% 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_51__5184740_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:15:50.479

% Could-be-implicit typings (9)
thf(ty_n_t__Set__Oset_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_J, type,
    set_Pr851393385le_alt : $tType).
thf(ty_n_t__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,
    produc541234227le_alt : $tType).
thf(ty_n_t__Set__Oset_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_J, type,
    set_Pr448479039le_alt : $tType).
thf(ty_n_t__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,
    produc1556433673le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se2071012361le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Pr367596371le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc16571293le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    set_Ar1665529862le_alt : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    arrow_1857593510le_alt : $tType).

% Explicit typings (40)
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OLin, type,
    arrow_1848678355le_Lin : set_se2071012361le_alt).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    ord_le1885758387le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    ord_le1836905577le_alt : set_se2071012361le_alt > set_se2071012361le_alt > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_Eo_J, type,
    top_to1074038850_alt_o : produc16571293le_alt > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_M_Eo_J, type,
    top_to1900088076_alt_o : set_Pr367596371le_alt > $o).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    top_to224369155le_alt : set_Pr367596371le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    top_to469035705le_alt : set_se2071012361le_alt).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1494124311le_alt : arrow_1857593510le_alt > arrow_1857593510le_alt > produc16571293le_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__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_Oapfst_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1245692284le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_Oapsnd_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1710313402le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc16571293le_alt > produc16571293le_alt).
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_Omap__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1074667658le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001_Eo, type,
    produc624247124_alt_o : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > produc16571293le_alt > $o).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_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,
    produc860300173le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt) > produc16571293le_alt > set_Pr367596371le_alt).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc1042938349le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt) > produc16571293le_alt > set_se2071012361le_alt).
thf(sy_c_Product__Type_Oprod_Ofst_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc2071652395le_alt : produc16571293le_alt > arrow_1857593510le_alt).
thf(sy_c_Product__Type_Oprod_Osnd_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1272650601le_alt : produc16571293le_alt > arrow_1857593510le_alt).
thf(sy_c_Product__Type_Oprod_Oswap_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1794822519le_alt : produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Relation_OId__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    id_on_426682691le_alt : set_Ar1665529862le_alt > set_Pr367596371le_alt).
thf(sy_c_Relation_OId__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    id_on_714194496le_alt : set_Pr367596371le_alt > set_Pr448479039le_alt).
thf(sy_c_Relation_OId__on_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    id_on_1531570678le_alt : set_se2071012361le_alt > set_Pr851393385le_alt).
thf(sy_c_Relation_Oantisym_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    antisy1745863240le_alt : set_Pr367596371le_alt > $o).
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__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__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_Set_Oimage_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,
    image_1873259469le_alt : (produc16571293le_alt > produc16571293le_alt) > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Set_Oimage_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,
    image_715032109le_alt : (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr367596371le_alt > set_se2071012361le_alt).
thf(sy_c_Set_Oimage_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,
    image_2105633431le_alt : (set_Pr367596371le_alt > produc16571293le_alt) > set_se2071012361le_alt > set_Pr367596371le_alt).
thf(sy_c_Set_Oimage_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,
    image_71834871le_alt : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se2071012361le_alt > set_se2071012361le_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__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_L, type,
    l : set_Pr367596371le_alt).
thf(sy_v_a, type,
    a : arrow_1857593510le_alt).
thf(sy_v_b, type,
    b : arrow_1857593510le_alt).

% Relevant facts (102)
thf(fact_0_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_1_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_2_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_3_surj__pair, axiom,
    ((![P : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_4_prod__cases, axiom,
    ((![P2 : produc16571293le_alt > $o, P : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_5_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_6_old_Oprod_Oinducts, axiom,
    ((![P2 : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_7_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_8_ssubst__Pair__rhs, axiom,
    ((![R : arrow_1857593510le_alt, S : arrow_1857593510le_alt, R2 : set_Pr367596371le_alt, S2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ R @ S) @ R2) => ((S2 = S) => (member2048039092le_alt @ (produc1494124311le_alt @ R @ S2) @ R2)))))). % ssubst_Pair_rhs
thf(fact_9_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_10_swap__simp, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1794822519le_alt @ (produc1494124311le_alt @ X @ Y)) = (produc1494124311le_alt @ Y @ X))))). % swap_simp
thf(fact_11_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_12_apsnd__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1710313402le_alt @ F @ (produc1494124311le_alt @ X @ Y)) = (produc1494124311le_alt @ X @ (F @ Y)))))). % apsnd_conv
thf(fact_13_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_14_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_15_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_16_converse__converse, axiom,
    ((![R : set_Pr367596371le_alt]: ((conver1781819635le_alt @ (conver1781819635le_alt @ R)) = R)))). % converse_converse
thf(fact_17_converse__inject, axiom,
    ((![R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: (((conver1781819635le_alt @ R) = (conver1781819635le_alt @ S)) = (R = S))))). % converse_inject
thf(fact_18_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_19_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_20_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_21_converse_Osimps, axiom,
    ((![A1 : arrow_1857593510le_alt, A22 : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A1 @ A22) @ (conver1781819635le_alt @ R)) = (?[A4 : arrow_1857593510le_alt]: (?[B4 : arrow_1857593510le_alt]: (((A1 = B4)) & ((((A22 = A4)) & ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ R))))))))))). % converse.simps
thf(fact_22_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_23_converse_Oinducts, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt, R : set_Pr367596371le_alt, P2 : 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) => (P2 @ B3 @ A3))) => (P2 @ X1 @ X2)))))). % converse.inducts
thf(fact_24_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_25_pair__in__swap__image, axiom,
    ((![Y : arrow_1857593510le_alt, X : arrow_1857593510le_alt, A5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ (image_1873259469le_alt @ produc1794822519le_alt @ A5)) = (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ A5))))). % pair_in_swap_image
thf(fact_26_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_27_mem__Collect__eq, axiom,
    ((![A : set_Pr367596371le_alt, P2 : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ A @ (collec1399441576le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_28_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P2 : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_29_Collect__mem__eq, axiom,
    ((![A5 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (member1334244458le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_30_Collect__mem__eq, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_31_converse__Id__on, axiom,
    ((![A5 : set_Ar1665529862le_alt]: ((conver1781819635le_alt @ (id_on_426682691le_alt @ A5)) = (id_on_426682691le_alt @ A5))))). % converse_Id_on
thf(fact_32_antisym__converse, axiom,
    ((![R : set_Pr367596371le_alt]: ((antisy1745863240le_alt @ (conver1781819635le_alt @ R)) = (antisy1745863240le_alt @ R))))). % antisym_converse
thf(fact_33_Id__onI, axiom,
    ((![A : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((member1334244458le_alt @ A @ A5) => (member1392960970le_alt @ (produc1931840741le_alt @ A @ A) @ (id_on_1531570678le_alt @ A5)))))). % Id_onI
thf(fact_34_Id__onI, axiom,
    ((![A : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ A @ A5) => (member2146260128le_alt @ (produc41061307le_alt @ A @ A) @ (id_on_714194496le_alt @ A5)))))). % Id_onI
thf(fact_35_Id__onI, axiom,
    ((![A : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt]: ((member519365071le_alt @ A @ A5) => (member2048039092le_alt @ (produc1494124311le_alt @ A @ A) @ (id_on_426682691le_alt @ A5)))))). % Id_onI
thf(fact_36_mem__case__prodE, axiom,
    ((![Z : set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt, P : produc16571293le_alt]: ((member1334244458le_alt @ Z @ (produc1042938349le_alt @ C @ P)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((member1334244458le_alt @ Z @ (C @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_37_mem__case__prodE, axiom,
    ((![Z : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt, P : produc16571293le_alt]: ((member2048039092le_alt @ Z @ (produc860300173le_alt @ C @ P)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((member2048039092le_alt @ Z @ (C @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_38_antisym__def, axiom,
    ((antisy1745863240le_alt = (^[R3 : set_Pr367596371le_alt]: (![X4 : arrow_1857593510le_alt]: (![Y4 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ R3)) => ((((member2048039092le_alt @ (produc1494124311le_alt @ Y4 @ X4) @ R3)) => ((X4 = Y4))))))))))). % antisym_def
thf(fact_39_antisymI, axiom,
    ((![R : set_Pr367596371le_alt]: ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y3 @ X3) @ R) => (X3 = Y3)))) => (antisy1745863240le_alt @ R))))). % antisymI
thf(fact_40_antisymD, axiom,
    ((![R : set_Pr367596371le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((antisy1745863240le_alt @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ R) => (A = B))))))). % antisymD
thf(fact_41_Id__onE, axiom,
    ((![C : produc541234227le_alt, A5 : set_se2071012361le_alt]: ((member1392960970le_alt @ C @ (id_on_1531570678le_alt @ A5)) => (~ ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (~ ((C = (produc1931840741le_alt @ X3 @ X3)))))))))))). % Id_onE
thf(fact_42_Id__onE, axiom,
    ((![C : produc1556433673le_alt, A5 : set_Pr367596371le_alt]: ((member2146260128le_alt @ C @ (id_on_714194496le_alt @ A5)) => (~ ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (~ ((C = (produc41061307le_alt @ X3 @ X3)))))))))))). % Id_onE
thf(fact_43_Id__onE, axiom,
    ((![C : produc16571293le_alt, A5 : set_Ar1665529862le_alt]: ((member2048039092le_alt @ C @ (id_on_426682691le_alt @ A5)) => (~ ((![X3 : arrow_1857593510le_alt]: ((member519365071le_alt @ X3 @ A5) => (~ ((C = (produc1494124311le_alt @ X3 @ X3)))))))))))). % Id_onE
thf(fact_44_Id__on__eqI, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((A = B) => ((member1334244458le_alt @ A @ A5) => (member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ (id_on_1531570678le_alt @ A5))))))). % Id_on_eqI
thf(fact_45_Id__on__eqI, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((A = B) => ((member2048039092le_alt @ A @ A5) => (member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (id_on_714194496le_alt @ A5))))))). % Id_on_eqI
thf(fact_46_Id__on__eqI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt]: ((A = B) => ((member519365071le_alt @ A @ A5) => (member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (id_on_426682691le_alt @ A5))))))). % Id_on_eqI
thf(fact_47_Id__on__iff, axiom,
    ((![X : set_Pr367596371le_alt, Y : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ X @ Y) @ (id_on_1531570678le_alt @ A5)) = (((X = Y)) & ((member1334244458le_alt @ X @ A5))))))). % Id_on_iff
thf(fact_48_Id__on__iff, axiom,
    ((![X : produc16571293le_alt, Y : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ X @ Y) @ (id_on_714194496le_alt @ A5)) = (((X = Y)) & ((member2048039092le_alt @ X @ A5))))))). % Id_on_iff
thf(fact_49_Id__on__iff, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (id_on_426682691le_alt @ A5)) = (((X = Y)) & ((member519365071le_alt @ X @ A5))))))). % Id_on_iff
thf(fact_50_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_51_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_52_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_53_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_54_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_55_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_56_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_57_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_58_UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % UNIV_I
thf(fact_59_UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % UNIV_I
thf(fact_60_converse__UNIV, axiom,
    (((conver1781819635le_alt @ top_to224369155le_alt) = top_to224369155le_alt))). % converse_UNIV
thf(fact_61_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_62_UNIV__eq__I, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A5)) => (top_to224369155le_alt = A5))))). % UNIV_eq_I
thf(fact_63_UNIV__witness, axiom,
    ((?[X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_64_UNIV__witness, axiom,
    ((?[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_65_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_66_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_67_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_68_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_69_iso__tuple__UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % iso_tuple_UNIV_I
thf(fact_70_iso__tuple__UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_71_top__empty__eq, axiom,
    ((top_to1900088076_alt_o = (^[X4 : set_Pr367596371le_alt]: (member1334244458le_alt @ X4 @ top_to469035705le_alt))))). % top_empty_eq
thf(fact_72_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_73_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_74_prod_Ocollapse, axiom,
    ((![Prod : produc16571293le_alt]: ((produc1494124311le_alt @ (produc2071652395le_alt @ Prod) @ (produc1272650601le_alt @ Prod)) = Prod)))). % prod.collapse
thf(fact_75_map__prod__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R2 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R2) => (member2048039092le_alt @ (produc1494124311le_alt @ (F @ A) @ (G @ B)) @ (image_1873259469le_alt @ (produc1074667658le_alt @ F @ G) @ R2)))))). % map_prod_imageI
thf(fact_76_surjective__pairing, axiom,
    ((![T : produc16571293le_alt]: (T = (produc1494124311le_alt @ (produc2071652395le_alt @ T) @ (produc1272650601le_alt @ T)))))). % surjective_pairing
thf(fact_77_prod_Oexhaust__sel, axiom,
    ((![Prod : produc16571293le_alt]: (Prod = (produc1494124311le_alt @ (produc2071652395le_alt @ Prod) @ (produc1272650601le_alt @ Prod)))))). % prod.exhaust_sel
thf(fact_78_fst__eqD, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, A : arrow_1857593510le_alt]: (((produc2071652395le_alt @ (produc1494124311le_alt @ X @ Y)) = A) => (X = A))))). % fst_eqD
thf(fact_79_fst__conv, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt]: ((produc2071652395le_alt @ (produc1494124311le_alt @ X1 @ X2)) = X1)))). % fst_conv
thf(fact_80_snd__eqD, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, A : arrow_1857593510le_alt]: (((produc1272650601le_alt @ (produc1494124311le_alt @ X @ Y)) = A) => (Y = A))))). % snd_eqD
thf(fact_81_snd__conv, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt]: ((produc1272650601le_alt @ (produc1494124311le_alt @ X1 @ X2)) = X2)))). % snd_conv
thf(fact_82_prod_Oswap__def, axiom,
    ((produc1794822519le_alt = (^[P3 : produc16571293le_alt]: (produc1494124311le_alt @ (produc1272650601le_alt @ P3) @ (produc2071652395le_alt @ P3)))))). % prod.swap_def
thf(fact_83_Product__Type_OCollect__case__prodD, axiom,
    ((![X : produc16571293le_alt, A5 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((member2048039092le_alt @ X @ (collec531981554le_alt @ (produc624247124_alt_o @ A5))) => (A5 @ (produc2071652395le_alt @ X) @ (produc1272650601le_alt @ X)))))). % Product_Type.Collect_case_prodD
thf(fact_84_prod__fun__imageE, axiom,
    ((![C : produc16571293le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt, R2 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (image_1873259469le_alt @ (produc1074667658le_alt @ F @ G) @ R2)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((C = (produc1494124311le_alt @ (F @ X3) @ (G @ Y3))) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R2))))))))))). % prod_fun_imageE
thf(fact_85_BNF__Greatest__Fixpoint_Osubst__Pair, axiom,
    ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, A : produc16571293le_alt]: ((P2 @ X @ Y) => ((A = (produc1494124311le_alt @ X @ Y)) => (P2 @ (produc2071652395le_alt @ A) @ (produc1272650601le_alt @ A))))))). % BNF_Greatest_Fixpoint.subst_Pair
thf(fact_86_conjI__realizer, axiom,
    ((![P2 : arrow_1857593510le_alt > $o, P : arrow_1857593510le_alt, Q : arrow_1857593510le_alt > $o, Q2 : arrow_1857593510le_alt]: ((P2 @ P) => ((Q @ Q2) => ((P2 @ (produc2071652395le_alt @ (produc1494124311le_alt @ P @ Q2))) & (Q @ (produc1272650601le_alt @ (produc1494124311le_alt @ P @ Q2))))))))). % conjI_realizer
thf(fact_87_exI__realizer, axiom,
    ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, Y : arrow_1857593510le_alt, X : arrow_1857593510le_alt]: ((P2 @ Y @ X) => (P2 @ (produc1272650601le_alt @ (produc1494124311le_alt @ X @ Y)) @ (produc2071652395le_alt @ (produc1494124311le_alt @ X @ Y))))))). % exI_realizer
thf(fact_88_apfst__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1245692284le_alt @ F @ (produc1494124311le_alt @ X @ Y)) = (produc1494124311le_alt @ (F @ X) @ Y))))). % apfst_conv
thf(fact_89_sndI, axiom,
    ((![X : produc16571293le_alt, Y : arrow_1857593510le_alt, Z : arrow_1857593510le_alt]: ((X = (produc1494124311le_alt @ Y @ Z)) => ((produc1272650601le_alt @ X) = Z))))). % sndI
thf(fact_90_eq__snd__iff, axiom,
    ((![B : arrow_1857593510le_alt, P : produc16571293le_alt]: ((B = (produc1272650601le_alt @ P)) = (?[A4 : arrow_1857593510le_alt]: (P = (produc1494124311le_alt @ A4 @ B))))))). % eq_snd_iff
thf(fact_91_eq__fst__iff, axiom,
    ((![A : arrow_1857593510le_alt, P : produc16571293le_alt]: ((A = (produc2071652395le_alt @ P)) = (?[B4 : arrow_1857593510le_alt]: (P = (produc1494124311le_alt @ A @ B4))))))). % eq_fst_iff
thf(fact_92_fstI, axiom,
    ((![X : produc16571293le_alt, Y : arrow_1857593510le_alt, Z : arrow_1857593510le_alt]: ((X = (produc1494124311le_alt @ Y @ Z)) => ((produc2071652395le_alt @ X) = Y))))). % fstI
thf(fact_93_subsetI, axiom,
    ((![A5 : set_se2071012361le_alt, B5 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ X3 @ B5))) => (ord_le1836905577le_alt @ A5 @ B5))))). % subsetI
thf(fact_94_subsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ X3 @ B5))) => (ord_le1885758387le_alt @ A5 @ B5))))). % subsetI
thf(fact_95_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_96_image__subsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F @ X3) @ B5))) => (ord_le1836905577le_alt @ (image_71834871le_alt @ F @ A5) @ B5))))). % image_subsetI
thf(fact_97_image__subsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F @ X3) @ B5))) => (ord_le1885758387le_alt @ (image_2105633431le_alt @ F @ A5) @ B5))))). % image_subsetI
thf(fact_98_image__subsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F @ X3) @ B5))) => (ord_le1836905577le_alt @ (image_715032109le_alt @ F @ A5) @ B5))))). % image_subsetI
thf(fact_99_image__subsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F : produc16571293le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F @ X3) @ B5))) => (ord_le1885758387le_alt @ (image_1873259469le_alt @ F @ A5) @ B5))))). % image_subsetI
thf(fact_100_in__mono, axiom,
    ((![A5 : set_se2071012361le_alt, B5 : set_se2071012361le_alt, X : set_Pr367596371le_alt]: ((ord_le1836905577le_alt @ A5 @ B5) => ((member1334244458le_alt @ X @ A5) => (member1334244458le_alt @ X @ B5)))))). % in_mono
thf(fact_101_in__mono, axiom,
    ((![A5 : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt, X : produc16571293le_alt]: ((ord_le1885758387le_alt @ A5 @ B5) => ((member2048039092le_alt @ X @ A5) => (member2048039092le_alt @ X @ B5)))))). % in_mono

% Conjectures (4)
thf(conj_0, hypothesis,
    ((member1334244458le_alt @ l @ arrow_1848678355le_Lin))).
thf(conj_1, hypothesis,
    ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ l))).
thf(conj_2, hypothesis,
    ((member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ l))).
thf(conj_3, conjecture,
    ($false)).
