Number of types : 28 ( 27 usr)
% Number of type conns : 1139 (1139 >; 0 *; 0 +; 0 <<)
% Number of symbols : 226 ( 223 usr; 14 con; 0-4 aty)
% Number of variables : 3838 ( 456 ^;3255 !; 127 ?;3838 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2023-01-19 16:12:20.630
%------------------------------------------------------------------------------
% Could-be-implicit typings (27)
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% Explicit typings (223)
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stalnaker_Ax_2_i: epistemic_fm_i > $o ).
thf(sy_c_Stalnaker__Logic_Oconjunct_001tf__i,type,
stalnaker_conjunct_i: list_Epistemic_fm_i > epistemic_fm_i ).
thf(sy_c_Zorn_Ochain__subset_001t__Epistemic____Logic__Ofm_Itf__i_J,type,
chain_7805378461283022331c_fm_i: set_se3485332733965609186c_fm_i > $o ).
thf(sy_c_Zorn_Ochains_001t__Epistemic____Logic__Ofm_Itf__i_J,type,
chains830531755891748338c_fm_i: set_se3485332733965609186c_fm_i > set_se7339729205154126530c_fm_i ).
thf(sy_c_member_001_062_It__Epistemic____Logic__Ofm_Itf__i_J_M_Eo_J,type,
member633939095840083442fm_i_o: ( epistemic_fm_i > $o ) > set_Epistemic_fm_i_o > $o ).
thf(sy_c_member_001_062_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__i_J_J_M_Eo_J,type,
member5074877863442670610fm_i_o: ( set_Epistemic_fm_i > $o ) > set_se4360409073116726705fm_i_o > $o ).
thf(sy_c_member_001t__Epistemic____Logic__Ofm_Itf__i_J,type,
member6642669606046002379c_fm_i: epistemic_fm_i > set_Epistemic_fm_i > $o ).
thf(sy_c_member_001t__List__Olist_It__Epistemic____Logic__Ofm_Itf__i_J_J,type,
member6475149752759350353c_fm_i: list_Epistemic_fm_i > set_li8269783359719514504c_fm_i > $o ).
thf(sy_c_member_001t__List__Olist_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__i_J_J_J,type,
member605545779687026225c_fm_i: list_s8081015415394010888c_fm_i > set_li2934481837907835752c_fm_i > $o ).
thf(sy_c_member_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__i_J_J,type,
member1104366573291651755c_fm_i: set_Epistemic_fm_i > set_se3485332733965609186c_fm_i > $o ).
thf(sy_c_member_001t__Set__Oset_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__i_J_J_J,type,
member794313724012529841c_fm_i: set_li8269783359719514504c_fm_i > set_se3663484335793657320c_fm_i > $o ).
thf(sy_c_member_001t__Set__Oset_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__i_J_J_J,type,
member1461078328125707403c_fm_i: set_se3485332733965609186c_fm_i > set_se7339729205154126530c_fm_i > $o ).
thf(sy_c_member_001t__Set__Oset_It__Set__Oset_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__i_J_J_J_J,type,
member2074520630381716075c_fm_i: set_se7339729205154126530c_fm_i > set_se8293749906924980386c_fm_i > $o ).
thf(sy_c_member_001tf__i,type,
member_i: i > set_i > $o ).
thf(sy_v_A,type,
a: epistemic_fm_i > $o ).
thf(sy_v_U,type,
u: set_Epistemic_fm_i ).
thf(sy_v_V,type,
v: set_Epistemic_fm_i ).
thf(sy_v_W,type,
w: set_Epistemic_fm_i ).
thf(sy_v_i,type,
i2: i ).
thf(sy_v_thesis____,type,
thesis: $o ).
% Relevant facts (1278)
thf(fact_0_assms_I1_J,axiom,
! [P: epistemic_fm_i] :
( ( stalnaker_Ax_2_i @ P )
=> ( a @ P ) ) ).
% assms(1)
thf(fact_1_assms_I9_J,axiom,
( member1104366573291651755c_fm_i @ u
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ i2 @ P2 ) @ v ) ) ) ) ) ).
% assms(9)
thf(fact_2_assms_I8_J,axiom,
( member1104366573291651755c_fm_i @ w
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ i2 @ P2 ) @ v ) ) ) ) ) ).
% assms(8)
thf(fact_3_assms_I6_J,axiom,
episte2285483198712856234tent_i @ a @ u ).
% assms(6)
thf(fact_4_assms_I4_J,axiom,
episte2285483198712856234tent_i @ a @ w ).
% assms(4)
thf(fact_5__092_060open_062_092_060not_062_Aconsistent_AA_A_Iknown_AW_Ai_A_092_060union_062_Aknown_AU_Ai_J_092_060close_062,axiom,
~ ( episte2285483198712856234tent_i @ a
@ ( sup_su1936195050962291414c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ i2 @ P2 ) @ w ) )
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ i2 @ P2 ) @ u ) ) ) ) ).
% \<open>\<not> consistent A (known W i \<union> known U i)\<close>
thf(fact_6_finite__Collect__subsets,axiom,
! [A: set_se8476610928908190011c_fm_i] :
( ( finite5517585301071133084c_fm_i @ A )
=> ( finite3693969766958446546c_fm_i
@ ( collec5714284441206222864c_fm_i
@ ^ [B: set_se8476610928908190011c_fm_i] : ( ord_le2967411346902147483c_fm_i @ B @ A ) ) ) ) ).
% finite_Collect_subsets
thf(fact_7_finite__Collect__subsets,axiom,
! [A: set_Ep2190104726579546907c_fm_i] :
( ( finite4369126853184676732c_fm_i @ A )
=> ( finite2986264657457470898c_fm_i
@ ( collec4377899601863806448c_fm_i
@ ^ [B: set_Ep2190104726579546907c_fm_i] : ( ord_le4359956957808536443c_fm_i @ B @ A ) ) ) ) ).
% finite_Collect_subsets
thf(fact_8_finite__Collect__subsets,axiom,
! [A: set_se7339729205154126530c_fm_i] :
( ( finite9087983574947184523c_fm_i @ A )
=> ( finite523845223739985259c_fm_i
@ ( collec7169927098055193517c_fm_i
@ ^ [B: set_se7339729205154126530c_fm_i] : ( ord_le2772500130360476258c_fm_i @ B @ A ) ) ) ) ).
% finite_Collect_subsets
thf(fact_9_finite__Collect__subsets,axiom,
! [A: set_li8269783359719514504c_fm_i] :
( ( finite3106398504192302929c_fm_i @ A )
=> ( finite5297363955932591025c_fm_i
@ ( collec2389093812960846067c_fm_i
@ ^ [B: set_li8269783359719514504c_fm_i] : ( ord_le1209247765174941992c_fm_i @ B @ A ) ) ) ) ).
% finite_Collect_subsets
thf(fact_10_finite__Collect__subsets,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( finite9087983574947184523c_fm_i
@ ( collec2761885132556217805c_fm_i
@ ^ [B: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ B @ A ) ) ) ) ).
% finite_Collect_subsets
thf(fact_11_finite__Collect__subsets,axiom,
! [A: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ A )
=> ( finite7933139204641697195c_fm_i
@ ( collec3087743281813070829c_fm_i
@ ^ [B: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ B @ A ) ) ) ) ).
% finite_Collect_subsets
thf(fact_12_Un__subset__iff,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ ( sup_su2582925890723967158c_fm_i @ A @ B2 ) @ C )
= ( ( ord_le5389487502678872194c_fm_i @ A @ C )
& ( ord_le5389487502678872194c_fm_i @ B2 @ C ) ) ) ).
% Un_subset_iff
thf(fact_13_Un__subset__iff,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i,C: set_se7339729205154126530c_fm_i] :
( ( ord_le2772500130360476258c_fm_i @ ( sup_su2317974602288960150c_fm_i @ A @ B2 ) @ C )
= ( ( ord_le2772500130360476258c_fm_i @ A @ C )
& ( ord_le2772500130360476258c_fm_i @ B2 @ C ) ) ) ).
% Un_subset_iff
thf(fact_14_Un__subset__iff,axiom,
! [A: set_li8269783359719514504c_fm_i,B2: set_li8269783359719514504c_fm_i,C: set_li8269783359719514504c_fm_i] :
( ( ord_le1209247765174941992c_fm_i @ ( sup_su33170788683693916c_fm_i @ A @ B2 ) @ C )
= ( ( ord_le1209247765174941992c_fm_i @ A @ C )
& ( ord_le1209247765174941992c_fm_i @ B2 @ C ) ) ) ).
% Un_subset_iff
thf(fact_15_Un__subset__iff,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) @ C )
= ( ( ord_le3843937902494030498c_fm_i @ A @ C )
& ( ord_le3843937902494030498c_fm_i @ B2 @ C ) ) ) ).
% Un_subset_iff
thf(fact_16_finite__Un,axiom,
! [F: set_se8476610928908190011c_fm_i,G: set_se8476610928908190011c_fm_i] :
( ( finite5517585301071133084c_fm_i @ ( sup_su892458105919474279c_fm_i @ F @ G ) )
= ( ( finite5517585301071133084c_fm_i @ F )
& ( finite5517585301071133084c_fm_i @ G ) ) ) ).
% finite_Un
thf(fact_17_finite__Un,axiom,
! [F: set_Ep2190104726579546907c_fm_i,G: set_Ep2190104726579546907c_fm_i] :
( ( finite4369126853184676732c_fm_i @ ( sup_su5011873955875882055c_fm_i @ F @ G ) )
= ( ( finite4369126853184676732c_fm_i @ F )
& ( finite4369126853184676732c_fm_i @ G ) ) ) ).
% finite_Un
thf(fact_18_finite__Un,axiom,
! [F: set_se7339729205154126530c_fm_i,G: set_se7339729205154126530c_fm_i] :
( ( finite9087983574947184523c_fm_i @ ( sup_su2317974602288960150c_fm_i @ F @ G ) )
= ( ( finite9087983574947184523c_fm_i @ F )
& ( finite9087983574947184523c_fm_i @ G ) ) ) ).
% finite_Un
thf(fact_19_finite__Un,axiom,
! [F: set_se3485332733965609186c_fm_i,G: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ ( sup_su2582925890723967158c_fm_i @ F @ G ) )
= ( ( finite7933139204641697195c_fm_i @ F )
& ( finite7933139204641697195c_fm_i @ G ) ) ) ).
% finite_Un
thf(fact_20_finite__Un,axiom,
! [F: set_Epistemic_fm_i,G: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ ( sup_su1936195050962291414c_fm_i @ F @ G ) )
= ( ( finite3304564979551393739c_fm_i @ F )
& ( finite3304564979551393739c_fm_i @ G ) ) ) ).
% finite_Un
thf(fact_21_List_Ofinite__set,axiom,
! [Xs: list_l4360594050116504750c_fm_i] : ( finite3106398504192302929c_fm_i @ ( set_li9010496130497932989c_fm_i @ Xs ) ) ).
% List.finite_set
thf(fact_22_List_Ofinite__set,axiom,
! [Xs: list_s8635415444435394792c_fm_i] : ( finite9087983574947184523c_fm_i @ ( set_se5076022966804059383c_fm_i @ Xs ) ) ).
% List.finite_set
thf(fact_23_List_Ofinite__set,axiom,
! [Xs: list_s6079497109814496917c_fm_i] : ( finite5517585301071133084c_fm_i @ ( set_se1663946760828023600c_fm_i @ Xs ) ) ).
% List.finite_set
thf(fact_24_List_Ofinite__set,axiom,
! [Xs: list_E6081740836645470325c_fm_i] : ( finite4369126853184676732c_fm_i @ ( set_Ep2053541840733318416c_fm_i @ Xs ) ) ).
% List.finite_set
thf(fact_25_List_Ofinite__set,axiom,
! [Xs: list_s8081015415394010888c_fm_i] : ( finite7933139204641697195c_fm_i @ ( set_se200842218512397079c_fm_i @ Xs ) ) ).
% List.finite_set
thf(fact_26_List_Ofinite__set,axiom,
! [Xs: list_Epistemic_fm_i] : ( finite3304564979551393739c_fm_i @ ( set_Epistemic_fm_i2 @ Xs ) ) ).
% List.finite_set
thf(fact_27_le__sup__iff,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ ( sup_su2582925890723967158c_fm_i @ X @ Y ) @ Z )
= ( ( ord_le5389487502678872194c_fm_i @ X @ Z )
& ( ord_le5389487502678872194c_fm_i @ Y @ Z ) ) ) ).
% le_sup_iff
thf(fact_28_le__sup__iff,axiom,
! [X: epistemic_fm_i > $o,Y: epistemic_fm_i > $o,Z: epistemic_fm_i > $o] :
( ( ord_le190830114487426235fm_i_o @ ( sup_su2844414564337698183fm_i_o @ X @ Y ) @ Z )
= ( ( ord_le190830114487426235fm_i_o @ X @ Z )
& ( ord_le190830114487426235fm_i_o @ Y @ Z ) ) ) ).
% le_sup_iff
thf(fact_29_le__sup__iff,axiom,
! [X: set_Epistemic_fm_i > $o,Y: set_Epistemic_fm_i > $o,Z: set_Epistemic_fm_i > $o] :
( ( ord_le5706303257367236315fm_i_o @ ( sup_su6723579903606884263fm_i_o @ X @ Y ) @ Z )
= ( ( ord_le5706303257367236315fm_i_o @ X @ Z )
& ( ord_le5706303257367236315fm_i_o @ Y @ Z ) ) ) ).
% le_sup_iff
thf(fact_30_le__sup__iff,axiom,
! [X: set_se7339729205154126530c_fm_i,Y: set_se7339729205154126530c_fm_i,Z: set_se7339729205154126530c_fm_i] :
( ( ord_le2772500130360476258c_fm_i @ ( sup_su2317974602288960150c_fm_i @ X @ Y ) @ Z )
= ( ( ord_le2772500130360476258c_fm_i @ X @ Z )
& ( ord_le2772500130360476258c_fm_i @ Y @ Z ) ) ) ).
% le_sup_iff
thf(fact_31_le__sup__iff,axiom,
! [X: set_li8269783359719514504c_fm_i,Y: set_li8269783359719514504c_fm_i,Z: set_li8269783359719514504c_fm_i] :
( ( ord_le1209247765174941992c_fm_i @ ( sup_su33170788683693916c_fm_i @ X @ Y ) @ Z )
= ( ( ord_le1209247765174941992c_fm_i @ X @ Z )
& ( ord_le1209247765174941992c_fm_i @ Y @ Z ) ) ) ).
% le_sup_iff
thf(fact_32_le__sup__iff,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ X @ Y ) @ Z )
= ( ( ord_le3843937902494030498c_fm_i @ X @ Z )
& ( ord_le3843937902494030498c_fm_i @ Y @ Z ) ) ) ).
% le_sup_iff
thf(fact_33_sup_Obounded__iff,axiom,
! [B3: set_se3485332733965609186c_fm_i,C2: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ ( sup_su2582925890723967158c_fm_i @ B3 @ C2 ) @ A2 )
= ( ( ord_le5389487502678872194c_fm_i @ B3 @ A2 )
& ( ord_le5389487502678872194c_fm_i @ C2 @ A2 ) ) ) ).
% sup.bounded_iff
thf(fact_34_sup_Obounded__iff,axiom,
! [B3: epistemic_fm_i > $o,C2: epistemic_fm_i > $o,A2: epistemic_fm_i > $o] :
( ( ord_le190830114487426235fm_i_o @ ( sup_su2844414564337698183fm_i_o @ B3 @ C2 ) @ A2 )
= ( ( ord_le190830114487426235fm_i_o @ B3 @ A2 )
& ( ord_le190830114487426235fm_i_o @ C2 @ A2 ) ) ) ).
% sup.bounded_iff
thf(fact_35_sup_Obounded__iff,axiom,
! [B3: set_Epistemic_fm_i > $o,C2: set_Epistemic_fm_i > $o,A2: set_Epistemic_fm_i > $o] :
( ( ord_le5706303257367236315fm_i_o @ ( sup_su6723579903606884263fm_i_o @ B3 @ C2 ) @ A2 )
= ( ( ord_le5706303257367236315fm_i_o @ B3 @ A2 )
& ( ord_le5706303257367236315fm_i_o @ C2 @ A2 ) ) ) ).
% sup.bounded_iff
thf(fact_36_sup_Obounded__iff,axiom,
! [B3: set_se7339729205154126530c_fm_i,C2: set_se7339729205154126530c_fm_i,A2: set_se7339729205154126530c_fm_i] :
( ( ord_le2772500130360476258c_fm_i @ ( sup_su2317974602288960150c_fm_i @ B3 @ C2 ) @ A2 )
= ( ( ord_le2772500130360476258c_fm_i @ B3 @ A2 )
& ( ord_le2772500130360476258c_fm_i @ C2 @ A2 ) ) ) ).
% sup.bounded_iff
thf(fact_37_sup_Obounded__iff,axiom,
! [B3: set_li8269783359719514504c_fm_i,C2: set_li8269783359719514504c_fm_i,A2: set_li8269783359719514504c_fm_i] :
( ( ord_le1209247765174941992c_fm_i @ ( sup_su33170788683693916c_fm_i @ B3 @ C2 ) @ A2 )
= ( ( ord_le1209247765174941992c_fm_i @ B3 @ A2 )
& ( ord_le1209247765174941992c_fm_i @ C2 @ A2 ) ) ) ).
% sup.bounded_iff
thf(fact_38_sup_Obounded__iff,axiom,
! [B3: set_Epistemic_fm_i,C2: set_Epistemic_fm_i,A2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ B3 @ C2 ) @ A2 )
= ( ( ord_le3843937902494030498c_fm_i @ B3 @ A2 )
& ( ord_le3843937902494030498c_fm_i @ C2 @ A2 ) ) ) ).
% sup.bounded_iff
thf(fact_39_K__imply__weaken,axiom,
! [A: epistemic_fm_i > $o,Ps: list_Epistemic_fm_i,Q: epistemic_fm_i,Ps2: list_Epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_imply_i @ Ps @ Q ) )
=> ( ( ord_le3843937902494030498c_fm_i @ ( set_Epistemic_fm_i2 @ Ps ) @ ( set_Epistemic_fm_i2 @ Ps2 ) )
=> ( epistemic_AK_i @ A @ ( epistemic_imply_i @ Ps2 @ Q ) ) ) ) ).
% K_imply_weaken
thf(fact_40_finite__Collect__conjI,axiom,
! [P3: list_Epistemic_fm_i > $o,Q2: list_Epistemic_fm_i > $o] :
( ( ( finite3106398504192302929c_fm_i @ ( collec5759350117362652307c_fm_i @ P3 ) )
| ( finite3106398504192302929c_fm_i @ ( collec5759350117362652307c_fm_i @ Q2 ) ) )
=> ( finite3106398504192302929c_fm_i
@ ( collec5759350117362652307c_fm_i
@ ^ [X2: list_Epistemic_fm_i] :
( ( P3 @ X2 )
& ( Q2 @ X2 ) ) ) ) ) ).
% finite_Collect_conjI
thf(fact_41_finite__Collect__conjI,axiom,
! [P3: set_se3485332733965609186c_fm_i > $o,Q2: set_se3485332733965609186c_fm_i > $o] :
( ( ( finite9087983574947184523c_fm_i @ ( collec2761885132556217805c_fm_i @ P3 ) )
| ( finite9087983574947184523c_fm_i @ ( collec2761885132556217805c_fm_i @ Q2 ) ) )
=> ( finite9087983574947184523c_fm_i
@ ( collec2761885132556217805c_fm_i
@ ^ [X2: set_se3485332733965609186c_fm_i] :
( ( P3 @ X2 )
& ( Q2 @ X2 ) ) ) ) ) ).
% finite_Collect_conjI
thf(fact_42_finite__Collect__conjI,axiom,
! [P3: ( set_Epistemic_fm_i > epistemic_fm_i ) > $o,Q2: ( set_Epistemic_fm_i > epistemic_fm_i ) > $o] :
( ( ( finite5517585301071133084c_fm_i @ ( collec6909220245477468634c_fm_i @ P3 ) )
| ( finite5517585301071133084c_fm_i @ ( collec6909220245477468634c_fm_i @ Q2 ) ) )
=> ( finite5517585301071133084c_fm_i
@ ( collec6909220245477468634c_fm_i
@ ^ [X2: set_Epistemic_fm_i > epistemic_fm_i] :
( ( P3 @ X2 )
& ( Q2 @ X2 ) ) ) ) ) ).
% finite_Collect_conjI
thf(fact_43_finite__Collect__conjI,axiom,
! [P3: ( epistemic_fm_i > epistemic_fm_i ) > $o,Q2: ( epistemic_fm_i > epistemic_fm_i ) > $o] :
( ( ( finite4369126853184676732c_fm_i @ ( collec4821997688893311930c_fm_i @ P3 ) )
| ( finite4369126853184676732c_fm_i @ ( collec4821997688893311930c_fm_i @ Q2 ) ) )
=> ( finite4369126853184676732c_fm_i
@ ( collec4821997688893311930c_fm_i
@ ^ [X2: epistemic_fm_i > epistemic_fm_i] :
( ( P3 @ X2 )
& ( Q2 @ X2 ) ) ) ) ) ).
% finite_Collect_conjI
thf(fact_44_finite__Collect__conjI,axiom,
! [P3: epistemic_fm_i > $o,Q2: epistemic_fm_i > $o] :
( ( ( finite3304564979551393739c_fm_i @ ( collec4904205187116291597c_fm_i @ P3 ) )
| ( finite3304564979551393739c_fm_i @ ( collec4904205187116291597c_fm_i @ Q2 ) ) )
=> ( finite3304564979551393739c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( P3 @ X2 )
& ( Q2 @ X2 ) ) ) ) ) ).
% finite_Collect_conjI
thf(fact_45_finite__Collect__conjI,axiom,
! [P3: set_Epistemic_fm_i > $o,Q2: set_Epistemic_fm_i > $o] :
( ( ( finite7933139204641697195c_fm_i @ ( collec3087743281813070829c_fm_i @ P3 ) )
| ( finite7933139204641697195c_fm_i @ ( collec3087743281813070829c_fm_i @ Q2 ) ) )
=> ( finite7933139204641697195c_fm_i
@ ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( P3 @ X2 )
& ( Q2 @ X2 ) ) ) ) ) ).
% finite_Collect_conjI
thf(fact_46_finite__Collect__disjI,axiom,
! [P3: list_Epistemic_fm_i > $o,Q2: list_Epistemic_fm_i > $o] :
( ( finite3106398504192302929c_fm_i
@ ( collec5759350117362652307c_fm_i
@ ^ [X2: list_Epistemic_fm_i] :
( ( P3 @ X2 )
| ( Q2 @ X2 ) ) ) )
= ( ( finite3106398504192302929c_fm_i @ ( collec5759350117362652307c_fm_i @ P3 ) )
& ( finite3106398504192302929c_fm_i @ ( collec5759350117362652307c_fm_i @ Q2 ) ) ) ) ).
% finite_Collect_disjI
thf(fact_47_finite__Collect__disjI,axiom,
! [P3: set_se3485332733965609186c_fm_i > $o,Q2: set_se3485332733965609186c_fm_i > $o] :
( ( finite9087983574947184523c_fm_i
@ ( collec2761885132556217805c_fm_i
@ ^ [X2: set_se3485332733965609186c_fm_i] :
( ( P3 @ X2 )
| ( Q2 @ X2 ) ) ) )
= ( ( finite9087983574947184523c_fm_i @ ( collec2761885132556217805c_fm_i @ P3 ) )
& ( finite9087983574947184523c_fm_i @ ( collec2761885132556217805c_fm_i @ Q2 ) ) ) ) ).
% finite_Collect_disjI
thf(fact_48_finite__Collect__disjI,axiom,
! [P3: ( set_Epistemic_fm_i > epistemic_fm_i ) > $o,Q2: ( set_Epistemic_fm_i > epistemic_fm_i ) > $o] :
( ( finite5517585301071133084c_fm_i
@ ( collec6909220245477468634c_fm_i
@ ^ [X2: set_Epistemic_fm_i > epistemic_fm_i] :
( ( P3 @ X2 )
| ( Q2 @ X2 ) ) ) )
= ( ( finite5517585301071133084c_fm_i @ ( collec6909220245477468634c_fm_i @ P3 ) )
& ( finite5517585301071133084c_fm_i @ ( collec6909220245477468634c_fm_i @ Q2 ) ) ) ) ).
% finite_Collect_disjI
thf(fact_49_finite__Collect__disjI,axiom,
! [P3: ( epistemic_fm_i > epistemic_fm_i ) > $o,Q2: ( epistemic_fm_i > epistemic_fm_i ) > $o] :
( ( finite4369126853184676732c_fm_i
@ ( collec4821997688893311930c_fm_i
@ ^ [X2: epistemic_fm_i > epistemic_fm_i] :
( ( P3 @ X2 )
| ( Q2 @ X2 ) ) ) )
= ( ( finite4369126853184676732c_fm_i @ ( collec4821997688893311930c_fm_i @ P3 ) )
& ( finite4369126853184676732c_fm_i @ ( collec4821997688893311930c_fm_i @ Q2 ) ) ) ) ).
% finite_Collect_disjI
thf(fact_50_finite__Collect__disjI,axiom,
! [P3: epistemic_fm_i > $o,Q2: epistemic_fm_i > $o] :
( ( finite3304564979551393739c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( P3 @ X2 )
| ( Q2 @ X2 ) ) ) )
= ( ( finite3304564979551393739c_fm_i @ ( collec4904205187116291597c_fm_i @ P3 ) )
& ( finite3304564979551393739c_fm_i @ ( collec4904205187116291597c_fm_i @ Q2 ) ) ) ) ).
% finite_Collect_disjI
thf(fact_51_finite__Collect__disjI,axiom,
! [P3: set_Epistemic_fm_i > $o,Q2: set_Epistemic_fm_i > $o] :
( ( finite7933139204641697195c_fm_i
@ ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( P3 @ X2 )
| ( Q2 @ X2 ) ) ) )
= ( ( finite7933139204641697195c_fm_i @ ( collec3087743281813070829c_fm_i @ P3 ) )
& ( finite7933139204641697195c_fm_i @ ( collec3087743281813070829c_fm_i @ Q2 ) ) ) ) ).
% finite_Collect_disjI
thf(fact_52_fm_Oinject_I5_J,axiom,
! [X61: set_Epistemic_fm_i,X62: episte4276422356747265950c_fm_i,Y61: set_Epistemic_fm_i,Y62: episte4276422356747265950c_fm_i] :
( ( ( episte3581967596712343542c_fm_i @ X61 @ X62 )
= ( episte3581967596712343542c_fm_i @ Y61 @ Y62 ) )
= ( ( X61 = Y61 )
& ( X62 = Y62 ) ) ) ).
% fm.inject(5)
thf(fact_53_fm_Oinject_I5_J,axiom,
! [X61: epistemic_fm_i,X62: episte1308613106011496894c_fm_i,Y61: epistemic_fm_i,Y62: episte1308613106011496894c_fm_i] :
( ( ( episte5657488666450005526c_fm_i @ X61 @ X62 )
= ( episte5657488666450005526c_fm_i @ Y61 @ Y62 ) )
= ( ( X61 = Y61 )
& ( X62 = Y62 ) ) ) ).
% fm.inject(5)
thf(fact_54_fm_Oinject_I5_J,axiom,
! [X61: i,X62: epistemic_fm_i,Y61: i,Y62: epistemic_fm_i] :
( ( ( epistemic_K_i @ X61 @ X62 )
= ( epistemic_K_i @ Y61 @ Y62 ) )
= ( ( X61 = Y61 )
& ( X62 = Y62 ) ) ) ).
% fm.inject(5)
thf(fact_55_UnCI,axiom,
! [C2: i,B2: set_i,A: set_i] :
( ( ~ ( member_i @ C2 @ B2 )
=> ( member_i @ C2 @ A ) )
=> ( member_i @ C2 @ ( sup_sup_set_i @ A @ B2 ) ) ) ).
% UnCI
thf(fact_56_UnCI,axiom,
! [C2: list_s8081015415394010888c_fm_i,B2: set_li2934481837907835752c_fm_i,A: set_li2934481837907835752c_fm_i] :
( ( ~ ( member605545779687026225c_fm_i @ C2 @ B2 )
=> ( member605545779687026225c_fm_i @ C2 @ A ) )
=> ( member605545779687026225c_fm_i @ C2 @ ( sup_su6123556432952969532c_fm_i @ A @ B2 ) ) ) ).
% UnCI
thf(fact_57_UnCI,axiom,
! [C2: list_Epistemic_fm_i,B2: set_li8269783359719514504c_fm_i,A: set_li8269783359719514504c_fm_i] :
( ( ~ ( member6475149752759350353c_fm_i @ C2 @ B2 )
=> ( member6475149752759350353c_fm_i @ C2 @ A ) )
=> ( member6475149752759350353c_fm_i @ C2 @ ( sup_su33170788683693916c_fm_i @ A @ B2 ) ) ) ).
% UnCI
thf(fact_58_UnCI,axiom,
! [C2: set_se3485332733965609186c_fm_i,B2: set_se7339729205154126530c_fm_i,A: set_se7339729205154126530c_fm_i] :
( ( ~ ( member1461078328125707403c_fm_i @ C2 @ B2 )
=> ( member1461078328125707403c_fm_i @ C2 @ A ) )
=> ( member1461078328125707403c_fm_i @ C2 @ ( sup_su2317974602288960150c_fm_i @ A @ B2 ) ) ) ).
% UnCI
thf(fact_59_UnCI,axiom,
! [C2: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( ~ ( member1104366573291651755c_fm_i @ C2 @ B2 )
=> ( member1104366573291651755c_fm_i @ C2 @ A ) )
=> ( member1104366573291651755c_fm_i @ C2 @ ( sup_su2582925890723967158c_fm_i @ A @ B2 ) ) ) ).
% UnCI
thf(fact_60_UnCI,axiom,
! [C2: epistemic_fm_i,B2: set_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( ~ ( member6642669606046002379c_fm_i @ C2 @ B2 )
=> ( member6642669606046002379c_fm_i @ C2 @ A ) )
=> ( member6642669606046002379c_fm_i @ C2 @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) ) ) ).
% UnCI
thf(fact_61_assms_I2_J,axiom,
episte2285483198712856234tent_i @ a @ v ).
% assms(2)
thf(fact_62_subset__antisym,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A @ B2 )
=> ( ( ord_le5389487502678872194c_fm_i @ B2 @ A )
=> ( A = B2 ) ) ) ).
% subset_antisym
thf(fact_63_subset__antisym,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i] :
( ( ord_le2772500130360476258c_fm_i @ A @ B2 )
=> ( ( ord_le2772500130360476258c_fm_i @ B2 @ A )
=> ( A = B2 ) ) ) ).
% subset_antisym
thf(fact_64_subset__antisym,axiom,
! [A: set_li8269783359719514504c_fm_i,B2: set_li8269783359719514504c_fm_i] :
( ( ord_le1209247765174941992c_fm_i @ A @ B2 )
=> ( ( ord_le1209247765174941992c_fm_i @ B2 @ A )
=> ( A = B2 ) ) ) ).
% subset_antisym
thf(fact_65_subset__antisym,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ( ord_le3843937902494030498c_fm_i @ B2 @ A )
=> ( A = B2 ) ) ) ).
% subset_antisym
thf(fact_66_subsetI,axiom,
! [A: set_i,B2: set_i] :
( ! [X3: i] :
( ( member_i @ X3 @ A )
=> ( member_i @ X3 @ B2 ) )
=> ( ord_less_eq_set_i @ A @ B2 ) ) ).
% subsetI
thf(fact_67_subsetI,axiom,
! [A: set_li2934481837907835752c_fm_i,B2: set_li2934481837907835752c_fm_i] :
( ! [X3: list_s8081015415394010888c_fm_i] :
( ( member605545779687026225c_fm_i @ X3 @ A )
=> ( member605545779687026225c_fm_i @ X3 @ B2 ) )
=> ( ord_le1241842563113145096c_fm_i @ A @ B2 ) ) ).
% subsetI
thf(fact_68_subsetI,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i] :
( ! [X3: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ X3 @ A )
=> ( member1461078328125707403c_fm_i @ X3 @ B2 ) )
=> ( ord_le2772500130360476258c_fm_i @ A @ B2 ) ) ).
% subsetI
thf(fact_69_subsetI,axiom,
! [A: set_li8269783359719514504c_fm_i,B2: set_li8269783359719514504c_fm_i] :
( ! [X3: list_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ X3 @ A )
=> ( member6475149752759350353c_fm_i @ X3 @ B2 ) )
=> ( ord_le1209247765174941992c_fm_i @ A @ B2 ) ) ).
% subsetI
thf(fact_70_subsetI,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ! [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
=> ( member1104366573291651755c_fm_i @ X3 @ B2 ) )
=> ( ord_le5389487502678872194c_fm_i @ A @ B2 ) ) ).
% subsetI
thf(fact_71_subsetI,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ! [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ A )
=> ( member6642669606046002379c_fm_i @ X3 @ B2 ) )
=> ( ord_le3843937902494030498c_fm_i @ A @ B2 ) ) ).
% subsetI
thf(fact_72_sup__apply,axiom,
( sup_su2844414564337698183fm_i_o
= ( ^ [F2: epistemic_fm_i > $o,G2: epistemic_fm_i > $o,X2: epistemic_fm_i] : ( sup_sup_o @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ).
% sup_apply
thf(fact_73_sup__apply,axiom,
( sup_su6723579903606884263fm_i_o
= ( ^ [F2: set_Epistemic_fm_i > $o,G2: set_Epistemic_fm_i > $o,X2: set_Epistemic_fm_i] : ( sup_sup_o @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ).
% sup_apply
thf(fact_74_sup_Oright__idem,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ ( sup_su2582925890723967158c_fm_i @ A2 @ B3 ) @ B3 )
= ( sup_su2582925890723967158c_fm_i @ A2 @ B3 ) ) ).
% sup.right_idem
thf(fact_75_sup_Oright__idem,axiom,
! [A2: epistemic_fm_i > $o,B3: epistemic_fm_i > $o] :
( ( sup_su2844414564337698183fm_i_o @ ( sup_su2844414564337698183fm_i_o @ A2 @ B3 ) @ B3 )
= ( sup_su2844414564337698183fm_i_o @ A2 @ B3 ) ) ).
% sup.right_idem
thf(fact_76_sup_Oright__idem,axiom,
! [A2: set_Epistemic_fm_i > $o,B3: set_Epistemic_fm_i > $o] :
( ( sup_su6723579903606884263fm_i_o @ ( sup_su6723579903606884263fm_i_o @ A2 @ B3 ) @ B3 )
= ( sup_su6723579903606884263fm_i_o @ A2 @ B3 ) ) ).
% sup.right_idem
thf(fact_77_sup_Oright__idem,axiom,
! [A2: set_se7339729205154126530c_fm_i,B3: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ ( sup_su2317974602288960150c_fm_i @ A2 @ B3 ) @ B3 )
= ( sup_su2317974602288960150c_fm_i @ A2 @ B3 ) ) ).
% sup.right_idem
thf(fact_78_sup_Oright__idem,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) @ B3 )
= ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) ) ).
% sup.right_idem
thf(fact_79_sup__left__idem,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ X @ ( sup_su2582925890723967158c_fm_i @ X @ Y ) )
= ( sup_su2582925890723967158c_fm_i @ X @ Y ) ) ).
% sup_left_idem
thf(fact_80_sup__left__idem,axiom,
! [X: epistemic_fm_i > $o,Y: epistemic_fm_i > $o] :
( ( sup_su2844414564337698183fm_i_o @ X @ ( sup_su2844414564337698183fm_i_o @ X @ Y ) )
= ( sup_su2844414564337698183fm_i_o @ X @ Y ) ) ).
% sup_left_idem
thf(fact_81_sup__left__idem,axiom,
! [X: set_Epistemic_fm_i > $o,Y: set_Epistemic_fm_i > $o] :
( ( sup_su6723579903606884263fm_i_o @ X @ ( sup_su6723579903606884263fm_i_o @ X @ Y ) )
= ( sup_su6723579903606884263fm_i_o @ X @ Y ) ) ).
% sup_left_idem
thf(fact_82_sup__left__idem,axiom,
! [X: set_se7339729205154126530c_fm_i,Y: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ X @ ( sup_su2317974602288960150c_fm_i @ X @ Y ) )
= ( sup_su2317974602288960150c_fm_i @ X @ Y ) ) ).
% sup_left_idem
thf(fact_83_sup__left__idem,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ X @ Y ) )
= ( sup_su1936195050962291414c_fm_i @ X @ Y ) ) ).
% sup_left_idem
thf(fact_84_sup_Oleft__idem,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ A2 @ ( sup_su2582925890723967158c_fm_i @ A2 @ B3 ) )
= ( sup_su2582925890723967158c_fm_i @ A2 @ B3 ) ) ).
% sup.left_idem
thf(fact_85_sup_Oleft__idem,axiom,
! [A2: epistemic_fm_i > $o,B3: epistemic_fm_i > $o] :
( ( sup_su2844414564337698183fm_i_o @ A2 @ ( sup_su2844414564337698183fm_i_o @ A2 @ B3 ) )
= ( sup_su2844414564337698183fm_i_o @ A2 @ B3 ) ) ).
% sup.left_idem
thf(fact_86_sup_Oleft__idem,axiom,
! [A2: set_Epistemic_fm_i > $o,B3: set_Epistemic_fm_i > $o] :
( ( sup_su6723579903606884263fm_i_o @ A2 @ ( sup_su6723579903606884263fm_i_o @ A2 @ B3 ) )
= ( sup_su6723579903606884263fm_i_o @ A2 @ B3 ) ) ).
% sup.left_idem
thf(fact_87_sup_Oleft__idem,axiom,
! [A2: set_se7339729205154126530c_fm_i,B3: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ A2 @ ( sup_su2317974602288960150c_fm_i @ A2 @ B3 ) )
= ( sup_su2317974602288960150c_fm_i @ A2 @ B3 ) ) ).
% sup.left_idem
thf(fact_88_sup_Oleft__idem,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ A2 @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) )
= ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) ) ).
% sup.left_idem
thf(fact_89_sup__idem,axiom,
! [X: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ X @ X )
= X ) ).
% sup_idem
thf(fact_90_sup__idem,axiom,
! [X: epistemic_fm_i > $o] :
( ( sup_su2844414564337698183fm_i_o @ X @ X )
= X ) ).
% sup_idem
thf(fact_91_sup__idem,axiom,
! [X: set_Epistemic_fm_i > $o] :
( ( sup_su6723579903606884263fm_i_o @ X @ X )
= X ) ).
% sup_idem
thf(fact_92_sup__idem,axiom,
! [X: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ X @ X )
= X ) ).
% sup_idem
thf(fact_93_sup__idem,axiom,
! [X: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ X @ X )
= X ) ).
% sup_idem
thf(fact_94_sup_Oidem,axiom,
! [A2: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ A2 @ A2 )
= A2 ) ).
% sup.idem
thf(fact_95_sup_Oidem,axiom,
! [A2: epistemic_fm_i > $o] :
( ( sup_su2844414564337698183fm_i_o @ A2 @ A2 )
= A2 ) ).
% sup.idem
thf(fact_96_sup_Oidem,axiom,
! [A2: set_Epistemic_fm_i > $o] :
( ( sup_su6723579903606884263fm_i_o @ A2 @ A2 )
= A2 ) ).
% sup.idem
thf(fact_97_sup_Oidem,axiom,
! [A2: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ A2 @ A2 )
= A2 ) ).
% sup.idem
thf(fact_98_sup_Oidem,axiom,
! [A2: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ A2 @ A2 )
= A2 ) ).
% sup.idem
thf(fact_99_Un__iff,axiom,
! [C2: i,A: set_i,B2: set_i] :
( ( member_i @ C2 @ ( sup_sup_set_i @ A @ B2 ) )
= ( ( member_i @ C2 @ A )
| ( member_i @ C2 @ B2 ) ) ) ).
% Un_iff
thf(fact_100_Un__iff,axiom,
! [C2: list_s8081015415394010888c_fm_i,A: set_li2934481837907835752c_fm_i,B2: set_li2934481837907835752c_fm_i] :
( ( member605545779687026225c_fm_i @ C2 @ ( sup_su6123556432952969532c_fm_i @ A @ B2 ) )
= ( ( member605545779687026225c_fm_i @ C2 @ A )
| ( member605545779687026225c_fm_i @ C2 @ B2 ) ) ) ).
% Un_iff
thf(fact_101_Un__iff,axiom,
! [C2: list_Epistemic_fm_i,A: set_li8269783359719514504c_fm_i,B2: set_li8269783359719514504c_fm_i] :
( ( member6475149752759350353c_fm_i @ C2 @ ( sup_su33170788683693916c_fm_i @ A @ B2 ) )
= ( ( member6475149752759350353c_fm_i @ C2 @ A )
| ( member6475149752759350353c_fm_i @ C2 @ B2 ) ) ) ).
% Un_iff
thf(fact_102_Un__iff,axiom,
! [C2: set_se3485332733965609186c_fm_i,A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i] :
( ( member1461078328125707403c_fm_i @ C2 @ ( sup_su2317974602288960150c_fm_i @ A @ B2 ) )
= ( ( member1461078328125707403c_fm_i @ C2 @ A )
| ( member1461078328125707403c_fm_i @ C2 @ B2 ) ) ) ).
% Un_iff
thf(fact_103_Un__iff,axiom,
! [C2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ C2 @ ( sup_su2582925890723967158c_fm_i @ A @ B2 ) )
= ( ( member1104366573291651755c_fm_i @ C2 @ A )
| ( member1104366573291651755c_fm_i @ C2 @ B2 ) ) ) ).
% Un_iff
thf(fact_104_Un__iff,axiom,
! [C2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ C2 @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) )
= ( ( member6642669606046002379c_fm_i @ C2 @ A )
| ( member6642669606046002379c_fm_i @ C2 @ B2 ) ) ) ).
% Un_iff
thf(fact_105_assms_I5_J,axiom,
maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ a ) @ w ).
% assms(5)
thf(fact_106_assms_I7_J,axiom,
maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ a ) @ u ).
% assms(7)
thf(fact_107_assms_I3_J,axiom,
maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ a ) @ v ).
% assms(3)
thf(fact_108_consistent__hereditary,axiom,
! [A: epistemic_fm_i > $o,S: set_Epistemic_fm_i,S2: set_Epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ A @ S )
=> ( ( ord_le3843937902494030498c_fm_i @ S2 @ S )
=> ( episte2285483198712856234tent_i @ A @ S2 ) ) ) ).
% consistent_hereditary
thf(fact_109_sup__set__def,axiom,
( sup_sup_set_i
= ( ^ [A3: set_i,B: set_i] :
( collect_i
@ ( sup_sup_i_o
@ ^ [X2: i] : ( member_i @ X2 @ A3 )
@ ^ [X2: i] : ( member_i @ X2 @ B ) ) ) ) ) ).
% sup_set_def
thf(fact_110_sup__set__def,axiom,
( sup_su6123556432952969532c_fm_i
= ( ^ [A3: set_li2934481837907835752c_fm_i,B: set_li2934481837907835752c_fm_i] :
( collec2200325868635342451c_fm_i
@ ( sup_su2317072595969462433fm_i_o
@ ^ [X2: list_s8081015415394010888c_fm_i] : ( member605545779687026225c_fm_i @ X2 @ A3 )
@ ^ [X2: list_s8081015415394010888c_fm_i] : ( member605545779687026225c_fm_i @ X2 @ B ) ) ) ) ) ).
% sup_set_def
thf(fact_111_sup__set__def,axiom,
( sup_su33170788683693916c_fm_i
= ( ^ [A3: set_li8269783359719514504c_fm_i,B: set_li8269783359719514504c_fm_i] :
( collec5759350117362652307c_fm_i
@ ( sup_su7027133776084382337fm_i_o
@ ^ [X2: list_Epistemic_fm_i] : ( member6475149752759350353c_fm_i @ X2 @ A3 )
@ ^ [X2: list_Epistemic_fm_i] : ( member6475149752759350353c_fm_i @ X2 @ B ) ) ) ) ) ).
% sup_set_def
thf(fact_112_sup__set__def,axiom,
( sup_su2317974602288960150c_fm_i
= ( ^ [A3: set_se7339729205154126530c_fm_i,B: set_se7339729205154126530c_fm_i] :
( collec2761885132556217805c_fm_i
@ ( sup_su5020628091962035655fm_i_o
@ ^ [X2: set_se3485332733965609186c_fm_i] : ( member1461078328125707403c_fm_i @ X2 @ A3 )
@ ^ [X2: set_se3485332733965609186c_fm_i] : ( member1461078328125707403c_fm_i @ X2 @ B ) ) ) ) ) ).
% sup_set_def
thf(fact_113_sup__set__def,axiom,
( sup_su2582925890723967158c_fm_i
= ( ^ [A3: set_se3485332733965609186c_fm_i,B: set_se3485332733965609186c_fm_i] :
( collec3087743281813070829c_fm_i
@ ( sup_su6723579903606884263fm_i_o
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ A3 )
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ B ) ) ) ) ) ).
% sup_set_def
thf(fact_114_sup__set__def,axiom,
( sup_su1936195050962291414c_fm_i
= ( ^ [A3: set_Epistemic_fm_i,B: set_Epistemic_fm_i] :
( collec4904205187116291597c_fm_i
@ ( sup_su2844414564337698183fm_i_o
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ A3 )
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ B ) ) ) ) ) ).
% sup_set_def
thf(fact_115_less__eq__set__def,axiom,
( ord_less_eq_set_i
= ( ^ [A3: set_i,B: set_i] :
( ord_less_eq_i_o
@ ^ [X2: i] : ( member_i @ X2 @ A3 )
@ ^ [X2: i] : ( member_i @ X2 @ B ) ) ) ) ).
% less_eq_set_def
thf(fact_116_less__eq__set__def,axiom,
( ord_le1241842563113145096c_fm_i
= ( ^ [A3: set_li2934481837907835752c_fm_i,B: set_li2934481837907835752c_fm_i] :
( ord_le1881634118666284501fm_i_o
@ ^ [X2: list_s8081015415394010888c_fm_i] : ( member605545779687026225c_fm_i @ X2 @ A3 )
@ ^ [X2: list_s8081015415394010888c_fm_i] : ( member605545779687026225c_fm_i @ X2 @ B ) ) ) ) ).
% less_eq_set_def
thf(fact_117_less__eq__set__def,axiom,
( ord_le2772500130360476258c_fm_i
= ( ^ [A3: set_se7339729205154126530c_fm_i,B: set_se7339729205154126530c_fm_i] :
( ord_le1814827286658909435fm_i_o
@ ^ [X2: set_se3485332733965609186c_fm_i] : ( member1461078328125707403c_fm_i @ X2 @ A3 )
@ ^ [X2: set_se3485332733965609186c_fm_i] : ( member1461078328125707403c_fm_i @ X2 @ B ) ) ) ) ).
% less_eq_set_def
thf(fact_118_less__eq__set__def,axiom,
( ord_le1209247765174941992c_fm_i
= ( ^ [A3: set_li8269783359719514504c_fm_i,B: set_li8269783359719514504c_fm_i] :
( ord_le204167446249480117fm_i_o
@ ^ [X2: list_Epistemic_fm_i] : ( member6475149752759350353c_fm_i @ X2 @ A3 )
@ ^ [X2: list_Epistemic_fm_i] : ( member6475149752759350353c_fm_i @ X2 @ B ) ) ) ) ).
% less_eq_set_def
thf(fact_119_less__eq__set__def,axiom,
( ord_le5389487502678872194c_fm_i
= ( ^ [A3: set_se3485332733965609186c_fm_i,B: set_se3485332733965609186c_fm_i] :
( ord_le5706303257367236315fm_i_o
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ A3 )
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ B ) ) ) ) ).
% less_eq_set_def
thf(fact_120_less__eq__set__def,axiom,
( ord_le3843937902494030498c_fm_i
= ( ^ [A3: set_Epistemic_fm_i,B: set_Epistemic_fm_i] :
( ord_le190830114487426235fm_i_o
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ A3 )
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ B ) ) ) ) ).
% less_eq_set_def
thf(fact_121_inconsistent__finite,axiom,
! [A: epistemic_fm_i > $o,S: set_Epistemic_fm_i] :
( ~ ( episte2285483198712856234tent_i @ A @ S )
=> ? [S3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ S3 @ S )
& ( finite3304564979551393739c_fm_i @ S3 )
& ~ ( episte2285483198712856234tent_i @ A @ S3 ) ) ) ).
% inconsistent_finite
thf(fact_122_Collect__mono__iff,axiom,
! [P3: set_se3485332733965609186c_fm_i > $o,Q2: set_se3485332733965609186c_fm_i > $o] :
( ( ord_le2772500130360476258c_fm_i @ ( collec2761885132556217805c_fm_i @ P3 ) @ ( collec2761885132556217805c_fm_i @ Q2 ) )
= ( ! [X2: set_se3485332733965609186c_fm_i] :
( ( P3 @ X2 )
=> ( Q2 @ X2 ) ) ) ) ).
% Collect_mono_iff
thf(fact_123_Collect__mono__iff,axiom,
! [P3: list_Epistemic_fm_i > $o,Q2: list_Epistemic_fm_i > $o] :
( ( ord_le1209247765174941992c_fm_i @ ( collec5759350117362652307c_fm_i @ P3 ) @ ( collec5759350117362652307c_fm_i @ Q2 ) )
= ( ! [X2: list_Epistemic_fm_i] :
( ( P3 @ X2 )
=> ( Q2 @ X2 ) ) ) ) ).
% Collect_mono_iff
thf(fact_124_Collect__mono__iff,axiom,
! [P3: set_Epistemic_fm_i > $o,Q2: set_Epistemic_fm_i > $o] :
( ( ord_le5389487502678872194c_fm_i @ ( collec3087743281813070829c_fm_i @ P3 ) @ ( collec3087743281813070829c_fm_i @ Q2 ) )
= ( ! [X2: set_Epistemic_fm_i] :
( ( P3 @ X2 )
=> ( Q2 @ X2 ) ) ) ) ).
% Collect_mono_iff
thf(fact_125_Collect__mono__iff,axiom,
! [P3: epistemic_fm_i > $o,Q2: epistemic_fm_i > $o] :
( ( ord_le3843937902494030498c_fm_i @ ( collec4904205187116291597c_fm_i @ P3 ) @ ( collec4904205187116291597c_fm_i @ Q2 ) )
= ( ! [X2: epistemic_fm_i] :
( ( P3 @ X2 )
=> ( Q2 @ X2 ) ) ) ) ).
% Collect_mono_iff
thf(fact_126_set__eq__subset,axiom,
( ( ^ [Y2: set_se3485332733965609186c_fm_i,Z2: set_se3485332733965609186c_fm_i] : ( Y2 = Z2 ) )
= ( ^ [A3: set_se3485332733965609186c_fm_i,B: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A3 @ B )
& ( ord_le5389487502678872194c_fm_i @ B @ A3 ) ) ) ) ).
% set_eq_subset
thf(fact_127_set__eq__subset,axiom,
( ( ^ [Y2: set_se7339729205154126530c_fm_i,Z2: set_se7339729205154126530c_fm_i] : ( Y2 = Z2 ) )
= ( ^ [A3: set_se7339729205154126530c_fm_i,B: set_se7339729205154126530c_fm_i] :
( ( ord_le2772500130360476258c_fm_i @ A3 @ B )
& ( ord_le2772500130360476258c_fm_i @ B @ A3 ) ) ) ) ).
% set_eq_subset
thf(fact_128_set__eq__subset,axiom,
( ( ^ [Y2: set_li8269783359719514504c_fm_i,Z2: set_li8269783359719514504c_fm_i] : ( Y2 = Z2 ) )
= ( ^ [A3: set_li8269783359719514504c_fm_i,B: set_li8269783359719514504c_fm_i] :
( ( ord_le1209247765174941992c_fm_i @ A3 @ B )
& ( ord_le1209247765174941992c_fm_i @ B @ A3 ) ) ) ) ).
% set_eq_subset
thf(fact_129_set__eq__subset,axiom,
( ( ^ [Y2: set_Epistemic_fm_i,Z2: set_Epistemic_fm_i] : ( Y2 = Z2 ) )
= ( ^ [A3: set_Epistemic_fm_i,B: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A3 @ B )
& ( ord_le3843937902494030498c_fm_i @ B @ A3 ) ) ) ) ).
% set_eq_subset
thf(fact_130_subset__trans,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A @ B2 )
=> ( ( ord_le5389487502678872194c_fm_i @ B2 @ C )
=> ( ord_le5389487502678872194c_fm_i @ A @ C ) ) ) ).
% subset_trans
thf(fact_131_subset__trans,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i,C: set_se7339729205154126530c_fm_i] :
( ( ord_le2772500130360476258c_fm_i @ A @ B2 )
=> ( ( ord_le2772500130360476258c_fm_i @ B2 @ C )
=> ( ord_le2772500130360476258c_fm_i @ A @ C ) ) ) ).
% subset_trans
thf(fact_132_subset__trans,axiom,
! [A: set_li8269783359719514504c_fm_i,B2: set_li8269783359719514504c_fm_i,C: set_li8269783359719514504c_fm_i] :
( ( ord_le1209247765174941992c_fm_i @ A @ B2 )
=> ( ( ord_le1209247765174941992c_fm_i @ B2 @ C )
=> ( ord_le1209247765174941992c_fm_i @ A @ C ) ) ) ).
% subset_trans
thf(fact_133_subset__trans,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ( ord_le3843937902494030498c_fm_i @ B2 @ C )
=> ( ord_le3843937902494030498c_fm_i @ A @ C ) ) ) ).
% subset_trans
thf(fact_134_Collect__mono,axiom,
! [P3: set_se3485332733965609186c_fm_i > $o,Q2: set_se3485332733965609186c_fm_i > $o] :
( ! [X3: set_se3485332733965609186c_fm_i] :
( ( P3 @ X3 )
=> ( Q2 @ X3 ) )
=> ( ord_le2772500130360476258c_fm_i @ ( collec2761885132556217805c_fm_i @ P3 ) @ ( collec2761885132556217805c_fm_i @ Q2 ) ) ) ).
% Collect_mono
thf(fact_135_Collect__mono,axiom,
! [P3: list_Epistemic_fm_i > $o,Q2: list_Epistemic_fm_i > $o] :
( ! [X3: list_Epistemic_fm_i] :
( ( P3 @ X3 )
=> ( Q2 @ X3 ) )
=> ( ord_le1209247765174941992c_fm_i @ ( collec5759350117362652307c_fm_i @ P3 ) @ ( collec5759350117362652307c_fm_i @ Q2 ) ) ) ).
% Collect_mono
thf(fact_136_Collect__mono,axiom,
! [P3: set_Epistemic_fm_i > $o,Q2: set_Epistemic_fm_i > $o] :
( ! [X3: set_Epistemic_fm_i] :
( ( P3 @ X3 )
=> ( Q2 @ X3 ) )
=> ( ord_le5389487502678872194c_fm_i @ ( collec3087743281813070829c_fm_i @ P3 ) @ ( collec3087743281813070829c_fm_i @ Q2 ) ) ) ).
% Collect_mono
thf(fact_137_Collect__mono,axiom,
! [P3: epistemic_fm_i > $o,Q2: epistemic_fm_i > $o] :
( ! [X3: epistemic_fm_i] :
( ( P3 @ X3 )
=> ( Q2 @ X3 ) )
=> ( ord_le3843937902494030498c_fm_i @ ( collec4904205187116291597c_fm_i @ P3 ) @ ( collec4904205187116291597c_fm_i @ Q2 ) ) ) ).
% Collect_mono
thf(fact_138_subset__refl,axiom,
! [A: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ A @ A ) ).
% subset_refl
thf(fact_139_subset__refl,axiom,
! [A: set_se7339729205154126530c_fm_i] : ( ord_le2772500130360476258c_fm_i @ A @ A ) ).
% subset_refl
thf(fact_140_subset__refl,axiom,
! [A: set_li8269783359719514504c_fm_i] : ( ord_le1209247765174941992c_fm_i @ A @ A ) ).
% subset_refl
thf(fact_141_subset__refl,axiom,
! [A: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ A @ A ) ).
% subset_refl
thf(fact_142_subset__iff,axiom,
( ord_less_eq_set_i
= ( ^ [A3: set_i,B: set_i] :
! [T: i] :
( ( member_i @ T @ A3 )
=> ( member_i @ T @ B ) ) ) ) ).
% subset_iff
thf(fact_143_subset__iff,axiom,
( ord_le1241842563113145096c_fm_i
= ( ^ [A3: set_li2934481837907835752c_fm_i,B: set_li2934481837907835752c_fm_i] :
! [T: list_s8081015415394010888c_fm_i] :
( ( member605545779687026225c_fm_i @ T @ A3 )
=> ( member605545779687026225c_fm_i @ T @ B ) ) ) ) ).
% subset_iff
thf(fact_144_subset__iff,axiom,
( ord_le2772500130360476258c_fm_i
= ( ^ [A3: set_se7339729205154126530c_fm_i,B: set_se7339729205154126530c_fm_i] :
! [T: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ T @ A3 )
=> ( member1461078328125707403c_fm_i @ T @ B ) ) ) ) ).
% subset_iff
thf(fact_145_subset__iff,axiom,
( ord_le1209247765174941992c_fm_i
= ( ^ [A3: set_li8269783359719514504c_fm_i,B: set_li8269783359719514504c_fm_i] :
! [T: list_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ T @ A3 )
=> ( member6475149752759350353c_fm_i @ T @ B ) ) ) ) ).
% subset_iff
thf(fact_146_subset__iff,axiom,
( ord_le5389487502678872194c_fm_i
= ( ^ [A3: set_se3485332733965609186c_fm_i,B: set_se3485332733965609186c_fm_i] :
! [T: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ T @ A3 )
=> ( member1104366573291651755c_fm_i @ T @ B ) ) ) ) ).
% subset_iff
thf(fact_147_subset__iff,axiom,
( ord_le3843937902494030498c_fm_i
= ( ^ [A3: set_Epistemic_fm_i,B: set_Epistemic_fm_i] :
! [T: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ T @ A3 )
=> ( member6642669606046002379c_fm_i @ T @ B ) ) ) ) ).
% subset_iff
thf(fact_148_equalityD2,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( A = B2 )
=> ( ord_le5389487502678872194c_fm_i @ B2 @ A ) ) ).
% equalityD2
thf(fact_149_equalityD2,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i] :
( ( A = B2 )
=> ( ord_le2772500130360476258c_fm_i @ B2 @ A ) ) ).
% equalityD2
thf(fact_150_equalityD2,axiom,
! [A: set_li8269783359719514504c_fm_i,B2: set_li8269783359719514504c_fm_i] :
( ( A = B2 )
=> ( ord_le1209247765174941992c_fm_i @ B2 @ A ) ) ).
% equalityD2
thf(fact_151_equalityD2,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( A = B2 )
=> ( ord_le3843937902494030498c_fm_i @ B2 @ A ) ) ).
% equalityD2
thf(fact_152_equalityD1,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( A = B2 )
=> ( ord_le5389487502678872194c_fm_i @ A @ B2 ) ) ).
% equalityD1
thf(fact_153_equalityD1,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i] :
( ( A = B2 )
=> ( ord_le2772500130360476258c_fm_i @ A @ B2 ) ) ).
% equalityD1
thf(fact_154_equalityD1,axiom,
! [A: set_li8269783359719514504c_fm_i,B2: set_li8269783359719514504c_fm_i] :
( ( A = B2 )
=> ( ord_le1209247765174941992c_fm_i @ A @ B2 ) ) ).
% equalityD1
thf(fact_155_equalityD1,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( A = B2 )
=> ( ord_le3843937902494030498c_fm_i @ A @ B2 ) ) ).
% equalityD1
thf(fact_156_mem__Collect__eq,axiom,
! [A2: i,P3: i > $o] :
( ( member_i @ A2 @ ( collect_i @ P3 ) )
= ( P3 @ A2 ) ) ).
% mem_Collect_eq
thf(fact_157_mem__Collect__eq,axiom,
! [A2: list_s8081015415394010888c_fm_i,P3: list_s8081015415394010888c_fm_i > $o] :
( ( member605545779687026225c_fm_i @ A2 @ ( collec2200325868635342451c_fm_i @ P3 ) )
= ( P3 @ A2 ) ) ).
% mem_Collect_eq
thf(fact_158_mem__Collect__eq,axiom,
! [A2: set_se3485332733965609186c_fm_i,P3: set_se3485332733965609186c_fm_i > $o] :
( ( member1461078328125707403c_fm_i @ A2 @ ( collec2761885132556217805c_fm_i @ P3 ) )
= ( P3 @ A2 ) ) ).
% mem_Collect_eq
thf(fact_159_mem__Collect__eq,axiom,
! [A2: list_Epistemic_fm_i,P3: list_Epistemic_fm_i > $o] :
( ( member6475149752759350353c_fm_i @ A2 @ ( collec5759350117362652307c_fm_i @ P3 ) )
= ( P3 @ A2 ) ) ).
% mem_Collect_eq
thf(fact_160_mem__Collect__eq,axiom,
! [A2: epistemic_fm_i,P3: epistemic_fm_i > $o] :
( ( member6642669606046002379c_fm_i @ A2 @ ( collec4904205187116291597c_fm_i @ P3 ) )
= ( P3 @ A2 ) ) ).
% mem_Collect_eq
thf(fact_161_mem__Collect__eq,axiom,
! [A2: set_Epistemic_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( member1104366573291651755c_fm_i @ A2 @ ( collec3087743281813070829c_fm_i @ P3 ) )
= ( P3 @ A2 ) ) ).
% mem_Collect_eq
thf(fact_162_Collect__mem__eq,axiom,
! [A: set_i] :
( ( collect_i
@ ^ [X2: i] : ( member_i @ X2 @ A ) )
= A ) ).
% Collect_mem_eq
thf(fact_163_Collect__mem__eq,axiom,
! [A: set_li2934481837907835752c_fm_i] :
( ( collec2200325868635342451c_fm_i
@ ^ [X2: list_s8081015415394010888c_fm_i] : ( member605545779687026225c_fm_i @ X2 @ A ) )
= A ) ).
% Collect_mem_eq
thf(fact_164_Collect__mem__eq,axiom,
! [A: set_se7339729205154126530c_fm_i] :
( ( collec2761885132556217805c_fm_i
@ ^ [X2: set_se3485332733965609186c_fm_i] : ( member1461078328125707403c_fm_i @ X2 @ A ) )
= A ) ).
% Collect_mem_eq
thf(fact_165_Collect__mem__eq,axiom,
! [A: set_li8269783359719514504c_fm_i] :
( ( collec5759350117362652307c_fm_i
@ ^ [X2: list_Epistemic_fm_i] : ( member6475149752759350353c_fm_i @ X2 @ A ) )
= A ) ).
% Collect_mem_eq
thf(fact_166_Collect__mem__eq,axiom,
! [A: set_Epistemic_fm_i] :
( ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ A ) )
= A ) ).
% Collect_mem_eq
thf(fact_167_Collect__mem__eq,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ A ) )
= A ) ).
% Collect_mem_eq
thf(fact_168_Collect__cong,axiom,
! [P3: set_se3485332733965609186c_fm_i > $o,Q2: set_se3485332733965609186c_fm_i > $o] :
( ! [X3: set_se3485332733965609186c_fm_i] :
( ( P3 @ X3 )
= ( Q2 @ X3 ) )
=> ( ( collec2761885132556217805c_fm_i @ P3 )
= ( collec2761885132556217805c_fm_i @ Q2 ) ) ) ).
% Collect_cong
thf(fact_169_Collect__cong,axiom,
! [P3: list_Epistemic_fm_i > $o,Q2: list_Epistemic_fm_i > $o] :
( ! [X3: list_Epistemic_fm_i] :
( ( P3 @ X3 )
= ( Q2 @ X3 ) )
=> ( ( collec5759350117362652307c_fm_i @ P3 )
= ( collec5759350117362652307c_fm_i @ Q2 ) ) ) ).
% Collect_cong
thf(fact_170_Collect__cong,axiom,
! [P3: epistemic_fm_i > $o,Q2: epistemic_fm_i > $o] :
( ! [X3: epistemic_fm_i] :
( ( P3 @ X3 )
= ( Q2 @ X3 ) )
=> ( ( collec4904205187116291597c_fm_i @ P3 )
= ( collec4904205187116291597c_fm_i @ Q2 ) ) ) ).
% Collect_cong
thf(fact_171_Collect__cong,axiom,
! [P3: set_Epistemic_fm_i > $o,Q2: set_Epistemic_fm_i > $o] :
( ! [X3: set_Epistemic_fm_i] :
( ( P3 @ X3 )
= ( Q2 @ X3 ) )
=> ( ( collec3087743281813070829c_fm_i @ P3 )
= ( collec3087743281813070829c_fm_i @ Q2 ) ) ) ).
% Collect_cong
thf(fact_172_subset__eq,axiom,
( ord_less_eq_set_i
= ( ^ [A3: set_i,B: set_i] :
! [X2: i] :
( ( member_i @ X2 @ A3 )
=> ( member_i @ X2 @ B ) ) ) ) ).
% subset_eq
thf(fact_173_subset__eq,axiom,
( ord_le1241842563113145096c_fm_i
= ( ^ [A3: set_li2934481837907835752c_fm_i,B: set_li2934481837907835752c_fm_i] :
! [X2: list_s8081015415394010888c_fm_i] :
( ( member605545779687026225c_fm_i @ X2 @ A3 )
=> ( member605545779687026225c_fm_i @ X2 @ B ) ) ) ) ).
% subset_eq
thf(fact_174_subset__eq,axiom,
( ord_le2772500130360476258c_fm_i
= ( ^ [A3: set_se7339729205154126530c_fm_i,B: set_se7339729205154126530c_fm_i] :
! [X2: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ X2 @ A3 )
=> ( member1461078328125707403c_fm_i @ X2 @ B ) ) ) ) ).
% subset_eq
thf(fact_175_subset__eq,axiom,
( ord_le1209247765174941992c_fm_i
= ( ^ [A3: set_li8269783359719514504c_fm_i,B: set_li8269783359719514504c_fm_i] :
! [X2: list_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ X2 @ A3 )
=> ( member6475149752759350353c_fm_i @ X2 @ B ) ) ) ) ).
% subset_eq
thf(fact_176_subset__eq,axiom,
( ord_le5389487502678872194c_fm_i
= ( ^ [A3: set_se3485332733965609186c_fm_i,B: set_se3485332733965609186c_fm_i] :
! [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A3 )
=> ( member1104366573291651755c_fm_i @ X2 @ B ) ) ) ) ).
% subset_eq
thf(fact_177_subset__eq,axiom,
( ord_le3843937902494030498c_fm_i
= ( ^ [A3: set_Epistemic_fm_i,B: set_Epistemic_fm_i] :
! [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ A3 )
=> ( member6642669606046002379c_fm_i @ X2 @ B ) ) ) ) ).
% subset_eq
thf(fact_178_equalityE,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( A = B2 )
=> ~ ( ( ord_le5389487502678872194c_fm_i @ A @ B2 )
=> ~ ( ord_le5389487502678872194c_fm_i @ B2 @ A ) ) ) ).
% equalityE
thf(fact_179_equalityE,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i] :
( ( A = B2 )
=> ~ ( ( ord_le2772500130360476258c_fm_i @ A @ B2 )
=> ~ ( ord_le2772500130360476258c_fm_i @ B2 @ A ) ) ) ).
% equalityE
thf(fact_180_equalityE,axiom,
! [A: set_li8269783359719514504c_fm_i,B2: set_li8269783359719514504c_fm_i] :
( ( A = B2 )
=> ~ ( ( ord_le1209247765174941992c_fm_i @ A @ B2 )
=> ~ ( ord_le1209247765174941992c_fm_i @ B2 @ A ) ) ) ).
% equalityE
thf(fact_181_equalityE,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( A = B2 )
=> ~ ( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ~ ( ord_le3843937902494030498c_fm_i @ B2 @ A ) ) ) ).
% equalityE
thf(fact_182_subsetD,axiom,
! [A: set_i,B2: set_i,C2: i] :
( ( ord_less_eq_set_i @ A @ B2 )
=> ( ( member_i @ C2 @ A )
=> ( member_i @ C2 @ B2 ) ) ) ).
% subsetD
thf(fact_183_subsetD,axiom,
! [A: set_li2934481837907835752c_fm_i,B2: set_li2934481837907835752c_fm_i,C2: list_s8081015415394010888c_fm_i] :
( ( ord_le1241842563113145096c_fm_i @ A @ B2 )
=> ( ( member605545779687026225c_fm_i @ C2 @ A )
=> ( member605545779687026225c_fm_i @ C2 @ B2 ) ) ) ).
% subsetD
thf(fact_184_subsetD,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i,C2: set_se3485332733965609186c_fm_i] :
( ( ord_le2772500130360476258c_fm_i @ A @ B2 )
=> ( ( member1461078328125707403c_fm_i @ C2 @ A )
=> ( member1461078328125707403c_fm_i @ C2 @ B2 ) ) ) ).
% subsetD
thf(fact_185_subsetD,axiom,
! [A: set_li8269783359719514504c_fm_i,B2: set_li8269783359719514504c_fm_i,C2: list_Epistemic_fm_i] :
( ( ord_le1209247765174941992c_fm_i @ A @ B2 )
=> ( ( member6475149752759350353c_fm_i @ C2 @ A )
=> ( member6475149752759350353c_fm_i @ C2 @ B2 ) ) ) ).
% subsetD
thf(fact_186_subsetD,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C2: set_Epistemic_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A @ B2 )
=> ( ( member1104366573291651755c_fm_i @ C2 @ A )
=> ( member1104366573291651755c_fm_i @ C2 @ B2 ) ) ) ).
% subsetD
thf(fact_187_subsetD,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,C2: epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ( member6642669606046002379c_fm_i @ C2 @ A )
=> ( member6642669606046002379c_fm_i @ C2 @ B2 ) ) ) ).
% subsetD
thf(fact_188_in__mono,axiom,
! [A: set_i,B2: set_i,X: i] :
( ( ord_less_eq_set_i @ A @ B2 )
=> ( ( member_i @ X @ A )
=> ( member_i @ X @ B2 ) ) ) ).
% in_mono
thf(fact_189_in__mono,axiom,
! [A: set_li2934481837907835752c_fm_i,B2: set_li2934481837907835752c_fm_i,X: list_s8081015415394010888c_fm_i] :
( ( ord_le1241842563113145096c_fm_i @ A @ B2 )
=> ( ( member605545779687026225c_fm_i @ X @ A )
=> ( member605545779687026225c_fm_i @ X @ B2 ) ) ) ).
% in_mono
thf(fact_190_in__mono,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i,X: set_se3485332733965609186c_fm_i] :
( ( ord_le2772500130360476258c_fm_i @ A @ B2 )
=> ( ( member1461078328125707403c_fm_i @ X @ A )
=> ( member1461078328125707403c_fm_i @ X @ B2 ) ) ) ).
% in_mono
thf(fact_191_in__mono,axiom,
! [A: set_li8269783359719514504c_fm_i,B2: set_li8269783359719514504c_fm_i,X: list_Epistemic_fm_i] :
( ( ord_le1209247765174941992c_fm_i @ A @ B2 )
=> ( ( member6475149752759350353c_fm_i @ X @ A )
=> ( member6475149752759350353c_fm_i @ X @ B2 ) ) ) ).
% in_mono
thf(fact_192_in__mono,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A @ B2 )
=> ( ( member1104366573291651755c_fm_i @ X @ A )
=> ( member1104366573291651755c_fm_i @ X @ B2 ) ) ) ).
% in_mono
thf(fact_193_in__mono,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,X: epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ( member6642669606046002379c_fm_i @ X @ A )
=> ( member6642669606046002379c_fm_i @ X @ B2 ) ) ) ).
% in_mono
thf(fact_194_sup__fun__def,axiom,
( sup_su2844414564337698183fm_i_o
= ( ^ [F2: epistemic_fm_i > $o,G2: epistemic_fm_i > $o,X2: epistemic_fm_i] : ( sup_sup_o @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ).
% sup_fun_def
thf(fact_195_sup__fun__def,axiom,
( sup_su6723579903606884263fm_i_o
= ( ^ [F2: set_Epistemic_fm_i > $o,G2: set_Epistemic_fm_i > $o,X2: set_Epistemic_fm_i] : ( sup_sup_o @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ).
% sup_fun_def
thf(fact_196_sup__left__commute,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ X @ ( sup_su2582925890723967158c_fm_i @ Y @ Z ) )
= ( sup_su2582925890723967158c_fm_i @ Y @ ( sup_su2582925890723967158c_fm_i @ X @ Z ) ) ) ).
% sup_left_commute
thf(fact_197_sup__left__commute,axiom,
! [X: epistemic_fm_i > $o,Y: epistemic_fm_i > $o,Z: epistemic_fm_i > $o] :
( ( sup_su2844414564337698183fm_i_o @ X @ ( sup_su2844414564337698183fm_i_o @ Y @ Z ) )
= ( sup_su2844414564337698183fm_i_o @ Y @ ( sup_su2844414564337698183fm_i_o @ X @ Z ) ) ) ).
% sup_left_commute
thf(fact_198_sup__left__commute,axiom,
! [X: set_Epistemic_fm_i > $o,Y: set_Epistemic_fm_i > $o,Z: set_Epistemic_fm_i > $o] :
( ( sup_su6723579903606884263fm_i_o @ X @ ( sup_su6723579903606884263fm_i_o @ Y @ Z ) )
= ( sup_su6723579903606884263fm_i_o @ Y @ ( sup_su6723579903606884263fm_i_o @ X @ Z ) ) ) ).
% sup_left_commute
thf(fact_199_sup__left__commute,axiom,
! [X: set_se7339729205154126530c_fm_i,Y: set_se7339729205154126530c_fm_i,Z: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ X @ ( sup_su2317974602288960150c_fm_i @ Y @ Z ) )
= ( sup_su2317974602288960150c_fm_i @ Y @ ( sup_su2317974602288960150c_fm_i @ X @ Z ) ) ) ).
% sup_left_commute
thf(fact_200_sup__left__commute,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ Y @ Z ) )
= ( sup_su1936195050962291414c_fm_i @ Y @ ( sup_su1936195050962291414c_fm_i @ X @ Z ) ) ) ).
% sup_left_commute
thf(fact_201_sup_Oleft__commute,axiom,
! [B3: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i,C2: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ B3 @ ( sup_su2582925890723967158c_fm_i @ A2 @ C2 ) )
= ( sup_su2582925890723967158c_fm_i @ A2 @ ( sup_su2582925890723967158c_fm_i @ B3 @ C2 ) ) ) ).
% sup.left_commute
thf(fact_202_sup_Oleft__commute,axiom,
! [B3: epistemic_fm_i > $o,A2: epistemic_fm_i > $o,C2: epistemic_fm_i > $o] :
( ( sup_su2844414564337698183fm_i_o @ B3 @ ( sup_su2844414564337698183fm_i_o @ A2 @ C2 ) )
= ( sup_su2844414564337698183fm_i_o @ A2 @ ( sup_su2844414564337698183fm_i_o @ B3 @ C2 ) ) ) ).
% sup.left_commute
thf(fact_203_sup_Oleft__commute,axiom,
! [B3: set_Epistemic_fm_i > $o,A2: set_Epistemic_fm_i > $o,C2: set_Epistemic_fm_i > $o] :
( ( sup_su6723579903606884263fm_i_o @ B3 @ ( sup_su6723579903606884263fm_i_o @ A2 @ C2 ) )
= ( sup_su6723579903606884263fm_i_o @ A2 @ ( sup_su6723579903606884263fm_i_o @ B3 @ C2 ) ) ) ).
% sup.left_commute
thf(fact_204_sup_Oleft__commute,axiom,
! [B3: set_se7339729205154126530c_fm_i,A2: set_se7339729205154126530c_fm_i,C2: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ B3 @ ( sup_su2317974602288960150c_fm_i @ A2 @ C2 ) )
= ( sup_su2317974602288960150c_fm_i @ A2 @ ( sup_su2317974602288960150c_fm_i @ B3 @ C2 ) ) ) ).
% sup.left_commute
thf(fact_205_sup_Oleft__commute,axiom,
! [B3: set_Epistemic_fm_i,A2: set_Epistemic_fm_i,C2: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ B3 @ ( sup_su1936195050962291414c_fm_i @ A2 @ C2 ) )
= ( sup_su1936195050962291414c_fm_i @ A2 @ ( sup_su1936195050962291414c_fm_i @ B3 @ C2 ) ) ) ).
% sup.left_commute
thf(fact_206_sup__commute,axiom,
( sup_su2582925890723967158c_fm_i
= ( ^ [X2: set_se3485332733965609186c_fm_i,Y3: set_se3485332733965609186c_fm_i] : ( sup_su2582925890723967158c_fm_i @ Y3 @ X2 ) ) ) ).
% sup_commute
thf(fact_207_sup__commute,axiom,
( sup_su2844414564337698183fm_i_o
= ( ^ [X2: epistemic_fm_i > $o,Y3: epistemic_fm_i > $o] : ( sup_su2844414564337698183fm_i_o @ Y3 @ X2 ) ) ) ).
% sup_commute
thf(fact_208_sup__commute,axiom,
( sup_su6723579903606884263fm_i_o
= ( ^ [X2: set_Epistemic_fm_i > $o,Y3: set_Epistemic_fm_i > $o] : ( sup_su6723579903606884263fm_i_o @ Y3 @ X2 ) ) ) ).
% sup_commute
thf(fact_209_sup__commute,axiom,
( sup_su2317974602288960150c_fm_i
= ( ^ [X2: set_se7339729205154126530c_fm_i,Y3: set_se7339729205154126530c_fm_i] : ( sup_su2317974602288960150c_fm_i @ Y3 @ X2 ) ) ) ).
% sup_commute
thf(fact_210_sup__commute,axiom,
( sup_su1936195050962291414c_fm_i
= ( ^ [X2: set_Epistemic_fm_i,Y3: set_Epistemic_fm_i] : ( sup_su1936195050962291414c_fm_i @ Y3 @ X2 ) ) ) ).
% sup_commute
thf(fact_211_sup_Ocommute,axiom,
( sup_su2582925890723967158c_fm_i
= ( ^ [A4: set_se3485332733965609186c_fm_i,B4: set_se3485332733965609186c_fm_i] : ( sup_su2582925890723967158c_fm_i @ B4 @ A4 ) ) ) ).
% sup.commute
thf(fact_212_sup_Ocommute,axiom,
( sup_su2844414564337698183fm_i_o
= ( ^ [A4: epistemic_fm_i > $o,B4: epistemic_fm_i > $o] : ( sup_su2844414564337698183fm_i_o @ B4 @ A4 ) ) ) ).
% sup.commute
thf(fact_213_sup_Ocommute,axiom,
( sup_su6723579903606884263fm_i_o
= ( ^ [A4: set_Epistemic_fm_i > $o,B4: set_Epistemic_fm_i > $o] : ( sup_su6723579903606884263fm_i_o @ B4 @ A4 ) ) ) ).
% sup.commute
thf(fact_214_sup_Ocommute,axiom,
( sup_su2317974602288960150c_fm_i
= ( ^ [A4: set_se7339729205154126530c_fm_i,B4: set_se7339729205154126530c_fm_i] : ( sup_su2317974602288960150c_fm_i @ B4 @ A4 ) ) ) ).
% sup.commute
thf(fact_215_sup_Ocommute,axiom,
( sup_su1936195050962291414c_fm_i
= ( ^ [A4: set_Epistemic_fm_i,B4: set_Epistemic_fm_i] : ( sup_su1936195050962291414c_fm_i @ B4 @ A4 ) ) ) ).
% sup.commute
thf(fact_216_sup__assoc,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ ( sup_su2582925890723967158c_fm_i @ X @ Y ) @ Z )
= ( sup_su2582925890723967158c_fm_i @ X @ ( sup_su2582925890723967158c_fm_i @ Y @ Z ) ) ) ).
% sup_assoc
thf(fact_217_sup__assoc,axiom,
! [X: epistemic_fm_i > $o,Y: epistemic_fm_i > $o,Z: epistemic_fm_i > $o] :
( ( sup_su2844414564337698183fm_i_o @ ( sup_su2844414564337698183fm_i_o @ X @ Y ) @ Z )
= ( sup_su2844414564337698183fm_i_o @ X @ ( sup_su2844414564337698183fm_i_o @ Y @ Z ) ) ) ).
% sup_assoc
thf(fact_218_sup__assoc,axiom,
! [X: set_Epistemic_fm_i > $o,Y: set_Epistemic_fm_i > $o,Z: set_Epistemic_fm_i > $o] :
( ( sup_su6723579903606884263fm_i_o @ ( sup_su6723579903606884263fm_i_o @ X @ Y ) @ Z )
= ( sup_su6723579903606884263fm_i_o @ X @ ( sup_su6723579903606884263fm_i_o @ Y @ Z ) ) ) ).
% sup_assoc
thf(fact_219_sup__assoc,axiom,
! [X: set_se7339729205154126530c_fm_i,Y: set_se7339729205154126530c_fm_i,Z: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ ( sup_su2317974602288960150c_fm_i @ X @ Y ) @ Z )
= ( sup_su2317974602288960150c_fm_i @ X @ ( sup_su2317974602288960150c_fm_i @ Y @ Z ) ) ) ).
% sup_assoc
thf(fact_220_sup__assoc,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( sup_su1936195050962291414c_fm_i @ X @ Y ) @ Z )
= ( sup_su1936195050962291414c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ Y @ Z ) ) ) ).
% sup_assoc
thf(fact_221_sup_Oassoc,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i,C2: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ ( sup_su2582925890723967158c_fm_i @ A2 @ B3 ) @ C2 )
= ( sup_su2582925890723967158c_fm_i @ A2 @ ( sup_su2582925890723967158c_fm_i @ B3 @ C2 ) ) ) ).
% sup.assoc
thf(fact_222_sup_Oassoc,axiom,
! [A2: epistemic_fm_i > $o,B3: epistemic_fm_i > $o,C2: epistemic_fm_i > $o] :
( ( sup_su2844414564337698183fm_i_o @ ( sup_su2844414564337698183fm_i_o @ A2 @ B3 ) @ C2 )
= ( sup_su2844414564337698183fm_i_o @ A2 @ ( sup_su2844414564337698183fm_i_o @ B3 @ C2 ) ) ) ).
% sup.assoc
thf(fact_223_sup_Oassoc,axiom,
! [A2: set_Epistemic_fm_i > $o,B3: set_Epistemic_fm_i > $o,C2: set_Epistemic_fm_i > $o] :
( ( sup_su6723579903606884263fm_i_o @ ( sup_su6723579903606884263fm_i_o @ A2 @ B3 ) @ C2 )
= ( sup_su6723579903606884263fm_i_o @ A2 @ ( sup_su6723579903606884263fm_i_o @ B3 @ C2 ) ) ) ).
% sup.assoc
thf(fact_224_sup_Oassoc,axiom,
! [A2: set_se7339729205154126530c_fm_i,B3: set_se7339729205154126530c_fm_i,C2: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ ( sup_su2317974602288960150c_fm_i @ A2 @ B3 ) @ C2 )
= ( sup_su2317974602288960150c_fm_i @ A2 @ ( sup_su2317974602288960150c_fm_i @ B3 @ C2 ) ) ) ).
% sup.assoc
thf(fact_225_sup_Oassoc,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,C2: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) @ C2 )
= ( sup_su1936195050962291414c_fm_i @ A2 @ ( sup_su1936195050962291414c_fm_i @ B3 @ C2 ) ) ) ).
% sup.assoc
thf(fact_226_inf__sup__aci_I5_J,axiom,
( sup_su2582925890723967158c_fm_i
= ( ^ [X2: set_se3485332733965609186c_fm_i,Y3: set_se3485332733965609186c_fm_i] : ( sup_su2582925890723967158c_fm_i @ Y3 @ X2 ) ) ) ).
% inf_sup_aci(5)
thf(fact_227_inf__sup__aci_I5_J,axiom,
( sup_su2844414564337698183fm_i_o
= ( ^ [X2: epistemic_fm_i > $o,Y3: epistemic_fm_i > $o] : ( sup_su2844414564337698183fm_i_o @ Y3 @ X2 ) ) ) ).
% inf_sup_aci(5)
thf(fact_228_inf__sup__aci_I5_J,axiom,
( sup_su6723579903606884263fm_i_o
= ( ^ [X2: set_Epistemic_fm_i > $o,Y3: set_Epistemic_fm_i > $o] : ( sup_su6723579903606884263fm_i_o @ Y3 @ X2 ) ) ) ).
% inf_sup_aci(5)
thf(fact_229_inf__sup__aci_I5_J,axiom,
( sup_su2317974602288960150c_fm_i
= ( ^ [X2: set_se7339729205154126530c_fm_i,Y3: set_se7339729205154126530c_fm_i] : ( sup_su2317974602288960150c_fm_i @ Y3 @ X2 ) ) ) ).
% inf_sup_aci(5)
thf(fact_230_inf__sup__aci_I5_J,axiom,
( sup_su1936195050962291414c_fm_i
= ( ^ [X2: set_Epistemic_fm_i,Y3: set_Epistemic_fm_i] : ( sup_su1936195050962291414c_fm_i @ Y3 @ X2 ) ) ) ).
% inf_sup_aci(5)
thf(fact_231_inf__sup__aci_I6_J,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ ( sup_su2582925890723967158c_fm_i @ X @ Y ) @ Z )
= ( sup_su2582925890723967158c_fm_i @ X @ ( sup_su2582925890723967158c_fm_i @ Y @ Z ) ) ) ).
% inf_sup_aci(6)
thf(fact_232_inf__sup__aci_I6_J,axiom,
! [X: epistemic_fm_i > $o,Y: epistemic_fm_i > $o,Z: epistemic_fm_i > $o] :
( ( sup_su2844414564337698183fm_i_o @ ( sup_su2844414564337698183fm_i_o @ X @ Y ) @ Z )
= ( sup_su2844414564337698183fm_i_o @ X @ ( sup_su2844414564337698183fm_i_o @ Y @ Z ) ) ) ).
% inf_sup_aci(6)
thf(fact_233_inf__sup__aci_I6_J,axiom,
! [X: set_Epistemic_fm_i > $o,Y: set_Epistemic_fm_i > $o,Z: set_Epistemic_fm_i > $o] :
( ( sup_su6723579903606884263fm_i_o @ ( sup_su6723579903606884263fm_i_o @ X @ Y ) @ Z )
= ( sup_su6723579903606884263fm_i_o @ X @ ( sup_su6723579903606884263fm_i_o @ Y @ Z ) ) ) ).
% inf_sup_aci(6)
thf(fact_234_inf__sup__aci_I6_J,axiom,
! [X: set_se7339729205154126530c_fm_i,Y: set_se7339729205154126530c_fm_i,Z: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ ( sup_su2317974602288960150c_fm_i @ X @ Y ) @ Z )
= ( sup_su2317974602288960150c_fm_i @ X @ ( sup_su2317974602288960150c_fm_i @ Y @ Z ) ) ) ).
% inf_sup_aci(6)
thf(fact_235_inf__sup__aci_I6_J,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( sup_su1936195050962291414c_fm_i @ X @ Y ) @ Z )
= ( sup_su1936195050962291414c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ Y @ Z ) ) ) ).
% inf_sup_aci(6)
thf(fact_236_inf__sup__aci_I7_J,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ X @ ( sup_su2582925890723967158c_fm_i @ Y @ Z ) )
= ( sup_su2582925890723967158c_fm_i @ Y @ ( sup_su2582925890723967158c_fm_i @ X @ Z ) ) ) ).
% inf_sup_aci(7)
thf(fact_237_inf__sup__aci_I7_J,axiom,
! [X: epistemic_fm_i > $o,Y: epistemic_fm_i > $o,Z: epistemic_fm_i > $o] :
( ( sup_su2844414564337698183fm_i_o @ X @ ( sup_su2844414564337698183fm_i_o @ Y @ Z ) )
= ( sup_su2844414564337698183fm_i_o @ Y @ ( sup_su2844414564337698183fm_i_o @ X @ Z ) ) ) ).
% inf_sup_aci(7)
thf(fact_238_inf__sup__aci_I7_J,axiom,
! [X: set_Epistemic_fm_i > $o,Y: set_Epistemic_fm_i > $o,Z: set_Epistemic_fm_i > $o] :
( ( sup_su6723579903606884263fm_i_o @ X @ ( sup_su6723579903606884263fm_i_o @ Y @ Z ) )
= ( sup_su6723579903606884263fm_i_o @ Y @ ( sup_su6723579903606884263fm_i_o @ X @ Z ) ) ) ).
% inf_sup_aci(7)
thf(fact_239_inf__sup__aci_I7_J,axiom,
! [X: set_se7339729205154126530c_fm_i,Y: set_se7339729205154126530c_fm_i,Z: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ X @ ( sup_su2317974602288960150c_fm_i @ Y @ Z ) )
= ( sup_su2317974602288960150c_fm_i @ Y @ ( sup_su2317974602288960150c_fm_i @ X @ Z ) ) ) ).
% inf_sup_aci(7)
thf(fact_240_inf__sup__aci_I7_J,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ Y @ Z ) )
= ( sup_su1936195050962291414c_fm_i @ Y @ ( sup_su1936195050962291414c_fm_i @ X @ Z ) ) ) ).
% inf_sup_aci(7)
thf(fact_241_inf__sup__aci_I8_J,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ X @ ( sup_su2582925890723967158c_fm_i @ X @ Y ) )
= ( sup_su2582925890723967158c_fm_i @ X @ Y ) ) ).
% inf_sup_aci(8)
thf(fact_242_inf__sup__aci_I8_J,axiom,
! [X: epistemic_fm_i > $o,Y: epistemic_fm_i > $o] :
( ( sup_su2844414564337698183fm_i_o @ X @ ( sup_su2844414564337698183fm_i_o @ X @ Y ) )
= ( sup_su2844414564337698183fm_i_o @ X @ Y ) ) ).
% inf_sup_aci(8)
thf(fact_243_inf__sup__aci_I8_J,axiom,
! [X: set_Epistemic_fm_i > $o,Y: set_Epistemic_fm_i > $o] :
( ( sup_su6723579903606884263fm_i_o @ X @ ( sup_su6723579903606884263fm_i_o @ X @ Y ) )
= ( sup_su6723579903606884263fm_i_o @ X @ Y ) ) ).
% inf_sup_aci(8)
thf(fact_244_inf__sup__aci_I8_J,axiom,
! [X: set_se7339729205154126530c_fm_i,Y: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ X @ ( sup_su2317974602288960150c_fm_i @ X @ Y ) )
= ( sup_su2317974602288960150c_fm_i @ X @ Y ) ) ).
% inf_sup_aci(8)
thf(fact_245_inf__sup__aci_I8_J,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ X @ Y ) )
= ( sup_su1936195050962291414c_fm_i @ X @ Y ) ) ).
% inf_sup_aci(8)
thf(fact_246_Un__left__commute,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ A @ ( sup_su2582925890723967158c_fm_i @ B2 @ C ) )
= ( sup_su2582925890723967158c_fm_i @ B2 @ ( sup_su2582925890723967158c_fm_i @ A @ C ) ) ) ).
% Un_left_commute
thf(fact_247_Un__left__commute,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i,C: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ A @ ( sup_su2317974602288960150c_fm_i @ B2 @ C ) )
= ( sup_su2317974602288960150c_fm_i @ B2 @ ( sup_su2317974602288960150c_fm_i @ A @ C ) ) ) ).
% Un_left_commute
thf(fact_248_Un__left__commute,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ A @ ( sup_su1936195050962291414c_fm_i @ B2 @ C ) )
= ( sup_su1936195050962291414c_fm_i @ B2 @ ( sup_su1936195050962291414c_fm_i @ A @ C ) ) ) ).
% Un_left_commute
thf(fact_249_Un__left__absorb,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ A @ ( sup_su2582925890723967158c_fm_i @ A @ B2 ) )
= ( sup_su2582925890723967158c_fm_i @ A @ B2 ) ) ).
% Un_left_absorb
thf(fact_250_Un__left__absorb,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ A @ ( sup_su2317974602288960150c_fm_i @ A @ B2 ) )
= ( sup_su2317974602288960150c_fm_i @ A @ B2 ) ) ).
% Un_left_absorb
thf(fact_251_Un__left__absorb,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ A @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) )
= ( sup_su1936195050962291414c_fm_i @ A @ B2 ) ) ).
% Un_left_absorb
thf(fact_252_Un__commute,axiom,
( sup_su2582925890723967158c_fm_i
= ( ^ [A3: set_se3485332733965609186c_fm_i,B: set_se3485332733965609186c_fm_i] : ( sup_su2582925890723967158c_fm_i @ B @ A3 ) ) ) ).
% Un_commute
thf(fact_253_Un__commute,axiom,
( sup_su2317974602288960150c_fm_i
= ( ^ [A3: set_se7339729205154126530c_fm_i,B: set_se7339729205154126530c_fm_i] : ( sup_su2317974602288960150c_fm_i @ B @ A3 ) ) ) ).
% Un_commute
thf(fact_254_Un__commute,axiom,
( sup_su1936195050962291414c_fm_i
= ( ^ [A3: set_Epistemic_fm_i,B: set_Epistemic_fm_i] : ( sup_su1936195050962291414c_fm_i @ B @ A3 ) ) ) ).
% Un_commute
thf(fact_255_Un__absorb,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ A @ A )
= A ) ).
% Un_absorb
thf(fact_256_Un__absorb,axiom,
! [A: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ A @ A )
= A ) ).
% Un_absorb
thf(fact_257_Un__absorb,axiom,
! [A: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ A @ A )
= A ) ).
% Un_absorb
thf(fact_258_Un__assoc,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ ( sup_su2582925890723967158c_fm_i @ A @ B2 ) @ C )
= ( sup_su2582925890723967158c_fm_i @ A @ ( sup_su2582925890723967158c_fm_i @ B2 @ C ) ) ) ).
% Un_assoc
thf(fact_259_Un__assoc,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i,C: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ ( sup_su2317974602288960150c_fm_i @ A @ B2 ) @ C )
= ( sup_su2317974602288960150c_fm_i @ A @ ( sup_su2317974602288960150c_fm_i @ B2 @ C ) ) ) ).
% Un_assoc
thf(fact_260_Un__assoc,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) @ C )
= ( sup_su1936195050962291414c_fm_i @ A @ ( sup_su1936195050962291414c_fm_i @ B2 @ C ) ) ) ).
% Un_assoc
thf(fact_261_ball__Un,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( ! [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ ( sup_su2582925890723967158c_fm_i @ A @ B2 ) )
=> ( P3 @ X2 ) ) )
= ( ! [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A )
=> ( P3 @ X2 ) )
& ! [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ B2 )
=> ( P3 @ X2 ) ) ) ) ).
% ball_Un
thf(fact_262_ball__Un,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i,P3: set_se3485332733965609186c_fm_i > $o] :
( ( ! [X2: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ X2 @ ( sup_su2317974602288960150c_fm_i @ A @ B2 ) )
=> ( P3 @ X2 ) ) )
= ( ! [X2: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ X2 @ A )
=> ( P3 @ X2 ) )
& ! [X2: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ X2 @ B2 )
=> ( P3 @ X2 ) ) ) ) ).
% ball_Un
thf(fact_263_ball__Un,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,P3: epistemic_fm_i > $o] :
( ( ! [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) )
=> ( P3 @ X2 ) ) )
= ( ! [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ A )
=> ( P3 @ X2 ) )
& ! [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ B2 )
=> ( P3 @ X2 ) ) ) ) ).
% ball_Un
thf(fact_264_bex__Un,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( ? [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ ( sup_su2582925890723967158c_fm_i @ A @ B2 ) )
& ( P3 @ X2 ) ) )
= ( ? [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A )
& ( P3 @ X2 ) )
| ? [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ B2 )
& ( P3 @ X2 ) ) ) ) ).
% bex_Un
thf(fact_265_bex__Un,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i,P3: set_se3485332733965609186c_fm_i > $o] :
( ( ? [X2: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ X2 @ ( sup_su2317974602288960150c_fm_i @ A @ B2 ) )
& ( P3 @ X2 ) ) )
= ( ? [X2: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ X2 @ A )
& ( P3 @ X2 ) )
| ? [X2: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ X2 @ B2 )
& ( P3 @ X2 ) ) ) ) ).
% bex_Un
thf(fact_266_bex__Un,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,P3: epistemic_fm_i > $o] :
( ( ? [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) )
& ( P3 @ X2 ) ) )
= ( ? [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ A )
& ( P3 @ X2 ) )
| ? [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ B2 )
& ( P3 @ X2 ) ) ) ) ).
% bex_Un
thf(fact_267_UnI2,axiom,
! [C2: i,B2: set_i,A: set_i] :
( ( member_i @ C2 @ B2 )
=> ( member_i @ C2 @ ( sup_sup_set_i @ A @ B2 ) ) ) ).
% UnI2
thf(fact_268_UnI2,axiom,
! [C2: list_s8081015415394010888c_fm_i,B2: set_li2934481837907835752c_fm_i,A: set_li2934481837907835752c_fm_i] :
( ( member605545779687026225c_fm_i @ C2 @ B2 )
=> ( member605545779687026225c_fm_i @ C2 @ ( sup_su6123556432952969532c_fm_i @ A @ B2 ) ) ) ).
% UnI2
thf(fact_269_UnI2,axiom,
! [C2: list_Epistemic_fm_i,B2: set_li8269783359719514504c_fm_i,A: set_li8269783359719514504c_fm_i] :
( ( member6475149752759350353c_fm_i @ C2 @ B2 )
=> ( member6475149752759350353c_fm_i @ C2 @ ( sup_su33170788683693916c_fm_i @ A @ B2 ) ) ) ).
% UnI2
thf(fact_270_UnI2,axiom,
! [C2: set_se3485332733965609186c_fm_i,B2: set_se7339729205154126530c_fm_i,A: set_se7339729205154126530c_fm_i] :
( ( member1461078328125707403c_fm_i @ C2 @ B2 )
=> ( member1461078328125707403c_fm_i @ C2 @ ( sup_su2317974602288960150c_fm_i @ A @ B2 ) ) ) ).
% UnI2
thf(fact_271_UnI2,axiom,
! [C2: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ C2 @ B2 )
=> ( member1104366573291651755c_fm_i @ C2 @ ( sup_su2582925890723967158c_fm_i @ A @ B2 ) ) ) ).
% UnI2
thf(fact_272_UnI2,axiom,
! [C2: epistemic_fm_i,B2: set_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ C2 @ B2 )
=> ( member6642669606046002379c_fm_i @ C2 @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) ) ) ).
% UnI2
thf(fact_273_UnI1,axiom,
! [C2: i,A: set_i,B2: set_i] :
( ( member_i @ C2 @ A )
=> ( member_i @ C2 @ ( sup_sup_set_i @ A @ B2 ) ) ) ).
% UnI1
thf(fact_274_UnI1,axiom,
! [C2: list_s8081015415394010888c_fm_i,A: set_li2934481837907835752c_fm_i,B2: set_li2934481837907835752c_fm_i] :
( ( member605545779687026225c_fm_i @ C2 @ A )
=> ( member605545779687026225c_fm_i @ C2 @ ( sup_su6123556432952969532c_fm_i @ A @ B2 ) ) ) ).
% UnI1
thf(fact_275_UnI1,axiom,
! [C2: list_Epistemic_fm_i,A: set_li8269783359719514504c_fm_i,B2: set_li8269783359719514504c_fm_i] :
( ( member6475149752759350353c_fm_i @ C2 @ A )
=> ( member6475149752759350353c_fm_i @ C2 @ ( sup_su33170788683693916c_fm_i @ A @ B2 ) ) ) ).
% UnI1
thf(fact_276_UnI1,axiom,
! [C2: set_se3485332733965609186c_fm_i,A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i] :
( ( member1461078328125707403c_fm_i @ C2 @ A )
=> ( member1461078328125707403c_fm_i @ C2 @ ( sup_su2317974602288960150c_fm_i @ A @ B2 ) ) ) ).
% UnI1
thf(fact_277_UnI1,axiom,
! [C2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ C2 @ A )
=> ( member1104366573291651755c_fm_i @ C2 @ ( sup_su2582925890723967158c_fm_i @ A @ B2 ) ) ) ).
% UnI1
thf(fact_278_UnI1,axiom,
! [C2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ C2 @ A )
=> ( member6642669606046002379c_fm_i @ C2 @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) ) ) ).
% UnI1
thf(fact_279_UnE,axiom,
! [C2: i,A: set_i,B2: set_i] :
( ( member_i @ C2 @ ( sup_sup_set_i @ A @ B2 ) )
=> ( ~ ( member_i @ C2 @ A )
=> ( member_i @ C2 @ B2 ) ) ) ).
% UnE
thf(fact_280_UnE,axiom,
! [C2: list_s8081015415394010888c_fm_i,A: set_li2934481837907835752c_fm_i,B2: set_li2934481837907835752c_fm_i] :
( ( member605545779687026225c_fm_i @ C2 @ ( sup_su6123556432952969532c_fm_i @ A @ B2 ) )
=> ( ~ ( member605545779687026225c_fm_i @ C2 @ A )
=> ( member605545779687026225c_fm_i @ C2 @ B2 ) ) ) ).
% UnE
thf(fact_281_UnE,axiom,
! [C2: list_Epistemic_fm_i,A: set_li8269783359719514504c_fm_i,B2: set_li8269783359719514504c_fm_i] :
( ( member6475149752759350353c_fm_i @ C2 @ ( sup_su33170788683693916c_fm_i @ A @ B2 ) )
=> ( ~ ( member6475149752759350353c_fm_i @ C2 @ A )
=> ( member6475149752759350353c_fm_i @ C2 @ B2 ) ) ) ).
% UnE
thf(fact_282_UnE,axiom,
! [C2: set_se3485332733965609186c_fm_i,A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i] :
( ( member1461078328125707403c_fm_i @ C2 @ ( sup_su2317974602288960150c_fm_i @ A @ B2 ) )
=> ( ~ ( member1461078328125707403c_fm_i @ C2 @ A )
=> ( member1461078328125707403c_fm_i @ C2 @ B2 ) ) ) ).
% UnE
thf(fact_283_UnE,axiom,
! [C2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ C2 @ ( sup_su2582925890723967158c_fm_i @ A @ B2 ) )
=> ( ~ ( member1104366573291651755c_fm_i @ C2 @ A )
=> ( member1104366573291651755c_fm_i @ C2 @ B2 ) ) ) ).
% UnE
thf(fact_284_UnE,axiom,
! [C2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ C2 @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) )
=> ( ~ ( member6642669606046002379c_fm_i @ C2 @ A )
=> ( member6642669606046002379c_fm_i @ C2 @ B2 ) ) ) ).
% UnE
thf(fact_285_consistent__def,axiom,
( episte2285483198712856234tent_i
= ( ^ [A3: epistemic_fm_i > $o,S4: set_Epistemic_fm_i] :
~ ? [Qs: list_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( set_Epistemic_fm_i2 @ Qs ) @ S4 )
& ( epistemic_AK_i @ A3 @ ( epistemic_imply_i @ Qs @ epistemic_FF_i ) ) ) ) ) ).
% consistent_def
thf(fact_286_Ax,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i] :
( ( A @ P4 )
=> ( epistemic_AK_i @ A @ P4 ) ) ).
% Ax
thf(fact_287_pigeonhole__infinite__rel,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,R: epistemic_fm_i > epistemic_fm_i > $o] :
( ~ ( finite3304564979551393739c_fm_i @ A )
=> ( ( finite3304564979551393739c_fm_i @ B2 )
=> ( ! [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ A )
=> ? [Xa: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ Xa @ B2 )
& ( R @ X3 @ Xa ) ) )
=> ? [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ B2 )
& ~ ( finite3304564979551393739c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [A4: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A4 @ A )
& ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite_rel
thf(fact_288_pigeonhole__infinite__rel,axiom,
! [A: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i,R: epistemic_fm_i > set_Epistemic_fm_i > $o] :
( ~ ( finite3304564979551393739c_fm_i @ A )
=> ( ( finite7933139204641697195c_fm_i @ B2 )
=> ( ! [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ A )
=> ? [Xa: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Xa @ B2 )
& ( R @ X3 @ Xa ) ) )
=> ? [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ B2 )
& ~ ( finite3304564979551393739c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [A4: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A4 @ A )
& ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite_rel
thf(fact_289_pigeonhole__infinite__rel,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_Epistemic_fm_i,R: set_Epistemic_fm_i > epistemic_fm_i > $o] :
( ~ ( finite7933139204641697195c_fm_i @ A )
=> ( ( finite3304564979551393739c_fm_i @ B2 )
=> ( ! [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
=> ? [Xa: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ Xa @ B2 )
& ( R @ X3 @ Xa ) ) )
=> ? [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ B2 )
& ~ ( finite7933139204641697195c_fm_i
@ ( collec3087743281813070829c_fm_i
@ ^ [A4: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A4 @ A )
& ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite_rel
thf(fact_290_pigeonhole__infinite__rel,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,R: set_Epistemic_fm_i > set_Epistemic_fm_i > $o] :
( ~ ( finite7933139204641697195c_fm_i @ A )
=> ( ( finite7933139204641697195c_fm_i @ B2 )
=> ( ! [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
=> ? [Xa: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Xa @ B2 )
& ( R @ X3 @ Xa ) ) )
=> ? [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ B2 )
& ~ ( finite7933139204641697195c_fm_i
@ ( collec3087743281813070829c_fm_i
@ ^ [A4: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A4 @ A )
& ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite_rel
thf(fact_291_pigeonhole__infinite__rel,axiom,
! [A: set_i,B2: set_Epistemic_fm_i,R: i > epistemic_fm_i > $o] :
( ~ ( finite_finite_i @ A )
=> ( ( finite3304564979551393739c_fm_i @ B2 )
=> ( ! [X3: i] :
( ( member_i @ X3 @ A )
=> ? [Xa: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ Xa @ B2 )
& ( R @ X3 @ Xa ) ) )
=> ? [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ B2 )
& ~ ( finite_finite_i
@ ( collect_i
@ ^ [A4: i] :
( ( member_i @ A4 @ A )
& ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite_rel
thf(fact_292_pigeonhole__infinite__rel,axiom,
! [A: set_i,B2: set_se3485332733965609186c_fm_i,R: i > set_Epistemic_fm_i > $o] :
( ~ ( finite_finite_i @ A )
=> ( ( finite7933139204641697195c_fm_i @ B2 )
=> ( ! [X3: i] :
( ( member_i @ X3 @ A )
=> ? [Xa: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Xa @ B2 )
& ( R @ X3 @ Xa ) ) )
=> ? [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ B2 )
& ~ ( finite_finite_i
@ ( collect_i
@ ^ [A4: i] :
( ( member_i @ A4 @ A )
& ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite_rel
thf(fact_293_pigeonhole__infinite__rel,axiom,
! [A: set_li8269783359719514504c_fm_i,B2: set_Epistemic_fm_i,R: list_Epistemic_fm_i > epistemic_fm_i > $o] :
( ~ ( finite3106398504192302929c_fm_i @ A )
=> ( ( finite3304564979551393739c_fm_i @ B2 )
=> ( ! [X3: list_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ X3 @ A )
=> ? [Xa: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ Xa @ B2 )
& ( R @ X3 @ Xa ) ) )
=> ? [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ B2 )
& ~ ( finite3106398504192302929c_fm_i
@ ( collec5759350117362652307c_fm_i
@ ^ [A4: list_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ A4 @ A )
& ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite_rel
thf(fact_294_pigeonhole__infinite__rel,axiom,
! [A: set_i,B2: set_se7339729205154126530c_fm_i,R: i > set_se3485332733965609186c_fm_i > $o] :
( ~ ( finite_finite_i @ A )
=> ( ( finite9087983574947184523c_fm_i @ B2 )
=> ( ! [X3: i] :
( ( member_i @ X3 @ A )
=> ? [Xa: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ Xa @ B2 )
& ( R @ X3 @ Xa ) ) )
=> ? [X3: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ X3 @ B2 )
& ~ ( finite_finite_i
@ ( collect_i
@ ^ [A4: i] :
( ( member_i @ A4 @ A )
& ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite_rel
thf(fact_295_pigeonhole__infinite__rel,axiom,
! [A: set_li2934481837907835752c_fm_i,B2: set_Epistemic_fm_i,R: list_s8081015415394010888c_fm_i > epistemic_fm_i > $o] :
( ~ ( finite5108596011607087409c_fm_i @ A )
=> ( ( finite3304564979551393739c_fm_i @ B2 )
=> ( ! [X3: list_s8081015415394010888c_fm_i] :
( ( member605545779687026225c_fm_i @ X3 @ A )
=> ? [Xa: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ Xa @ B2 )
& ( R @ X3 @ Xa ) ) )
=> ? [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ B2 )
& ~ ( finite5108596011607087409c_fm_i
@ ( collec2200325868635342451c_fm_i
@ ^ [A4: list_s8081015415394010888c_fm_i] :
( ( member605545779687026225c_fm_i @ A4 @ A )
& ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite_rel
thf(fact_296_pigeonhole__infinite__rel,axiom,
! [A: set_li8269783359719514504c_fm_i,B2: set_se3485332733965609186c_fm_i,R: list_Epistemic_fm_i > set_Epistemic_fm_i > $o] :
( ~ ( finite3106398504192302929c_fm_i @ A )
=> ( ( finite7933139204641697195c_fm_i @ B2 )
=> ( ! [X3: list_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ X3 @ A )
=> ? [Xa: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Xa @ B2 )
& ( R @ X3 @ Xa ) ) )
=> ? [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ B2 )
& ~ ( finite3106398504192302929c_fm_i
@ ( collec5759350117362652307c_fm_i
@ ^ [A4: list_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ A4 @ A )
& ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite_rel
thf(fact_297_not__finite__existsD,axiom,
! [P3: list_Epistemic_fm_i > $o] :
( ~ ( finite3106398504192302929c_fm_i @ ( collec5759350117362652307c_fm_i @ P3 ) )
=> ? [X_1: list_Epistemic_fm_i] : ( P3 @ X_1 ) ) ).
% not_finite_existsD
thf(fact_298_not__finite__existsD,axiom,
! [P3: set_se3485332733965609186c_fm_i > $o] :
( ~ ( finite9087983574947184523c_fm_i @ ( collec2761885132556217805c_fm_i @ P3 ) )
=> ? [X_1: set_se3485332733965609186c_fm_i] : ( P3 @ X_1 ) ) ).
% not_finite_existsD
thf(fact_299_not__finite__existsD,axiom,
! [P3: ( set_Epistemic_fm_i > epistemic_fm_i ) > $o] :
( ~ ( finite5517585301071133084c_fm_i @ ( collec6909220245477468634c_fm_i @ P3 ) )
=> ? [X_1: set_Epistemic_fm_i > epistemic_fm_i] : ( P3 @ X_1 ) ) ).
% not_finite_existsD
thf(fact_300_not__finite__existsD,axiom,
! [P3: ( epistemic_fm_i > epistemic_fm_i ) > $o] :
( ~ ( finite4369126853184676732c_fm_i @ ( collec4821997688893311930c_fm_i @ P3 ) )
=> ? [X_1: epistemic_fm_i > epistemic_fm_i] : ( P3 @ X_1 ) ) ).
% not_finite_existsD
thf(fact_301_not__finite__existsD,axiom,
! [P3: epistemic_fm_i > $o] :
( ~ ( finite3304564979551393739c_fm_i @ ( collec4904205187116291597c_fm_i @ P3 ) )
=> ? [X_1: epistemic_fm_i] : ( P3 @ X_1 ) ) ).
% not_finite_existsD
thf(fact_302_not__finite__existsD,axiom,
! [P3: set_Epistemic_fm_i > $o] :
( ~ ( finite7933139204641697195c_fm_i @ ( collec3087743281813070829c_fm_i @ P3 ) )
=> ? [X_1: set_Epistemic_fm_i] : ( P3 @ X_1 ) ) ).
% not_finite_existsD
thf(fact_303_Collect__subset,axiom,
! [A: set_i,P3: i > $o] :
( ord_less_eq_set_i
@ ( collect_i
@ ^ [X2: i] :
( ( member_i @ X2 @ A )
& ( P3 @ X2 ) ) )
@ A ) ).
% Collect_subset
thf(fact_304_Collect__subset,axiom,
! [A: set_li2934481837907835752c_fm_i,P3: list_s8081015415394010888c_fm_i > $o] :
( ord_le1241842563113145096c_fm_i
@ ( collec2200325868635342451c_fm_i
@ ^ [X2: list_s8081015415394010888c_fm_i] :
( ( member605545779687026225c_fm_i @ X2 @ A )
& ( P3 @ X2 ) ) )
@ A ) ).
% Collect_subset
thf(fact_305_Collect__subset,axiom,
! [A: set_se7339729205154126530c_fm_i,P3: set_se3485332733965609186c_fm_i > $o] :
( ord_le2772500130360476258c_fm_i
@ ( collec2761885132556217805c_fm_i
@ ^ [X2: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ X2 @ A )
& ( P3 @ X2 ) ) )
@ A ) ).
% Collect_subset
thf(fact_306_Collect__subset,axiom,
! [A: set_li8269783359719514504c_fm_i,P3: list_Epistemic_fm_i > $o] :
( ord_le1209247765174941992c_fm_i
@ ( collec5759350117362652307c_fm_i
@ ^ [X2: list_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ X2 @ A )
& ( P3 @ X2 ) ) )
@ A ) ).
% Collect_subset
thf(fact_307_Collect__subset,axiom,
! [A: set_se3485332733965609186c_fm_i,P3: set_Epistemic_fm_i > $o] :
( ord_le5389487502678872194c_fm_i
@ ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A )
& ( P3 @ X2 ) ) )
@ A ) ).
% Collect_subset
thf(fact_308_Collect__subset,axiom,
! [A: set_Epistemic_fm_i,P3: epistemic_fm_i > $o] :
( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ A )
& ( P3 @ X2 ) ) )
@ A ) ).
% Collect_subset
thf(fact_309_Collect__disj__eq,axiom,
! [P3: list_Epistemic_fm_i > $o,Q2: list_Epistemic_fm_i > $o] :
( ( collec5759350117362652307c_fm_i
@ ^ [X2: list_Epistemic_fm_i] :
( ( P3 @ X2 )
| ( Q2 @ X2 ) ) )
= ( sup_su33170788683693916c_fm_i @ ( collec5759350117362652307c_fm_i @ P3 ) @ ( collec5759350117362652307c_fm_i @ Q2 ) ) ) ).
% Collect_disj_eq
thf(fact_310_Collect__disj__eq,axiom,
! [P3: set_se3485332733965609186c_fm_i > $o,Q2: set_se3485332733965609186c_fm_i > $o] :
( ( collec2761885132556217805c_fm_i
@ ^ [X2: set_se3485332733965609186c_fm_i] :
( ( P3 @ X2 )
| ( Q2 @ X2 ) ) )
= ( sup_su2317974602288960150c_fm_i @ ( collec2761885132556217805c_fm_i @ P3 ) @ ( collec2761885132556217805c_fm_i @ Q2 ) ) ) ).
% Collect_disj_eq
thf(fact_311_Collect__disj__eq,axiom,
! [P3: set_Epistemic_fm_i > $o,Q2: set_Epistemic_fm_i > $o] :
( ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( P3 @ X2 )
| ( Q2 @ X2 ) ) )
= ( sup_su2582925890723967158c_fm_i @ ( collec3087743281813070829c_fm_i @ P3 ) @ ( collec3087743281813070829c_fm_i @ Q2 ) ) ) ).
% Collect_disj_eq
thf(fact_312_Collect__disj__eq,axiom,
! [P3: epistemic_fm_i > $o,Q2: epistemic_fm_i > $o] :
( ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( P3 @ X2 )
| ( Q2 @ X2 ) ) )
= ( sup_su1936195050962291414c_fm_i @ ( collec4904205187116291597c_fm_i @ P3 ) @ ( collec4904205187116291597c_fm_i @ Q2 ) ) ) ).
% Collect_disj_eq
thf(fact_313_Un__def,axiom,
( sup_sup_set_i
= ( ^ [A3: set_i,B: set_i] :
( collect_i
@ ^ [X2: i] :
( ( member_i @ X2 @ A3 )
| ( member_i @ X2 @ B ) ) ) ) ) ).
% Un_def
thf(fact_314_Un__def,axiom,
( sup_su6123556432952969532c_fm_i
= ( ^ [A3: set_li2934481837907835752c_fm_i,B: set_li2934481837907835752c_fm_i] :
( collec2200325868635342451c_fm_i
@ ^ [X2: list_s8081015415394010888c_fm_i] :
( ( member605545779687026225c_fm_i @ X2 @ A3 )
| ( member605545779687026225c_fm_i @ X2 @ B ) ) ) ) ) ).
% Un_def
thf(fact_315_Un__def,axiom,
( sup_su33170788683693916c_fm_i
= ( ^ [A3: set_li8269783359719514504c_fm_i,B: set_li8269783359719514504c_fm_i] :
( collec5759350117362652307c_fm_i
@ ^ [X2: list_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ X2 @ A3 )
| ( member6475149752759350353c_fm_i @ X2 @ B ) ) ) ) ) ).
% Un_def
thf(fact_316_Un__def,axiom,
( sup_su2317974602288960150c_fm_i
= ( ^ [A3: set_se7339729205154126530c_fm_i,B: set_se7339729205154126530c_fm_i] :
( collec2761885132556217805c_fm_i
@ ^ [X2: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ X2 @ A3 )
| ( member1461078328125707403c_fm_i @ X2 @ B ) ) ) ) ) ).
% Un_def
thf(fact_317_Un__def,axiom,
( sup_su2582925890723967158c_fm_i
= ( ^ [A3: set_se3485332733965609186c_fm_i,B: set_se3485332733965609186c_fm_i] :
( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A3 )
| ( member1104366573291651755c_fm_i @ X2 @ B ) ) ) ) ) ).
% Un_def
thf(fact_318_Un__def,axiom,
( sup_su1936195050962291414c_fm_i
= ( ^ [A3: set_Epistemic_fm_i,B: set_Epistemic_fm_i] :
( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ A3 )
| ( member6642669606046002379c_fm_i @ X2 @ B ) ) ) ) ) ).
% Un_def
thf(fact_319_finite__has__minimal2,axiom,
! [A: set_se7339729205154126530c_fm_i,A2: set_se3485332733965609186c_fm_i] :
( ( finite9087983574947184523c_fm_i @ A )
=> ( ( member1461078328125707403c_fm_i @ A2 @ A )
=> ? [X3: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ X3 @ A )
& ( ord_le5389487502678872194c_fm_i @ X3 @ A2 )
& ! [Xa: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ Xa @ A )
=> ( ( ord_le5389487502678872194c_fm_i @ Xa @ X3 )
=> ( X3 = Xa ) ) ) ) ) ) ).
% finite_has_minimal2
thf(fact_320_finite__has__minimal2,axiom,
! [A: set_Epistemic_fm_i_o,A2: epistemic_fm_i > $o] :
( ( finite1554648870599795442fm_i_o @ A )
=> ( ( member633939095840083442fm_i_o @ A2 @ A )
=> ? [X3: epistemic_fm_i > $o] :
( ( member633939095840083442fm_i_o @ X3 @ A )
& ( ord_le190830114487426235fm_i_o @ X3 @ A2 )
& ! [Xa: epistemic_fm_i > $o] :
( ( member633939095840083442fm_i_o @ Xa @ A )
=> ( ( ord_le190830114487426235fm_i_o @ Xa @ X3 )
=> ( X3 = Xa ) ) ) ) ) ) ).
% finite_has_minimal2
thf(fact_321_finite__has__minimal2,axiom,
! [A: set_se4360409073116726705fm_i_o,A2: set_Epistemic_fm_i > $o] :
( ( finite6832145847383406866fm_i_o @ A )
=> ( ( member5074877863442670610fm_i_o @ A2 @ A )
=> ? [X3: set_Epistemic_fm_i > $o] :
( ( member5074877863442670610fm_i_o @ X3 @ A )
& ( ord_le5706303257367236315fm_i_o @ X3 @ A2 )
& ! [Xa: set_Epistemic_fm_i > $o] :
( ( member5074877863442670610fm_i_o @ Xa @ A )
=> ( ( ord_le5706303257367236315fm_i_o @ Xa @ X3 )
=> ( X3 = Xa ) ) ) ) ) ) ).
% finite_has_minimal2
thf(fact_322_finite__has__minimal2,axiom,
! [A: set_se8293749906924980386c_fm_i,A2: set_se7339729205154126530c_fm_i] :
( ( finite523845223739985259c_fm_i @ A )
=> ( ( member2074520630381716075c_fm_i @ A2 @ A )
=> ? [X3: set_se7339729205154126530c_fm_i] :
( ( member2074520630381716075c_fm_i @ X3 @ A )
& ( ord_le2772500130360476258c_fm_i @ X3 @ A2 )
& ! [Xa: set_se7339729205154126530c_fm_i] :
( ( member2074520630381716075c_fm_i @ Xa @ A )
=> ( ( ord_le2772500130360476258c_fm_i @ Xa @ X3 )
=> ( X3 = Xa ) ) ) ) ) ) ).
% finite_has_minimal2
thf(fact_323_finite__has__minimal2,axiom,
! [A: set_se3663484335793657320c_fm_i,A2: set_li8269783359719514504c_fm_i] :
( ( finite5297363955932591025c_fm_i @ A )
=> ( ( member794313724012529841c_fm_i @ A2 @ A )
=> ? [X3: set_li8269783359719514504c_fm_i] :
( ( member794313724012529841c_fm_i @ X3 @ A )
& ( ord_le1209247765174941992c_fm_i @ X3 @ A2 )
& ! [Xa: set_li8269783359719514504c_fm_i] :
( ( member794313724012529841c_fm_i @ Xa @ A )
=> ( ( ord_le1209247765174941992c_fm_i @ Xa @ X3 )
=> ( X3 = Xa ) ) ) ) ) ) ).
% finite_has_minimal2
thf(fact_324_finite__has__minimal2,axiom,
! [A: set_se3485332733965609186c_fm_i,A2: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( member1104366573291651755c_fm_i @ A2 @ A )
=> ? [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
& ( ord_le3843937902494030498c_fm_i @ X3 @ A2 )
& ! [Xa: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Xa @ A )
=> ( ( ord_le3843937902494030498c_fm_i @ Xa @ X3 )
=> ( X3 = Xa ) ) ) ) ) ) ).
% finite_has_minimal2
thf(fact_325_finite__has__maximal2,axiom,
! [A: set_se7339729205154126530c_fm_i,A2: set_se3485332733965609186c_fm_i] :
( ( finite9087983574947184523c_fm_i @ A )
=> ( ( member1461078328125707403c_fm_i @ A2 @ A )
=> ? [X3: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ X3 @ A )
& ( ord_le5389487502678872194c_fm_i @ A2 @ X3 )
& ! [Xa: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ Xa @ A )
=> ( ( ord_le5389487502678872194c_fm_i @ X3 @ Xa )
=> ( X3 = Xa ) ) ) ) ) ) ).
% finite_has_maximal2
thf(fact_326_finite__has__maximal2,axiom,
! [A: set_Epistemic_fm_i_o,A2: epistemic_fm_i > $o] :
( ( finite1554648870599795442fm_i_o @ A )
=> ( ( member633939095840083442fm_i_o @ A2 @ A )
=> ? [X3: epistemic_fm_i > $o] :
( ( member633939095840083442fm_i_o @ X3 @ A )
& ( ord_le190830114487426235fm_i_o @ A2 @ X3 )
& ! [Xa: epistemic_fm_i > $o] :
( ( member633939095840083442fm_i_o @ Xa @ A )
=> ( ( ord_le190830114487426235fm_i_o @ X3 @ Xa )
=> ( X3 = Xa ) ) ) ) ) ) ).
% finite_has_maximal2
thf(fact_327_finite__has__maximal2,axiom,
! [A: set_se4360409073116726705fm_i_o,A2: set_Epistemic_fm_i > $o] :
( ( finite6832145847383406866fm_i_o @ A )
=> ( ( member5074877863442670610fm_i_o @ A2 @ A )
=> ? [X3: set_Epistemic_fm_i > $o] :
( ( member5074877863442670610fm_i_o @ X3 @ A )
& ( ord_le5706303257367236315fm_i_o @ A2 @ X3 )
& ! [Xa: set_Epistemic_fm_i > $o] :
( ( member5074877863442670610fm_i_o @ Xa @ A )
=> ( ( ord_le5706303257367236315fm_i_o @ X3 @ Xa )
=> ( X3 = Xa ) ) ) ) ) ) ).
% finite_has_maximal2
thf(fact_328_finite__has__maximal2,axiom,
! [A: set_se8293749906924980386c_fm_i,A2: set_se7339729205154126530c_fm_i] :
( ( finite523845223739985259c_fm_i @ A )
=> ( ( member2074520630381716075c_fm_i @ A2 @ A )
=> ? [X3: set_se7339729205154126530c_fm_i] :
( ( member2074520630381716075c_fm_i @ X3 @ A )
& ( ord_le2772500130360476258c_fm_i @ A2 @ X3 )
& ! [Xa: set_se7339729205154126530c_fm_i] :
( ( member2074520630381716075c_fm_i @ Xa @ A )
=> ( ( ord_le2772500130360476258c_fm_i @ X3 @ Xa )
=> ( X3 = Xa ) ) ) ) ) ) ).
% finite_has_maximal2
thf(fact_329_finite__has__maximal2,axiom,
! [A: set_se3663484335793657320c_fm_i,A2: set_li8269783359719514504c_fm_i] :
( ( finite5297363955932591025c_fm_i @ A )
=> ( ( member794313724012529841c_fm_i @ A2 @ A )
=> ? [X3: set_li8269783359719514504c_fm_i] :
( ( member794313724012529841c_fm_i @ X3 @ A )
& ( ord_le1209247765174941992c_fm_i @ A2 @ X3 )
& ! [Xa: set_li8269783359719514504c_fm_i] :
( ( member794313724012529841c_fm_i @ Xa @ A )
=> ( ( ord_le1209247765174941992c_fm_i @ X3 @ Xa )
=> ( X3 = Xa ) ) ) ) ) ) ).
% finite_has_maximal2
thf(fact_330_finite__has__maximal2,axiom,
! [A: set_se3485332733965609186c_fm_i,A2: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( member1104366573291651755c_fm_i @ A2 @ A )
=> ? [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
& ( ord_le3843937902494030498c_fm_i @ A2 @ X3 )
& ! [Xa: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Xa @ A )
=> ( ( ord_le3843937902494030498c_fm_i @ X3 @ Xa )
=> ( X3 = Xa ) ) ) ) ) ) ).
% finite_has_maximal2
thf(fact_331_sup_OcoboundedI2,axiom,
! [C2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ C2 @ B3 )
=> ( ord_le5389487502678872194c_fm_i @ C2 @ ( sup_su2582925890723967158c_fm_i @ A2 @ B3 ) ) ) ).
% sup.coboundedI2
thf(fact_332_sup_OcoboundedI2,axiom,
! [C2: epistemic_fm_i > $o,B3: epistemic_fm_i > $o,A2: epistemic_fm_i > $o] :
( ( ord_le190830114487426235fm_i_o @ C2 @ B3 )
=> ( ord_le190830114487426235fm_i_o @ C2 @ ( sup_su2844414564337698183fm_i_o @ A2 @ B3 ) ) ) ).
% sup.coboundedI2
thf(fact_333_sup_OcoboundedI2,axiom,
! [C2: set_Epistemic_fm_i > $o,B3: set_Epistemic_fm_i > $o,A2: set_Epistemic_fm_i > $o] :
( ( ord_le5706303257367236315fm_i_o @ C2 @ B3 )
=> ( ord_le5706303257367236315fm_i_o @ C2 @ ( sup_su6723579903606884263fm_i_o @ A2 @ B3 ) ) ) ).
% sup.coboundedI2
thf(fact_334_sup_OcoboundedI2,axiom,
! [C2: set_se7339729205154126530c_fm_i,B3: set_se7339729205154126530c_fm_i,A2: set_se7339729205154126530c_fm_i] :
( ( ord_le2772500130360476258c_fm_i @ C2 @ B3 )
=> ( ord_le2772500130360476258c_fm_i @ C2 @ ( sup_su2317974602288960150c_fm_i @ A2 @ B3 ) ) ) ).
% sup.coboundedI2
thf(fact_335_sup_OcoboundedI2,axiom,
! [C2: set_li8269783359719514504c_fm_i,B3: set_li8269783359719514504c_fm_i,A2: set_li8269783359719514504c_fm_i] :
( ( ord_le1209247765174941992c_fm_i @ C2 @ B3 )
=> ( ord_le1209247765174941992c_fm_i @ C2 @ ( sup_su33170788683693916c_fm_i @ A2 @ B3 ) ) ) ).
% sup.coboundedI2
thf(fact_336_sup_OcoboundedI2,axiom,
! [C2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,A2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ C2 @ B3 )
=> ( ord_le3843937902494030498c_fm_i @ C2 @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) ) ) ).
% sup.coboundedI2
thf(fact_337_sup_OcoboundedI1,axiom,
! [C2: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ C2 @ A2 )
=> ( ord_le5389487502678872194c_fm_i @ C2 @ ( sup_su2582925890723967158c_fm_i @ A2 @ B3 ) ) ) ).
% sup.coboundedI1
thf(fact_338_sup_OcoboundedI1,axiom,
! [C2: epistemic_fm_i > $o,A2: epistemic_fm_i > $o,B3: epistemic_fm_i > $o] :
( ( ord_le190830114487426235fm_i_o @ C2 @ A2 )
=> ( ord_le190830114487426235fm_i_o @ C2 @ ( sup_su2844414564337698183fm_i_o @ A2 @ B3 ) ) ) ).
% sup.coboundedI1
thf(fact_339_sup_OcoboundedI1,axiom,
! [C2: set_Epistemic_fm_i > $o,A2: set_Epistemic_fm_i > $o,B3: set_Epistemic_fm_i > $o] :
( ( ord_le5706303257367236315fm_i_o @ C2 @ A2 )
=> ( ord_le5706303257367236315fm_i_o @ C2 @ ( sup_su6723579903606884263fm_i_o @ A2 @ B3 ) ) ) ).
% sup.coboundedI1
thf(fact_340_sup_OcoboundedI1,axiom,
! [C2: set_se7339729205154126530c_fm_i,A2: set_se7339729205154126530c_fm_i,B3: set_se7339729205154126530c_fm_i] :
( ( ord_le2772500130360476258c_fm_i @ C2 @ A2 )
=> ( ord_le2772500130360476258c_fm_i @ C2 @ ( sup_su2317974602288960150c_fm_i @ A2 @ B3 ) ) ) ).
% sup.coboundedI1
thf(fact_341_sup_OcoboundedI1,axiom,
! [C2: set_li8269783359719514504c_fm_i,A2: set_li8269783359719514504c_fm_i,B3: set_li8269783359719514504c_fm_i] :
( ( ord_le1209247765174941992c_fm_i @ C2 @ A2 )
=> ( ord_le1209247765174941992c_fm_i @ C2 @ ( sup_su33170788683693916c_fm_i @ A2 @ B3 ) ) ) ).
% sup.coboundedI1
thf(fact_342_sup_OcoboundedI1,axiom,
! [C2: set_Epistemic_fm_i,A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ C2 @ A2 )
=> ( ord_le3843937902494030498c_fm_i @ C2 @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) ) ) ).
% sup.coboundedI1
thf(fact_343_sup_Oabsorb__iff2,axiom,
( ord_le5389487502678872194c_fm_i
= ( ^ [A4: set_se3485332733965609186c_fm_i,B4: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ A4 @ B4 )
= B4 ) ) ) ).
% sup.absorb_iff2
thf(fact_344_sup_Oabsorb__iff2,axiom,
( ord_le190830114487426235fm_i_o
= ( ^ [A4: epistemic_fm_i > $o,B4: epistemic_fm_i > $o] :
( ( sup_su2844414564337698183fm_i_o @ A4 @ B4 )
= B4 ) ) ) ).
% sup.absorb_iff2
thf(fact_345_sup_Oabsorb__iff2,axiom,
( ord_le5706303257367236315fm_i_o
= ( ^ [A4: set_Epistemic_fm_i > $o,B4: set_Epistemic_fm_i > $o] :
( ( sup_su6723579903606884263fm_i_o @ A4 @ B4 )
= B4 ) ) ) ).
% sup.absorb_iff2
thf(fact_346_sup_Oabsorb__iff2,axiom,
( ord_le2772500130360476258c_fm_i
= ( ^ [A4: set_se7339729205154126530c_fm_i,B4: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ A4 @ B4 )
= B4 ) ) ) ).
% sup.absorb_iff2
thf(fact_347_sup_Oabsorb__iff2,axiom,
( ord_le1209247765174941992c_fm_i
= ( ^ [A4: set_li8269783359719514504c_fm_i,B4: set_li8269783359719514504c_fm_i] :
( ( sup_su33170788683693916c_fm_i @ A4 @ B4 )
= B4 ) ) ) ).
% sup.absorb_iff2
thf(fact_348_sup_Oabsorb__iff2,axiom,
( ord_le3843937902494030498c_fm_i
= ( ^ [A4: set_Epistemic_fm_i,B4: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ A4 @ B4 )
= B4 ) ) ) ).
% sup.absorb_iff2
thf(fact_349_sup_Oabsorb__iff1,axiom,
( ord_le5389487502678872194c_fm_i
= ( ^ [B4: set_se3485332733965609186c_fm_i,A4: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ A4 @ B4 )
= A4 ) ) ) ).
% sup.absorb_iff1
thf(fact_350_sup_Oabsorb__iff1,axiom,
( ord_le190830114487426235fm_i_o
= ( ^ [B4: epistemic_fm_i > $o,A4: epistemic_fm_i > $o] :
( ( sup_su2844414564337698183fm_i_o @ A4 @ B4 )
= A4 ) ) ) ).
% sup.absorb_iff1
thf(fact_351_sup_Oabsorb__iff1,axiom,
( ord_le5706303257367236315fm_i_o
= ( ^ [B4: set_Epistemic_fm_i > $o,A4: set_Epistemic_fm_i > $o] :
( ( sup_su6723579903606884263fm_i_o @ A4 @ B4 )
= A4 ) ) ) ).
% sup.absorb_iff1
thf(fact_352_sup_Oabsorb__iff1,axiom,
( ord_le2772500130360476258c_fm_i
= ( ^ [B4: set_se7339729205154126530c_fm_i,A4: set_se7339729205154126530c_fm_i] :
( ( sup_su2317974602288960150c_fm_i @ A4 @ B4 )
= A4 ) ) ) ).
% sup.absorb_iff1
thf(fact_353_sup_Oabsorb__iff1,axiom,
( ord_le1209247765174941992c_fm_i
= ( ^ [B4: set_li8269783359719514504c_fm_i,A4: set_li8269783359719514504c_fm_i] :
( ( sup_su33170788683693916c_fm_i @ A4 @ B4 )
= A4 ) ) ) ).
% sup.absorb_iff1
thf(fact_354_sup_Oabsorb__iff1,axiom,
( ord_le3843937902494030498c_fm_i
= ( ^ [B4: set_Epistemic_fm_i,A4: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ A4 @ B4 )
= A4 ) ) ) ).
% sup.absorb_iff1
thf(fact_355_sup_Ocobounded2,axiom,
! [B3: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ B3 @ ( sup_su2582925890723967158c_fm_i @ A2 @ B3 ) ) ).
% sup.cobounded2
thf(fact_356_sup_Ocobounded2,axiom,
! [B3: epistemic_fm_i > $o,A2: epistemic_fm_i > $o] : ( ord_le190830114487426235fm_i_o @ B3 @ ( sup_su2844414564337698183fm_i_o @ A2 @ B3 ) ) ).
% sup.cobounded2
thf(fact_357_sup_Ocobounded2,axiom,
! [B3: set_Epistemic_fm_i > $o,A2: set_Epistemic_fm_i > $o] : ( ord_le5706303257367236315fm_i_o @ B3 @ ( sup_su6723579903606884263fm_i_o @ A2 @ B3 ) ) ).
% sup.cobounded2
thf(fact_358_sup_Ocobounded2,axiom,
! [B3: set_se7339729205154126530c_fm_i,A2: set_se7339729205154126530c_fm_i] : ( ord_le2772500130360476258c_fm_i @ B3 @ ( sup_su2317974602288960150c_fm_i @ A2 @ B3 ) ) ).
% sup.cobounded2
thf(fact_359_sup_Ocobounded2,axiom,
! [B3: set_li8269783359719514504c_fm_i,A2: set_li8269783359719514504c_fm_i] : ( ord_le1209247765174941992c_fm_i @ B3 @ ( sup_su33170788683693916c_fm_i @ A2 @ B3 ) ) ).
% sup.cobounded2
thf(fact_360_sup_Ocobounded2,axiom,
! [B3: set_Epistemic_fm_i,A2: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ B3 @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) ) ).
% sup.cobounded2
thf(fact_361_sup_Ocobounded1,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ A2 @ ( sup_su2582925890723967158c_fm_i @ A2 @ B3 ) ) ).
% sup.cobounded1
thf(fact_362_sup_Ocobounded1,axiom,
! [A2: epistemic_fm_i > $o,B3: epistemic_fm_i > $o] : ( ord_le190830114487426235fm_i_o @ A2 @ ( sup_su2844414564337698183fm_i_o @ A2 @ B3 ) ) ).
% sup.cobounded1
thf(fact_363_sup_Ocobounded1,axiom,
! [A2: set_Epistemic_fm_i > $o,B3: set_Epistemic_fm_i > $o] : ( ord_le5706303257367236315fm_i_o @ A2 @ ( sup_su6723579903606884263fm_i_o @ A2 @ B3 ) ) ).
% sup.cobounded1
thf(fact_364_sup_Ocobounded1,axiom,
! [A2: set_se7339729205154126530c_fm_i,B3: set_se7339729205154126530c_fm_i] : ( ord_le2772500130360476258c_fm_i @ A2 @ ( sup_su2317974602288960150c_fm_i @ A2 @ B3 ) ) ).
% sup.cobounded1
thf(fact_365_sup_Ocobounded1,axiom,
! [A2: set_li8269783359719514504c_fm_i,B3: set_li8269783359719514504c_fm_i] : ( ord_le1209247765174941992c_fm_i @ A2 @ ( sup_su33170788683693916c_fm_i @ A2 @ B3 ) ) ).
% sup.cobounded1
thf(fact_366_sup_Ocobounded1,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ A2 @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) ) ).
% sup.cobounded1
thf(fact_367_sup_Oorder__iff,axiom,
( ord_le5389487502678872194c_fm_i
= ( ^ [B4: set_se3485332733965609186c_fm_i,A4: set_se3485332733965609186c_fm_i] :
( A4
= ( sup_su2582925890723967158c_fm_i @ A4 @ B4 ) ) ) ) ).
% sup.order_iff
thf(fact_368_sup_Oorder__iff,axiom,
( ord_le190830114487426235fm_i_o
= ( ^ [B4: epistemic_fm_i > $o,A4: epistemic_fm_i > $o] :
( A4
= ( sup_su2844414564337698183fm_i_o @ A4 @ B4 ) ) ) ) ).
% sup.order_iff
thf(fact_369_sup_Oorder__iff,axiom,
( ord_le5706303257367236315fm_i_o
= ( ^ [B4: set_Epistemic_fm_i > $o,A4: set_Epistemic_fm_i > $o] :
( A4
= ( sup_su6723579903606884263fm_i_o @ A4 @ B4 ) ) ) ) ).
% sup.order_iff
thf(fact_370_sup_Oorder__iff,axiom,
( ord_le2772500130360476258c_fm_i
= ( ^ [B4: set_se7339729205154126530c_fm_i,A4: set_se7339729205154126530c_fm_i] :
( A4
= ( sup_su2317974602288960150c_fm_i @ A4 @ B4 ) ) ) ) ).
% sup.order_iff
thf(fact_371_sup_Oorder__iff,axiom,
( ord_le1209247765174941992c_fm_i
= ( ^ [B4: set_li8269783359719514504c_fm_i,A4: set_li8269783359719514504c_fm_i] :
( A4
= ( sup_su33170788683693916c_fm_i @ A4 @ B4 ) ) ) ) ).
% sup.order_iff
thf(fact_372_sup_Oorder__iff,axiom,
( ord_le3843937902494030498c_fm_i
= ( ^ [B4: set_Epistemic_fm_i,A4: set_Epistemic_fm_i] :
( A4
= ( sup_su1936195050962291414c_fm_i @ A4 @ B4 ) ) ) ) ).
% sup.order_iff
thf(fact_373_sup_OboundedI,axiom,
! [B3: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i,C2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ B3 @ A2 )
=> ( ( ord_le5389487502678872194c_fm_i @ C2 @ A2 )
=> ( ord_le5389487502678872194c_fm_i @ ( sup_su2582925890723967158c_fm_i @ B3 @ C2 ) @ A2 ) ) ) ).
% sup.boundedI
thf(fact_374_sup_OboundedI,axiom,
! [B3: epistemic_fm_i > $o,A2: epistemic_fm_i > $o,C2: epistemic_fm_i > $o] :
( ( ord_le190830114487426235fm_i_o @ B3 @ A2 )
=> ( ( ord_le190830114487426235fm_i_o @ C2 @ A2 )
=> ( ord_le190830114487426235fm_i_o @ ( sup_su2844414564337698183fm_i_o @ B3 @ C2 ) @ A2 ) ) ) ).
% sup.boundedI
thf(fact_375_sup_OboundedI,axiom,
! [B3: set_Epistemic_fm_i > $o,A2: set_Epistemic_fm_i > $o,C2: set_Epistemic_fm_i > $o] :
( ( ord_le5706303257367236315fm_i_o @ B3 @ A2 )
=> ( ( ord_le5706303257367236315fm_i_o @ C2 @ A2 )
=> ( ord_le5706303257367236315fm_i_o @ ( sup_su6723579903606884263fm_i_o @ B3 @ C2 ) @ A2 ) ) ) ).
% sup.boundedI
thf(fact_376_sup_OboundedI,axiom,
! [B3: set_se7339729205154126530c_fm_i,A2: set_se7339729205154126530c_fm_i,C2: set_se7339729205154126530c_fm_i] :
( ( ord_le2772500130360476258c_fm_i @ B3 @ A2 )
=> ( ( ord_le2772500130360476258c_fm_i @ C2 @ A2 )
=> ( ord_le2772500130360476258c_fm_i @ ( sup_su2317974602288960150c_fm_i @ B3 @ C2 ) @ A2 ) ) ) ).
% sup.boundedI
thf(fact_377_sup_OboundedI,axiom,
! [B3: set_li8269783359719514504c_fm_i,A2: set_li8269783359719514504c_fm_i,C2: set_li8269783359719514504c_fm_i] :
( ( ord_le1209247765174941992c_fm_i @ B3 @ A2 )
=> ( ( ord_le1209247765174941992c_fm_i @ C2 @ A2 )
=> ( ord_le1209247765174941992c_fm_i @ ( sup_su33170788683693916c_fm_i @ B3 @ C2 ) @ A2 ) ) ) ).
% sup.boundedI
thf(fact_378_sup_OboundedI,axiom,
! [B3: set_Epistemic_fm_i,A2: set_Epistemic_fm_i,C2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B3 @ A2 )
=> ( ( ord_le3843937902494030498c_fm_i @ C2 @ A2 )
=> ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ B3 @ C2 ) @ A2 ) ) ) ).
% sup.boundedI
thf(fact_379_sup_OboundedE,axiom,
! [B3: set_se3485332733965609186c_fm_i,C2: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ ( sup_su2582925890723967158c_fm_i @ B3 @ C2 ) @ A2 )
=> ~ ( ( ord_le5389487502678872194c_fm_i @ B3 @ A2 )
=> ~ ( ord_le5389487502678872194c_fm_i @ C2 @ A2 ) ) ) ).
% sup.boundedE
thf(fact_380_sup_OboundedE,axiom,
! [B3: epistemic_fm_i > $o,C2: epistemic_fm_i > $o,A2: epistemic_fm_i > $o] :
( ( ord_le190830114487426235fm_i_o @ ( sup_su2844414564337698183fm_i_o @ B3 @ C2 ) @ A2 )
=> ~ ( ( ord_le190830114487426235fm_i_o @ B3 @ A2 )
=> ~ ( ord_le190830114487426235fm_i_o @ C2 @ A2 ) ) ) ).
% sup.boundedE
thf(fact_381_sup_OboundedE,axiom,
! [B3: set_Epistemic_fm_i > $o,C2: set_Epistemic_fm_i > $o,A2: set_Epistemic_fm_i > $o] :
( ( ord_le5706303257367236315fm_i_o @ ( sup_su6723579903606884263fm_i_o @ B3 @ C2 ) @ A2 )
=> ~ ( ( ord_le5706303257367236315fm_i_o @ B3 @ A2 )
=> ~ ( ord_le5706303257367236315fm_i_o @ C2 @ A2 ) ) ) ).
% sup.boundedE
thf(fact_382_sup_OboundedE,axiom,
! [B3: set_se7339729205154126530c_fm_i,C2: set_se7339729205154126530c_fm_i,A2: set_se7339729205154126530c_fm_i] :
( ( ord_le2772500130360476258c_fm_i @ ( sup_su2317974602288960150c_fm_i @ B3 @ C2 ) @ A2 )
=> ~ ( ( ord_le2772500130360476258c_fm_i @ B3 @ A2 )
=> ~ ( ord_le2772500130360476258c_fm_i @ C2 @ A2 ) ) ) ).
% sup.boundedE
thf(fact_383_sup_OboundedE,axiom,
! [B3: set_li8269783359719514504c_fm_i,C2: set_li8269783359719514504c_fm_i,A2: set_li8269783359719514504c_fm_i] :
( ( ord_le1209247765174941992c_fm_i @ ( sup_su33170788683693916c_fm_i @ B3 @ C2 ) @ A2 )
=> ~ ( ( ord_le1209247765174941992c_fm_i @ B3 @ A2 )
=> ~ ( ord_le1209247765174941992c_fm_i @ C2 @ A2 ) ) ) ).
% sup.boundedE
thf(fact_384_sup_OboundedE,axiom,
! [B3: set_Epistemic_fm_i,C2: set_Epistemic_fm_i,A2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ B3 @ C2 ) @ A2 )
=> ~ ( ( ord_le3843937902494030498c_fm_i @ B3 @ A2 )
=> ~ ( ord_le3843937902494030498c_fm_i @ C2 @ A2 ) ) ) ).
% sup.boundedE
thf(fact_385_sup__absorb2,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ X @ Y )
=> ( ( sup_su2582925890723967158c_fm_i @ X @ Y )
= Y ) ) ).
% sup_absorb2
thf(fact_386_sup__absorb2,axiom,
! [X: epistemic_fm_i > $o,Y: epistemic_fm_i > $o] :
( ( ord_le190830114487426235fm_i_o @ X @ Y )
=> ( ( sup_su2844414564337698183fm_i_o @ X @ Y )
= Y ) ) ).
% sup_absorb2
thf(fact_387_sup__absorb2,axiom,
! [X: set_Epistemic_fm_i > $o,Y: set_Epistemic_fm_i > $o] :
( ( ord_le5706303257367236315fm_i_o @ X @ Y )
=> ( ( sup_su6723579903606884263fm_i_o @ X @ Y )
= Y ) ) ).
% sup_absorb2
thf(fact_388_sup__absorb2,axiom,
! [X: set_se7339729205154126530c_fm_i,Y: set_se7339729205154126530c_fm_i] :
( ( ord_le2772500130360476258c_fm_i @ X @ Y )
=> ( ( sup_su2317974602288960150c_fm_i @ X @ Y )
= Y ) ) ).
% sup_absorb2
thf(fact_389_sup__absorb2,axiom,
! [X: set_li8269783359719514504c_fm_i,Y: set_li8269783359719514504c_fm_i] :
( ( ord_le1209247765174941992c_fm_i @ X @ Y )
=> ( ( sup_su33170788683693916c_fm_i @ X @ Y )
= Y ) ) ).
% sup_absorb2
thf(fact_390_sup__absorb2,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X @ Y )
=> ( ( sup_su1936195050962291414c_fm_i @ X @ Y )
= Y ) ) ).
% sup_absorb2
thf(fact_391_sup__absorb1,axiom,
! [Y: set_se3485332733965609186c_fm_i,X: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ Y @ X )
=> ( ( sup_su2582925890723967158c_fm_i @ X @ Y )
= X ) ) ).
% sup_absorb1
thf(fact_392_sup__absorb1,axiom,
! [Y: epistemic_fm_i > $o,X: epistemic_fm_i > $o] :
( ( ord_le190830114487426235fm_i_o @ Y @ X )
=> ( ( sup_su2844414564337698183fm_i_o @ X @ Y )
= X ) ) ).
% sup_absorb1
thf(fact_393_sup__absorb1,axiom,
! [Y: set_Epistemic_fm_i > $o,X: set_Epistemic_fm_i > $o] :
( ( ord_le5706303257367236315fm_i_o @ Y @ X )
=> ( ( sup_su6723579903606884263fm_i_o @ X @ Y )
= X ) ) ).
% sup_absorb1
thf(fact_394_sup__absorb1,axiom,
! [Y: set_se7339729205154126530c_fm_i,X: set_se7339729205154126530c_fm_i] :
( ( ord_le2772500130360476258c_fm_i @ Y @ X )
=> ( ( sup_su2317974602288960150c_fm_i @ X @ Y )
= X ) ) ).
% sup_absorb1
thf(fact_395_sup__absorb1,axiom,
! [Y: set_li8269783359719514504c_fm_i,X: set_li8269783359719514504c_fm_i] :
( ( ord_le1209247765174941992c_fm_i @ Y @ X )
=> ( ( sup_su33170788683693916c_fm_i @ X @ Y )
= X ) ) ).
% sup_absorb1
thf(fact_396_sup__absorb1,axiom,
! [Y: set_Epistemic_fm_i,X: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ Y @ X )
=> ( ( sup_su1936195050962291414c_fm_i @ X @ Y )
= X ) ) ).
% sup_absorb1
thf(fact_397_sup_Oabsorb2,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ B3 )
=> ( ( sup_su1936195050962291414c_fm_i @ A2 @ B3 )
= B3 ) ) ).
% sup.absorb2
thf(fact_398_sup_Oabsorb1,axiom,
! [B3: set_Epistemic_fm_i,A2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B3 @ A2 )
=> ( ( sup_su1936195050962291414c_fm_i @ A2 @ B3 )
= A2 ) ) ).
% sup.absorb1
thf(fact_399_sup__unique,axiom,
! [F3: set_Epistemic_fm_i > set_Epistemic_fm_i > set_Epistemic_fm_i,X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ X3 @ ( F3 @ X3 @ Y4 ) )
=> ( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ Y4 @ ( F3 @ X3 @ Y4 ) )
=> ( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i,Z3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ Y4 @ X3 )
=> ( ( ord_le3843937902494030498c_fm_i @ Z3 @ X3 )
=> ( ord_le3843937902494030498c_fm_i @ ( F3 @ Y4 @ Z3 ) @ X3 ) ) )
=> ( ( sup_su1936195050962291414c_fm_i @ X @ Y )
= ( F3 @ X @ Y ) ) ) ) ) ).
% sup_unique
thf(fact_400_sup_OorderI,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( A2
= ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) )
=> ( ord_le3843937902494030498c_fm_i @ B3 @ A2 ) ) ).
% sup.orderI
thf(fact_401_sup_OorderE,axiom,
! [B3: set_Epistemic_fm_i,A2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B3 @ A2 )
=> ( A2
= ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) ) ) ).
% sup.orderE
thf(fact_402_le__iff__sup,axiom,
( ord_le3843937902494030498c_fm_i
= ( ^ [X2: set_Epistemic_fm_i,Y3: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ X2 @ Y3 )
= Y3 ) ) ) ).
% le_iff_sup
thf(fact_403_sup__least,axiom,
! [Y: set_Epistemic_fm_i,X: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ Y @ X )
=> ( ( ord_le3843937902494030498c_fm_i @ Z @ X )
=> ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ Y @ Z ) @ X ) ) ) ).
% sup_least
thf(fact_404_sup__mono,axiom,
! [A2: set_Epistemic_fm_i,C2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,D: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ C2 )
=> ( ( ord_le3843937902494030498c_fm_i @ B3 @ D )
=> ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) @ ( sup_su1936195050962291414c_fm_i @ C2 @ D ) ) ) ) ).
% sup_mono
thf(fact_405_sup_Omono,axiom,
! [C2: set_Epistemic_fm_i,A2: set_Epistemic_fm_i,D: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ C2 @ A2 )
=> ( ( ord_le3843937902494030498c_fm_i @ D @ B3 )
=> ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ C2 @ D ) @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) ) ) ) ).
% sup.mono
thf(fact_406_le__supI2,axiom,
! [X: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,A2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X @ B3 )
=> ( ord_le3843937902494030498c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) ) ) ).
% le_supI2
thf(fact_407_le__supI1,axiom,
! [X: set_Epistemic_fm_i,A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X @ A2 )
=> ( ord_le3843937902494030498c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) ) ) ).
% le_supI1
thf(fact_408_sup__ge2,axiom,
! [Y: set_Epistemic_fm_i,X: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ Y @ ( sup_su1936195050962291414c_fm_i @ X @ Y ) ) ).
% sup_ge2
thf(fact_409_sup__ge1,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ X @ Y ) ) ).
% sup_ge1
thf(fact_410_le__supI,axiom,
! [A2: set_Epistemic_fm_i,X: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ X )
=> ( ( ord_le3843937902494030498c_fm_i @ B3 @ X )
=> ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) @ X ) ) ) ).
% le_supI
thf(fact_411_le__supE,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,X: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) @ X )
=> ~ ( ( ord_le3843937902494030498c_fm_i @ A2 @ X )
=> ~ ( ord_le3843937902494030498c_fm_i @ B3 @ X ) ) ) ).
% le_supE
thf(fact_412_inf__sup__ord_I3_J,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ X @ Y ) ) ).
% inf_sup_ord(3)
thf(fact_413_inf__sup__ord_I4_J,axiom,
! [Y: set_Epistemic_fm_i,X: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ Y @ ( sup_su1936195050962291414c_fm_i @ X @ Y ) ) ).
% inf_sup_ord(4)
thf(fact_414_rev__finite__subset,axiom,
! [B2: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ B2 )
=> ( ( ord_le5389487502678872194c_fm_i @ A @ B2 )
=> ( finite7933139204641697195c_fm_i @ A ) ) ) ).
% rev_finite_subset
thf(fact_415_rev__finite__subset,axiom,
! [B2: set_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ B2 )
=> ( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( finite3304564979551393739c_fm_i @ A ) ) ) ).
% rev_finite_subset
thf(fact_416_infinite__super,axiom,
! [S: set_se3485332733965609186c_fm_i,T2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ S @ T2 )
=> ( ~ ( finite7933139204641697195c_fm_i @ S )
=> ~ ( finite7933139204641697195c_fm_i @ T2 ) ) ) ).
% infinite_super
thf(fact_417_infinite__super,axiom,
! [S: set_Epistemic_fm_i,T2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ S @ T2 )
=> ( ~ ( finite3304564979551393739c_fm_i @ S )
=> ~ ( finite3304564979551393739c_fm_i @ T2 ) ) ) ).
% infinite_super
thf(fact_418_finite__subset,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A @ B2 )
=> ( ( finite7933139204641697195c_fm_i @ B2 )
=> ( finite7933139204641697195c_fm_i @ A ) ) ) ).
% finite_subset
thf(fact_419_finite__subset,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ( finite3304564979551393739c_fm_i @ B2 )
=> ( finite3304564979551393739c_fm_i @ A ) ) ) ).
% finite_subset
thf(fact_420_finite__list,axiom,
! [A: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ A )
=> ? [Xs2: list_Epistemic_fm_i] :
( ( set_Epistemic_fm_i2 @ Xs2 )
= A ) ) ).
% finite_list
thf(fact_421_finite__list,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ? [Xs2: list_s8081015415394010888c_fm_i] :
( ( set_se200842218512397079c_fm_i @ Xs2 )
= A ) ) ).
% finite_list
thf(fact_422_subset__code_I1_J,axiom,
! [Xs: list_s8081015415394010888c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ ( set_se200842218512397079c_fm_i @ Xs ) @ B2 )
= ( ! [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ ( set_se200842218512397079c_fm_i @ Xs ) )
=> ( member1104366573291651755c_fm_i @ X2 @ B2 ) ) ) ) ).
% subset_code(1)
thf(fact_423_subset__code_I1_J,axiom,
! [Xs: list_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( set_Epistemic_fm_i2 @ Xs ) @ B2 )
= ( ! [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ ( set_Epistemic_fm_i2 @ Xs ) )
=> ( member6642669606046002379c_fm_i @ X2 @ B2 ) ) ) ) ).
% subset_code(1)
thf(fact_424_infinite__Un,axiom,
! [S: set_se3485332733965609186c_fm_i,T2: set_se3485332733965609186c_fm_i] :
( ( ~ ( finite7933139204641697195c_fm_i @ ( sup_su2582925890723967158c_fm_i @ S @ T2 ) ) )
= ( ~ ( finite7933139204641697195c_fm_i @ S )
| ~ ( finite7933139204641697195c_fm_i @ T2 ) ) ) ).
% infinite_Un
thf(fact_425_infinite__Un,axiom,
! [S: set_Epistemic_fm_i,T2: set_Epistemic_fm_i] :
( ( ~ ( finite3304564979551393739c_fm_i @ ( sup_su1936195050962291414c_fm_i @ S @ T2 ) ) )
= ( ~ ( finite3304564979551393739c_fm_i @ S )
| ~ ( finite3304564979551393739c_fm_i @ T2 ) ) ) ).
% infinite_Un
thf(fact_426_Un__infinite,axiom,
! [S: set_se3485332733965609186c_fm_i,T2: set_se3485332733965609186c_fm_i] :
( ~ ( finite7933139204641697195c_fm_i @ S )
=> ~ ( finite7933139204641697195c_fm_i @ ( sup_su2582925890723967158c_fm_i @ S @ T2 ) ) ) ).
% Un_infinite
thf(fact_427_Un__infinite,axiom,
! [S: set_Epistemic_fm_i,T2: set_Epistemic_fm_i] :
( ~ ( finite3304564979551393739c_fm_i @ S )
=> ~ ( finite3304564979551393739c_fm_i @ ( sup_su1936195050962291414c_fm_i @ S @ T2 ) ) ) ).
% Un_infinite
thf(fact_428_finite__UnI,axiom,
! [F: set_se3485332733965609186c_fm_i,G: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ F )
=> ( ( finite7933139204641697195c_fm_i @ G )
=> ( finite7933139204641697195c_fm_i @ ( sup_su2582925890723967158c_fm_i @ F @ G ) ) ) ) ).
% finite_UnI
thf(fact_429_finite__UnI,axiom,
! [F: set_Epistemic_fm_i,G: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ F )
=> ( ( finite3304564979551393739c_fm_i @ G )
=> ( finite3304564979551393739c_fm_i @ ( sup_su1936195050962291414c_fm_i @ F @ G ) ) ) ) ).
% finite_UnI
thf(fact_430_subset__Un__eq,axiom,
( ord_le3843937902494030498c_fm_i
= ( ^ [A3: set_Epistemic_fm_i,B: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ A3 @ B )
= B ) ) ) ).
% subset_Un_eq
thf(fact_431_subset__UnE,axiom,
! [C: set_Epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ C @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) )
=> ~ ! [A5: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A5 @ A )
=> ! [B5: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B5 @ B2 )
=> ( C
!= ( sup_su1936195050962291414c_fm_i @ A5 @ B5 ) ) ) ) ) ).
% subset_UnE
thf(fact_432_Un__absorb2,axiom,
! [B2: set_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B2 @ A )
=> ( ( sup_su1936195050962291414c_fm_i @ A @ B2 )
= A ) ) ).
% Un_absorb2
thf(fact_433_Un__absorb1,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ( sup_su1936195050962291414c_fm_i @ A @ B2 )
= B2 ) ) ).
% Un_absorb1
thf(fact_434_Un__upper2,axiom,
! [B2: set_Epistemic_fm_i,A: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ B2 @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) ) ).
% Un_upper2
thf(fact_435_Un__upper1,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ A @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) ) ).
% Un_upper1
thf(fact_436_Un__least,axiom,
! [A: set_Epistemic_fm_i,C: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ C )
=> ( ( ord_le3843937902494030498c_fm_i @ B2 @ C )
=> ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) @ C ) ) ) ).
% Un_least
thf(fact_437_Un__mono,axiom,
! [A: set_Epistemic_fm_i,C: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,D2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ C )
=> ( ( ord_le3843937902494030498c_fm_i @ B2 @ D2 )
=> ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) @ ( sup_su1936195050962291414c_fm_i @ C @ D2 ) ) ) ) ).
% Un_mono
thf(fact_438_fm_Odistinct_I9_J,axiom,
! [X61: i,X62: epistemic_fm_i] :
( epistemic_FF_i
!= ( epistemic_K_i @ X61 @ X62 ) ) ).
% fm.distinct(9)
thf(fact_439_R2,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,I: i] :
( ( epistemic_AK_i @ A @ P4 )
=> ( epistemic_AK_i @ A @ ( epistemic_K_i @ I @ P4 ) ) ) ).
% R2
thf(fact_440__092_060open_062_092_060nexists_062X_O_Aconsistent_AA_AX_A_092_060and_062_Amaximal_AA_AX_A_092_060and_062_AX_A_092_060in_062_A_123Wa_O_Aknown_AW_Ai_A_092_060subseteq_062_AWa_125_A_092_060inter_062_A_123W_O_Aknown_AU_Ai_A_092_060subseteq_062_AW_125_092_060close_062,axiom,
~ ? [X4: set_Epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ a @ X4 )
& ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ a ) @ X4 )
& ( member1104366573291651755c_fm_i @ X4
@ ( inf_in161960956874937808c_fm_i
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ i2 @ P2 ) @ w ) ) ) )
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ i2 @ P2 ) @ u ) ) ) ) ) ) ) ).
% \<open>\<nexists>X. consistent A X \<and> maximal A X \<and> X \<in> {Wa. known W i \<subseteq> Wa} \<inter> {W. known U i \<subseteq> W}\<close>
thf(fact_441_set__union,axiom,
! [Xs: list_Epistemic_fm_i,Ys: list_Epistemic_fm_i] :
( ( set_Epistemic_fm_i2 @ ( union_Epistemic_fm_i @ Xs @ Ys ) )
= ( sup_su1936195050962291414c_fm_i @ ( set_Epistemic_fm_i2 @ Xs ) @ ( set_Epistemic_fm_i2 @ Ys ) ) ) ).
% set_union
thf(fact_442_dual__order_Orefl,axiom,
! [A2: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ A2 @ A2 ) ).
% dual_order.refl
thf(fact_443_order__refl,axiom,
! [X: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ X @ X ) ).
% order_refl
thf(fact_444_sup__Un__eq,axiom,
! [R: set_se3485332733965609186c_fm_i,S: set_se3485332733965609186c_fm_i] :
( ( sup_su6723579903606884263fm_i_o
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ R )
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ S ) )
= ( ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ ( sup_su2582925890723967158c_fm_i @ R @ S ) ) ) ) ).
% sup_Un_eq
thf(fact_445_sup__Un__eq,axiom,
! [R: set_Epistemic_fm_i,S: set_Epistemic_fm_i] :
( ( sup_su2844414564337698183fm_i_o
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ R )
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ S ) )
= ( ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ ( sup_su1936195050962291414c_fm_i @ R @ S ) ) ) ) ).
% sup_Un_eq
thf(fact_446_pred__subset__eq,axiom,
! [R: set_se3485332733965609186c_fm_i,S: set_se3485332733965609186c_fm_i] :
( ( ord_le5706303257367236315fm_i_o
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ R )
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ S ) )
= ( ord_le5389487502678872194c_fm_i @ R @ S ) ) ).
% pred_subset_eq
thf(fact_447_pred__subset__eq,axiom,
! [R: set_Epistemic_fm_i,S: set_Epistemic_fm_i] :
( ( ord_le190830114487426235fm_i_o
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ R )
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ S ) )
= ( ord_le3843937902494030498c_fm_i @ R @ S ) ) ).
% pred_subset_eq
thf(fact_448_subset__Collect__iff,axiom,
! [B2: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( ord_le5389487502678872194c_fm_i @ B2 @ A )
=> ( ( ord_le5389487502678872194c_fm_i @ B2
@ ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A )
& ( P3 @ X2 ) ) ) )
= ( ! [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ B2 )
=> ( P3 @ X2 ) ) ) ) ) ).
% subset_Collect_iff
thf(fact_449_subset__Collect__iff,axiom,
! [B2: set_Epistemic_fm_i,A: set_Epistemic_fm_i,P3: epistemic_fm_i > $o] :
( ( ord_le3843937902494030498c_fm_i @ B2 @ A )
=> ( ( ord_le3843937902494030498c_fm_i @ B2
@ ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ A )
& ( P3 @ X2 ) ) ) )
= ( ! [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ B2 )
=> ( P3 @ X2 ) ) ) ) ) ).
% subset_Collect_iff
thf(fact_450_subset__CollectI,axiom,
! [B2: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i,Q2: set_Epistemic_fm_i > $o,P3: set_Epistemic_fm_i > $o] :
( ( ord_le5389487502678872194c_fm_i @ B2 @ A )
=> ( ! [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ B2 )
=> ( ( Q2 @ X3 )
=> ( P3 @ X3 ) ) )
=> ( ord_le5389487502678872194c_fm_i
@ ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ B2 )
& ( Q2 @ X2 ) ) )
@ ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A )
& ( P3 @ X2 ) ) ) ) ) ) ).
% subset_CollectI
thf(fact_451_subset__CollectI,axiom,
! [B2: set_Epistemic_fm_i,A: set_Epistemic_fm_i,Q2: epistemic_fm_i > $o,P3: epistemic_fm_i > $o] :
( ( ord_le3843937902494030498c_fm_i @ B2 @ A )
=> ( ! [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ B2 )
=> ( ( Q2 @ X3 )
=> ( P3 @ X3 ) ) )
=> ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ B2 )
& ( Q2 @ X2 ) ) )
@ ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ A )
& ( P3 @ X2 ) ) ) ) ) ) ).
% subset_CollectI
thf(fact_452_Collect__restrict,axiom,
! [X5: set_se3485332733965609186c_fm_i,P3: set_Epistemic_fm_i > $o] :
( ord_le5389487502678872194c_fm_i
@ ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ X5 )
& ( P3 @ X2 ) ) )
@ X5 ) ).
% Collect_restrict
thf(fact_453_Collect__restrict,axiom,
! [X5: set_Epistemic_fm_i,P3: epistemic_fm_i > $o] :
( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ X5 )
& ( P3 @ X2 ) ) )
@ X5 ) ).
% Collect_restrict
thf(fact_454_prop__restrict,axiom,
! [X: set_Epistemic_fm_i,Z4: set_se3485332733965609186c_fm_i,X5: set_se3485332733965609186c_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( member1104366573291651755c_fm_i @ X @ Z4 )
=> ( ( ord_le5389487502678872194c_fm_i @ Z4
@ ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ X5 )
& ( P3 @ X2 ) ) ) )
=> ( P3 @ X ) ) ) ).
% prop_restrict
thf(fact_455_prop__restrict,axiom,
! [X: epistemic_fm_i,Z4: set_Epistemic_fm_i,X5: set_Epistemic_fm_i,P3: epistemic_fm_i > $o] :
( ( member6642669606046002379c_fm_i @ X @ Z4 )
=> ( ( ord_le3843937902494030498c_fm_i @ Z4
@ ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ X5 )
& ( P3 @ X2 ) ) ) )
=> ( P3 @ X ) ) ) ).
% prop_restrict
thf(fact_456_conj__subset__def,axiom,
! [A: set_se3485332733965609186c_fm_i,P3: set_Epistemic_fm_i > $o,Q2: set_Epistemic_fm_i > $o] :
( ( ord_le5389487502678872194c_fm_i @ A
@ ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( P3 @ X2 )
& ( Q2 @ X2 ) ) ) )
= ( ( ord_le5389487502678872194c_fm_i @ A @ ( collec3087743281813070829c_fm_i @ P3 ) )
& ( ord_le5389487502678872194c_fm_i @ A @ ( collec3087743281813070829c_fm_i @ Q2 ) ) ) ) ).
% conj_subset_def
thf(fact_457_conj__subset__def,axiom,
! [A: set_Epistemic_fm_i,P3: epistemic_fm_i > $o,Q2: epistemic_fm_i > $o] :
( ( ord_le3843937902494030498c_fm_i @ A
@ ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( P3 @ X2 )
& ( Q2 @ X2 ) ) ) )
= ( ( ord_le3843937902494030498c_fm_i @ A @ ( collec4904205187116291597c_fm_i @ P3 ) )
& ( ord_le3843937902494030498c_fm_i @ A @ ( collec4904205187116291597c_fm_i @ Q2 ) ) ) ) ).
% conj_subset_def
thf(fact_458_inf_Oidem,axiom,
! [A2: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ A2 @ A2 )
= A2 ) ).
% inf.idem
thf(fact_459_inf__idem,axiom,
! [X: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ X @ X )
= X ) ).
% inf_idem
thf(fact_460_inf_Oleft__idem,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ A2 @ ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) )
= ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) ) ).
% inf.left_idem
thf(fact_461_inf__left__idem,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ X @ Y ) )
= ( inf_in161960956874937808c_fm_i @ X @ Y ) ) ).
% inf_left_idem
thf(fact_462_inf_Oright__idem,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) @ B3 )
= ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) ) ).
% inf.right_idem
thf(fact_463_inf__right__idem,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ ( inf_in161960956874937808c_fm_i @ X @ Y ) @ Y )
= ( inf_in161960956874937808c_fm_i @ X @ Y ) ) ).
% inf_right_idem
thf(fact_464_IntI,axiom,
! [C2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ C2 @ A )
=> ( ( member6642669606046002379c_fm_i @ C2 @ B2 )
=> ( member6642669606046002379c_fm_i @ C2 @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) ) ) ) ).
% IntI
thf(fact_465_IntI,axiom,
! [C2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ C2 @ A )
=> ( ( member1104366573291651755c_fm_i @ C2 @ B2 )
=> ( member1104366573291651755c_fm_i @ C2 @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) ) ) ) ).
% IntI
thf(fact_466_Int__iff,axiom,
! [C2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ C2 @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) )
= ( ( member6642669606046002379c_fm_i @ C2 @ A )
& ( member6642669606046002379c_fm_i @ C2 @ B2 ) ) ) ).
% Int_iff
thf(fact_467_Int__iff,axiom,
! [C2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ C2 @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) )
= ( ( member1104366573291651755c_fm_i @ C2 @ A )
& ( member1104366573291651755c_fm_i @ C2 @ B2 ) ) ) ).
% Int_iff
thf(fact_468_le__inf__iff,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ Y @ Z ) )
= ( ( ord_le5389487502678872194c_fm_i @ X @ Y )
& ( ord_le5389487502678872194c_fm_i @ X @ Z ) ) ) ).
% le_inf_iff
thf(fact_469_le__inf__iff,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X @ ( inf_in3450601097109690352c_fm_i @ Y @ Z ) )
= ( ( ord_le3843937902494030498c_fm_i @ X @ Y )
& ( ord_le3843937902494030498c_fm_i @ X @ Z ) ) ) ).
% le_inf_iff
thf(fact_470_inf_Obounded__iff,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i,C2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A2 @ ( inf_in161960956874937808c_fm_i @ B3 @ C2 ) )
= ( ( ord_le5389487502678872194c_fm_i @ A2 @ B3 )
& ( ord_le5389487502678872194c_fm_i @ A2 @ C2 ) ) ) ).
% inf.bounded_iff
thf(fact_471_inf_Obounded__iff,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,C2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ ( inf_in3450601097109690352c_fm_i @ B3 @ C2 ) )
= ( ( ord_le3843937902494030498c_fm_i @ A2 @ B3 )
& ( ord_le3843937902494030498c_fm_i @ A2 @ C2 ) ) ) ).
% inf.bounded_iff
thf(fact_472_inf__sup__absorb,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ X @ ( sup_su2582925890723967158c_fm_i @ X @ Y ) )
= X ) ).
% inf_sup_absorb
thf(fact_473_inf__sup__absorb,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ X @ Y ) )
= X ) ).
% inf_sup_absorb
thf(fact_474_sup__inf__absorb,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ X @ Y ) )
= X ) ).
% sup_inf_absorb
thf(fact_475_sup__inf__absorb,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ X @ ( inf_in3450601097109690352c_fm_i @ X @ Y ) )
= X ) ).
% sup_inf_absorb
thf(fact_476_finite__Int,axiom,
! [F: set_Epistemic_fm_i,G: set_Epistemic_fm_i] :
( ( ( finite3304564979551393739c_fm_i @ F )
| ( finite3304564979551393739c_fm_i @ G ) )
=> ( finite3304564979551393739c_fm_i @ ( inf_in3450601097109690352c_fm_i @ F @ G ) ) ) ).
% finite_Int
thf(fact_477_finite__Int,axiom,
! [F: set_se3485332733965609186c_fm_i,G: set_se3485332733965609186c_fm_i] :
( ( ( finite7933139204641697195c_fm_i @ F )
| ( finite7933139204641697195c_fm_i @ G ) )
=> ( finite7933139204641697195c_fm_i @ ( inf_in161960956874937808c_fm_i @ F @ G ) ) ) ).
% finite_Int
thf(fact_478_Int__subset__iff,axiom,
! [C: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ C @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) )
= ( ( ord_le5389487502678872194c_fm_i @ C @ A )
& ( ord_le5389487502678872194c_fm_i @ C @ B2 ) ) ) ).
% Int_subset_iff
thf(fact_479_Int__subset__iff,axiom,
! [C: set_Epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ C @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) )
= ( ( ord_le3843937902494030498c_fm_i @ C @ A )
& ( ord_le3843937902494030498c_fm_i @ C @ B2 ) ) ) ).
% Int_subset_iff
thf(fact_480_Int__Un__eq_I4_J,axiom,
! [T2: set_se3485332733965609186c_fm_i,S: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ T2 @ ( inf_in161960956874937808c_fm_i @ S @ T2 ) )
= T2 ) ).
% Int_Un_eq(4)
thf(fact_481_Int__Un__eq_I4_J,axiom,
! [T2: set_Epistemic_fm_i,S: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ T2 @ ( inf_in3450601097109690352c_fm_i @ S @ T2 ) )
= T2 ) ).
% Int_Un_eq(4)
thf(fact_482_Int__Un__eq_I3_J,axiom,
! [S: set_se3485332733965609186c_fm_i,T2: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ S @ ( inf_in161960956874937808c_fm_i @ S @ T2 ) )
= S ) ).
% Int_Un_eq(3)
thf(fact_483_Int__Un__eq_I3_J,axiom,
! [S: set_Epistemic_fm_i,T2: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ S @ ( inf_in3450601097109690352c_fm_i @ S @ T2 ) )
= S ) ).
% Int_Un_eq(3)
thf(fact_484_Int__Un__eq_I2_J,axiom,
! [S: set_se3485332733965609186c_fm_i,T2: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ S @ T2 ) @ T2 )
= T2 ) ).
% Int_Un_eq(2)
thf(fact_485_Int__Un__eq_I2_J,axiom,
! [S: set_Epistemic_fm_i,T2: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ S @ T2 ) @ T2 )
= T2 ) ).
% Int_Un_eq(2)
thf(fact_486_Int__Un__eq_I1_J,axiom,
! [S: set_se3485332733965609186c_fm_i,T2: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ S @ T2 ) @ S )
= S ) ).
% Int_Un_eq(1)
thf(fact_487_Int__Un__eq_I1_J,axiom,
! [S: set_Epistemic_fm_i,T2: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ S @ T2 ) @ S )
= S ) ).
% Int_Un_eq(1)
thf(fact_488_Un__Int__eq_I4_J,axiom,
! [T2: set_se3485332733965609186c_fm_i,S: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ T2 @ ( sup_su2582925890723967158c_fm_i @ S @ T2 ) )
= T2 ) ).
% Un_Int_eq(4)
thf(fact_489_Un__Int__eq_I4_J,axiom,
! [T2: set_Epistemic_fm_i,S: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ T2 @ ( sup_su1936195050962291414c_fm_i @ S @ T2 ) )
= T2 ) ).
% Un_Int_eq(4)
thf(fact_490_Un__Int__eq_I3_J,axiom,
! [S: set_se3485332733965609186c_fm_i,T2: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ S @ ( sup_su2582925890723967158c_fm_i @ S @ T2 ) )
= S ) ).
% Un_Int_eq(3)
thf(fact_491_Un__Int__eq_I3_J,axiom,
! [S: set_Epistemic_fm_i,T2: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ S @ ( sup_su1936195050962291414c_fm_i @ S @ T2 ) )
= S ) ).
% Un_Int_eq(3)
thf(fact_492_Un__Int__eq_I2_J,axiom,
! [S: set_se3485332733965609186c_fm_i,T2: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ S @ T2 ) @ T2 )
= T2 ) ).
% Un_Int_eq(2)
thf(fact_493_Un__Int__eq_I2_J,axiom,
! [S: set_Epistemic_fm_i,T2: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ S @ T2 ) @ T2 )
= T2 ) ).
% Un_Int_eq(2)
thf(fact_494_Un__Int__eq_I1_J,axiom,
! [S: set_se3485332733965609186c_fm_i,T2: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ S @ T2 ) @ S )
= S ) ).
% Un_Int_eq(1)
thf(fact_495_Un__Int__eq_I1_J,axiom,
! [S: set_Epistemic_fm_i,T2: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ S @ T2 ) @ S )
= S ) ).
% Un_Int_eq(1)
thf(fact_496_inf__sup__aci_I4_J,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ X @ Y ) )
= ( inf_in161960956874937808c_fm_i @ X @ Y ) ) ).
% inf_sup_aci(4)
thf(fact_497_inf__sup__aci_I3_J,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ Y @ Z ) )
= ( inf_in161960956874937808c_fm_i @ Y @ ( inf_in161960956874937808c_fm_i @ X @ Z ) ) ) ).
% inf_sup_aci(3)
thf(fact_498_inf__sup__aci_I2_J,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ ( inf_in161960956874937808c_fm_i @ X @ Y ) @ Z )
= ( inf_in161960956874937808c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ Y @ Z ) ) ) ).
% inf_sup_aci(2)
thf(fact_499_inf__sup__aci_I1_J,axiom,
( inf_in161960956874937808c_fm_i
= ( ^ [X2: set_se3485332733965609186c_fm_i,Y3: set_se3485332733965609186c_fm_i] : ( inf_in161960956874937808c_fm_i @ Y3 @ X2 ) ) ) ).
% inf_sup_aci(1)
thf(fact_500_inf_Oassoc,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i,C2: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) @ C2 )
= ( inf_in161960956874937808c_fm_i @ A2 @ ( inf_in161960956874937808c_fm_i @ B3 @ C2 ) ) ) ).
% inf.assoc
thf(fact_501_inf__assoc,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ ( inf_in161960956874937808c_fm_i @ X @ Y ) @ Z )
= ( inf_in161960956874937808c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ Y @ Z ) ) ) ).
% inf_assoc
thf(fact_502_inf_Ocommute,axiom,
( inf_in161960956874937808c_fm_i
= ( ^ [A4: set_se3485332733965609186c_fm_i,B4: set_se3485332733965609186c_fm_i] : ( inf_in161960956874937808c_fm_i @ B4 @ A4 ) ) ) ).
% inf.commute
thf(fact_503_inf__commute,axiom,
( inf_in161960956874937808c_fm_i
= ( ^ [X2: set_se3485332733965609186c_fm_i,Y3: set_se3485332733965609186c_fm_i] : ( inf_in161960956874937808c_fm_i @ Y3 @ X2 ) ) ) ).
% inf_commute
thf(fact_504_inf_Oleft__commute,axiom,
! [B3: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i,C2: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ B3 @ ( inf_in161960956874937808c_fm_i @ A2 @ C2 ) )
= ( inf_in161960956874937808c_fm_i @ A2 @ ( inf_in161960956874937808c_fm_i @ B3 @ C2 ) ) ) ).
% inf.left_commute
thf(fact_505_inf__left__commute,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ Y @ Z ) )
= ( inf_in161960956874937808c_fm_i @ Y @ ( inf_in161960956874937808c_fm_i @ X @ Z ) ) ) ).
% inf_left_commute
thf(fact_506_IntE,axiom,
! [C2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ C2 @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) )
=> ~ ( ( member6642669606046002379c_fm_i @ C2 @ A )
=> ~ ( member6642669606046002379c_fm_i @ C2 @ B2 ) ) ) ).
% IntE
thf(fact_507_IntE,axiom,
! [C2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ C2 @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) )
=> ~ ( ( member1104366573291651755c_fm_i @ C2 @ A )
=> ~ ( member1104366573291651755c_fm_i @ C2 @ B2 ) ) ) ).
% IntE
thf(fact_508_IntD1,axiom,
! [C2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ C2 @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) )
=> ( member6642669606046002379c_fm_i @ C2 @ A ) ) ).
% IntD1
thf(fact_509_IntD1,axiom,
! [C2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ C2 @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) )
=> ( member1104366573291651755c_fm_i @ C2 @ A ) ) ).
% IntD1
thf(fact_510_IntD2,axiom,
! [C2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ C2 @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) )
=> ( member6642669606046002379c_fm_i @ C2 @ B2 ) ) ).
% IntD2
thf(fact_511_IntD2,axiom,
! [C2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ C2 @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) )
=> ( member1104366573291651755c_fm_i @ C2 @ B2 ) ) ).
% IntD2
thf(fact_512_Int__assoc,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) @ C )
= ( inf_in161960956874937808c_fm_i @ A @ ( inf_in161960956874937808c_fm_i @ B2 @ C ) ) ) ).
% Int_assoc
thf(fact_513_Int__absorb,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ A @ A )
= A ) ).
% Int_absorb
thf(fact_514_Int__commute,axiom,
( inf_in161960956874937808c_fm_i
= ( ^ [A3: set_se3485332733965609186c_fm_i,B: set_se3485332733965609186c_fm_i] : ( inf_in161960956874937808c_fm_i @ B @ A3 ) ) ) ).
% Int_commute
thf(fact_515_Int__left__absorb,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ A @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) )
= ( inf_in161960956874937808c_fm_i @ A @ B2 ) ) ).
% Int_left_absorb
thf(fact_516_Int__left__commute,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ A @ ( inf_in161960956874937808c_fm_i @ B2 @ C ) )
= ( inf_in161960956874937808c_fm_i @ B2 @ ( inf_in161960956874937808c_fm_i @ A @ C ) ) ) ).
% Int_left_commute
thf(fact_517_consequent__in__maximal,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,P4: epistemic_fm_i,Q: epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ V )
=> ( ( member6642669606046002379c_fm_i @ P4 @ V )
=> ( ( member6642669606046002379c_fm_i @ ( epistemic_Imp_i @ P4 @ Q ) @ V )
=> ( member6642669606046002379c_fm_i @ Q @ V ) ) ) ) ) ).
% consequent_in_maximal
thf(fact_518_Collect__conj__eq,axiom,
! [P3: epistemic_fm_i > $o,Q2: epistemic_fm_i > $o] :
( ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( P3 @ X2 )
& ( Q2 @ X2 ) ) )
= ( inf_in3450601097109690352c_fm_i @ ( collec4904205187116291597c_fm_i @ P3 ) @ ( collec4904205187116291597c_fm_i @ Q2 ) ) ) ).
% Collect_conj_eq
thf(fact_519_Collect__conj__eq,axiom,
! [P3: set_Epistemic_fm_i > $o,Q2: set_Epistemic_fm_i > $o] :
( ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( P3 @ X2 )
& ( Q2 @ X2 ) ) )
= ( inf_in161960956874937808c_fm_i @ ( collec3087743281813070829c_fm_i @ P3 ) @ ( collec3087743281813070829c_fm_i @ Q2 ) ) ) ).
% Collect_conj_eq
thf(fact_520_Int__Collect,axiom,
! [X: epistemic_fm_i,A: set_Epistemic_fm_i,P3: epistemic_fm_i > $o] :
( ( member6642669606046002379c_fm_i @ X @ ( inf_in3450601097109690352c_fm_i @ A @ ( collec4904205187116291597c_fm_i @ P3 ) ) )
= ( ( member6642669606046002379c_fm_i @ X @ A )
& ( P3 @ X ) ) ) ).
% Int_Collect
thf(fact_521_Int__Collect,axiom,
! [X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( member1104366573291651755c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ A @ ( collec3087743281813070829c_fm_i @ P3 ) ) )
= ( ( member1104366573291651755c_fm_i @ X @ A )
& ( P3 @ X ) ) ) ).
% Int_Collect
thf(fact_522_Int__def,axiom,
( inf_in3450601097109690352c_fm_i
= ( ^ [A3: set_Epistemic_fm_i,B: set_Epistemic_fm_i] :
( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ A3 )
& ( member6642669606046002379c_fm_i @ X2 @ B ) ) ) ) ) ).
% Int_def
thf(fact_523_Int__def,axiom,
( inf_in161960956874937808c_fm_i
= ( ^ [A3: set_se3485332733965609186c_fm_i,B: set_se3485332733965609186c_fm_i] :
( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A3 )
& ( member1104366573291651755c_fm_i @ X2 @ B ) ) ) ) ) ).
% Int_def
thf(fact_524_inf__sup__ord_I2_J,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ X @ Y ) @ Y ) ).
% inf_sup_ord(2)
thf(fact_525_inf__sup__ord_I2_J,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ X @ Y ) @ Y ) ).
% inf_sup_ord(2)
thf(fact_526_inf__sup__ord_I1_J,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ X @ Y ) @ X ) ).
% inf_sup_ord(1)
thf(fact_527_inf__sup__ord_I1_J,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ X @ Y ) @ X ) ).
% inf_sup_ord(1)
thf(fact_528_inf__le1,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ X @ Y ) @ X ) ).
% inf_le1
thf(fact_529_inf__le1,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ X @ Y ) @ X ) ).
% inf_le1
thf(fact_530_inf__le2,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ X @ Y ) @ Y ) ).
% inf_le2
thf(fact_531_inf__le2,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ X @ Y ) @ Y ) ).
% inf_le2
thf(fact_532_le__infE,axiom,
! [X: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) )
=> ~ ( ( ord_le5389487502678872194c_fm_i @ X @ A2 )
=> ~ ( ord_le5389487502678872194c_fm_i @ X @ B3 ) ) ) ).
% le_infE
thf(fact_533_le__infE,axiom,
! [X: set_Epistemic_fm_i,A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X @ ( inf_in3450601097109690352c_fm_i @ A2 @ B3 ) )
=> ~ ( ( ord_le3843937902494030498c_fm_i @ X @ A2 )
=> ~ ( ord_le3843937902494030498c_fm_i @ X @ B3 ) ) ) ).
% le_infE
thf(fact_534_le__infI,axiom,
! [X: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ X @ A2 )
=> ( ( ord_le5389487502678872194c_fm_i @ X @ B3 )
=> ( ord_le5389487502678872194c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) ) ) ) ).
% le_infI
thf(fact_535_le__infI,axiom,
! [X: set_Epistemic_fm_i,A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X @ A2 )
=> ( ( ord_le3843937902494030498c_fm_i @ X @ B3 )
=> ( ord_le3843937902494030498c_fm_i @ X @ ( inf_in3450601097109690352c_fm_i @ A2 @ B3 ) ) ) ) ).
% le_infI
thf(fact_536_inf__mono,axiom,
! [A2: set_se3485332733965609186c_fm_i,C2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i,D: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A2 @ C2 )
=> ( ( ord_le5389487502678872194c_fm_i @ B3 @ D )
=> ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) @ ( inf_in161960956874937808c_fm_i @ C2 @ D ) ) ) ) ).
% inf_mono
thf(fact_537_inf__mono,axiom,
! [A2: set_Epistemic_fm_i,C2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,D: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ C2 )
=> ( ( ord_le3843937902494030498c_fm_i @ B3 @ D )
=> ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A2 @ B3 ) @ ( inf_in3450601097109690352c_fm_i @ C2 @ D ) ) ) ) ).
% inf_mono
thf(fact_538_le__infI1,axiom,
! [A2: set_se3485332733965609186c_fm_i,X: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A2 @ X )
=> ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) @ X ) ) ).
% le_infI1
thf(fact_539_le__infI1,axiom,
! [A2: set_Epistemic_fm_i,X: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ X )
=> ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A2 @ B3 ) @ X ) ) ).
% le_infI1
thf(fact_540_le__infI2,axiom,
! [B3: set_se3485332733965609186c_fm_i,X: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ B3 @ X )
=> ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) @ X ) ) ).
% le_infI2
thf(fact_541_le__infI2,axiom,
! [B3: set_Epistemic_fm_i,X: set_Epistemic_fm_i,A2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B3 @ X )
=> ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A2 @ B3 ) @ X ) ) ).
% le_infI2
thf(fact_542_inf_OorderE,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A2 @ B3 )
=> ( A2
= ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) ) ) ).
% inf.orderE
thf(fact_543_inf_OorderE,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ B3 )
=> ( A2
= ( inf_in3450601097109690352c_fm_i @ A2 @ B3 ) ) ) ).
% inf.orderE
thf(fact_544_inf_OorderI,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] :
( ( A2
= ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) )
=> ( ord_le5389487502678872194c_fm_i @ A2 @ B3 ) ) ).
% inf.orderI
thf(fact_545_inf_OorderI,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( A2
= ( inf_in3450601097109690352c_fm_i @ A2 @ B3 ) )
=> ( ord_le3843937902494030498c_fm_i @ A2 @ B3 ) ) ).
% inf.orderI
thf(fact_546_inf__unique,axiom,
! [F3: set_se3485332733965609186c_fm_i > set_se3485332733965609186c_fm_i > set_se3485332733965609186c_fm_i,X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] :
( ! [X3: set_se3485332733965609186c_fm_i,Y4: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ ( F3 @ X3 @ Y4 ) @ X3 )
=> ( ! [X3: set_se3485332733965609186c_fm_i,Y4: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ ( F3 @ X3 @ Y4 ) @ Y4 )
=> ( ! [X3: set_se3485332733965609186c_fm_i,Y4: set_se3485332733965609186c_fm_i,Z3: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ X3 @ Y4 )
=> ( ( ord_le5389487502678872194c_fm_i @ X3 @ Z3 )
=> ( ord_le5389487502678872194c_fm_i @ X3 @ ( F3 @ Y4 @ Z3 ) ) ) )
=> ( ( inf_in161960956874937808c_fm_i @ X @ Y )
= ( F3 @ X @ Y ) ) ) ) ) ).
% inf_unique
thf(fact_547_inf__unique,axiom,
! [F3: set_Epistemic_fm_i > set_Epistemic_fm_i > set_Epistemic_fm_i,X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( F3 @ X3 @ Y4 ) @ X3 )
=> ( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( F3 @ X3 @ Y4 ) @ Y4 )
=> ( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i,Z3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X3 @ Y4 )
=> ( ( ord_le3843937902494030498c_fm_i @ X3 @ Z3 )
=> ( ord_le3843937902494030498c_fm_i @ X3 @ ( F3 @ Y4 @ Z3 ) ) ) )
=> ( ( inf_in3450601097109690352c_fm_i @ X @ Y )
= ( F3 @ X @ Y ) ) ) ) ) ).
% inf_unique
thf(fact_548_le__iff__inf,axiom,
( ord_le5389487502678872194c_fm_i
= ( ^ [X2: set_se3485332733965609186c_fm_i,Y3: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ X2 @ Y3 )
= X2 ) ) ) ).
% le_iff_inf
thf(fact_549_le__iff__inf,axiom,
( ord_le3843937902494030498c_fm_i
= ( ^ [X2: set_Epistemic_fm_i,Y3: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ X2 @ Y3 )
= X2 ) ) ) ).
% le_iff_inf
thf(fact_550_inf_Oabsorb1,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A2 @ B3 )
=> ( ( inf_in161960956874937808c_fm_i @ A2 @ B3 )
= A2 ) ) ).
% inf.absorb1
thf(fact_551_inf_Oabsorb1,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ B3 )
=> ( ( inf_in3450601097109690352c_fm_i @ A2 @ B3 )
= A2 ) ) ).
% inf.absorb1
thf(fact_552_inf_Oabsorb2,axiom,
! [B3: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ B3 @ A2 )
=> ( ( inf_in161960956874937808c_fm_i @ A2 @ B3 )
= B3 ) ) ).
% inf.absorb2
thf(fact_553_inf_Oabsorb2,axiom,
! [B3: set_Epistemic_fm_i,A2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B3 @ A2 )
=> ( ( inf_in3450601097109690352c_fm_i @ A2 @ B3 )
= B3 ) ) ).
% inf.absorb2
thf(fact_554_inf__absorb1,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ X @ Y )
=> ( ( inf_in161960956874937808c_fm_i @ X @ Y )
= X ) ) ).
% inf_absorb1
thf(fact_555_inf__absorb1,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X @ Y )
=> ( ( inf_in3450601097109690352c_fm_i @ X @ Y )
= X ) ) ).
% inf_absorb1
thf(fact_556_inf__absorb2,axiom,
! [Y: set_se3485332733965609186c_fm_i,X: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ Y @ X )
=> ( ( inf_in161960956874937808c_fm_i @ X @ Y )
= Y ) ) ).
% inf_absorb2
thf(fact_557_inf__absorb2,axiom,
! [Y: set_Epistemic_fm_i,X: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ Y @ X )
=> ( ( inf_in3450601097109690352c_fm_i @ X @ Y )
= Y ) ) ).
% inf_absorb2
thf(fact_558_inf_OboundedE,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i,C2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A2 @ ( inf_in161960956874937808c_fm_i @ B3 @ C2 ) )
=> ~ ( ( ord_le5389487502678872194c_fm_i @ A2 @ B3 )
=> ~ ( ord_le5389487502678872194c_fm_i @ A2 @ C2 ) ) ) ).
% inf.boundedE
thf(fact_559_inf_OboundedE,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,C2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ ( inf_in3450601097109690352c_fm_i @ B3 @ C2 ) )
=> ~ ( ( ord_le3843937902494030498c_fm_i @ A2 @ B3 )
=> ~ ( ord_le3843937902494030498c_fm_i @ A2 @ C2 ) ) ) ).
% inf.boundedE
thf(fact_560_inf_OboundedI,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i,C2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A2 @ B3 )
=> ( ( ord_le5389487502678872194c_fm_i @ A2 @ C2 )
=> ( ord_le5389487502678872194c_fm_i @ A2 @ ( inf_in161960956874937808c_fm_i @ B3 @ C2 ) ) ) ) ).
% inf.boundedI
thf(fact_561_inf_OboundedI,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,C2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ B3 )
=> ( ( ord_le3843937902494030498c_fm_i @ A2 @ C2 )
=> ( ord_le3843937902494030498c_fm_i @ A2 @ ( inf_in3450601097109690352c_fm_i @ B3 @ C2 ) ) ) ) ).
% inf.boundedI
thf(fact_562_inf__greatest,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ X @ Y )
=> ( ( ord_le5389487502678872194c_fm_i @ X @ Z )
=> ( ord_le5389487502678872194c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ Y @ Z ) ) ) ) ).
% inf_greatest
thf(fact_563_inf__greatest,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X @ Y )
=> ( ( ord_le3843937902494030498c_fm_i @ X @ Z )
=> ( ord_le3843937902494030498c_fm_i @ X @ ( inf_in3450601097109690352c_fm_i @ Y @ Z ) ) ) ) ).
% inf_greatest
thf(fact_564_inf_Oorder__iff,axiom,
( ord_le5389487502678872194c_fm_i
= ( ^ [A4: set_se3485332733965609186c_fm_i,B4: set_se3485332733965609186c_fm_i] :
( A4
= ( inf_in161960956874937808c_fm_i @ A4 @ B4 ) ) ) ) ).
% inf.order_iff
thf(fact_565_inf_Oorder__iff,axiom,
( ord_le3843937902494030498c_fm_i
= ( ^ [A4: set_Epistemic_fm_i,B4: set_Epistemic_fm_i] :
( A4
= ( inf_in3450601097109690352c_fm_i @ A4 @ B4 ) ) ) ) ).
% inf.order_iff
thf(fact_566_inf_Ocobounded1,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) @ A2 ) ).
% inf.cobounded1
thf(fact_567_inf_Ocobounded1,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A2 @ B3 ) @ A2 ) ).
% inf.cobounded1
thf(fact_568_inf_Ocobounded2,axiom,
! [A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) @ B3 ) ).
% inf.cobounded2
thf(fact_569_inf_Ocobounded2,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A2 @ B3 ) @ B3 ) ).
% inf.cobounded2
thf(fact_570_inf_Oabsorb__iff1,axiom,
( ord_le5389487502678872194c_fm_i
= ( ^ [A4: set_se3485332733965609186c_fm_i,B4: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ A4 @ B4 )
= A4 ) ) ) ).
% inf.absorb_iff1
thf(fact_571_inf_Oabsorb__iff1,axiom,
( ord_le3843937902494030498c_fm_i
= ( ^ [A4: set_Epistemic_fm_i,B4: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ A4 @ B4 )
= A4 ) ) ) ).
% inf.absorb_iff1
thf(fact_572_inf_Oabsorb__iff2,axiom,
( ord_le5389487502678872194c_fm_i
= ( ^ [B4: set_se3485332733965609186c_fm_i,A4: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ A4 @ B4 )
= B4 ) ) ) ).
% inf.absorb_iff2
thf(fact_573_inf_Oabsorb__iff2,axiom,
( ord_le3843937902494030498c_fm_i
= ( ^ [B4: set_Epistemic_fm_i,A4: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ A4 @ B4 )
= B4 ) ) ) ).
% inf.absorb_iff2
thf(fact_574_inf_OcoboundedI1,axiom,
! [A2: set_se3485332733965609186c_fm_i,C2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A2 @ C2 )
=> ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) @ C2 ) ) ).
% inf.coboundedI1
thf(fact_575_inf_OcoboundedI1,axiom,
! [A2: set_Epistemic_fm_i,C2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ C2 )
=> ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A2 @ B3 ) @ C2 ) ) ).
% inf.coboundedI1
thf(fact_576_inf_OcoboundedI2,axiom,
! [B3: set_se3485332733965609186c_fm_i,C2: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ B3 @ C2 )
=> ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) @ C2 ) ) ).
% inf.coboundedI2
thf(fact_577_inf_OcoboundedI2,axiom,
! [B3: set_Epistemic_fm_i,C2: set_Epistemic_fm_i,A2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B3 @ C2 )
=> ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A2 @ B3 ) @ C2 ) ) ).
% inf.coboundedI2
thf(fact_578_exactly__one__in__maximal,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,P4: epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ V )
=> ( ( member6642669606046002379c_fm_i @ P4 @ V )
= ( ~ ( member6642669606046002379c_fm_i @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) @ V ) ) ) ) ) ).
% exactly_one_in_maximal
thf(fact_579_distrib__imp1,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ! [X3: set_se3485332733965609186c_fm_i,Y4: set_se3485332733965609186c_fm_i,Z3: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ X3 @ ( sup_su2582925890723967158c_fm_i @ Y4 @ Z3 ) )
= ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ X3 @ Y4 ) @ ( inf_in161960956874937808c_fm_i @ X3 @ Z3 ) ) )
=> ( ( sup_su2582925890723967158c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ Y @ Z ) )
= ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ X @ Y ) @ ( sup_su2582925890723967158c_fm_i @ X @ Z ) ) ) ) ).
% distrib_imp1
thf(fact_580_distrib__imp1,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i,Z3: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ X3 @ ( sup_su1936195050962291414c_fm_i @ Y4 @ Z3 ) )
= ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ X3 @ Y4 ) @ ( inf_in3450601097109690352c_fm_i @ X3 @ Z3 ) ) )
=> ( ( sup_su1936195050962291414c_fm_i @ X @ ( inf_in3450601097109690352c_fm_i @ Y @ Z ) )
= ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ X @ Y ) @ ( sup_su1936195050962291414c_fm_i @ X @ Z ) ) ) ) ).
% distrib_imp1
thf(fact_581_distrib__imp2,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ! [X3: set_se3485332733965609186c_fm_i,Y4: set_se3485332733965609186c_fm_i,Z3: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ X3 @ ( inf_in161960956874937808c_fm_i @ Y4 @ Z3 ) )
= ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ X3 @ Y4 ) @ ( sup_su2582925890723967158c_fm_i @ X3 @ Z3 ) ) )
=> ( ( inf_in161960956874937808c_fm_i @ X @ ( sup_su2582925890723967158c_fm_i @ Y @ Z ) )
= ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ X @ Y ) @ ( inf_in161960956874937808c_fm_i @ X @ Z ) ) ) ) ).
% distrib_imp2
thf(fact_582_distrib__imp2,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i,Z3: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ X3 @ ( inf_in3450601097109690352c_fm_i @ Y4 @ Z3 ) )
= ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ X3 @ Y4 ) @ ( sup_su1936195050962291414c_fm_i @ X3 @ Z3 ) ) )
=> ( ( inf_in3450601097109690352c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ Y @ Z ) )
= ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ X @ Y ) @ ( inf_in3450601097109690352c_fm_i @ X @ Z ) ) ) ) ).
% distrib_imp2
thf(fact_583_inf__sup__distrib1,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ X @ ( sup_su2582925890723967158c_fm_i @ Y @ Z ) )
= ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ X @ Y ) @ ( inf_in161960956874937808c_fm_i @ X @ Z ) ) ) ).
% inf_sup_distrib1
thf(fact_584_inf__sup__distrib1,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ Y @ Z ) )
= ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ X @ Y ) @ ( inf_in3450601097109690352c_fm_i @ X @ Z ) ) ) ).
% inf_sup_distrib1
thf(fact_585_inf__sup__distrib2,axiom,
! [Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i,X: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ Y @ Z ) @ X )
= ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ Y @ X ) @ ( inf_in161960956874937808c_fm_i @ Z @ X ) ) ) ).
% inf_sup_distrib2
thf(fact_586_inf__sup__distrib2,axiom,
! [Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i,X: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ Y @ Z ) @ X )
= ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ Y @ X ) @ ( inf_in3450601097109690352c_fm_i @ Z @ X ) ) ) ).
% inf_sup_distrib2
thf(fact_587_sup__inf__distrib1,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ Y @ Z ) )
= ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ X @ Y ) @ ( sup_su2582925890723967158c_fm_i @ X @ Z ) ) ) ).
% sup_inf_distrib1
thf(fact_588_sup__inf__distrib1,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ X @ ( inf_in3450601097109690352c_fm_i @ Y @ Z ) )
= ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ X @ Y ) @ ( sup_su1936195050962291414c_fm_i @ X @ Z ) ) ) ).
% sup_inf_distrib1
thf(fact_589_sup__inf__distrib2,axiom,
! [Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i,X: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ Y @ Z ) @ X )
= ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ Y @ X ) @ ( sup_su2582925890723967158c_fm_i @ Z @ X ) ) ) ).
% sup_inf_distrib2
thf(fact_590_sup__inf__distrib2,axiom,
! [Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i,X: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ Y @ Z ) @ X )
= ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ Y @ X ) @ ( sup_su1936195050962291414c_fm_i @ Z @ X ) ) ) ).
% sup_inf_distrib2
thf(fact_591_Int__mono,axiom,
! [A: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,D2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A @ C )
=> ( ( ord_le5389487502678872194c_fm_i @ B2 @ D2 )
=> ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) @ ( inf_in161960956874937808c_fm_i @ C @ D2 ) ) ) ) ).
% Int_mono
thf(fact_592_Int__mono,axiom,
! [A: set_Epistemic_fm_i,C: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,D2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ C )
=> ( ( ord_le3843937902494030498c_fm_i @ B2 @ D2 )
=> ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) @ ( inf_in3450601097109690352c_fm_i @ C @ D2 ) ) ) ) ).
% Int_mono
thf(fact_593_Int__lower1,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) @ A ) ).
% Int_lower1
thf(fact_594_Int__lower1,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) @ A ) ).
% Int_lower1
thf(fact_595_Int__lower2,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) @ B2 ) ).
% Int_lower2
thf(fact_596_Int__lower2,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) @ B2 ) ).
% Int_lower2
thf(fact_597_Int__absorb1,axiom,
! [B2: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ B2 @ A )
=> ( ( inf_in161960956874937808c_fm_i @ A @ B2 )
= B2 ) ) ).
% Int_absorb1
thf(fact_598_Int__absorb1,axiom,
! [B2: set_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B2 @ A )
=> ( ( inf_in3450601097109690352c_fm_i @ A @ B2 )
= B2 ) ) ).
% Int_absorb1
thf(fact_599_Int__absorb2,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A @ B2 )
=> ( ( inf_in161960956874937808c_fm_i @ A @ B2 )
= A ) ) ).
% Int_absorb2
thf(fact_600_Int__absorb2,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ( inf_in3450601097109690352c_fm_i @ A @ B2 )
= A ) ) ).
% Int_absorb2
thf(fact_601_Int__greatest,axiom,
! [C: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ C @ A )
=> ( ( ord_le5389487502678872194c_fm_i @ C @ B2 )
=> ( ord_le5389487502678872194c_fm_i @ C @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) ) ) ) ).
% Int_greatest
thf(fact_602_Int__greatest,axiom,
! [C: set_Epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ C @ A )
=> ( ( ord_le3843937902494030498c_fm_i @ C @ B2 )
=> ( ord_le3843937902494030498c_fm_i @ C @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) ) ) ) ).
% Int_greatest
thf(fact_603_Int__Collect__mono,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,P3: set_Epistemic_fm_i > $o,Q2: set_Epistemic_fm_i > $o] :
( ( ord_le5389487502678872194c_fm_i @ A @ B2 )
=> ( ! [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
=> ( ( P3 @ X3 )
=> ( Q2 @ X3 ) ) )
=> ( ord_le5389487502678872194c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ ( collec3087743281813070829c_fm_i @ P3 ) ) @ ( inf_in161960956874937808c_fm_i @ B2 @ ( collec3087743281813070829c_fm_i @ Q2 ) ) ) ) ) ).
% Int_Collect_mono
thf(fact_604_Int__Collect__mono,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,P3: epistemic_fm_i > $o,Q2: epistemic_fm_i > $o] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ! [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ A )
=> ( ( P3 @ X3 )
=> ( Q2 @ X3 ) ) )
=> ( ord_le3843937902494030498c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A @ ( collec4904205187116291597c_fm_i @ P3 ) ) @ ( inf_in3450601097109690352c_fm_i @ B2 @ ( collec4904205187116291597c_fm_i @ Q2 ) ) ) ) ) ).
% Int_Collect_mono
thf(fact_605_fm_Odistinct_I29_J,axiom,
! [X51: epistemic_fm_i,X52: epistemic_fm_i,X61: i,X62: epistemic_fm_i] :
( ( epistemic_Imp_i @ X51 @ X52 )
!= ( epistemic_K_i @ X61 @ X62 ) ) ).
% fm.distinct(29)
thf(fact_606_Un__Int__crazy,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) @ ( inf_in161960956874937808c_fm_i @ B2 @ C ) ) @ ( inf_in161960956874937808c_fm_i @ C @ A ) )
= ( inf_in161960956874937808c_fm_i @ ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ A @ B2 ) @ ( sup_su2582925890723967158c_fm_i @ B2 @ C ) ) @ ( sup_su2582925890723967158c_fm_i @ C @ A ) ) ) ).
% Un_Int_crazy
thf(fact_607_Un__Int__crazy,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) @ ( inf_in3450601097109690352c_fm_i @ B2 @ C ) ) @ ( inf_in3450601097109690352c_fm_i @ C @ A ) )
= ( inf_in3450601097109690352c_fm_i @ ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) @ ( sup_su1936195050962291414c_fm_i @ B2 @ C ) ) @ ( sup_su1936195050962291414c_fm_i @ C @ A ) ) ) ).
% Un_Int_crazy
thf(fact_608_Int__Un__distrib,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ A @ ( sup_su2582925890723967158c_fm_i @ B2 @ C ) )
= ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) @ ( inf_in161960956874937808c_fm_i @ A @ C ) ) ) ).
% Int_Un_distrib
thf(fact_609_Int__Un__distrib,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ A @ ( sup_su1936195050962291414c_fm_i @ B2 @ C ) )
= ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) @ ( inf_in3450601097109690352c_fm_i @ A @ C ) ) ) ).
% Int_Un_distrib
thf(fact_610_Un__Int__distrib,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ A @ ( inf_in161960956874937808c_fm_i @ B2 @ C ) )
= ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ A @ B2 ) @ ( sup_su2582925890723967158c_fm_i @ A @ C ) ) ) ).
% Un_Int_distrib
thf(fact_611_Un__Int__distrib,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ A @ ( inf_in3450601097109690352c_fm_i @ B2 @ C ) )
= ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) @ ( sup_su1936195050962291414c_fm_i @ A @ C ) ) ) ).
% Un_Int_distrib
thf(fact_612_Int__Un__distrib2,axiom,
! [B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ B2 @ C ) @ A )
= ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ B2 @ A ) @ ( inf_in161960956874937808c_fm_i @ C @ A ) ) ) ).
% Int_Un_distrib2
thf(fact_613_Int__Un__distrib2,axiom,
! [B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ B2 @ C ) @ A )
= ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ B2 @ A ) @ ( inf_in3450601097109690352c_fm_i @ C @ A ) ) ) ).
% Int_Un_distrib2
thf(fact_614_Un__Int__distrib2,axiom,
! [B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ B2 @ C ) @ A )
= ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ B2 @ A ) @ ( sup_su2582925890723967158c_fm_i @ C @ A ) ) ) ).
% Un_Int_distrib2
thf(fact_615_Un__Int__distrib2,axiom,
! [B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ B2 @ C ) @ A )
= ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ B2 @ A ) @ ( sup_su1936195050962291414c_fm_i @ C @ A ) ) ) ).
% Un_Int_distrib2
thf(fact_616_fm_Odistinct_I7_J,axiom,
! [X51: epistemic_fm_i,X52: epistemic_fm_i] :
( epistemic_FF_i
!= ( epistemic_Imp_i @ X51 @ X52 ) ) ).
% fm.distinct(7)
thf(fact_617_K__imp__trans,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,Q: epistemic_fm_i,R2: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ P4 @ Q ) )
=> ( ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ Q @ R2 ) )
=> ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ P4 @ R2 ) ) ) ) ).
% K_imp_trans
thf(fact_618_K__imp__trans_H,axiom,
! [A: epistemic_fm_i > $o,Q: epistemic_fm_i,R2: epistemic_fm_i,P4: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ Q @ R2 ) )
=> ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ P4 @ Q ) @ ( epistemic_Imp_i @ P4 @ R2 ) ) ) ) ).
% K_imp_trans'
thf(fact_619_R1,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,Q: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ P4 )
=> ( ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ P4 @ Q ) )
=> ( epistemic_AK_i @ A @ Q ) ) ) ).
% R1
thf(fact_620_K__trans,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,Q: epistemic_fm_i,R2: epistemic_fm_i] : ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ P4 @ Q ) @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ Q @ R2 ) @ ( epistemic_Imp_i @ P4 @ R2 ) ) ) ) ).
% K_trans
thf(fact_621_ax__in__maximal,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,P4: epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ V )
=> ( ( A @ P4 )
=> ( member6642669606046002379c_fm_i @ P4 @ V ) ) ) ) ).
% ax_in_maximal
thf(fact_622_distrib__inf__le,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ X @ Y ) @ ( inf_in161960956874937808c_fm_i @ X @ Z ) ) @ ( inf_in161960956874937808c_fm_i @ X @ ( sup_su2582925890723967158c_fm_i @ Y @ Z ) ) ) ).
% distrib_inf_le
thf(fact_623_distrib__inf__le,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ X @ Y ) @ ( inf_in3450601097109690352c_fm_i @ X @ Z ) ) @ ( inf_in3450601097109690352c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ Y @ Z ) ) ) ).
% distrib_inf_le
thf(fact_624_distrib__sup__le,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ ( sup_su2582925890723967158c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ Y @ Z ) ) @ ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ X @ Y ) @ ( sup_su2582925890723967158c_fm_i @ X @ Z ) ) ) ).
% distrib_sup_le
thf(fact_625_distrib__sup__le,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ X @ ( inf_in3450601097109690352c_fm_i @ Y @ Z ) ) @ ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ X @ Y ) @ ( sup_su1936195050962291414c_fm_i @ X @ Z ) ) ) ).
% distrib_sup_le
thf(fact_626_Un__Int__assoc__eq,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) @ C )
= ( inf_in161960956874937808c_fm_i @ A @ ( sup_su2582925890723967158c_fm_i @ B2 @ C ) ) )
= ( ord_le5389487502678872194c_fm_i @ C @ A ) ) ).
% Un_Int_assoc_eq
thf(fact_627_Un__Int__assoc__eq,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) @ C )
= ( inf_in3450601097109690352c_fm_i @ A @ ( sup_su1936195050962291414c_fm_i @ B2 @ C ) ) )
= ( ord_le3843937902494030498c_fm_i @ C @ A ) ) ).
% Un_Int_assoc_eq
thf(fact_628_K__A2_H,axiom,
! [A: epistemic_fm_i > $o,I: i,P4: epistemic_fm_i,Q: epistemic_fm_i] : ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ P4 @ Q ) ) @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ P4 ) @ ( epistemic_K_i @ I @ Q ) ) ) ) ).
% K_A2'
thf(fact_629_K__map,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,Q: epistemic_fm_i,I: i] :
( ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ P4 @ Q ) )
=> ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ P4 ) @ ( epistemic_K_i @ I @ Q ) ) ) ) ).
% K_map
thf(fact_630_K__right__mp,axiom,
! [A: epistemic_fm_i > $o,Ps: list_Epistemic_fm_i,P4: epistemic_fm_i,Q: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_imply_i @ Ps @ P4 ) )
=> ( ( epistemic_AK_i @ A @ ( epistemic_imply_i @ Ps @ ( epistemic_Imp_i @ P4 @ Q ) ) )
=> ( epistemic_AK_i @ A @ ( epistemic_imply_i @ Ps @ Q ) ) ) ) ).
% K_right_mp
thf(fact_631_dual__reach,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,I: i,P4: epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ V )
=> ( ( member6642669606046002379c_fm_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ V )
=> ? [W: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ W
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ I @ P2 ) @ V ) ) ) ) )
& ( member6642669606046002379c_fm_i @ P4 @ W ) ) ) ) ) ).
% dual_reach
thf(fact_632_reach__dualK,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,W2: set_Epistemic_fm_i,I: i] :
( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ V )
=> ( ( episte2285483198712856234tent_i @ A @ W2 )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ W2 )
=> ( ( member1104366573291651755c_fm_i @ W2
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ I @ P2 ) @ V ) ) ) ) )
=> ! [P: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ P @ W2 )
=> ( member6642669606046002379c_fm_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ P @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ V ) ) ) ) ) ) ) ).
% reach_dualK
thf(fact_633_deriv__in__maximal,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,P4: epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ V )
=> ( ( epistemic_AK_i @ A @ P4 )
=> ( member6642669606046002379c_fm_i @ P4 @ V ) ) ) ) ).
% deriv_in_maximal
thf(fact_634_maximal__extension,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ A @ V )
=> ~ ! [W: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ V @ W )
=> ( ( episte2285483198712856234tent_i @ A @ W )
=> ~ ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ W ) ) ) ) ).
% maximal_extension
thf(fact_635_K__LK,axiom,
! [A: epistemic_fm_i > $o,I: i,P4: epistemic_fm_i] : ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ P4 ) @ epistemic_FF_i ) ) ) ).
% K_LK
thf(fact_636_K__L__dual,axiom,
! [A: epistemic_fm_i > $o,I: i,P4: epistemic_fm_i] : ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ epistemic_FF_i ) @ ( epistemic_K_i @ I @ P4 ) ) ) ).
% K_L_dual
thf(fact_637_order__class_Oorder__eq__iff,axiom,
( ( ^ [Y2: set_Epistemic_fm_i,Z2: set_Epistemic_fm_i] : ( Y2 = Z2 ) )
= ( ^ [X2: set_Epistemic_fm_i,Y3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X2 @ Y3 )
& ( ord_le3843937902494030498c_fm_i @ Y3 @ X2 ) ) ) ) ).
% order_class.order_eq_iff
thf(fact_638_ord__eq__le__trans,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,C2: set_Epistemic_fm_i] :
( ( A2 = B3 )
=> ( ( ord_le3843937902494030498c_fm_i @ B3 @ C2 )
=> ( ord_le3843937902494030498c_fm_i @ A2 @ C2 ) ) ) ).
% ord_eq_le_trans
thf(fact_639_ord__le__eq__trans,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,C2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ B3 )
=> ( ( B3 = C2 )
=> ( ord_le3843937902494030498c_fm_i @ A2 @ C2 ) ) ) ).
% ord_le_eq_trans
thf(fact_640_order__antisym,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X @ Y )
=> ( ( ord_le3843937902494030498c_fm_i @ Y @ X )
=> ( X = Y ) ) ) ).
% order_antisym
thf(fact_641_order_Otrans,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,C2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ B3 )
=> ( ( ord_le3843937902494030498c_fm_i @ B3 @ C2 )
=> ( ord_le3843937902494030498c_fm_i @ A2 @ C2 ) ) ) ).
% order.trans
thf(fact_642_order__trans,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X @ Y )
=> ( ( ord_le3843937902494030498c_fm_i @ Y @ Z )
=> ( ord_le3843937902494030498c_fm_i @ X @ Z ) ) ) ).
% order_trans
thf(fact_643_dual__order_Oeq__iff,axiom,
( ( ^ [Y2: set_Epistemic_fm_i,Z2: set_Epistemic_fm_i] : ( Y2 = Z2 ) )
= ( ^ [A4: set_Epistemic_fm_i,B4: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B4 @ A4 )
& ( ord_le3843937902494030498c_fm_i @ A4 @ B4 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_644_dual__order_Oantisym,axiom,
! [B3: set_Epistemic_fm_i,A2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B3 @ A2 )
=> ( ( ord_le3843937902494030498c_fm_i @ A2 @ B3 )
=> ( A2 = B3 ) ) ) ).
% dual_order.antisym
thf(fact_645_dual__order_Otrans,axiom,
! [B3: set_Epistemic_fm_i,A2: set_Epistemic_fm_i,C2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B3 @ A2 )
=> ( ( ord_le3843937902494030498c_fm_i @ C2 @ B3 )
=> ( ord_le3843937902494030498c_fm_i @ C2 @ A2 ) ) ) ).
% dual_order.trans
thf(fact_646_antisym,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ B3 )
=> ( ( ord_le3843937902494030498c_fm_i @ B3 @ A2 )
=> ( A2 = B3 ) ) ) ).
% antisym
thf(fact_647_Orderings_Oorder__eq__iff,axiom,
( ( ^ [Y2: set_Epistemic_fm_i,Z2: set_Epistemic_fm_i] : ( Y2 = Z2 ) )
= ( ^ [A4: set_Epistemic_fm_i,B4: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A4 @ B4 )
& ( ord_le3843937902494030498c_fm_i @ B4 @ A4 ) ) ) ) ).
% Orderings.order_eq_iff
thf(fact_648_order__subst1,axiom,
! [A2: set_Epistemic_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i,B3: set_Epistemic_fm_i,C2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ ( F3 @ B3 ) )
=> ( ( ord_le3843937902494030498c_fm_i @ B3 @ C2 )
=> ( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X3 @ Y4 )
=> ( ord_le3843937902494030498c_fm_i @ ( F3 @ X3 ) @ ( F3 @ Y4 ) ) )
=> ( ord_le3843937902494030498c_fm_i @ A2 @ ( F3 @ C2 ) ) ) ) ) ).
% order_subst1
thf(fact_649_order__subst2,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i,C2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ B3 )
=> ( ( ord_le3843937902494030498c_fm_i @ ( F3 @ B3 ) @ C2 )
=> ( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X3 @ Y4 )
=> ( ord_le3843937902494030498c_fm_i @ ( F3 @ X3 ) @ ( F3 @ Y4 ) ) )
=> ( ord_le3843937902494030498c_fm_i @ ( F3 @ A2 ) @ C2 ) ) ) ) ).
% order_subst2
thf(fact_650_order__eq__refl,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ( X = Y )
=> ( ord_le3843937902494030498c_fm_i @ X @ Y ) ) ).
% order_eq_refl
thf(fact_651_ord__eq__le__subst,axiom,
! [A2: set_Epistemic_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i,B3: set_Epistemic_fm_i,C2: set_Epistemic_fm_i] :
( ( A2
= ( F3 @ B3 ) )
=> ( ( ord_le3843937902494030498c_fm_i @ B3 @ C2 )
=> ( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X3 @ Y4 )
=> ( ord_le3843937902494030498c_fm_i @ ( F3 @ X3 ) @ ( F3 @ Y4 ) ) )
=> ( ord_le3843937902494030498c_fm_i @ A2 @ ( F3 @ C2 ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_652_ord__le__eq__subst,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i,C2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ B3 )
=> ( ( ( F3 @ B3 )
= C2 )
=> ( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X3 @ Y4 )
=> ( ord_le3843937902494030498c_fm_i @ ( F3 @ X3 ) @ ( F3 @ Y4 ) ) )
=> ( ord_le3843937902494030498c_fm_i @ ( F3 @ A2 ) @ C2 ) ) ) ) ).
% ord_le_eq_subst
thf(fact_653_order__antisym__conv,axiom,
! [Y: set_Epistemic_fm_i,X: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ Y @ X )
=> ( ( ord_le3843937902494030498c_fm_i @ X @ Y )
= ( X = Y ) ) ) ).
% order_antisym_conv
thf(fact_654_Ax__2_Ocases,axiom,
! [A2: epistemic_fm_i] :
( ( stalnaker_Ax_2_i @ A2 )
=> ~ ! [I2: i,P5: epistemic_fm_i] :
( A2
!= ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I2 @ ( epistemic_Imp_i @ ( epistemic_K_i @ I2 @ P5 ) @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ ( epistemic_K_i @ I2 @ ( epistemic_Imp_i @ ( epistemic_K_i @ I2 @ ( epistemic_Imp_i @ P5 @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) ) ) ) ).
% Ax_2.cases
thf(fact_655_Ax__2_Osimps,axiom,
( stalnaker_Ax_2_i
= ( ^ [A4: epistemic_fm_i] :
? [I3: i,P2: epistemic_fm_i] :
( A4
= ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I3 @ ( epistemic_Imp_i @ ( epistemic_K_i @ I3 @ P2 ) @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ ( epistemic_K_i @ I3 @ ( epistemic_Imp_i @ ( epistemic_K_i @ I3 @ ( epistemic_Imp_i @ P2 @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) ) ) ) ) ).
% Ax_2.simps
thf(fact_656_Ax__2_Ointros,axiom,
! [I: i,P4: epistemic_fm_i] : ( stalnaker_Ax_2_i @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ P4 ) @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) ) ) ).
% Ax_2.intros
thf(fact_657_mcs__conjunction__mult,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,S: list_Epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ V )
=> ( ( ( ord_le3843937902494030498c_fm_i @ ( set_Epistemic_fm_i2 @ S ) @ V )
& ( finite3304564979551393739c_fm_i @ ( set_Epistemic_fm_i2 @ S ) ) )
=> ( member6642669606046002379c_fm_i @ ( stalnaker_conjunct_i @ S ) @ V ) ) ) ) ).
% mcs_conjunction_mult
thf(fact_658_AxB__symmetric_H,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,W2: set_Epistemic_fm_i,I: i] :
( ( ord_le190830114487426235fm_i_o @ epistemic_AxB_i @ A )
=> ( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ V )
=> ( ( episte2285483198712856234tent_i @ A @ W2 )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ W2 )
=> ( ( member1104366573291651755c_fm_i @ W2
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ I @ P2 ) @ V ) ) ) ) )
=> ( member1104366573291651755c_fm_i @ V
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ I @ P2 ) @ W2 ) ) ) ) ) ) ) ) ) ) ) ).
% AxB_symmetric'
thf(fact_659_boolean__algebra_Oconj__disj__distrib,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ X @ ( sup_su2582925890723967158c_fm_i @ Y @ Z ) )
= ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ X @ Y ) @ ( inf_in161960956874937808c_fm_i @ X @ Z ) ) ) ).
% boolean_algebra.conj_disj_distrib
thf(fact_660_boolean__algebra_Oconj__disj__distrib,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ X @ ( sup_su1936195050962291414c_fm_i @ Y @ Z ) )
= ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ X @ Y ) @ ( inf_in3450601097109690352c_fm_i @ X @ Z ) ) ) ).
% boolean_algebra.conj_disj_distrib
thf(fact_661_boolean__algebra_Odisj__conj__distrib,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ X @ ( inf_in161960956874937808c_fm_i @ Y @ Z ) )
= ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ X @ Y ) @ ( sup_su2582925890723967158c_fm_i @ X @ Z ) ) ) ).
% boolean_algebra.disj_conj_distrib
thf(fact_662_boolean__algebra_Odisj__conj__distrib,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ X @ ( inf_in3450601097109690352c_fm_i @ Y @ Z ) )
= ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ X @ Y ) @ ( sup_su1936195050962291414c_fm_i @ X @ Z ) ) ) ).
% boolean_algebra.disj_conj_distrib
thf(fact_663_boolean__algebra_Oconj__disj__distrib2,axiom,
! [Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i,X: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ Y @ Z ) @ X )
= ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ Y @ X ) @ ( inf_in161960956874937808c_fm_i @ Z @ X ) ) ) ).
% boolean_algebra.conj_disj_distrib2
thf(fact_664_boolean__algebra_Oconj__disj__distrib2,axiom,
! [Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i,X: set_Epistemic_fm_i] :
( ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ Y @ Z ) @ X )
= ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ Y @ X ) @ ( inf_in3450601097109690352c_fm_i @ Z @ X ) ) ) ).
% boolean_algebra.conj_disj_distrib2
thf(fact_665_boolean__algebra_Odisj__conj__distrib2,axiom,
! [Y: set_se3485332733965609186c_fm_i,Z: set_se3485332733965609186c_fm_i,X: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ Y @ Z ) @ X )
= ( inf_in161960956874937808c_fm_i @ ( sup_su2582925890723967158c_fm_i @ Y @ X ) @ ( sup_su2582925890723967158c_fm_i @ Z @ X ) ) ) ).
% boolean_algebra.disj_conj_distrib2
thf(fact_666_boolean__algebra_Odisj__conj__distrib2,axiom,
! [Y: set_Epistemic_fm_i,Z: set_Epistemic_fm_i,X: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ Y @ Z ) @ X )
= ( inf_in3450601097109690352c_fm_i @ ( sup_su1936195050962291414c_fm_i @ Y @ X ) @ ( sup_su1936195050962291414c_fm_i @ Z @ X ) ) ) ).
% boolean_algebra.disj_conj_distrib2
thf(fact_667_Ax5__Euclidean,axiom,
! [A: epistemic_fm_i > $o,U: set_Epistemic_fm_i,V: set_Epistemic_fm_i,W2: set_Epistemic_fm_i,I: i] :
( ( ord_le190830114487426235fm_i_o @ epistemic_Ax5_i @ A )
=> ( ( episte2285483198712856234tent_i @ A @ U )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ U )
=> ( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ V )
=> ( ( episte2285483198712856234tent_i @ A @ W2 )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ W2 )
=> ( ( member1104366573291651755c_fm_i @ V
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ I @ P2 ) @ U ) ) ) ) )
=> ( ( member1104366573291651755c_fm_i @ W2
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ I @ P2 ) @ U ) ) ) ) )
=> ( member1104366573291651755c_fm_i @ W2
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ I @ P2 ) @ V ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% Ax5_Euclidean
thf(fact_668_Ax4__transitive,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,W2: set_Epistemic_fm_i,I: i,U: set_Epistemic_fm_i] :
( ( ord_le190830114487426235fm_i_o @ epistemic_Ax4_i @ A )
=> ( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ V )
=> ( ( member1104366573291651755c_fm_i @ W2
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ I @ P2 ) @ V ) ) ) ) )
=> ( ( member1104366573291651755c_fm_i @ U
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ I @ P2 ) @ W2 ) ) ) ) )
=> ( member1104366573291651755c_fm_i @ U
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ I @ P2 ) @ V ) ) ) ) ) ) ) ) ) ) ).
% Ax4_transitive
thf(fact_669_inf__Int__eq,axiom,
! [R: set_Epistemic_fm_i,S: set_Epistemic_fm_i] :
( ( inf_in8976956063904982253fm_i_o
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ R )
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ S ) )
= ( ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ ( inf_in3450601097109690352c_fm_i @ R @ S ) ) ) ) ).
% inf_Int_eq
thf(fact_670_inf__Int__eq,axiom,
! [R: set_se3485332733965609186c_fm_i,S: set_se3485332733965609186c_fm_i] :
( ( inf_in853329969422372621fm_i_o
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ R )
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ S ) )
= ( ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ ( inf_in161960956874937808c_fm_i @ R @ S ) ) ) ) ).
% inf_Int_eq
thf(fact_671_inf__set__def,axiom,
( inf_in3450601097109690352c_fm_i
= ( ^ [A3: set_Epistemic_fm_i,B: set_Epistemic_fm_i] :
( collec4904205187116291597c_fm_i
@ ( inf_in8976956063904982253fm_i_o
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ A3 )
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ B ) ) ) ) ) ).
% inf_set_def
thf(fact_672_inf__set__def,axiom,
( inf_in161960956874937808c_fm_i
= ( ^ [A3: set_se3485332733965609186c_fm_i,B: set_se3485332733965609186c_fm_i] :
( collec3087743281813070829c_fm_i
@ ( inf_in853329969422372621fm_i_o
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ A3 )
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ B ) ) ) ) ) ).
% inf_set_def
thf(fact_673_KB4__5,axiom,
! [A: epistemic_fm_i > $o,I: i,P4: epistemic_fm_i] :
( ( ord_le190830114487426235fm_i_o @ epistemic_AxB_i @ A )
=> ( ( ord_le190830114487426235fm_i_o @ epistemic_Ax4_i @ A )
=> ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) ) ) ) ) ).
% KB4_5
thf(fact_674_Ax4_Ocases,axiom,
! [A2: epistemic_fm_i] :
( ( epistemic_Ax4_i @ A2 )
=> ~ ! [I2: i,P5: epistemic_fm_i] :
( A2
!= ( epistemic_Imp_i @ ( epistemic_K_i @ I2 @ P5 ) @ ( epistemic_K_i @ I2 @ ( epistemic_K_i @ I2 @ P5 ) ) ) ) ) ).
% Ax4.cases
thf(fact_675_Ax4_Osimps,axiom,
( epistemic_Ax4_i
= ( ^ [A4: epistemic_fm_i] :
? [I3: i,P2: epistemic_fm_i] :
( A4
= ( epistemic_Imp_i @ ( epistemic_K_i @ I3 @ P2 ) @ ( epistemic_K_i @ I3 @ ( epistemic_K_i @ I3 @ P2 ) ) ) ) ) ) ).
% Ax4.simps
thf(fact_676_Ax4_Ointros,axiom,
! [I: i,P4: epistemic_fm_i] : ( epistemic_Ax4_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ P4 ) @ ( epistemic_K_i @ I @ ( epistemic_K_i @ I @ P4 ) ) ) ) ).
% Ax4.intros
thf(fact_677_boolean__algebra__cancel_Oinf1,axiom,
! [A: set_se3485332733965609186c_fm_i,K: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i] :
( ( A
= ( inf_in161960956874937808c_fm_i @ K @ A2 ) )
=> ( ( inf_in161960956874937808c_fm_i @ A @ B3 )
= ( inf_in161960956874937808c_fm_i @ K @ ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) ) ) ) ).
% boolean_algebra_cancel.inf1
thf(fact_678_boolean__algebra__cancel_Oinf2,axiom,
! [B2: set_se3485332733965609186c_fm_i,K: set_se3485332733965609186c_fm_i,B3: set_se3485332733965609186c_fm_i,A2: set_se3485332733965609186c_fm_i] :
( ( B2
= ( inf_in161960956874937808c_fm_i @ K @ B3 ) )
=> ( ( inf_in161960956874937808c_fm_i @ A2 @ B2 )
= ( inf_in161960956874937808c_fm_i @ K @ ( inf_in161960956874937808c_fm_i @ A2 @ B3 ) ) ) ) ).
% boolean_algebra_cancel.inf2
thf(fact_679_boolean__algebra__cancel_Osup2,axiom,
! [B2: set_Epistemic_fm_i,K: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,A2: set_Epistemic_fm_i] :
( ( B2
= ( sup_su1936195050962291414c_fm_i @ K @ B3 ) )
=> ( ( sup_su1936195050962291414c_fm_i @ A2 @ B2 )
= ( sup_su1936195050962291414c_fm_i @ K @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) ) ) ) ).
% boolean_algebra_cancel.sup2
thf(fact_680_boolean__algebra__cancel_Osup1,axiom,
! [A: set_Epistemic_fm_i,K: set_Epistemic_fm_i,A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( A
= ( sup_su1936195050962291414c_fm_i @ K @ A2 ) )
=> ( ( sup_su1936195050962291414c_fm_i @ A @ B3 )
= ( sup_su1936195050962291414c_fm_i @ K @ ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) ) ) ) ).
% boolean_algebra_cancel.sup1
thf(fact_681_Ax5_Ointros,axiom,
! [I: i,P4: epistemic_fm_i] : ( epistemic_Ax5_i @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) ) ) ).
% Ax5.intros
thf(fact_682_Ax5_Osimps,axiom,
( epistemic_Ax5_i
= ( ^ [A4: epistemic_fm_i] :
? [I3: i,P2: epistemic_fm_i] :
( A4
= ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I3 @ ( epistemic_Imp_i @ P2 @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ ( epistemic_K_i @ I3 @ ( epistemic_Imp_i @ ( epistemic_K_i @ I3 @ ( epistemic_Imp_i @ P2 @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) ) ) ) ) ).
% Ax5.simps
thf(fact_683_Ax5_Ocases,axiom,
! [A2: epistemic_fm_i] :
( ( epistemic_Ax5_i @ A2 )
=> ~ ! [I2: i,P5: epistemic_fm_i] :
( A2
!= ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I2 @ ( epistemic_Imp_i @ P5 @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ ( epistemic_K_i @ I2 @ ( epistemic_Imp_i @ ( epistemic_K_i @ I2 @ ( epistemic_Imp_i @ P5 @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) ) ) ) ).
% Ax5.cases
thf(fact_684_AxB_Ointros,axiom,
! [P4: epistemic_fm_i,I: i] : ( epistemic_AxB_i @ ( epistemic_Imp_i @ P4 @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) ) ) ).
% AxB.intros
thf(fact_685_AxB_Osimps,axiom,
( epistemic_AxB_i
= ( ^ [A4: epistemic_fm_i] :
? [P2: epistemic_fm_i,I3: i] :
( A4
= ( epistemic_Imp_i @ P2 @ ( epistemic_K_i @ I3 @ ( epistemic_Imp_i @ ( epistemic_K_i @ I3 @ ( epistemic_Imp_i @ P2 @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) ) ) ) ) ).
% AxB.simps
thf(fact_686_AxB_Ocases,axiom,
! [A2: epistemic_fm_i] :
( ( epistemic_AxB_i @ A2 )
=> ~ ! [P5: epistemic_fm_i,I2: i] :
( A2
!= ( epistemic_Imp_i @ P5 @ ( epistemic_K_i @ I2 @ ( epistemic_Imp_i @ ( epistemic_K_i @ I2 @ ( epistemic_Imp_i @ P5 @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) ) ) ) ).
% AxB.cases
thf(fact_687_K__imply__conjunct,axiom,
! [A: epistemic_fm_i > $o,G: list_Epistemic_fm_i,P4: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_imply_i @ G @ P4 ) )
=> ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( stalnaker_conjunct_i @ G ) @ P4 ) ) ) ).
% K_imply_conjunct
thf(fact_688_K__conjunct__imply,axiom,
! [A: epistemic_fm_i > $o,G: list_Epistemic_fm_i,P4: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( stalnaker_conjunct_i @ G ) @ P4 ) )
=> ( epistemic_AK_i @ A @ ( epistemic_imply_i @ G @ P4 ) ) ) ).
% K_conjunct_imply
thf(fact_689_K4__L,axiom,
! [A: epistemic_fm_i > $o,I: i,P4: epistemic_fm_i] :
( ( ord_le190830114487426235fm_i_o @ epistemic_Ax4_i @ A )
=> ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) ) ) ).
% K4_L
thf(fact_690_K5__L,axiom,
! [A: epistemic_fm_i > $o,I: i,P4: epistemic_fm_i] :
( ( ord_le190830114487426235fm_i_o @ epistemic_Ax5_i @ A )
=> ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ P4 ) @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ ( epistemic_K_i @ I @ P4 ) ) ) ) ).
% K5_L
thf(fact_691_S5__S5_H__assms,axiom,
! [G: set_Epistemic_fm_i,P4: epistemic_fm_i] :
( ( ? [Qs: list_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( set_Epistemic_fm_i2 @ Qs ) @ G )
& ( epistemic_AK_i
@ ^ [P2: epistemic_fm_i] :
( ( epistemic_AxT_i @ P2 )
| ( epistemic_AxB_i @ P2 )
| ( epistemic_Ax4_i @ P2 ) )
@ ( epistemic_imply_i @ Qs @ P4 ) ) ) )
= ( ? [Qs: list_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( set_Epistemic_fm_i2 @ Qs ) @ G )
& ( epistemic_AK_i
@ ^ [P2: epistemic_fm_i] :
( ( epistemic_AxT_i @ P2 )
| ( epistemic_Ax5_i @ P2 ) )
@ ( epistemic_imply_i @ Qs @ P4 ) ) ) ) ) ).
% S5_S5'_assms
thf(fact_692_S5_H__B,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,I: i] :
( ( ord_le190830114487426235fm_i_o @ epistemic_AxT_i @ A )
=> ( ( ord_le190830114487426235fm_i_o @ epistemic_Ax5_i @ A )
=> ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ P4 @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) ) ) ) ) ).
% S5'_B
thf(fact_693_AxT__reflexive,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,I: i] :
( ( ord_le190830114487426235fm_i_o @ epistemic_AxT_i @ A )
=> ( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ V )
=> ( member1104366573291651755c_fm_i @ V
@ ( collec3087743281813070829c_fm_i
@ ( ord_le3843937902494030498c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ I @ P2 ) @ V ) ) ) ) ) ) ) ) ).
% AxT_reflexive
thf(fact_694_S5_H__4,axiom,
! [A: epistemic_fm_i > $o,I: i,P4: epistemic_fm_i] :
( ( ord_le190830114487426235fm_i_o @ epistemic_AxT_i @ A )
=> ( ( ord_le190830114487426235fm_i_o @ epistemic_Ax5_i @ A )
=> ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ P4 ) @ ( epistemic_K_i @ I @ ( epistemic_K_i @ I @ P4 ) ) ) ) ) ) ).
% S5'_4
thf(fact_695_T__L,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,I: i] :
( ( ord_le190830114487426235fm_i_o @ epistemic_AxT_i @ A )
=> ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ P4 @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) ) ) ).
% T_L
thf(fact_696_S5__S5_H,axiom,
! [P4: epistemic_fm_i] :
( ( epistemic_AK_i
@ ^ [P2: epistemic_fm_i] :
( ( epistemic_AxT_i @ P2 )
| ( epistemic_AxB_i @ P2 )
| ( epistemic_Ax4_i @ P2 ) )
@ P4 )
=> ( epistemic_AK_i
@ ^ [P2: epistemic_fm_i] :
( ( epistemic_AxT_i @ P2 )
| ( epistemic_Ax5_i @ P2 ) )
@ P4 ) ) ).
% S5_S5'
thf(fact_697_AxT_Ointros,axiom,
! [I: i,P4: epistemic_fm_i] : ( epistemic_AxT_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ P4 ) @ P4 ) ) ).
% AxT.intros
thf(fact_698_AxT_Osimps,axiom,
( epistemic_AxT_i
= ( ^ [A4: epistemic_fm_i] :
? [I3: i,P2: epistemic_fm_i] :
( A4
= ( epistemic_Imp_i @ ( epistemic_K_i @ I3 @ P2 ) @ P2 ) ) ) ) ).
% AxT.simps
thf(fact_699_AxT_Ocases,axiom,
! [A2: epistemic_fm_i] :
( ( epistemic_AxT_i @ A2 )
=> ~ ! [I2: i,P5: epistemic_fm_i] :
( A2
!= ( epistemic_Imp_i @ ( epistemic_K_i @ I2 @ P5 ) @ P5 ) ) ) ).
% AxT.cases
thf(fact_700_S5_H__S5,axiom,
! [P4: epistemic_fm_i] :
( ( epistemic_AK_i
@ ^ [P2: epistemic_fm_i] :
( ( epistemic_AxT_i @ P2 )
| ( epistemic_Ax5_i @ P2 ) )
@ P4 )
=> ( epistemic_AK_i
@ ^ [P2: epistemic_fm_i] :
( ( epistemic_AxT_i @ P2 )
| ( epistemic_AxB_i @ P2 )
| ( epistemic_Ax4_i @ P2 ) )
@ P4 ) ) ).
% S5'_S5
thf(fact_701_tautology__imply__superset,axiom,
! [Ps: list_Epistemic_fm_i,Qs2: list_Epistemic_fm_i,R2: epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( set_Epistemic_fm_i2 @ Ps ) @ ( set_Epistemic_fm_i2 @ Qs2 ) )
=> ! [G3: list_char > $o,H: epistemic_fm_i > $o] : ( epistemic_eval_i @ G3 @ H @ ( epistemic_Imp_i @ ( epistemic_imply_i @ Ps @ R2 ) @ ( epistemic_imply_i @ Qs2 @ R2 ) ) ) ) ).
% tautology_imply_superset
thf(fact_702_inter__Set__filter,axiom,
! [B2: set_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ B2 )
=> ( ( inf_in3450601097109690352c_fm_i @ A @ B2 )
= ( filter6053540608743173075c_fm_i
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ A )
@ B2 ) ) ) ).
% inter_Set_filter
thf(fact_703_inter__Set__filter,axiom,
! [B2: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ B2 )
=> ( ( inf_in161960956874937808c_fm_i @ A @ B2 )
= ( filter8450032351001387443c_fm_i
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ A )
@ B2 ) ) ) ).
% inter_Set_filter
thf(fact_704_conjunct__imply,axiom,
! [G: list_Epistemic_fm_i,P4: epistemic_fm_i,G3: list_char > $o,H: epistemic_fm_i > $o] : ( epistemic_eval_i @ G3 @ H @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( stalnaker_conjunct_i @ G ) @ P4 ) @ ( epistemic_imply_i @ G @ P4 ) ) ) ).
% conjunct_imply
thf(fact_705_imply__conjunct,axiom,
! [G: list_Epistemic_fm_i,P4: epistemic_fm_i,G3: list_char > $o,H: epistemic_fm_i > $o] : ( epistemic_eval_i @ G3 @ H @ ( epistemic_Imp_i @ ( epistemic_imply_i @ G @ P4 ) @ ( epistemic_Imp_i @ ( stalnaker_conjunct_i @ G ) @ P4 ) ) ) ).
% imply_conjunct
thf(fact_706_K__thm,axiom,
! [A: epistemic_fm_i > $o,I: i,P4: epistemic_fm_i,Q: epistemic_fm_i] : ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_Con_i @ ( epistemic_K_i @ I @ P4 ) @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ Q @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ ( epistemic_Con_i @ P4 @ Q ) @ epistemic_FF_i ) ) @ epistemic_FF_i ) ) ) ).
% K_thm
thf(fact_707_K__Boole,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,G: list_Epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_imply_i @ ( cons_Epistemic_fm_i @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) @ G ) @ epistemic_FF_i ) )
=> ( epistemic_AK_i @ A @ ( epistemic_imply_i @ G @ P4 ) ) ) ).
% K_Boole
thf(fact_708_member__filter,axiom,
! [X: epistemic_fm_i,P3: epistemic_fm_i > $o,A: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X @ ( filter6053540608743173075c_fm_i @ P3 @ A ) )
= ( ( member6642669606046002379c_fm_i @ X @ A )
& ( P3 @ X ) ) ) ).
% member_filter
thf(fact_709_member__filter,axiom,
! [X: set_Epistemic_fm_i,P3: set_Epistemic_fm_i > $o,A: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ X @ ( filter8450032351001387443c_fm_i @ P3 @ A ) )
= ( ( member1104366573291651755c_fm_i @ X @ A )
& ( P3 @ X ) ) ) ).
% member_filter
thf(fact_710_set__ConsD,axiom,
! [Y: set_Epistemic_fm_i,X: set_Epistemic_fm_i,Xs: list_s8081015415394010888c_fm_i] :
( ( member1104366573291651755c_fm_i @ Y @ ( set_se200842218512397079c_fm_i @ ( cons_s4962720389763977656c_fm_i @ X @ Xs ) ) )
=> ( ( Y = X )
| ( member1104366573291651755c_fm_i @ Y @ ( set_se200842218512397079c_fm_i @ Xs ) ) ) ) ).
% set_ConsD
thf(fact_711_set__ConsD,axiom,
! [Y: epistemic_fm_i,X: epistemic_fm_i,Xs: list_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ Y @ ( set_Epistemic_fm_i2 @ ( cons_Epistemic_fm_i @ X @ Xs ) ) )
=> ( ( Y = X )
| ( member6642669606046002379c_fm_i @ Y @ ( set_Epistemic_fm_i2 @ Xs ) ) ) ) ).
% set_ConsD
thf(fact_712_list_Oset__cases,axiom,
! [E: set_Epistemic_fm_i,A2: list_s8081015415394010888c_fm_i] :
( ( member1104366573291651755c_fm_i @ E @ ( set_se200842218512397079c_fm_i @ A2 ) )
=> ( ! [Z22: list_s8081015415394010888c_fm_i] :
( A2
!= ( cons_s4962720389763977656c_fm_i @ E @ Z22 ) )
=> ~ ! [Z1: set_Epistemic_fm_i,Z22: list_s8081015415394010888c_fm_i] :
( ( A2
= ( cons_s4962720389763977656c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member1104366573291651755c_fm_i @ E @ ( set_se200842218512397079c_fm_i @ Z22 ) ) ) ) ) ).
% list.set_cases
thf(fact_713_list_Oset__cases,axiom,
! [E: epistemic_fm_i,A2: list_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ E @ ( set_Epistemic_fm_i2 @ A2 ) )
=> ( ! [Z22: list_Epistemic_fm_i] :
( A2
!= ( cons_Epistemic_fm_i @ E @ Z22 ) )
=> ~ ! [Z1: epistemic_fm_i,Z22: list_Epistemic_fm_i] :
( ( A2
= ( cons_Epistemic_fm_i @ Z1 @ Z22 ) )
=> ~ ( member6642669606046002379c_fm_i @ E @ ( set_Epistemic_fm_i2 @ Z22 ) ) ) ) ) ).
% list.set_cases
thf(fact_714_list_Oset__intros_I1_J,axiom,
! [X21: set_Epistemic_fm_i,X22: list_s8081015415394010888c_fm_i] : ( member1104366573291651755c_fm_i @ X21 @ ( set_se200842218512397079c_fm_i @ ( cons_s4962720389763977656c_fm_i @ X21 @ X22 ) ) ) ).
% list.set_intros(1)
thf(fact_715_list_Oset__intros_I1_J,axiom,
! [X21: epistemic_fm_i,X22: list_Epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X21 @ ( set_Epistemic_fm_i2 @ ( cons_Epistemic_fm_i @ X21 @ X22 ) ) ) ).
% list.set_intros(1)
thf(fact_716_list_Oset__intros_I2_J,axiom,
! [Y: set_Epistemic_fm_i,X22: list_s8081015415394010888c_fm_i,X21: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Y @ ( set_se200842218512397079c_fm_i @ X22 ) )
=> ( member1104366573291651755c_fm_i @ Y @ ( set_se200842218512397079c_fm_i @ ( cons_s4962720389763977656c_fm_i @ X21 @ X22 ) ) ) ) ).
% list.set_intros(2)
thf(fact_717_list_Oset__intros_I2_J,axiom,
! [Y: epistemic_fm_i,X22: list_Epistemic_fm_i,X21: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ Y @ ( set_Epistemic_fm_i2 @ X22 ) )
=> ( member6642669606046002379c_fm_i @ Y @ ( set_Epistemic_fm_i2 @ ( cons_Epistemic_fm_i @ X21 @ X22 ) ) ) ) ).
% list.set_intros(2)
thf(fact_718_Set_Ofilter__def,axiom,
( filter6053540608743173075c_fm_i
= ( ^ [P6: epistemic_fm_i > $o,A3: set_Epistemic_fm_i] :
( collec4904205187116291597c_fm_i
@ ^ [A4: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A4 @ A3 )
& ( P6 @ A4 ) ) ) ) ) ).
% Set.filter_def
thf(fact_719_Set_Ofilter__def,axiom,
( filter8450032351001387443c_fm_i
= ( ^ [P6: set_Epistemic_fm_i > $o,A3: set_se3485332733965609186c_fm_i] :
( collec3087743281813070829c_fm_i
@ ^ [A4: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A4 @ A3 )
& ( P6 @ A4 ) ) ) ) ) ).
% Set.filter_def
thf(fact_720_fm_Odistinct_I27_J,axiom,
! [X41: epistemic_fm_i,X42: epistemic_fm_i,X61: i,X62: epistemic_fm_i] :
( ( epistemic_Con_i @ X41 @ X42 )
!= ( epistemic_K_i @ X61 @ X62 ) ) ).
% fm.distinct(27)
thf(fact_721_fm_Odistinct_I5_J,axiom,
! [X41: epistemic_fm_i,X42: epistemic_fm_i] :
( epistemic_FF_i
!= ( epistemic_Con_i @ X41 @ X42 ) ) ).
% fm.distinct(5)
thf(fact_722_eval_Osimps_I6_J,axiom,
! [Ux: list_char > $o,H2: epistemic_fm_i > $o,I: i,P4: epistemic_fm_i] :
( ( epistemic_eval_i @ Ux @ H2 @ ( epistemic_K_i @ I @ P4 ) )
= ( H2 @ ( epistemic_K_i @ I @ P4 ) ) ) ).
% eval.simps(6)
thf(fact_723_eval_Osimps_I1_J,axiom,
! [Uu: list_char > $o,Uv: epistemic_fm_i > $o] :
~ ( epistemic_eval_i @ Uu @ Uv @ epistemic_FF_i ) ).
% eval.simps(1)
thf(fact_724_A1,axiom,
! [P4: epistemic_fm_i,A: epistemic_fm_i > $o] :
( ! [G4: list_char > $o,H3: epistemic_fm_i > $o] : ( epistemic_eval_i @ G4 @ H3 @ P4 )
=> ( epistemic_AK_i @ A @ P4 ) ) ).
% A1
thf(fact_725_AK_Osimps,axiom,
( epistemic_AK_i
= ( ^ [A3: epistemic_fm_i > $o,A4: epistemic_fm_i] :
( ? [P2: epistemic_fm_i] :
( ( A4 = P2 )
& ! [G2: list_char > $o,H4: epistemic_fm_i > $o] : ( epistemic_eval_i @ G2 @ H4 @ P2 ) )
| ? [I3: i,P2: epistemic_fm_i,Q3: epistemic_fm_i] :
( A4
= ( epistemic_Imp_i @ ( epistemic_Con_i @ ( epistemic_K_i @ I3 @ P2 ) @ ( epistemic_K_i @ I3 @ ( epistemic_Imp_i @ P2 @ Q3 ) ) ) @ ( epistemic_K_i @ I3 @ Q3 ) ) )
| ? [P2: epistemic_fm_i] :
( ( A4 = P2 )
& ( A3 @ P2 ) )
| ? [P2: epistemic_fm_i,Q3: epistemic_fm_i] :
( ( A4 = Q3 )
& ( epistemic_AK_i @ A3 @ P2 )
& ( epistemic_AK_i @ A3 @ ( epistemic_Imp_i @ P2 @ Q3 ) ) )
| ? [P2: epistemic_fm_i,I3: i] :
( ( A4
= ( epistemic_K_i @ I3 @ P2 ) )
& ( epistemic_AK_i @ A3 @ P2 ) ) ) ) ) ).
% AK.simps
thf(fact_726_AK_Ocases,axiom,
! [A: epistemic_fm_i > $o,A2: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ A2 )
=> ( ~ ! [G3: list_char > $o,H: epistemic_fm_i > $o] : ( epistemic_eval_i @ G3 @ H @ A2 )
=> ( ! [I2: i,P5: epistemic_fm_i,Q4: epistemic_fm_i] :
( A2
!= ( epistemic_Imp_i @ ( epistemic_Con_i @ ( epistemic_K_i @ I2 @ P5 ) @ ( epistemic_K_i @ I2 @ ( epistemic_Imp_i @ P5 @ Q4 ) ) ) @ ( epistemic_K_i @ I2 @ Q4 ) ) )
=> ( ~ ( A @ A2 )
=> ( ! [P5: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ P5 )
=> ~ ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ P5 @ A2 ) ) )
=> ~ ! [P5: epistemic_fm_i] :
( ? [I2: i] :
( A2
= ( epistemic_K_i @ I2 @ P5 ) )
=> ~ ( epistemic_AK_i @ A @ P5 ) ) ) ) ) ) ) ).
% AK.cases
thf(fact_727_set__subset__Cons,axiom,
! [Xs: list_Epistemic_fm_i,X: epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( set_Epistemic_fm_i2 @ Xs ) @ ( set_Epistemic_fm_i2 @ ( cons_Epistemic_fm_i @ X @ Xs ) ) ) ).
% set_subset_Cons
thf(fact_728_finite__filter,axiom,
! [S: set_Epistemic_fm_i,P3: epistemic_fm_i > $o] :
( ( finite3304564979551393739c_fm_i @ S )
=> ( finite3304564979551393739c_fm_i @ ( filter6053540608743173075c_fm_i @ P3 @ S ) ) ) ).
% finite_filter
thf(fact_729_finite__filter,axiom,
! [S: set_se3485332733965609186c_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( finite7933139204641697195c_fm_i @ S )
=> ( finite7933139204641697195c_fm_i @ ( filter8450032351001387443c_fm_i @ P3 @ S ) ) ) ).
% finite_filter
thf(fact_730_imply_Osimps_I2_J,axiom,
! [P4: epistemic_fm_i,Ps: list_Epistemic_fm_i,Q: epistemic_fm_i] :
( ( epistemic_imply_i @ ( cons_Epistemic_fm_i @ P4 @ Ps ) @ Q )
= ( epistemic_Imp_i @ P4 @ ( epistemic_imply_i @ Ps @ Q ) ) ) ).
% imply.simps(2)
thf(fact_731_K__multi__imply,axiom,
! [A: epistemic_fm_i > $o,A2: epistemic_fm_i,B3: epistemic_fm_i,C2: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ A2 @ ( epistemic_Imp_i @ B3 @ C2 ) ) )
=> ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_Con_i @ A2 @ B3 ) @ C2 ) ) ) ).
% K_multi_imply
thf(fact_732_K__imply__multi,axiom,
! [A: epistemic_fm_i > $o,A2: epistemic_fm_i,B3: epistemic_fm_i,C2: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ A2 @ B3 ) )
=> ( ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ A2 @ C2 ) )
=> ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ A2 @ ( epistemic_Con_i @ B3 @ C2 ) ) ) ) ) ).
% K_imply_multi
thf(fact_733_K__imply__head,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,Ps: list_Epistemic_fm_i] : ( epistemic_AK_i @ A @ ( epistemic_imply_i @ ( cons_Epistemic_fm_i @ P4 @ Ps ) @ P4 ) ) ).
% K_imply_head
thf(fact_734_K__imply__Cons,axiom,
! [A: epistemic_fm_i > $o,Ps: list_Epistemic_fm_i,Q: epistemic_fm_i,P4: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_imply_i @ Ps @ Q ) )
=> ( epistemic_AK_i @ A @ ( epistemic_imply_i @ ( cons_Epistemic_fm_i @ P4 @ Ps ) @ Q ) ) ) ).
% K_imply_Cons
thf(fact_735_K__swap,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,Q: epistemic_fm_i,G: list_Epistemic_fm_i,R2: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_imply_i @ ( cons_Epistemic_fm_i @ P4 @ ( cons_Epistemic_fm_i @ Q @ G ) ) @ R2 ) )
=> ( epistemic_AK_i @ A @ ( epistemic_imply_i @ ( cons_Epistemic_fm_i @ Q @ ( cons_Epistemic_fm_i @ P4 @ G ) ) @ R2 ) ) ) ).
% K_swap
thf(fact_736_mcs__conjunction,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,P4: epistemic_fm_i,Q: epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ V )
=> ( ( ( member6642669606046002379c_fm_i @ P4 @ V )
& ( member6642669606046002379c_fm_i @ Q @ V ) )
=> ( member6642669606046002379c_fm_i @ ( epistemic_Con_i @ P4 @ Q ) @ V ) ) ) ) ).
% mcs_conjunction
thf(fact_737_A2,axiom,
! [A: epistemic_fm_i > $o,I: i,P4: epistemic_fm_i,Q: epistemic_fm_i] : ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_Con_i @ ( epistemic_K_i @ I @ P4 ) @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ P4 @ Q ) ) ) @ ( epistemic_K_i @ I @ Q ) ) ) ).
% A2
thf(fact_738_K__conj__imply__factor,axiom,
! [A: epistemic_fm_i > $o,I: i,P4: epistemic_fm_i,Q: epistemic_fm_i,R2: epistemic_fm_i] : ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_Con_i @ ( epistemic_K_i @ I @ P4 ) @ ( epistemic_K_i @ I @ Q ) ) @ R2 ) @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Con_i @ P4 @ Q ) ) @ R2 ) ) ) ).
% K_conj_imply_factor
thf(fact_739_K__conjunction__out,axiom,
! [A: epistemic_fm_i > $o,I: i,P4: epistemic_fm_i,Q: epistemic_fm_i] : ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_Con_i @ ( epistemic_K_i @ I @ P4 ) @ ( epistemic_K_i @ I @ Q ) ) @ ( epistemic_K_i @ I @ ( epistemic_Con_i @ P4 @ Q ) ) ) ) ).
% K_conjunction_out
thf(fact_740_K__conjunction__in,axiom,
! [A: epistemic_fm_i > $o,I: i,P4: epistemic_fm_i,Q: epistemic_fm_i] : ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Con_i @ P4 @ Q ) ) @ ( epistemic_Con_i @ ( epistemic_K_i @ I @ P4 ) @ ( epistemic_K_i @ I @ Q ) ) ) ) ).
% K_conjunction_in
thf(fact_741_K__ImpI,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,G: list_Epistemic_fm_i,Q: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_imply_i @ ( cons_Epistemic_fm_i @ P4 @ G ) @ Q ) )
=> ( epistemic_AK_i @ A @ ( epistemic_imply_i @ G @ ( epistemic_Imp_i @ P4 @ Q ) ) ) ) ).
% K_ImpI
thf(fact_742_K__mp,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,Q: epistemic_fm_i,G: list_Epistemic_fm_i] : ( epistemic_AK_i @ A @ ( epistemic_imply_i @ ( cons_Epistemic_fm_i @ P4 @ ( cons_Epistemic_fm_i @ ( epistemic_Imp_i @ P4 @ Q ) @ G ) ) @ Q ) ) ).
% K_mp
thf(fact_743_duality__taut,axiom,
! [I: i,P4: epistemic_fm_i,Q: epistemic_fm_i,G3: list_char > $o,H: epistemic_fm_i > $o] : ( epistemic_eval_i @ G3 @ H @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ P4 ) @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ Q @ epistemic_FF_i ) ) ) @ ( epistemic_Imp_i @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( epistemic_Imp_i @ Q @ epistemic_FF_i ) ) @ epistemic_FF_i ) @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ P4 ) @ epistemic_FF_i ) ) ) ) ).
% duality_taut
thf(fact_744_not__in__set__insert,axiom,
! [X: set_Epistemic_fm_i,Xs: list_s8081015415394010888c_fm_i] :
( ~ ( member1104366573291651755c_fm_i @ X @ ( set_se200842218512397079c_fm_i @ Xs ) )
=> ( ( insert2436375702790685214c_fm_i @ X @ Xs )
= ( cons_s4962720389763977656c_fm_i @ X @ Xs ) ) ) ).
% not_in_set_insert
thf(fact_745_not__in__set__insert,axiom,
! [X: epistemic_fm_i,Xs: list_Epistemic_fm_i] :
( ~ ( member6642669606046002379c_fm_i @ X @ ( set_Epistemic_fm_i2 @ Xs ) )
=> ( ( insert177310195918387262c_fm_i @ X @ Xs )
= ( cons_Epistemic_fm_i @ X @ Xs ) ) ) ).
% not_in_set_insert
thf(fact_746_inconsistent__subset,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,P4: epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ A @ V )
=> ( ~ ( episte2285483198712856234tent_i @ A @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ P4 @ bot_bo4194595901900360558c_fm_i ) @ V ) )
=> ~ ! [V2: list_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( set_Epistemic_fm_i2 @ V2 ) @ V )
=> ~ ( epistemic_AK_i @ A @ ( epistemic_imply_i @ ( cons_Epistemic_fm_i @ P4 @ V2 ) @ epistemic_FF_i ) ) ) ) ) ).
% inconsistent_subset
thf(fact_747_K__conjunction__out__mult,axiom,
! [A: epistemic_fm_i > $o,I: i,G: list_Epistemic_fm_i] : ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( stalnaker_conjunct_i @ ( map_Ep2755178516647988292c_fm_i @ ( epistemic_K_i @ I ) @ G ) ) @ ( epistemic_K_i @ I @ ( stalnaker_conjunct_i @ G ) ) ) ) ).
% K_conjunction_out_mult
thf(fact_748_empty__iff,axiom,
! [C2: epistemic_fm_i] :
~ ( member6642669606046002379c_fm_i @ C2 @ bot_bo4194595901900360558c_fm_i ) ).
% empty_iff
thf(fact_749_empty__iff,axiom,
! [C2: set_Epistemic_fm_i] :
~ ( member1104366573291651755c_fm_i @ C2 @ bot_bo145720340923748686c_fm_i ) ).
% empty_iff
thf(fact_750_all__not__in__conv,axiom,
! [A: set_Epistemic_fm_i] :
( ( ! [X2: epistemic_fm_i] :
~ ( member6642669606046002379c_fm_i @ X2 @ A ) )
= ( A = bot_bo4194595901900360558c_fm_i ) ) ).
% all_not_in_conv
thf(fact_751_all__not__in__conv,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( ! [X2: set_Epistemic_fm_i] :
~ ( member1104366573291651755c_fm_i @ X2 @ A ) )
= ( A = bot_bo145720340923748686c_fm_i ) ) ).
% all_not_in_conv
thf(fact_752_Collect__empty__eq,axiom,
! [P3: epistemic_fm_i > $o] :
( ( ( collec4904205187116291597c_fm_i @ P3 )
= bot_bo4194595901900360558c_fm_i )
= ( ! [X2: epistemic_fm_i] :
~ ( P3 @ X2 ) ) ) ).
% Collect_empty_eq
thf(fact_753_Collect__empty__eq,axiom,
! [P3: set_Epistemic_fm_i > $o] :
( ( ( collec3087743281813070829c_fm_i @ P3 )
= bot_bo145720340923748686c_fm_i )
= ( ! [X2: set_Epistemic_fm_i] :
~ ( P3 @ X2 ) ) ) ).
% Collect_empty_eq
thf(fact_754_empty__Collect__eq,axiom,
! [P3: epistemic_fm_i > $o] :
( ( bot_bo4194595901900360558c_fm_i
= ( collec4904205187116291597c_fm_i @ P3 ) )
= ( ! [X2: epistemic_fm_i] :
~ ( P3 @ X2 ) ) ) ).
% empty_Collect_eq
thf(fact_755_empty__Collect__eq,axiom,
! [P3: set_Epistemic_fm_i > $o] :
( ( bot_bo145720340923748686c_fm_i
= ( collec3087743281813070829c_fm_i @ P3 ) )
= ( ! [X2: set_Epistemic_fm_i] :
~ ( P3 @ X2 ) ) ) ).
% empty_Collect_eq
thf(fact_756_insertCI,axiom,
! [A2: epistemic_fm_i,B2: set_Epistemic_fm_i,B3: epistemic_fm_i] :
( ( ~ ( member6642669606046002379c_fm_i @ A2 @ B2 )
=> ( A2 = B3 ) )
=> ( member6642669606046002379c_fm_i @ A2 @ ( insert7817948997695205106c_fm_i @ B3 @ B2 ) ) ) ).
% insertCI
thf(fact_757_insertCI,axiom,
! [A2: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i,B3: set_Epistemic_fm_i] :
( ( ~ ( member1104366573291651755c_fm_i @ A2 @ B2 )
=> ( A2 = B3 ) )
=> ( member1104366573291651755c_fm_i @ A2 @ ( insert7698009978809854162c_fm_i @ B3 @ B2 ) ) ) ).
% insertCI
thf(fact_758_insert__iff,axiom,
! [A2: epistemic_fm_i,B3: epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A2 @ ( insert7817948997695205106c_fm_i @ B3 @ A ) )
= ( ( A2 = B3 )
| ( member6642669606046002379c_fm_i @ A2 @ A ) ) ) ).
% insert_iff
thf(fact_759_insert__iff,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ A2 @ ( insert7698009978809854162c_fm_i @ B3 @ A ) )
= ( ( A2 = B3 )
| ( member1104366573291651755c_fm_i @ A2 @ A ) ) ) ).
% insert_iff
thf(fact_760_subset__empty,axiom,
! [A: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ bot_bo4194595901900360558c_fm_i )
= ( A = bot_bo4194595901900360558c_fm_i ) ) ).
% subset_empty
thf(fact_761_empty__subsetI,axiom,
! [A: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ bot_bo4194595901900360558c_fm_i @ A ) ).
% empty_subsetI
thf(fact_762_inf__bot__left,axiom,
! [X: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ bot_bo145720340923748686c_fm_i @ X )
= bot_bo145720340923748686c_fm_i ) ).
% inf_bot_left
thf(fact_763_inf__bot__right,axiom,
! [X: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ X @ bot_bo145720340923748686c_fm_i )
= bot_bo145720340923748686c_fm_i ) ).
% inf_bot_right
thf(fact_764_boolean__algebra_Oconj__zero__right,axiom,
! [X: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ X @ bot_bo145720340923748686c_fm_i )
= bot_bo145720340923748686c_fm_i ) ).
% boolean_algebra.conj_zero_right
thf(fact_765_boolean__algebra_Oconj__zero__left,axiom,
! [X: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ bot_bo145720340923748686c_fm_i @ X )
= bot_bo145720340923748686c_fm_i ) ).
% boolean_algebra.conj_zero_left
thf(fact_766_sup__bot__left,axiom,
! [X: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ bot_bo4194595901900360558c_fm_i @ X )
= X ) ).
% sup_bot_left
thf(fact_767_sup__bot__right,axiom,
! [X: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ X @ bot_bo4194595901900360558c_fm_i )
= X ) ).
% sup_bot_right
thf(fact_768_bot__eq__sup__iff,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ( bot_bo4194595901900360558c_fm_i
= ( sup_su1936195050962291414c_fm_i @ X @ Y ) )
= ( ( X = bot_bo4194595901900360558c_fm_i )
& ( Y = bot_bo4194595901900360558c_fm_i ) ) ) ).
% bot_eq_sup_iff
thf(fact_769_sup__eq__bot__iff,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ( ( sup_su1936195050962291414c_fm_i @ X @ Y )
= bot_bo4194595901900360558c_fm_i )
= ( ( X = bot_bo4194595901900360558c_fm_i )
& ( Y = bot_bo4194595901900360558c_fm_i ) ) ) ).
% sup_eq_bot_iff
thf(fact_770_sup__bot_Oeq__neutr__iff,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( ( sup_su1936195050962291414c_fm_i @ A2 @ B3 )
= bot_bo4194595901900360558c_fm_i )
= ( ( A2 = bot_bo4194595901900360558c_fm_i )
& ( B3 = bot_bo4194595901900360558c_fm_i ) ) ) ).
% sup_bot.eq_neutr_iff
thf(fact_771_sup__bot_Oleft__neutral,axiom,
! [A2: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ bot_bo4194595901900360558c_fm_i @ A2 )
= A2 ) ).
% sup_bot.left_neutral
thf(fact_772_sup__bot_Oneutr__eq__iff,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i] :
( ( bot_bo4194595901900360558c_fm_i
= ( sup_su1936195050962291414c_fm_i @ A2 @ B3 ) )
= ( ( A2 = bot_bo4194595901900360558c_fm_i )
& ( B3 = bot_bo4194595901900360558c_fm_i ) ) ) ).
% sup_bot.neutr_eq_iff
thf(fact_773_sup__bot_Oright__neutral,axiom,
! [A2: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i )
= A2 ) ).
% sup_bot.right_neutral
thf(fact_774_singletonI,axiom,
! [A2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ A2 @ ( insert7817948997695205106c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i ) ) ).
% singletonI
thf(fact_775_singletonI,axiom,
! [A2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ A2 @ ( insert7698009978809854162c_fm_i @ A2 @ bot_bo145720340923748686c_fm_i ) ) ).
% singletonI
thf(fact_776_finite__insert,axiom,
! [A2: epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ ( insert7817948997695205106c_fm_i @ A2 @ A ) )
= ( finite3304564979551393739c_fm_i @ A ) ) ).
% finite_insert
thf(fact_777_finite__insert,axiom,
! [A2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ ( insert7698009978809854162c_fm_i @ A2 @ A ) )
= ( finite7933139204641697195c_fm_i @ A ) ) ).
% finite_insert
thf(fact_778_insert__subset,axiom,
! [X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) @ B2 )
= ( ( member1104366573291651755c_fm_i @ X @ B2 )
& ( ord_le5389487502678872194c_fm_i @ A @ B2 ) ) ) ).
% insert_subset
thf(fact_779_insert__subset,axiom,
! [X: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( insert7817948997695205106c_fm_i @ X @ A ) @ B2 )
= ( ( member6642669606046002379c_fm_i @ X @ B2 )
& ( ord_le3843937902494030498c_fm_i @ A @ B2 ) ) ) ).
% insert_subset
thf(fact_780_Un__empty,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ( sup_su1936195050962291414c_fm_i @ A @ B2 )
= bot_bo4194595901900360558c_fm_i )
= ( ( A = bot_bo4194595901900360558c_fm_i )
& ( B2 = bot_bo4194595901900360558c_fm_i ) ) ) ).
% Un_empty
thf(fact_781_Int__insert__left__if0,axiom,
! [A2: epistemic_fm_i,C: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ~ ( member6642669606046002379c_fm_i @ A2 @ C )
=> ( ( inf_in3450601097109690352c_fm_i @ ( insert7817948997695205106c_fm_i @ A2 @ B2 ) @ C )
= ( inf_in3450601097109690352c_fm_i @ B2 @ C ) ) ) ).
% Int_insert_left_if0
thf(fact_782_Int__insert__left__if0,axiom,
! [A2: set_Epistemic_fm_i,C: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ~ ( member1104366573291651755c_fm_i @ A2 @ C )
=> ( ( inf_in161960956874937808c_fm_i @ ( insert7698009978809854162c_fm_i @ A2 @ B2 ) @ C )
= ( inf_in161960956874937808c_fm_i @ B2 @ C ) ) ) ).
% Int_insert_left_if0
thf(fact_783_Int__insert__left__if1,axiom,
! [A2: epistemic_fm_i,C: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A2 @ C )
=> ( ( inf_in3450601097109690352c_fm_i @ ( insert7817948997695205106c_fm_i @ A2 @ B2 ) @ C )
= ( insert7817948997695205106c_fm_i @ A2 @ ( inf_in3450601097109690352c_fm_i @ B2 @ C ) ) ) ) ).
% Int_insert_left_if1
thf(fact_784_Int__insert__left__if1,axiom,
! [A2: set_Epistemic_fm_i,C: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ A2 @ C )
=> ( ( inf_in161960956874937808c_fm_i @ ( insert7698009978809854162c_fm_i @ A2 @ B2 ) @ C )
= ( insert7698009978809854162c_fm_i @ A2 @ ( inf_in161960956874937808c_fm_i @ B2 @ C ) ) ) ) ).
% Int_insert_left_if1
thf(fact_785_insert__inter__insert,axiom,
! [A2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ ( insert7698009978809854162c_fm_i @ A2 @ A ) @ ( insert7698009978809854162c_fm_i @ A2 @ B2 ) )
= ( insert7698009978809854162c_fm_i @ A2 @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) ) ) ).
% insert_inter_insert
thf(fact_786_Int__insert__right__if0,axiom,
! [A2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ~ ( member6642669606046002379c_fm_i @ A2 @ A )
=> ( ( inf_in3450601097109690352c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ A2 @ B2 ) )
= ( inf_in3450601097109690352c_fm_i @ A @ B2 ) ) ) ).
% Int_insert_right_if0
thf(fact_787_Int__insert__right__if0,axiom,
! [A2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ~ ( member1104366573291651755c_fm_i @ A2 @ A )
=> ( ( inf_in161960956874937808c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ A2 @ B2 ) )
= ( inf_in161960956874937808c_fm_i @ A @ B2 ) ) ) ).
% Int_insert_right_if0
thf(fact_788_Int__insert__right__if1,axiom,
! [A2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A2 @ A )
=> ( ( inf_in3450601097109690352c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ A2 @ B2 ) )
= ( insert7817948997695205106c_fm_i @ A2 @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) ) ) ) ).
% Int_insert_right_if1
thf(fact_789_Int__insert__right__if1,axiom,
! [A2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ A2 @ A )
=> ( ( inf_in161960956874937808c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ A2 @ B2 ) )
= ( insert7698009978809854162c_fm_i @ A2 @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) ) ) ) ).
% Int_insert_right_if1
thf(fact_790_Un__insert__left,axiom,
! [A2: epistemic_fm_i,B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ A2 @ B2 ) @ C )
= ( insert7817948997695205106c_fm_i @ A2 @ ( sup_su1936195050962291414c_fm_i @ B2 @ C ) ) ) ).
% Un_insert_left
thf(fact_791_Un__insert__right,axiom,
! [A: set_Epistemic_fm_i,A2: epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ A2 @ B2 ) )
= ( insert7817948997695205106c_fm_i @ A2 @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) ) ) ).
% Un_insert_right
thf(fact_792_singleton__conv,axiom,
! [A2: epistemic_fm_i] :
( ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] : ( X2 = A2 ) )
= ( insert7817948997695205106c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i ) ) ).
% singleton_conv
thf(fact_793_singleton__conv,axiom,
! [A2: set_Epistemic_fm_i] :
( ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] : ( X2 = A2 ) )
= ( insert7698009978809854162c_fm_i @ A2 @ bot_bo145720340923748686c_fm_i ) ) ).
% singleton_conv
thf(fact_794_singleton__conv2,axiom,
! [A2: epistemic_fm_i] :
( ( collec4904205187116291597c_fm_i
@ ( ^ [Y2: epistemic_fm_i,Z2: epistemic_fm_i] : ( Y2 = Z2 )
@ A2 ) )
= ( insert7817948997695205106c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i ) ) ).
% singleton_conv2
thf(fact_795_singleton__conv2,axiom,
! [A2: set_Epistemic_fm_i] :
( ( collec3087743281813070829c_fm_i
@ ( ^ [Y2: set_Epistemic_fm_i,Z2: set_Epistemic_fm_i] : ( Y2 = Z2 )
@ A2 ) )
= ( insert7698009978809854162c_fm_i @ A2 @ bot_bo145720340923748686c_fm_i ) ) ).
% singleton_conv2
thf(fact_796_in__set__insert,axiom,
! [X: set_Epistemic_fm_i,Xs: list_s8081015415394010888c_fm_i] :
( ( member1104366573291651755c_fm_i @ X @ ( set_se200842218512397079c_fm_i @ Xs ) )
=> ( ( insert2436375702790685214c_fm_i @ X @ Xs )
= Xs ) ) ).
% in_set_insert
thf(fact_797_in__set__insert,axiom,
! [X: epistemic_fm_i,Xs: list_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X @ ( set_Epistemic_fm_i2 @ Xs ) )
=> ( ( insert177310195918387262c_fm_i @ X @ Xs )
= Xs ) ) ).
% in_set_insert
thf(fact_798_singleton__insert__inj__eq_H,axiom,
! [A2: epistemic_fm_i,A: set_Epistemic_fm_i,B3: epistemic_fm_i] :
( ( ( insert7817948997695205106c_fm_i @ A2 @ A )
= ( insert7817948997695205106c_fm_i @ B3 @ bot_bo4194595901900360558c_fm_i ) )
= ( ( A2 = B3 )
& ( ord_le3843937902494030498c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ B3 @ bot_bo4194595901900360558c_fm_i ) ) ) ) ).
% singleton_insert_inj_eq'
thf(fact_799_singleton__insert__inj__eq,axiom,
! [B3: epistemic_fm_i,A2: epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( ( insert7817948997695205106c_fm_i @ B3 @ bot_bo4194595901900360558c_fm_i )
= ( insert7817948997695205106c_fm_i @ A2 @ A ) )
= ( ( A2 = B3 )
& ( ord_le3843937902494030498c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ B3 @ bot_bo4194595901900360558c_fm_i ) ) ) ) ).
% singleton_insert_inj_eq
thf(fact_800_insert__disjoint_I1_J,axiom,
! [A2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ( inf_in3450601097109690352c_fm_i @ ( insert7817948997695205106c_fm_i @ A2 @ A ) @ B2 )
= bot_bo4194595901900360558c_fm_i )
= ( ~ ( member6642669606046002379c_fm_i @ A2 @ B2 )
& ( ( inf_in3450601097109690352c_fm_i @ A @ B2 )
= bot_bo4194595901900360558c_fm_i ) ) ) ).
% insert_disjoint(1)
thf(fact_801_insert__disjoint_I1_J,axiom,
! [A2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ( inf_in161960956874937808c_fm_i @ ( insert7698009978809854162c_fm_i @ A2 @ A ) @ B2 )
= bot_bo145720340923748686c_fm_i )
= ( ~ ( member1104366573291651755c_fm_i @ A2 @ B2 )
& ( ( inf_in161960956874937808c_fm_i @ A @ B2 )
= bot_bo145720340923748686c_fm_i ) ) ) ).
% insert_disjoint(1)
thf(fact_802_insert__disjoint_I2_J,axiom,
! [A2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( bot_bo4194595901900360558c_fm_i
= ( inf_in3450601097109690352c_fm_i @ ( insert7817948997695205106c_fm_i @ A2 @ A ) @ B2 ) )
= ( ~ ( member6642669606046002379c_fm_i @ A2 @ B2 )
& ( bot_bo4194595901900360558c_fm_i
= ( inf_in3450601097109690352c_fm_i @ A @ B2 ) ) ) ) ).
% insert_disjoint(2)
thf(fact_803_insert__disjoint_I2_J,axiom,
! [A2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( bot_bo145720340923748686c_fm_i
= ( inf_in161960956874937808c_fm_i @ ( insert7698009978809854162c_fm_i @ A2 @ A ) @ B2 ) )
= ( ~ ( member1104366573291651755c_fm_i @ A2 @ B2 )
& ( bot_bo145720340923748686c_fm_i
= ( inf_in161960956874937808c_fm_i @ A @ B2 ) ) ) ) ).
% insert_disjoint(2)
thf(fact_804_disjoint__insert_I1_J,axiom,
! [B2: set_Epistemic_fm_i,A2: epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( ( inf_in3450601097109690352c_fm_i @ B2 @ ( insert7817948997695205106c_fm_i @ A2 @ A ) )
= bot_bo4194595901900360558c_fm_i )
= ( ~ ( member6642669606046002379c_fm_i @ A2 @ B2 )
& ( ( inf_in3450601097109690352c_fm_i @ B2 @ A )
= bot_bo4194595901900360558c_fm_i ) ) ) ).
% disjoint_insert(1)
thf(fact_805_disjoint__insert_I1_J,axiom,
! [B2: set_se3485332733965609186c_fm_i,A2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( ( inf_in161960956874937808c_fm_i @ B2 @ ( insert7698009978809854162c_fm_i @ A2 @ A ) )
= bot_bo145720340923748686c_fm_i )
= ( ~ ( member1104366573291651755c_fm_i @ A2 @ B2 )
& ( ( inf_in161960956874937808c_fm_i @ B2 @ A )
= bot_bo145720340923748686c_fm_i ) ) ) ).
% disjoint_insert(1)
thf(fact_806_disjoint__insert_I2_J,axiom,
! [A: set_Epistemic_fm_i,B3: epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( bot_bo4194595901900360558c_fm_i
= ( inf_in3450601097109690352c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ B3 @ B2 ) ) )
= ( ~ ( member6642669606046002379c_fm_i @ B3 @ A )
& ( bot_bo4194595901900360558c_fm_i
= ( inf_in3450601097109690352c_fm_i @ A @ B2 ) ) ) ) ).
% disjoint_insert(2)
thf(fact_807_disjoint__insert_I2_J,axiom,
! [A: set_se3485332733965609186c_fm_i,B3: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( bot_bo145720340923748686c_fm_i
= ( inf_in161960956874937808c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ B3 @ B2 ) ) )
= ( ~ ( member1104366573291651755c_fm_i @ B3 @ A )
& ( bot_bo145720340923748686c_fm_i
= ( inf_in161960956874937808c_fm_i @ A @ B2 ) ) ) ) ).
% disjoint_insert(2)
thf(fact_808_list_Osimps_I15_J,axiom,
! [X21: epistemic_fm_i,X22: list_Epistemic_fm_i] :
( ( set_Epistemic_fm_i2 @ ( cons_Epistemic_fm_i @ X21 @ X22 ) )
= ( insert7817948997695205106c_fm_i @ X21 @ ( set_Epistemic_fm_i2 @ X22 ) ) ) ).
% list.simps(15)
thf(fact_809_List_Oset__insert,axiom,
! [X: epistemic_fm_i,Xs: list_Epistemic_fm_i] :
( ( set_Epistemic_fm_i2 @ ( insert177310195918387262c_fm_i @ X @ Xs ) )
= ( insert7817948997695205106c_fm_i @ X @ ( set_Epistemic_fm_i2 @ Xs ) ) ) ).
% List.set_insert
thf(fact_810_finite__subset__induct_H,axiom,
! [F: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i,P3: set_se3485332733965609186c_fm_i > $o] :
( ( finite7933139204641697195c_fm_i @ F )
=> ( ( ord_le5389487502678872194c_fm_i @ F @ A )
=> ( ( P3 @ bot_bo145720340923748686c_fm_i )
=> ( ! [A6: set_Epistemic_fm_i,F4: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ F4 )
=> ( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ( ord_le5389487502678872194c_fm_i @ F4 @ A )
=> ( ~ ( member1104366573291651755c_fm_i @ A6 @ F4 )
=> ( ( P3 @ F4 )
=> ( P3 @ ( insert7698009978809854162c_fm_i @ A6 @ F4 ) ) ) ) ) ) )
=> ( P3 @ F ) ) ) ) ) ).
% finite_subset_induct'
thf(fact_811_finite__subset__induct_H,axiom,
! [F: set_Epistemic_fm_i,A: set_Epistemic_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( finite3304564979551393739c_fm_i @ F )
=> ( ( ord_le3843937902494030498c_fm_i @ F @ A )
=> ( ( P3 @ bot_bo4194595901900360558c_fm_i )
=> ( ! [A6: epistemic_fm_i,F4: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ F4 )
=> ( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ( ( ord_le3843937902494030498c_fm_i @ F4 @ A )
=> ( ~ ( member6642669606046002379c_fm_i @ A6 @ F4 )
=> ( ( P3 @ F4 )
=> ( P3 @ ( insert7817948997695205106c_fm_i @ A6 @ F4 ) ) ) ) ) ) )
=> ( P3 @ F ) ) ) ) ) ).
% finite_subset_induct'
thf(fact_812_finite__subset__induct,axiom,
! [F: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i,P3: set_se3485332733965609186c_fm_i > $o] :
( ( finite7933139204641697195c_fm_i @ F )
=> ( ( ord_le5389487502678872194c_fm_i @ F @ A )
=> ( ( P3 @ bot_bo145720340923748686c_fm_i )
=> ( ! [A6: set_Epistemic_fm_i,F4: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ F4 )
=> ( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ~ ( member1104366573291651755c_fm_i @ A6 @ F4 )
=> ( ( P3 @ F4 )
=> ( P3 @ ( insert7698009978809854162c_fm_i @ A6 @ F4 ) ) ) ) ) )
=> ( P3 @ F ) ) ) ) ) ).
% finite_subset_induct
thf(fact_813_finite__subset__induct,axiom,
! [F: set_Epistemic_fm_i,A: set_Epistemic_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( finite3304564979551393739c_fm_i @ F )
=> ( ( ord_le3843937902494030498c_fm_i @ F @ A )
=> ( ( P3 @ bot_bo4194595901900360558c_fm_i )
=> ( ! [A6: epistemic_fm_i,F4: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ F4 )
=> ( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ( ~ ( member6642669606046002379c_fm_i @ A6 @ F4 )
=> ( ( P3 @ F4 )
=> ( P3 @ ( insert7817948997695205106c_fm_i @ A6 @ F4 ) ) ) ) ) )
=> ( P3 @ F ) ) ) ) ) ).
% finite_subset_induct
thf(fact_814_subset__singleton__iff,axiom,
! [X5: set_Epistemic_fm_i,A2: epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X5 @ ( insert7817948997695205106c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i ) )
= ( ( X5 = bot_bo4194595901900360558c_fm_i )
| ( X5
= ( insert7817948997695205106c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i ) ) ) ) ).
% subset_singleton_iff
thf(fact_815_subset__singletonD,axiom,
! [A: set_Epistemic_fm_i,X: epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) )
=> ( ( A = bot_bo4194595901900360558c_fm_i )
| ( A
= ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) ) ) ) ).
% subset_singletonD
thf(fact_816_empty__def,axiom,
( bot_bo4194595901900360558c_fm_i
= ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] : $false ) ) ).
% empty_def
thf(fact_817_empty__def,axiom,
( bot_bo145720340923748686c_fm_i
= ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] : $false ) ) ).
% empty_def
thf(fact_818_emptyE,axiom,
! [A2: epistemic_fm_i] :
~ ( member6642669606046002379c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i ) ).
% emptyE
thf(fact_819_emptyE,axiom,
! [A2: set_Epistemic_fm_i] :
~ ( member1104366573291651755c_fm_i @ A2 @ bot_bo145720340923748686c_fm_i ) ).
% emptyE
thf(fact_820_insertE,axiom,
! [A2: epistemic_fm_i,B3: epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A2 @ ( insert7817948997695205106c_fm_i @ B3 @ A ) )
=> ( ( A2 != B3 )
=> ( member6642669606046002379c_fm_i @ A2 @ A ) ) ) ).
% insertE
thf(fact_821_insertE,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ A2 @ ( insert7698009978809854162c_fm_i @ B3 @ A ) )
=> ( ( A2 != B3 )
=> ( member1104366573291651755c_fm_i @ A2 @ A ) ) ) ).
% insertE
thf(fact_822_equals0D,axiom,
! [A: set_Epistemic_fm_i,A2: epistemic_fm_i] :
( ( A = bot_bo4194595901900360558c_fm_i )
=> ~ ( member6642669606046002379c_fm_i @ A2 @ A ) ) ).
% equals0D
thf(fact_823_equals0D,axiom,
! [A: set_se3485332733965609186c_fm_i,A2: set_Epistemic_fm_i] :
( ( A = bot_bo145720340923748686c_fm_i )
=> ~ ( member1104366573291651755c_fm_i @ A2 @ A ) ) ).
% equals0D
thf(fact_824_equals0I,axiom,
! [A: set_Epistemic_fm_i] :
( ! [Y4: epistemic_fm_i] :
~ ( member6642669606046002379c_fm_i @ Y4 @ A )
=> ( A = bot_bo4194595901900360558c_fm_i ) ) ).
% equals0I
thf(fact_825_equals0I,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ! [Y4: set_Epistemic_fm_i] :
~ ( member1104366573291651755c_fm_i @ Y4 @ A )
=> ( A = bot_bo145720340923748686c_fm_i ) ) ).
% equals0I
thf(fact_826_insertI1,axiom,
! [A2: epistemic_fm_i,B2: set_Epistemic_fm_i] : ( member6642669606046002379c_fm_i @ A2 @ ( insert7817948997695205106c_fm_i @ A2 @ B2 ) ) ).
% insertI1
thf(fact_827_insertI1,axiom,
! [A2: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i] : ( member1104366573291651755c_fm_i @ A2 @ ( insert7698009978809854162c_fm_i @ A2 @ B2 ) ) ).
% insertI1
thf(fact_828_insertI2,axiom,
! [A2: epistemic_fm_i,B2: set_Epistemic_fm_i,B3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A2 @ B2 )
=> ( member6642669606046002379c_fm_i @ A2 @ ( insert7817948997695205106c_fm_i @ B3 @ B2 ) ) ) ).
% insertI2
thf(fact_829_insertI2,axiom,
! [A2: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i,B3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A2 @ B2 )
=> ( member1104366573291651755c_fm_i @ A2 @ ( insert7698009978809854162c_fm_i @ B3 @ B2 ) ) ) ).
% insertI2
thf(fact_830_ex__in__conv,axiom,
! [A: set_Epistemic_fm_i] :
( ( ? [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ A ) )
= ( A != bot_bo4194595901900360558c_fm_i ) ) ).
% ex_in_conv
thf(fact_831_ex__in__conv,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( ? [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ A ) )
= ( A != bot_bo145720340923748686c_fm_i ) ) ).
% ex_in_conv
thf(fact_832_Set_Oset__insert,axiom,
! [X: epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X @ A )
=> ~ ! [B6: set_Epistemic_fm_i] :
( ( A
= ( insert7817948997695205106c_fm_i @ X @ B6 ) )
=> ( member6642669606046002379c_fm_i @ X @ B6 ) ) ) ).
% Set.set_insert
thf(fact_833_Set_Oset__insert,axiom,
! [X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ X @ A )
=> ~ ! [B6: set_se3485332733965609186c_fm_i] :
( ( A
= ( insert7698009978809854162c_fm_i @ X @ B6 ) )
=> ( member1104366573291651755c_fm_i @ X @ B6 ) ) ) ).
% Set.set_insert
thf(fact_834_singletonD,axiom,
! [B3: epistemic_fm_i,A2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ B3 @ ( insert7817948997695205106c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i ) )
=> ( B3 = A2 ) ) ).
% singletonD
thf(fact_835_singletonD,axiom,
! [B3: set_Epistemic_fm_i,A2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ B3 @ ( insert7698009978809854162c_fm_i @ A2 @ bot_bo145720340923748686c_fm_i ) )
=> ( B3 = A2 ) ) ).
% singletonD
thf(fact_836_insert__ident,axiom,
! [X: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ~ ( member6642669606046002379c_fm_i @ X @ A )
=> ( ~ ( member6642669606046002379c_fm_i @ X @ B2 )
=> ( ( ( insert7817948997695205106c_fm_i @ X @ A )
= ( insert7817948997695205106c_fm_i @ X @ B2 ) )
= ( A = B2 ) ) ) ) ).
% insert_ident
thf(fact_837_insert__ident,axiom,
! [X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ~ ( member1104366573291651755c_fm_i @ X @ A )
=> ( ~ ( member1104366573291651755c_fm_i @ X @ B2 )
=> ( ( ( insert7698009978809854162c_fm_i @ X @ A )
= ( insert7698009978809854162c_fm_i @ X @ B2 ) )
= ( A = B2 ) ) ) ) ).
% insert_ident
thf(fact_838_insert__absorb,axiom,
! [A2: epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A2 @ A )
=> ( ( insert7817948997695205106c_fm_i @ A2 @ A )
= A ) ) ).
% insert_absorb
thf(fact_839_insert__absorb,axiom,
! [A2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ A2 @ A )
=> ( ( insert7698009978809854162c_fm_i @ A2 @ A )
= A ) ) ).
% insert_absorb
thf(fact_840_insert__eq__iff,axiom,
! [A2: epistemic_fm_i,A: set_Epistemic_fm_i,B3: epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ~ ( member6642669606046002379c_fm_i @ A2 @ A )
=> ( ~ ( member6642669606046002379c_fm_i @ B3 @ B2 )
=> ( ( ( insert7817948997695205106c_fm_i @ A2 @ A )
= ( insert7817948997695205106c_fm_i @ B3 @ B2 ) )
= ( ( ( A2 = B3 )
=> ( A = B2 ) )
& ( ( A2 != B3 )
=> ? [C3: set_Epistemic_fm_i] :
( ( A
= ( insert7817948997695205106c_fm_i @ B3 @ C3 ) )
& ~ ( member6642669606046002379c_fm_i @ B3 @ C3 )
& ( B2
= ( insert7817948997695205106c_fm_i @ A2 @ C3 ) )
& ~ ( member6642669606046002379c_fm_i @ A2 @ C3 ) ) ) ) ) ) ) ).
% insert_eq_iff
thf(fact_841_insert__eq__iff,axiom,
! [A2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B3: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ~ ( member1104366573291651755c_fm_i @ A2 @ A )
=> ( ~ ( member1104366573291651755c_fm_i @ B3 @ B2 )
=> ( ( ( insert7698009978809854162c_fm_i @ A2 @ A )
= ( insert7698009978809854162c_fm_i @ B3 @ B2 ) )
= ( ( ( A2 = B3 )
=> ( A = B2 ) )
& ( ( A2 != B3 )
=> ? [C3: set_se3485332733965609186c_fm_i] :
( ( A
= ( insert7698009978809854162c_fm_i @ B3 @ C3 ) )
& ~ ( member1104366573291651755c_fm_i @ B3 @ C3 )
& ( B2
= ( insert7698009978809854162c_fm_i @ A2 @ C3 ) )
& ~ ( member1104366573291651755c_fm_i @ A2 @ C3 ) ) ) ) ) ) ) ).
% insert_eq_iff
thf(fact_842_singleton__iff,axiom,
! [B3: epistemic_fm_i,A2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ B3 @ ( insert7817948997695205106c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i ) )
= ( B3 = A2 ) ) ).
% singleton_iff
thf(fact_843_singleton__iff,axiom,
! [B3: set_Epistemic_fm_i,A2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ B3 @ ( insert7698009978809854162c_fm_i @ A2 @ bot_bo145720340923748686c_fm_i ) )
= ( B3 = A2 ) ) ).
% singleton_iff
thf(fact_844_Collect__conv__if,axiom,
! [P3: epistemic_fm_i > $o,A2: epistemic_fm_i] :
( ( ( P3 @ A2 )
=> ( ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( X2 = A2 )
& ( P3 @ X2 ) ) )
= ( insert7817948997695205106c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i ) ) )
& ( ~ ( P3 @ A2 )
=> ( ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( X2 = A2 )
& ( P3 @ X2 ) ) )
= bot_bo4194595901900360558c_fm_i ) ) ) ).
% Collect_conv_if
thf(fact_845_Collect__conv__if,axiom,
! [P3: set_Epistemic_fm_i > $o,A2: set_Epistemic_fm_i] :
( ( ( P3 @ A2 )
=> ( ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( X2 = A2 )
& ( P3 @ X2 ) ) )
= ( insert7698009978809854162c_fm_i @ A2 @ bot_bo145720340923748686c_fm_i ) ) )
& ( ~ ( P3 @ A2 )
=> ( ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( X2 = A2 )
& ( P3 @ X2 ) ) )
= bot_bo145720340923748686c_fm_i ) ) ) ).
% Collect_conv_if
thf(fact_846_Collect__conv__if2,axiom,
! [P3: epistemic_fm_i > $o,A2: epistemic_fm_i] :
( ( ( P3 @ A2 )
=> ( ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( A2 = X2 )
& ( P3 @ X2 ) ) )
= ( insert7817948997695205106c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i ) ) )
& ( ~ ( P3 @ A2 )
=> ( ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( A2 = X2 )
& ( P3 @ X2 ) ) )
= bot_bo4194595901900360558c_fm_i ) ) ) ).
% Collect_conv_if2
thf(fact_847_Collect__conv__if2,axiom,
! [P3: set_Epistemic_fm_i > $o,A2: set_Epistemic_fm_i] :
( ( ( P3 @ A2 )
=> ( ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( A2 = X2 )
& ( P3 @ X2 ) ) )
= ( insert7698009978809854162c_fm_i @ A2 @ bot_bo145720340923748686c_fm_i ) ) )
& ( ~ ( P3 @ A2 )
=> ( ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( A2 = X2 )
& ( P3 @ X2 ) ) )
= bot_bo145720340923748686c_fm_i ) ) ) ).
% Collect_conv_if2
thf(fact_848_mk__disjoint__insert,axiom,
! [A2: epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A2 @ A )
=> ? [B6: set_Epistemic_fm_i] :
( ( A
= ( insert7817948997695205106c_fm_i @ A2 @ B6 ) )
& ~ ( member6642669606046002379c_fm_i @ A2 @ B6 ) ) ) ).
% mk_disjoint_insert
thf(fact_849_mk__disjoint__insert,axiom,
! [A2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ A2 @ A )
=> ? [B6: set_se3485332733965609186c_fm_i] :
( ( A
= ( insert7698009978809854162c_fm_i @ A2 @ B6 ) )
& ~ ( member1104366573291651755c_fm_i @ A2 @ B6 ) ) ) ).
% mk_disjoint_insert
thf(fact_850_insert__compr,axiom,
( insert7817948997695205106c_fm_i
= ( ^ [A4: epistemic_fm_i,B: set_Epistemic_fm_i] :
( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( X2 = A4 )
| ( member6642669606046002379c_fm_i @ X2 @ B ) ) ) ) ) ).
% insert_compr
thf(fact_851_insert__compr,axiom,
( insert7698009978809854162c_fm_i
= ( ^ [A4: set_Epistemic_fm_i,B: set_se3485332733965609186c_fm_i] :
( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( X2 = A4 )
| ( member1104366573291651755c_fm_i @ X2 @ B ) ) ) ) ) ).
% insert_compr
thf(fact_852_insert__Collect,axiom,
! [A2: epistemic_fm_i,P3: epistemic_fm_i > $o] :
( ( insert7817948997695205106c_fm_i @ A2 @ ( collec4904205187116291597c_fm_i @ P3 ) )
= ( collec4904205187116291597c_fm_i
@ ^ [U2: epistemic_fm_i] :
( ( U2 != A2 )
=> ( P3 @ U2 ) ) ) ) ).
% insert_Collect
thf(fact_853_insert__Collect,axiom,
! [A2: set_Epistemic_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( insert7698009978809854162c_fm_i @ A2 @ ( collec3087743281813070829c_fm_i @ P3 ) )
= ( collec3087743281813070829c_fm_i
@ ^ [U2: set_Epistemic_fm_i] :
( ( U2 != A2 )
=> ( P3 @ U2 ) ) ) ) ).
% insert_Collect
thf(fact_854_insert__is__Un,axiom,
( insert7817948997695205106c_fm_i
= ( ^ [A4: epistemic_fm_i] : ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ A4 @ bot_bo4194595901900360558c_fm_i ) ) ) ) ).
% insert_is_Un
thf(fact_855_Un__singleton__iff,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,X: epistemic_fm_i] :
( ( ( sup_su1936195050962291414c_fm_i @ A @ B2 )
= ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) )
= ( ( ( A = bot_bo4194595901900360558c_fm_i )
& ( B2
= ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) ) )
| ( ( A
= ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) )
& ( B2 = bot_bo4194595901900360558c_fm_i ) )
| ( ( A
= ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) )
& ( B2
= ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) ) ) ) ) ).
% Un_singleton_iff
thf(fact_856_singleton__Un__iff,axiom,
! [X: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i )
= ( sup_su1936195050962291414c_fm_i @ A @ B2 ) )
= ( ( ( A = bot_bo4194595901900360558c_fm_i )
& ( B2
= ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) ) )
| ( ( A
= ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) )
& ( B2 = bot_bo4194595901900360558c_fm_i ) )
| ( ( A
= ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) )
& ( B2
= ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) ) ) ) ) ).
% singleton_Un_iff
thf(fact_857_finite_Ocases,axiom,
! [A2: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ A2 )
=> ( ( A2 != bot_bo4194595901900360558c_fm_i )
=> ~ ! [A7: set_Epistemic_fm_i] :
( ? [A6: epistemic_fm_i] :
( A2
= ( insert7817948997695205106c_fm_i @ A6 @ A7 ) )
=> ~ ( finite3304564979551393739c_fm_i @ A7 ) ) ) ) ).
% finite.cases
thf(fact_858_finite_Ocases,axiom,
! [A2: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A2 )
=> ( ( A2 != bot_bo145720340923748686c_fm_i )
=> ~ ! [A7: set_se3485332733965609186c_fm_i] :
( ? [A6: set_Epistemic_fm_i] :
( A2
= ( insert7698009978809854162c_fm_i @ A6 @ A7 ) )
=> ~ ( finite7933139204641697195c_fm_i @ A7 ) ) ) ) ).
% finite.cases
thf(fact_859_finite_Osimps,axiom,
( finite3304564979551393739c_fm_i
= ( ^ [A4: set_Epistemic_fm_i] :
( ( A4 = bot_bo4194595901900360558c_fm_i )
| ? [A3: set_Epistemic_fm_i,B4: epistemic_fm_i] :
( ( A4
= ( insert7817948997695205106c_fm_i @ B4 @ A3 ) )
& ( finite3304564979551393739c_fm_i @ A3 ) ) ) ) ) ).
% finite.simps
thf(fact_860_finite_Osimps,axiom,
( finite7933139204641697195c_fm_i
= ( ^ [A4: set_se3485332733965609186c_fm_i] :
( ( A4 = bot_bo145720340923748686c_fm_i )
| ? [A3: set_se3485332733965609186c_fm_i,B4: set_Epistemic_fm_i] :
( ( A4
= ( insert7698009978809854162c_fm_i @ B4 @ A3 ) )
& ( finite7933139204641697195c_fm_i @ A3 ) ) ) ) ) ).
% finite.simps
thf(fact_861_finite__induct,axiom,
! [F: set_Epistemic_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( finite3304564979551393739c_fm_i @ F )
=> ( ( P3 @ bot_bo4194595901900360558c_fm_i )
=> ( ! [X3: epistemic_fm_i,F4: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ F4 )
=> ( ~ ( member6642669606046002379c_fm_i @ X3 @ F4 )
=> ( ( P3 @ F4 )
=> ( P3 @ ( insert7817948997695205106c_fm_i @ X3 @ F4 ) ) ) ) )
=> ( P3 @ F ) ) ) ) ).
% finite_induct
thf(fact_862_finite__induct,axiom,
! [F: set_se3485332733965609186c_fm_i,P3: set_se3485332733965609186c_fm_i > $o] :
( ( finite7933139204641697195c_fm_i @ F )
=> ( ( P3 @ bot_bo145720340923748686c_fm_i )
=> ( ! [X3: set_Epistemic_fm_i,F4: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ F4 )
=> ( ~ ( member1104366573291651755c_fm_i @ X3 @ F4 )
=> ( ( P3 @ F4 )
=> ( P3 @ ( insert7698009978809854162c_fm_i @ X3 @ F4 ) ) ) ) )
=> ( P3 @ F ) ) ) ) ).
% finite_induct
thf(fact_863_finite__ne__induct,axiom,
! [F: set_Epistemic_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( finite3304564979551393739c_fm_i @ F )
=> ( ( F != bot_bo4194595901900360558c_fm_i )
=> ( ! [X3: epistemic_fm_i] : ( P3 @ ( insert7817948997695205106c_fm_i @ X3 @ bot_bo4194595901900360558c_fm_i ) )
=> ( ! [X3: epistemic_fm_i,F4: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ F4 )
=> ( ( F4 != bot_bo4194595901900360558c_fm_i )
=> ( ~ ( member6642669606046002379c_fm_i @ X3 @ F4 )
=> ( ( P3 @ F4 )
=> ( P3 @ ( insert7817948997695205106c_fm_i @ X3 @ F4 ) ) ) ) ) )
=> ( P3 @ F ) ) ) ) ) ).
% finite_ne_induct
thf(fact_864_finite__ne__induct,axiom,
! [F: set_se3485332733965609186c_fm_i,P3: set_se3485332733965609186c_fm_i > $o] :
( ( finite7933139204641697195c_fm_i @ F )
=> ( ( F != bot_bo145720340923748686c_fm_i )
=> ( ! [X3: set_Epistemic_fm_i] : ( P3 @ ( insert7698009978809854162c_fm_i @ X3 @ bot_bo145720340923748686c_fm_i ) )
=> ( ! [X3: set_Epistemic_fm_i,F4: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ F4 )
=> ( ( F4 != bot_bo145720340923748686c_fm_i )
=> ( ~ ( member1104366573291651755c_fm_i @ X3 @ F4 )
=> ( ( P3 @ F4 )
=> ( P3 @ ( insert7698009978809854162c_fm_i @ X3 @ F4 ) ) ) ) ) )
=> ( P3 @ F ) ) ) ) ) ).
% finite_ne_induct
thf(fact_865_infinite__finite__induct,axiom,
! [P3: set_Epistemic_fm_i > $o,A: set_Epistemic_fm_i] :
( ! [A7: set_Epistemic_fm_i] :
( ~ ( finite3304564979551393739c_fm_i @ A7 )
=> ( P3 @ A7 ) )
=> ( ( P3 @ bot_bo4194595901900360558c_fm_i )
=> ( ! [X3: epistemic_fm_i,F4: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ F4 )
=> ( ~ ( member6642669606046002379c_fm_i @ X3 @ F4 )
=> ( ( P3 @ F4 )
=> ( P3 @ ( insert7817948997695205106c_fm_i @ X3 @ F4 ) ) ) ) )
=> ( P3 @ A ) ) ) ) ).
% infinite_finite_induct
thf(fact_866_infinite__finite__induct,axiom,
! [P3: set_se3485332733965609186c_fm_i > $o,A: set_se3485332733965609186c_fm_i] :
( ! [A7: set_se3485332733965609186c_fm_i] :
( ~ ( finite7933139204641697195c_fm_i @ A7 )
=> ( P3 @ A7 ) )
=> ( ( P3 @ bot_bo145720340923748686c_fm_i )
=> ( ! [X3: set_Epistemic_fm_i,F4: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ F4 )
=> ( ~ ( member1104366573291651755c_fm_i @ X3 @ F4 )
=> ( ( P3 @ F4 )
=> ( P3 @ ( insert7698009978809854162c_fm_i @ X3 @ F4 ) ) ) ) )
=> ( P3 @ A ) ) ) ) ).
% infinite_finite_induct
thf(fact_867_list_Omap__ident__strong,axiom,
! [T3: list_s8081015415394010888c_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i] :
( ! [Z3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Z3 @ ( set_se200842218512397079c_fm_i @ T3 ) )
=> ( ( F3 @ Z3 )
= Z3 ) )
=> ( ( map_se1449444348732536900c_fm_i @ F3 @ T3 )
= T3 ) ) ).
% list.map_ident_strong
thf(fact_868_list_Omap__ident__strong,axiom,
! [T3: list_Epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i] :
( ! [Z3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ Z3 @ ( set_Epistemic_fm_i2 @ T3 ) )
=> ( ( F3 @ Z3 )
= Z3 ) )
=> ( ( map_Ep2755178516647988292c_fm_i @ F3 @ T3 )
= T3 ) ) ).
% list.map_ident_strong
thf(fact_869_map__idI,axiom,
! [Xs: list_s8081015415394010888c_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i] :
( ! [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ ( set_se200842218512397079c_fm_i @ Xs ) )
=> ( ( F3 @ X3 )
= X3 ) )
=> ( ( map_se1449444348732536900c_fm_i @ F3 @ Xs )
= Xs ) ) ).
% map_idI
thf(fact_870_map__idI,axiom,
! [Xs: list_Epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i] :
( ! [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ ( set_Epistemic_fm_i2 @ Xs ) )
=> ( ( F3 @ X3 )
= X3 ) )
=> ( ( map_Ep2755178516647988292c_fm_i @ F3 @ Xs )
= Xs ) ) ).
% map_idI
thf(fact_871_bot_Oextremum,axiom,
! [A2: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ bot_bo4194595901900360558c_fm_i @ A2 ) ).
% bot.extremum
thf(fact_872_bot_Oextremum__unique,axiom,
! [A2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i )
= ( A2 = bot_bo4194595901900360558c_fm_i ) ) ).
% bot.extremum_unique
thf(fact_873_bot_Oextremum__uniqueI,axiom,
! [A2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i )
=> ( A2 = bot_bo4194595901900360558c_fm_i ) ) ).
% bot.extremum_uniqueI
thf(fact_874_boolean__algebra_Odisj__zero__right,axiom,
! [X: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ X @ bot_bo4194595901900360558c_fm_i )
= X ) ).
% boolean_algebra.disj_zero_right
thf(fact_875_finite_OinsertI,axiom,
! [A: set_Epistemic_fm_i,A2: epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ A )
=> ( finite3304564979551393739c_fm_i @ ( insert7817948997695205106c_fm_i @ A2 @ A ) ) ) ).
% finite.insertI
thf(fact_876_finite_OinsertI,axiom,
! [A: set_se3485332733965609186c_fm_i,A2: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( finite7933139204641697195c_fm_i @ ( insert7698009978809854162c_fm_i @ A2 @ A ) ) ) ).
% finite.insertI
thf(fact_877_insert__subsetI,axiom,
! [X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,X5: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ X @ A )
=> ( ( ord_le5389487502678872194c_fm_i @ X5 @ A )
=> ( ord_le5389487502678872194c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ X5 ) @ A ) ) ) ).
% insert_subsetI
thf(fact_878_insert__subsetI,axiom,
! [X: epistemic_fm_i,A: set_Epistemic_fm_i,X5: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X @ A )
=> ( ( ord_le3843937902494030498c_fm_i @ X5 @ A )
=> ( ord_le3843937902494030498c_fm_i @ ( insert7817948997695205106c_fm_i @ X @ X5 ) @ A ) ) ) ).
% insert_subsetI
thf(fact_879_insert__mono,axiom,
! [C: set_Epistemic_fm_i,D2: set_Epistemic_fm_i,A2: epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ C @ D2 )
=> ( ord_le3843937902494030498c_fm_i @ ( insert7817948997695205106c_fm_i @ A2 @ C ) @ ( insert7817948997695205106c_fm_i @ A2 @ D2 ) ) ) ).
% insert_mono
thf(fact_880_subset__insert,axiom,
! [X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ~ ( member1104366573291651755c_fm_i @ X @ A )
=> ( ( ord_le5389487502678872194c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ B2 ) )
= ( ord_le5389487502678872194c_fm_i @ A @ B2 ) ) ) ).
% subset_insert
thf(fact_881_subset__insert,axiom,
! [X: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ~ ( member6642669606046002379c_fm_i @ X @ A )
=> ( ( ord_le3843937902494030498c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ X @ B2 ) )
= ( ord_le3843937902494030498c_fm_i @ A @ B2 ) ) ) ).
% subset_insert
thf(fact_882_subset__insertI,axiom,
! [B2: set_Epistemic_fm_i,A2: epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ B2 @ ( insert7817948997695205106c_fm_i @ A2 @ B2 ) ) ).
% subset_insertI
thf(fact_883_subset__insertI2,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,B3: epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ord_le3843937902494030498c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ B3 @ B2 ) ) ) ).
% subset_insertI2
thf(fact_884_Int__insert__left,axiom,
! [A2: epistemic_fm_i,C: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ( member6642669606046002379c_fm_i @ A2 @ C )
=> ( ( inf_in3450601097109690352c_fm_i @ ( insert7817948997695205106c_fm_i @ A2 @ B2 ) @ C )
= ( insert7817948997695205106c_fm_i @ A2 @ ( inf_in3450601097109690352c_fm_i @ B2 @ C ) ) ) )
& ( ~ ( member6642669606046002379c_fm_i @ A2 @ C )
=> ( ( inf_in3450601097109690352c_fm_i @ ( insert7817948997695205106c_fm_i @ A2 @ B2 ) @ C )
= ( inf_in3450601097109690352c_fm_i @ B2 @ C ) ) ) ) ).
% Int_insert_left
thf(fact_885_Int__insert__left,axiom,
! [A2: set_Epistemic_fm_i,C: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ( member1104366573291651755c_fm_i @ A2 @ C )
=> ( ( inf_in161960956874937808c_fm_i @ ( insert7698009978809854162c_fm_i @ A2 @ B2 ) @ C )
= ( insert7698009978809854162c_fm_i @ A2 @ ( inf_in161960956874937808c_fm_i @ B2 @ C ) ) ) )
& ( ~ ( member1104366573291651755c_fm_i @ A2 @ C )
=> ( ( inf_in161960956874937808c_fm_i @ ( insert7698009978809854162c_fm_i @ A2 @ B2 ) @ C )
= ( inf_in161960956874937808c_fm_i @ B2 @ C ) ) ) ) ).
% Int_insert_left
thf(fact_886_Int__insert__right,axiom,
! [A2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ( member6642669606046002379c_fm_i @ A2 @ A )
=> ( ( inf_in3450601097109690352c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ A2 @ B2 ) )
= ( insert7817948997695205106c_fm_i @ A2 @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) ) ) )
& ( ~ ( member6642669606046002379c_fm_i @ A2 @ A )
=> ( ( inf_in3450601097109690352c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ A2 @ B2 ) )
= ( inf_in3450601097109690352c_fm_i @ A @ B2 ) ) ) ) ).
% Int_insert_right
thf(fact_887_Int__insert__right,axiom,
! [A2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ( member1104366573291651755c_fm_i @ A2 @ A )
=> ( ( inf_in161960956874937808c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ A2 @ B2 ) )
= ( insert7698009978809854162c_fm_i @ A2 @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) ) ) )
& ( ~ ( member1104366573291651755c_fm_i @ A2 @ A )
=> ( ( inf_in161960956874937808c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ A2 @ B2 ) )
= ( inf_in161960956874937808c_fm_i @ A @ B2 ) ) ) ) ).
% Int_insert_right
thf(fact_888_finite_OemptyI,axiom,
finite3304564979551393739c_fm_i @ bot_bo4194595901900360558c_fm_i ).
% finite.emptyI
thf(fact_889_finite_OemptyI,axiom,
finite7933139204641697195c_fm_i @ bot_bo145720340923748686c_fm_i ).
% finite.emptyI
thf(fact_890_infinite__imp__nonempty,axiom,
! [S: set_Epistemic_fm_i] :
( ~ ( finite3304564979551393739c_fm_i @ S )
=> ( S != bot_bo4194595901900360558c_fm_i ) ) ).
% infinite_imp_nonempty
thf(fact_891_infinite__imp__nonempty,axiom,
! [S: set_se3485332733965609186c_fm_i] :
( ~ ( finite7933139204641697195c_fm_i @ S )
=> ( S != bot_bo145720340923748686c_fm_i ) ) ).
% infinite_imp_nonempty
thf(fact_892_subset__emptyI,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ! [X3: set_Epistemic_fm_i] :
~ ( member1104366573291651755c_fm_i @ X3 @ A )
=> ( ord_le5389487502678872194c_fm_i @ A @ bot_bo145720340923748686c_fm_i ) ) ).
% subset_emptyI
thf(fact_893_subset__emptyI,axiom,
! [A: set_Epistemic_fm_i] :
( ! [X3: epistemic_fm_i] :
~ ( member6642669606046002379c_fm_i @ X3 @ A )
=> ( ord_le3843937902494030498c_fm_i @ A @ bot_bo4194595901900360558c_fm_i ) ) ).
% subset_emptyI
thf(fact_894_Int__emptyI,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ! [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ A )
=> ~ ( member6642669606046002379c_fm_i @ X3 @ B2 ) )
=> ( ( inf_in3450601097109690352c_fm_i @ A @ B2 )
= bot_bo4194595901900360558c_fm_i ) ) ).
% Int_emptyI
thf(fact_895_Int__emptyI,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ! [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
=> ~ ( member1104366573291651755c_fm_i @ X3 @ B2 ) )
=> ( ( inf_in161960956874937808c_fm_i @ A @ B2 )
= bot_bo145720340923748686c_fm_i ) ) ).
% Int_emptyI
thf(fact_896_disjoint__iff,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ( inf_in3450601097109690352c_fm_i @ A @ B2 )
= bot_bo4194595901900360558c_fm_i )
= ( ! [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ A )
=> ~ ( member6642669606046002379c_fm_i @ X2 @ B2 ) ) ) ) ).
% disjoint_iff
thf(fact_897_disjoint__iff,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ( inf_in161960956874937808c_fm_i @ A @ B2 )
= bot_bo145720340923748686c_fm_i )
= ( ! [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A )
=> ~ ( member1104366573291651755c_fm_i @ X2 @ B2 ) ) ) ) ).
% disjoint_iff
thf(fact_898_Int__empty__left,axiom,
! [B2: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ bot_bo145720340923748686c_fm_i @ B2 )
= bot_bo145720340923748686c_fm_i ) ).
% Int_empty_left
thf(fact_899_Int__empty__right,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ A @ bot_bo145720340923748686c_fm_i )
= bot_bo145720340923748686c_fm_i ) ).
% Int_empty_right
thf(fact_900_disjoint__iff__not__equal,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ( inf_in161960956874937808c_fm_i @ A @ B2 )
= bot_bo145720340923748686c_fm_i )
= ( ! [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A )
=> ! [Y3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Y3 @ B2 )
=> ( X2 != Y3 ) ) ) ) ) ).
% disjoint_iff_not_equal
thf(fact_901_Un__empty__left,axiom,
! [B2: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ bot_bo4194595901900360558c_fm_i @ B2 )
= B2 ) ).
% Un_empty_left
thf(fact_902_Un__empty__right,axiom,
! [A: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ A @ bot_bo4194595901900360558c_fm_i )
= A ) ).
% Un_empty_right
thf(fact_903_insert__def,axiom,
( insert7698009978809854162c_fm_i
= ( ^ [A4: set_Epistemic_fm_i] :
( sup_su2582925890723967158c_fm_i
@ ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] : ( X2 = A4 ) ) ) ) ) ).
% insert_def
thf(fact_904_insert__def,axiom,
( insert7817948997695205106c_fm_i
= ( ^ [A4: epistemic_fm_i] :
( sup_su1936195050962291414c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] : ( X2 = A4 ) ) ) ) ) ).
% insert_def
thf(fact_905_maximal__def,axiom,
! [A: epistemic_fm_i > $o,S: set_Epistemic_fm_i] :
( ( maxima3264069618988350929c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ S )
= ( ! [P2: epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ A @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ P2 @ bot_bo4194595901900360558c_fm_i ) @ S ) )
=> ( member6642669606046002379c_fm_i @ P2 @ S ) ) ) ) ).
% maximal_def
thf(fact_906_finite__has__maximal,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ? [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
& ! [Xa: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Xa @ A )
=> ( ( ord_le3843937902494030498c_fm_i @ X3 @ Xa )
=> ( X3 = Xa ) ) ) ) ) ) ).
% finite_has_maximal
thf(fact_907_finite__has__minimal,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ? [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
& ! [Xa: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Xa @ A )
=> ( ( ord_le3843937902494030498c_fm_i @ Xa @ X3 )
=> ( X3 = Xa ) ) ) ) ) ) ).
% finite_has_minimal
thf(fact_908_consistent__consequent,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,P4: epistemic_fm_i,Q: epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( member6642669606046002379c_fm_i @ P4 @ V )
=> ( ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ P4 @ Q ) )
=> ( episte2285483198712856234tent_i @ A @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ Q @ bot_bo4194595901900360558c_fm_i ) @ V ) ) ) ) ) ).
% consistent_consequent
thf(fact_909_consistent__consequent_H,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,P4: epistemic_fm_i,Q: epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( member6642669606046002379c_fm_i @ P4 @ V )
=> ( ! [G4: list_char > $o,H3: epistemic_fm_i > $o] : ( epistemic_eval_i @ G4 @ H3 @ ( epistemic_Imp_i @ P4 @ Q ) )
=> ( episte2285483198712856234tent_i @ A @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ Q @ bot_bo4194595901900360558c_fm_i ) @ V ) ) ) ) ) ).
% consistent_consequent'
thf(fact_910_K__distrib__K__imp,axiom,
! [A: epistemic_fm_i > $o,I: i,G: list_Epistemic_fm_i,Q: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_K_i @ I @ ( epistemic_imply_i @ G @ Q ) ) )
=> ( epistemic_AK_i @ A @ ( epistemic_imply_i @ ( map_Ep2755178516647988292c_fm_i @ ( epistemic_K_i @ I ) @ G ) @ ( epistemic_K_i @ I @ Q ) ) ) ) ).
% K_distrib_K_imp
thf(fact_911_List_Oinsert__def,axiom,
( insert2436375702790685214c_fm_i
= ( ^ [X2: set_Epistemic_fm_i,Xs3: list_s8081015415394010888c_fm_i] : ( if_lis2088983353317256142c_fm_i @ ( member1104366573291651755c_fm_i @ X2 @ ( set_se200842218512397079c_fm_i @ Xs3 ) ) @ Xs3 @ ( cons_s4962720389763977656c_fm_i @ X2 @ Xs3 ) ) ) ) ).
% List.insert_def
thf(fact_912_List_Oinsert__def,axiom,
( insert177310195918387262c_fm_i
= ( ^ [X2: epistemic_fm_i,Xs3: list_Epistemic_fm_i] : ( if_lis3446954105117697518c_fm_i @ ( member6642669606046002379c_fm_i @ X2 @ ( set_Epistemic_fm_i2 @ Xs3 ) ) @ Xs3 @ ( cons_Epistemic_fm_i @ X2 @ Xs3 ) ) ) ) ).
% List.insert_def
thf(fact_913_exists__finite__inconsistent,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,V: set_Epistemic_fm_i] :
( ~ ( episte2285483198712856234tent_i @ A @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) @ bot_bo4194595901900360558c_fm_i ) @ V ) )
=> ~ ! [W: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) @ bot_bo4194595901900360558c_fm_i ) @ W ) @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) @ bot_bo4194595901900360558c_fm_i ) @ V ) )
=> ( ~ ( member6642669606046002379c_fm_i @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) @ W )
=> ( ( finite3304564979551393739c_fm_i @ W )
=> ( episte2285483198712856234tent_i @ A @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) @ bot_bo4194595901900360558c_fm_i ) @ W ) ) ) ) ) ) ).
% exists_finite_inconsistent
thf(fact_914_inconsistent__imply,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,G: list_Epistemic_fm_i] :
( ~ ( episte2285483198712856234tent_i @ A @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ ( epistemic_Imp_i @ P4 @ epistemic_FF_i ) @ bot_bo4194595901900360558c_fm_i ) @ ( set_Epistemic_fm_i2 @ G ) ) )
=> ( epistemic_AK_i @ A @ ( epistemic_imply_i @ G @ P4 ) ) ) ).
% inconsistent_imply
thf(fact_915_K__conjunction__in__mult,axiom,
! [A: epistemic_fm_i > $o,I: i,G: list_Epistemic_fm_i] : ( epistemic_AK_i @ A @ ( epistemic_Imp_i @ ( epistemic_K_i @ I @ ( stalnaker_conjunct_i @ G ) ) @ ( stalnaker_conjunct_i @ ( map_Ep2755178516647988292c_fm_i @ ( epistemic_K_i @ I ) @ G ) ) ) ) ).
% K_conjunction_in_mult
thf(fact_916_extendS__def,axiom,
! [A: epistemic_fm_i > $o,N: epistemic_fm_i,Prev: set_Epistemic_fm_i,S: set_Epistemic_fm_i] :
( ( ( episte2285483198712856234tent_i @ A @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ N @ bot_bo4194595901900360558c_fm_i ) @ Prev ) )
=> ( ( maxima5458213620894205884c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ S @ N @ Prev )
= ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ N @ bot_bo4194595901900360558c_fm_i ) @ Prev ) ) )
& ( ~ ( episte2285483198712856234tent_i @ A @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ N @ bot_bo4194595901900360558c_fm_i ) @ Prev ) )
=> ( ( maxima5458213620894205884c_fm_i @ ( episte2285483198712856234tent_i @ A ) @ S @ N @ Prev )
= Prev ) ) ) ).
% extendS_def
thf(fact_917_bot__set__def,axiom,
( bot_bo4194595901900360558c_fm_i
= ( collec4904205187116291597c_fm_i @ bot_bo2580527446789968623fm_i_o ) ) ).
% bot_set_def
thf(fact_918_bot__set__def,axiom,
( bot_bo145720340923748686c_fm_i
= ( collec3087743281813070829c_fm_i @ bot_bo6089404950617257231fm_i_o ) ) ).
% bot_set_def
thf(fact_919_bot__empty__eq,axiom,
( bot_bo2580527446789968623fm_i_o
= ( ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ bot_bo4194595901900360558c_fm_i ) ) ) ).
% bot_empty_eq
thf(fact_920_bot__empty__eq,axiom,
( bot_bo6089404950617257231fm_i_o
= ( ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ bot_bo145720340923748686c_fm_i ) ) ) ).
% bot_empty_eq
thf(fact_921_is__singletonI_H,axiom,
! [A: set_Epistemic_fm_i] :
( ( A != bot_bo4194595901900360558c_fm_i )
=> ( ! [X3: epistemic_fm_i,Y4: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ A )
=> ( ( member6642669606046002379c_fm_i @ Y4 @ A )
=> ( X3 = Y4 ) ) )
=> ( is_sin4923117429174228502c_fm_i @ A ) ) ) ).
% is_singletonI'
thf(fact_922_is__singletonI_H,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( A != bot_bo145720340923748686c_fm_i )
=> ( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
=> ( ( member1104366573291651755c_fm_i @ Y4 @ A )
=> ( X3 = Y4 ) ) )
=> ( is_sin2358732406619996150c_fm_i @ A ) ) ) ).
% is_singletonI'
thf(fact_923_set__rec,axiom,
( set_Epistemic_fm_i2
= ( rec_li5834409330748533462c_fm_i @ bot_bo4194595901900360558c_fm_i
@ ^ [X2: epistemic_fm_i,Uu2: list_Epistemic_fm_i] : ( insert7817948997695205106c_fm_i @ X2 ) ) ) ).
% set_rec
thf(fact_924_Sup__fin_Oinsert,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ( lattic3744900211830597177c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) )
= ( sup_su1936195050962291414c_fm_i @ X @ ( lattic3744900211830597177c_fm_i @ A ) ) ) ) ) ).
% Sup_fin.insert
thf(fact_925_Inf__fin_Oinsert,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ( lattic8495942116038605215c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) )
= ( inf_in3450601097109690352c_fm_i @ X @ ( lattic8495942116038605215c_fm_i @ A ) ) ) ) ) ).
% Inf_fin.insert
thf(fact_926_Inf__fin_Oinsert,axiom,
! [A: set_se7339729205154126530c_fm_i,X: set_se3485332733965609186c_fm_i] :
( ( finite9087983574947184523c_fm_i @ A )
=> ( ( A != bot_bo4781621276559889198c_fm_i )
=> ( ( lattic7860428167660714879c_fm_i @ ( insert7111703059596746418c_fm_i @ X @ A ) )
= ( inf_in161960956874937808c_fm_i @ X @ ( lattic7860428167660714879c_fm_i @ A ) ) ) ) ) ).
% Inf_fin.insert
thf(fact_927_inf__Sup__absorb,axiom,
! [A: set_se3485332733965609186c_fm_i,A2: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( member1104366573291651755c_fm_i @ A2 @ A )
=> ( ( inf_in3450601097109690352c_fm_i @ A2 @ ( lattic3744900211830597177c_fm_i @ A ) )
= A2 ) ) ) ).
% inf_Sup_absorb
thf(fact_928_inf__Sup__absorb,axiom,
! [A: set_se7339729205154126530c_fm_i,A2: set_se3485332733965609186c_fm_i] :
( ( finite9087983574947184523c_fm_i @ A )
=> ( ( member1461078328125707403c_fm_i @ A2 @ A )
=> ( ( inf_in161960956874937808c_fm_i @ A2 @ ( lattic5920028816461561881c_fm_i @ A ) )
= A2 ) ) ) ).
% inf_Sup_absorb
thf(fact_929_sup__Inf__absorb,axiom,
! [A: set_se3485332733965609186c_fm_i,A2: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( member1104366573291651755c_fm_i @ A2 @ A )
=> ( ( sup_su1936195050962291414c_fm_i @ ( lattic8495942116038605215c_fm_i @ A ) @ A2 )
= A2 ) ) ) ).
% sup_Inf_absorb
thf(fact_930_Inf__fin__le__Sup__fin,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ord_le3843937902494030498c_fm_i @ ( lattic8495942116038605215c_fm_i @ A ) @ ( lattic3744900211830597177c_fm_i @ A ) ) ) ) ).
% Inf_fin_le_Sup_fin
thf(fact_931_Inf__fin_OcoboundedI,axiom,
! [A: set_se3485332733965609186c_fm_i,A2: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( member1104366573291651755c_fm_i @ A2 @ A )
=> ( ord_le3843937902494030498c_fm_i @ ( lattic8495942116038605215c_fm_i @ A ) @ A2 ) ) ) ).
% Inf_fin.coboundedI
thf(fact_932_Sup__fin_OcoboundedI,axiom,
! [A: set_se3485332733965609186c_fm_i,A2: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( member1104366573291651755c_fm_i @ A2 @ A )
=> ( ord_le3843937902494030498c_fm_i @ A2 @ ( lattic3744900211830597177c_fm_i @ A ) ) ) ) ).
% Sup_fin.coboundedI
thf(fact_933_Inf__fin_Oin__idem,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( member1104366573291651755c_fm_i @ X @ A )
=> ( ( inf_in3450601097109690352c_fm_i @ X @ ( lattic8495942116038605215c_fm_i @ A ) )
= ( lattic8495942116038605215c_fm_i @ A ) ) ) ) ).
% Inf_fin.in_idem
thf(fact_934_Inf__fin_Oin__idem,axiom,
! [A: set_se7339729205154126530c_fm_i,X: set_se3485332733965609186c_fm_i] :
( ( finite9087983574947184523c_fm_i @ A )
=> ( ( member1461078328125707403c_fm_i @ X @ A )
=> ( ( inf_in161960956874937808c_fm_i @ X @ ( lattic7860428167660714879c_fm_i @ A ) )
= ( lattic7860428167660714879c_fm_i @ A ) ) ) ) ).
% Inf_fin.in_idem
thf(fact_935_Sup__fin_Oin__idem,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( member1104366573291651755c_fm_i @ X @ A )
=> ( ( sup_su1936195050962291414c_fm_i @ X @ ( lattic3744900211830597177c_fm_i @ A ) )
= ( lattic3744900211830597177c_fm_i @ A ) ) ) ) ).
% Sup_fin.in_idem
thf(fact_936_Sup__fin_Obounded__iff,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ( ord_le3843937902494030498c_fm_i @ ( lattic3744900211830597177c_fm_i @ A ) @ X )
= ( ! [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A )
=> ( ord_le3843937902494030498c_fm_i @ X2 @ X ) ) ) ) ) ) ).
% Sup_fin.bounded_iff
thf(fact_937_Inf__fin_Obounded__iff,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ( ord_le3843937902494030498c_fm_i @ X @ ( lattic8495942116038605215c_fm_i @ A ) )
= ( ! [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A )
=> ( ord_le3843937902494030498c_fm_i @ X @ X2 ) ) ) ) ) ) ).
% Inf_fin.bounded_iff
thf(fact_938_Sup__fin_OboundedI,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ! [A6: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ord_le3843937902494030498c_fm_i @ A6 @ X ) )
=> ( ord_le3843937902494030498c_fm_i @ ( lattic3744900211830597177c_fm_i @ A ) @ X ) ) ) ) ).
% Sup_fin.boundedI
thf(fact_939_Sup__fin_OboundedE,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ( ord_le3843937902494030498c_fm_i @ ( lattic3744900211830597177c_fm_i @ A ) @ X )
=> ! [A8: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A8 @ A )
=> ( ord_le3843937902494030498c_fm_i @ A8 @ X ) ) ) ) ) ).
% Sup_fin.boundedE
thf(fact_940_Inf__fin_OboundedI,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ! [A6: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ord_le3843937902494030498c_fm_i @ X @ A6 ) )
=> ( ord_le3843937902494030498c_fm_i @ X @ ( lattic8495942116038605215c_fm_i @ A ) ) ) ) ) ).
% Inf_fin.boundedI
thf(fact_941_Inf__fin_OboundedE,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ( ord_le3843937902494030498c_fm_i @ X @ ( lattic8495942116038605215c_fm_i @ A ) )
=> ! [A8: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A8 @ A )
=> ( ord_le3843937902494030498c_fm_i @ X @ A8 ) ) ) ) ) ).
% Inf_fin.boundedE
thf(fact_942_Inf__fin_Osubset__imp,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A @ B2 )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ( finite7933139204641697195c_fm_i @ B2 )
=> ( ord_le3843937902494030498c_fm_i @ ( lattic8495942116038605215c_fm_i @ B2 ) @ ( lattic8495942116038605215c_fm_i @ A ) ) ) ) ) ).
% Inf_fin.subset_imp
thf(fact_943_Sup__fin_Osubset__imp,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A @ B2 )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ( finite7933139204641697195c_fm_i @ B2 )
=> ( ord_le3843937902494030498c_fm_i @ ( lattic3744900211830597177c_fm_i @ A ) @ ( lattic3744900211830597177c_fm_i @ B2 ) ) ) ) ) ).
% Sup_fin.subset_imp
thf(fact_944_Inf__fin_Osubset,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( B2 != bot_bo145720340923748686c_fm_i )
=> ( ( ord_le5389487502678872194c_fm_i @ B2 @ A )
=> ( ( inf_in3450601097109690352c_fm_i @ ( lattic8495942116038605215c_fm_i @ B2 ) @ ( lattic8495942116038605215c_fm_i @ A ) )
= ( lattic8495942116038605215c_fm_i @ A ) ) ) ) ) ).
% Inf_fin.subset
thf(fact_945_Inf__fin_Osubset,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i] :
( ( finite9087983574947184523c_fm_i @ A )
=> ( ( B2 != bot_bo4781621276559889198c_fm_i )
=> ( ( ord_le2772500130360476258c_fm_i @ B2 @ A )
=> ( ( inf_in161960956874937808c_fm_i @ ( lattic7860428167660714879c_fm_i @ B2 ) @ ( lattic7860428167660714879c_fm_i @ A ) )
= ( lattic7860428167660714879c_fm_i @ A ) ) ) ) ) ).
% Inf_fin.subset
thf(fact_946_Sup__fin_Osubset,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( B2 != bot_bo145720340923748686c_fm_i )
=> ( ( ord_le5389487502678872194c_fm_i @ B2 @ A )
=> ( ( sup_su1936195050962291414c_fm_i @ ( lattic3744900211830597177c_fm_i @ B2 ) @ ( lattic3744900211830597177c_fm_i @ A ) )
= ( lattic3744900211830597177c_fm_i @ A ) ) ) ) ) ).
% Sup_fin.subset
thf(fact_947_Inf__fin_Oinsert__not__elem,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ~ ( member1104366573291651755c_fm_i @ X @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ( lattic8495942116038605215c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) )
= ( inf_in3450601097109690352c_fm_i @ X @ ( lattic8495942116038605215c_fm_i @ A ) ) ) ) ) ) ).
% Inf_fin.insert_not_elem
thf(fact_948_Inf__fin_Oinsert__not__elem,axiom,
! [A: set_se7339729205154126530c_fm_i,X: set_se3485332733965609186c_fm_i] :
( ( finite9087983574947184523c_fm_i @ A )
=> ( ~ ( member1461078328125707403c_fm_i @ X @ A )
=> ( ( A != bot_bo4781621276559889198c_fm_i )
=> ( ( lattic7860428167660714879c_fm_i @ ( insert7111703059596746418c_fm_i @ X @ A ) )
= ( inf_in161960956874937808c_fm_i @ X @ ( lattic7860428167660714879c_fm_i @ A ) ) ) ) ) ) ).
% Inf_fin.insert_not_elem
thf(fact_949_Inf__fin_Oclosed,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ ( inf_in3450601097109690352c_fm_i @ X3 @ Y4 ) @ ( insert7698009978809854162c_fm_i @ X3 @ ( insert7698009978809854162c_fm_i @ Y4 @ bot_bo145720340923748686c_fm_i ) ) )
=> ( member1104366573291651755c_fm_i @ ( lattic8495942116038605215c_fm_i @ A ) @ A ) ) ) ) ).
% Inf_fin.closed
thf(fact_950_Inf__fin_Oclosed,axiom,
! [A: set_se7339729205154126530c_fm_i] :
( ( finite9087983574947184523c_fm_i @ A )
=> ( ( A != bot_bo4781621276559889198c_fm_i )
=> ( ! [X3: set_se3485332733965609186c_fm_i,Y4: set_se3485332733965609186c_fm_i] : ( member1461078328125707403c_fm_i @ ( inf_in161960956874937808c_fm_i @ X3 @ Y4 ) @ ( insert7111703059596746418c_fm_i @ X3 @ ( insert7111703059596746418c_fm_i @ Y4 @ bot_bo4781621276559889198c_fm_i ) ) )
=> ( member1461078328125707403c_fm_i @ ( lattic7860428167660714879c_fm_i @ A ) @ A ) ) ) ) ).
% Inf_fin.closed
thf(fact_951_Sup__fin_Oinsert__not__elem,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ~ ( member1104366573291651755c_fm_i @ X @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ( lattic3744900211830597177c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) )
= ( sup_su1936195050962291414c_fm_i @ X @ ( lattic3744900211830597177c_fm_i @ A ) ) ) ) ) ) ).
% Sup_fin.insert_not_elem
thf(fact_952_Sup__fin_Oclosed,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ ( sup_su1936195050962291414c_fm_i @ X3 @ Y4 ) @ ( insert7698009978809854162c_fm_i @ X3 @ ( insert7698009978809854162c_fm_i @ Y4 @ bot_bo145720340923748686c_fm_i ) ) )
=> ( member1104366573291651755c_fm_i @ ( lattic3744900211830597177c_fm_i @ A ) @ A ) ) ) ) ).
% Sup_fin.closed
thf(fact_953_Inf__fin_Ounion,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ( finite7933139204641697195c_fm_i @ B2 )
=> ( ( B2 != bot_bo145720340923748686c_fm_i )
=> ( ( lattic8495942116038605215c_fm_i @ ( sup_su2582925890723967158c_fm_i @ A @ B2 ) )
= ( inf_in3450601097109690352c_fm_i @ ( lattic8495942116038605215c_fm_i @ A ) @ ( lattic8495942116038605215c_fm_i @ B2 ) ) ) ) ) ) ) ).
% Inf_fin.union
thf(fact_954_Inf__fin_Ounion,axiom,
! [A: set_se7339729205154126530c_fm_i,B2: set_se7339729205154126530c_fm_i] :
( ( finite9087983574947184523c_fm_i @ A )
=> ( ( A != bot_bo4781621276559889198c_fm_i )
=> ( ( finite9087983574947184523c_fm_i @ B2 )
=> ( ( B2 != bot_bo4781621276559889198c_fm_i )
=> ( ( lattic7860428167660714879c_fm_i @ ( sup_su2317974602288960150c_fm_i @ A @ B2 ) )
= ( inf_in161960956874937808c_fm_i @ ( lattic7860428167660714879c_fm_i @ A ) @ ( lattic7860428167660714879c_fm_i @ B2 ) ) ) ) ) ) ) ).
% Inf_fin.union
thf(fact_955_Sup__fin_Ounion,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( A != bot_bo145720340923748686c_fm_i )
=> ( ( finite7933139204641697195c_fm_i @ B2 )
=> ( ( B2 != bot_bo145720340923748686c_fm_i )
=> ( ( lattic3744900211830597177c_fm_i @ ( sup_su2582925890723967158c_fm_i @ A @ B2 ) )
= ( sup_su1936195050962291414c_fm_i @ ( lattic3744900211830597177c_fm_i @ A ) @ ( lattic3744900211830597177c_fm_i @ B2 ) ) ) ) ) ) ) ).
% Sup_fin.union
thf(fact_956_consistent__disjuncts,axiom,
! [A: epistemic_fm_i > $o,V: set_Epistemic_fm_i,P4: epistemic_fm_i,Q: epistemic_fm_i] :
( ( episte2285483198712856234tent_i @ A @ V )
=> ( ( member6642669606046002379c_fm_i @ ( epistemic_Dis_i @ P4 @ Q ) @ V )
=> ( ( episte2285483198712856234tent_i @ A @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ P4 @ bot_bo4194595901900360558c_fm_i ) @ V ) )
| ( episte2285483198712856234tent_i @ A @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ Q @ bot_bo4194595901900360558c_fm_i ) @ V ) ) ) ) ) ).
% consistent_disjuncts
thf(fact_957_subset__singleton__iff__Uniq,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( ? [A4: set_Epistemic_fm_i] : ( ord_le5389487502678872194c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ A4 @ bot_bo145720340923748686c_fm_i ) ) )
= ( uniq_s5891897140743797767c_fm_i
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ A ) ) ) ).
% subset_singleton_iff_Uniq
thf(fact_958_subset__singleton__iff__Uniq,axiom,
! [A: set_Epistemic_fm_i] :
( ( ? [A4: epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ A4 @ bot_bo4194595901900360558c_fm_i ) ) )
= ( uniq_Epistemic_fm_i
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ A ) ) ) ).
% subset_singleton_iff_Uniq
thf(fact_959_Sup__fin_Oinsert__remove,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( ( ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) )
= bot_bo145720340923748686c_fm_i )
=> ( ( lattic3744900211830597177c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) )
= X ) )
& ( ( ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) )
!= bot_bo145720340923748686c_fm_i )
=> ( ( lattic3744900211830597177c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) )
= ( sup_su1936195050962291414c_fm_i @ X @ ( lattic3744900211830597177c_fm_i @ ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) ) ) ) ) ) ) ) ).
% Sup_fin.insert_remove
thf(fact_960_Diff__iff,axiom,
! [C2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ C2 @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) )
= ( ( member6642669606046002379c_fm_i @ C2 @ A )
& ~ ( member6642669606046002379c_fm_i @ C2 @ B2 ) ) ) ).
% Diff_iff
thf(fact_961_Diff__iff,axiom,
! [C2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ C2 @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) )
= ( ( member1104366573291651755c_fm_i @ C2 @ A )
& ~ ( member1104366573291651755c_fm_i @ C2 @ B2 ) ) ) ).
% Diff_iff
thf(fact_962_DiffI,axiom,
! [C2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ C2 @ A )
=> ( ~ ( member6642669606046002379c_fm_i @ C2 @ B2 )
=> ( member6642669606046002379c_fm_i @ C2 @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) ) ) ) ).
% DiffI
thf(fact_963_DiffI,axiom,
! [C2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ C2 @ A )
=> ( ~ ( member1104366573291651755c_fm_i @ C2 @ B2 )
=> ( member1104366573291651755c_fm_i @ C2 @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) ) ) ) ).
% DiffI
thf(fact_964_finite__Diff,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ A )
=> ( finite3304564979551393739c_fm_i @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) ) ) ).
% finite_Diff
thf(fact_965_finite__Diff,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( finite7933139204641697195c_fm_i @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) ) ) ).
% finite_Diff
thf(fact_966_finite__Diff2,axiom,
! [B2: set_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ B2 )
=> ( ( finite3304564979551393739c_fm_i @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) )
= ( finite3304564979551393739c_fm_i @ A ) ) ) ).
% finite_Diff2
thf(fact_967_finite__Diff2,axiom,
! [B2: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ B2 )
=> ( ( finite7933139204641697195c_fm_i @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) )
= ( finite7933139204641697195c_fm_i @ A ) ) ) ).
% finite_Diff2
thf(fact_968_Diff__insert0,axiom,
! [X: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ~ ( member6642669606046002379c_fm_i @ X @ A )
=> ( ( minus_1543973939109951465c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ X @ B2 ) )
= ( minus_1543973939109951465c_fm_i @ A @ B2 ) ) ) ).
% Diff_insert0
thf(fact_969_Diff__insert0,axiom,
! [X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ~ ( member1104366573291651755c_fm_i @ X @ A )
=> ( ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ B2 ) )
= ( minus_1073301138667672009c_fm_i @ A @ B2 ) ) ) ).
% Diff_insert0
thf(fact_970_insert__Diff1,axiom,
! [X: epistemic_fm_i,B2: set_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X @ B2 )
=> ( ( minus_1543973939109951465c_fm_i @ ( insert7817948997695205106c_fm_i @ X @ A ) @ B2 )
= ( minus_1543973939109951465c_fm_i @ A @ B2 ) ) ) ).
% insert_Diff1
thf(fact_971_insert__Diff1,axiom,
! [X: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ X @ B2 )
=> ( ( minus_1073301138667672009c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) @ B2 )
= ( minus_1073301138667672009c_fm_i @ A @ B2 ) ) ) ).
% insert_Diff1
thf(fact_972_Un__Diff__cancel,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ A @ ( minus_1543973939109951465c_fm_i @ B2 @ A ) )
= ( sup_su1936195050962291414c_fm_i @ A @ B2 ) ) ).
% Un_Diff_cancel
thf(fact_973_Un__Diff__cancel2,axiom,
! [B2: set_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( minus_1543973939109951465c_fm_i @ B2 @ A ) @ A )
= ( sup_su1936195050962291414c_fm_i @ B2 @ A ) ) ).
% Un_Diff_cancel2
thf(fact_974_Diff__eq__empty__iff,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ( minus_1543973939109951465c_fm_i @ A @ B2 )
= bot_bo4194595901900360558c_fm_i )
= ( ord_le3843937902494030498c_fm_i @ A @ B2 ) ) ).
% Diff_eq_empty_iff
thf(fact_975_finite__Diff__insert,axiom,
! [A: set_Epistemic_fm_i,A2: epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ ( minus_1543973939109951465c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ A2 @ B2 ) ) )
= ( finite3304564979551393739c_fm_i @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) ) ) ).
% finite_Diff_insert
thf(fact_976_finite__Diff__insert,axiom,
! [A: set_se3485332733965609186c_fm_i,A2: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ A2 @ B2 ) ) )
= ( finite7933139204641697195c_fm_i @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) ) ) ).
% finite_Diff_insert
thf(fact_977_Diff__disjoint,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ A @ ( minus_1073301138667672009c_fm_i @ B2 @ A ) )
= bot_bo145720340923748686c_fm_i ) ).
% Diff_disjoint
thf(fact_978_set__diff__eq,axiom,
( minus_1543973939109951465c_fm_i
= ( ^ [A3: set_Epistemic_fm_i,B: set_Epistemic_fm_i] :
( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ A3 )
& ~ ( member6642669606046002379c_fm_i @ X2 @ B ) ) ) ) ) ).
% set_diff_eq
thf(fact_979_set__diff__eq,axiom,
( minus_1073301138667672009c_fm_i
= ( ^ [A3: set_se3485332733965609186c_fm_i,B: set_se3485332733965609186c_fm_i] :
( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A3 )
& ~ ( member1104366573291651755c_fm_i @ X2 @ B ) ) ) ) ) ).
% set_diff_eq
thf(fact_980_DiffD2,axiom,
! [C2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ C2 @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) )
=> ~ ( member6642669606046002379c_fm_i @ C2 @ B2 ) ) ).
% DiffD2
thf(fact_981_DiffD2,axiom,
! [C2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ C2 @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) )
=> ~ ( member1104366573291651755c_fm_i @ C2 @ B2 ) ) ).
% DiffD2
thf(fact_982_DiffD1,axiom,
! [C2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ C2 @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) )
=> ( member6642669606046002379c_fm_i @ C2 @ A ) ) ).
% DiffD1
thf(fact_983_DiffD1,axiom,
! [C2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ C2 @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) )
=> ( member1104366573291651755c_fm_i @ C2 @ A ) ) ).
% DiffD1
thf(fact_984_DiffE,axiom,
! [C2: epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ C2 @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) )
=> ~ ( ( member6642669606046002379c_fm_i @ C2 @ A )
=> ( member6642669606046002379c_fm_i @ C2 @ B2 ) ) ) ).
% DiffE
thf(fact_985_DiffE,axiom,
! [C2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ C2 @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) )
=> ~ ( ( member1104366573291651755c_fm_i @ C2 @ A )
=> ( member1104366573291651755c_fm_i @ C2 @ B2 ) ) ) ).
% DiffE
thf(fact_986_fm_Odistinct_I3_J,axiom,
! [X31: epistemic_fm_i,X32: epistemic_fm_i] :
( epistemic_FF_i
!= ( epistemic_Dis_i @ X31 @ X32 ) ) ).
% fm.distinct(3)
thf(fact_987_fm_Odistinct_I23_J,axiom,
! [X31: epistemic_fm_i,X32: epistemic_fm_i,X61: i,X62: epistemic_fm_i] :
( ( epistemic_Dis_i @ X31 @ X32 )
!= ( epistemic_K_i @ X61 @ X62 ) ) ).
% fm.distinct(23)
thf(fact_988_Un__Diff,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( minus_1543973939109951465c_fm_i @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) @ C )
= ( sup_su1936195050962291414c_fm_i @ ( minus_1543973939109951465c_fm_i @ A @ C ) @ ( minus_1543973939109951465c_fm_i @ B2 @ C ) ) ) ).
% Un_Diff
thf(fact_989_Int__Diff,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( minus_1073301138667672009c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) @ C )
= ( inf_in161960956874937808c_fm_i @ A @ ( minus_1073301138667672009c_fm_i @ B2 @ C ) ) ) ).
% Int_Diff
thf(fact_990_Diff__Int2,axiom,
! [A: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( minus_1073301138667672009c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ C ) @ ( inf_in161960956874937808c_fm_i @ B2 @ C ) )
= ( minus_1073301138667672009c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ C ) @ B2 ) ) ).
% Diff_Int2
thf(fact_991_Diff__Diff__Int,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( minus_1073301138667672009c_fm_i @ A @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) )
= ( inf_in161960956874937808c_fm_i @ A @ B2 ) ) ).
% Diff_Diff_Int
thf(fact_992_Diff__Int__distrib,axiom,
! [C: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ C @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) )
= ( minus_1073301138667672009c_fm_i @ ( inf_in161960956874937808c_fm_i @ C @ A ) @ ( inf_in161960956874937808c_fm_i @ C @ B2 ) ) ) ).
% Diff_Int_distrib
thf(fact_993_Diff__Int__distrib2,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) @ C )
= ( minus_1073301138667672009c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ C ) @ ( inf_in161960956874937808c_fm_i @ B2 @ C ) ) ) ).
% Diff_Int_distrib2
thf(fact_994_insert__Diff__if,axiom,
! [X: epistemic_fm_i,B2: set_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( ( member6642669606046002379c_fm_i @ X @ B2 )
=> ( ( minus_1543973939109951465c_fm_i @ ( insert7817948997695205106c_fm_i @ X @ A ) @ B2 )
= ( minus_1543973939109951465c_fm_i @ A @ B2 ) ) )
& ( ~ ( member6642669606046002379c_fm_i @ X @ B2 )
=> ( ( minus_1543973939109951465c_fm_i @ ( insert7817948997695205106c_fm_i @ X @ A ) @ B2 )
= ( insert7817948997695205106c_fm_i @ X @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) ) ) ) ) ).
% insert_Diff_if
thf(fact_995_insert__Diff__if,axiom,
! [X: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( ( member1104366573291651755c_fm_i @ X @ B2 )
=> ( ( minus_1073301138667672009c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) @ B2 )
= ( minus_1073301138667672009c_fm_i @ A @ B2 ) ) )
& ( ~ ( member1104366573291651755c_fm_i @ X @ B2 )
=> ( ( minus_1073301138667672009c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) @ B2 )
= ( insert7698009978809854162c_fm_i @ X @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) ) ) ) ) ).
% insert_Diff_if
thf(fact_996_Diff__mono,axiom,
! [A: set_Epistemic_fm_i,C: set_Epistemic_fm_i,D2: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ C )
=> ( ( ord_le3843937902494030498c_fm_i @ D2 @ B2 )
=> ( ord_le3843937902494030498c_fm_i @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) @ ( minus_1543973939109951465c_fm_i @ C @ D2 ) ) ) ) ).
% Diff_mono
thf(fact_997_Diff__subset,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) @ A ) ).
% Diff_subset
thf(fact_998_double__diff,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ( ord_le3843937902494030498c_fm_i @ B2 @ C )
=> ( ( minus_1543973939109951465c_fm_i @ B2 @ ( minus_1543973939109951465c_fm_i @ C @ A ) )
= A ) ) ) ).
% double_diff
thf(fact_999_Diff__infinite__finite,axiom,
! [T2: set_Epistemic_fm_i,S: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ T2 )
=> ( ~ ( finite3304564979551393739c_fm_i @ S )
=> ~ ( finite3304564979551393739c_fm_i @ ( minus_1543973939109951465c_fm_i @ S @ T2 ) ) ) ) ).
% Diff_infinite_finite
thf(fact_1000_Diff__infinite__finite,axiom,
! [T2: set_se3485332733965609186c_fm_i,S: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ T2 )
=> ( ~ ( finite7933139204641697195c_fm_i @ S )
=> ~ ( finite7933139204641697195c_fm_i @ ( minus_1073301138667672009c_fm_i @ S @ T2 ) ) ) ) ).
% Diff_infinite_finite
thf(fact_1001_diff__shunt__var,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ( ( minus_1543973939109951465c_fm_i @ X @ Y )
= bot_bo4194595901900360558c_fm_i )
= ( ord_le3843937902494030498c_fm_i @ X @ Y ) ) ).
% diff_shunt_var
thf(fact_1002_Diff__insert__absorb,axiom,
! [X: epistemic_fm_i,A: set_Epistemic_fm_i] :
( ~ ( member6642669606046002379c_fm_i @ X @ A )
=> ( ( minus_1543973939109951465c_fm_i @ ( insert7817948997695205106c_fm_i @ X @ A ) @ ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) )
= A ) ) ).
% Diff_insert_absorb
thf(fact_1003_Diff__insert__absorb,axiom,
! [X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ~ ( member1104366573291651755c_fm_i @ X @ A )
=> ( ( minus_1073301138667672009c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) )
= A ) ) ).
% Diff_insert_absorb
thf(fact_1004_insert__Diff,axiom,
! [A2: epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A2 @ A )
=> ( ( insert7817948997695205106c_fm_i @ A2 @ ( minus_1543973939109951465c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i ) ) )
= A ) ) ).
% insert_Diff
thf(fact_1005_insert__Diff,axiom,
! [A2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ A2 @ A )
=> ( ( insert7698009978809854162c_fm_i @ A2 @ ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ A2 @ bot_bo145720340923748686c_fm_i ) ) )
= A ) ) ).
% insert_Diff
thf(fact_1006_subset__Diff__insert,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A @ ( minus_1073301138667672009c_fm_i @ B2 @ ( insert7698009978809854162c_fm_i @ X @ C ) ) )
= ( ( ord_le5389487502678872194c_fm_i @ A @ ( minus_1073301138667672009c_fm_i @ B2 @ C ) )
& ~ ( member1104366573291651755c_fm_i @ X @ A ) ) ) ).
% subset_Diff_insert
thf(fact_1007_subset__Diff__insert,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,X: epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ ( minus_1543973939109951465c_fm_i @ B2 @ ( insert7817948997695205106c_fm_i @ X @ C ) ) )
= ( ( ord_le3843937902494030498c_fm_i @ A @ ( minus_1543973939109951465c_fm_i @ B2 @ C ) )
& ~ ( member6642669606046002379c_fm_i @ X @ A ) ) ) ).
% subset_Diff_insert
thf(fact_1008_Diff__triv,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ( inf_in161960956874937808c_fm_i @ A @ B2 )
= bot_bo145720340923748686c_fm_i )
=> ( ( minus_1073301138667672009c_fm_i @ A @ B2 )
= A ) ) ).
% Diff_triv
thf(fact_1009_Int__Diff__disjoint,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) )
= bot_bo145720340923748686c_fm_i ) ).
% Int_Diff_disjoint
thf(fact_1010_Diff__subset__conv,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) @ C )
= ( ord_le3843937902494030498c_fm_i @ A @ ( sup_su1936195050962291414c_fm_i @ B2 @ C ) ) ) ).
% Diff_subset_conv
thf(fact_1011_Diff__partition,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ( sup_su1936195050962291414c_fm_i @ A @ ( minus_1543973939109951465c_fm_i @ B2 @ A ) )
= B2 ) ) ).
% Diff_partition
thf(fact_1012_Diff__Un,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( minus_1073301138667672009c_fm_i @ A @ ( sup_su2582925890723967158c_fm_i @ B2 @ C ) )
= ( inf_in161960956874937808c_fm_i @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) @ ( minus_1073301138667672009c_fm_i @ A @ C ) ) ) ).
% Diff_Un
thf(fact_1013_Diff__Un,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( minus_1543973939109951465c_fm_i @ A @ ( sup_su1936195050962291414c_fm_i @ B2 @ C ) )
= ( inf_in3450601097109690352c_fm_i @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) @ ( minus_1543973939109951465c_fm_i @ A @ C ) ) ) ).
% Diff_Un
thf(fact_1014_Diff__Int,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,C: set_se3485332733965609186c_fm_i] :
( ( minus_1073301138667672009c_fm_i @ A @ ( inf_in161960956874937808c_fm_i @ B2 @ C ) )
= ( sup_su2582925890723967158c_fm_i @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) @ ( minus_1073301138667672009c_fm_i @ A @ C ) ) ) ).
% Diff_Int
thf(fact_1015_Diff__Int,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,C: set_Epistemic_fm_i] :
( ( minus_1543973939109951465c_fm_i @ A @ ( inf_in3450601097109690352c_fm_i @ B2 @ C ) )
= ( sup_su1936195050962291414c_fm_i @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) @ ( minus_1543973939109951465c_fm_i @ A @ C ) ) ) ).
% Diff_Int
thf(fact_1016_Int__Diff__Un,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) )
= A ) ).
% Int_Diff_Un
thf(fact_1017_Int__Diff__Un,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) )
= A ) ).
% Int_Diff_Un
thf(fact_1018_Un__Diff__Int,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( sup_su2582925890723967158c_fm_i @ ( minus_1073301138667672009c_fm_i @ A @ B2 ) @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) )
= A ) ).
% Un_Diff_Int
thf(fact_1019_Un__Diff__Int,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( minus_1543973939109951465c_fm_i @ A @ B2 ) @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) )
= A ) ).
% Un_Diff_Int
thf(fact_1020_infinite__remove,axiom,
! [S: set_Epistemic_fm_i,A2: epistemic_fm_i] :
( ~ ( finite3304564979551393739c_fm_i @ S )
=> ~ ( finite3304564979551393739c_fm_i @ ( minus_1543973939109951465c_fm_i @ S @ ( insert7817948997695205106c_fm_i @ A2 @ bot_bo4194595901900360558c_fm_i ) ) ) ) ).
% infinite_remove
thf(fact_1021_infinite__remove,axiom,
! [S: set_se3485332733965609186c_fm_i,A2: set_Epistemic_fm_i] :
( ~ ( finite7933139204641697195c_fm_i @ S )
=> ~ ( finite7933139204641697195c_fm_i @ ( minus_1073301138667672009c_fm_i @ S @ ( insert7698009978809854162c_fm_i @ A2 @ bot_bo145720340923748686c_fm_i ) ) ) ) ).
% infinite_remove
thf(fact_1022_infinite__coinduct,axiom,
! [X5: set_Epistemic_fm_i > $o,A: set_Epistemic_fm_i] :
( ( X5 @ A )
=> ( ! [A7: set_Epistemic_fm_i] :
( ( X5 @ A7 )
=> ? [X6: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X6 @ A7 )
& ( ( X5 @ ( minus_1543973939109951465c_fm_i @ A7 @ ( insert7817948997695205106c_fm_i @ X6 @ bot_bo4194595901900360558c_fm_i ) ) )
| ~ ( finite3304564979551393739c_fm_i @ ( minus_1543973939109951465c_fm_i @ A7 @ ( insert7817948997695205106c_fm_i @ X6 @ bot_bo4194595901900360558c_fm_i ) ) ) ) ) )
=> ~ ( finite3304564979551393739c_fm_i @ A ) ) ) ).
% infinite_coinduct
thf(fact_1023_infinite__coinduct,axiom,
! [X5: set_se3485332733965609186c_fm_i > $o,A: set_se3485332733965609186c_fm_i] :
( ( X5 @ A )
=> ( ! [A7: set_se3485332733965609186c_fm_i] :
( ( X5 @ A7 )
=> ? [X6: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X6 @ A7 )
& ( ( X5 @ ( minus_1073301138667672009c_fm_i @ A7 @ ( insert7698009978809854162c_fm_i @ X6 @ bot_bo145720340923748686c_fm_i ) ) )
| ~ ( finite7933139204641697195c_fm_i @ ( minus_1073301138667672009c_fm_i @ A7 @ ( insert7698009978809854162c_fm_i @ X6 @ bot_bo145720340923748686c_fm_i ) ) ) ) ) )
=> ~ ( finite7933139204641697195c_fm_i @ A ) ) ) ).
% infinite_coinduct
thf(fact_1024_finite__empty__induct,axiom,
! [A: set_Epistemic_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( finite3304564979551393739c_fm_i @ A )
=> ( ( P3 @ A )
=> ( ! [A6: epistemic_fm_i,A7: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ A7 )
=> ( ( member6642669606046002379c_fm_i @ A6 @ A7 )
=> ( ( P3 @ A7 )
=> ( P3 @ ( minus_1543973939109951465c_fm_i @ A7 @ ( insert7817948997695205106c_fm_i @ A6 @ bot_bo4194595901900360558c_fm_i ) ) ) ) ) )
=> ( P3 @ bot_bo4194595901900360558c_fm_i ) ) ) ) ).
% finite_empty_induct
thf(fact_1025_finite__empty__induct,axiom,
! [A: set_se3485332733965609186c_fm_i,P3: set_se3485332733965609186c_fm_i > $o] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( P3 @ A )
=> ( ! [A6: set_Epistemic_fm_i,A7: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A7 )
=> ( ( member1104366573291651755c_fm_i @ A6 @ A7 )
=> ( ( P3 @ A7 )
=> ( P3 @ ( minus_1073301138667672009c_fm_i @ A7 @ ( insert7698009978809854162c_fm_i @ A6 @ bot_bo145720340923748686c_fm_i ) ) ) ) ) )
=> ( P3 @ bot_bo145720340923748686c_fm_i ) ) ) ) ).
% finite_empty_induct
thf(fact_1026_Diff__single__insert,axiom,
! [A: set_Epistemic_fm_i,X: epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ ( minus_1543973939109951465c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) ) @ B2 )
=> ( ord_le3843937902494030498c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ X @ B2 ) ) ) ).
% Diff_single_insert
thf(fact_1027_subset__insert__iff,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ B2 ) )
= ( ( ( member1104366573291651755c_fm_i @ X @ A )
=> ( ord_le5389487502678872194c_fm_i @ ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) ) @ B2 ) )
& ( ~ ( member1104366573291651755c_fm_i @ X @ A )
=> ( ord_le5389487502678872194c_fm_i @ A @ B2 ) ) ) ) ).
% subset_insert_iff
thf(fact_1028_subset__insert__iff,axiom,
! [A: set_Epistemic_fm_i,X: epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ X @ B2 ) )
= ( ( ( member6642669606046002379c_fm_i @ X @ A )
=> ( ord_le3843937902494030498c_fm_i @ ( minus_1543973939109951465c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) ) @ B2 ) )
& ( ~ ( member6642669606046002379c_fm_i @ X @ A )
=> ( ord_le3843937902494030498c_fm_i @ A @ B2 ) ) ) ) ).
% subset_insert_iff
thf(fact_1029_K__DisL,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,Ps: list_Epistemic_fm_i,Q: epistemic_fm_i,P7: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_imply_i @ ( cons_Epistemic_fm_i @ P4 @ Ps ) @ Q ) )
=> ( ( epistemic_AK_i @ A @ ( epistemic_imply_i @ ( cons_Epistemic_fm_i @ P7 @ Ps ) @ Q ) )
=> ( epistemic_AK_i @ A @ ( epistemic_imply_i @ ( cons_Epistemic_fm_i @ ( epistemic_Dis_i @ P4 @ P7 ) @ Ps ) @ Q ) ) ) ) ).
% K_DisL
thf(fact_1030_K__DisE,axiom,
! [A: epistemic_fm_i > $o,P4: epistemic_fm_i,G: list_Epistemic_fm_i,R2: epistemic_fm_i,Q: epistemic_fm_i] :
( ( epistemic_AK_i @ A @ ( epistemic_imply_i @ ( cons_Epistemic_fm_i @ P4 @ G ) @ R2 ) )
=> ( ( epistemic_AK_i @ A @ ( epistemic_imply_i @ ( cons_Epistemic_fm_i @ Q @ G ) @ R2 ) )
=> ( ( epistemic_AK_i @ A @ ( epistemic_imply_i @ G @ ( epistemic_Dis_i @ P4 @ Q ) ) )
=> ( epistemic_AK_i @ A @ ( epistemic_imply_i @ G @ R2 ) ) ) ) ) ).
% K_DisE
thf(fact_1031_finite__remove__induct,axiom,
! [B2: set_se3485332733965609186c_fm_i,P3: set_se3485332733965609186c_fm_i > $o] :
( ( finite7933139204641697195c_fm_i @ B2 )
=> ( ( P3 @ bot_bo145720340923748686c_fm_i )
=> ( ! [A7: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A7 )
=> ( ( A7 != bot_bo145720340923748686c_fm_i )
=> ( ( ord_le5389487502678872194c_fm_i @ A7 @ B2 )
=> ( ! [X6: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X6 @ A7 )
=> ( P3 @ ( minus_1073301138667672009c_fm_i @ A7 @ ( insert7698009978809854162c_fm_i @ X6 @ bot_bo145720340923748686c_fm_i ) ) ) )
=> ( P3 @ A7 ) ) ) ) )
=> ( P3 @ B2 ) ) ) ) ).
% finite_remove_induct
thf(fact_1032_finite__remove__induct,axiom,
! [B2: set_Epistemic_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( finite3304564979551393739c_fm_i @ B2 )
=> ( ( P3 @ bot_bo4194595901900360558c_fm_i )
=> ( ! [A7: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ A7 )
=> ( ( A7 != bot_bo4194595901900360558c_fm_i )
=> ( ( ord_le3843937902494030498c_fm_i @ A7 @ B2 )
=> ( ! [X6: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X6 @ A7 )
=> ( P3 @ ( minus_1543973939109951465c_fm_i @ A7 @ ( insert7817948997695205106c_fm_i @ X6 @ bot_bo4194595901900360558c_fm_i ) ) ) )
=> ( P3 @ A7 ) ) ) ) )
=> ( P3 @ B2 ) ) ) ) ).
% finite_remove_induct
thf(fact_1033_remove__induct,axiom,
! [P3: set_se3485332733965609186c_fm_i > $o,B2: set_se3485332733965609186c_fm_i] :
( ( P3 @ bot_bo145720340923748686c_fm_i )
=> ( ( ~ ( finite7933139204641697195c_fm_i @ B2 )
=> ( P3 @ B2 ) )
=> ( ! [A7: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A7 )
=> ( ( A7 != bot_bo145720340923748686c_fm_i )
=> ( ( ord_le5389487502678872194c_fm_i @ A7 @ B2 )
=> ( ! [X6: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X6 @ A7 )
=> ( P3 @ ( minus_1073301138667672009c_fm_i @ A7 @ ( insert7698009978809854162c_fm_i @ X6 @ bot_bo145720340923748686c_fm_i ) ) ) )
=> ( P3 @ A7 ) ) ) ) )
=> ( P3 @ B2 ) ) ) ) ).
% remove_induct
thf(fact_1034_remove__induct,axiom,
! [P3: set_Epistemic_fm_i > $o,B2: set_Epistemic_fm_i] :
( ( P3 @ bot_bo4194595901900360558c_fm_i )
=> ( ( ~ ( finite3304564979551393739c_fm_i @ B2 )
=> ( P3 @ B2 ) )
=> ( ! [A7: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ A7 )
=> ( ( A7 != bot_bo4194595901900360558c_fm_i )
=> ( ( ord_le3843937902494030498c_fm_i @ A7 @ B2 )
=> ( ! [X6: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X6 @ A7 )
=> ( P3 @ ( minus_1543973939109951465c_fm_i @ A7 @ ( insert7817948997695205106c_fm_i @ X6 @ bot_bo4194595901900360558c_fm_i ) ) ) )
=> ( P3 @ A7 ) ) ) ) )
=> ( P3 @ B2 ) ) ) ) ).
% remove_induct
thf(fact_1035_Inf__fin_Oremove,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( member1104366573291651755c_fm_i @ X @ A )
=> ( ( ( ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) )
= bot_bo145720340923748686c_fm_i )
=> ( ( lattic8495942116038605215c_fm_i @ A )
= X ) )
& ( ( ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) )
!= bot_bo145720340923748686c_fm_i )
=> ( ( lattic8495942116038605215c_fm_i @ A )
= ( inf_in3450601097109690352c_fm_i @ X @ ( lattic8495942116038605215c_fm_i @ ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) ) ) ) ) ) ) ) ) ).
% Inf_fin.remove
thf(fact_1036_Inf__fin_Oremove,axiom,
! [A: set_se7339729205154126530c_fm_i,X: set_se3485332733965609186c_fm_i] :
( ( finite9087983574947184523c_fm_i @ A )
=> ( ( member1461078328125707403c_fm_i @ X @ A )
=> ( ( ( ( minus_8476896128438495145c_fm_i @ A @ ( insert7111703059596746418c_fm_i @ X @ bot_bo4781621276559889198c_fm_i ) )
= bot_bo4781621276559889198c_fm_i )
=> ( ( lattic7860428167660714879c_fm_i @ A )
= X ) )
& ( ( ( minus_8476896128438495145c_fm_i @ A @ ( insert7111703059596746418c_fm_i @ X @ bot_bo4781621276559889198c_fm_i ) )
!= bot_bo4781621276559889198c_fm_i )
=> ( ( lattic7860428167660714879c_fm_i @ A )
= ( inf_in161960956874937808c_fm_i @ X @ ( lattic7860428167660714879c_fm_i @ ( minus_8476896128438495145c_fm_i @ A @ ( insert7111703059596746418c_fm_i @ X @ bot_bo4781621276559889198c_fm_i ) ) ) ) ) ) ) ) ) ).
% Inf_fin.remove
thf(fact_1037_Inf__fin_Oinsert__remove,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( ( ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) )
= bot_bo145720340923748686c_fm_i )
=> ( ( lattic8495942116038605215c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) )
= X ) )
& ( ( ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) )
!= bot_bo145720340923748686c_fm_i )
=> ( ( lattic8495942116038605215c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) )
= ( inf_in3450601097109690352c_fm_i @ X @ ( lattic8495942116038605215c_fm_i @ ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) ) ) ) ) ) ) ) ).
% Inf_fin.insert_remove
thf(fact_1038_Inf__fin_Oinsert__remove,axiom,
! [A: set_se7339729205154126530c_fm_i,X: set_se3485332733965609186c_fm_i] :
( ( finite9087983574947184523c_fm_i @ A )
=> ( ( ( ( minus_8476896128438495145c_fm_i @ A @ ( insert7111703059596746418c_fm_i @ X @ bot_bo4781621276559889198c_fm_i ) )
= bot_bo4781621276559889198c_fm_i )
=> ( ( lattic7860428167660714879c_fm_i @ ( insert7111703059596746418c_fm_i @ X @ A ) )
= X ) )
& ( ( ( minus_8476896128438495145c_fm_i @ A @ ( insert7111703059596746418c_fm_i @ X @ bot_bo4781621276559889198c_fm_i ) )
!= bot_bo4781621276559889198c_fm_i )
=> ( ( lattic7860428167660714879c_fm_i @ ( insert7111703059596746418c_fm_i @ X @ A ) )
= ( inf_in161960956874937808c_fm_i @ X @ ( lattic7860428167660714879c_fm_i @ ( minus_8476896128438495145c_fm_i @ A @ ( insert7111703059596746418c_fm_i @ X @ bot_bo4781621276559889198c_fm_i ) ) ) ) ) ) ) ) ).
% Inf_fin.insert_remove
thf(fact_1039_Sup__fin_Oremove,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( member1104366573291651755c_fm_i @ X @ A )
=> ( ( ( ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) )
= bot_bo145720340923748686c_fm_i )
=> ( ( lattic3744900211830597177c_fm_i @ A )
= X ) )
& ( ( ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) )
!= bot_bo145720340923748686c_fm_i )
=> ( ( lattic3744900211830597177c_fm_i @ A )
= ( sup_su1936195050962291414c_fm_i @ X @ ( lattic3744900211830597177c_fm_i @ ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) ) ) ) ) ) ) ) ) ).
% Sup_fin.remove
thf(fact_1040_set__removeAll,axiom,
! [X: epistemic_fm_i,Xs: list_Epistemic_fm_i] :
( ( set_Epistemic_fm_i2 @ ( remove817376155714978094c_fm_i @ X @ Xs ) )
= ( minus_1543973939109951465c_fm_i @ ( set_Epistemic_fm_i2 @ Xs ) @ ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) ) ) ).
% set_removeAll
thf(fact_1041_removeAll__id,axiom,
! [X: set_Epistemic_fm_i,Xs: list_s8081015415394010888c_fm_i] :
( ~ ( member1104366573291651755c_fm_i @ X @ ( set_se200842218512397079c_fm_i @ Xs ) )
=> ( ( remove6226062834164189966c_fm_i @ X @ Xs )
= Xs ) ) ).
% removeAll_id
thf(fact_1042_removeAll__id,axiom,
! [X: epistemic_fm_i,Xs: list_Epistemic_fm_i] :
( ~ ( member6642669606046002379c_fm_i @ X @ ( set_Epistemic_fm_i2 @ Xs ) )
=> ( ( remove817376155714978094c_fm_i @ X @ Xs )
= Xs ) ) ).
% removeAll_id
thf(fact_1043_minus__set__def,axiom,
( minus_1543973939109951465c_fm_i
= ( ^ [A3: set_Epistemic_fm_i,B: set_Epistemic_fm_i] :
( collec4904205187116291597c_fm_i
@ ( minus_6519238007984220724fm_i_o
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ A3 )
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ B ) ) ) ) ) ).
% minus_set_def
thf(fact_1044_minus__set__def,axiom,
( minus_1073301138667672009c_fm_i
= ( ^ [A3: set_se3485332733965609186c_fm_i,B: set_se3485332733965609186c_fm_i] :
( collec3087743281813070829c_fm_i
@ ( minus_5671197887077578836fm_i_o
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ A3 )
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ B ) ) ) ) ) ).
% minus_set_def
thf(fact_1045_fm_Oexhaust,axiom,
! [Y: epistemic_fm_i] :
( ( Y != epistemic_FF_i )
=> ( ! [X23: list_char] :
( Y
!= ( epistemic_Pro_i @ X23 ) )
=> ( ! [X312: epistemic_fm_i,X322: epistemic_fm_i] :
( Y
!= ( epistemic_Dis_i @ X312 @ X322 ) )
=> ( ! [X412: epistemic_fm_i,X422: epistemic_fm_i] :
( Y
!= ( epistemic_Con_i @ X412 @ X422 ) )
=> ( ! [X512: epistemic_fm_i,X522: epistemic_fm_i] :
( Y
!= ( epistemic_Imp_i @ X512 @ X522 ) )
=> ~ ! [X612: i,X622: epistemic_fm_i] :
( Y
!= ( epistemic_K_i @ X612 @ X622 ) ) ) ) ) ) ) ).
% fm.exhaust
thf(fact_1046_member__remove,axiom,
! [X: epistemic_fm_i,Y: epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X @ ( remove5552923401211475591c_fm_i @ Y @ A ) )
= ( ( member6642669606046002379c_fm_i @ X @ A )
& ( X != Y ) ) ) ).
% member_remove
thf(fact_1047_member__remove,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ X @ ( remove1392734035364174951c_fm_i @ Y @ A ) )
= ( ( member1104366573291651755c_fm_i @ X @ A )
& ( X != Y ) ) ) ).
% member_remove
thf(fact_1048_fm_Odistinct_I1_J,axiom,
! [X24: list_char] :
( epistemic_FF_i
!= ( epistemic_Pro_i @ X24 ) ) ).
% fm.distinct(1)
thf(fact_1049_fm_Odistinct_I17_J,axiom,
! [X24: list_char,X61: i,X62: epistemic_fm_i] :
( ( epistemic_Pro_i @ X24 )
!= ( epistemic_K_i @ X61 @ X62 ) ) ).
% fm.distinct(17)
thf(fact_1050_remove__code_I1_J,axiom,
! [X: epistemic_fm_i,Xs: list_Epistemic_fm_i] :
( ( remove5552923401211475591c_fm_i @ X @ ( set_Epistemic_fm_i2 @ Xs ) )
= ( set_Epistemic_fm_i2 @ ( remove817376155714978094c_fm_i @ X @ Xs ) ) ) ).
% remove_code(1)
thf(fact_1051_fm_Orel__induct,axiom,
! [R: i > i > $o,X: epistemic_fm_i,Y: epistemic_fm_i,Q2: epistemic_fm_i > epistemic_fm_i > $o] :
( ( epistemic_rel_fm_i_i @ R @ X @ Y )
=> ( ( Q2 @ epistemic_FF_i @ epistemic_FF_i )
=> ( ! [A22: list_char,B22: list_char] :
( ( A22 = B22 )
=> ( Q2 @ ( epistemic_Pro_i @ A22 ) @ ( epistemic_Pro_i @ B22 ) ) )
=> ( ! [A31: epistemic_fm_i,A32: epistemic_fm_i,B31: epistemic_fm_i,B32: epistemic_fm_i] :
( ( Q2 @ A31 @ B31 )
=> ( ( Q2 @ A32 @ B32 )
=> ( Q2 @ ( epistemic_Dis_i @ A31 @ A32 ) @ ( epistemic_Dis_i @ B31 @ B32 ) ) ) )
=> ( ! [A41: epistemic_fm_i,A42: epistemic_fm_i,B41: epistemic_fm_i,B42: epistemic_fm_i] :
( ( Q2 @ A41 @ B41 )
=> ( ( Q2 @ A42 @ B42 )
=> ( Q2 @ ( epistemic_Con_i @ A41 @ A42 ) @ ( epistemic_Con_i @ B41 @ B42 ) ) ) )
=> ( ! [A51: epistemic_fm_i,A52: epistemic_fm_i,B51: epistemic_fm_i,B52: epistemic_fm_i] :
( ( Q2 @ A51 @ B51 )
=> ( ( Q2 @ A52 @ B52 )
=> ( Q2 @ ( epistemic_Imp_i @ A51 @ A52 ) @ ( epistemic_Imp_i @ B51 @ B52 ) ) ) )
=> ( ! [A61: i,A62: epistemic_fm_i,B61: i,B62: epistemic_fm_i] :
( ( R @ A61 @ B61 )
=> ( ( Q2 @ A62 @ B62 )
=> ( Q2 @ ( epistemic_K_i @ A61 @ A62 ) @ ( epistemic_K_i @ B61 @ B62 ) ) ) )
=> ( Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% fm.rel_induct
thf(fact_1052_fm_Orel__cases,axiom,
! [R: i > i > $o,A2: epistemic_fm_i,B3: epistemic_fm_i] :
( ( epistemic_rel_fm_i_i @ R @ A2 @ B3 )
=> ( ( ( A2 = epistemic_FF_i )
=> ( B3 != epistemic_FF_i ) )
=> ( ! [X3: list_char] :
( ( A2
= ( epistemic_Pro_i @ X3 ) )
=> ! [Y4: list_char] :
( ( B3
= ( epistemic_Pro_i @ Y4 ) )
=> ( X3 != Y4 ) ) )
=> ( ! [X1: epistemic_fm_i,X2a: epistemic_fm_i] :
( ( A2
= ( epistemic_Dis_i @ X1 @ X2a ) )
=> ! [Y1: epistemic_fm_i,Y2a: epistemic_fm_i] :
( ( B3
= ( epistemic_Dis_i @ Y1 @ Y2a ) )
=> ( ( epistemic_rel_fm_i_i @ R @ X1 @ Y1 )
=> ~ ( epistemic_rel_fm_i_i @ R @ X2a @ Y2a ) ) ) )
=> ( ! [X1a: epistemic_fm_i,X2b: epistemic_fm_i] :
( ( A2
= ( epistemic_Con_i @ X1a @ X2b ) )
=> ! [Y1a: epistemic_fm_i,Y2b: epistemic_fm_i] :
( ( B3
= ( epistemic_Con_i @ Y1a @ Y2b ) )
=> ( ( epistemic_rel_fm_i_i @ R @ X1a @ Y1a )
=> ~ ( epistemic_rel_fm_i_i @ R @ X2b @ Y2b ) ) ) )
=> ( ! [X1b: epistemic_fm_i,X2c: epistemic_fm_i] :
( ( A2
= ( epistemic_Imp_i @ X1b @ X2c ) )
=> ! [Y1b: epistemic_fm_i,Y2c: epistemic_fm_i] :
( ( B3
= ( epistemic_Imp_i @ Y1b @ Y2c ) )
=> ( ( epistemic_rel_fm_i_i @ R @ X1b @ Y1b )
=> ~ ( epistemic_rel_fm_i_i @ R @ X2c @ Y2c ) ) ) )
=> ~ ! [X1c: i,X2d: epistemic_fm_i] :
( ( A2
= ( epistemic_K_i @ X1c @ X2d ) )
=> ! [Y1c: i,Y2d: epistemic_fm_i] :
( ( B3
= ( epistemic_K_i @ Y1c @ Y2d ) )
=> ( ( R @ X1c @ Y1c )
=> ~ ( epistemic_rel_fm_i_i @ R @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).
% fm.rel_cases
thf(fact_1053_fm_Octr__transfer_I1_J,axiom,
! [R: i > i > $o] : ( epistemic_rel_fm_i_i @ R @ epistemic_FF_i @ epistemic_FF_i ) ).
% fm.ctr_transfer(1)
thf(fact_1054_fm_Orel__intros_I6_J,axiom,
! [R: i > i > $o,X61: i,Y61: i,X62: epistemic_fm_i,Y62: epistemic_fm_i] :
( ( R @ X61 @ Y61 )
=> ( ( epistemic_rel_fm_i_i @ R @ X62 @ Y62 )
=> ( epistemic_rel_fm_i_i @ R @ ( epistemic_K_i @ X61 @ X62 ) @ ( epistemic_K_i @ Y61 @ Y62 ) ) ) ) ).
% fm.rel_intros(6)
thf(fact_1055_fm_Orel__inject_I6_J,axiom,
! [R: i > i > $o,X61: i,X62: epistemic_fm_i,Y61: i,Y62: epistemic_fm_i] :
( ( epistemic_rel_fm_i_i @ R @ ( epistemic_K_i @ X61 @ X62 ) @ ( epistemic_K_i @ Y61 @ Y62 ) )
= ( ( R @ X61 @ Y61 )
& ( epistemic_rel_fm_i_i @ R @ X62 @ Y62 ) ) ) ).
% fm.rel_inject(6)
thf(fact_1056_fm_Orel__distinct_I10_J,axiom,
! [R: i > i > $o,Y61: i,Y62: epistemic_fm_i] :
~ ( epistemic_rel_fm_i_i @ R @ ( epistemic_K_i @ Y61 @ Y62 ) @ epistemic_FF_i ) ).
% fm.rel_distinct(10)
thf(fact_1057_fm_Orel__distinct_I9_J,axiom,
! [R: i > i > $o,Y61: i,Y62: epistemic_fm_i] :
~ ( epistemic_rel_fm_i_i @ R @ epistemic_FF_i @ ( epistemic_K_i @ Y61 @ Y62 ) ) ).
% fm.rel_distinct(9)
thf(fact_1058_MCS_Omaximal__def,axiom,
! [Consistent: set_se3485332733965609186c_fm_i > $o,S: set_se3485332733965609186c_fm_i] :
( ( maxima5540402109999912942c_fm_i @ Consistent )
=> ( ( maxima7741914846562630577c_fm_i @ Consistent @ S )
= ( ! [P2: set_Epistemic_fm_i] :
( ( Consistent @ ( sup_su2582925890723967158c_fm_i @ ( insert7698009978809854162c_fm_i @ P2 @ bot_bo145720340923748686c_fm_i ) @ S ) )
=> ( member1104366573291651755c_fm_i @ P2 @ S ) ) ) ) ) ).
% MCS.maximal_def
thf(fact_1059_MCS_Omaximal__def,axiom,
! [Consistent: set_Epistemic_fm_i > $o,S: set_Epistemic_fm_i] :
( ( maxima1924290493700099598c_fm_i @ Consistent )
=> ( ( maxima3264069618988350929c_fm_i @ Consistent @ S )
= ( ! [P2: epistemic_fm_i] :
( ( Consistent @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ P2 @ bot_bo4194595901900360558c_fm_i ) @ S ) )
=> ( member6642669606046002379c_fm_i @ P2 @ S ) ) ) ) ) ).
% MCS.maximal_def
thf(fact_1060_MCS__axioms,axiom,
! [A: epistemic_fm_i > $o] : ( maxima1924290493700099598c_fm_i @ ( episte2285483198712856234tent_i @ A ) ) ).
% MCS_axioms
thf(fact_1061_MCS_Omaximal_Ocong,axiom,
maxima3264069618988350929c_fm_i = maxima3264069618988350929c_fm_i ).
% MCS.maximal.cong
thf(fact_1062_is__empty__set,axiom,
! [Xs: list_Epistemic_fm_i] :
( ( is_emp7643256682846039796c_fm_i @ ( set_Epistemic_fm_i2 @ Xs ) )
= ( null_Epistemic_fm_i @ Xs ) ) ).
% is_empty_set
thf(fact_1063_MCS__Lim__Ord_OextendS__def,axiom,
! [R2: set_Pr4658907567593863815c_fm_i,Consistent: set_Epistemic_fm_i > $o,N: epistemic_fm_i,Prev: set_Epistemic_fm_i,S: set_Epistemic_fm_i] :
( ( maxima8116622286610175645c_fm_i @ R2 @ Consistent )
=> ( ( ( Consistent @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ N @ bot_bo4194595901900360558c_fm_i ) @ Prev ) )
=> ( ( maxima5458213620894205884c_fm_i @ Consistent @ S @ N @ Prev )
= ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ N @ bot_bo4194595901900360558c_fm_i ) @ Prev ) ) )
& ( ~ ( Consistent @ ( sup_su1936195050962291414c_fm_i @ ( insert7817948997695205106c_fm_i @ N @ bot_bo4194595901900360558c_fm_i ) @ Prev ) )
=> ( ( maxima5458213620894205884c_fm_i @ Consistent @ S @ N @ Prev )
= Prev ) ) ) ) ).
% MCS_Lim_Ord.extendS_def
thf(fact_1064_MCS__Lim__Ord_Oconsistent__hereditary,axiom,
! [R2: set_Pr4658907567593863815c_fm_i,Consistent: set_Epistemic_fm_i > $o,S: set_Epistemic_fm_i,S2: set_Epistemic_fm_i] :
( ( maxima8116622286610175645c_fm_i @ R2 @ Consistent )
=> ( ( Consistent @ S )
=> ( ( ord_le3843937902494030498c_fm_i @ S2 @ S )
=> ( Consistent @ S2 ) ) ) ) ).
% MCS_Lim_Ord.consistent_hereditary
thf(fact_1065_MCS__Lim__Ord_Oinconsistent__finite,axiom,
! [R2: set_Pr3972831103112126087c_fm_i,Consistent: set_se3485332733965609186c_fm_i > $o,S: set_se3485332733965609186c_fm_i] :
( ( maxima9073963094320882813c_fm_i @ R2 @ Consistent )
=> ( ~ ( Consistent @ S )
=> ? [S3: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ S3 @ S )
& ( finite7933139204641697195c_fm_i @ S3 )
& ~ ( Consistent @ S3 ) ) ) ) ).
% MCS_Lim_Ord.inconsistent_finite
thf(fact_1066_MCS__Lim__Ord_Oinconsistent__finite,axiom,
! [R2: set_Pr4658907567593863815c_fm_i,Consistent: set_Epistemic_fm_i > $o,S: set_Epistemic_fm_i] :
( ( maxima8116622286610175645c_fm_i @ R2 @ Consistent )
=> ( ~ ( Consistent @ S )
=> ? [S3: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ S3 @ S )
& ( finite3304564979551393739c_fm_i @ S3 )
& ~ ( Consistent @ S3 ) ) ) ) ).
% MCS_Lim_Ord.inconsistent_finite
thf(fact_1067_Set__filter__fold,axiom,
! [A: set_Epistemic_fm_i,P3: epistemic_fm_i > $o] :
( ( finite3304564979551393739c_fm_i @ A )
=> ( ( filter6053540608743173075c_fm_i @ P3 @ A )
= ( finite6274917443777430184c_fm_i
@ ^ [X2: epistemic_fm_i,A9: set_Epistemic_fm_i] : ( if_set2943457721768014536c_fm_i @ ( P3 @ X2 ) @ ( insert7817948997695205106c_fm_i @ X2 @ A9 ) @ A9 )
@ bot_bo4194595901900360558c_fm_i
@ A ) ) ) ).
% Set_filter_fold
thf(fact_1068_Set__filter__fold,axiom,
! [A: set_se3485332733965609186c_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( filter8450032351001387443c_fm_i @ P3 @ A )
= ( finite28738107572603560c_fm_i
@ ^ [X2: set_Epistemic_fm_i,A9: set_se3485332733965609186c_fm_i] : ( if_set3792857027667890344c_fm_i @ ( P3 @ X2 ) @ ( insert7698009978809854162c_fm_i @ X2 @ A9 ) @ A9 )
@ bot_bo145720340923748686c_fm_i
@ A ) ) ) ).
% Set_filter_fold
thf(fact_1069_fm_Oset__cases,axiom,
! [E: epistemic_fm_i,A2: episte1308613106011496894c_fm_i] :
( ( member6642669606046002379c_fm_i @ E @ ( episte9089240992906287960c_fm_i @ A2 ) )
=> ( ! [Z1: episte1308613106011496894c_fm_i] :
( ? [Z22: episte1308613106011496894c_fm_i] :
( A2
= ( episte6088726798904853267c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member6642669606046002379c_fm_i @ E @ ( episte9089240992906287960c_fm_i @ Z1 ) ) )
=> ( ! [Z1: episte1308613106011496894c_fm_i,Z22: episte1308613106011496894c_fm_i] :
( ( A2
= ( episte6088726798904853267c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member6642669606046002379c_fm_i @ E @ ( episte9089240992906287960c_fm_i @ Z22 ) ) )
=> ( ! [Z1: episte1308613106011496894c_fm_i] :
( ? [Z22: episte1308613106011496894c_fm_i] :
( A2
= ( episte3685526521632971807c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member6642669606046002379c_fm_i @ E @ ( episte9089240992906287960c_fm_i @ Z1 ) ) )
=> ( ! [Z1: episte1308613106011496894c_fm_i,Z22: episte1308613106011496894c_fm_i] :
( ( A2
= ( episte3685526521632971807c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member6642669606046002379c_fm_i @ E @ ( episte9089240992906287960c_fm_i @ Z22 ) ) )
=> ( ! [Z1: episte1308613106011496894c_fm_i] :
( ? [Z22: episte1308613106011496894c_fm_i] :
( A2
= ( episte260752253203357973c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member6642669606046002379c_fm_i @ E @ ( episte9089240992906287960c_fm_i @ Z1 ) ) )
=> ( ! [Z1: episte1308613106011496894c_fm_i,Z22: episte1308613106011496894c_fm_i] :
( ( A2
= ( episte260752253203357973c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member6642669606046002379c_fm_i @ E @ ( episte9089240992906287960c_fm_i @ Z22 ) ) )
=> ( ! [Z22: episte1308613106011496894c_fm_i] :
( A2
!= ( episte5657488666450005526c_fm_i @ E @ Z22 ) )
=> ~ ! [Z1: epistemic_fm_i,Z22: episte1308613106011496894c_fm_i] :
( ( A2
= ( episte5657488666450005526c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member6642669606046002379c_fm_i @ E @ ( episte9089240992906287960c_fm_i @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).
% fm.set_cases
thf(fact_1070_fm_Oset__cases,axiom,
! [E: set_Epistemic_fm_i,A2: episte4276422356747265950c_fm_i] :
( ( member1104366573291651755c_fm_i @ E @ ( episte6795552051664633144c_fm_i @ A2 ) )
=> ( ! [Z1: episte4276422356747265950c_fm_i] :
( ? [Z22: episte4276422356747265950c_fm_i] :
( A2
= ( episte535002356104313075c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member1104366573291651755c_fm_i @ E @ ( episte6795552051664633144c_fm_i @ Z1 ) ) )
=> ( ! [Z1: episte4276422356747265950c_fm_i,Z22: episte4276422356747265950c_fm_i] :
( ( A2
= ( episte535002356104313075c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member1104366573291651755c_fm_i @ E @ ( episte6795552051664633144c_fm_i @ Z22 ) ) )
=> ( ! [Z1: episte4276422356747265950c_fm_i] :
( ? [Z22: episte4276422356747265950c_fm_i] :
( A2
= ( episte64184772710425087c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member1104366573291651755c_fm_i @ E @ ( episte6795552051664633144c_fm_i @ Z1 ) ) )
=> ( ! [Z1: episte4276422356747265950c_fm_i,Z22: episte4276422356747265950c_fm_i] :
( ( A2
= ( episte64184772710425087c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member1104366573291651755c_fm_i @ E @ ( episte6795552051664633144c_fm_i @ Z22 ) ) )
=> ( ! [Z1: episte4276422356747265950c_fm_i] :
( ? [Z22: episte4276422356747265950c_fm_i] :
( A2
= ( episte5768433346120044277c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member1104366573291651755c_fm_i @ E @ ( episte6795552051664633144c_fm_i @ Z1 ) ) )
=> ( ! [Z1: episte4276422356747265950c_fm_i,Z22: episte4276422356747265950c_fm_i] :
( ( A2
= ( episte5768433346120044277c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member1104366573291651755c_fm_i @ E @ ( episte6795552051664633144c_fm_i @ Z22 ) ) )
=> ( ! [Z22: episte4276422356747265950c_fm_i] :
( A2
!= ( episte3581967596712343542c_fm_i @ E @ Z22 ) )
=> ~ ! [Z1: set_Epistemic_fm_i,Z22: episte4276422356747265950c_fm_i] :
( ( A2
= ( episte3581967596712343542c_fm_i @ Z1 @ Z22 ) )
=> ~ ( member1104366573291651755c_fm_i @ E @ ( episte6795552051664633144c_fm_i @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).
% fm.set_cases
thf(fact_1071_fm_Oset__cases,axiom,
! [E: i,A2: epistemic_fm_i] :
( ( member_i @ E @ ( epistemic_set_fm_i @ A2 ) )
=> ( ! [Z1: epistemic_fm_i] :
( ? [Z22: epistemic_fm_i] :
( A2
= ( epistemic_Dis_i @ Z1 @ Z22 ) )
=> ~ ( member_i @ E @ ( epistemic_set_fm_i @ Z1 ) ) )
=> ( ! [Z1: epistemic_fm_i,Z22: epistemic_fm_i] :
( ( A2
= ( epistemic_Dis_i @ Z1 @ Z22 ) )
=> ~ ( member_i @ E @ ( epistemic_set_fm_i @ Z22 ) ) )
=> ( ! [Z1: epistemic_fm_i] :
( ? [Z22: epistemic_fm_i] :
( A2
= ( epistemic_Con_i @ Z1 @ Z22 ) )
=> ~ ( member_i @ E @ ( epistemic_set_fm_i @ Z1 ) ) )
=> ( ! [Z1: epistemic_fm_i,Z22: epistemic_fm_i] :
( ( A2
= ( epistemic_Con_i @ Z1 @ Z22 ) )
=> ~ ( member_i @ E @ ( epistemic_set_fm_i @ Z22 ) ) )
=> ( ! [Z1: epistemic_fm_i] :
( ? [Z22: epistemic_fm_i] :
( A2
= ( epistemic_Imp_i @ Z1 @ Z22 ) )
=> ~ ( member_i @ E @ ( epistemic_set_fm_i @ Z1 ) ) )
=> ( ! [Z1: epistemic_fm_i,Z22: epistemic_fm_i] :
( ( A2
= ( epistemic_Imp_i @ Z1 @ Z22 ) )
=> ~ ( member_i @ E @ ( epistemic_set_fm_i @ Z22 ) ) )
=> ( ! [Z22: epistemic_fm_i] :
( A2
!= ( epistemic_K_i @ E @ Z22 ) )
=> ~ ! [Z1: i,Z22: epistemic_fm_i] :
( ( A2
= ( epistemic_K_i @ Z1 @ Z22 ) )
=> ~ ( member_i @ E @ ( epistemic_set_fm_i @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).
% fm.set_cases
thf(fact_1072_fm_Osimps_I95_J,axiom,
! [X61: i,X62: epistemic_fm_i] :
( ( epistemic_set_fm_i @ ( epistemic_K_i @ X61 @ X62 ) )
= ( insert_i @ X61 @ ( epistemic_set_fm_i @ X62 ) ) ) ).
% fm.simps(95)
thf(fact_1073_fm_Orel__cong,axiom,
! [X: episte1308613106011496894c_fm_i,Ya: episte1308613106011496894c_fm_i,Y: episte1308613106011496894c_fm_i,Xa2: episte1308613106011496894c_fm_i,R: epistemic_fm_i > epistemic_fm_i > $o,Ra: epistemic_fm_i > epistemic_fm_i > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: epistemic_fm_i,Yb: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ Z3 @ ( episte9089240992906287960c_fm_i @ Ya ) )
=> ( ( member6642669606046002379c_fm_i @ Yb @ ( episte9089240992906287960c_fm_i @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( episte3445413862081925600c_fm_i @ R @ X @ Y )
= ( episte3445413862081925600c_fm_i @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% fm.rel_cong
thf(fact_1074_fm_Orel__cong,axiom,
! [X: episte1308613106011496894c_fm_i,Ya: episte1308613106011496894c_fm_i,Y: episte4276422356747265950c_fm_i,Xa2: episte4276422356747265950c_fm_i,R: epistemic_fm_i > set_Epistemic_fm_i > $o,Ra: epistemic_fm_i > set_Epistemic_fm_i > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: epistemic_fm_i,Yb: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ Z3 @ ( episte9089240992906287960c_fm_i @ Ya ) )
=> ( ( member1104366573291651755c_fm_i @ Yb @ ( episte6795552051664633144c_fm_i @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( episte6079896185807049664c_fm_i @ R @ X @ Y )
= ( episte6079896185807049664c_fm_i @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% fm.rel_cong
thf(fact_1075_fm_Orel__cong,axiom,
! [X: episte4276422356747265950c_fm_i,Ya: episte4276422356747265950c_fm_i,Y: episte1308613106011496894c_fm_i,Xa2: episte1308613106011496894c_fm_i,R: set_Epistemic_fm_i > epistemic_fm_i > $o,Ra: set_Epistemic_fm_i > epistemic_fm_i > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: set_Epistemic_fm_i,Yb: epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Z3 @ ( episte6795552051664633144c_fm_i @ Ya ) )
=> ( ( member6642669606046002379c_fm_i @ Yb @ ( episte9089240992906287960c_fm_i @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( episte3976198365643398144c_fm_i @ R @ X @ Y )
= ( episte3976198365643398144c_fm_i @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% fm.rel_cong
thf(fact_1076_fm_Orel__cong,axiom,
! [X: episte4276422356747265950c_fm_i,Ya: episte4276422356747265950c_fm_i,Y: episte4276422356747265950c_fm_i,Xa2: episte4276422356747265950c_fm_i,R: set_Epistemic_fm_i > set_Epistemic_fm_i > $o,Ra: set_Epistemic_fm_i > set_Epistemic_fm_i > $o] :
( ( X = Ya )
=> ( ( Y = Xa2 )
=> ( ! [Z3: set_Epistemic_fm_i,Yb: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Z3 @ ( episte6795552051664633144c_fm_i @ Ya ) )
=> ( ( member1104366573291651755c_fm_i @ Yb @ ( episte6795552051664633144c_fm_i @ Xa2 ) )
=> ( ( R @ Z3 @ Yb )
= ( Ra @ Z3 @ Yb ) ) ) )
=> ( ( episte2362472030976073184c_fm_i @ R @ X @ Y )
= ( episte2362472030976073184c_fm_i @ Ra @ Ya @ Xa2 ) ) ) ) ) ).
% fm.rel_cong
thf(fact_1077_fm_Orel__mono__strong,axiom,
! [R: epistemic_fm_i > epistemic_fm_i > $o,X: episte1308613106011496894c_fm_i,Y: episte1308613106011496894c_fm_i,Ra: epistemic_fm_i > epistemic_fm_i > $o] :
( ( episte3445413862081925600c_fm_i @ R @ X @ Y )
=> ( ! [Z3: epistemic_fm_i,Yb: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ Z3 @ ( episte9089240992906287960c_fm_i @ X ) )
=> ( ( member6642669606046002379c_fm_i @ Yb @ ( episte9089240992906287960c_fm_i @ Y ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( episte3445413862081925600c_fm_i @ Ra @ X @ Y ) ) ) ).
% fm.rel_mono_strong
thf(fact_1078_fm_Orel__mono__strong,axiom,
! [R: epistemic_fm_i > set_Epistemic_fm_i > $o,X: episte1308613106011496894c_fm_i,Y: episte4276422356747265950c_fm_i,Ra: epistemic_fm_i > set_Epistemic_fm_i > $o] :
( ( episte6079896185807049664c_fm_i @ R @ X @ Y )
=> ( ! [Z3: epistemic_fm_i,Yb: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ Z3 @ ( episte9089240992906287960c_fm_i @ X ) )
=> ( ( member1104366573291651755c_fm_i @ Yb @ ( episte6795552051664633144c_fm_i @ Y ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( episte6079896185807049664c_fm_i @ Ra @ X @ Y ) ) ) ).
% fm.rel_mono_strong
thf(fact_1079_fm_Orel__mono__strong,axiom,
! [R: set_Epistemic_fm_i > epistemic_fm_i > $o,X: episte4276422356747265950c_fm_i,Y: episte1308613106011496894c_fm_i,Ra: set_Epistemic_fm_i > epistemic_fm_i > $o] :
( ( episte3976198365643398144c_fm_i @ R @ X @ Y )
=> ( ! [Z3: set_Epistemic_fm_i,Yb: epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Z3 @ ( episte6795552051664633144c_fm_i @ X ) )
=> ( ( member6642669606046002379c_fm_i @ Yb @ ( episte9089240992906287960c_fm_i @ Y ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( episte3976198365643398144c_fm_i @ Ra @ X @ Y ) ) ) ).
% fm.rel_mono_strong
thf(fact_1080_fm_Orel__mono__strong,axiom,
! [R: set_Epistemic_fm_i > set_Epistemic_fm_i > $o,X: episte4276422356747265950c_fm_i,Y: episte4276422356747265950c_fm_i,Ra: set_Epistemic_fm_i > set_Epistemic_fm_i > $o] :
( ( episte2362472030976073184c_fm_i @ R @ X @ Y )
=> ( ! [Z3: set_Epistemic_fm_i,Yb: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Z3 @ ( episte6795552051664633144c_fm_i @ X ) )
=> ( ( member1104366573291651755c_fm_i @ Yb @ ( episte6795552051664633144c_fm_i @ Y ) )
=> ( ( R @ Z3 @ Yb )
=> ( Ra @ Z3 @ Yb ) ) ) )
=> ( episte2362472030976073184c_fm_i @ Ra @ X @ Y ) ) ) ).
% fm.rel_mono_strong
thf(fact_1081_fm_Orel__refl__strong,axiom,
! [X: episte1308613106011496894c_fm_i,Ra: epistemic_fm_i > epistemic_fm_i > $o] :
( ! [Z3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ Z3 @ ( episte9089240992906287960c_fm_i @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( episte3445413862081925600c_fm_i @ Ra @ X @ X ) ) ).
% fm.rel_refl_strong
thf(fact_1082_fm_Orel__refl__strong,axiom,
! [X: episte4276422356747265950c_fm_i,Ra: set_Epistemic_fm_i > set_Epistemic_fm_i > $o] :
( ! [Z3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Z3 @ ( episte6795552051664633144c_fm_i @ X ) )
=> ( Ra @ Z3 @ Z3 ) )
=> ( episte2362472030976073184c_fm_i @ Ra @ X @ X ) ) ).
% fm.rel_refl_strong
thf(fact_1083_fold__closed__eq,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i > epistemic_fm_i,G5: epistemic_fm_i > epistemic_fm_i > epistemic_fm_i,Z: epistemic_fm_i] :
( ! [A6: epistemic_fm_i,B7: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ( ( member6642669606046002379c_fm_i @ B7 @ B2 )
=> ( ( F3 @ A6 @ B7 )
= ( G5 @ A6 @ B7 ) ) ) )
=> ( ! [A6: epistemic_fm_i,B7: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ( ( member6642669606046002379c_fm_i @ B7 @ B2 )
=> ( member6642669606046002379c_fm_i @ ( G5 @ A6 @ B7 ) @ B2 ) ) )
=> ( ( member6642669606046002379c_fm_i @ Z @ B2 )
=> ( ( finite2135258021436235976c_fm_i @ F3 @ Z @ A )
= ( finite2135258021436235976c_fm_i @ G5 @ Z @ A ) ) ) ) ) ).
% fold_closed_eq
thf(fact_1084_fold__closed__eq,axiom,
! [A: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i,F3: epistemic_fm_i > set_Epistemic_fm_i > set_Epistemic_fm_i,G5: epistemic_fm_i > set_Epistemic_fm_i > set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ! [A6: epistemic_fm_i,B7: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ( ( member1104366573291651755c_fm_i @ B7 @ B2 )
=> ( ( F3 @ A6 @ B7 )
= ( G5 @ A6 @ B7 ) ) ) )
=> ( ! [A6: epistemic_fm_i,B7: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ( ( member1104366573291651755c_fm_i @ B7 @ B2 )
=> ( member1104366573291651755c_fm_i @ ( G5 @ A6 @ B7 ) @ B2 ) ) )
=> ( ( member1104366573291651755c_fm_i @ Z @ B2 )
=> ( ( finite6274917443777430184c_fm_i @ F3 @ Z @ A )
= ( finite6274917443777430184c_fm_i @ G5 @ Z @ A ) ) ) ) ) ).
% fold_closed_eq
thf(fact_1085_fold__closed__eq,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_Epistemic_fm_i,F3: set_Epistemic_fm_i > epistemic_fm_i > epistemic_fm_i,G5: set_Epistemic_fm_i > epistemic_fm_i > epistemic_fm_i,Z: epistemic_fm_i] :
( ! [A6: set_Epistemic_fm_i,B7: epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ( member6642669606046002379c_fm_i @ B7 @ B2 )
=> ( ( F3 @ A6 @ B7 )
= ( G5 @ A6 @ B7 ) ) ) )
=> ( ! [A6: set_Epistemic_fm_i,B7: epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ( member6642669606046002379c_fm_i @ B7 @ B2 )
=> ( member6642669606046002379c_fm_i @ ( G5 @ A6 @ B7 ) @ B2 ) ) )
=> ( ( member6642669606046002379c_fm_i @ Z @ B2 )
=> ( ( finite4171219623613778664c_fm_i @ F3 @ Z @ A )
= ( finite4171219623613778664c_fm_i @ G5 @ Z @ A ) ) ) ) ) ).
% fold_closed_eq
thf(fact_1086_fold__closed__eq,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i > set_Epistemic_fm_i,G5: set_Epistemic_fm_i > set_Epistemic_fm_i > set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ! [A6: set_Epistemic_fm_i,B7: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ( member1104366573291651755c_fm_i @ B7 @ B2 )
=> ( ( F3 @ A6 @ B7 )
= ( G5 @ A6 @ B7 ) ) ) )
=> ( ! [A6: set_Epistemic_fm_i,B7: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ( member1104366573291651755c_fm_i @ B7 @ B2 )
=> ( member1104366573291651755c_fm_i @ ( G5 @ A6 @ B7 ) @ B2 ) ) )
=> ( ( member1104366573291651755c_fm_i @ Z @ B2 )
=> ( ( finite2237691025846545608c_fm_i @ F3 @ Z @ A )
= ( finite2237691025846545608c_fm_i @ G5 @ Z @ A ) ) ) ) ) ).
% fold_closed_eq
thf(fact_1087_fm_Oset__intros_I4_J,axiom,
! [Yd: epistemic_fm_i,X42: episte1308613106011496894c_fm_i,X41: episte1308613106011496894c_fm_i] :
( ( member6642669606046002379c_fm_i @ Yd @ ( episte9089240992906287960c_fm_i @ X42 ) )
=> ( member6642669606046002379c_fm_i @ Yd @ ( episte9089240992906287960c_fm_i @ ( episte3685526521632971807c_fm_i @ X41 @ X42 ) ) ) ) ).
% fm.set_intros(4)
thf(fact_1088_fm_Oset__intros_I4_J,axiom,
! [Yd: set_Epistemic_fm_i,X42: episte4276422356747265950c_fm_i,X41: episte4276422356747265950c_fm_i] :
( ( member1104366573291651755c_fm_i @ Yd @ ( episte6795552051664633144c_fm_i @ X42 ) )
=> ( member1104366573291651755c_fm_i @ Yd @ ( episte6795552051664633144c_fm_i @ ( episte64184772710425087c_fm_i @ X41 @ X42 ) ) ) ) ).
% fm.set_intros(4)
thf(fact_1089_fm_Oset__intros_I3_J,axiom,
! [Yc: epistemic_fm_i,X41: episte1308613106011496894c_fm_i,X42: episte1308613106011496894c_fm_i] :
( ( member6642669606046002379c_fm_i @ Yc @ ( episte9089240992906287960c_fm_i @ X41 ) )
=> ( member6642669606046002379c_fm_i @ Yc @ ( episte9089240992906287960c_fm_i @ ( episte3685526521632971807c_fm_i @ X41 @ X42 ) ) ) ) ).
% fm.set_intros(3)
thf(fact_1090_fm_Oset__intros_I3_J,axiom,
! [Yc: set_Epistemic_fm_i,X41: episte4276422356747265950c_fm_i,X42: episte4276422356747265950c_fm_i] :
( ( member1104366573291651755c_fm_i @ Yc @ ( episte6795552051664633144c_fm_i @ X41 ) )
=> ( member1104366573291651755c_fm_i @ Yc @ ( episte6795552051664633144c_fm_i @ ( episte64184772710425087c_fm_i @ X41 @ X42 ) ) ) ) ).
% fm.set_intros(3)
thf(fact_1091_fm_Oset__intros_I8_J,axiom,
! [Yg: epistemic_fm_i,X62: episte1308613106011496894c_fm_i,X61: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ Yg @ ( episte9089240992906287960c_fm_i @ X62 ) )
=> ( member6642669606046002379c_fm_i @ Yg @ ( episte9089240992906287960c_fm_i @ ( episte5657488666450005526c_fm_i @ X61 @ X62 ) ) ) ) ).
% fm.set_intros(8)
thf(fact_1092_fm_Oset__intros_I8_J,axiom,
! [Yg: set_Epistemic_fm_i,X62: episte4276422356747265950c_fm_i,X61: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Yg @ ( episte6795552051664633144c_fm_i @ X62 ) )
=> ( member1104366573291651755c_fm_i @ Yg @ ( episte6795552051664633144c_fm_i @ ( episte3581967596712343542c_fm_i @ X61 @ X62 ) ) ) ) ).
% fm.set_intros(8)
thf(fact_1093_fm_Oset__intros_I8_J,axiom,
! [Yg: i,X62: epistemic_fm_i,X61: i] :
( ( member_i @ Yg @ ( epistemic_set_fm_i @ X62 ) )
=> ( member_i @ Yg @ ( epistemic_set_fm_i @ ( epistemic_K_i @ X61 @ X62 ) ) ) ) ).
% fm.set_intros(8)
thf(fact_1094_fm_Oset__intros_I7_J,axiom,
! [X61: epistemic_fm_i,X62: episte1308613106011496894c_fm_i] : ( member6642669606046002379c_fm_i @ X61 @ ( episte9089240992906287960c_fm_i @ ( episte5657488666450005526c_fm_i @ X61 @ X62 ) ) ) ).
% fm.set_intros(7)
thf(fact_1095_fm_Oset__intros_I7_J,axiom,
! [X61: set_Epistemic_fm_i,X62: episte4276422356747265950c_fm_i] : ( member1104366573291651755c_fm_i @ X61 @ ( episte6795552051664633144c_fm_i @ ( episte3581967596712343542c_fm_i @ X61 @ X62 ) ) ) ).
% fm.set_intros(7)
thf(fact_1096_fm_Oset__intros_I7_J,axiom,
! [X61: i,X62: epistemic_fm_i] : ( member_i @ X61 @ ( epistemic_set_fm_i @ ( epistemic_K_i @ X61 @ X62 ) ) ) ).
% fm.set_intros(7)
thf(fact_1097_fm_Oset__intros_I6_J,axiom,
! [Yf: epistemic_fm_i,X52: episte1308613106011496894c_fm_i,X51: episte1308613106011496894c_fm_i] :
( ( member6642669606046002379c_fm_i @ Yf @ ( episte9089240992906287960c_fm_i @ X52 ) )
=> ( member6642669606046002379c_fm_i @ Yf @ ( episte9089240992906287960c_fm_i @ ( episte260752253203357973c_fm_i @ X51 @ X52 ) ) ) ) ).
% fm.set_intros(6)
thf(fact_1098_fm_Oset__intros_I6_J,axiom,
! [Yf: set_Epistemic_fm_i,X52: episte4276422356747265950c_fm_i,X51: episte4276422356747265950c_fm_i] :
( ( member1104366573291651755c_fm_i @ Yf @ ( episte6795552051664633144c_fm_i @ X52 ) )
=> ( member1104366573291651755c_fm_i @ Yf @ ( episte6795552051664633144c_fm_i @ ( episte5768433346120044277c_fm_i @ X51 @ X52 ) ) ) ) ).
% fm.set_intros(6)
thf(fact_1099_fm_Oset__intros_I5_J,axiom,
! [Ye: epistemic_fm_i,X51: episte1308613106011496894c_fm_i,X52: episte1308613106011496894c_fm_i] :
( ( member6642669606046002379c_fm_i @ Ye @ ( episte9089240992906287960c_fm_i @ X51 ) )
=> ( member6642669606046002379c_fm_i @ Ye @ ( episte9089240992906287960c_fm_i @ ( episte260752253203357973c_fm_i @ X51 @ X52 ) ) ) ) ).
% fm.set_intros(5)
thf(fact_1100_fm_Oset__intros_I5_J,axiom,
! [Ye: set_Epistemic_fm_i,X51: episte4276422356747265950c_fm_i,X52: episte4276422356747265950c_fm_i] :
( ( member1104366573291651755c_fm_i @ Ye @ ( episte6795552051664633144c_fm_i @ X51 ) )
=> ( member1104366573291651755c_fm_i @ Ye @ ( episte6795552051664633144c_fm_i @ ( episte5768433346120044277c_fm_i @ X51 @ X52 ) ) ) ) ).
% fm.set_intros(5)
thf(fact_1101_fm_Oset__intros_I2_J,axiom,
! [Yb2: epistemic_fm_i,X32: episte1308613106011496894c_fm_i,X31: episte1308613106011496894c_fm_i] :
( ( member6642669606046002379c_fm_i @ Yb2 @ ( episte9089240992906287960c_fm_i @ X32 ) )
=> ( member6642669606046002379c_fm_i @ Yb2 @ ( episte9089240992906287960c_fm_i @ ( episte6088726798904853267c_fm_i @ X31 @ X32 ) ) ) ) ).
% fm.set_intros(2)
thf(fact_1102_fm_Oset__intros_I2_J,axiom,
! [Yb2: set_Epistemic_fm_i,X32: episte4276422356747265950c_fm_i,X31: episte4276422356747265950c_fm_i] :
( ( member1104366573291651755c_fm_i @ Yb2 @ ( episte6795552051664633144c_fm_i @ X32 ) )
=> ( member1104366573291651755c_fm_i @ Yb2 @ ( episte6795552051664633144c_fm_i @ ( episte535002356104313075c_fm_i @ X31 @ X32 ) ) ) ) ).
% fm.set_intros(2)
thf(fact_1103_fm_Oset__intros_I1_J,axiom,
! [Ya: epistemic_fm_i,X31: episte1308613106011496894c_fm_i,X32: episte1308613106011496894c_fm_i] :
( ( member6642669606046002379c_fm_i @ Ya @ ( episte9089240992906287960c_fm_i @ X31 ) )
=> ( member6642669606046002379c_fm_i @ Ya @ ( episte9089240992906287960c_fm_i @ ( episte6088726798904853267c_fm_i @ X31 @ X32 ) ) ) ) ).
% fm.set_intros(1)
thf(fact_1104_fm_Oset__intros_I1_J,axiom,
! [Ya: set_Epistemic_fm_i,X31: episte4276422356747265950c_fm_i,X32: episte4276422356747265950c_fm_i] :
( ( member1104366573291651755c_fm_i @ Ya @ ( episte6795552051664633144c_fm_i @ X31 ) )
=> ( member1104366573291651755c_fm_i @ Ya @ ( episte6795552051664633144c_fm_i @ ( episte535002356104313075c_fm_i @ X31 @ X32 ) ) ) ) ).
% fm.set_intros(1)
thf(fact_1105_fm_Osimps_I90_J,axiom,
( ( epistemic_set_fm_i @ epistemic_FF_i )
= bot_bot_set_i ) ).
% fm.simps(90)
thf(fact_1106_fm_Osimps_I94_J,axiom,
! [X51: episte1308613106011496894c_fm_i,X52: episte1308613106011496894c_fm_i] :
( ( episte9089240992906287960c_fm_i @ ( episte260752253203357973c_fm_i @ X51 @ X52 ) )
= ( sup_su1936195050962291414c_fm_i @ ( episte9089240992906287960c_fm_i @ X51 ) @ ( episte9089240992906287960c_fm_i @ X52 ) ) ) ).
% fm.simps(94)
thf(fact_1107_fm_Osimps_I93_J,axiom,
! [X41: episte1308613106011496894c_fm_i,X42: episte1308613106011496894c_fm_i] :
( ( episte9089240992906287960c_fm_i @ ( episte3685526521632971807c_fm_i @ X41 @ X42 ) )
= ( sup_su1936195050962291414c_fm_i @ ( episte9089240992906287960c_fm_i @ X41 ) @ ( episte9089240992906287960c_fm_i @ X42 ) ) ) ).
% fm.simps(93)
thf(fact_1108_fm_Osimps_I92_J,axiom,
! [X31: episte1308613106011496894c_fm_i,X32: episte1308613106011496894c_fm_i] :
( ( episte9089240992906287960c_fm_i @ ( episte6088726798904853267c_fm_i @ X31 @ X32 ) )
= ( sup_su1936195050962291414c_fm_i @ ( episte9089240992906287960c_fm_i @ X31 ) @ ( episte9089240992906287960c_fm_i @ X32 ) ) ) ).
% fm.simps(92)
thf(fact_1109_union__fold__insert,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( sup_su2582925890723967158c_fm_i @ A @ B2 )
= ( finite28738107572603560c_fm_i @ insert7698009978809854162c_fm_i @ B2 @ A ) ) ) ).
% union_fold_insert
thf(fact_1110_union__fold__insert,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ A )
=> ( ( sup_su1936195050962291414c_fm_i @ A @ B2 )
= ( finite6274917443777430184c_fm_i @ insert7817948997695205106c_fm_i @ B2 @ A ) ) ) ).
% union_fold_insert
thf(fact_1111_subset__code_I2_J,axiom,
! [A: set_se3485332733965609186c_fm_i,Ys: list_s8081015415394010888c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ A @ ( coset_1342939534705115381c_fm_i @ Ys ) )
= ( ! [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ ( set_se200842218512397079c_fm_i @ Ys ) )
=> ~ ( member1104366573291651755c_fm_i @ X2 @ A ) ) ) ) ).
% subset_code(2)
thf(fact_1112_subset__code_I2_J,axiom,
! [A: set_Epistemic_fm_i,Ys: list_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ ( coset_Epistemic_fm_i @ Ys ) )
= ( ! [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ ( set_Epistemic_fm_i2 @ Ys ) )
=> ~ ( member6642669606046002379c_fm_i @ X2 @ A ) ) ) ) ).
% subset_code(2)
thf(fact_1113_minus__fold__remove,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ A )
=> ( ( minus_1543973939109951465c_fm_i @ B2 @ A )
= ( finite6274917443777430184c_fm_i @ remove5552923401211475591c_fm_i @ B2 @ A ) ) ) ).
% minus_fold_remove
thf(fact_1114_minus__fold__remove,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( minus_1073301138667672009c_fm_i @ B2 @ A )
= ( finite28738107572603560c_fm_i @ remove1392734035364174951c_fm_i @ B2 @ A ) ) ) ).
% minus_fold_remove
thf(fact_1115_Inf__fin_Oeq__fold,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( lattic8495942116038605215c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) )
= ( finite2237691025846545608c_fm_i @ inf_in3450601097109690352c_fm_i @ X @ A ) ) ) ).
% Inf_fin.eq_fold
thf(fact_1116_Inf__fin_Oeq__fold,axiom,
! [A: set_se7339729205154126530c_fm_i,X: set_se3485332733965609186c_fm_i] :
( ( finite9087983574947184523c_fm_i @ A )
=> ( ( lattic7860428167660714879c_fm_i @ ( insert7111703059596746418c_fm_i @ X @ A ) )
= ( finite436508220448094408c_fm_i @ inf_in161960956874937808c_fm_i @ X @ A ) ) ) ).
% Inf_fin.eq_fold
thf(fact_1117_Sup__fin_Oeq__fold,axiom,
! [A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( lattic3744900211830597177c_fm_i @ ( insert7698009978809854162c_fm_i @ X @ A ) )
= ( finite2237691025846545608c_fm_i @ sup_su1936195050962291414c_fm_i @ X @ A ) ) ) ).
% Sup_fin.eq_fold
thf(fact_1118_fold__graph__closed__lemma,axiom,
! [G5: epistemic_fm_i > epistemic_fm_i > epistemic_fm_i,Z: epistemic_fm_i,A: set_Epistemic_fm_i,X: epistemic_fm_i,B2: set_Epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i > epistemic_fm_i] :
( ( finite4898207529229619782c_fm_i @ G5 @ Z @ A @ X )
=> ( ! [A6: epistemic_fm_i,B7: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ( ( member6642669606046002379c_fm_i @ B7 @ B2 )
=> ( ( F3 @ A6 @ B7 )
= ( G5 @ A6 @ B7 ) ) ) )
=> ( ! [A6: epistemic_fm_i,B7: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ( ( member6642669606046002379c_fm_i @ B7 @ B2 )
=> ( member6642669606046002379c_fm_i @ ( G5 @ A6 @ B7 ) @ B2 ) ) )
=> ( ( member6642669606046002379c_fm_i @ Z @ B2 )
=> ( ( finite4898207529229619782c_fm_i @ F3 @ Z @ A @ X )
& ( member6642669606046002379c_fm_i @ X @ B2 ) ) ) ) ) ) ).
% fold_graph_closed_lemma
thf(fact_1119_fold__graph__closed__lemma,axiom,
! [G5: epistemic_fm_i > set_Epistemic_fm_i > set_Epistemic_fm_i,Z: set_Epistemic_fm_i,A: set_Epistemic_fm_i,X: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i,F3: epistemic_fm_i > set_Epistemic_fm_i > set_Epistemic_fm_i] :
( ( finite3073240682113661990c_fm_i @ G5 @ Z @ A @ X )
=> ( ! [A6: epistemic_fm_i,B7: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ( ( member1104366573291651755c_fm_i @ B7 @ B2 )
=> ( ( F3 @ A6 @ B7 )
= ( G5 @ A6 @ B7 ) ) ) )
=> ( ! [A6: epistemic_fm_i,B7: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ( ( member1104366573291651755c_fm_i @ B7 @ B2 )
=> ( member1104366573291651755c_fm_i @ ( G5 @ A6 @ B7 ) @ B2 ) ) )
=> ( ( member1104366573291651755c_fm_i @ Z @ B2 )
=> ( ( finite3073240682113661990c_fm_i @ F3 @ Z @ A @ X )
& ( member1104366573291651755c_fm_i @ X @ B2 ) ) ) ) ) ) ).
% fold_graph_closed_lemma
thf(fact_1120_fold__graph__closed__lemma,axiom,
! [G5: set_Epistemic_fm_i > epistemic_fm_i > epistemic_fm_i,Z: epistemic_fm_i,A: set_se3485332733965609186c_fm_i,X: epistemic_fm_i,B2: set_Epistemic_fm_i,F3: set_Epistemic_fm_i > epistemic_fm_i > epistemic_fm_i] :
( ( finite969542861950010470c_fm_i @ G5 @ Z @ A @ X )
=> ( ! [A6: set_Epistemic_fm_i,B7: epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ( member6642669606046002379c_fm_i @ B7 @ B2 )
=> ( ( F3 @ A6 @ B7 )
= ( G5 @ A6 @ B7 ) ) ) )
=> ( ! [A6: set_Epistemic_fm_i,B7: epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ( member6642669606046002379c_fm_i @ B7 @ B2 )
=> ( member6642669606046002379c_fm_i @ ( G5 @ A6 @ B7 ) @ B2 ) ) )
=> ( ( member6642669606046002379c_fm_i @ Z @ B2 )
=> ( ( finite969542861950010470c_fm_i @ F3 @ Z @ A @ X )
& ( member6642669606046002379c_fm_i @ X @ B2 ) ) ) ) ) ) ).
% fold_graph_closed_lemma
thf(fact_1121_fold__graph__closed__lemma,axiom,
! [G5: set_Epistemic_fm_i > set_Epistemic_fm_i > set_Epistemic_fm_i,Z: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i > set_Epistemic_fm_i] :
( ( finite5960466103032163910c_fm_i @ G5 @ Z @ A @ X )
=> ( ! [A6: set_Epistemic_fm_i,B7: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ( member1104366573291651755c_fm_i @ B7 @ B2 )
=> ( ( F3 @ A6 @ B7 )
= ( G5 @ A6 @ B7 ) ) ) )
=> ( ! [A6: set_Epistemic_fm_i,B7: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ( member1104366573291651755c_fm_i @ B7 @ B2 )
=> ( member1104366573291651755c_fm_i @ ( G5 @ A6 @ B7 ) @ B2 ) ) )
=> ( ( member1104366573291651755c_fm_i @ Z @ B2 )
=> ( ( finite5960466103032163910c_fm_i @ F3 @ Z @ A @ X )
& ( member1104366573291651755c_fm_i @ X @ B2 ) ) ) ) ) ) ).
% fold_graph_closed_lemma
thf(fact_1122_fold__graph__closed__eq,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i > epistemic_fm_i,G5: epistemic_fm_i > epistemic_fm_i > epistemic_fm_i,Z: epistemic_fm_i] :
( ! [A6: epistemic_fm_i,B7: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ( ( member6642669606046002379c_fm_i @ B7 @ B2 )
=> ( ( F3 @ A6 @ B7 )
= ( G5 @ A6 @ B7 ) ) ) )
=> ( ! [A6: epistemic_fm_i,B7: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ( ( member6642669606046002379c_fm_i @ B7 @ B2 )
=> ( member6642669606046002379c_fm_i @ ( G5 @ A6 @ B7 ) @ B2 ) ) )
=> ( ( member6642669606046002379c_fm_i @ Z @ B2 )
=> ( ( finite4898207529229619782c_fm_i @ F3 @ Z @ A )
= ( finite4898207529229619782c_fm_i @ G5 @ Z @ A ) ) ) ) ) ).
% fold_graph_closed_eq
thf(fact_1123_fold__graph__closed__eq,axiom,
! [A: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i,F3: epistemic_fm_i > set_Epistemic_fm_i > set_Epistemic_fm_i,G5: epistemic_fm_i > set_Epistemic_fm_i > set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ! [A6: epistemic_fm_i,B7: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ( ( member1104366573291651755c_fm_i @ B7 @ B2 )
=> ( ( F3 @ A6 @ B7 )
= ( G5 @ A6 @ B7 ) ) ) )
=> ( ! [A6: epistemic_fm_i,B7: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ( ( member1104366573291651755c_fm_i @ B7 @ B2 )
=> ( member1104366573291651755c_fm_i @ ( G5 @ A6 @ B7 ) @ B2 ) ) )
=> ( ( member1104366573291651755c_fm_i @ Z @ B2 )
=> ( ( finite3073240682113661990c_fm_i @ F3 @ Z @ A )
= ( finite3073240682113661990c_fm_i @ G5 @ Z @ A ) ) ) ) ) ).
% fold_graph_closed_eq
thf(fact_1124_fold__graph__closed__eq,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_Epistemic_fm_i,F3: set_Epistemic_fm_i > epistemic_fm_i > epistemic_fm_i,G5: set_Epistemic_fm_i > epistemic_fm_i > epistemic_fm_i,Z: epistemic_fm_i] :
( ! [A6: set_Epistemic_fm_i,B7: epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ( member6642669606046002379c_fm_i @ B7 @ B2 )
=> ( ( F3 @ A6 @ B7 )
= ( G5 @ A6 @ B7 ) ) ) )
=> ( ! [A6: set_Epistemic_fm_i,B7: epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ( member6642669606046002379c_fm_i @ B7 @ B2 )
=> ( member6642669606046002379c_fm_i @ ( G5 @ A6 @ B7 ) @ B2 ) ) )
=> ( ( member6642669606046002379c_fm_i @ Z @ B2 )
=> ( ( finite969542861950010470c_fm_i @ F3 @ Z @ A )
= ( finite969542861950010470c_fm_i @ G5 @ Z @ A ) ) ) ) ) ).
% fold_graph_closed_eq
thf(fact_1125_fold__graph__closed__eq,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i > set_Epistemic_fm_i,G5: set_Epistemic_fm_i > set_Epistemic_fm_i > set_Epistemic_fm_i,Z: set_Epistemic_fm_i] :
( ! [A6: set_Epistemic_fm_i,B7: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ( member1104366573291651755c_fm_i @ B7 @ B2 )
=> ( ( F3 @ A6 @ B7 )
= ( G5 @ A6 @ B7 ) ) ) )
=> ( ! [A6: set_Epistemic_fm_i,B7: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ( ( member1104366573291651755c_fm_i @ B7 @ B2 )
=> ( member1104366573291651755c_fm_i @ ( G5 @ A6 @ B7 ) @ B2 ) ) )
=> ( ( member1104366573291651755c_fm_i @ Z @ B2 )
=> ( ( finite5960466103032163910c_fm_i @ F3 @ Z @ A )
= ( finite5960466103032163910c_fm_i @ G5 @ Z @ A ) ) ) ) ) ).
% fold_graph_closed_eq
thf(fact_1126_union__set__fold,axiom,
! [Xs: list_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( sup_su1936195050962291414c_fm_i @ ( set_Epistemic_fm_i2 @ Xs ) @ A )
= ( fold_E3768464346039846891c_fm_i @ insert7817948997695205106c_fm_i @ Xs @ A ) ) ).
% union_set_fold
thf(fact_1127_minus__set__fold,axiom,
! [A: set_Epistemic_fm_i,Xs: list_Epistemic_fm_i] :
( ( minus_1543973939109951465c_fm_i @ A @ ( set_Epistemic_fm_i2 @ Xs ) )
= ( fold_E3768464346039846891c_fm_i @ remove5552923401211475591c_fm_i @ Xs @ A ) ) ).
% minus_set_fold
thf(fact_1128_inter__coset__fold,axiom,
! [A: set_se3485332733965609186c_fm_i,Xs: list_s8081015415394010888c_fm_i] :
( ( inf_in161960956874937808c_fm_i @ A @ ( coset_1342939534705115381c_fm_i @ Xs ) )
= ( fold_s1063232419846502379c_fm_i @ remove1392734035364174951c_fm_i @ Xs @ A ) ) ).
% inter_coset_fold
thf(fact_1129_Inf__fin_Oset__eq__fold,axiom,
! [X: set_se3485332733965609186c_fm_i,Xs: list_s8635415444435394792c_fm_i] :
( ( lattic7860428167660714879c_fm_i @ ( set_se5076022966804059383c_fm_i @ ( cons_s5806790718070763416c_fm_i @ X @ Xs ) ) )
= ( fold_s7712222339821836811c_fm_i @ inf_in161960956874937808c_fm_i @ Xs @ X ) ) ).
% Inf_fin.set_eq_fold
thf(fact_1130_Sup__fin_Oset__eq__fold,axiom,
! [X: set_Epistemic_fm_i,Xs: list_s8081015415394010888c_fm_i] :
( ( lattic3744900211830597177c_fm_i @ ( set_se200842218512397079c_fm_i @ ( cons_s4962720389763977656c_fm_i @ X @ Xs ) ) )
= ( fold_s1768690285866886667c_fm_i @ sup_su1936195050962291414c_fm_i @ Xs @ X ) ) ).
% Sup_fin.set_eq_fold
thf(fact_1131_set__remdups,axiom,
! [Xs: list_Epistemic_fm_i] :
( ( set_Epistemic_fm_i2 @ ( remdup2862625226703050045c_fm_i @ Xs ) )
= ( set_Epistemic_fm_i2 @ Xs ) ) ).
% set_remdups
thf(fact_1132_remdups_Osimps_I2_J,axiom,
! [X: set_Epistemic_fm_i,Xs: list_s8081015415394010888c_fm_i] :
( ( ( member1104366573291651755c_fm_i @ X @ ( set_se200842218512397079c_fm_i @ Xs ) )
=> ( ( remdup493799568840827677c_fm_i @ ( cons_s4962720389763977656c_fm_i @ X @ Xs ) )
= ( remdup493799568840827677c_fm_i @ Xs ) ) )
& ( ~ ( member1104366573291651755c_fm_i @ X @ ( set_se200842218512397079c_fm_i @ Xs ) )
=> ( ( remdup493799568840827677c_fm_i @ ( cons_s4962720389763977656c_fm_i @ X @ Xs ) )
= ( cons_s4962720389763977656c_fm_i @ X @ ( remdup493799568840827677c_fm_i @ Xs ) ) ) ) ) ).
% remdups.simps(2)
thf(fact_1133_remdups_Osimps_I2_J,axiom,
! [X: epistemic_fm_i,Xs: list_Epistemic_fm_i] :
( ( ( member6642669606046002379c_fm_i @ X @ ( set_Epistemic_fm_i2 @ Xs ) )
=> ( ( remdup2862625226703050045c_fm_i @ ( cons_Epistemic_fm_i @ X @ Xs ) )
= ( remdup2862625226703050045c_fm_i @ Xs ) ) )
& ( ~ ( member6642669606046002379c_fm_i @ X @ ( set_Epistemic_fm_i2 @ Xs ) )
=> ( ( remdup2862625226703050045c_fm_i @ ( cons_Epistemic_fm_i @ X @ Xs ) )
= ( cons_Epistemic_fm_i @ X @ ( remdup2862625226703050045c_fm_i @ Xs ) ) ) ) ) ).
% remdups.simps(2)
thf(fact_1134_flat__lub__def,axiom,
( partia2237093934842463950c_fm_i
= ( ^ [B4: set_Epistemic_fm_i,A3: set_se3485332733965609186c_fm_i] :
( if_set2943457721768014536c_fm_i @ ( ord_le5389487502678872194c_fm_i @ A3 @ ( insert7698009978809854162c_fm_i @ B4 @ bot_bo145720340923748686c_fm_i ) ) @ B4
@ ( the_se2508142961706643081c_fm_i
@ ^ [X2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ X2 @ ( minus_1073301138667672009c_fm_i @ A3 @ ( insert7698009978809854162c_fm_i @ B4 @ bot_bo145720340923748686c_fm_i ) ) ) ) ) ) ) ).
% flat_lub_def
thf(fact_1135_flat__lub__def,axiom,
( partia6511039473171299566c_fm_i
= ( ^ [B4: epistemic_fm_i,A3: set_Epistemic_fm_i] :
( if_Epistemic_fm_i @ ( ord_le3843937902494030498c_fm_i @ A3 @ ( insert7817948997695205106c_fm_i @ B4 @ bot_bo4194595901900360558c_fm_i ) ) @ B4
@ ( the_Epistemic_fm_i
@ ^ [X2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ X2 @ ( minus_1543973939109951465c_fm_i @ A3 @ ( insert7817948997695205106c_fm_i @ B4 @ bot_bo4194595901900360558c_fm_i ) ) ) ) ) ) ) ).
% flat_lub_def
thf(fact_1136_image__eqI,axiom,
! [B3: epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i,X: epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( B3
= ( F3 @ X ) )
=> ( ( member6642669606046002379c_fm_i @ X @ A )
=> ( member6642669606046002379c_fm_i @ B3 @ ( image_120052958407486725c_fm_i @ F3 @ A ) ) ) ) ).
% image_eqI
thf(fact_1137_image__eqI,axiom,
! [B3: set_Epistemic_fm_i,F3: epistemic_fm_i > set_Epistemic_fm_i,X: epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( B3
= ( F3 @ X ) )
=> ( ( member6642669606046002379c_fm_i @ X @ A )
=> ( member1104366573291651755c_fm_i @ B3 @ ( image_2913337242412145381c_fm_i @ F3 @ A ) ) ) ) ).
% image_eqI
thf(fact_1138_image__eqI,axiom,
! [B3: epistemic_fm_i,F3: set_Epistemic_fm_i > epistemic_fm_i,X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( B3
= ( F3 @ X ) )
=> ( ( member1104366573291651755c_fm_i @ X @ A )
=> ( member6642669606046002379c_fm_i @ B3 @ ( image_809639422248493861c_fm_i @ F3 @ A ) ) ) ) ).
% image_eqI
thf(fact_1139_image__eqI,axiom,
! [B3: set_Epistemic_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i,X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( B3
= ( F3 @ X ) )
=> ( ( member1104366573291651755c_fm_i @ X @ A )
=> ( member1104366573291651755c_fm_i @ B3 @ ( image_2698589095351095557c_fm_i @ F3 @ A ) ) ) ) ).
% image_eqI
thf(fact_1140_finite__imageI,axiom,
! [F: set_Epistemic_fm_i,H2: epistemic_fm_i > epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ F )
=> ( finite3304564979551393739c_fm_i @ ( image_120052958407486725c_fm_i @ H2 @ F ) ) ) ).
% finite_imageI
thf(fact_1141_finite__imageI,axiom,
! [F: set_Epistemic_fm_i,H2: epistemic_fm_i > set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ F )
=> ( finite7933139204641697195c_fm_i @ ( image_2913337242412145381c_fm_i @ H2 @ F ) ) ) ).
% finite_imageI
thf(fact_1142_finite__imageI,axiom,
! [F: set_se3485332733965609186c_fm_i,H2: set_Epistemic_fm_i > epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ F )
=> ( finite3304564979551393739c_fm_i @ ( image_809639422248493861c_fm_i @ H2 @ F ) ) ) ).
% finite_imageI
thf(fact_1143_finite__imageI,axiom,
! [F: set_se3485332733965609186c_fm_i,H2: set_Epistemic_fm_i > set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ F )
=> ( finite7933139204641697195c_fm_i @ ( image_2698589095351095557c_fm_i @ H2 @ F ) ) ) ).
% finite_imageI
thf(fact_1144_list_Oset__map,axiom,
! [F3: epistemic_fm_i > epistemic_fm_i,V3: list_Epistemic_fm_i] :
( ( set_Epistemic_fm_i2 @ ( map_Ep2755178516647988292c_fm_i @ F3 @ V3 ) )
= ( image_120052958407486725c_fm_i @ F3 @ ( set_Epistemic_fm_i2 @ V3 ) ) ) ).
% list.set_map
thf(fact_1145_if__image__distrib,axiom,
! [P3: epistemic_fm_i > $o,F3: epistemic_fm_i > epistemic_fm_i,G5: epistemic_fm_i > epistemic_fm_i,S: set_Epistemic_fm_i] :
( ( image_120052958407486725c_fm_i
@ ^ [X2: epistemic_fm_i] : ( if_Epistemic_fm_i @ ( P3 @ X2 ) @ ( F3 @ X2 ) @ ( G5 @ X2 ) )
@ S )
= ( sup_su1936195050962291414c_fm_i @ ( image_120052958407486725c_fm_i @ F3 @ ( inf_in3450601097109690352c_fm_i @ S @ ( collec4904205187116291597c_fm_i @ P3 ) ) )
@ ( image_120052958407486725c_fm_i @ G5
@ ( inf_in3450601097109690352c_fm_i @ S
@ ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
~ ( P3 @ X2 ) ) ) ) ) ) ).
% if_image_distrib
thf(fact_1146_if__image__distrib,axiom,
! [P3: set_Epistemic_fm_i > $o,F3: set_Epistemic_fm_i > epistemic_fm_i,G5: set_Epistemic_fm_i > epistemic_fm_i,S: set_se3485332733965609186c_fm_i] :
( ( image_809639422248493861c_fm_i
@ ^ [X2: set_Epistemic_fm_i] : ( if_Epistemic_fm_i @ ( P3 @ X2 ) @ ( F3 @ X2 ) @ ( G5 @ X2 ) )
@ S )
= ( sup_su1936195050962291414c_fm_i @ ( image_809639422248493861c_fm_i @ F3 @ ( inf_in161960956874937808c_fm_i @ S @ ( collec3087743281813070829c_fm_i @ P3 ) ) )
@ ( image_809639422248493861c_fm_i @ G5
@ ( inf_in161960956874937808c_fm_i @ S
@ ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
~ ( P3 @ X2 ) ) ) ) ) ) ).
% if_image_distrib
thf(fact_1147_image__mono,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ord_le3843937902494030498c_fm_i @ ( image_120052958407486725c_fm_i @ F3 @ A ) @ ( image_120052958407486725c_fm_i @ F3 @ B2 ) ) ) ).
% image_mono
thf(fact_1148_image__subsetI,axiom,
! [A: set_Epistemic_fm_i,F3: epistemic_fm_i > set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ! [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ A )
=> ( member1104366573291651755c_fm_i @ ( F3 @ X3 ) @ B2 ) )
=> ( ord_le5389487502678872194c_fm_i @ ( image_2913337242412145381c_fm_i @ F3 @ A ) @ B2 ) ) ).
% image_subsetI
thf(fact_1149_image__subsetI,axiom,
! [A: set_se3485332733965609186c_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ! [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
=> ( member1104366573291651755c_fm_i @ ( F3 @ X3 ) @ B2 ) )
=> ( ord_le5389487502678872194c_fm_i @ ( image_2698589095351095557c_fm_i @ F3 @ A ) @ B2 ) ) ).
% image_subsetI
thf(fact_1150_image__subsetI,axiom,
! [A: set_Epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ! [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ A )
=> ( member6642669606046002379c_fm_i @ ( F3 @ X3 ) @ B2 ) )
=> ( ord_le3843937902494030498c_fm_i @ ( image_120052958407486725c_fm_i @ F3 @ A ) @ B2 ) ) ).
% image_subsetI
thf(fact_1151_image__subsetI,axiom,
! [A: set_se3485332733965609186c_fm_i,F3: set_Epistemic_fm_i > epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ! [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
=> ( member6642669606046002379c_fm_i @ ( F3 @ X3 ) @ B2 ) )
=> ( ord_le3843937902494030498c_fm_i @ ( image_809639422248493861c_fm_i @ F3 @ A ) @ B2 ) ) ).
% image_subsetI
thf(fact_1152_subset__imageE,axiom,
! [B2: set_Epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B2 @ ( image_120052958407486725c_fm_i @ F3 @ A ) )
=> ~ ! [C4: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ C4 @ A )
=> ( B2
!= ( image_120052958407486725c_fm_i @ F3 @ C4 ) ) ) ) ).
% subset_imageE
thf(fact_1153_subset__image__iff,axiom,
! [B2: set_Epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B2 @ ( image_120052958407486725c_fm_i @ F3 @ A ) )
= ( ? [AA: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ AA @ A )
& ( B2
= ( image_120052958407486725c_fm_i @ F3 @ AA ) ) ) ) ) ).
% subset_image_iff
thf(fact_1154_all__subset__image,axiom,
! [F3: epistemic_fm_i > epistemic_fm_i,A: set_Epistemic_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( ! [B: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B @ ( image_120052958407486725c_fm_i @ F3 @ A ) )
=> ( P3 @ B ) ) )
= ( ! [B: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ B @ A )
=> ( P3 @ ( image_120052958407486725c_fm_i @ F3 @ B ) ) ) ) ) ).
% all_subset_image
thf(fact_1155_image__Collect__subsetI,axiom,
! [P3: epistemic_fm_i > $o,F3: epistemic_fm_i > set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ! [X3: epistemic_fm_i] :
( ( P3 @ X3 )
=> ( member1104366573291651755c_fm_i @ ( F3 @ X3 ) @ B2 ) )
=> ( ord_le5389487502678872194c_fm_i @ ( image_2913337242412145381c_fm_i @ F3 @ ( collec4904205187116291597c_fm_i @ P3 ) ) @ B2 ) ) ).
% image_Collect_subsetI
thf(fact_1156_image__Collect__subsetI,axiom,
! [P3: set_Epistemic_fm_i > $o,F3: set_Epistemic_fm_i > set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ! [X3: set_Epistemic_fm_i] :
( ( P3 @ X3 )
=> ( member1104366573291651755c_fm_i @ ( F3 @ X3 ) @ B2 ) )
=> ( ord_le5389487502678872194c_fm_i @ ( image_2698589095351095557c_fm_i @ F3 @ ( collec3087743281813070829c_fm_i @ P3 ) ) @ B2 ) ) ).
% image_Collect_subsetI
thf(fact_1157_image__Collect__subsetI,axiom,
! [P3: epistemic_fm_i > $o,F3: epistemic_fm_i > epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ! [X3: epistemic_fm_i] :
( ( P3 @ X3 )
=> ( member6642669606046002379c_fm_i @ ( F3 @ X3 ) @ B2 ) )
=> ( ord_le3843937902494030498c_fm_i @ ( image_120052958407486725c_fm_i @ F3 @ ( collec4904205187116291597c_fm_i @ P3 ) ) @ B2 ) ) ).
% image_Collect_subsetI
thf(fact_1158_image__Collect__subsetI,axiom,
! [P3: set_Epistemic_fm_i > $o,F3: set_Epistemic_fm_i > epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ! [X3: set_Epistemic_fm_i] :
( ( P3 @ X3 )
=> ( member6642669606046002379c_fm_i @ ( F3 @ X3 ) @ B2 ) )
=> ( ord_le3843937902494030498c_fm_i @ ( image_809639422248493861c_fm_i @ F3 @ ( collec3087743281813070829c_fm_i @ P3 ) ) @ B2 ) ) ).
% image_Collect_subsetI
thf(fact_1159_all__finite__subset__image,axiom,
! [F3: set_Epistemic_fm_i > set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,P3: set_se3485332733965609186c_fm_i > $o] :
( ( ! [B: set_se3485332733965609186c_fm_i] :
( ( ( finite7933139204641697195c_fm_i @ B )
& ( ord_le5389487502678872194c_fm_i @ B @ ( image_2698589095351095557c_fm_i @ F3 @ A ) ) )
=> ( P3 @ B ) ) )
= ( ! [B: set_se3485332733965609186c_fm_i] :
( ( ( finite7933139204641697195c_fm_i @ B )
& ( ord_le5389487502678872194c_fm_i @ B @ A ) )
=> ( P3 @ ( image_2698589095351095557c_fm_i @ F3 @ B ) ) ) ) ) ).
% all_finite_subset_image
thf(fact_1160_all__finite__subset__image,axiom,
! [F3: epistemic_fm_i > set_Epistemic_fm_i,A: set_Epistemic_fm_i,P3: set_se3485332733965609186c_fm_i > $o] :
( ( ! [B: set_se3485332733965609186c_fm_i] :
( ( ( finite7933139204641697195c_fm_i @ B )
& ( ord_le5389487502678872194c_fm_i @ B @ ( image_2913337242412145381c_fm_i @ F3 @ A ) ) )
=> ( P3 @ B ) ) )
= ( ! [B: set_Epistemic_fm_i] :
( ( ( finite3304564979551393739c_fm_i @ B )
& ( ord_le3843937902494030498c_fm_i @ B @ A ) )
=> ( P3 @ ( image_2913337242412145381c_fm_i @ F3 @ B ) ) ) ) ) ).
% all_finite_subset_image
thf(fact_1161_all__finite__subset__image,axiom,
! [F3: set_Epistemic_fm_i > epistemic_fm_i,A: set_se3485332733965609186c_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( ! [B: set_Epistemic_fm_i] :
( ( ( finite3304564979551393739c_fm_i @ B )
& ( ord_le3843937902494030498c_fm_i @ B @ ( image_809639422248493861c_fm_i @ F3 @ A ) ) )
=> ( P3 @ B ) ) )
= ( ! [B: set_se3485332733965609186c_fm_i] :
( ( ( finite7933139204641697195c_fm_i @ B )
& ( ord_le5389487502678872194c_fm_i @ B @ A ) )
=> ( P3 @ ( image_809639422248493861c_fm_i @ F3 @ B ) ) ) ) ) ).
% all_finite_subset_image
thf(fact_1162_all__finite__subset__image,axiom,
! [F3: epistemic_fm_i > epistemic_fm_i,A: set_Epistemic_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( ! [B: set_Epistemic_fm_i] :
( ( ( finite3304564979551393739c_fm_i @ B )
& ( ord_le3843937902494030498c_fm_i @ B @ ( image_120052958407486725c_fm_i @ F3 @ A ) ) )
=> ( P3 @ B ) ) )
= ( ! [B: set_Epistemic_fm_i] :
( ( ( finite3304564979551393739c_fm_i @ B )
& ( ord_le3843937902494030498c_fm_i @ B @ A ) )
=> ( P3 @ ( image_120052958407486725c_fm_i @ F3 @ B ) ) ) ) ) ).
% all_finite_subset_image
thf(fact_1163_ex__finite__subset__image,axiom,
! [F3: set_Epistemic_fm_i > set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,P3: set_se3485332733965609186c_fm_i > $o] :
( ( ? [B: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ B )
& ( ord_le5389487502678872194c_fm_i @ B @ ( image_2698589095351095557c_fm_i @ F3 @ A ) )
& ( P3 @ B ) ) )
= ( ? [B: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ B )
& ( ord_le5389487502678872194c_fm_i @ B @ A )
& ( P3 @ ( image_2698589095351095557c_fm_i @ F3 @ B ) ) ) ) ) ).
% ex_finite_subset_image
thf(fact_1164_ex__finite__subset__image,axiom,
! [F3: epistemic_fm_i > set_Epistemic_fm_i,A: set_Epistemic_fm_i,P3: set_se3485332733965609186c_fm_i > $o] :
( ( ? [B: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ B )
& ( ord_le5389487502678872194c_fm_i @ B @ ( image_2913337242412145381c_fm_i @ F3 @ A ) )
& ( P3 @ B ) ) )
= ( ? [B: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ B )
& ( ord_le3843937902494030498c_fm_i @ B @ A )
& ( P3 @ ( image_2913337242412145381c_fm_i @ F3 @ B ) ) ) ) ) ).
% ex_finite_subset_image
thf(fact_1165_ex__finite__subset__image,axiom,
! [F3: set_Epistemic_fm_i > epistemic_fm_i,A: set_se3485332733965609186c_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( ? [B: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ B )
& ( ord_le3843937902494030498c_fm_i @ B @ ( image_809639422248493861c_fm_i @ F3 @ A ) )
& ( P3 @ B ) ) )
= ( ? [B: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ B )
& ( ord_le5389487502678872194c_fm_i @ B @ A )
& ( P3 @ ( image_809639422248493861c_fm_i @ F3 @ B ) ) ) ) ) ).
% ex_finite_subset_image
thf(fact_1166_ex__finite__subset__image,axiom,
! [F3: epistemic_fm_i > epistemic_fm_i,A: set_Epistemic_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( ? [B: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ B )
& ( ord_le3843937902494030498c_fm_i @ B @ ( image_120052958407486725c_fm_i @ F3 @ A ) )
& ( P3 @ B ) ) )
= ( ? [B: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ B )
& ( ord_le3843937902494030498c_fm_i @ B @ A )
& ( P3 @ ( image_120052958407486725c_fm_i @ F3 @ B ) ) ) ) ) ).
% ex_finite_subset_image
thf(fact_1167_finite__subset__image,axiom,
! [B2: set_se3485332733965609186c_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ B2 )
=> ( ( ord_le5389487502678872194c_fm_i @ B2 @ ( image_2698589095351095557c_fm_i @ F3 @ A ) )
=> ? [C4: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ C4 @ A )
& ( finite7933139204641697195c_fm_i @ C4 )
& ( B2
= ( image_2698589095351095557c_fm_i @ F3 @ C4 ) ) ) ) ) ).
% finite_subset_image
thf(fact_1168_finite__subset__image,axiom,
! [B2: set_se3485332733965609186c_fm_i,F3: epistemic_fm_i > set_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ B2 )
=> ( ( ord_le5389487502678872194c_fm_i @ B2 @ ( image_2913337242412145381c_fm_i @ F3 @ A ) )
=> ? [C4: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ C4 @ A )
& ( finite3304564979551393739c_fm_i @ C4 )
& ( B2
= ( image_2913337242412145381c_fm_i @ F3 @ C4 ) ) ) ) ) ).
% finite_subset_image
thf(fact_1169_finite__subset__image,axiom,
! [B2: set_Epistemic_fm_i,F3: set_Epistemic_fm_i > epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( finite3304564979551393739c_fm_i @ B2 )
=> ( ( ord_le3843937902494030498c_fm_i @ B2 @ ( image_809639422248493861c_fm_i @ F3 @ A ) )
=> ? [C4: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ C4 @ A )
& ( finite7933139204641697195c_fm_i @ C4 )
& ( B2
= ( image_809639422248493861c_fm_i @ F3 @ C4 ) ) ) ) ) ).
% finite_subset_image
thf(fact_1170_finite__subset__image,axiom,
! [B2: set_Epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ B2 )
=> ( ( ord_le3843937902494030498c_fm_i @ B2 @ ( image_120052958407486725c_fm_i @ F3 @ A ) )
=> ? [C4: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ C4 @ A )
& ( finite3304564979551393739c_fm_i @ C4 )
& ( B2
= ( image_120052958407486725c_fm_i @ F3 @ C4 ) ) ) ) ) ).
% finite_subset_image
thf(fact_1171_finite__surj,axiom,
! [A: set_Epistemic_fm_i,B2: set_se3485332733965609186c_fm_i,F3: epistemic_fm_i > set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ A )
=> ( ( ord_le5389487502678872194c_fm_i @ B2 @ ( image_2913337242412145381c_fm_i @ F3 @ A ) )
=> ( finite7933139204641697195c_fm_i @ B2 ) ) ) ).
% finite_surj
thf(fact_1172_finite__surj,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( ord_le5389487502678872194c_fm_i @ B2 @ ( image_2698589095351095557c_fm_i @ F3 @ A ) )
=> ( finite7933139204641697195c_fm_i @ B2 ) ) ) ).
% finite_surj
thf(fact_1173_finite__surj,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ A )
=> ( ( ord_le3843937902494030498c_fm_i @ B2 @ ( image_120052958407486725c_fm_i @ F3 @ A ) )
=> ( finite3304564979551393739c_fm_i @ B2 ) ) ) ).
% finite_surj
thf(fact_1174_finite__surj,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_Epistemic_fm_i,F3: set_Epistemic_fm_i > epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( ord_le3843937902494030498c_fm_i @ B2 @ ( image_809639422248493861c_fm_i @ F3 @ A ) )
=> ( finite3304564979551393739c_fm_i @ B2 ) ) ) ).
% finite_surj
thf(fact_1175_image__Int__subset,axiom,
! [F3: set_Epistemic_fm_i > set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] : ( ord_le5389487502678872194c_fm_i @ ( image_2698589095351095557c_fm_i @ F3 @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) ) @ ( inf_in161960956874937808c_fm_i @ ( image_2698589095351095557c_fm_i @ F3 @ A ) @ ( image_2698589095351095557c_fm_i @ F3 @ B2 ) ) ) ).
% image_Int_subset
thf(fact_1176_image__Int__subset,axiom,
! [F3: set_Epistemic_fm_i > epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( image_809639422248493861c_fm_i @ F3 @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) ) @ ( inf_in3450601097109690352c_fm_i @ ( image_809639422248493861c_fm_i @ F3 @ A ) @ ( image_809639422248493861c_fm_i @ F3 @ B2 ) ) ) ).
% image_Int_subset
thf(fact_1177_image__set,axiom,
! [F3: epistemic_fm_i > epistemic_fm_i,Xs: list_Epistemic_fm_i] :
( ( image_120052958407486725c_fm_i @ F3 @ ( set_Epistemic_fm_i2 @ Xs ) )
= ( set_Epistemic_fm_i2 @ ( map_Ep2755178516647988292c_fm_i @ F3 @ Xs ) ) ) ).
% image_set
thf(fact_1178_image__Un,axiom,
! [F3: epistemic_fm_i > epistemic_fm_i,A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( image_120052958407486725c_fm_i @ F3 @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) )
= ( sup_su1936195050962291414c_fm_i @ ( image_120052958407486725c_fm_i @ F3 @ A ) @ ( image_120052958407486725c_fm_i @ F3 @ B2 ) ) ) ).
% image_Un
thf(fact_1179_pigeonhole__infinite,axiom,
! [A: set_Epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i] :
( ~ ( finite3304564979551393739c_fm_i @ A )
=> ( ( finite3304564979551393739c_fm_i @ ( image_120052958407486725c_fm_i @ F3 @ A ) )
=> ? [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ A )
& ~ ( finite3304564979551393739c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [A4: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A4 @ A )
& ( ( F3 @ A4 )
= ( F3 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite
thf(fact_1180_pigeonhole__infinite,axiom,
! [A: set_Epistemic_fm_i,F3: epistemic_fm_i > set_Epistemic_fm_i] :
( ~ ( finite3304564979551393739c_fm_i @ A )
=> ( ( finite7933139204641697195c_fm_i @ ( image_2913337242412145381c_fm_i @ F3 @ A ) )
=> ? [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ A )
& ~ ( finite3304564979551393739c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [A4: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A4 @ A )
& ( ( F3 @ A4 )
= ( F3 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite
thf(fact_1181_pigeonhole__infinite,axiom,
! [A: set_se3485332733965609186c_fm_i,F3: set_Epistemic_fm_i > epistemic_fm_i] :
( ~ ( finite7933139204641697195c_fm_i @ A )
=> ( ( finite3304564979551393739c_fm_i @ ( image_809639422248493861c_fm_i @ F3 @ A ) )
=> ? [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
& ~ ( finite7933139204641697195c_fm_i
@ ( collec3087743281813070829c_fm_i
@ ^ [A4: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A4 @ A )
& ( ( F3 @ A4 )
= ( F3 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite
thf(fact_1182_pigeonhole__infinite,axiom,
! [A: set_se3485332733965609186c_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i] :
( ~ ( finite7933139204641697195c_fm_i @ A )
=> ( ( finite7933139204641697195c_fm_i @ ( image_2698589095351095557c_fm_i @ F3 @ A ) )
=> ? [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
& ~ ( finite7933139204641697195c_fm_i
@ ( collec3087743281813070829c_fm_i
@ ^ [A4: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A4 @ A )
& ( ( F3 @ A4 )
= ( F3 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite
thf(fact_1183_imageI,axiom,
! [X: epistemic_fm_i,A: set_Epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X @ A )
=> ( member6642669606046002379c_fm_i @ ( F3 @ X ) @ ( image_120052958407486725c_fm_i @ F3 @ A ) ) ) ).
% imageI
thf(fact_1184_imageI,axiom,
! [X: epistemic_fm_i,A: set_Epistemic_fm_i,F3: epistemic_fm_i > set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X @ A )
=> ( member1104366573291651755c_fm_i @ ( F3 @ X ) @ ( image_2913337242412145381c_fm_i @ F3 @ A ) ) ) ).
% imageI
thf(fact_1185_imageI,axiom,
! [X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,F3: set_Epistemic_fm_i > epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X @ A )
=> ( member6642669606046002379c_fm_i @ ( F3 @ X ) @ ( image_809639422248493861c_fm_i @ F3 @ A ) ) ) ).
% imageI
thf(fact_1186_imageI,axiom,
! [X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X @ A )
=> ( member1104366573291651755c_fm_i @ ( F3 @ X ) @ ( image_2698589095351095557c_fm_i @ F3 @ A ) ) ) ).
% imageI
thf(fact_1187_rev__image__eqI,axiom,
! [X: epistemic_fm_i,A: set_Epistemic_fm_i,B3: epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X @ A )
=> ( ( B3
= ( F3 @ X ) )
=> ( member6642669606046002379c_fm_i @ B3 @ ( image_120052958407486725c_fm_i @ F3 @ A ) ) ) ) ).
% rev_image_eqI
thf(fact_1188_rev__image__eqI,axiom,
! [X: epistemic_fm_i,A: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,F3: epistemic_fm_i > set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X @ A )
=> ( ( B3
= ( F3 @ X ) )
=> ( member1104366573291651755c_fm_i @ B3 @ ( image_2913337242412145381c_fm_i @ F3 @ A ) ) ) ) ).
% rev_image_eqI
thf(fact_1189_rev__image__eqI,axiom,
! [X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B3: epistemic_fm_i,F3: set_Epistemic_fm_i > epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X @ A )
=> ( ( B3
= ( F3 @ X ) )
=> ( member6642669606046002379c_fm_i @ B3 @ ( image_809639422248493861c_fm_i @ F3 @ A ) ) ) ) ).
% rev_image_eqI
thf(fact_1190_rev__image__eqI,axiom,
! [X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,B3: set_Epistemic_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X @ A )
=> ( ( B3
= ( F3 @ X ) )
=> ( member1104366573291651755c_fm_i @ B3 @ ( image_2698589095351095557c_fm_i @ F3 @ A ) ) ) ) ).
% rev_image_eqI
thf(fact_1191_imageE,axiom,
! [B3: epistemic_fm_i,F3: epistemic_fm_i > epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ B3 @ ( image_120052958407486725c_fm_i @ F3 @ A ) )
=> ~ ! [X3: epistemic_fm_i] :
( ( B3
= ( F3 @ X3 ) )
=> ~ ( member6642669606046002379c_fm_i @ X3 @ A ) ) ) ).
% imageE
thf(fact_1192_imageE,axiom,
! [B3: epistemic_fm_i,F3: set_Epistemic_fm_i > epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member6642669606046002379c_fm_i @ B3 @ ( image_809639422248493861c_fm_i @ F3 @ A ) )
=> ~ ! [X3: set_Epistemic_fm_i] :
( ( B3
= ( F3 @ X3 ) )
=> ~ ( member1104366573291651755c_fm_i @ X3 @ A ) ) ) ).
% imageE
thf(fact_1193_imageE,axiom,
! [B3: set_Epistemic_fm_i,F3: epistemic_fm_i > set_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ B3 @ ( image_2913337242412145381c_fm_i @ F3 @ A ) )
=> ~ ! [X3: epistemic_fm_i] :
( ( B3
= ( F3 @ X3 ) )
=> ~ ( member6642669606046002379c_fm_i @ X3 @ A ) ) ) ).
% imageE
thf(fact_1194_imageE,axiom,
! [B3: set_Epistemic_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member1104366573291651755c_fm_i @ B3 @ ( image_2698589095351095557c_fm_i @ F3 @ A ) )
=> ~ ! [X3: set_Epistemic_fm_i] :
( ( B3
= ( F3 @ X3 ) )
=> ~ ( member1104366573291651755c_fm_i @ X3 @ A ) ) ) ).
% imageE
thf(fact_1195_Compr__image__eq,axiom,
! [F3: epistemic_fm_i > epistemic_fm_i,A: set_Epistemic_fm_i,P3: epistemic_fm_i > $o] :
( ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ ( image_120052958407486725c_fm_i @ F3 @ A ) )
& ( P3 @ X2 ) ) )
= ( image_120052958407486725c_fm_i @ F3
@ ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ A )
& ( P3 @ ( F3 @ X2 ) ) ) ) ) ) ).
% Compr_image_eq
thf(fact_1196_Compr__image__eq,axiom,
! [F3: set_Epistemic_fm_i > epistemic_fm_i,A: set_se3485332733965609186c_fm_i,P3: epistemic_fm_i > $o] :
( ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ ( image_809639422248493861c_fm_i @ F3 @ A ) )
& ( P3 @ X2 ) ) )
= ( image_809639422248493861c_fm_i @ F3
@ ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A )
& ( P3 @ ( F3 @ X2 ) ) ) ) ) ) ).
% Compr_image_eq
thf(fact_1197_Compr__image__eq,axiom,
! [F3: epistemic_fm_i > set_Epistemic_fm_i,A: set_Epistemic_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ ( image_2913337242412145381c_fm_i @ F3 @ A ) )
& ( P3 @ X2 ) ) )
= ( image_2913337242412145381c_fm_i @ F3
@ ( collec4904205187116291597c_fm_i
@ ^ [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ A )
& ( P3 @ ( F3 @ X2 ) ) ) ) ) ) ).
% Compr_image_eq
thf(fact_1198_Compr__image__eq,axiom,
! [F3: set_Epistemic_fm_i > set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,P3: set_Epistemic_fm_i > $o] :
( ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ ( image_2698589095351095557c_fm_i @ F3 @ A ) )
& ( P3 @ X2 ) ) )
= ( image_2698589095351095557c_fm_i @ F3
@ ( collec3087743281813070829c_fm_i
@ ^ [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ A )
& ( P3 @ ( F3 @ X2 ) ) ) ) ) ) ).
% Compr_image_eq
thf(fact_1199_in__image__insert__iff,axiom,
! [B2: set_se7339729205154126530c_fm_i,X: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i] :
( ! [C4: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ C4 @ B2 )
=> ~ ( member1104366573291651755c_fm_i @ X @ C4 ) )
=> ( ( member1461078328125707403c_fm_i @ A @ ( image_6052327717552338181c_fm_i @ ( insert7698009978809854162c_fm_i @ X ) @ B2 ) )
= ( ( member1104366573291651755c_fm_i @ X @ A )
& ( member1461078328125707403c_fm_i @ ( minus_1073301138667672009c_fm_i @ A @ ( insert7698009978809854162c_fm_i @ X @ bot_bo145720340923748686c_fm_i ) ) @ B2 ) ) ) ) ).
% in_image_insert_iff
thf(fact_1200_in__image__insert__iff,axiom,
! [B2: set_se3485332733965609186c_fm_i,X: epistemic_fm_i,A: set_Epistemic_fm_i] :
( ! [C4: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ C4 @ B2 )
=> ~ ( member6642669606046002379c_fm_i @ X @ C4 ) )
=> ( ( member1104366573291651755c_fm_i @ A @ ( image_2698589095351095557c_fm_i @ ( insert7817948997695205106c_fm_i @ X ) @ B2 ) )
= ( ( member6642669606046002379c_fm_i @ X @ A )
& ( member1104366573291651755c_fm_i @ ( minus_1543973939109951465c_fm_i @ A @ ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) ) @ B2 ) ) ) ) ).
% in_image_insert_iff
thf(fact_1201_Inf__fin_Ohom__commute,axiom,
! [H2: set_Epistemic_fm_i > set_Epistemic_fm_i,N2: set_se3485332733965609186c_fm_i] :
( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i] :
( ( H2 @ ( inf_in3450601097109690352c_fm_i @ X3 @ Y4 ) )
= ( inf_in3450601097109690352c_fm_i @ ( H2 @ X3 ) @ ( H2 @ Y4 ) ) )
=> ( ( finite7933139204641697195c_fm_i @ N2 )
=> ( ( N2 != bot_bo145720340923748686c_fm_i )
=> ( ( H2 @ ( lattic8495942116038605215c_fm_i @ N2 ) )
= ( lattic8495942116038605215c_fm_i @ ( image_2698589095351095557c_fm_i @ H2 @ N2 ) ) ) ) ) ) ).
% Inf_fin.hom_commute
thf(fact_1202_Inf__fin_Ohom__commute,axiom,
! [H2: set_se3485332733965609186c_fm_i > set_se3485332733965609186c_fm_i,N2: set_se7339729205154126530c_fm_i] :
( ! [X3: set_se3485332733965609186c_fm_i,Y4: set_se3485332733965609186c_fm_i] :
( ( H2 @ ( inf_in161960956874937808c_fm_i @ X3 @ Y4 ) )
= ( inf_in161960956874937808c_fm_i @ ( H2 @ X3 ) @ ( H2 @ Y4 ) ) )
=> ( ( finite9087983574947184523c_fm_i @ N2 )
=> ( ( N2 != bot_bo4781621276559889198c_fm_i )
=> ( ( H2 @ ( lattic7860428167660714879c_fm_i @ N2 ) )
= ( lattic7860428167660714879c_fm_i @ ( image_6052327717552338181c_fm_i @ H2 @ N2 ) ) ) ) ) ) ).
% Inf_fin.hom_commute
thf(fact_1203_Sup__fin_Ohom__commute,axiom,
! [H2: set_Epistemic_fm_i > set_Epistemic_fm_i,N2: set_se3485332733965609186c_fm_i] :
( ! [X3: set_Epistemic_fm_i,Y4: set_Epistemic_fm_i] :
( ( H2 @ ( sup_su1936195050962291414c_fm_i @ X3 @ Y4 ) )
= ( sup_su1936195050962291414c_fm_i @ ( H2 @ X3 ) @ ( H2 @ Y4 ) ) )
=> ( ( finite7933139204641697195c_fm_i @ N2 )
=> ( ( N2 != bot_bo145720340923748686c_fm_i )
=> ( ( H2 @ ( lattic3744900211830597177c_fm_i @ N2 ) )
= ( lattic3744900211830597177c_fm_i @ ( image_2698589095351095557c_fm_i @ H2 @ N2 ) ) ) ) ) ) ).
% Sup_fin.hom_commute
thf(fact_1204_Pow__set_I2_J,axiom,
! [X: epistemic_fm_i,Xs: list_Epistemic_fm_i] :
( ( pow_Epistemic_fm_i @ ( set_Epistemic_fm_i2 @ ( cons_Epistemic_fm_i @ X @ Xs ) ) )
= ( sup_su2582925890723967158c_fm_i @ ( pow_Epistemic_fm_i @ ( set_Epistemic_fm_i2 @ Xs ) ) @ ( image_2698589095351095557c_fm_i @ ( insert7817948997695205106c_fm_i @ X ) @ ( pow_Epistemic_fm_i @ ( set_Epistemic_fm_i2 @ Xs ) ) ) ) ) ).
% Pow_set(2)
thf(fact_1205_PowI,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( member1104366573291651755c_fm_i @ A @ ( pow_Epistemic_fm_i @ B2 ) ) ) ).
% PowI
thf(fact_1206_Pow__iff,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A @ ( pow_Epistemic_fm_i @ B2 ) )
= ( ord_le3843937902494030498c_fm_i @ A @ B2 ) ) ).
% Pow_iff
thf(fact_1207_finite__Pow__iff,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( finite9087983574947184523c_fm_i @ ( pow_se279538576771467295c_fm_i @ A ) )
= ( finite7933139204641697195c_fm_i @ A ) ) ).
% finite_Pow_iff
thf(fact_1208_finite__Pow__iff,axiom,
! [A: set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ ( pow_Epistemic_fm_i @ A ) )
= ( finite3304564979551393739c_fm_i @ A ) ) ).
% finite_Pow_iff
thf(fact_1209_Pow__Int__eq,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( pow_Epistemic_fm_i @ ( inf_in3450601097109690352c_fm_i @ A @ B2 ) )
= ( inf_in161960956874937808c_fm_i @ ( pow_Epistemic_fm_i @ A ) @ ( pow_Epistemic_fm_i @ B2 ) ) ) ).
% Pow_Int_eq
thf(fact_1210_Pow__Int__eq,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( pow_se279538576771467295c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) )
= ( inf_in5373734518419001264c_fm_i @ ( pow_se279538576771467295c_fm_i @ A ) @ ( pow_se279538576771467295c_fm_i @ B2 ) ) ) ).
% Pow_Int_eq
thf(fact_1211_Un__Pow__subset,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] : ( ord_le5389487502678872194c_fm_i @ ( sup_su2582925890723967158c_fm_i @ ( pow_Epistemic_fm_i @ A ) @ ( pow_Epistemic_fm_i @ B2 ) ) @ ( pow_Epistemic_fm_i @ ( sup_su1936195050962291414c_fm_i @ A @ B2 ) ) ) ).
% Un_Pow_subset
thf(fact_1212_PowD,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ A @ ( pow_Epistemic_fm_i @ B2 ) )
=> ( ord_le3843937902494030498c_fm_i @ A @ B2 ) ) ).
% PowD
thf(fact_1213_Pow__mono,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ord_le5389487502678872194c_fm_i @ ( pow_Epistemic_fm_i @ A ) @ ( pow_Epistemic_fm_i @ B2 ) ) ) ).
% Pow_mono
thf(fact_1214_Pow__def,axiom,
( pow_Epistemic_fm_i
= ( ^ [A3: set_Epistemic_fm_i] :
( collec3087743281813070829c_fm_i
@ ^ [B: set_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ B @ A3 ) ) ) ) ).
% Pow_def
thf(fact_1215_Pow__top,axiom,
! [A: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ A @ ( pow_Epistemic_fm_i @ A ) ) ).
% Pow_top
thf(fact_1216_Pow__bottom,axiom,
! [B2: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ bot_bo4194595901900360558c_fm_i @ ( pow_Epistemic_fm_i @ B2 ) ) ).
% Pow_bottom
thf(fact_1217_finite__bind,axiom,
! [S: set_Epistemic_fm_i,F3: epistemic_fm_i > set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ S )
=> ( ! [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ S )
=> ( finite3304564979551393739c_fm_i @ ( F3 @ X3 ) ) )
=> ( finite3304564979551393739c_fm_i @ ( bind_E4051058263104957139c_fm_i @ S @ F3 ) ) ) ) ).
% finite_bind
thf(fact_1218_finite__bind,axiom,
! [S: set_Epistemic_fm_i,F3: epistemic_fm_i > set_se3485332733965609186c_fm_i] :
( ( finite3304564979551393739c_fm_i @ S )
=> ( ! [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ S )
=> ( finite7933139204641697195c_fm_i @ ( F3 @ X3 ) ) )
=> ( finite7933139204641697195c_fm_i @ ( bind_E1456725107580952755c_fm_i @ S @ F3 ) ) ) ) ).
% finite_bind
thf(fact_1219_finite__bind,axiom,
! [S: set_se3485332733965609186c_fm_i,F3: set_Epistemic_fm_i > set_Epistemic_fm_i] :
( ( finite7933139204641697195c_fm_i @ S )
=> ( ! [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ S )
=> ( finite3304564979551393739c_fm_i @ ( F3 @ X3 ) ) )
=> ( finite3304564979551393739c_fm_i @ ( bind_s8576399324272077043c_fm_i @ S @ F3 ) ) ) ) ).
% finite_bind
thf(fact_1220_finite__bind,axiom,
! [S: set_se3485332733965609186c_fm_i,F3: set_Epistemic_fm_i > set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ S )
=> ( ! [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ S )
=> ( finite7933139204641697195c_fm_i @ ( F3 @ X3 ) ) )
=> ( finite7933139204641697195c_fm_i @ ( bind_s8077422299240980179c_fm_i @ S @ F3 ) ) ) ) ).
% finite_bind
thf(fact_1221_Pow__fold,axiom,
! [A: set_Epistemic_fm_i] :
( ( finite3304564979551393739c_fm_i @ A )
=> ( ( pow_Epistemic_fm_i @ A )
= ( finite296791182991827080c_fm_i
@ ^ [X2: epistemic_fm_i,A3: set_se3485332733965609186c_fm_i] : ( sup_su2582925890723967158c_fm_i @ A3 @ ( image_2698589095351095557c_fm_i @ ( insert7817948997695205106c_fm_i @ X2 ) @ A3 ) )
@ ( insert7698009978809854162c_fm_i @ bot_bo4194595901900360558c_fm_i @ bot_bo145720340923748686c_fm_i )
@ A ) ) ) ).
% Pow_fold
thf(fact_1222_Pow__fold,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ( finite7933139204641697195c_fm_i @ A )
=> ( ( pow_se279538576771467295c_fm_i @ A )
= ( finite8679521513121883272c_fm_i
@ ^ [X2: set_Epistemic_fm_i,A3: set_se7339729205154126530c_fm_i] : ( sup_su2317974602288960150c_fm_i @ A3 @ ( image_6052327717552338181c_fm_i @ ( insert7698009978809854162c_fm_i @ X2 ) @ A3 ) )
@ ( insert7111703059596746418c_fm_i @ bot_bo145720340923748686c_fm_i @ bot_bo4781621276559889198c_fm_i )
@ A ) ) ) ).
% Pow_fold
thf(fact_1223_infinite__Pow,axiom,
! [A: set_Epistemic_fm_i] :
( ~ ( finite3304564979551393739c_fm_i @ A )
=> ~ ( finite7933139204641697195c_fm_i @ ( pow_Epistemic_fm_i @ A ) ) ) ).
% infinite_Pow
thf(fact_1224_infinite__Pow,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ~ ( finite7933139204641697195c_fm_i @ A )
=> ~ ( finite9087983574947184523c_fm_i @ ( pow_se279538576771467295c_fm_i @ A ) ) ) ).
% infinite_Pow
thf(fact_1225_Pow__set_I1_J,axiom,
( ( pow_Epistemic_fm_i @ ( set_Epistemic_fm_i2 @ nil_Epistemic_fm_i ) )
= ( insert7698009978809854162c_fm_i @ bot_bo4194595901900360558c_fm_i @ bot_bo145720340923748686c_fm_i ) ) ).
% Pow_set(1)
thf(fact_1226_chains__extend,axiom,
! [C2: set_se3485332733965609186c_fm_i,S: set_se3485332733965609186c_fm_i,Z: set_Epistemic_fm_i] :
( ( member1461078328125707403c_fm_i @ C2 @ ( chains830531755891748338c_fm_i @ S ) )
=> ( ( member1104366573291651755c_fm_i @ Z @ S )
=> ( ! [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ C2 )
=> ( ord_le3843937902494030498c_fm_i @ X3 @ Z ) )
=> ( member1461078328125707403c_fm_i @ ( sup_su2582925890723967158c_fm_i @ ( insert7698009978809854162c_fm_i @ Z @ bot_bo145720340923748686c_fm_i ) @ C2 ) @ ( chains830531755891748338c_fm_i @ S ) ) ) ) ) ).
% chains_extend
thf(fact_1227_set__empty2,axiom,
! [Xs: list_Epistemic_fm_i] :
( ( bot_bo4194595901900360558c_fm_i
= ( set_Epistemic_fm_i2 @ Xs ) )
= ( Xs = nil_Epistemic_fm_i ) ) ).
% set_empty2
thf(fact_1228_set__empty,axiom,
! [Xs: list_Epistemic_fm_i] :
( ( ( set_Epistemic_fm_i2 @ Xs )
= bot_bo4194595901900360558c_fm_i )
= ( Xs = nil_Epistemic_fm_i ) ) ).
% set_empty
thf(fact_1229_Zorn__Lemma2,axiom,
! [A: set_se3485332733965609186c_fm_i] :
( ! [X3: set_se3485332733965609186c_fm_i] :
( ( member1461078328125707403c_fm_i @ X3 @ ( chains830531755891748338c_fm_i @ A ) )
=> ? [Xa: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Xa @ A )
& ! [Xb: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Xb @ X3 )
=> ( ord_le3843937902494030498c_fm_i @ Xb @ Xa ) ) ) )
=> ? [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ A )
& ! [Xa: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Xa @ A )
=> ( ( ord_le3843937902494030498c_fm_i @ X3 @ Xa )
=> ( Xa = X3 ) ) ) ) ) ).
% Zorn_Lemma2
thf(fact_1230_chainsD,axiom,
! [C2: set_se3485332733965609186c_fm_i,S: set_se3485332733965609186c_fm_i,X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ( member1461078328125707403c_fm_i @ C2 @ ( chains830531755891748338c_fm_i @ S ) )
=> ( ( member1104366573291651755c_fm_i @ X @ C2 )
=> ( ( member1104366573291651755c_fm_i @ Y @ C2 )
=> ( ( ord_le3843937902494030498c_fm_i @ X @ Y )
| ( ord_le3843937902494030498c_fm_i @ Y @ X ) ) ) ) ) ).
% chainsD
thf(fact_1231_empty__set,axiom,
( bot_bo4194595901900360558c_fm_i
= ( set_Epistemic_fm_i2 @ nil_Epistemic_fm_i ) ) ).
% empty_set
thf(fact_1232_imply_Osimps_I1_J,axiom,
! [Q: epistemic_fm_i] :
( ( epistemic_imply_i @ nil_Epistemic_fm_i @ Q )
= Q ) ).
% imply.simps(1)
thf(fact_1233_empty__Shift,axiom,
! [Kl: set_li8269783359719514504c_fm_i,K: epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ nil_Epistemic_fm_i @ Kl )
=> ( ( member6642669606046002379c_fm_i @ K @ ( bNF_Gr1093487169986386109c_fm_i @ Kl @ nil_Epistemic_fm_i ) )
=> ( member6475149752759350353c_fm_i @ nil_Epistemic_fm_i @ ( bNF_Gr8437504169225076033c_fm_i @ Kl @ K ) ) ) ) ).
% empty_Shift
thf(fact_1234_empty__Shift,axiom,
! [Kl: set_li2934481837907835752c_fm_i,K: set_Epistemic_fm_i] :
( ( member605545779687026225c_fm_i @ nil_se670848885773549064c_fm_i @ Kl )
=> ( ( member1104366573291651755c_fm_i @ K @ ( bNF_Gr2376118584863155869c_fm_i @ Kl @ nil_se670848885773549064c_fm_i ) )
=> ( member605545779687026225c_fm_i @ nil_se670848885773549064c_fm_i @ ( bNF_Gr8275819806307007265c_fm_i @ Kl @ K ) ) ) ) ).
% empty_Shift
thf(fact_1235_subset__code_I3_J,axiom,
~ ( ord_le3843937902494030498c_fm_i @ ( coset_Epistemic_fm_i @ nil_Epistemic_fm_i ) @ ( set_Epistemic_fm_i2 @ nil_Epistemic_fm_i ) ) ).
% subset_code(3)
thf(fact_1236_conjunct_Osimps_I1_J,axiom,
( ( stalnaker_conjunct_i @ nil_Epistemic_fm_i )
= ( epistemic_Imp_i @ epistemic_FF_i @ epistemic_FF_i ) ) ).
% conjunct.simps(1)
thf(fact_1237_the__elem__set,axiom,
! [X: epistemic_fm_i] :
( ( the_el2173195912186371479c_fm_i @ ( set_Epistemic_fm_i2 @ ( cons_Epistemic_fm_i @ X @ nil_Epistemic_fm_i ) ) )
= X ) ).
% the_elem_set
thf(fact_1238_chain__subset__def,axiom,
( chain_7805378461283022331c_fm_i
= ( ^ [C3: set_se3485332733965609186c_fm_i] :
! [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ C3 )
=> ! [Y3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ Y3 @ C3 )
=> ( ( ord_le3843937902494030498c_fm_i @ X2 @ Y3 )
| ( ord_le3843937902494030498c_fm_i @ Y3 @ X2 ) ) ) ) ) ) ).
% chain_subset_def
thf(fact_1239_Fpow__mono,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ord_le5389487502678872194c_fm_i @ ( finite7994277067554142856c_fm_i @ A ) @ ( finite7994277067554142856c_fm_i @ B2 ) ) ) ).
% Fpow_mono
thf(fact_1240_empty__in__Fpow,axiom,
! [A: set_Epistemic_fm_i] : ( member1104366573291651755c_fm_i @ bot_bo4194595901900360558c_fm_i @ ( finite7994277067554142856c_fm_i @ A ) ) ).
% empty_in_Fpow
thf(fact_1241_Fpow__def,axiom,
( finite7612387961876094056c_fm_i
= ( ^ [A3: set_se3485332733965609186c_fm_i] :
( collec2761885132556217805c_fm_i
@ ^ [X7: set_se3485332733965609186c_fm_i] :
( ( ord_le5389487502678872194c_fm_i @ X7 @ A3 )
& ( finite7933139204641697195c_fm_i @ X7 ) ) ) ) ) ).
% Fpow_def
thf(fact_1242_Fpow__def,axiom,
( finite7994277067554142856c_fm_i
= ( ^ [A3: set_Epistemic_fm_i] :
( collec3087743281813070829c_fm_i
@ ^ [X7: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X7 @ A3 )
& ( finite3304564979551393739c_fm_i @ X7 ) ) ) ) ) ).
% Fpow_def
thf(fact_1243_subset__subseqs,axiom,
! [X5: set_Epistemic_fm_i,Xs: list_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ X5 @ ( set_Epistemic_fm_i2 @ Xs ) )
=> ( member1104366573291651755c_fm_i @ X5 @ ( image_4310783338035737183c_fm_i @ set_Epistemic_fm_i2 @ ( set_li9010496130497932989c_fm_i @ ( subseq859285874047815415c_fm_i @ Xs ) ) ) ) ) ).
% subset_subseqs
thf(fact_1244_subseqs__powset,axiom,
! [Xs: list_Epistemic_fm_i] :
( ( image_4310783338035737183c_fm_i @ set_Epistemic_fm_i2 @ ( set_li9010496130497932989c_fm_i @ ( subseq859285874047815415c_fm_i @ Xs ) ) )
= ( pow_Epistemic_fm_i @ ( set_Epistemic_fm_i2 @ Xs ) ) ) ).
% subseqs_powset
thf(fact_1245_Fpow__Pow__finite,axiom,
( finite7612387961876094056c_fm_i
= ( ^ [A3: set_se3485332733965609186c_fm_i] : ( inf_in5373734518419001264c_fm_i @ ( pow_se279538576771467295c_fm_i @ A3 ) @ ( collec2761885132556217805c_fm_i @ finite7933139204641697195c_fm_i ) ) ) ) ).
% Fpow_Pow_finite
thf(fact_1246_Fpow__Pow__finite,axiom,
( finite7994277067554142856c_fm_i
= ( ^ [A3: set_Epistemic_fm_i] : ( inf_in161960956874937808c_fm_i @ ( pow_Epistemic_fm_i @ A3 ) @ ( collec3087743281813070829c_fm_i @ finite3304564979551393739c_fm_i ) ) ) ) ).
% Fpow_Pow_finite
thf(fact_1247_Cons__in__lists__iff,axiom,
! [X: epistemic_fm_i,Xs: list_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ ( cons_Epistemic_fm_i @ X @ Xs ) @ ( lists_Epistemic_fm_i @ A ) )
= ( ( member6642669606046002379c_fm_i @ X @ A )
& ( member6475149752759350353c_fm_i @ Xs @ ( lists_Epistemic_fm_i @ A ) ) ) ) ).
% Cons_in_lists_iff
thf(fact_1248_Cons__in__lists__iff,axiom,
! [X: set_Epistemic_fm_i,Xs: list_s8081015415394010888c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member605545779687026225c_fm_i @ ( cons_s4962720389763977656c_fm_i @ X @ Xs ) @ ( lists_3378462843525889270c_fm_i @ A ) )
= ( ( member1104366573291651755c_fm_i @ X @ A )
& ( member605545779687026225c_fm_i @ Xs @ ( lists_3378462843525889270c_fm_i @ A ) ) ) ) ).
% Cons_in_lists_iff
thf(fact_1249_in__listsI,axiom,
! [Xs: list_s8081015415394010888c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ! [X3: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X3 @ ( set_se200842218512397079c_fm_i @ Xs ) )
=> ( member1104366573291651755c_fm_i @ X3 @ A ) )
=> ( member605545779687026225c_fm_i @ Xs @ ( lists_3378462843525889270c_fm_i @ A ) ) ) ).
% in_listsI
thf(fact_1250_in__listsI,axiom,
! [Xs: list_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ! [X3: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X3 @ ( set_Epistemic_fm_i2 @ Xs ) )
=> ( member6642669606046002379c_fm_i @ X3 @ A ) )
=> ( member6475149752759350353c_fm_i @ Xs @ ( lists_Epistemic_fm_i @ A ) ) ) ).
% in_listsI
thf(fact_1251_lists__Int__eq,axiom,
! [A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( lists_3378462843525889270c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) )
= ( inf_in3319901132148857174c_fm_i @ ( lists_3378462843525889270c_fm_i @ A ) @ ( lists_3378462843525889270c_fm_i @ B2 ) ) ) ).
% lists_Int_eq
thf(fact_1252_lists_Ocases,axiom,
! [A2: list_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ A2 @ ( lists_Epistemic_fm_i @ A ) )
=> ( ( A2 != nil_Epistemic_fm_i )
=> ~ ! [A6: epistemic_fm_i,L: list_Epistemic_fm_i] :
( ( A2
= ( cons_Epistemic_fm_i @ A6 @ L ) )
=> ( ( member6642669606046002379c_fm_i @ A6 @ A )
=> ~ ( member6475149752759350353c_fm_i @ L @ ( lists_Epistemic_fm_i @ A ) ) ) ) ) ) ).
% lists.cases
thf(fact_1253_lists_Ocases,axiom,
! [A2: list_s8081015415394010888c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member605545779687026225c_fm_i @ A2 @ ( lists_3378462843525889270c_fm_i @ A ) )
=> ( ( A2 != nil_se670848885773549064c_fm_i )
=> ~ ! [A6: set_Epistemic_fm_i,L: list_s8081015415394010888c_fm_i] :
( ( A2
= ( cons_s4962720389763977656c_fm_i @ A6 @ L ) )
=> ( ( member1104366573291651755c_fm_i @ A6 @ A )
=> ~ ( member605545779687026225c_fm_i @ L @ ( lists_3378462843525889270c_fm_i @ A ) ) ) ) ) ) ).
% lists.cases
thf(fact_1254_lists_Osimps,axiom,
! [A2: list_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ A2 @ ( lists_Epistemic_fm_i @ A ) )
= ( ( A2 = nil_Epistemic_fm_i )
| ? [A4: epistemic_fm_i,L2: list_Epistemic_fm_i] :
( ( A2
= ( cons_Epistemic_fm_i @ A4 @ L2 ) )
& ( member6642669606046002379c_fm_i @ A4 @ A )
& ( member6475149752759350353c_fm_i @ L2 @ ( lists_Epistemic_fm_i @ A ) ) ) ) ) ).
% lists.simps
thf(fact_1255_lists_Osimps,axiom,
! [A2: list_s8081015415394010888c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member605545779687026225c_fm_i @ A2 @ ( lists_3378462843525889270c_fm_i @ A ) )
= ( ( A2 = nil_se670848885773549064c_fm_i )
| ? [A4: set_Epistemic_fm_i,L2: list_s8081015415394010888c_fm_i] :
( ( A2
= ( cons_s4962720389763977656c_fm_i @ A4 @ L2 ) )
& ( member1104366573291651755c_fm_i @ A4 @ A )
& ( member605545779687026225c_fm_i @ L2 @ ( lists_3378462843525889270c_fm_i @ A ) ) ) ) ) ).
% lists.simps
thf(fact_1256_listsE,axiom,
! [X: epistemic_fm_i,L3: list_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ ( cons_Epistemic_fm_i @ X @ L3 ) @ ( lists_Epistemic_fm_i @ A ) )
=> ~ ( ( member6642669606046002379c_fm_i @ X @ A )
=> ~ ( member6475149752759350353c_fm_i @ L3 @ ( lists_Epistemic_fm_i @ A ) ) ) ) ).
% listsE
thf(fact_1257_listsE,axiom,
! [X: set_Epistemic_fm_i,L3: list_s8081015415394010888c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member605545779687026225c_fm_i @ ( cons_s4962720389763977656c_fm_i @ X @ L3 ) @ ( lists_3378462843525889270c_fm_i @ A ) )
=> ~ ( ( member1104366573291651755c_fm_i @ X @ A )
=> ~ ( member605545779687026225c_fm_i @ L3 @ ( lists_3378462843525889270c_fm_i @ A ) ) ) ) ).
% listsE
thf(fact_1258_lists_OCons,axiom,
! [A2: epistemic_fm_i,A: set_Epistemic_fm_i,L3: list_Epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ A2 @ A )
=> ( ( member6475149752759350353c_fm_i @ L3 @ ( lists_Epistemic_fm_i @ A ) )
=> ( member6475149752759350353c_fm_i @ ( cons_Epistemic_fm_i @ A2 @ L3 ) @ ( lists_Epistemic_fm_i @ A ) ) ) ) ).
% lists.Cons
thf(fact_1259_lists_OCons,axiom,
! [A2: set_Epistemic_fm_i,A: set_se3485332733965609186c_fm_i,L3: list_s8081015415394010888c_fm_i] :
( ( member1104366573291651755c_fm_i @ A2 @ A )
=> ( ( member605545779687026225c_fm_i @ L3 @ ( lists_3378462843525889270c_fm_i @ A ) )
=> ( member605545779687026225c_fm_i @ ( cons_s4962720389763977656c_fm_i @ A2 @ L3 ) @ ( lists_3378462843525889270c_fm_i @ A ) ) ) ) ).
% lists.Cons
thf(fact_1260_lists__IntI,axiom,
! [L3: list_s8081015415394010888c_fm_i,A: set_se3485332733965609186c_fm_i,B2: set_se3485332733965609186c_fm_i] :
( ( member605545779687026225c_fm_i @ L3 @ ( lists_3378462843525889270c_fm_i @ A ) )
=> ( ( member605545779687026225c_fm_i @ L3 @ ( lists_3378462843525889270c_fm_i @ B2 ) )
=> ( member605545779687026225c_fm_i @ L3 @ ( lists_3378462843525889270c_fm_i @ ( inf_in161960956874937808c_fm_i @ A @ B2 ) ) ) ) ) ).
% lists_IntI
thf(fact_1261_lists__mono,axiom,
! [A: set_Epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ( ord_le3843937902494030498c_fm_i @ A @ B2 )
=> ( ord_le1209247765174941992c_fm_i @ ( lists_Epistemic_fm_i @ A ) @ ( lists_Epistemic_fm_i @ B2 ) ) ) ).
% lists_mono
thf(fact_1262_lists__def2,axiom,
( lists_Epistemic_fm_i
= ( ^ [A3: set_Epistemic_fm_i] :
( collec5759350117362652307c_fm_i
@ ^ [L2: list_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( set_Epistemic_fm_i2 @ L2 ) @ A3 ) ) ) ) ).
% lists_def2
thf(fact_1263_in__lists__conv__set,axiom,
! [Xs: list_s8081015415394010888c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member605545779687026225c_fm_i @ Xs @ ( lists_3378462843525889270c_fm_i @ A ) )
= ( ! [X2: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X2 @ ( set_se200842218512397079c_fm_i @ Xs ) )
=> ( member1104366573291651755c_fm_i @ X2 @ A ) ) ) ) ).
% in_lists_conv_set
thf(fact_1264_in__lists__conv__set,axiom,
! [Xs: list_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ Xs @ ( lists_Epistemic_fm_i @ A ) )
= ( ! [X2: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X2 @ ( set_Epistemic_fm_i2 @ Xs ) )
=> ( member6642669606046002379c_fm_i @ X2 @ A ) ) ) ) ).
% in_lists_conv_set
thf(fact_1265_in__listsD,axiom,
! [Xs: list_s8081015415394010888c_fm_i,A: set_se3485332733965609186c_fm_i] :
( ( member605545779687026225c_fm_i @ Xs @ ( lists_3378462843525889270c_fm_i @ A ) )
=> ! [X6: set_Epistemic_fm_i] :
( ( member1104366573291651755c_fm_i @ X6 @ ( set_se200842218512397079c_fm_i @ Xs ) )
=> ( member1104366573291651755c_fm_i @ X6 @ A ) ) ) ).
% in_listsD
thf(fact_1266_in__listsD,axiom,
! [Xs: list_Epistemic_fm_i,A: set_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ Xs @ ( lists_Epistemic_fm_i @ A ) )
=> ! [X6: epistemic_fm_i] :
( ( member6642669606046002379c_fm_i @ X6 @ ( set_Epistemic_fm_i2 @ Xs ) )
=> ( member6642669606046002379c_fm_i @ X6 @ A ) ) ) ).
% in_listsD
thf(fact_1267_infinite__Func,axiom,
! [A: set_Epistemic_fm_i,B1: epistemic_fm_i,B23: epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ~ ( finite3304564979551393739c_fm_i @ A )
=> ( ( ord_le3843937902494030498c_fm_i @ ( insert7817948997695205106c_fm_i @ B1 @ ( insert7817948997695205106c_fm_i @ B23 @ bot_bo4194595901900360558c_fm_i ) ) @ B2 )
=> ( ( B1 != B23 )
=> ~ ( finite4369126853184676732c_fm_i @ ( bNF_We489590214134045204c_fm_i @ A @ B2 ) ) ) ) ) ).
% infinite_Func
thf(fact_1268_infinite__Func,axiom,
! [A: set_se3485332733965609186c_fm_i,B1: epistemic_fm_i,B23: epistemic_fm_i,B2: set_Epistemic_fm_i] :
( ~ ( finite7933139204641697195c_fm_i @ A )
=> ( ( ord_le3843937902494030498c_fm_i @ ( insert7817948997695205106c_fm_i @ B1 @ ( insert7817948997695205106c_fm_i @ B23 @ bot_bo4194595901900360558c_fm_i ) ) @ B2 )
=> ( ( B1 != B23 )
=> ~ ( finite5517585301071133084c_fm_i @ ( bNF_We7251144373225460788c_fm_i @ A @ B2 ) ) ) ) ) ).
% infinite_Func
thf(fact_1269_set__shuffles,axiom,
! [Zs: list_Epistemic_fm_i,Xs: list_Epistemic_fm_i,Ys: list_Epistemic_fm_i] :
( ( member6475149752759350353c_fm_i @ Zs @ ( shuffl511019056595460925c_fm_i @ Xs @ Ys ) )
=> ( ( set_Epistemic_fm_i2 @ Zs )
= ( sup_su1936195050962291414c_fm_i @ ( set_Epistemic_fm_i2 @ Xs ) @ ( set_Epistemic_fm_i2 @ Ys ) ) ) ) ).
% set_shuffles
thf(fact_1270_in__set__remove1,axiom,
! [A2: set_Epistemic_fm_i,B3: set_Epistemic_fm_i,Xs: list_s8081015415394010888c_fm_i] :
( ( A2 != B3 )
=> ( ( member1104366573291651755c_fm_i @ A2 @ ( set_se200842218512397079c_fm_i @ ( remove2021789187851727006c_fm_i @ B3 @ Xs ) ) )
= ( member1104366573291651755c_fm_i @ A2 @ ( set_se200842218512397079c_fm_i @ Xs ) ) ) ) ).
% in_set_remove1
thf(fact_1271_in__set__remove1,axiom,
! [A2: epistemic_fm_i,B3: epistemic_fm_i,Xs: list_Epistemic_fm_i] :
( ( A2 != B3 )
=> ( ( member6642669606046002379c_fm_i @ A2 @ ( set_Epistemic_fm_i2 @ ( remove8001893566138066622c_fm_i @ B3 @ Xs ) ) )
= ( member6642669606046002379c_fm_i @ A2 @ ( set_Epistemic_fm_i2 @ Xs ) ) ) ) ).
% in_set_remove1
thf(fact_1272_remove1__idem,axiom,
! [X: set_Epistemic_fm_i,Xs: list_s8081015415394010888c_fm_i] :
( ~ ( member1104366573291651755c_fm_i @ X @ ( set_se200842218512397079c_fm_i @ Xs ) )
=> ( ( remove2021789187851727006c_fm_i @ X @ Xs )
= Xs ) ) ).
% remove1_idem
thf(fact_1273_remove1__idem,axiom,
! [X: epistemic_fm_i,Xs: list_Epistemic_fm_i] :
( ~ ( member6642669606046002379c_fm_i @ X @ ( set_Epistemic_fm_i2 @ Xs ) )
=> ( ( remove8001893566138066622c_fm_i @ X @ Xs )
= Xs ) ) ).
% remove1_idem
thf(fact_1274_notin__set__remove1,axiom,
! [X: set_Epistemic_fm_i,Xs: list_s8081015415394010888c_fm_i,Y: set_Epistemic_fm_i] :
( ~ ( member1104366573291651755c_fm_i @ X @ ( set_se200842218512397079c_fm_i @ Xs ) )
=> ~ ( member1104366573291651755c_fm_i @ X @ ( set_se200842218512397079c_fm_i @ ( remove2021789187851727006c_fm_i @ Y @ Xs ) ) ) ) ).
% notin_set_remove1
thf(fact_1275_notin__set__remove1,axiom,
! [X: epistemic_fm_i,Xs: list_Epistemic_fm_i,Y: epistemic_fm_i] :
( ~ ( member6642669606046002379c_fm_i @ X @ ( set_Epistemic_fm_i2 @ Xs ) )
=> ~ ( member6642669606046002379c_fm_i @ X @ ( set_Epistemic_fm_i2 @ ( remove8001893566138066622c_fm_i @ Y @ Xs ) ) ) ) ).
% notin_set_remove1
thf(fact_1276_set__remove1__subset,axiom,
! [X: epistemic_fm_i,Xs: list_Epistemic_fm_i] : ( ord_le3843937902494030498c_fm_i @ ( set_Epistemic_fm_i2 @ ( remove8001893566138066622c_fm_i @ X @ Xs ) ) @ ( set_Epistemic_fm_i2 @ Xs ) ) ).
% set_remove1_subset
thf(fact_1277_set__remove1__eq,axiom,
! [Xs: list_Epistemic_fm_i,X: epistemic_fm_i] :
( ( distin5379319190628067867c_fm_i @ Xs )
=> ( ( set_Epistemic_fm_i2 @ ( remove8001893566138066622c_fm_i @ X @ Xs ) )
= ( minus_1543973939109951465c_fm_i @ ( set_Epistemic_fm_i2 @ Xs ) @ ( insert7817948997695205106c_fm_i @ X @ bot_bo4194595901900360558c_fm_i ) ) ) ) ).
% set_remove1_eq
% Helper facts (11)
thf(help_If_2_1_If_001t__Epistemic____Logic__Ofm_Itf__i_J_T,axiom,
! [X: epistemic_fm_i,Y: epistemic_fm_i] :
( ( if_Epistemic_fm_i @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Epistemic____Logic__Ofm_Itf__i_J_T,axiom,
! [X: epistemic_fm_i,Y: epistemic_fm_i] :
( ( if_Epistemic_fm_i @ $true @ X @ Y )
= X ) ).
thf(help_If_2_1_If_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__i_J_J_T,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ( if_set2943457721768014536c_fm_i @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__i_J_J_T,axiom,
! [X: set_Epistemic_fm_i,Y: set_Epistemic_fm_i] :
( ( if_set2943457721768014536c_fm_i @ $true @ X @ Y )
= X ) ).
thf(help_If_2_1_If_001t__List__Olist_It__Epistemic____Logic__Ofm_Itf__i_J_J_T,axiom,
! [X: list_Epistemic_fm_i,Y: list_Epistemic_fm_i] :
( ( if_lis3446954105117697518c_fm_i @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__List__Olist_It__Epistemic____Logic__Ofm_Itf__i_J_J_T,axiom,
! [X: list_Epistemic_fm_i,Y: list_Epistemic_fm_i] :
( ( if_lis3446954105117697518c_fm_i @ $true @ X @ Y )
= X ) ).
thf(help_If_2_1_If_001t__Set__Oset_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__i_J_J_J_T,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] :
( ( if_set3792857027667890344c_fm_i @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Set__Oset_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__i_J_J_J_T,axiom,
! [X: set_se3485332733965609186c_fm_i,Y: set_se3485332733965609186c_fm_i] :
( ( if_set3792857027667890344c_fm_i @ $true @ X @ Y )
= X ) ).
thf(help_If_3_1_If_001t__List__Olist_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__i_J_J_J_T,axiom,
! [P3: $o] :
( ( P3 = $true )
| ( P3 = $false ) ) ).
thf(help_If_2_1_If_001t__List__Olist_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__i_J_J_J_T,axiom,
! [X: list_s8081015415394010888c_fm_i,Y: list_s8081015415394010888c_fm_i] :
( ( if_lis2088983353317256142c_fm_i @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__List__Olist_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__i_J_J_J_T,axiom,
! [X: list_s8081015415394010888c_fm_i,Y: list_s8081015415394010888c_fm_i] :
( ( if_lis2088983353317256142c_fm_i @ $true @ X @ Y )
= X ) ).
% Conjectures (2)
thf(conj_0,hypothesis,
! [S5: list_Epistemic_fm_i] :
( ( epistemic_AK_i @ a @ ( epistemic_imply_i @ S5 @ epistemic_FF_i ) )
=> ( ( ord_le3843937902494030498c_fm_i @ ( set_Epistemic_fm_i2 @ S5 )
@ ( sup_su1936195050962291414c_fm_i
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ i2 @ P2 ) @ w ) )
@ ( collec4904205187116291597c_fm_i
@ ^ [P2: epistemic_fm_i] : ( member6642669606046002379c_fm_i @ ( epistemic_K_i @ i2 @ P2 ) @ u ) ) ) )
=> ( ( finite3304564979551393739c_fm_i @ ( set_Epistemic_fm_i2 @ S5 ) )
=> thesis ) ) ) ).
thf(conj_1,conjecture,
thesis ).
%------------------------------------------------------------------------------