% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/Arrow_Order/prob_55__5184764_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:15:51.411

% Could-be-implicit typings (22)
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thf(ty_n_t__Product____Type__Ounit, type,
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% Explicit typings (80)
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OLin, type,
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    produc78632318le_alt : produc16571293le_alt > arrow_1857593510le_alt > produc2034271302le_alt).
thf(sy_c_Product__Type_OPair_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,
    produc41061307le_alt : produc16571293le_alt > produc16571293le_alt > produc1556433673le_alt).
thf(sy_c_Product__Type_OPair_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,
    produc268611099le_alt : produc16571293le_alt > set_Pr367596371le_alt > produc1114386793le_alt).
thf(sy_c_Product__Type_OPair_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,
    produc226079796le_alt : set_Pr367596371le_alt > arrow_1857593510le_alt > produc366337788le_alt).
thf(sy_c_Product__Type_OPair_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,
    produc1659212421le_alt : set_Pr367596371le_alt > produc16571293le_alt > produc670815699le_alt).
thf(sy_c_Product__Type_OPair_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,
    produc1931840741le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > produc541234227le_alt).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc2062971558le_alt : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar1665529862le_alt) > set_Pr367596371le_alt).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc2023643283le_alt : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Pr367596371le_alt) > set_Pr1508209746le_alt).
thf(sy_c_Product__Type_OSigma_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,
    produc1741626099le_alt : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_se2071012361le_alt) > set_Pr858239666le_alt).
thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc195787183le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Ar1665529862le_alt) > set_Pr346863910le_alt).
thf(sy_c_Product__Type_OSigma_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,
    produc1360152522le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr448479039le_alt).
thf(sy_c_Product__Type_OSigma_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,
    produc1173532202le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_se2071012361le_alt) > set_Pr1043548575le_alt).
thf(sy_c_Product__Type_OSigma_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,
    produc1568937061le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Ar1665529862le_alt) > set_Pr2094056668le_alt).
thf(sy_c_Product__Type_OSigma_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,
    produc416649876le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_Pr1113807113le_alt).
thf(sy_c_Product__Type_OSigma_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,
    produc223727860le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_se2071012361le_alt) > set_Pr851393385le_alt).
thf(sy_c_Product__Type_OUnity, type,
    product_Unity : product_unit).
thf(sy_c_Product__Type_Ocurry_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001_Eo, type,
    produc392997491_alt_o : (produc16571293le_alt > $o) > arrow_1857593510le_alt > arrow_1857593510le_alt > $o).
thf(sy_c_Product__Type_Oproduct_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc961482780le_alt : set_Ar1665529862le_alt > set_Ar1665529862le_alt > set_Pr367596371le_alt).
thf(sy_c_Product__Type_Ounit_OAbs__unit, type,
    product_Abs_unit : $o > product_unit).
thf(sy_c_Relation_Oconverse_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    conver1781819635le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Relation_Oinv__image_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    inv_im155136540le_alt : set_Pr367596371le_alt > (arrow_1857593510le_alt > arrow_1857593510le_alt) > set_Pr367596371le_alt).
thf(sy_c_Set_OCollect_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    collec1364151825le_alt : (arrow_1857593510le_alt > $o) > set_Ar1665529862le_alt).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    collec531981554le_alt : (produc16571293le_alt > $o) > set_Pr367596371le_alt).
thf(sy_c_Set_OCollect_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,
    collec824848862le_alt : (produc1556433673le_alt > $o) > set_Pr448479039le_alt).
thf(sy_c_Set_OCollect_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,
    collec454808328le_alt : (produc541234227le_alt > $o) > set_Pr851393385le_alt).
thf(sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    collec1399441576le_alt : (set_Pr367596371le_alt > $o) > set_se2071012361le_alt).
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_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_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__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1000073755le_alt : produc1158092146le_alt > set_Pr1508209746le_alt > $o).
thf(sy_c_member_001t__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, type,
    member1361938555le_alt : produc1816647634le_alt > set_Pr858239666le_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__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    member1876252911le_alt : produc2034271302le_alt > set_Pr346863910le_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__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, type,
    member1923768064le_alt : produc1114386793le_alt > set_Pr1043548575le_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__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    member2059112357le_alt : produc366337788le_alt > set_Pr2094056668le_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__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1480196970le_alt : produc670815699le_alt > set_Pr1113807113le_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).

% Relevant facts (183)
thf(fact_0_converse__in__Lin, axiom,
    ((![L : set_Pr367596371le_alt]: ((member1334244458le_alt @ (conver1781819635le_alt @ L) @ arrow_1848678355le_Lin) = (member1334244458le_alt @ L @ arrow_1848678355le_Lin))))). % converse_in_Lin
thf(fact_1_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_2_notin__Lin__iff, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((~ ((X = Y))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ L))))))). % notin_Lin_iff
thf(fact_3_Lin__def, axiom,
    ((arrow_1848678355le_Lin = (collec1399441576le_alt @ (order_257197092le_alt @ top_to958727510le_alt))))). % Lin_def
thf(fact_4__092_060open_062_092_060exists_062r_O_Awell__order_Ar_092_060close_062, axiom,
    ((?[X_1 : set_Pr367596371le_alt]: (order_1185271620le_alt @ top_to958727510le_alt @ X_1)))). % \<open>\<exists>r. well_order r\<close>
thf(fact_5_converse__iff, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (conver1781819635le_alt @ R)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ R))))). % converse_iff
thf(fact_6_converse__inject, axiom,
    ((![R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: (((conver1781819635le_alt @ R) = (conver1781819635le_alt @ S)) = (R = S))))). % converse_inject
thf(fact_7_converse__converse, axiom,
    ((![R : set_Pr367596371le_alt]: ((conver1781819635le_alt @ (conver1781819635le_alt @ R)) = R)))). % converse_converse
thf(fact_8_UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % UNIV_I
thf(fact_9_UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % UNIV_I
thf(fact_10_UNIV__I, axiom,
    ((![X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt)))). % UNIV_I
thf(fact_11_iso__tuple__UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % iso_tuple_UNIV_I
thf(fact_12_iso__tuple__UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_13_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt)))). % iso_tuple_UNIV_I
thf(fact_14_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_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_converseD, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (conver1781819635le_alt @ R)) => (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ R))))). % converseD
thf(fact_17_converseE, axiom,
    ((![Yx : produc16571293le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ Yx @ (conver1781819635le_alt @ R)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((Yx = (produc1494124311le_alt @ Y3 @ X3)) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R))))))))))). % converseE
thf(fact_18_converse_Ocases, axiom,
    ((![A1 : arrow_1857593510le_alt, A22 : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A1 @ A22) @ (conver1781819635le_alt @ R)) => (member2048039092le_alt @ (produc1494124311le_alt @ A22 @ A1) @ R))))). % converse.cases
thf(fact_19_converse__UNIV, axiom,
    (((conver1781819635le_alt @ top_to224369155le_alt) = top_to224369155le_alt))). % converse_UNIV
thf(fact_20_top__empty__eq2, axiom,
    ((top_to701951606_alt_o = (^[X4 : arrow_1857593510le_alt]: (^[Y4 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ top_to224369155le_alt)))))). % top_empty_eq2
thf(fact_21_top__empty__eq, axiom,
    ((top_to516240647_alt_o = (^[X4 : arrow_1857593510le_alt]: (member519365071le_alt @ X4 @ top_to958727510le_alt))))). % top_empty_eq
thf(fact_22_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_23_top__empty__eq, axiom,
    ((top_to1900088076_alt_o = (^[X4 : set_Pr367596371le_alt]: (member1334244458le_alt @ X4 @ top_to469035705le_alt))))). % top_empty_eq
thf(fact_24_top__set__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ top_to516240647_alt_o)))). % top_set_def
thf(fact_25_top__set__def, axiom,
    ((top_to224369155le_alt = (collec531981554le_alt @ top_to1074038850_alt_o)))). % top_set_def
thf(fact_26_top__set__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ top_to1900088076_alt_o)))). % top_set_def
thf(fact_27_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_28_old_Oprod_Oexhaust, axiom,
    ((![Y : produc16571293le_alt]: (~ ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (~ ((Y = (produc1494124311le_alt @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_29_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_30_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_31_surj__pair, axiom,
    ((![P2 : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P2 = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_32_UNIV__witness, axiom,
    ((?[X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ top_to958727510le_alt)))). % UNIV_witness
thf(fact_33_UNIV__witness, axiom,
    ((?[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_34_UNIV__witness, axiom,
    ((?[X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_35_UNIV__eq__I, axiom,
    ((![A4 : set_Ar1665529862le_alt]: ((![X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ A4)) => (top_to958727510le_alt = A4))))). % UNIV_eq_I
thf(fact_36_UNIV__eq__I, axiom,
    ((![A4 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A4)) => (top_to224369155le_alt = A4))))). % UNIV_eq_I
thf(fact_37_UNIV__eq__I, axiom,
    ((![A4 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ A4)) => (top_to469035705le_alt = A4))))). % UNIV_eq_I
thf(fact_38_pred__equals__eq2, axiom,
    ((![R2 : set_Pr367596371le_alt, S2 : set_Pr367596371le_alt]: (((^[X4 : arrow_1857593510le_alt]: (^[Y4 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ R2))) = (^[X4 : arrow_1857593510le_alt]: (^[Y4 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ S2)))) = (R2 = S2))))). % pred_equals_eq2
thf(fact_39_UNIV__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ (^[X4 : arrow_1857593510le_alt]: $true))))). % UNIV_def
thf(fact_40_UNIV__def, axiom,
    ((top_to224369155le_alt = (collec531981554le_alt @ (^[X4 : produc16571293le_alt]: $true))))). % UNIV_def
thf(fact_41_UNIV__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: $true))))). % UNIV_def
thf(fact_42_converse_Oinducts, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt, R : set_Pr367596371le_alt, P : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((member2048039092le_alt @ (produc1494124311le_alt @ X1 @ X2) @ (conver1781819635le_alt @ R)) => ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ R) => (P @ B3 @ A3))) => (P @ X1 @ X2)))))). % converse.inducts
thf(fact_43_converse_Ointros, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R) => (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (conver1781819635le_alt @ R)))))). % converse.intros
thf(fact_44_converse_Osimps, axiom,
    ((![A1 : arrow_1857593510le_alt, A22 : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A1 @ A22) @ (conver1781819635le_alt @ R)) = (?[A5 : arrow_1857593510le_alt]: (?[B4 : arrow_1857593510le_alt]: (((A1 = B4)) & ((((A22 = A5)) & ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ R))))))))))). % converse.simps
thf(fact_45_well__order__on__domain, axiom,
    ((![A4 : set_se2071012361le_alt, R : set_Pr851393385le_alt, A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((order_980048949le_alt @ A4 @ R) => ((member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ R) => ((member1334244458le_alt @ A @ A4) & (member1334244458le_alt @ B @ A4))))))). % well_order_on_domain
thf(fact_46_well__order__on__domain, axiom,
    ((![A4 : set_Pr367596371le_alt, R : set_Pr448479039le_alt, A : produc16571293le_alt, B : produc16571293le_alt]: ((order_901950591le_alt @ A4 @ R) => ((member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ R) => ((member2048039092le_alt @ A @ A4) & (member2048039092le_alt @ B @ A4))))))). % well_order_on_domain
thf(fact_47_well__order__on__domain, axiom,
    ((![A4 : set_Ar1665529862le_alt, R : set_Pr367596371le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((order_1185271620le_alt @ A4 @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R) => ((member519365071le_alt @ A @ A4) & (member519365071le_alt @ B @ A4))))))). % well_order_on_domain
thf(fact_48_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_49_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_50_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_51_Collect__mem__eq, axiom,
    ((![A4 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_52_Collect__mem__eq, axiom,
    ((![A4 : set_Ar1665529862le_alt]: ((collec1364151825le_alt @ (^[X4 : arrow_1857593510le_alt]: (member519365071le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_53_Collect__mem__eq, axiom,
    ((![A4 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (member1334244458le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_54_Collect__cong, axiom,
    ((![P : set_Pr367596371le_alt > $o, Q : set_Pr367596371le_alt > $o]: ((![X3 : set_Pr367596371le_alt]: ((P @ X3) = (Q @ X3))) => ((collec1399441576le_alt @ P) = (collec1399441576le_alt @ Q)))))). % Collect_cong
thf(fact_55_well__order__on, axiom,
    ((![A4 : set_Ar1665529862le_alt]: (?[X_1 : set_Pr367596371le_alt]: (order_1185271620le_alt @ A4 @ X_1))))). % well_order_on
thf(fact_56_ssubst__Pair__rhs, axiom,
    ((![R : arrow_1857593510le_alt, S : arrow_1857593510le_alt, R2 : set_Pr367596371le_alt, S3 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ R @ S) @ R2) => ((S3 = S) => (member2048039092le_alt @ (produc1494124311le_alt @ R @ S3) @ R2)))))). % ssubst_Pair_rhs
thf(fact_57_converse__inv__image, axiom,
    ((![R2 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((conver1781819635le_alt @ (inv_im155136540le_alt @ R2 @ F)) = (inv_im155136540le_alt @ (conver1781819635le_alt @ R2) @ F))))). % converse_inv_image
thf(fact_58_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_59_in__inv__image, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (inv_im155136540le_alt @ R @ F)) = (member2048039092le_alt @ (produc1494124311le_alt @ (F @ X) @ (F @ Y)) @ R))))). % in_inv_image
thf(fact_60_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_61_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_62_aboveS__def, axiom,
    ((order_1390665000le_alt = (^[R3 : set_Pr851393385le_alt]: (^[A5 : set_Pr367596371le_alt]: (collec1399441576le_alt @ (^[B4 : set_Pr367596371le_alt]: (((~ ((B4 = A5)))) & ((member1392960970le_alt @ (produc1931840741le_alt @ A5 @ B4) @ R3)))))))))). % aboveS_def
thf(fact_63_aboveS__def, axiom,
    ((order_1629231505le_alt = (^[R3 : set_Pr367596371le_alt]: (^[A5 : arrow_1857593510le_alt]: (collec1364151825le_alt @ (^[B4 : arrow_1857593510le_alt]: (((~ ((B4 = A5)))) & ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ R3)))))))))). % aboveS_def
thf(fact_64_above__def, axiom,
    ((order_1714391123le_alt = (^[R3 : set_Pr851393385le_alt]: (^[A5 : set_Pr367596371le_alt]: (collec1399441576le_alt @ (^[B4 : set_Pr367596371le_alt]: (member1392960970le_alt @ (produc1931840741le_alt @ A5 @ B4) @ R3)))))))). % above_def
thf(fact_65_above__def, axiom,
    ((order_1686956966le_alt = (^[R3 : set_Pr367596371le_alt]: (^[A5 : arrow_1857593510le_alt]: (collec1364151825le_alt @ (^[B4 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ R3)))))))). % above_def
thf(fact_66_preorder__on__converse, axiom,
    ((![A4 : set_Ar1665529862le_alt, R : set_Pr367596371le_alt]: ((order_1371535037le_alt @ A4 @ (conver1781819635le_alt @ R)) = (order_1371535037le_alt @ A4 @ R))))). % preorder_on_converse
thf(fact_67_UNIV__Times__UNIV, axiom,
    (((produc2062971558le_alt @ top_to958727510le_alt @ (^[Uu : arrow_1857593510le_alt]: top_to958727510le_alt)) = top_to224369155le_alt))). % UNIV_Times_UNIV
thf(fact_68_UNIV__Times__UNIV, axiom,
    (((produc2023643283le_alt @ top_to958727510le_alt @ (^[Uu : arrow_1857593510le_alt]: top_to224369155le_alt)) = top_to1544444322le_alt))). % UNIV_Times_UNIV
thf(fact_69_UNIV__Times__UNIV, axiom,
    (((produc1741626099le_alt @ top_to958727510le_alt @ (^[Uu : arrow_1857593510le_alt]: top_to469035705le_alt)) = top_to2022922242le_alt))). % UNIV_Times_UNIV
thf(fact_70_UNIV__Times__UNIV, axiom,
    (((produc195787183le_alt @ top_to224369155le_alt @ (^[Uu : produc16571293le_alt]: top_to958727510le_alt)) = top_to383098486le_alt))). % UNIV_Times_UNIV
thf(fact_71_UNIV__Times__UNIV, axiom,
    (((produc1360152522le_alt @ top_to224369155le_alt @ (^[Uu : produc16571293le_alt]: top_to224369155le_alt)) = top_to960359919le_alt))). % UNIV_Times_UNIV
thf(fact_72_UNIV__Times__UNIV, axiom,
    (((produc1173532202le_alt @ top_to224369155le_alt @ (^[Uu : produc16571293le_alt]: top_to469035705le_alt)) = top_to19085391le_alt))). % UNIV_Times_UNIV
thf(fact_73_UNIV__Times__UNIV, axiom,
    (((produc1568937061le_alt @ top_to469035705le_alt @ (^[Uu : set_Pr367596371le_alt]: top_to958727510le_alt)) = top_to1111255596le_alt))). % UNIV_Times_UNIV
thf(fact_74_UNIV__Times__UNIV, axiom,
    (((produc416649876le_alt @ top_to469035705le_alt @ (^[Uu : set_Pr367596371le_alt]: top_to224369155le_alt)) = top_to89343929le_alt))). % UNIV_Times_UNIV
thf(fact_75_UNIV__Times__UNIV, axiom,
    (((produc223727860le_alt @ top_to469035705le_alt @ (^[Uu : set_Pr367596371le_alt]: top_to469035705le_alt)) = top_to1159490073le_alt))). % UNIV_Times_UNIV
thf(fact_76_mem__Sigma__iff, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ (produc223727860le_alt @ A4 @ B5)) = (((member1334244458le_alt @ A @ A4)) & ((member1334244458le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_77_mem__Sigma__iff, axiom,
    ((![A : set_Pr367596371le_alt, B : produc16571293le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1480196970le_alt @ (produc1659212421le_alt @ A @ B) @ (produc416649876le_alt @ A4 @ B5)) = (((member1334244458le_alt @ A @ A4)) & ((member2048039092le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_78_mem__Sigma__iff, axiom,
    ((![A : set_Pr367596371le_alt, B : arrow_1857593510le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar1665529862le_alt]: ((member2059112357le_alt @ (produc226079796le_alt @ A @ B) @ (produc1568937061le_alt @ A4 @ B5)) = (((member1334244458le_alt @ A @ A4)) & ((member519365071le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_79_mem__Sigma__iff, axiom,
    ((![A : produc16571293le_alt, B : set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member1923768064le_alt @ (produc268611099le_alt @ A @ B) @ (produc1173532202le_alt @ A4 @ B5)) = (((member2048039092le_alt @ A @ A4)) & ((member1334244458le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_80_mem__Sigma__iff, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (produc1360152522le_alt @ A4 @ B5)) = (((member2048039092le_alt @ A @ A4)) & ((member2048039092le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_81_mem__Sigma__iff, axiom,
    ((![A : produc16571293le_alt, B : arrow_1857593510le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar1665529862le_alt]: ((member1876252911le_alt @ (produc78632318le_alt @ A @ B) @ (produc195787183le_alt @ A4 @ B5)) = (((member2048039092le_alt @ A @ A4)) & ((member519365071le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_82_mem__Sigma__iff, axiom,
    ((![A : arrow_1857593510le_alt, B : set_Pr367596371le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_se2071012361le_alt]: ((member1361938555le_alt @ (produc398768834le_alt @ A @ B) @ (produc1741626099le_alt @ A4 @ B5)) = (((member519365071le_alt @ A @ A4)) & ((member1334244458le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_83_mem__Sigma__iff, axiom,
    ((![A : arrow_1857593510le_alt, B : produc16571293le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((member1000073755le_alt @ (produc1906488418le_alt @ A @ B) @ (produc2023643283le_alt @ A4 @ B5)) = (((member519365071le_alt @ A @ A4)) & ((member2048039092le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_84_mem__Sigma__iff, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A4 @ B5)) = (((member519365071le_alt @ A @ A4)) & ((member519365071le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_85_SigmaI, axiom,
    ((![A : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1334244458le_alt @ A @ A4) => ((member1334244458le_alt @ B @ (B5 @ A)) => (member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ (produc223727860le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_86_SigmaI, axiom,
    ((![A : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B : produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ A @ A4) => ((member2048039092le_alt @ B @ (B5 @ A)) => (member1480196970le_alt @ (produc1659212421le_alt @ A @ B) @ (produc416649876le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_87_SigmaI, axiom,
    ((![A : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B : arrow_1857593510le_alt, B5 : set_Pr367596371le_alt > set_Ar1665529862le_alt]: ((member1334244458le_alt @ A @ A4) => ((member519365071le_alt @ B @ (B5 @ A)) => (member2059112357le_alt @ (produc226079796le_alt @ A @ B) @ (produc1568937061le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_88_SigmaI, axiom,
    ((![A : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member2048039092le_alt @ A @ A4) => ((member1334244458le_alt @ B @ (B5 @ A)) => (member1923768064le_alt @ (produc268611099le_alt @ A @ B) @ (produc1173532202le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_89_SigmaI, axiom,
    ((![A : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ A @ A4) => ((member2048039092le_alt @ B @ (B5 @ A)) => (member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (produc1360152522le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_90_SigmaI, axiom,
    ((![A : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : arrow_1857593510le_alt, B5 : produc16571293le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ A @ A4) => ((member519365071le_alt @ B @ (B5 @ A)) => (member1876252911le_alt @ (produc78632318le_alt @ A @ B) @ (produc195787183le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_91_SigmaI, axiom,
    ((![A : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt, B : set_Pr367596371le_alt, B5 : arrow_1857593510le_alt > set_se2071012361le_alt]: ((member519365071le_alt @ A @ A4) => ((member1334244458le_alt @ B @ (B5 @ A)) => (member1361938555le_alt @ (produc398768834le_alt @ A @ B) @ (produc1741626099le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_92_SigmaI, axiom,
    ((![A : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt, B : produc16571293le_alt, B5 : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((member519365071le_alt @ A @ A4) => ((member2048039092le_alt @ B @ (B5 @ A)) => (member1000073755le_alt @ (produc1906488418le_alt @ A @ B) @ (produc2023643283le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_93_SigmaI, axiom,
    ((![A : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt, B : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member519365071le_alt @ A @ A4) => ((member519365071le_alt @ B @ (B5 @ A)) => (member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_94_SigmaE, axiom,
    ((![C : produc541234227le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1392960970le_alt @ C @ (produc223727860le_alt @ A4 @ B5)) => (~ ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A4) => (![Y3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc1931840741le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_95_SigmaE, axiom,
    ((![C : produc670815699le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1480196970le_alt @ C @ (produc416649876le_alt @ A4 @ B5)) => (~ ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A4) => (![Y3 : produc16571293le_alt]: ((member2048039092le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc1659212421le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_96_SigmaE, axiom,
    ((![C : produc366337788le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar1665529862le_alt]: ((member2059112357le_alt @ C @ (produc1568937061le_alt @ A4 @ B5)) => (~ ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A4) => (![Y3 : arrow_1857593510le_alt]: ((member519365071le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc226079796le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_97_SigmaE, axiom,
    ((![C : produc1114386793le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member1923768064le_alt @ C @ (produc1173532202le_alt @ A4 @ B5)) => (~ ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A4) => (![Y3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc268611099le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_98_SigmaE, axiom,
    ((![C : produc1556433673le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2146260128le_alt @ C @ (produc1360152522le_alt @ A4 @ B5)) => (~ ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A4) => (![Y3 : produc16571293le_alt]: ((member2048039092le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc41061307le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_99_SigmaE, axiom,
    ((![C : produc2034271302le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar1665529862le_alt]: ((member1876252911le_alt @ C @ (produc195787183le_alt @ A4 @ B5)) => (~ ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A4) => (![Y3 : arrow_1857593510le_alt]: ((member519365071le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc78632318le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_100_SigmaE, axiom,
    ((![C : produc1816647634le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_se2071012361le_alt]: ((member1361938555le_alt @ C @ (produc1741626099le_alt @ A4 @ B5)) => (~ ((![X3 : arrow_1857593510le_alt]: ((member519365071le_alt @ X3 @ A4) => (![Y3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc398768834le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_101_SigmaE, axiom,
    ((![C : produc1158092146le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((member1000073755le_alt @ C @ (produc2023643283le_alt @ A4 @ B5)) => (~ ((![X3 : arrow_1857593510le_alt]: ((member519365071le_alt @ X3 @ A4) => (![Y3 : produc16571293le_alt]: ((member2048039092le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc1906488418le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_102_SigmaE, axiom,
    ((![C : produc16571293le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ C @ (produc2062971558le_alt @ A4 @ B5)) => (~ ((![X3 : arrow_1857593510le_alt]: ((member519365071le_alt @ X3 @ A4) => (![Y3 : arrow_1857593510le_alt]: ((member519365071le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc1494124311le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_103_SigmaD1, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A4 @ B5)) => (member519365071le_alt @ A @ A4))))). % SigmaD1
thf(fact_104_SigmaD2, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A4 @ B5)) => (member519365071le_alt @ B @ (B5 @ A)))))). % SigmaD2
thf(fact_105_SigmaE2, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ (produc223727860le_alt @ A4 @ B5)) => (~ (((member1334244458le_alt @ A @ A4) => (~ ((member1334244458le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_106_SigmaE2, axiom,
    ((![A : set_Pr367596371le_alt, B : produc16571293le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1480196970le_alt @ (produc1659212421le_alt @ A @ B) @ (produc416649876le_alt @ A4 @ B5)) => (~ (((member1334244458le_alt @ A @ A4) => (~ ((member2048039092le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_107_SigmaE2, axiom,
    ((![A : set_Pr367596371le_alt, B : arrow_1857593510le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar1665529862le_alt]: ((member2059112357le_alt @ (produc226079796le_alt @ A @ B) @ (produc1568937061le_alt @ A4 @ B5)) => (~ (((member1334244458le_alt @ A @ A4) => (~ ((member519365071le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_108_SigmaE2, axiom,
    ((![A : produc16571293le_alt, B : set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member1923768064le_alt @ (produc268611099le_alt @ A @ B) @ (produc1173532202le_alt @ A4 @ B5)) => (~ (((member2048039092le_alt @ A @ A4) => (~ ((member1334244458le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_109_SigmaE2, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (produc1360152522le_alt @ A4 @ B5)) => (~ (((member2048039092le_alt @ A @ A4) => (~ ((member2048039092le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_110_SigmaE2, axiom,
    ((![A : produc16571293le_alt, B : arrow_1857593510le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar1665529862le_alt]: ((member1876252911le_alt @ (produc78632318le_alt @ A @ B) @ (produc195787183le_alt @ A4 @ B5)) => (~ (((member2048039092le_alt @ A @ A4) => (~ ((member519365071le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_111_SigmaE2, axiom,
    ((![A : arrow_1857593510le_alt, B : set_Pr367596371le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_se2071012361le_alt]: ((member1361938555le_alt @ (produc398768834le_alt @ A @ B) @ (produc1741626099le_alt @ A4 @ B5)) => (~ (((member519365071le_alt @ A @ A4) => (~ ((member1334244458le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_112_SigmaE2, axiom,
    ((![A : arrow_1857593510le_alt, B : produc16571293le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((member1000073755le_alt @ (produc1906488418le_alt @ A @ B) @ (produc2023643283le_alt @ A4 @ B5)) => (~ (((member519365071le_alt @ A @ A4) => (~ ((member2048039092le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_113_SigmaE2, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A4 @ B5)) => (~ (((member519365071le_alt @ A @ A4) => (~ ((member519365071le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_114_converse__Times, axiom,
    ((![A4 : set_Ar1665529862le_alt, B5 : set_Ar1665529862le_alt]: ((conver1781819635le_alt @ (produc2062971558le_alt @ A4 @ (^[Uu : arrow_1857593510le_alt]: B5))) = (produc2062971558le_alt @ B5 @ (^[Uu : arrow_1857593510le_alt]: A4)))))). % converse_Times
thf(fact_115_member__product, axiom,
    ((![X : produc16571293le_alt, A4 : set_Ar1665529862le_alt, B5 : set_Ar1665529862le_alt]: ((member2048039092le_alt @ X @ (produc961482780le_alt @ A4 @ B5)) = (member2048039092le_alt @ X @ (produc2062971558le_alt @ A4 @ (^[Uu : arrow_1857593510le_alt]: B5))))))). % member_product
thf(fact_116_same__fstI, axiom,
    ((![P : arrow_1857593510le_alt > $o, X : arrow_1857593510le_alt, Y5 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R2 : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((P @ X) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y5 @ Y) @ (R2 @ X)) => (member2146260128le_alt @ (produc41061307le_alt @ (produc1494124311le_alt @ X @ Y5) @ (produc1494124311le_alt @ X @ Y)) @ (same_f554660482le_alt @ P @ R2))))))). % same_fstI
thf(fact_117_image2__eqI, axiom,
    ((![B : arrow_1857593510le_alt, F : set_Pr367596371le_alt > arrow_1857593510le_alt, X : set_Pr367596371le_alt, C : arrow_1857593510le_alt, G : set_Pr367596371le_alt > arrow_1857593510le_alt, A4 : set_se2071012361le_alt]: ((B = (F @ X)) => ((C = (G @ X)) => ((member1334244458le_alt @ X @ A4) => (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (bNF_Gr1763718335le_alt @ A4 @ F @ G)))))))). % image2_eqI
thf(fact_118_image2__eqI, axiom,
    ((![B : arrow_1857593510le_alt, F : produc16571293le_alt > arrow_1857593510le_alt, X : produc16571293le_alt, C : arrow_1857593510le_alt, G : produc16571293le_alt > arrow_1857593510le_alt, A4 : set_Pr367596371le_alt]: ((B = (F @ X)) => ((C = (G @ X)) => ((member2048039092le_alt @ X @ A4) => (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (bNF_Gr2045826825le_alt @ A4 @ F @ G)))))))). % image2_eqI
thf(fact_119_image2__eqI, axiom,
    ((![B : arrow_1857593510le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt, C : arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt]: ((B = (F @ X)) => ((C = (G @ X)) => ((member519365071le_alt @ X @ A4) => (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (bNF_Gr1049083998le_alt @ A4 @ F @ G)))))))). % image2_eqI
thf(fact_120_top__unit__def, axiom,
    ((top_top_Product_unit = product_Unity))). % top_unit_def
thf(fact_121_old_Ounit_Oexhaust, axiom,
    ((![Y : product_unit]: (Y = product_Unity)))). % old.unit.exhaust
thf(fact_122_old_Ounit_Oinducts, axiom,
    ((![P : product_unit > $o, Unit : product_unit]: ((P @ product_Unity) => (P @ Unit))))). % old.unit.inducts
thf(fact_123_unit__all__impI, axiom,
    ((![P : product_unit > $o, Q : product_unit > $o]: (((P @ product_Unity) => (Q @ product_Unity)) => (![X5 : product_unit]: ((P @ X5) => (Q @ X5))))))). % unit_all_impI
thf(fact_124_eq__sym__Unity__conv, axiom,
    ((![X : $o]: ((X = (product_Unity = product_Unity)) = X)))). % eq_sym_Unity_conv
thf(fact_125_default__unit__def, axiom,
    ((defaul1399868459t_unit = product_Unity))). % default_unit_def
thf(fact_126_in__lex__prod, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ (produc1494124311le_alt @ A @ B) @ (produc1494124311le_alt @ A2 @ B2)) @ (lex_pr3395839le_alt @ R @ S)) = (((member2048039092le_alt @ (produc1494124311le_alt @ A @ A2) @ R)) | ((((A = A2)) & ((member2048039092le_alt @ (produc1494124311le_alt @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_127_image2__def, axiom,
    ((bNF_Gr1763718335le_alt = (^[A6 : set_se2071012361le_alt]: (^[F2 : set_Pr367596371le_alt > arrow_1857593510le_alt]: (^[G2 : set_Pr367596371le_alt > arrow_1857593510le_alt]: (collec531981554le_alt @ (^[Uu : produc16571293le_alt]: (?[A5 : set_Pr367596371le_alt]: (((Uu = (produc1494124311le_alt @ (F2 @ A5) @ (G2 @ A5)))) & ((member1334244458le_alt @ A5 @ A6)))))))))))). % image2_def
thf(fact_128_image2__def, axiom,
    ((bNF_Gr2045826825le_alt = (^[A6 : set_Pr367596371le_alt]: (^[F2 : produc16571293le_alt > arrow_1857593510le_alt]: (^[G2 : produc16571293le_alt > arrow_1857593510le_alt]: (collec531981554le_alt @ (^[Uu : produc16571293le_alt]: (?[A5 : produc16571293le_alt]: (((Uu = (produc1494124311le_alt @ (F2 @ A5) @ (G2 @ A5)))) & ((member2048039092le_alt @ A5 @ A6)))))))))))). % image2_def
thf(fact_129_image2__def, axiom,
    ((bNF_Gr1049083998le_alt = (^[A6 : set_Ar1665529862le_alt]: (^[F2 : arrow_1857593510le_alt > arrow_1857593510le_alt]: (^[G2 : arrow_1857593510le_alt > arrow_1857593510le_alt]: (collec531981554le_alt @ (^[Uu : produc16571293le_alt]: (?[A5 : arrow_1857593510le_alt]: (((Uu = (produc1494124311le_alt @ (F2 @ A5) @ (G2 @ A5)))) & ((member519365071le_alt @ A5 @ A6)))))))))))). % image2_def
thf(fact_130_Unity__def, axiom,
    ((product_Unity = (product_Abs_unit @ $true)))). % Unity_def
thf(fact_131_relImage__def, axiom,
    ((bNF_Gr960124042le_alt = (^[R4 : set_Pr367596371le_alt]: (^[F2 : arrow_1857593510le_alt > arrow_1857593510le_alt]: (collec531981554le_alt @ (^[Uu : produc16571293le_alt]: (?[A12 : arrow_1857593510le_alt]: (?[A23 : arrow_1857593510le_alt]: (((Uu = (produc1494124311le_alt @ (F2 @ A12) @ (F2 @ A23)))) & ((member2048039092le_alt @ (produc1494124311le_alt @ A12 @ A23) @ R4)))))))))))). % relImage_def
thf(fact_132_relInvImage__def, axiom,
    ((bNF_Gr1688359262le_alt = (^[A6 : set_se2071012361le_alt]: (^[R4 : set_Pr367596371le_alt]: (^[F2 : set_Pr367596371le_alt > arrow_1857593510le_alt]: (collec454808328le_alt @ (^[Uu : produc541234227le_alt]: (?[A12 : set_Pr367596371le_alt]: (?[A23 : set_Pr367596371le_alt]: (((Uu = (produc1931840741le_alt @ A12 @ A23))) & ((((member1334244458le_alt @ A12 @ A6)) & ((((member1334244458le_alt @ A23 @ A6)) & ((member2048039092le_alt @ (produc1494124311le_alt @ (F2 @ A12) @ (F2 @ A23)) @ R4))))))))))))))))). % relInvImage_def
thf(fact_133_relInvImage__def, axiom,
    ((bNF_Gr1884428968le_alt = (^[A6 : set_Pr367596371le_alt]: (^[R4 : set_Pr367596371le_alt]: (^[F2 : produc16571293le_alt > arrow_1857593510le_alt]: (collec824848862le_alt @ (^[Uu : produc1556433673le_alt]: (?[A12 : produc16571293le_alt]: (?[A23 : produc16571293le_alt]: (((Uu = (produc41061307le_alt @ A12 @ A23))) & ((((member2048039092le_alt @ A12 @ A6)) & ((((member2048039092le_alt @ A23 @ A6)) & ((member2048039092le_alt @ (produc1494124311le_alt @ (F2 @ A12) @ (F2 @ A23)) @ R4))))))))))))))))). % relInvImage_def
thf(fact_134_relInvImage__def, axiom,
    ((bNF_Gr1969491821le_alt = (^[A6 : set_Ar1665529862le_alt]: (^[R4 : set_Pr367596371le_alt]: (^[F2 : arrow_1857593510le_alt > arrow_1857593510le_alt]: (collec531981554le_alt @ (^[Uu : produc16571293le_alt]: (?[A12 : arrow_1857593510le_alt]: (?[A23 : arrow_1857593510le_alt]: (((Uu = (produc1494124311le_alt @ A12 @ A23))) & ((((member519365071le_alt @ A12 @ A6)) & ((((member519365071le_alt @ A23 @ A6)) & ((member2048039092le_alt @ (produc1494124311le_alt @ (F2 @ A12) @ (F2 @ A23)) @ R4))))))))))))))))). % relInvImage_def
thf(fact_135_subsetI, axiom,
    ((![A4 : set_se2071012361le_alt, B5 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A4) => (member1334244458le_alt @ X3 @ B5))) => (ord_le1836905577le_alt @ A4 @ B5))))). % subsetI
thf(fact_136_subsetI, axiom,
    ((![A4 : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A4) => (member2048039092le_alt @ X3 @ B5))) => (ord_le1885758387le_alt @ A4 @ B5))))). % subsetI
thf(fact_137_subsetI, axiom,
    ((![A4 : set_Ar1665529862le_alt, B5 : set_Ar1665529862le_alt]: ((![X3 : arrow_1857593510le_alt]: ((member519365071le_alt @ X3 @ A4) => (member519365071le_alt @ X3 @ B5))) => (ord_le142020518le_alt @ A4 @ B5))))). % subsetI
thf(fact_138_converse__mono, axiom,
    ((![R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: ((ord_le1885758387le_alt @ (conver1781819635le_alt @ R) @ (conver1781819635le_alt @ S)) = (ord_le1885758387le_alt @ R @ S))))). % converse_mono
thf(fact_139_top_Oextremum__uniqueI, axiom,
    ((![A : set_Ar1665529862le_alt]: ((ord_le142020518le_alt @ top_to958727510le_alt @ A) => (A = top_to958727510le_alt))))). % top.extremum_uniqueI
thf(fact_140_top_Oextremum__uniqueI, axiom,
    ((![A : product_unit]: ((ord_le1997193645t_unit @ top_top_Product_unit @ A) => (A = top_top_Product_unit))))). % top.extremum_uniqueI
thf(fact_141_top_Oextremum__uniqueI, axiom,
    ((![A : set_Pr367596371le_alt]: ((ord_le1885758387le_alt @ top_to224369155le_alt @ A) => (A = top_to224369155le_alt))))). % top.extremum_uniqueI
thf(fact_142_top_Oextremum__uniqueI, axiom,
    ((![A : set_se2071012361le_alt]: ((ord_le1836905577le_alt @ top_to469035705le_alt @ A) => (A = top_to469035705le_alt))))). % top.extremum_uniqueI
thf(fact_143_top_Oextremum__unique, axiom,
    ((![A : set_Ar1665529862le_alt]: ((ord_le142020518le_alt @ top_to958727510le_alt @ A) = (A = top_to958727510le_alt))))). % top.extremum_unique
thf(fact_144_top_Oextremum__unique, axiom,
    ((![A : product_unit]: ((ord_le1997193645t_unit @ top_top_Product_unit @ A) = (A = top_top_Product_unit))))). % top.extremum_unique
thf(fact_145_top_Oextremum__unique, axiom,
    ((![A : set_Pr367596371le_alt]: ((ord_le1885758387le_alt @ top_to224369155le_alt @ A) = (A = top_to224369155le_alt))))). % top.extremum_unique
thf(fact_146_top_Oextremum__unique, axiom,
    ((![A : set_se2071012361le_alt]: ((ord_le1836905577le_alt @ top_to469035705le_alt @ A) = (A = top_to469035705le_alt))))). % top.extremum_unique
thf(fact_147_top__greatest, axiom,
    ((![A : set_Ar1665529862le_alt]: (ord_le142020518le_alt @ A @ top_to958727510le_alt)))). % top_greatest
thf(fact_148_top__greatest, axiom,
    ((![A : product_unit]: (ord_le1997193645t_unit @ A @ top_top_Product_unit)))). % top_greatest
thf(fact_149_top__greatest, axiom,
    ((![A : set_Pr367596371le_alt]: (ord_le1885758387le_alt @ A @ top_to224369155le_alt)))). % top_greatest
thf(fact_150_top__greatest, axiom,
    ((![A : set_se2071012361le_alt]: (ord_le1836905577le_alt @ A @ top_to469035705le_alt)))). % top_greatest
thf(fact_151_subset__UNIV, axiom,
    ((![A4 : set_Ar1665529862le_alt]: (ord_le142020518le_alt @ A4 @ top_to958727510le_alt)))). % subset_UNIV
thf(fact_152_subset__UNIV, axiom,
    ((![A4 : set_Pr367596371le_alt]: (ord_le1885758387le_alt @ A4 @ top_to224369155le_alt)))). % subset_UNIV
thf(fact_153_subset__UNIV, axiom,
    ((![A4 : set_se2071012361le_alt]: (ord_le1836905577le_alt @ A4 @ top_to469035705le_alt)))). % subset_UNIV
thf(fact_154_subset__Collect__iff, axiom,
    ((![B5 : set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, P : produc16571293le_alt > $o]: ((ord_le1885758387le_alt @ B5 @ A4) => ((ord_le1885758387le_alt @ B5 @ (collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ A4)) & ((P @ X4)))))) = (![X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ B5)) => ((P @ X4))))))))). % subset_Collect_iff
thf(fact_155_subset__Collect__iff, axiom,
    ((![B5 : set_Ar1665529862le_alt, A4 : set_Ar1665529862le_alt, P : arrow_1857593510le_alt > $o]: ((ord_le142020518le_alt @ B5 @ A4) => ((ord_le142020518le_alt @ B5 @ (collec1364151825le_alt @ (^[X4 : arrow_1857593510le_alt]: (((member519365071le_alt @ X4 @ A4)) & ((P @ X4)))))) = (![X4 : arrow_1857593510le_alt]: (((member519365071le_alt @ X4 @ B5)) => ((P @ X4))))))))). % subset_Collect_iff
thf(fact_156_subset__Collect__iff, axiom,
    ((![B5 : set_se2071012361le_alt, A4 : set_se2071012361le_alt, P : set_Pr367596371le_alt > $o]: ((ord_le1836905577le_alt @ B5 @ A4) => ((ord_le1836905577le_alt @ B5 @ (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ A4)) & ((P @ X4)))))) = (![X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ B5)) => ((P @ X4))))))))). % subset_Collect_iff
thf(fact_157_subset__CollectI, axiom,
    ((![B5 : set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, Q : produc16571293le_alt > $o, P : produc16571293le_alt > $o]: ((ord_le1885758387le_alt @ B5 @ A4) => ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ B5) => ((Q @ X3) => (P @ X3)))) => (ord_le1885758387le_alt @ (collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ B5)) & ((Q @ X4))))) @ (collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ A4)) & ((P @ X4))))))))))). % subset_CollectI
thf(fact_158_subset__CollectI, axiom,
    ((![B5 : set_Ar1665529862le_alt, A4 : set_Ar1665529862le_alt, Q : arrow_1857593510le_alt > $o, P : arrow_1857593510le_alt > $o]: ((ord_le142020518le_alt @ B5 @ A4) => ((![X3 : arrow_1857593510le_alt]: ((member519365071le_alt @ X3 @ B5) => ((Q @ X3) => (P @ X3)))) => (ord_le142020518le_alt @ (collec1364151825le_alt @ (^[X4 : arrow_1857593510le_alt]: (((member519365071le_alt @ X4 @ B5)) & ((Q @ X4))))) @ (collec1364151825le_alt @ (^[X4 : arrow_1857593510le_alt]: (((member519365071le_alt @ X4 @ A4)) & ((P @ X4))))))))))). % subset_CollectI
thf(fact_159_subset__CollectI, axiom,
    ((![B5 : set_se2071012361le_alt, A4 : set_se2071012361le_alt, Q : set_Pr367596371le_alt > $o, P : set_Pr367596371le_alt > $o]: ((ord_le1836905577le_alt @ B5 @ A4) => ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ B5) => ((Q @ X3) => (P @ X3)))) => (ord_le1836905577le_alt @ (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ B5)) & ((Q @ X4))))) @ (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ A4)) & ((P @ X4))))))))))). % subset_CollectI
thf(fact_160_converse__subset__swap, axiom,
    ((![R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: ((ord_le1885758387le_alt @ R @ (conver1781819635le_alt @ S)) = (ord_le1885758387le_alt @ (conver1781819635le_alt @ R) @ S))))). % converse_subset_swap
thf(fact_161_Collect__restrict, axiom,
    ((![X6 : set_Pr367596371le_alt, P : produc16571293le_alt > $o]: (ord_le1885758387le_alt @ (collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ X6)) & ((P @ X4))))) @ X6)))). % Collect_restrict
thf(fact_162_Collect__restrict, axiom,
    ((![X6 : set_Ar1665529862le_alt, P : arrow_1857593510le_alt > $o]: (ord_le142020518le_alt @ (collec1364151825le_alt @ (^[X4 : arrow_1857593510le_alt]: (((member519365071le_alt @ X4 @ X6)) & ((P @ X4))))) @ X6)))). % Collect_restrict
thf(fact_163_Collect__restrict, axiom,
    ((![X6 : set_se2071012361le_alt, P : set_Pr367596371le_alt > $o]: (ord_le1836905577le_alt @ (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ X6)) & ((P @ X4))))) @ X6)))). % Collect_restrict
thf(fact_164_prop__restrict, axiom,
    ((![X : produc16571293le_alt, Z : set_Pr367596371le_alt, X6 : set_Pr367596371le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ X @ Z) => ((ord_le1885758387le_alt @ Z @ (collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ X6)) & ((P @ X4)))))) => (P @ X)))))). % prop_restrict
thf(fact_165_prop__restrict, axiom,
    ((![X : arrow_1857593510le_alt, Z : set_Ar1665529862le_alt, X6 : set_Ar1665529862le_alt, P : arrow_1857593510le_alt > $o]: ((member519365071le_alt @ X @ Z) => ((ord_le142020518le_alt @ Z @ (collec1364151825le_alt @ (^[X4 : arrow_1857593510le_alt]: (((member519365071le_alt @ X4 @ X6)) & ((P @ X4)))))) => (P @ X)))))). % prop_restrict
thf(fact_166_prop__restrict, axiom,
    ((![X : set_Pr367596371le_alt, Z : set_se2071012361le_alt, X6 : set_se2071012361le_alt, P : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ X @ Z) => ((ord_le1836905577le_alt @ Z @ (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ X6)) & ((P @ X4)))))) => (P @ X)))))). % prop_restrict
thf(fact_167_Collect__subset, axiom,
    ((![A4 : set_Pr367596371le_alt, P : produc16571293le_alt > $o]: (ord_le1885758387le_alt @ (collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ A4)) & ((P @ X4))))) @ A4)))). % Collect_subset
thf(fact_168_Collect__subset, axiom,
    ((![A4 : set_Ar1665529862le_alt, P : arrow_1857593510le_alt > $o]: (ord_le142020518le_alt @ (collec1364151825le_alt @ (^[X4 : arrow_1857593510le_alt]: (((member519365071le_alt @ X4 @ A4)) & ((P @ X4))))) @ A4)))). % Collect_subset
thf(fact_169_Collect__subset, axiom,
    ((![A4 : set_se2071012361le_alt, P : set_Pr367596371le_alt > $o]: (ord_le1836905577le_alt @ (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ A4)) & ((P @ X4))))) @ A4)))). % Collect_subset
thf(fact_170_in__mono, axiom,
    ((![A4 : set_se2071012361le_alt, B5 : set_se2071012361le_alt, X : set_Pr367596371le_alt]: ((ord_le1836905577le_alt @ A4 @ B5) => ((member1334244458le_alt @ X @ A4) => (member1334244458le_alt @ X @ B5)))))). % in_mono
thf(fact_171_in__mono, axiom,
    ((![A4 : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt, X : produc16571293le_alt]: ((ord_le1885758387le_alt @ A4 @ B5) => ((member2048039092le_alt @ X @ A4) => (member2048039092le_alt @ X @ B5)))))). % in_mono
thf(fact_172_in__mono, axiom,
    ((![A4 : set_Ar1665529862le_alt, B5 : set_Ar1665529862le_alt, X : arrow_1857593510le_alt]: ((ord_le142020518le_alt @ A4 @ B5) => ((member519365071le_alt @ X @ A4) => (member519365071le_alt @ X @ B5)))))). % in_mono
thf(fact_173_subsetD, axiom,
    ((![A4 : set_se2071012361le_alt, B5 : set_se2071012361le_alt, C : set_Pr367596371le_alt]: ((ord_le1836905577le_alt @ A4 @ B5) => ((member1334244458le_alt @ C @ A4) => (member1334244458le_alt @ C @ B5)))))). % subsetD
thf(fact_174_subsetD, axiom,
    ((![A4 : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt, C : produc16571293le_alt]: ((ord_le1885758387le_alt @ A4 @ B5) => ((member2048039092le_alt @ C @ A4) => (member2048039092le_alt @ C @ B5)))))). % subsetD
thf(fact_175_subsetD, axiom,
    ((![A4 : set_Ar1665529862le_alt, B5 : set_Ar1665529862le_alt, C : arrow_1857593510le_alt]: ((ord_le142020518le_alt @ A4 @ B5) => ((member519365071le_alt @ C @ A4) => (member519365071le_alt @ C @ B5)))))). % subsetD
thf(fact_176_subset__eq, axiom,
    ((ord_le1836905577le_alt = (^[A6 : set_se2071012361le_alt]: (^[B6 : set_se2071012361le_alt]: (![X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ A6)) => ((member1334244458le_alt @ X4 @ B6))))))))). % subset_eq
thf(fact_177_subset__eq, axiom,
    ((ord_le1885758387le_alt = (^[A6 : set_Pr367596371le_alt]: (^[B6 : set_Pr367596371le_alt]: (![X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ A6)) => ((member2048039092le_alt @ X4 @ B6))))))))). % subset_eq
thf(fact_178_subset__eq, axiom,
    ((ord_le142020518le_alt = (^[A6 : set_Ar1665529862le_alt]: (^[B6 : set_Ar1665529862le_alt]: (![X4 : arrow_1857593510le_alt]: (((member519365071le_alt @ X4 @ A6)) => ((member519365071le_alt @ X4 @ B6))))))))). % subset_eq
thf(fact_179_subset__iff, axiom,
    ((ord_le1836905577le_alt = (^[A6 : set_se2071012361le_alt]: (^[B6 : set_se2071012361le_alt]: (![T : set_Pr367596371le_alt]: (((member1334244458le_alt @ T @ A6)) => ((member1334244458le_alt @ T @ B6))))))))). % subset_iff
thf(fact_180_subset__iff, axiom,
    ((ord_le1885758387le_alt = (^[A6 : set_Pr367596371le_alt]: (^[B6 : set_Pr367596371le_alt]: (![T : produc16571293le_alt]: (((member2048039092le_alt @ T @ A6)) => ((member2048039092le_alt @ T @ B6))))))))). % subset_iff
thf(fact_181_subset__iff, axiom,
    ((ord_le142020518le_alt = (^[A6 : set_Ar1665529862le_alt]: (^[B6 : set_Ar1665529862le_alt]: (![T : arrow_1857593510le_alt]: (((member519365071le_alt @ T @ A6)) => ((member519365071le_alt @ T @ B6))))))))). % subset_iff
thf(fact_182_Collect__mono, axiom,
    ((![P : set_Pr367596371le_alt > $o, Q : set_Pr367596371le_alt > $o]: ((![X3 : set_Pr367596371le_alt]: ((P @ X3) => (Q @ X3))) => (ord_le1836905577le_alt @ (collec1399441576le_alt @ P) @ (collec1399441576le_alt @ Q)))))). % Collect_mono

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[L2 : set_Pr367596371le_alt]: (member1334244458le_alt @ L2 @ arrow_1848678355le_Lin)))).
