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% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:16:07.672

% Could-be-implicit typings (38)
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    produc751143617le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > (produc16571293le_alt > arrow_1857593510le_alt) > produc1158092146le_alt > produc16571293le_alt).
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    produc570876728le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > (produc16571293le_alt > produc16571293le_alt) > produc1158092146le_alt > produc1158092146le_alt).
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    produc1292660252le_alt : (produc16571293le_alt > set_Pr367596371le_alt) > (produc16571293le_alt > set_Pr367596371le_alt) > produc1556433673le_alt > produc541234227le_alt).
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    produc603630534le_alt : (set_Pr367596371le_alt > arrow_1857593510le_alt) > (set_Pr367596371le_alt > arrow_1857593510le_alt) > produc541234227le_alt > produc16571293le_alt).
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thf(sy_c_Wellfounded_Olex__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    lex_pr3395839le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr448479039le_alt).
thf(sy_c_Wellfounded_Olex__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    lex_pr788137082le_alt : set_Pr367596371le_alt > set_Pr448479039le_alt > set_Pr1042723573le_alt).
thf(sy_c_Wellfounded_Olex__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    lex_pr1024436954le_alt : set_Pr367596371le_alt > set_Pr851393385le_alt > set_Pr1831300021le_alt).
thf(sy_c_Wellfounded_Olex__prod_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    lex_pr1107764630le_alt : set_Pr448479039le_alt > set_Pr367596371le_alt > set_Pr1209604755le_alt).
thf(sy_c_Wellfounded_Olex__prod_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    lex_pr1691165091le_alt : set_Pr448479039le_alt > set_Pr448479039le_alt > set_Pr139735753le_alt).
thf(sy_c_Wellfounded_Olex__prod_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    lex_pr533832707le_alt : set_Pr448479039le_alt > set_Pr851393385le_alt > set_Pr2007558857le_alt).
thf(sy_c_Wellfounded_Olex__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    lex_pr851747916le_alt : set_Pr851393385le_alt > set_Pr367596371le_alt > set_Pr1906499753le_alt).
thf(sy_c_Wellfounded_Olex__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    lex_pr1924434029le_alt : set_Pr851393385le_alt > set_Pr448479039le_alt > set_Pr1836928287le_alt).
thf(sy_c_Wellfounded_Olex__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    lex_pr787014349le_alt : set_Pr851393385le_alt > set_Pr851393385le_alt > set_Pr1911117087le_alt).
thf(sy_c_Wfrec_Osame__fst_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    same_f554660482le_alt : (arrow_1857593510le_alt > $o) > (arrow_1857593510le_alt > set_Pr367596371le_alt) > set_Pr448479039le_alt).
thf(sy_c_Wfrec_Osame__fst_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    same_f1658501542le_alt : (produc16571293le_alt > $o) > (produc16571293le_alt > set_Pr448479039le_alt) > set_Pr139735753le_alt).
thf(sy_c_Wfrec_Osame__fst_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    same_f263414480le_alt : (set_Pr367596371le_alt > $o) > (set_Pr367596371le_alt > set_Pr851393385le_alt) > set_Pr1911117087le_alt).
thf(sy_c_member_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    member519365071le_alt : arrow_1857593510le_alt > set_Ar1665529862le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    member2048039092le_alt : produc16571293le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member2146260128le_alt : produc1556433673le_alt > set_Pr448479039le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member101850454le_alt : produc1453983551le_alt > set_Pr1042723573le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    member2124338710le_alt : produc209614847le_alt > set_Pr1831300021le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1220670452le_alt : produc425319901le_alt > set_Pr1209604755le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member1145282858le_alt : produc1196277395le_alt > set_Pr139735753le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    member2091907370le_alt : produc937807507le_alt > set_Pr2007558857le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1374323978le_alt : produc1607083763le_alt > set_Pr1906499753le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member1211213440le_alt : produc57113577le_alt > set_Pr1836928287le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    member593317504le_alt : produc16702441le_alt > set_Pr1911117087le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member1392960970le_alt : produc541234227le_alt > set_Pr851393385le_alt > $o).
thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1334244458le_alt : set_Pr367596371le_alt > set_se2071012361le_alt > $o).
thf(sy_v_F, type,
    f : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt).
thf(sy_v_P, type,
    p : arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_v_a, type,
    a : arrow_1857593510le_alt).
thf(sy_v_b, type,
    b : arrow_1857593510le_alt).
thf(sy_v_i, type,
    i : arrow_1429744205e_indi).

% Relevant facts (249)
thf(fact_0_UNIV__I, axiom,
    ((![X : produc541234227le_alt]: (member1392960970le_alt @ X @ top_to1159490073le_alt)))). % UNIV_I
thf(fact_1_UNIV__I, axiom,
    ((![X : produc1556433673le_alt]: (member2146260128le_alt @ X @ top_to960359919le_alt)))). % UNIV_I
thf(fact_2_UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % UNIV_I
thf(fact_3_UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % UNIV_I
thf(fact_4_UNIV__I, axiom,
    ((![X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt)))). % UNIV_I
thf(fact_5_iso__tuple__UNIV__I, axiom,
    ((![X : produc541234227le_alt]: (member1392960970le_alt @ X @ top_to1159490073le_alt)))). % iso_tuple_UNIV_I
thf(fact_6_iso__tuple__UNIV__I, axiom,
    ((![X : produc1556433673le_alt]: (member2146260128le_alt @ X @ top_to960359919le_alt)))). % iso_tuple_UNIV_I
thf(fact_7_iso__tuple__UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_8_iso__tuple__UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % iso_tuple_UNIV_I
thf(fact_9_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt)))). % iso_tuple_UNIV_I
thf(fact_10_prod_Oinject, axiom,
    ((![X1 : set_Pr367596371le_alt, X2 : set_Pr367596371le_alt, Y1 : set_Pr367596371le_alt, Y2 : set_Pr367596371le_alt]: (((produc1931840741le_alt @ X1 @ X2) = (produc1931840741le_alt @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_11_prod_Oinject, axiom,
    ((![X1 : produc16571293le_alt, X2 : produc16571293le_alt, Y1 : produc16571293le_alt, Y2 : produc16571293le_alt]: (((produc41061307le_alt @ X1 @ X2) = (produc41061307le_alt @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_12_prod_Oinject, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X1 @ X2) = (produc1494124311le_alt @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_13_old_Oprod_Oinject, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, A2 : set_Pr367596371le_alt, B2 : set_Pr367596371le_alt]: (((produc1931840741le_alt @ A @ B) = (produc1931840741le_alt @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_14_old_Oprod_Oinject, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, A2 : produc16571293le_alt, B2 : produc16571293le_alt]: (((produc41061307le_alt @ A @ B) = (produc41061307le_alt @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_15_old_Oprod_Oinject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_16_irreflI, axiom,
    ((![R : set_Pr851393385le_alt]: ((![A3 : set_Pr367596371le_alt]: (~ ((member1392960970le_alt @ (produc1931840741le_alt @ A3 @ A3) @ R)))) => (irrefl360196318le_alt @ R))))). % irreflI
thf(fact_17_irreflI, axiom,
    ((![R : set_Pr448479039le_alt]: ((![A3 : produc16571293le_alt]: (~ ((member2146260128le_alt @ (produc41061307le_alt @ A3 @ A3) @ R)))) => (irrefl1894751528le_alt @ R))))). % irreflI
thf(fact_18_irreflI, axiom,
    ((![R : set_Pr367596371le_alt]: ((![A3 : arrow_1857593510le_alt]: (~ ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ A3) @ R)))) => (irrefl1932292187le_alt @ R))))). % irreflI
thf(fact_19_irrefl__def, axiom,
    ((irrefl360196318le_alt = (^[R2 : set_Pr851393385le_alt]: (![A4 : set_Pr367596371le_alt]: (~ ((member1392960970le_alt @ (produc1931840741le_alt @ A4 @ A4) @ R2)))))))). % irrefl_def
thf(fact_20_irrefl__def, axiom,
    ((irrefl1894751528le_alt = (^[R2 : set_Pr448479039le_alt]: (![A4 : produc16571293le_alt]: (~ ((member2146260128le_alt @ (produc41061307le_alt @ A4 @ A4) @ R2)))))))). % irrefl_def
thf(fact_21_irrefl__def, axiom,
    ((irrefl1932292187le_alt = (^[R2 : set_Pr367596371le_alt]: (![A4 : arrow_1857593510le_alt]: (~ ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ A4) @ R2)))))))). % irrefl_def
thf(fact_22_total__onI, axiom,
    ((![A5 : set_Pr851393385le_alt, R3 : set_Pr1911117087le_alt]: ((![X3 : produc541234227le_alt, Y : produc541234227le_alt]: ((member1392960970le_alt @ X3 @ A5) => ((member1392960970le_alt @ Y @ A5) => ((~ ((X3 = Y))) => ((member593317504le_alt @ (produc1507879067le_alt @ X3 @ Y) @ R3) | (member593317504le_alt @ (produc1507879067le_alt @ Y @ X3) @ R3)))))) => (total_579958703le_alt @ A5 @ R3))))). % total_onI
thf(fact_23_total__onI, axiom,
    ((![A5 : set_Pr448479039le_alt, R3 : set_Pr139735753le_alt]: ((![X3 : produc1556433673le_alt, Y : produc1556433673le_alt]: ((member2146260128le_alt @ X3 @ A5) => ((member2146260128le_alt @ Y @ A5) => ((~ ((X3 = Y))) => ((member1145282858le_alt @ (produc579746629le_alt @ X3 @ Y) @ R3) | (member1145282858le_alt @ (produc579746629le_alt @ Y @ X3) @ R3)))))) => (total_581701253le_alt @ A5 @ R3))))). % total_onI
thf(fact_24_total__onI, axiom,
    ((![A5 : set_Pr367596371le_alt, R3 : set_Pr448479039le_alt]: ((![X3 : produc16571293le_alt, Y : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => ((member2048039092le_alt @ Y @ A5) => ((~ ((X3 = Y))) => ((member2146260128le_alt @ (produc41061307le_alt @ X3 @ Y) @ R3) | (member2146260128le_alt @ (produc41061307le_alt @ Y @ X3) @ R3)))))) => (total_608959769le_alt @ A5 @ R3))))). % total_onI
thf(fact_25_total__onI, axiom,
    ((![A5 : set_se2071012361le_alt, R3 : set_Pr851393385le_alt]: ((![X3 : set_Pr367596371le_alt, Y : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => ((member1334244458le_alt @ Y @ A5) => ((~ ((X3 = Y))) => ((member1392960970le_alt @ (produc1931840741le_alt @ X3 @ Y) @ R3) | (member1392960970le_alt @ (produc1931840741le_alt @ Y @ X3) @ R3)))))) => (total_51659983le_alt @ A5 @ R3))))). % total_onI
thf(fact_26_total__onI, axiom,
    ((![A5 : set_Ar1665529862le_alt, R3 : set_Pr367596371le_alt]: ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((member519365071le_alt @ X3 @ A5) => ((member519365071le_alt @ Y @ A5) => ((~ ((X3 = Y))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ R3) | (member2048039092le_alt @ (produc1494124311le_alt @ Y @ X3) @ R3)))))) => (total_2034085930le_alt @ A5 @ R3))))). % total_onI
thf(fact_27_total__on__def, axiom,
    ((total_51659983le_alt = (^[A6 : set_se2071012361le_alt]: (^[R2 : set_Pr851393385le_alt]: (![X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ A6)) => ((![Y3 : set_Pr367596371le_alt]: (((member1334244458le_alt @ Y3 @ A6)) => ((((~ ((X4 = Y3)))) => ((((member1392960970le_alt @ (produc1931840741le_alt @ X4 @ Y3) @ R2)) | ((member1392960970le_alt @ (produc1931840741le_alt @ Y3 @ X4) @ R2)))))))))))))))). % total_on_def
thf(fact_28_total__on__def, axiom,
    ((total_608959769le_alt = (^[A6 : set_Pr367596371le_alt]: (^[R2 : set_Pr448479039le_alt]: (![X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ A6)) => ((![Y3 : produc16571293le_alt]: (((member2048039092le_alt @ Y3 @ A6)) => ((((~ ((X4 = Y3)))) => ((((member2146260128le_alt @ (produc41061307le_alt @ X4 @ Y3) @ R2)) | ((member2146260128le_alt @ (produc41061307le_alt @ Y3 @ X4) @ R2)))))))))))))))). % total_on_def
thf(fact_29_total__on__def, axiom,
    ((total_2034085930le_alt = (^[A6 : set_Ar1665529862le_alt]: (^[R2 : set_Pr367596371le_alt]: (![X4 : arrow_1857593510le_alt]: (((member519365071le_alt @ X4 @ A6)) => ((![Y3 : arrow_1857593510le_alt]: (((member519365071le_alt @ Y3 @ A6)) => ((((~ ((X4 = Y3)))) => ((((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y3) @ R2)) | ((member2048039092le_alt @ (produc1494124311le_alt @ Y3 @ X4) @ R2)))))))))))))))). % total_on_def
thf(fact_30_transD, axiom,
    ((![R3 : set_Pr851393385le_alt, X : set_Pr367596371le_alt, Y4 : set_Pr367596371le_alt, Z : set_Pr367596371le_alt]: ((trans_88152500le_alt @ R3) => ((member1392960970le_alt @ (produc1931840741le_alt @ X @ Y4) @ R3) => ((member1392960970le_alt @ (produc1931840741le_alt @ Y4 @ Z) @ R3) => (member1392960970le_alt @ (produc1931840741le_alt @ X @ Z) @ R3))))))). % transD
thf(fact_31_transD, axiom,
    ((![R3 : set_Pr448479039le_alt, X : produc16571293le_alt, Y4 : produc16571293le_alt, Z : produc16571293le_alt]: ((trans_695657982le_alt @ R3) => ((member2146260128le_alt @ (produc41061307le_alt @ X @ Y4) @ R3) => ((member2146260128le_alt @ (produc41061307le_alt @ Y4 @ Z) @ R3) => (member2146260128le_alt @ (produc41061307le_alt @ X @ Z) @ R3))))))). % transD
thf(fact_32_transD, axiom,
    ((![R3 : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, Z : arrow_1857593510le_alt]: ((trans_1364318725le_alt @ R3) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ R3) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y4 @ Z) @ R3) => (member2048039092le_alt @ (produc1494124311le_alt @ X @ Z) @ R3))))))). % transD
thf(fact_33_transE, axiom,
    ((![R3 : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, Z : arrow_1857593510le_alt]: ((trans_1364318725le_alt @ R3) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ R3) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y4 @ Z) @ R3) => (member2048039092le_alt @ (produc1494124311le_alt @ X @ Z) @ R3))))))). % transE
thf(fact_34_transE, axiom,
    ((![R3 : set_Pr851393385le_alt, X : set_Pr367596371le_alt, Y4 : set_Pr367596371le_alt, Z : set_Pr367596371le_alt]: ((trans_88152500le_alt @ R3) => ((member1392960970le_alt @ (produc1931840741le_alt @ X @ Y4) @ R3) => ((member1392960970le_alt @ (produc1931840741le_alt @ Y4 @ Z) @ R3) => (member1392960970le_alt @ (produc1931840741le_alt @ X @ Z) @ R3))))))). % transE
thf(fact_35_transE, axiom,
    ((![R3 : set_Pr448479039le_alt, X : produc16571293le_alt, Y4 : produc16571293le_alt, Z : produc16571293le_alt]: ((trans_695657982le_alt @ R3) => ((member2146260128le_alt @ (produc41061307le_alt @ X @ Y4) @ R3) => ((member2146260128le_alt @ (produc41061307le_alt @ Y4 @ Z) @ R3) => (member2146260128le_alt @ (produc41061307le_alt @ X @ Z) @ R3))))))). % transE
thf(fact_36_transI, axiom,
    ((![R3 : set_Pr367596371le_alt]: ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, Z2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ R3) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ Z2) @ R3) => (member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Z2) @ R3)))) => (trans_1364318725le_alt @ R3))))). % transI
thf(fact_37_transI, axiom,
    ((![R3 : set_Pr851393385le_alt]: ((![X3 : set_Pr367596371le_alt, Y : set_Pr367596371le_alt, Z2 : set_Pr367596371le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ X3 @ Y) @ R3) => ((member1392960970le_alt @ (produc1931840741le_alt @ Y @ Z2) @ R3) => (member1392960970le_alt @ (produc1931840741le_alt @ X3 @ Z2) @ R3)))) => (trans_88152500le_alt @ R3))))). % transI
thf(fact_38_transI, axiom,
    ((![R3 : set_Pr448479039le_alt]: ((![X3 : produc16571293le_alt, Y : produc16571293le_alt, Z2 : produc16571293le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ X3 @ Y) @ R3) => ((member2146260128le_alt @ (produc41061307le_alt @ Y @ Z2) @ R3) => (member2146260128le_alt @ (produc41061307le_alt @ X3 @ Z2) @ R3)))) => (trans_695657982le_alt @ R3))))). % transI
thf(fact_39_top__empty__eq, axiom,
    ((top_to1303308716_alt_o = (^[X4 : produc541234227le_alt]: (member1392960970le_alt @ X4 @ top_to1159490073le_alt))))). % top_empty_eq
thf(fact_40_top__empty__eq, axiom,
    ((top_to1993937238_alt_o = (^[X4 : produc1556433673le_alt]: (member2146260128le_alt @ X4 @ top_to960359919le_alt))))). % top_empty_eq
thf(fact_41_top__empty__eq, axiom,
    ((top_to516240647_alt_o = (^[X4 : arrow_1857593510le_alt]: (member519365071le_alt @ X4 @ top_to958727510le_alt))))). % top_empty_eq
thf(fact_42_top__empty__eq, axiom,
    ((top_to1900088076_alt_o = (^[X4 : set_Pr367596371le_alt]: (member1334244458le_alt @ X4 @ top_to469035705le_alt))))). % top_empty_eq
thf(fact_43_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_44_top__set__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ top_to516240647_alt_o)))). % top_set_def
thf(fact_45_top__set__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ top_to1900088076_alt_o)))). % top_set_def
thf(fact_46_top__set__def, axiom,
    ((top_to224369155le_alt = (collec531981554le_alt @ top_to1074038850_alt_o)))). % top_set_def
thf(fact_47_old_Oprod_Oinducts, axiom,
    ((![P : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_48_old_Oprod_Oinducts, axiom,
    ((![P : produc541234227le_alt > $o, Prod : produc541234227le_alt]: ((![A3 : set_Pr367596371le_alt, B3 : set_Pr367596371le_alt]: (P @ (produc1931840741le_alt @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_49_old_Oprod_Oinducts, axiom,
    ((![P : produc1556433673le_alt > $o, Prod : produc1556433673le_alt]: ((![A3 : produc16571293le_alt, B3 : produc16571293le_alt]: (P @ (produc41061307le_alt @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_50_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc16571293le_alt]: (~ ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (~ ((Y4 = (produc1494124311le_alt @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_51_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc541234227le_alt]: (~ ((![A3 : set_Pr367596371le_alt, B3 : set_Pr367596371le_alt]: (~ ((Y4 = (produc1931840741le_alt @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_52_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc1556433673le_alt]: (~ ((![A3 : produc16571293le_alt, B3 : produc16571293le_alt]: (~ ((Y4 = (produc41061307le_alt @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_53_prod__induct3, axiom,
    ((![P : produc1556433673le_alt > $o, X : produc1556433673le_alt]: ((![A3 : produc16571293le_alt, B3 : arrow_1857593510le_alt, C : arrow_1857593510le_alt]: (P @ (produc41061307le_alt @ A3 @ (produc1494124311le_alt @ B3 @ C)))) => (P @ X))))). % prod_induct3
thf(fact_54_prod__cases3, axiom,
    ((![Y4 : produc1556433673le_alt]: (~ ((![A3 : produc16571293le_alt, B3 : arrow_1857593510le_alt, C : arrow_1857593510le_alt]: (~ ((Y4 = (produc41061307le_alt @ A3 @ (produc1494124311le_alt @ B3 @ C))))))))))). % prod_cases3
thf(fact_55_Pair__inject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_56_Pair__inject, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, A2 : set_Pr367596371le_alt, B2 : set_Pr367596371le_alt]: (((produc1931840741le_alt @ A @ B) = (produc1931840741le_alt @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_57_Pair__inject, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, A2 : produc16571293le_alt, B2 : produc16571293le_alt]: (((produc41061307le_alt @ A @ B) = (produc41061307le_alt @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_58_prod__cases, axiom,
    ((![P : produc16571293le_alt > $o, P2 : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_59_prod__cases, axiom,
    ((![P : produc541234227le_alt > $o, P2 : produc541234227le_alt]: ((![A3 : set_Pr367596371le_alt, B3 : set_Pr367596371le_alt]: (P @ (produc1931840741le_alt @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_60_prod__cases, axiom,
    ((![P : produc1556433673le_alt > $o, P2 : produc1556433673le_alt]: ((![A3 : produc16571293le_alt, B3 : produc16571293le_alt]: (P @ (produc41061307le_alt @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_61_surj__pair, axiom,
    ((![P2 : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: (P2 = (produc1494124311le_alt @ X3 @ Y)))))). % surj_pair
thf(fact_62_surj__pair, axiom,
    ((![P2 : produc541234227le_alt]: (?[X3 : set_Pr367596371le_alt, Y : set_Pr367596371le_alt]: (P2 = (produc1931840741le_alt @ X3 @ Y)))))). % surj_pair
thf(fact_63_surj__pair, axiom,
    ((![P2 : produc1556433673le_alt]: (?[X3 : produc16571293le_alt, Y : produc16571293le_alt]: (P2 = (produc41061307le_alt @ X3 @ Y)))))). % surj_pair
thf(fact_64_UNIV__witness, axiom,
    ((?[X3 : produc541234227le_alt]: (member1392960970le_alt @ X3 @ top_to1159490073le_alt)))). % UNIV_witness
thf(fact_65_UNIV__witness, axiom,
    ((?[X3 : produc1556433673le_alt]: (member2146260128le_alt @ X3 @ top_to960359919le_alt)))). % UNIV_witness
thf(fact_66_UNIV__witness, axiom,
    ((?[X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ top_to958727510le_alt)))). % UNIV_witness
thf(fact_67_UNIV__witness, axiom,
    ((?[X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_68_UNIV__witness, axiom,
    ((?[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_69_UNIV__eq__I, axiom,
    ((![A5 : set_Pr851393385le_alt]: ((![X3 : produc541234227le_alt]: (member1392960970le_alt @ X3 @ A5)) => (top_to1159490073le_alt = A5))))). % UNIV_eq_I
thf(fact_70_UNIV__eq__I, axiom,
    ((![A5 : set_Pr448479039le_alt]: ((![X3 : produc1556433673le_alt]: (member2146260128le_alt @ X3 @ A5)) => (top_to960359919le_alt = A5))))). % UNIV_eq_I
thf(fact_71_UNIV__eq__I, axiom,
    ((![A5 : set_Ar1665529862le_alt]: ((![X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ A5)) => (top_to958727510le_alt = A5))))). % UNIV_eq_I
thf(fact_72_UNIV__eq__I, axiom,
    ((![A5 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ A5)) => (top_to469035705le_alt = A5))))). % UNIV_eq_I
thf(fact_73_UNIV__eq__I, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A5)) => (top_to224369155le_alt = A5))))). % UNIV_eq_I
thf(fact_74_trans__def, axiom,
    ((trans_1364318725le_alt = (^[R2 : set_Pr367596371le_alt]: (![X4 : arrow_1857593510le_alt]: (![Y3 : arrow_1857593510le_alt]: (![Z3 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y3) @ R2)) => ((((member2048039092le_alt @ (produc1494124311le_alt @ Y3 @ Z3) @ R2)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Z3) @ R2)))))))))))). % trans_def
thf(fact_75_trans__def, axiom,
    ((trans_88152500le_alt = (^[R2 : set_Pr851393385le_alt]: (![X4 : set_Pr367596371le_alt]: (![Y3 : set_Pr367596371le_alt]: (![Z3 : set_Pr367596371le_alt]: (((member1392960970le_alt @ (produc1931840741le_alt @ X4 @ Y3) @ R2)) => ((((member1392960970le_alt @ (produc1931840741le_alt @ Y3 @ Z3) @ R2)) => ((member1392960970le_alt @ (produc1931840741le_alt @ X4 @ Z3) @ R2)))))))))))). % trans_def
thf(fact_76_trans__def, axiom,
    ((trans_695657982le_alt = (^[R2 : set_Pr448479039le_alt]: (![X4 : produc16571293le_alt]: (![Y3 : produc16571293le_alt]: (![Z3 : produc16571293le_alt]: (((member2146260128le_alt @ (produc41061307le_alt @ X4 @ Y3) @ R2)) => ((((member2146260128le_alt @ (produc41061307le_alt @ Y3 @ Z3) @ R2)) => ((member2146260128le_alt @ (produc41061307le_alt @ X4 @ Z3) @ R2)))))))))))). % trans_def
thf(fact_77_strict__linear__order__on__def, axiom,
    ((order_257197092le_alt = (^[A6 : set_Ar1665529862le_alt]: (^[R2 : set_Pr367596371le_alt]: (((trans_1364318725le_alt @ R2)) & ((((irrefl1932292187le_alt @ R2)) & ((total_2034085930le_alt @ A6 @ R2)))))))))). % strict_linear_order_on_def
thf(fact_78_strict__linear__order__on__def, axiom,
    ((order_882761557le_alt = (^[A6 : set_se2071012361le_alt]: (^[R2 : set_Pr851393385le_alt]: (((trans_88152500le_alt @ R2)) & ((((irrefl360196318le_alt @ R2)) & ((total_51659983le_alt @ A6 @ R2)))))))))). % strict_linear_order_on_def
thf(fact_79_strict__linear__order__on__def, axiom,
    ((order_1653780383le_alt = (^[A6 : set_Pr367596371le_alt]: (^[R2 : set_Pr448479039le_alt]: (((trans_695657982le_alt @ R2)) & ((((irrefl1894751528le_alt @ R2)) & ((total_608959769le_alt @ A6 @ R2)))))))))). % strict_linear_order_on_def
thf(fact_80_in__mktop, axiom,
    ((![X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ (arrow_992294841_mktop @ L @ Z)) = (((~ ((X = Z)))) & ((((((Y4 = Z)) => ((~ ((X = Y4)))))) & ((((~ ((Y4 = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ L))))))))))). % in_mktop
thf(fact_81_in__mkbot, axiom,
    ((![X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ (arrow_843587755_mkbot @ L @ Z)) = (((~ ((Y4 = Z)))) & ((((((X = Z)) => ((~ ((X = Y4)))))) & ((((~ ((X = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ L))))))))))). % in_mkbot
thf(fact_82_ssubst__Pair__rhs, axiom,
    ((![R3 : arrow_1857593510le_alt, S : arrow_1857593510le_alt, R : set_Pr367596371le_alt, S2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ R3 @ S) @ R) => ((S2 = S) => (member2048039092le_alt @ (produc1494124311le_alt @ R3 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_83_ssubst__Pair__rhs, axiom,
    ((![R3 : set_Pr367596371le_alt, S : set_Pr367596371le_alt, R : set_Pr851393385le_alt, S2 : set_Pr367596371le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ R3 @ S) @ R) => ((S2 = S) => (member1392960970le_alt @ (produc1931840741le_alt @ R3 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_84_ssubst__Pair__rhs, axiom,
    ((![R3 : produc16571293le_alt, S : produc16571293le_alt, R : set_Pr448479039le_alt, S2 : produc16571293le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ R3 @ S) @ R) => ((S2 = S) => (member2146260128le_alt @ (produc41061307le_alt @ R3 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_85_in__inv__image, axiom,
    ((![X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, R3 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ (inv_im155136540le_alt @ R3 @ F)) = (member2048039092le_alt @ (produc1494124311le_alt @ (F @ X) @ (F @ Y4)) @ R3))))). % in_inv_image
thf(fact_86_in__inv__image, axiom,
    ((![X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, R3 : set_Pr851393385le_alt, F : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ (inv_im2121417327le_alt @ R3 @ F)) = (member1392960970le_alt @ (produc1931840741le_alt @ (F @ X) @ (F @ Y4)) @ R3))))). % in_inv_image
thf(fact_87_in__inv__image, axiom,
    ((![X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, R3 : set_Pr448479039le_alt, F : arrow_1857593510le_alt > produc16571293le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ (inv_im1556533177le_alt @ R3 @ F)) = (member2146260128le_alt @ (produc41061307le_alt @ (F @ X) @ (F @ Y4)) @ R3))))). % in_inv_image
thf(fact_88_in__inv__image, axiom,
    ((![X : set_Pr367596371le_alt, Y4 : set_Pr367596371le_alt, R3 : set_Pr367596371le_alt, F : set_Pr367596371le_alt > arrow_1857593510le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ X @ Y4) @ (inv_im146622717le_alt @ R3 @ F)) = (member2048039092le_alt @ (produc1494124311le_alt @ (F @ X) @ (F @ Y4)) @ R3))))). % in_inv_image
thf(fact_89_in__inv__image, axiom,
    ((![X : set_Pr367596371le_alt, Y4 : set_Pr367596371le_alt, R3 : set_Pr851393385le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ X @ Y4) @ (inv_im1445991786le_alt @ R3 @ F)) = (member1392960970le_alt @ (produc1931840741le_alt @ (F @ X) @ (F @ Y4)) @ R3))))). % in_inv_image
thf(fact_90_in__inv__image, axiom,
    ((![X : set_Pr367596371le_alt, Y4 : set_Pr367596371le_alt, R3 : set_Pr448479039le_alt, F : set_Pr367596371le_alt > produc16571293le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ X @ Y4) @ (inv_im1437190816le_alt @ R3 @ F)) = (member2146260128le_alt @ (produc41061307le_alt @ (F @ X) @ (F @ Y4)) @ R3))))). % in_inv_image
thf(fact_91_in__inv__image, axiom,
    ((![X : produc16571293le_alt, Y4 : produc16571293le_alt, R3 : set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1857593510le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ X @ Y4) @ (inv_im1236905629le_alt @ R3 @ F)) = (member2048039092le_alt @ (produc1494124311le_alt @ (F @ X) @ (F @ Y4)) @ R3))))). % in_inv_image
thf(fact_92_in__inv__image, axiom,
    ((![X : produc16571293le_alt, Y4 : produc16571293le_alt, R3 : set_Pr851393385le_alt, F : produc16571293le_alt > set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ X @ Y4) @ (inv_im680308490le_alt @ R3 @ F)) = (member1392960970le_alt @ (produc1931840741le_alt @ (F @ X) @ (F @ Y4)) @ R3))))). % in_inv_image
thf(fact_93_in__inv__image, axiom,
    ((![X : produc16571293le_alt, Y4 : produc16571293le_alt, R3 : set_Pr448479039le_alt, F : produc16571293le_alt > produc16571293le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ X @ Y4) @ (inv_im1191590976le_alt @ R3 @ F)) = (member2146260128le_alt @ (produc41061307le_alt @ (F @ X) @ (F @ Y4)) @ R3))))). % in_inv_image
thf(fact_94_curryI, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F @ (produc1494124311le_alt @ A @ B)) => (produc392997491_alt_o @ F @ A @ B))))). % curryI
thf(fact_95_curryI, axiom,
    ((![F : produc541234227le_alt > $o, A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((F @ (produc1931840741le_alt @ A @ B)) => (produc1532412837_alt_o @ F @ A @ B))))). % curryI
thf(fact_96_curryI, axiom,
    ((![F : produc1556433673le_alt > $o, A : produc16571293le_alt, B : produc16571293le_alt]: ((F @ (produc41061307le_alt @ A @ B)) => (produc1079800655_alt_o @ F @ A @ B))))). % curryI
thf(fact_97_curryD, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F @ A @ B) => (F @ (produc1494124311le_alt @ A @ B)))))). % curryD
thf(fact_98_curryD, axiom,
    ((![F : produc541234227le_alt > $o, A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((produc1532412837_alt_o @ F @ A @ B) => (F @ (produc1931840741le_alt @ A @ B)))))). % curryD
thf(fact_99_curryD, axiom,
    ((![F : produc1556433673le_alt > $o, A : produc16571293le_alt, B : produc16571293le_alt]: ((produc1079800655_alt_o @ F @ A @ B) => (F @ (produc41061307le_alt @ A @ B)))))). % curryD
thf(fact_100_curryE, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F @ A @ B) => (F @ (produc1494124311le_alt @ A @ B)))))). % curryE
thf(fact_101_curryE, axiom,
    ((![F : produc541234227le_alt > $o, A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((produc1532412837_alt_o @ F @ A @ B) => (F @ (produc1931840741le_alt @ A @ B)))))). % curryE
thf(fact_102_curryE, axiom,
    ((![F : produc1556433673le_alt > $o, A : produc16571293le_alt, B : produc16571293le_alt]: ((produc1079800655_alt_o @ F @ A @ B) => (F @ (produc41061307le_alt @ A @ B)))))). % curryE
thf(fact_103_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_104_mem__Collect__eq, axiom,
    ((![A : set_Pr367596371le_alt, P : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ A @ (collec1399441576le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_105_mem__Collect__eq, axiom,
    ((![A : arrow_1857593510le_alt, P : arrow_1857593510le_alt > $o]: ((member519365071le_alt @ A @ (collec1364151825le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_106_mem__Collect__eq, axiom,
    ((![A : produc541234227le_alt, P : produc541234227le_alt > $o]: ((member1392960970le_alt @ A @ (collec454808328le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_107_mem__Collect__eq, axiom,
    ((![A : produc1556433673le_alt, P : produc1556433673le_alt > $o]: ((member2146260128le_alt @ A @ (collec824848862le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_108_Collect__mem__eq, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_109_Collect__mem__eq, axiom,
    ((![A5 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (member1334244458le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_110_Collect__mem__eq, axiom,
    ((![A5 : set_Ar1665529862le_alt]: ((collec1364151825le_alt @ (^[X4 : arrow_1857593510le_alt]: (member519365071le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_111_Collect__mem__eq, axiom,
    ((![A5 : set_Pr851393385le_alt]: ((collec454808328le_alt @ (^[X4 : produc541234227le_alt]: (member1392960970le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_112_Collect__mem__eq, axiom,
    ((![A5 : set_Pr448479039le_alt]: ((collec824848862le_alt @ (^[X4 : produc1556433673le_alt]: (member2146260128le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_113_trans__inv__image, axiom,
    ((![R3 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((trans_1364318725le_alt @ R3) => (trans_1364318725le_alt @ (inv_im155136540le_alt @ R3 @ F)))))). % trans_inv_image
thf(fact_114_total__inv__image, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, R3 : set_Pr367596371le_alt]: ((inj_on207902653le_alt @ F @ top_to958727510le_alt) => ((total_2034085930le_alt @ top_to958727510le_alt @ R3) => (total_2034085930le_alt @ top_to958727510le_alt @ (inv_im155136540le_alt @ R3 @ F))))))). % total_inv_image
thf(fact_115_total__inv__image, axiom,
    ((![F : arrow_1857593510le_alt > set_Pr367596371le_alt, R3 : set_Pr851393385le_alt]: ((inj_on1042719644le_alt @ F @ top_to958727510le_alt) => ((total_51659983le_alt @ top_to469035705le_alt @ R3) => (total_2034085930le_alt @ top_to958727510le_alt @ (inv_im2121417327le_alt @ R3 @ F))))))). % total_inv_image
thf(fact_116_total__inv__image, axiom,
    ((![F : arrow_1857593510le_alt > produc16571293le_alt, R3 : set_Pr448479039le_alt]: ((inj_on1409615164le_alt @ F @ top_to958727510le_alt) => ((total_608959769le_alt @ top_to224369155le_alt @ R3) => (total_2034085930le_alt @ top_to958727510le_alt @ (inv_im1556533177le_alt @ R3 @ F))))))). % total_inv_image
thf(fact_117_total__inv__image, axiom,
    ((![F : set_Pr367596371le_alt > arrow_1857593510le_alt, R3 : set_Pr367596371le_alt]: ((inj_on870030606le_alt @ F @ top_to469035705le_alt) => ((total_2034085930le_alt @ top_to958727510le_alt @ R3) => (total_51659983le_alt @ top_to469035705le_alt @ (inv_im146622717le_alt @ R3 @ F))))))). % total_inv_image
thf(fact_118_total__inv__image, axiom,
    ((![F : set_Pr367596371le_alt > set_Pr367596371le_alt, R3 : set_Pr851393385le_alt]: ((inj_on660490891le_alt @ F @ top_to469035705le_alt) => ((total_51659983le_alt @ top_to469035705le_alt @ R3) => (total_51659983le_alt @ top_to469035705le_alt @ (inv_im1445991786le_alt @ R3 @ F))))))). % total_inv_image
thf(fact_119_total__inv__image, axiom,
    ((![F : set_Pr367596371le_alt > produc16571293le_alt, R3 : set_Pr448479039le_alt]: ((inj_on351791147le_alt @ F @ top_to469035705le_alt) => ((total_608959769le_alt @ top_to224369155le_alt @ R3) => (total_51659983le_alt @ top_to469035705le_alt @ (inv_im1437190816le_alt @ R3 @ F))))))). % total_inv_image
thf(fact_120_total__inv__image, axiom,
    ((![F : produc16571293le_alt > arrow_1857593510le_alt, R3 : set_Pr367596371le_alt]: ((inj_on1729242712le_alt @ F @ top_to224369155le_alt) => ((total_2034085930le_alt @ top_to958727510le_alt @ R3) => (total_608959769le_alt @ top_to224369155le_alt @ (inv_im1236905629le_alt @ R3 @ F))))))). % total_inv_image
thf(fact_121_total__inv__image, axiom,
    ((![F : produc16571293le_alt > set_Pr367596371le_alt, R3 : set_Pr851393385le_alt]: ((inj_on1108673473le_alt @ F @ top_to224369155le_alt) => ((total_51659983le_alt @ top_to469035705le_alt @ R3) => (total_608959769le_alt @ top_to224369155le_alt @ (inv_im680308490le_alt @ R3 @ F))))))). % total_inv_image
thf(fact_122_total__inv__image, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, R3 : set_Pr448479039le_alt]: ((inj_on616462689le_alt @ F @ top_to224369155le_alt) => ((total_608959769le_alt @ top_to224369155le_alt @ R3) => (total_608959769le_alt @ top_to224369155le_alt @ (inv_im1191590976le_alt @ R3 @ F))))))). % total_inv_image
thf(fact_123_mktop__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_992294841_mktop @ L @ X) @ arrow_1848678355le_Lin))))). % mktop_Lin
thf(fact_124_mkbot__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_843587755_mkbot @ L @ X) @ arrow_1848678355le_Lin))))). % mkbot_Lin
thf(fact_125_total__lex__prod, axiom,
    ((![R3 : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: ((total_2034085930le_alt @ top_to958727510le_alt @ R3) => ((total_2034085930le_alt @ top_to958727510le_alt @ S) => (total_608959769le_alt @ top_to224369155le_alt @ (lex_pr3395839le_alt @ R3 @ S))))))). % total_lex_prod
thf(fact_126_total__lex__prod, axiom,
    ((![R3 : set_Pr367596371le_alt, S : set_Pr851393385le_alt]: ((total_2034085930le_alt @ top_to958727510le_alt @ R3) => ((total_51659983le_alt @ top_to469035705le_alt @ S) => (total_1223472470le_alt @ top_to2022922242le_alt @ (lex_pr1024436954le_alt @ R3 @ S))))))). % total_lex_prod
thf(fact_127_total__lex__prod, axiom,
    ((![R3 : set_Pr367596371le_alt, S : set_Pr448479039le_alt]: ((total_2034085930le_alt @ top_to958727510le_alt @ R3) => ((total_608959769le_alt @ top_to224369155le_alt @ S) => (total_1531183862le_alt @ top_to1544444322le_alt @ (lex_pr788137082le_alt @ R3 @ S))))))). % total_lex_prod
thf(fact_128_total__lex__prod, axiom,
    ((![R3 : set_Pr851393385le_alt, S : set_Pr367596371le_alt]: ((total_51659983le_alt @ top_to469035705le_alt @ R3) => ((total_2034085930le_alt @ top_to958727510le_alt @ S) => (total_1920646272le_alt @ top_to1111255596le_alt @ (lex_pr851747916le_alt @ R3 @ S))))))). % total_lex_prod
thf(fact_129_total__lex__prod, axiom,
    ((![R3 : set_Pr851393385le_alt, S : set_Pr851393385le_alt]: ((total_51659983le_alt @ top_to469035705le_alt @ R3) => ((total_51659983le_alt @ top_to469035705le_alt @ S) => (total_579958703le_alt @ top_to1159490073le_alt @ (lex_pr787014349le_alt @ R3 @ S))))))). % total_lex_prod
thf(fact_130_total__lex__prod, axiom,
    ((![R3 : set_Pr851393385le_alt, S : set_Pr448479039le_alt]: ((total_51659983le_alt @ top_to469035705le_alt @ R3) => ((total_608959769le_alt @ top_to224369155le_alt @ S) => (total_2016848207le_alt @ top_to89343929le_alt @ (lex_pr1924434029le_alt @ R3 @ S))))))). % total_lex_prod
thf(fact_131_total__lex__prod, axiom,
    ((![R3 : set_Pr448479039le_alt, S : set_Pr367596371le_alt]: ((total_608959769le_alt @ top_to224369155le_alt @ R3) => ((total_2034085930le_alt @ top_to958727510le_alt @ S) => (total_259879370le_alt @ top_to383098486le_alt @ (lex_pr1107764630le_alt @ R3 @ S))))))). % total_lex_prod
thf(fact_132_total__lex__prod, axiom,
    ((![R3 : set_Pr448479039le_alt, S : set_Pr851393385le_alt]: ((total_608959769le_alt @ top_to224369155le_alt @ R3) => ((total_51659983le_alt @ top_to469035705le_alt @ S) => (total_312935653le_alt @ top_to19085391le_alt @ (lex_pr533832707le_alt @ R3 @ S))))))). % total_lex_prod
thf(fact_133_total__lex__prod, axiom,
    ((![R3 : set_Pr448479039le_alt, S : set_Pr448479039le_alt]: ((total_608959769le_alt @ top_to224369155le_alt @ R3) => ((total_608959769le_alt @ top_to224369155le_alt @ S) => (total_581701253le_alt @ top_to960359919le_alt @ (lex_pr1691165091le_alt @ R3 @ S))))))). % total_lex_prod
thf(fact_134_in__lex__prod, axiom,
    ((![A : arrow_1857593510le_alt, B : set_Pr367596371le_alt, A2 : arrow_1857593510le_alt, B2 : set_Pr367596371le_alt, R3 : set_Pr367596371le_alt, S : set_Pr851393385le_alt]: ((member2124338710le_alt @ (produc2013791097le_alt @ (produc398768834le_alt @ A @ B) @ (produc398768834le_alt @ A2 @ B2)) @ (lex_pr1024436954le_alt @ R3 @ S)) = (((member2048039092le_alt @ (produc1494124311le_alt @ A @ A2) @ R3)) | ((((A = A2)) & ((member1392960970le_alt @ (produc1931840741le_alt @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_135_in__lex__prod, axiom,
    ((![A : arrow_1857593510le_alt, B : produc16571293le_alt, A2 : arrow_1857593510le_alt, B2 : produc16571293le_alt, R3 : set_Pr367596371le_alt, S : set_Pr448479039le_alt]: ((member101850454le_alt @ (produc1502411449le_alt @ (produc1906488418le_alt @ A @ B) @ (produc1906488418le_alt @ A2 @ B2)) @ (lex_pr788137082le_alt @ R3 @ S)) = (((member2048039092le_alt @ (produc1494124311le_alt @ A @ A2) @ R3)) | ((((A = A2)) & ((member2146260128le_alt @ (produc41061307le_alt @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_136_in__lex__prod, axiom,
    ((![A : set_Pr367596371le_alt, B : arrow_1857593510le_alt, A2 : set_Pr367596371le_alt, B2 : arrow_1857593510le_alt, R3 : set_Pr851393385le_alt, S : set_Pr367596371le_alt]: ((member1374323978le_alt @ (produc1704163181le_alt @ (produc226079796le_alt @ A @ B) @ (produc226079796le_alt @ A2 @ B2)) @ (lex_pr851747916le_alt @ R3 @ S)) = (((member1392960970le_alt @ (produc1931840741le_alt @ A @ A2) @ R3)) | ((((A = A2)) & ((member2048039092le_alt @ (produc1494124311le_alt @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_137_in__lex__prod, axiom,
    ((![A : set_Pr367596371le_alt, B : produc16571293le_alt, A2 : set_Pr367596371le_alt, B2 : produc16571293le_alt, R3 : set_Pr851393385le_alt, S : set_Pr448479039le_alt]: ((member1211213440le_alt @ (produc2051100827le_alt @ (produc1659212421le_alt @ A @ B) @ (produc1659212421le_alt @ A2 @ B2)) @ (lex_pr1924434029le_alt @ R3 @ S)) = (((member1392960970le_alt @ (produc1931840741le_alt @ A @ A2) @ R3)) | ((((A = A2)) & ((member2146260128le_alt @ (produc41061307le_alt @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_138_in__lex__prod, axiom,
    ((![A : produc16571293le_alt, B : arrow_1857593510le_alt, A2 : produc16571293le_alt, B2 : arrow_1857593510le_alt, R3 : set_Pr448479039le_alt, S : set_Pr367596371le_alt]: ((member1220670452le_alt @ (produc309761623le_alt @ (produc78632318le_alt @ A @ B) @ (produc78632318le_alt @ A2 @ B2)) @ (lex_pr1107764630le_alt @ R3 @ S)) = (((member2146260128le_alt @ (produc41061307le_alt @ A @ A2) @ R3)) | ((((A = A2)) & ((member2048039092le_alt @ (produc1494124311le_alt @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_139_in__lex__prod, axiom,
    ((![A : produc16571293le_alt, B : set_Pr367596371le_alt, A2 : produc16571293le_alt, B2 : set_Pr367596371le_alt, R3 : set_Pr448479039le_alt, S : set_Pr851393385le_alt]: ((member2091907370le_alt @ (produc1181614917le_alt @ (produc268611099le_alt @ A @ B) @ (produc268611099le_alt @ A2 @ B2)) @ (lex_pr533832707le_alt @ R3 @ S)) = (((member2146260128le_alt @ (produc41061307le_alt @ A @ A2) @ R3)) | ((((A = A2)) & ((member1392960970le_alt @ (produc1931840741le_alt @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_140_in__lex__prod, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, A2 : set_Pr367596371le_alt, B2 : set_Pr367596371le_alt, R3 : set_Pr851393385le_alt, S : set_Pr851393385le_alt]: ((member593317504le_alt @ (produc1507879067le_alt @ (produc1931840741le_alt @ A @ B) @ (produc1931840741le_alt @ A2 @ B2)) @ (lex_pr787014349le_alt @ R3 @ S)) = (((member1392960970le_alt @ (produc1931840741le_alt @ A @ A2) @ R3)) | ((((A = A2)) & ((member1392960970le_alt @ (produc1931840741le_alt @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_141_in__lex__prod, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, A2 : produc16571293le_alt, B2 : produc16571293le_alt, R3 : set_Pr448479039le_alt, S : set_Pr448479039le_alt]: ((member1145282858le_alt @ (produc579746629le_alt @ (produc41061307le_alt @ A @ B) @ (produc41061307le_alt @ A2 @ B2)) @ (lex_pr1691165091le_alt @ R3 @ S)) = (((member2146260128le_alt @ (produc41061307le_alt @ A @ A2) @ R3)) | ((((A = A2)) & ((member2146260128le_alt @ (produc41061307le_alt @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_142_in__lex__prod, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, R3 : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ (produc1494124311le_alt @ A @ B) @ (produc1494124311le_alt @ A2 @ B2)) @ (lex_pr3395839le_alt @ R3 @ S)) = (((member2048039092le_alt @ (produc1494124311le_alt @ A @ A2) @ R3)) | ((((A = A2)) & ((member2048039092le_alt @ (produc1494124311le_alt @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_143_trans__lex__prod, axiom,
    ((![R1 : set_Pr367596371le_alt, R22 : set_Pr367596371le_alt]: ((trans_1364318725le_alt @ R1) => ((trans_1364318725le_alt @ R22) => (trans_695657982le_alt @ (lex_pr3395839le_alt @ R1 @ R22))))))). % trans_lex_prod
thf(fact_144_linear__alt, axiom,
    ((?[L2 : set_Pr367596371le_alt]: (member1334244458le_alt @ L2 @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_145_notin__Lin__iff, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((~ ((X = Y4))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ L))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y4 @ X) @ L))))))). % notin_Lin_iff
thf(fact_146_Lin__irrefl, axiom,
    ((![L : set_Pr367596371le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ L) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ L)))))))). % Lin_irrefl
thf(fact_147_in__below, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ (arrow_887341619_below @ L @ A @ B)) = (((~ ((X = Y4)))) & ((((((Y4 = A)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ B) @ L)))) & ((((~ ((Y4 = A)))) => ((((((X = A)) => ((((Y4 = B)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y4) @ L)))))) & ((((~ ((X = A)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ L))))))))))))))))). % in_below
thf(fact_148_in__above, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ (arrow_1726226719_above @ L @ A @ B)) = (((~ ((X = Y4)))) & ((((((X = B)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y4) @ L)))) & ((((~ ((X = B)))) => ((((((Y4 = B)) => ((((X = A)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X @ A) @ L)))))) & ((((~ ((Y4 = B)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ L))))))))))))))))). % in_above
thf(fact_149_below__Lin, axiom,
    ((![X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X = Y4))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_887341619_below @ L @ X @ Y4) @ arrow_1848678355le_Lin)))))). % below_Lin
thf(fact_150_above__Lin, axiom,
    ((![X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X = Y4))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L @ X @ Y4) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_151_same__fstI, axiom,
    ((![P : arrow_1857593510le_alt > $o, X : arrow_1857593510le_alt, Y5 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, R : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((P @ X) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y5 @ Y4) @ (R @ X)) => (member2146260128le_alt @ (produc41061307le_alt @ (produc1494124311le_alt @ X @ Y5) @ (produc1494124311le_alt @ X @ Y4)) @ (same_f554660482le_alt @ P @ R))))))). % same_fstI
thf(fact_152_same__fstI, axiom,
    ((![P : set_Pr367596371le_alt > $o, X : set_Pr367596371le_alt, Y5 : set_Pr367596371le_alt, Y4 : set_Pr367596371le_alt, R : set_Pr367596371le_alt > set_Pr851393385le_alt]: ((P @ X) => ((member1392960970le_alt @ (produc1931840741le_alt @ Y5 @ Y4) @ (R @ X)) => (member593317504le_alt @ (produc1507879067le_alt @ (produc1931840741le_alt @ X @ Y5) @ (produc1931840741le_alt @ X @ Y4)) @ (same_f263414480le_alt @ P @ R))))))). % same_fstI
thf(fact_153_same__fstI, axiom,
    ((![P : produc16571293le_alt > $o, X : produc16571293le_alt, Y5 : produc16571293le_alt, Y4 : produc16571293le_alt, R : produc16571293le_alt > set_Pr448479039le_alt]: ((P @ X) => ((member2146260128le_alt @ (produc41061307le_alt @ Y5 @ Y4) @ (R @ X)) => (member1145282858le_alt @ (produc579746629le_alt @ (produc41061307le_alt @ X @ Y5) @ (produc41061307le_alt @ X @ Y4)) @ (same_f1658501542le_alt @ P @ R))))))). % same_fstI
thf(fact_154_swap__simp, axiom,
    ((![X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt]: ((produc1794822519le_alt @ (produc1494124311le_alt @ X @ Y4)) = (produc1494124311le_alt @ Y4 @ X))))). % swap_simp
thf(fact_155_swap__simp, axiom,
    ((![X : set_Pr367596371le_alt, Y4 : set_Pr367596371le_alt]: ((produc1671472965le_alt @ (produc1931840741le_alt @ X @ Y4)) = (produc1931840741le_alt @ Y4 @ X))))). % swap_simp
thf(fact_156_swap__simp, axiom,
    ((![X : produc16571293le_alt, Y4 : produc16571293le_alt]: ((produc237020699le_alt @ (produc41061307le_alt @ X @ Y4)) = (produc41061307le_alt @ Y4 @ X))))). % swap_simp
thf(fact_157_apfst__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt]: ((produc1245692284le_alt @ F @ (produc1494124311le_alt @ X @ Y4)) = (produc1494124311le_alt @ (F @ X) @ Y4))))). % apfst_conv
thf(fact_158_apfst__conv, axiom,
    ((![F : set_Pr367596371le_alt > set_Pr367596371le_alt, X : set_Pr367596371le_alt, Y4 : set_Pr367596371le_alt]: ((produc1497434703le_alt @ F @ (produc1931840741le_alt @ X @ Y4)) = (produc1931840741le_alt @ (F @ X) @ Y4))))). % apfst_conv
thf(fact_159_apfst__conv, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, X : produc16571293le_alt, Y4 : produc16571293le_alt]: ((produc890810265le_alt @ F @ (produc41061307le_alt @ X @ Y4)) = (produc41061307le_alt @ (F @ X) @ Y4))))). % apfst_conv
thf(fact_160_apsnd__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt]: ((produc1710313402le_alt @ F @ (produc1494124311le_alt @ X @ Y4)) = (produc1494124311le_alt @ X @ (F @ Y4)))))). % apsnd_conv
thf(fact_161_apsnd__conv, axiom,
    ((![F : set_Pr367596371le_alt > set_Pr367596371le_alt, X : set_Pr367596371le_alt, Y4 : set_Pr367596371le_alt]: ((produc1599863441le_alt @ F @ (produc1931840741le_alt @ X @ Y4)) = (produc1931840741le_alt @ X @ (F @ Y4)))))). % apsnd_conv
thf(fact_162_apsnd__conv, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, X : produc16571293le_alt, Y4 : produc16571293le_alt]: ((produc1783216091le_alt @ F @ (produc41061307le_alt @ X @ Y4)) = (produc41061307le_alt @ X @ (F @ Y4)))))). % apsnd_conv
thf(fact_163_surj__swap, axiom,
    (((image_1873259469le_alt @ produc1794822519le_alt @ top_to224369155le_alt) = top_to224369155le_alt))). % surj_swap
thf(fact_164_pair__in__swap__image, axiom,
    ((![Y4 : arrow_1857593510le_alt, X : arrow_1857593510le_alt, A5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ Y4 @ X) @ (image_1873259469le_alt @ produc1794822519le_alt @ A5)) = (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ A5))))). % pair_in_swap_image
thf(fact_165_pair__in__swap__image, axiom,
    ((![Y4 : set_Pr367596371le_alt, X : set_Pr367596371le_alt, A5 : set_Pr851393385le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ Y4 @ X) @ (image_863336109le_alt @ produc1671472965le_alt @ A5)) = (member1392960970le_alt @ (produc1931840741le_alt @ X @ Y4) @ A5))))). % pair_in_swap_image
thf(fact_166_pair__in__swap__image, axiom,
    ((![Y4 : produc16571293le_alt, X : produc16571293le_alt, A5 : set_Pr448479039le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ Y4 @ X) @ (image_2091411799le_alt @ produc237020699le_alt @ A5)) = (member2146260128le_alt @ (produc41061307le_alt @ X @ Y4) @ A5))))). % pair_in_swap_image
thf(fact_167_image__eqI, axiom,
    ((![B : arrow_1857593510le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt]: ((B = (F @ X)) => ((member519365071le_alt @ X @ A5) => (member519365071le_alt @ B @ (image_1918885929le_alt @ F @ A5))))))). % image_eqI
thf(fact_168_image__eqI, axiom,
    ((![B : arrow_1857593510le_alt, F : produc16571293le_alt > arrow_1857593510le_alt, X : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((B = (F @ X)) => ((member2048039092le_alt @ X @ A5) => (member519365071le_alt @ B @ (image_283060460le_alt @ F @ A5))))))). % image_eqI
thf(fact_169_image__eqI, axiom,
    ((![B : produc16571293le_alt, F : arrow_1857593510le_alt > produc16571293le_alt, X : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt]: ((B = (F @ X)) => ((member519365071le_alt @ X @ A5) => (member2048039092le_alt @ B @ (image_2110916560le_alt @ F @ A5))))))). % image_eqI
thf(fact_170_image__eqI, axiom,
    ((![B : arrow_1857593510le_alt, F : set_Pr367596371le_alt > arrow_1857593510le_alt, X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((B = (F @ X)) => ((member1334244458le_alt @ X @ A5) => (member519365071le_alt @ B @ (image_1689538466le_alt @ F @ A5))))))). % image_eqI
thf(fact_171_image__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : arrow_1857593510le_alt > set_Pr367596371le_alt, X : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt]: ((B = (F @ X)) => ((member519365071le_alt @ X @ A5) => (member1334244458le_alt @ B @ (image_1862227504le_alt @ F @ A5))))))). % image_eqI
thf(fact_172_image__eqI, axiom,
    ((![B : produc16571293le_alt, F : produc16571293le_alt > produc16571293le_alt, X : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((B = (F @ X)) => ((member2048039092le_alt @ X @ A5) => (member2048039092le_alt @ B @ (image_1873259469le_alt @ F @ A5))))))). % image_eqI
thf(fact_173_image__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, X : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((B = (F @ X)) => ((member2048039092le_alt @ X @ A5) => (member1334244458le_alt @ B @ (image_715032109le_alt @ F @ A5))))))). % image_eqI
thf(fact_174_image__eqI, axiom,
    ((![B : produc16571293le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((B = (F @ X)) => ((member1334244458le_alt @ X @ A5) => (member2048039092le_alt @ B @ (image_2105633431le_alt @ F @ A5))))))). % image_eqI
thf(fact_175_image__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((B = (F @ X)) => ((member1334244458le_alt @ X @ A5) => (member1334244458le_alt @ B @ (image_71834871le_alt @ F @ A5))))))). % image_eqI
thf(fact_176_image__eqI, axiom,
    ((![B : produc1556433673le_alt, F : arrow_1857593510le_alt > produc1556433673le_alt, X : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt]: ((B = (F @ X)) => ((member519365071le_alt @ X @ A5) => (member2146260128le_alt @ B @ (image_895735110le_alt @ F @ A5))))))). % image_eqI
thf(fact_177_map__prod__simp, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc1074667658le_alt @ F @ G @ (produc1494124311le_alt @ A @ B)) = (produc1494124311le_alt @ (F @ A) @ (G @ B)))))). % map_prod_simp
thf(fact_178_map__prod__simp, axiom,
    ((![F : arrow_1857593510le_alt > set_Pr367596371le_alt, G : arrow_1857593510le_alt > set_Pr367596371le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc1011675046le_alt @ F @ G @ (produc1494124311le_alt @ A @ B)) = (produc1931840741le_alt @ (F @ A) @ (G @ B)))))). % map_prod_simp
thf(fact_179_map__prod__simp, axiom,
    ((![F : arrow_1857593510le_alt > produc16571293le_alt, G : arrow_1857593510le_alt > produc16571293le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc1000623014le_alt @ F @ G @ (produc1494124311le_alt @ A @ B)) = (produc41061307le_alt @ (F @ A) @ (G @ B)))))). % map_prod_simp
thf(fact_180_map__prod__simp, axiom,
    ((![F : set_Pr367596371le_alt > arrow_1857593510le_alt, G : set_Pr367596371le_alt > arrow_1857593510le_alt, A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((produc603630534le_alt @ F @ G @ (produc1931840741le_alt @ A @ B)) = (produc1494124311le_alt @ (F @ A) @ (G @ B)))))). % map_prod_simp
thf(fact_181_map__prod__simp, axiom,
    ((![F : set_Pr367596371le_alt > set_Pr367596371le_alt, G : set_Pr367596371le_alt > set_Pr367596371le_alt, A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((produc804913030le_alt @ F @ G @ (produc1931840741le_alt @ A @ B)) = (produc1931840741le_alt @ (F @ A) @ (G @ B)))))). % map_prod_simp
thf(fact_182_map__prod__simp, axiom,
    ((![F : set_Pr367596371le_alt > produc16571293le_alt, G : set_Pr367596371le_alt > produc16571293le_alt, A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((produc446816966le_alt @ F @ G @ (produc1931840741le_alt @ A @ B)) = (produc41061307le_alt @ (F @ A) @ (G @ B)))))). % map_prod_simp
thf(fact_183_map__prod__simp, axiom,
    ((![F : produc16571293le_alt > arrow_1857593510le_alt, G : produc16571293le_alt > arrow_1857593510le_alt, A : produc16571293le_alt, B : produc16571293le_alt]: ((produc1767943324le_alt @ F @ G @ (produc41061307le_alt @ A @ B)) = (produc1494124311le_alt @ (F @ A) @ (G @ B)))))). % map_prod_simp
thf(fact_184_map__prod__simp, axiom,
    ((![F : produc16571293le_alt > set_Pr367596371le_alt, G : produc16571293le_alt > set_Pr367596371le_alt, A : produc16571293le_alt, B : produc16571293le_alt]: ((produc1292660252le_alt @ F @ G @ (produc41061307le_alt @ A @ B)) = (produc1931840741le_alt @ (F @ A) @ (G @ B)))))). % map_prod_simp
thf(fact_185_map__prod__simp, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, G : produc16571293le_alt > produc16571293le_alt, A : produc16571293le_alt, B : produc16571293le_alt]: ((produc374079836le_alt @ F @ G @ (produc41061307le_alt @ A @ B)) = (produc41061307le_alt @ (F @ A) @ (G @ B)))))). % map_prod_simp
thf(fact_186_map__prod__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R) => (member2048039092le_alt @ (produc1494124311le_alt @ (F @ A) @ (G @ B)) @ (image_1873259469le_alt @ (produc1074667658le_alt @ F @ G) @ R)))))). % map_prod_imageI
thf(fact_187_map__prod__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt, F : arrow_1857593510le_alt > set_Pr367596371le_alt, G : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R) => (member1392960970le_alt @ (produc1931840741le_alt @ (F @ A) @ (G @ B)) @ (image_639978179le_alt @ (produc1011675046le_alt @ F @ G) @ R)))))). % map_prod_imageI
thf(fact_188_map__prod__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt, F : arrow_1857593510le_alt > produc16571293le_alt, G : arrow_1857593510le_alt > produc16571293le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R) => (member2146260128le_alt @ (produc41061307le_alt @ (F @ A) @ (G @ B)) @ (image_442548931le_alt @ (produc1000623014le_alt @ F @ G) @ R)))))). % map_prod_imageI
thf(fact_189_map__prod__imageI, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, R : set_Pr851393385le_alt, F : set_Pr367596371le_alt > arrow_1857593510le_alt, G : set_Pr367596371le_alt > arrow_1857593510le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ R) => (member2048039092le_alt @ (produc1494124311le_alt @ (F @ A) @ (G @ B)) @ (image_283479223le_alt @ (produc603630534le_alt @ F @ G) @ R)))))). % map_prod_imageI
thf(fact_190_map__prod__imageI, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, R : set_Pr851393385le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, G : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ R) => (member1392960970le_alt @ (produc1931840741le_alt @ (F @ A) @ (G @ B)) @ (image_863336109le_alt @ (produc804913030le_alt @ F @ G) @ R)))))). % map_prod_imageI
thf(fact_191_map__prod__imageI, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, R : set_Pr851393385le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, G : set_Pr367596371le_alt > produc16571293le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ R) => (member2146260128le_alt @ (produc41061307le_alt @ (F @ A) @ (G @ B)) @ (image_1719287469le_alt @ (produc446816966le_alt @ F @ G) @ R)))))). % map_prod_imageI
thf(fact_192_map__prod__imageI, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, R : set_Pr448479039le_alt, F : produc16571293le_alt > arrow_1857593510le_alt, G : produc16571293le_alt > arrow_1857593510le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ R) => (member2048039092le_alt @ (produc1494124311le_alt @ (F @ A) @ (G @ B)) @ (image_1289845857le_alt @ (produc1767943324le_alt @ F @ G) @ R)))))). % map_prod_imageI
thf(fact_193_map__prod__imageI, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, R : set_Pr448479039le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, G : produc16571293le_alt > set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ R) => (member1392960970le_alt @ (produc1931840741le_alt @ (F @ A) @ (G @ B)) @ (image_379867479le_alt @ (produc1292660252le_alt @ F @ G) @ R)))))). % map_prod_imageI
thf(fact_194_map__prod__imageI, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, R : set_Pr448479039le_alt, F : produc16571293le_alt > produc16571293le_alt, G : produc16571293le_alt > produc16571293le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ R) => (member2146260128le_alt @ (produc41061307le_alt @ (F @ A) @ (G @ B)) @ (image_2091411799le_alt @ (produc374079836le_alt @ F @ G) @ R)))))). % map_prod_imageI
thf(fact_195_map__prod__surj, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt]: (((image_1918885929le_alt @ F @ top_to958727510le_alt) = top_to958727510le_alt) => (((image_1918885929le_alt @ G @ top_to958727510le_alt) = top_to958727510le_alt) => ((image_1873259469le_alt @ (produc1074667658le_alt @ F @ G) @ top_to224369155le_alt) = top_to224369155le_alt)))))). % map_prod_surj
thf(fact_196_map__prod__surj, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > produc16571293le_alt]: (((image_1918885929le_alt @ F @ top_to958727510le_alt) = top_to958727510le_alt) => (((image_2110916560le_alt @ G @ top_to958727510le_alt) = top_to224369155le_alt) => ((image_9179458le_alt @ (produc2077356975le_alt @ F @ G) @ top_to224369155le_alt) = top_to1544444322le_alt)))))). % map_prod_surj
thf(fact_197_map__prod__surj, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : produc16571293le_alt > arrow_1857593510le_alt]: (((image_1918885929le_alt @ F @ top_to958727510le_alt) = top_to958727510le_alt) => (((image_283060460le_alt @ G @ top_to224369155le_alt) = top_to958727510le_alt) => ((image_2106160388le_alt @ (produc751143617le_alt @ F @ G) @ top_to1544444322le_alt) = top_to224369155le_alt)))))). % map_prod_surj
thf(fact_198_map__prod__surj, axiom,
    ((![F : arrow_1857593510le_alt > produc16571293le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt]: (((image_2110916560le_alt @ F @ top_to958727510le_alt) = top_to224369155le_alt) => (((image_1918885929le_alt @ G @ top_to958727510le_alt) = top_to958727510le_alt) => ((image_1387001356le_alt @ (produc1135578835le_alt @ F @ G) @ top_to224369155le_alt) = top_to383098486le_alt)))))). % map_prod_surj
thf(fact_199_map__prod__surj, axiom,
    ((![F : produc16571293le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt]: (((image_283060460le_alt @ F @ top_to224369155le_alt) = top_to958727510le_alt) => (((image_1918885929le_alt @ G @ top_to958727510le_alt) = top_to958727510le_alt) => ((image_585251120le_alt @ (produc2060336111le_alt @ F @ G) @ top_to383098486le_alt) = top_to224369155le_alt)))))). % map_prod_surj
thf(fact_200_map__prod__surj, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > set_Pr367596371le_alt]: (((image_1918885929le_alt @ F @ top_to958727510le_alt) = top_to958727510le_alt) => (((image_1862227504le_alt @ G @ top_to958727510le_alt) = top_to469035705le_alt) => ((image_1534432162le_alt @ (produc1630029327le_alt @ F @ G) @ top_to224369155le_alt) = top_to2022922242le_alt)))))). % map_prod_surj
thf(fact_201_map__prod__surj, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : set_Pr367596371le_alt > arrow_1857593510le_alt]: (((image_1918885929le_alt @ F @ top_to958727510le_alt) = top_to958727510le_alt) => (((image_1689538466le_alt @ G @ top_to469035705le_alt) = top_to958727510le_alt) => ((image_1944994468le_alt @ (produc1152952609le_alt @ F @ G) @ top_to2022922242le_alt) = top_to224369155le_alt)))))). % map_prod_surj
thf(fact_202_map__prod__surj, axiom,
    ((![F : arrow_1857593510le_alt > set_Pr367596371le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt]: (((image_1862227504le_alt @ F @ top_to958727510le_alt) = top_to469035705le_alt) => (((image_1918885929le_alt @ G @ top_to958727510le_alt) = top_to958727510le_alt) => ((image_1927218284le_alt @ (produc113080627le_alt @ F @ G) @ top_to224369155le_alt) = top_to1111255596le_alt)))))). % map_prod_surj
thf(fact_203_map__prod__surj, axiom,
    ((![F : set_Pr367596371le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt]: (((image_1689538466le_alt @ F @ top_to469035705le_alt) = top_to958727510le_alt) => (((image_1918885929le_alt @ G @ top_to958727510le_alt) = top_to958727510le_alt) => ((image_1191240954le_alt @ (produc370912421le_alt @ F @ G) @ top_to1111255596le_alt) = top_to224369155le_alt)))))). % map_prod_surj
thf(fact_204_map__prod__surj, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : produc16571293le_alt > produc16571293le_alt]: (((image_1918885929le_alt @ F @ top_to958727510le_alt) = top_to958727510le_alt) => (((image_1873259469le_alt @ G @ top_to224369155le_alt) = top_to224369155le_alt) => ((image_1763336651le_alt @ (produc570876728le_alt @ F @ G) @ top_to1544444322le_alt) = top_to1544444322le_alt)))))). % map_prod_surj
thf(fact_205_imageI, axiom,
    ((![X : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member519365071le_alt @ X @ A5) => (member519365071le_alt @ (F @ X) @ (image_1918885929le_alt @ F @ A5)))))). % imageI
thf(fact_206_imageI, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ X @ A5) => (member519365071le_alt @ (F @ X) @ (image_283060460le_alt @ F @ A5)))))). % imageI
thf(fact_207_imageI, axiom,
    ((![X : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, F : arrow_1857593510le_alt > produc16571293le_alt]: ((member519365071le_alt @ X @ A5) => (member2048039092le_alt @ (F @ X) @ (image_2110916560le_alt @ F @ A5)))))). % imageI
thf(fact_208_imageI, axiom,
    ((![X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, F : set_Pr367596371le_alt > arrow_1857593510le_alt]: ((member1334244458le_alt @ X @ A5) => (member519365071le_alt @ (F @ X) @ (image_1689538466le_alt @ F @ A5)))))). % imageI
thf(fact_209_imageI, axiom,
    ((![X : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, F : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((member519365071le_alt @ X @ A5) => (member1334244458le_alt @ (F @ X) @ (image_1862227504le_alt @ F @ A5)))))). % imageI
thf(fact_210_imageI, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, F : produc16571293le_alt > produc16571293le_alt]: ((member2048039092le_alt @ X @ A5) => (member2048039092le_alt @ (F @ X) @ (image_1873259469le_alt @ F @ A5)))))). % imageI
thf(fact_211_imageI, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ X @ A5) => (member1334244458le_alt @ (F @ X) @ (image_715032109le_alt @ F @ A5)))))). % imageI
thf(fact_212_imageI, axiom,
    ((![X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, F : set_Pr367596371le_alt > produc16571293le_alt]: ((member1334244458le_alt @ X @ A5) => (member2048039092le_alt @ (F @ X) @ (image_2105633431le_alt @ F @ A5)))))). % imageI
thf(fact_213_imageI, axiom,
    ((![X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A5) => (member1334244458le_alt @ (F @ X) @ (image_71834871le_alt @ F @ A5)))))). % imageI
thf(fact_214_imageI, axiom,
    ((![X : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, F : arrow_1857593510le_alt > produc1556433673le_alt]: ((member519365071le_alt @ X @ A5) => (member2146260128le_alt @ (F @ X) @ (image_895735110le_alt @ F @ A5)))))). % imageI
thf(fact_215_rev__image__eqI, axiom,
    ((![X : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B : arrow_1857593510le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member519365071le_alt @ X @ A5) => ((B = (F @ X)) => (member519365071le_alt @ B @ (image_1918885929le_alt @ F @ A5))))))). % rev_image_eqI
thf(fact_216_rev__image__eqI, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, B : arrow_1857593510le_alt, F : produc16571293le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ X @ A5) => ((B = (F @ X)) => (member519365071le_alt @ B @ (image_283060460le_alt @ F @ A5))))))). % rev_image_eqI
thf(fact_217_rev__image__eqI, axiom,
    ((![X : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B : produc16571293le_alt, F : arrow_1857593510le_alt > produc16571293le_alt]: ((member519365071le_alt @ X @ A5) => ((B = (F @ X)) => (member2048039092le_alt @ B @ (image_2110916560le_alt @ F @ A5))))))). % rev_image_eqI
thf(fact_218_rev__image__eqI, axiom,
    ((![X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B : arrow_1857593510le_alt, F : set_Pr367596371le_alt > arrow_1857593510le_alt]: ((member1334244458le_alt @ X @ A5) => ((B = (F @ X)) => (member519365071le_alt @ B @ (image_1689538466le_alt @ F @ A5))))))). % rev_image_eqI
thf(fact_219_rev__image__eqI, axiom,
    ((![X : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B : set_Pr367596371le_alt, F : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((member519365071le_alt @ X @ A5) => ((B = (F @ X)) => (member1334244458le_alt @ B @ (image_1862227504le_alt @ F @ A5))))))). % rev_image_eqI
thf(fact_220_rev__image__eqI, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, B : produc16571293le_alt, F : produc16571293le_alt > produc16571293le_alt]: ((member2048039092le_alt @ X @ A5) => ((B = (F @ X)) => (member2048039092le_alt @ B @ (image_1873259469le_alt @ F @ A5))))))). % rev_image_eqI
thf(fact_221_rev__image__eqI, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, B : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ X @ A5) => ((B = (F @ X)) => (member1334244458le_alt @ B @ (image_715032109le_alt @ F @ A5))))))). % rev_image_eqI
thf(fact_222_rev__image__eqI, axiom,
    ((![X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B : produc16571293le_alt, F : set_Pr367596371le_alt > produc16571293le_alt]: ((member1334244458le_alt @ X @ A5) => ((B = (F @ X)) => (member2048039092le_alt @ B @ (image_2105633431le_alt @ F @ A5))))))). % rev_image_eqI
thf(fact_223_rev__image__eqI, axiom,
    ((![X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B : set_Pr367596371le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A5) => ((B = (F @ X)) => (member1334244458le_alt @ B @ (image_71834871le_alt @ F @ A5))))))). % rev_image_eqI
thf(fact_224_rev__image__eqI, axiom,
    ((![X : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B : produc1556433673le_alt, F : arrow_1857593510le_alt > produc1556433673le_alt]: ((member519365071le_alt @ X @ A5) => ((B = (F @ X)) => (member2146260128le_alt @ B @ (image_895735110le_alt @ F @ A5))))))). % rev_image_eqI
thf(fact_225_range__eqI, axiom,
    ((![B : arrow_1857593510le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt]: ((B = (F @ X)) => (member519365071le_alt @ B @ (image_1918885929le_alt @ F @ top_to958727510le_alt)))))). % range_eqI
thf(fact_226_range__eqI, axiom,
    ((![B : produc16571293le_alt, F : arrow_1857593510le_alt > produc16571293le_alt, X : arrow_1857593510le_alt]: ((B = (F @ X)) => (member2048039092le_alt @ B @ (image_2110916560le_alt @ F @ top_to958727510le_alt)))))). % range_eqI
thf(fact_227_range__eqI, axiom,
    ((![B : arrow_1857593510le_alt, F : produc16571293le_alt > arrow_1857593510le_alt, X : produc16571293le_alt]: ((B = (F @ X)) => (member519365071le_alt @ B @ (image_283060460le_alt @ F @ top_to224369155le_alt)))))). % range_eqI
thf(fact_228_range__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : arrow_1857593510le_alt > set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((B = (F @ X)) => (member1334244458le_alt @ B @ (image_1862227504le_alt @ F @ top_to958727510le_alt)))))). % range_eqI
thf(fact_229_range__eqI, axiom,
    ((![B : arrow_1857593510le_alt, F : set_Pr367596371le_alt > arrow_1857593510le_alt, X : set_Pr367596371le_alt]: ((B = (F @ X)) => (member519365071le_alt @ B @ (image_1689538466le_alt @ F @ top_to469035705le_alt)))))). % range_eqI
thf(fact_230_range__eqI, axiom,
    ((![B : produc16571293le_alt, F : produc16571293le_alt > produc16571293le_alt, X : produc16571293le_alt]: ((B = (F @ X)) => (member2048039092le_alt @ B @ (image_1873259469le_alt @ F @ top_to224369155le_alt)))))). % range_eqI
thf(fact_231_range__eqI, axiom,
    ((![B : produc16571293le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, X : set_Pr367596371le_alt]: ((B = (F @ X)) => (member2048039092le_alt @ B @ (image_2105633431le_alt @ F @ top_to469035705le_alt)))))). % range_eqI
thf(fact_232_range__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, X : produc16571293le_alt]: ((B = (F @ X)) => (member1334244458le_alt @ B @ (image_715032109le_alt @ F @ top_to224369155le_alt)))))). % range_eqI
thf(fact_233_range__eqI, axiom,
    ((![B : produc1556433673le_alt, F : arrow_1857593510le_alt > produc1556433673le_alt, X : arrow_1857593510le_alt]: ((B = (F @ X)) => (member2146260128le_alt @ B @ (image_895735110le_alt @ F @ top_to958727510le_alt)))))). % range_eqI
thf(fact_234_range__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, X : set_Pr367596371le_alt]: ((B = (F @ X)) => (member1334244458le_alt @ B @ (image_71834871le_alt @ F @ top_to469035705le_alt)))))). % range_eqI
thf(fact_235_rangeI, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt]: (member519365071le_alt @ (F @ X) @ (image_1918885929le_alt @ F @ top_to958727510le_alt))))). % rangeI
thf(fact_236_rangeI, axiom,
    ((![F : arrow_1857593510le_alt > produc16571293le_alt, X : arrow_1857593510le_alt]: (member2048039092le_alt @ (F @ X) @ (image_2110916560le_alt @ F @ top_to958727510le_alt))))). % rangeI
thf(fact_237_rangeI, axiom,
    ((![F : produc16571293le_alt > arrow_1857593510le_alt, X : produc16571293le_alt]: (member519365071le_alt @ (F @ X) @ (image_283060460le_alt @ F @ top_to224369155le_alt))))). % rangeI
thf(fact_238_rangeI, axiom,
    ((![F : arrow_1857593510le_alt > set_Pr367596371le_alt, X : arrow_1857593510le_alt]: (member1334244458le_alt @ (F @ X) @ (image_1862227504le_alt @ F @ top_to958727510le_alt))))). % rangeI
thf(fact_239_rangeI, axiom,
    ((![F : set_Pr367596371le_alt > arrow_1857593510le_alt, X : set_Pr367596371le_alt]: (member519365071le_alt @ (F @ X) @ (image_1689538466le_alt @ F @ top_to469035705le_alt))))). % rangeI
thf(fact_240_rangeI, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, X : produc16571293le_alt]: (member2048039092le_alt @ (F @ X) @ (image_1873259469le_alt @ F @ top_to224369155le_alt))))). % rangeI
thf(fact_241_rangeI, axiom,
    ((![F : set_Pr367596371le_alt > produc16571293le_alt, X : set_Pr367596371le_alt]: (member2048039092le_alt @ (F @ X) @ (image_2105633431le_alt @ F @ top_to469035705le_alt))))). % rangeI
thf(fact_242_rangeI, axiom,
    ((![F : produc16571293le_alt > set_Pr367596371le_alt, X : produc16571293le_alt]: (member1334244458le_alt @ (F @ X) @ (image_715032109le_alt @ F @ top_to224369155le_alt))))). % rangeI
thf(fact_243_rangeI, axiom,
    ((![F : arrow_1857593510le_alt > produc1556433673le_alt, X : arrow_1857593510le_alt]: (member2146260128le_alt @ (F @ X) @ (image_895735110le_alt @ F @ top_to958727510le_alt))))). % rangeI
thf(fact_244_rangeI, axiom,
    ((![F : set_Pr367596371le_alt > set_Pr367596371le_alt, X : set_Pr367596371le_alt]: (member1334244458le_alt @ (F @ X) @ (image_71834871le_alt @ F @ top_to469035705le_alt))))). % rangeI
thf(fact_245_prod__fun__imageE, axiom,
    ((![C2 : produc541234227le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, G : produc16571293le_alt > set_Pr367596371le_alt, R : set_Pr448479039le_alt]: ((member1392960970le_alt @ C2 @ (image_379867479le_alt @ (produc1292660252le_alt @ F @ G) @ R)) => (~ ((![X3 : produc16571293le_alt, Y : produc16571293le_alt]: ((C2 = (produc1931840741le_alt @ (F @ X3) @ (G @ Y))) => (~ ((member2146260128le_alt @ (produc41061307le_alt @ X3 @ Y) @ R))))))))))). % prod_fun_imageE
thf(fact_246_prod__fun__imageE, axiom,
    ((![C2 : produc1556433673le_alt, F : arrow_1857593510le_alt > produc16571293le_alt, G : arrow_1857593510le_alt > produc16571293le_alt, R : set_Pr367596371le_alt]: ((member2146260128le_alt @ C2 @ (image_442548931le_alt @ (produc1000623014le_alt @ F @ G) @ R)) => (~ ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((C2 = (produc41061307le_alt @ (F @ X3) @ (G @ Y))) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ R))))))))))). % prod_fun_imageE
thf(fact_247_prod__fun__imageE, axiom,
    ((![C2 : produc1556433673le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, G : set_Pr367596371le_alt > produc16571293le_alt, R : set_Pr851393385le_alt]: ((member2146260128le_alt @ C2 @ (image_1719287469le_alt @ (produc446816966le_alt @ F @ G) @ R)) => (~ ((![X3 : set_Pr367596371le_alt, Y : set_Pr367596371le_alt]: ((C2 = (produc41061307le_alt @ (F @ X3) @ (G @ Y))) => (~ ((member1392960970le_alt @ (produc1931840741le_alt @ X3 @ Y) @ R))))))))))). % prod_fun_imageE
thf(fact_248_prod__fun__imageE, axiom,
    ((![C2 : produc1556433673le_alt, F : produc16571293le_alt > produc16571293le_alt, G : produc16571293le_alt > produc16571293le_alt, R : set_Pr448479039le_alt]: ((member2146260128le_alt @ C2 @ (image_2091411799le_alt @ (produc374079836le_alt @ F @ G) @ R)) => (~ ((![X3 : produc16571293le_alt, Y : produc16571293le_alt]: ((C2 = (produc41061307le_alt @ (F @ X3) @ (G @ Y))) => (~ ((member2146260128le_alt @ (produc41061307le_alt @ X3 @ Y) @ R))))))))))). % prod_fun_imageE

% Conjectures (5)
thf(conj_0, hypothesis,
    ((![X5 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((![Xa : arrow_1429744205e_indi]: ((trans_1364318725le_alt @ (X5 @ Xa)) & ((irrefl1932292187le_alt @ (X5 @ Xa)) & (total_2034085930le_alt @ top_to958727510le_alt @ (X5 @ Xa))))) => ((trans_1364318725le_alt @ (f @ X5)) & ((irrefl1932292187le_alt @ (f @ X5)) & (total_2034085930le_alt @ top_to958727510le_alt @ (f @ X5)))))))).
thf(conj_1, hypothesis,
    ((![P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((![X3 : arrow_1429744205e_indi]: ((trans_1364318725le_alt @ (P3 @ X3)) & ((irrefl1932292187le_alt @ (P3 @ X3)) & (total_2034085930le_alt @ top_to958727510le_alt @ (P3 @ X3))))) => (![A7 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: ((~ ((A7 = B4))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A7 @ B4) @ (P3 @ i)) => (member2048039092le_alt @ (produc1494124311le_alt @ A7 @ B4) @ (f @ P3))))))))).
thf(conj_2, hypothesis,
    ((![X5 : arrow_1429744205e_indi]: ((trans_1364318725le_alt @ (p @ X5)) & ((irrefl1932292187le_alt @ (p @ X5)) & (total_2034085930le_alt @ top_to958727510le_alt @ (p @ X5))))))).
thf(conj_3, hypothesis,
    ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (f @ p)))).
thf(conj_4, conjecture,
    ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (p @ i)))).
