% 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_230__5188318_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:16:49.540

% Could-be-implicit typings (9)
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_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_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_Ar809243995le_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__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    produc851024659e_indi : $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__Oindi_J, type,
    set_Ar1007576579e_indi : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    arrow_1429744205e_indi : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    arrow_1857593510le_alt : $tType).

% Explicit typings (59)
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OIIA, type,
    arrow_1821794627le_IIA : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OLin, type,
    arrow_1848678355le_Lin : set_se2071012361le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OProf, type,
    arrow_1951607831e_Prof : set_Ar809243995le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Oabove, type,
    arrow_1726226719_above : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Obelow, type,
    arrow_887341619_below : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Odictator, type,
    arrow_960434986ctator : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Omkbot, type,
    arrow_843587755_mkbot : set_Pr367596371le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Omktop, type,
    arrow_992294841_mktop : set_Pr367596371le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Ounanimity, type,
    arrow_52334694nimity : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_Fun_Ocomp_001_062_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_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001_062_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__Oindi_J, type,
    comp_s735159582e_indi : ((set_Pr367596371le_alt > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt) > ((set_Pr367596371le_alt > arrow_1429744205e_indi) > set_Pr367596371le_alt > set_Pr367596371le_alt) > (set_Pr367596371le_alt > arrow_1429744205e_indi) > arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_c_Fun_Ocomp_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    comp_A721289968e_indi : (arrow_1429744205e_indi > arrow_1429744205e_indi) > (arrow_1429744205e_indi > arrow_1429744205e_indi) > arrow_1429744205e_indi > arrow_1429744205e_indi).
thf(sy_c_Fun_Ocomp_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_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__Oindi, type,
    comp_A1383563978e_indi : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > arrow_1429744205e_indi) > arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_c_Fun_Ocomp_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_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,
    comp_A396692848le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (set_Pr367596371le_alt > arrow_1429744205e_indi) > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Fun_Ocomp_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_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_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    comp_P2102120662e_indi : (produc541234227le_alt > produc541234227le_alt) > (produc851024659e_indi > produc541234227le_alt) > produc851024659e_indi > produc541234227le_alt).
thf(sy_c_Fun_Ocomp_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__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    comp_s1104322294e_indi : (set_Pr367596371le_alt > arrow_1429744205e_indi) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > arrow_1429744205e_indi).
thf(sy_c_Fun_Ocomp_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__Oindi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    comp_s1389889948le_alt : (set_Pr367596371le_alt > arrow_1429744205e_indi) > (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_Pr367596371le_alt > arrow_1429744205e_indi).
thf(sy_c_Fun_Ocomp_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_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    comp_s941199056e_indi : (set_Pr367596371le_alt > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_c_Fun_Ocomp_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_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    comp_s966035830le_alt : (set_Pr367596371le_alt > set_Pr367596371le_alt) > (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Fun_Omap__fun_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_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__Oindi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    map_fu1111161362le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > (set_Pr367596371le_alt > arrow_1429744205e_indi) > arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_c_Fun_Omap__fun_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_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_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    map_fu1049258476le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (set_Pr367596371le_alt > set_Pr367596371le_alt) > (set_Pr367596371le_alt > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_c_Fun_Omap__fun_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_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    map_fu51105932le_alt : (set_Pr367596371le_alt > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > (set_Pr367596371le_alt > arrow_1429744205e_indi) > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    top_to1799531699e_indi : set_Ar1007576579e_indi).
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_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_Omap__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_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__Oindi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc662251826le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc851024659e_indi > produc541234227le_alt).
thf(sy_c_Product__Type_Omap__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_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,
    produc804913030le_alt : (set_Pr367596371le_alt > set_Pr367596371le_alt) > (set_Pr367596371le_alt > set_Pr367596371le_alt) > produc541234227le_alt > produc541234227le_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_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    produc773314629le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar809243995le_alt) > produc16571293le_alt > set_Ar809243995le_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__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_Oasym_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    asym_A231202199le_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_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    collec1559089382le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > $o) > set_Ar809243995le_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__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    image_444707709le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar1007576579e_indi > 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__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_Typedef_Otype__definition_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    type_d271080816e_indi : (arrow_1429744205e_indi > arrow_1429744205e_indi) > (arrow_1429744205e_indi > arrow_1429744205e_indi) > set_Ar1007576579e_indi > $o).
thf(sy_c_Typedef_Otype__definition_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    type_d1784961046le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (set_Pr367596371le_alt > arrow_1429744205e_indi) > set_se2071012361le_alt > $o).
thf(sy_c_Typedef_Otype__definition_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__Oindi, type,
    type_d1560731370e_indi : (set_Pr367596371le_alt > arrow_1429744205e_indi) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar1007576579e_indi > $o).
thf(sy_c_Typedef_Otype__definition_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,
    type_d623995280le_alt : (set_Pr367596371le_alt > set_Pr367596371le_alt) > (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se2071012361le_alt > $o).
thf(sy_c_member_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member684274596le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt > $o).
thf(sy_c_member_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    member1966420836e_indi : arrow_1429744205e_indi > set_Ar1007576579e_indi > $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__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1334244458le_alt : set_Pr367596371le_alt > set_se2071012361le_alt > $o).
thf(sy_v_F, type,
    f : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt).
thf(sy_v_P_H____, type,
    p : arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_v_P____, type,
    p2 : arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_v_a____, type,
    a : arrow_1857593510le_alt).
thf(sy_v_b____, type,
    b : arrow_1857593510le_alt).
thf(sy_v_c____, type,
    c : arrow_1857593510le_alt).

% Relevant facts (126)
thf(fact_0_A_I5_J, axiom,
    ((member684274596le_alt @ p @ arrow_1951607831e_Prof))). % A(5)
thf(fact_1_A_I4_J, axiom,
    ((member684274596le_alt @ p2 @ arrow_1951607831e_Prof))). % A(4)
thf(fact_2_A_I2_J, axiom,
    ((~ ((b = c))))). % A(2)
thf(fact_3_A_I1_J, axiom,
    ((~ ((a = b))))). % A(1)
thf(fact_4_A_I3_J, axiom,
    ((~ ((a = c))))). % A(3)
thf(fact_5_iff, axiom,
    ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (p2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ b @ c) @ (p @ I)))))). % iff
thf(fact_6_assms_I3_J, axiom,
    ((arrow_1821794627le_IIA @ f))). % assms(3)
thf(fact_7_u, axiom,
    ((arrow_52334694nimity @ f))). % u
thf(fact_8_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_9_converse__inject, axiom,
    ((![R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: (((conver1781819635le_alt @ R) = (conver1781819635le_alt @ S)) = (R = S))))). % converse_inject
thf(fact_10_converse__converse, axiom,
    ((![R : set_Pr367596371le_alt]: ((conver1781819635le_alt @ (conver1781819635le_alt @ R)) = R)))). % converse_converse
thf(fact_11_comp__apply, axiom,
    ((comp_s941199056e_indi = (^[F : set_Pr367596371le_alt > set_Pr367596371le_alt]: (^[G : arrow_1429744205e_indi > set_Pr367596371le_alt]: (^[X : arrow_1429744205e_indi]: (F @ (G @ X)))))))). % comp_apply
thf(fact_12_prod_Oinject, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X1 @ X2) = (produc1494124311le_alt @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_13_old_Oprod_Oinject, axiom,
    ((![A : 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_14_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_15_converseE, axiom,
    ((![Yx : produc16571293le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ Yx @ (conver1781819635le_alt @ R)) => (~ ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((Yx = (produc1494124311le_alt @ Y @ X3)) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ R))))))))))). % converseE
thf(fact_16_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_17_converse_Osimps, axiom,
    ((![A1 : arrow_1857593510le_alt, A22 : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A1 @ A22) @ (conver1781819635le_alt @ R)) = (?[A3 : arrow_1857593510le_alt]: (?[B3 : arrow_1857593510le_alt]: (((A1 = B3)) & ((((A22 = A3)) & ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ R))))))))))). % converse.simps
thf(fact_18__C3_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (f @ P2)))))))))). % "3"
thf(fact_19__C2_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((~ ((A = B2))) => ((~ ((B = A2))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P2))))))))))))). % "2"
thf(fact_20__C1_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((~ ((A = B2))) => ((~ ((B = A2))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) => (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P2))))))))))))). % "1"
thf(fact_21_unanimity__def, axiom,
    ((arrow_52334694nimity = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ arrow_1951607831e_Prof)) => ((![A3 : arrow_1857593510le_alt]: (![B3 : arrow_1857593510le_alt]: (((![I3 : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X @ I3)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F2 @ X))))))))))))). % unanimity_def
thf(fact_22_IIA__def, axiom,
    ((arrow_1821794627le_IIA = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ arrow_1951607831e_Prof)) => ((![Y3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ Y3 @ arrow_1951607831e_Prof)) => ((![A3 : arrow_1857593510le_alt]: (![B3 : arrow_1857593510le_alt]: (((![I3 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X @ I3)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (Y3 @ I3))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F2 @ X)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F2 @ Y3))))))))))))))))). % IIA_def
thf(fact_23_old_Oprod_Oinducts, axiom,
    ((![P : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A4 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_24_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc16571293le_alt]: (~ ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (~ ((Y4 = (produc1494124311le_alt @ A4 @ B4)))))))))). % old.prod.exhaust
thf(fact_25_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_26_prod__cases, axiom,
    ((![P : produc16571293le_alt > $o, P3 : produc16571293le_alt]: ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A4 @ B4))) => (P @ P3))))). % prod_cases
thf(fact_27_surj__pair, axiom,
    ((![P3 : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: (P3 = (produc1494124311le_alt @ X3 @ Y)))))). % surj_pair
thf(fact_28_comp__eq__dest__lhs, axiom,
    ((![A : set_Pr367596371le_alt > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, C : arrow_1429744205e_indi > set_Pr367596371le_alt, V : arrow_1429744205e_indi]: (((comp_s941199056e_indi @ A @ B) = C) => ((A @ (B @ V)) = (C @ V)))))). % comp_eq_dest_lhs
thf(fact_29_comp__eq__elim, axiom,
    ((![A : set_Pr367596371le_alt > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, C : set_Pr367596371le_alt > set_Pr367596371le_alt, D : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((comp_s941199056e_indi @ A @ B) = (comp_s941199056e_indi @ C @ D)) => (![V2 : arrow_1429744205e_indi]: ((A @ (B @ V2)) = (C @ (D @ V2)))))))). % comp_eq_elim
thf(fact_30_comp__eq__dest, axiom,
    ((![A : set_Pr367596371le_alt > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, C : set_Pr367596371le_alt > set_Pr367596371le_alt, D : arrow_1429744205e_indi > set_Pr367596371le_alt, V : arrow_1429744205e_indi]: (((comp_s941199056e_indi @ A @ B) = (comp_s941199056e_indi @ C @ D)) => ((A @ (B @ V)) = (C @ (D @ V))))))). % comp_eq_dest
thf(fact_31_comp__assoc, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : arrow_1429744205e_indi > set_Pr367596371le_alt, H : arrow_1429744205e_indi > arrow_1429744205e_indi]: ((comp_A1383563978e_indi @ (comp_s941199056e_indi @ F3 @ G2) @ H) = (comp_s941199056e_indi @ F3 @ (comp_A1383563978e_indi @ G2 @ H)))))). % comp_assoc
thf(fact_32_comp__assoc, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, H : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((comp_s941199056e_indi @ (comp_s966035830le_alt @ F3 @ G2) @ H) = (comp_s941199056e_indi @ F3 @ (comp_s941199056e_indi @ G2 @ H)))))). % comp_assoc
thf(fact_33_comp__def, axiom,
    ((comp_s941199056e_indi = (^[F : set_Pr367596371le_alt > set_Pr367596371le_alt]: (^[G : arrow_1429744205e_indi > set_Pr367596371le_alt]: (^[X : arrow_1429744205e_indi]: (F @ (G @ X)))))))). % comp_def
thf(fact_34_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)) => ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ R) => (P @ B4 @ A4))) => (P @ X1 @ X2)))))). % converse.inducts
thf(fact_35_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_36_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_37_mem__Collect__eq, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, P : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((member684274596le_alt @ A @ (collec1559089382le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_38_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_39_Collect__mem__eq, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X : produc16571293le_alt]: (member2048039092le_alt @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_40_Collect__mem__eq, axiom,
    ((![A5 : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_41_Collect__mem__eq, axiom,
    ((![A5 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_42_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_43_dictator__def, axiom,
    ((arrow_960434986ctator = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (^[I3 : arrow_1429744205e_indi]: (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ arrow_1951607831e_Prof)) => (((F2 @ X) = (X @ I3)))))))))). % dictator_def
thf(fact_44_in__mktop, axiom,
    ((![X4 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ (arrow_992294841_mktop @ L @ Z)) = (((~ ((X4 = Z)))) & ((((((Y4 = Z)) => ((~ ((X4 = Y4)))))) & ((((~ ((Y4 = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ L))))))))))). % in_mktop
thf(fact_45_in__mkbot, axiom,
    ((![X4 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ (arrow_843587755_mkbot @ L @ Z)) = (((~ ((Y4 = Z)))) & ((((((X4 = Z)) => ((~ ((X4 = Y4)))))) & ((((~ ((X4 = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ L))))))))))). % in_mkbot
thf(fact_46_rewriteR__comp__comp2, axiom,
    ((![G2 : arrow_1429744205e_indi > set_Pr367596371le_alt, H : arrow_1429744205e_indi > arrow_1429744205e_indi, R1 : set_Pr367596371le_alt > set_Pr367596371le_alt, R2 : arrow_1429744205e_indi > set_Pr367596371le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, L2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: (((comp_A1383563978e_indi @ G2 @ H) = (comp_s941199056e_indi @ R1 @ R2)) => (((comp_s966035830le_alt @ F3 @ R1) = L2) => ((comp_A1383563978e_indi @ (comp_s941199056e_indi @ F3 @ G2) @ H) = (comp_s941199056e_indi @ L2 @ R2))))))). % rewriteR_comp_comp2
thf(fact_47_rewriteR__comp__comp2, axiom,
    ((![G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, H : arrow_1429744205e_indi > set_Pr367596371le_alt, R1 : arrow_1429744205e_indi > set_Pr367596371le_alt, R2 : arrow_1429744205e_indi > arrow_1429744205e_indi, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, L2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((comp_s941199056e_indi @ G2 @ H) = (comp_A1383563978e_indi @ R1 @ R2)) => (((comp_s941199056e_indi @ F3 @ R1) = L2) => ((comp_s941199056e_indi @ (comp_s966035830le_alt @ F3 @ G2) @ H) = (comp_A1383563978e_indi @ L2 @ R2))))))). % rewriteR_comp_comp2
thf(fact_48_rewriteR__comp__comp2, axiom,
    ((![G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, H : arrow_1429744205e_indi > set_Pr367596371le_alt, R1 : set_Pr367596371le_alt > set_Pr367596371le_alt, R2 : arrow_1429744205e_indi > set_Pr367596371le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, L2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: (((comp_s941199056e_indi @ G2 @ H) = (comp_s941199056e_indi @ R1 @ R2)) => (((comp_s966035830le_alt @ F3 @ R1) = L2) => ((comp_s941199056e_indi @ (comp_s966035830le_alt @ F3 @ G2) @ H) = (comp_s941199056e_indi @ L2 @ R2))))))). % rewriteR_comp_comp2
thf(fact_49_rewriteL__comp__comp2, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, L1 : set_Pr367596371le_alt > set_Pr367596371le_alt, L22 : set_Pr367596371le_alt > set_Pr367596371le_alt, H : arrow_1429744205e_indi > set_Pr367596371le_alt, R : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((comp_s966035830le_alt @ F3 @ G2) = (comp_s966035830le_alt @ L1 @ L22)) => (((comp_s941199056e_indi @ L22 @ H) = R) => ((comp_s941199056e_indi @ F3 @ (comp_s941199056e_indi @ G2 @ H)) = (comp_s941199056e_indi @ L1 @ R))))))). % rewriteL_comp_comp2
thf(fact_50_rewriteL__comp__comp2, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : arrow_1429744205e_indi > set_Pr367596371le_alt, L1 : set_Pr367596371le_alt > set_Pr367596371le_alt, L22 : arrow_1429744205e_indi > set_Pr367596371le_alt, H : arrow_1429744205e_indi > arrow_1429744205e_indi, R : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((comp_s941199056e_indi @ F3 @ G2) = (comp_s941199056e_indi @ L1 @ L22)) => (((comp_A1383563978e_indi @ L22 @ H) = R) => ((comp_s941199056e_indi @ F3 @ (comp_A1383563978e_indi @ G2 @ H)) = (comp_s941199056e_indi @ L1 @ R))))))). % rewriteL_comp_comp2
thf(fact_51_rewriteR__comp__comp, axiom,
    ((![G2 : arrow_1429744205e_indi > set_Pr367596371le_alt, H : arrow_1429744205e_indi > arrow_1429744205e_indi, R : arrow_1429744205e_indi > set_Pr367596371le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: (((comp_A1383563978e_indi @ G2 @ H) = R) => ((comp_A1383563978e_indi @ (comp_s941199056e_indi @ F3 @ G2) @ H) = (comp_s941199056e_indi @ F3 @ R)))))). % rewriteR_comp_comp
thf(fact_52_rewriteR__comp__comp, axiom,
    ((![G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, H : arrow_1429744205e_indi > set_Pr367596371le_alt, R : arrow_1429744205e_indi > set_Pr367596371le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: (((comp_s941199056e_indi @ G2 @ H) = R) => ((comp_s941199056e_indi @ (comp_s966035830le_alt @ F3 @ G2) @ H) = (comp_s941199056e_indi @ F3 @ R)))))). % rewriteR_comp_comp
thf(fact_53_linear__alt, axiom,
    ((?[L3 : set_Pr367596371le_alt]: (member1334244458le_alt @ L3 @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_54_mktop__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X4 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_992294841_mktop @ L @ X4) @ arrow_1848678355le_Lin))))). % mktop_Lin
thf(fact_55_mkbot__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X4 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_843587755_mkbot @ L @ X4) @ arrow_1848678355le_Lin))))). % mkbot_Lin
thf(fact_56_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_57_complete__Lin, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((~ ((A = B))) => (?[X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ arrow_1848678355le_Lin) & (member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ X3))))))). % complete_Lin
thf(fact_58_notin__Lin__iff, axiom,
    ((![L : set_Pr367596371le_alt, X4 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((~ ((X4 = Y4))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ L))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y4 @ X4) @ L))))))). % notin_Lin_iff
thf(fact_59_rewriteL__comp__comp, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, L2 : set_Pr367596371le_alt > set_Pr367596371le_alt, H : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((comp_s966035830le_alt @ F3 @ G2) = L2) => ((comp_s941199056e_indi @ F3 @ (comp_s941199056e_indi @ G2 @ H)) = (comp_s941199056e_indi @ L2 @ H)))))). % rewriteL_comp_comp
thf(fact_60_rewriteL__comp__comp, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : arrow_1429744205e_indi > set_Pr367596371le_alt, L2 : arrow_1429744205e_indi > set_Pr367596371le_alt, H : arrow_1429744205e_indi > arrow_1429744205e_indi]: (((comp_s941199056e_indi @ F3 @ G2) = L2) => ((comp_s941199056e_indi @ F3 @ (comp_A1383563978e_indi @ G2 @ H)) = (comp_A1383563978e_indi @ L2 @ H)))))). % rewriteL_comp_comp
thf(fact_61_in__above, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X4 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ (arrow_1726226719_above @ L @ A @ B)) = (((~ ((X4 = Y4)))) & ((((((X4 = B)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y4) @ L)))) & ((((~ ((X4 = B)))) => ((((((Y4 = B)) => ((((X4 = A)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ A) @ L)))))) & ((((~ ((Y4 = B)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ L))))))))))))))))). % in_above
thf(fact_62_in__below, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X4 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ (arrow_887341619_below @ L @ A @ B)) = (((~ ((X4 = Y4)))) & ((((((Y4 = A)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ B) @ L)))) & ((((~ ((Y4 = A)))) => ((((((X4 = A)) => ((((Y4 = B)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y4) @ L)))))) & ((((~ ((X4 = A)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ L))))))))))))))))). % in_below
thf(fact_63_below__Lin, axiom,
    ((![X4 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X4 = Y4))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_887341619_below @ L @ X4 @ Y4) @ arrow_1848678355le_Lin)))))). % below_Lin
thf(fact_64_above__Lin, axiom,
    ((![X4 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X4 = Y4))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L @ X4 @ Y4) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_65_comp__cong, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : arrow_1429744205e_indi > set_Pr367596371le_alt, X4 : arrow_1429744205e_indi, F4 : set_Pr367596371le_alt > set_Pr367596371le_alt, G3 : arrow_1429744205e_indi > set_Pr367596371le_alt, X5 : arrow_1429744205e_indi]: (((F3 @ (G2 @ X4)) = (F4 @ (G3 @ X5))) => ((comp_s941199056e_indi @ F3 @ G2 @ X4) = (comp_s941199056e_indi @ F4 @ G3 @ X5)))))). % comp_cong
thf(fact_66_type__copy__map__cong0, axiom,
    ((![M : arrow_1429744205e_indi > set_Pr367596371le_alt, G2 : arrow_1429744205e_indi > arrow_1429744205e_indi, X4 : arrow_1429744205e_indi, N : set_Pr367596371le_alt > set_Pr367596371le_alt, H : arrow_1429744205e_indi > set_Pr367596371le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: (((M @ (G2 @ X4)) = (N @ (H @ X4))) => ((comp_A1383563978e_indi @ (comp_s941199056e_indi @ F3 @ M) @ G2 @ X4) = (comp_s941199056e_indi @ (comp_s966035830le_alt @ F3 @ N) @ H @ X4)))))). % type_copy_map_cong0
thf(fact_67_type__copy__map__cong0, axiom,
    ((![M : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : arrow_1429744205e_indi > set_Pr367596371le_alt, X4 : arrow_1429744205e_indi, N : arrow_1429744205e_indi > set_Pr367596371le_alt, H : arrow_1429744205e_indi > arrow_1429744205e_indi, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: (((M @ (G2 @ X4)) = (N @ (H @ X4))) => ((comp_s941199056e_indi @ (comp_s966035830le_alt @ F3 @ M) @ G2 @ X4) = (comp_A1383563978e_indi @ (comp_s941199056e_indi @ F3 @ N) @ H @ X4)))))). % type_copy_map_cong0
thf(fact_68_function__factors__right, axiom,
    ((![G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((![X : arrow_1429744205e_indi]: (?[Y3 : set_Pr367596371le_alt]: ((G2 @ Y3) = (F3 @ X)))) = (?[H2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (F3 = (comp_s941199056e_indi @ G2 @ H2))))))). % function_factors_right
thf(fact_69_function__factors__left, axiom,
    ((![G2 : arrow_1429744205e_indi > set_Pr367596371le_alt, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((![X : arrow_1429744205e_indi]: (![Y3 : arrow_1429744205e_indi]: ((((G2 @ X) = (G2 @ Y3))) => (((F3 @ X) = (F3 @ Y3)))))) = (?[H2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: (F3 = (comp_s941199056e_indi @ H2 @ G2))))))). % function_factors_left
thf(fact_70_fun_Omap__comp, axiom,
    ((![G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, V : arrow_1429744205e_indi > arrow_1429744205e_indi]: ((comp_s941199056e_indi @ G2 @ (comp_A1383563978e_indi @ F3 @ V)) = (comp_A1383563978e_indi @ (comp_s941199056e_indi @ G2 @ F3) @ V))))). % fun.map_comp
thf(fact_71_fun_Omap__comp, axiom,
    ((![G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, V : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((comp_s941199056e_indi @ G2 @ (comp_s941199056e_indi @ F3 @ V)) = (comp_s941199056e_indi @ (comp_s966035830le_alt @ G2 @ F3) @ V))))). % fun.map_comp
thf(fact_72_comp__apply__eq, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : arrow_1429744205e_indi > set_Pr367596371le_alt, X4 : arrow_1429744205e_indi, H : set_Pr367596371le_alt > set_Pr367596371le_alt, K : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((F3 @ (G2 @ X4)) = (H @ (K @ X4))) => ((comp_s941199056e_indi @ F3 @ G2 @ X4) = (comp_s941199056e_indi @ H @ K @ X4)))))). % comp_apply_eq
thf(fact_73_ssubst__Pair__rhs, axiom,
    ((![R : arrow_1857593510le_alt, S : arrow_1857593510le_alt, R3 : set_Pr367596371le_alt, S2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ R @ S) @ R3) => ((S2 = S) => (member2048039092le_alt @ (produc1494124311le_alt @ R @ S2) @ R3)))))). % ssubst_Pair_rhs
thf(fact_74_curryI, axiom,
    ((![F3 : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F3 @ (produc1494124311le_alt @ A @ B)) => (produc392997491_alt_o @ F3 @ A @ B))))). % curryI
thf(fact_75_curryE, axiom,
    ((![F3 : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F3 @ A @ B) => (F3 @ (produc1494124311le_alt @ A @ B)))))). % curryE
thf(fact_76_curryD, axiom,
    ((![F3 : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F3 @ A @ B) => (F3 @ (produc1494124311le_alt @ A @ B)))))). % curryD
thf(fact_77_converse__inv__image, axiom,
    ((![R3 : set_Pr367596371le_alt, F3 : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((conver1781819635le_alt @ (inv_im155136540le_alt @ R3 @ F3)) = (inv_im155136540le_alt @ (conver1781819635le_alt @ R3) @ F3))))). % converse_inv_image
thf(fact_78_in__inv__image, axiom,
    ((![X4 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, R : set_Pr367596371le_alt, F3 : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ (inv_im155136540le_alt @ R @ F3)) = (member2048039092le_alt @ (produc1494124311le_alt @ (F3 @ X4) @ (F3 @ Y4)) @ R))))). % in_inv_image
thf(fact_79_swap__simp, axiom,
    ((![X4 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt]: ((produc1794822519le_alt @ (produc1494124311le_alt @ X4 @ Y4)) = (produc1494124311le_alt @ Y4 @ X4))))). % swap_simp
thf(fact_80_map__fun_Ocomp, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, H : set_Pr367596371le_alt > set_Pr367596371le_alt, I4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((comp_s735159582e_indi @ (map_fu1049258476le_alt @ F3 @ G2) @ (map_fu51105932le_alt @ H @ I4)) = (map_fu1111161362le_alt @ (comp_s941199056e_indi @ H @ F3) @ (comp_s941199056e_indi @ G2 @ I4)))))). % map_fun.comp
thf(fact_81_pair__in__swap__image, axiom,
    ((![Y4 : arrow_1857593510le_alt, X4 : arrow_1857593510le_alt, A5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ Y4 @ X4) @ (image_1873259469le_alt @ produc1794822519le_alt @ A5)) = (member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ A5))))). % pair_in_swap_image
thf(fact_82_map__fun_Ocompositionality, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, H : set_Pr367596371le_alt > set_Pr367596371le_alt, I4 : arrow_1429744205e_indi > set_Pr367596371le_alt, Fun : set_Pr367596371le_alt > arrow_1429744205e_indi]: ((map_fu1049258476le_alt @ F3 @ G2 @ (map_fu51105932le_alt @ H @ I4 @ Fun)) = (map_fu1111161362le_alt @ (comp_s941199056e_indi @ H @ F3) @ (comp_s941199056e_indi @ G2 @ I4) @ Fun))))). % map_fun.compositionality
thf(fact_83_image__eq__imp__comp, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, G2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar1007576579e_indi, H : set_Pr367596371le_alt > set_Pr367596371le_alt]: (((image_444707709le_alt @ F3 @ A5) = (image_444707709le_alt @ G2 @ B5)) => ((image_444707709le_alt @ (comp_s941199056e_indi @ H @ F3) @ A5) = (image_444707709le_alt @ (comp_s941199056e_indi @ H @ G2) @ B5)))))). % image_eq_imp_comp
thf(fact_84_image__comp, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : arrow_1429744205e_indi > set_Pr367596371le_alt, R : set_Ar1007576579e_indi]: ((image_71834871le_alt @ F3 @ (image_444707709le_alt @ G2 @ R)) = (image_444707709le_alt @ (comp_s941199056e_indi @ F3 @ G2) @ R))))). % image_comp
thf(fact_85_mem__case__prodE, axiom,
    ((![Z : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt, P3 : produc16571293le_alt]: ((member2048039092le_alt @ Z @ (produc860300173le_alt @ C @ P3)) => (~ ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ X3 @ Y)) => (~ ((member2048039092le_alt @ Z @ (C @ X3 @ Y)))))))))))). % mem_case_prodE
thf(fact_86_mem__case__prodE, axiom,
    ((![Z : arrow_1429744205e_indi > set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar809243995le_alt, P3 : produc16571293le_alt]: ((member684274596le_alt @ Z @ (produc773314629le_alt @ C @ P3)) => (~ ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ X3 @ Y)) => (~ ((member684274596le_alt @ Z @ (C @ X3 @ Y)))))))))))). % mem_case_prodE
thf(fact_87_mem__case__prodE, axiom,
    ((![Z : set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt, P3 : produc16571293le_alt]: ((member1334244458le_alt @ Z @ (produc1042938349le_alt @ C @ P3)) => (~ ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ X3 @ Y)) => (~ ((member1334244458le_alt @ Z @ (C @ X3 @ Y)))))))))))). % mem_case_prodE
thf(fact_88_asym_Oinducts, axiom,
    ((![X4 : set_Pr367596371le_alt, P : set_Pr367596371le_alt > $o]: ((asym_A231202199le_alt @ X4) => ((![R4 : set_Pr367596371le_alt]: ((![A6 : arrow_1857593510le_alt, B6 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A6 @ B6) @ R4) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B6 @ A6) @ R4))))) => (P @ R4))) => (P @ X4)))))). % asym.inducts
thf(fact_89_asym_Ointros, axiom,
    ((![R3 : set_Pr367596371le_alt]: ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ R3) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B4 @ A4) @ R3))))) => (asym_A231202199le_alt @ R3))))). % asym.intros
thf(fact_90_asym_Osimps, axiom,
    ((asym_A231202199le_alt = (^[A3 : set_Pr367596371le_alt]: (?[R5 : set_Pr367596371le_alt]: (((A3 = R5)) & ((![X : arrow_1857593510le_alt]: (![Y3 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y3) @ R5)) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ Y3 @ X) @ R5)))))))))))))). % asym.simps
thf(fact_91_asym_Ocases, axiom,
    ((![A : set_Pr367596371le_alt]: ((asym_A231202199le_alt @ A) => (![A6 : arrow_1857593510le_alt, B6 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A6 @ B6) @ A) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B6 @ A6) @ A))))))))). % asym.cases
thf(fact_92_asym__iff, axiom,
    ((asym_A231202199le_alt = (^[R5 : set_Pr367596371le_alt]: (![X : arrow_1857593510le_alt]: (![Y3 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y3) @ R5)) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ Y3 @ X) @ R5))))))))))). % asym_iff
thf(fact_93_asymD, axiom,
    ((![R3 : set_Pr367596371le_alt, X4 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt]: ((asym_A231202199le_alt @ R3) => ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ R3) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ Y4 @ X4) @ R3)))))))). % asymD
thf(fact_94_Sup_OSUP__image, axiom,
    ((![Sup : set_se2071012361le_alt > set_Pr367596371le_alt, G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi]: ((Sup @ (image_71834871le_alt @ G2 @ (image_444707709le_alt @ F3 @ A5))) = (Sup @ (image_444707709le_alt @ (comp_s941199056e_indi @ G2 @ F3) @ A5)))))). % Sup.SUP_image
thf(fact_95_Inf_OINF__image, axiom,
    ((![Inf : set_se2071012361le_alt > set_Pr367596371le_alt, G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi]: ((Inf @ (image_71834871le_alt @ G2 @ (image_444707709le_alt @ F3 @ A5))) = (Inf @ (image_444707709le_alt @ (comp_s941199056e_indi @ G2 @ F3) @ A5)))))). % Inf.INF_image
thf(fact_96_converse__UNIV, axiom,
    (((conver1781819635le_alt @ top_to224369155le_alt) = top_to224369155le_alt))). % converse_UNIV
thf(fact_97_fun_Oset__map, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, V : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((image_444707709le_alt @ (comp_s941199056e_indi @ F3 @ V) @ top_to1799531699e_indi) = (image_71834871le_alt @ F3 @ (image_444707709le_alt @ V @ top_to1799531699e_indi)))))). % fun.set_map
thf(fact_98_fun_Omap__cong, axiom,
    ((![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt, Ya : arrow_1429744205e_indi > set_Pr367596371le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((X4 = Ya) => ((![Z2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ Z2 @ (image_444707709le_alt @ Ya @ top_to1799531699e_indi)) => ((F3 @ Z2) = (G2 @ Z2)))) => ((comp_s941199056e_indi @ F3 @ X4) = (comp_s941199056e_indi @ G2 @ Ya))))))). % fun.map_cong
thf(fact_99_fun_Omap__cong0, axiom,
    ((![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![Z2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ Z2 @ (image_444707709le_alt @ X4 @ top_to1799531699e_indi)) => ((F3 @ Z2) = (G2 @ Z2)))) => ((comp_s941199056e_indi @ F3 @ X4) = (comp_s941199056e_indi @ G2 @ X4)))))). % fun.map_cong0
thf(fact_100_fun_Oinj__map__strong, axiom,
    ((![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt, Xa : arrow_1429744205e_indi > set_Pr367596371le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, Fa : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![Z2 : set_Pr367596371le_alt, Za : set_Pr367596371le_alt]: ((member1334244458le_alt @ Z2 @ (image_444707709le_alt @ X4 @ top_to1799531699e_indi)) => ((member1334244458le_alt @ Za @ (image_444707709le_alt @ Xa @ top_to1799531699e_indi)) => (((F3 @ Z2) = (Fa @ Za)) => (Z2 = Za))))) => (((comp_s941199056e_indi @ F3 @ X4) = (comp_s941199056e_indi @ Fa @ Xa)) => (X4 = Xa)))))). % fun.inj_map_strong
thf(fact_101_comp__surj, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, G2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: (((image_444707709le_alt @ F3 @ top_to1799531699e_indi) = top_to469035705le_alt) => (((image_71834871le_alt @ G2 @ top_to469035705le_alt) = top_to469035705le_alt) => ((image_444707709le_alt @ (comp_s941199056e_indi @ G2 @ F3) @ top_to1799531699e_indi) = top_to469035705le_alt)))))). % comp_surj
thf(fact_102_surj__fun__eq, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, X6 : set_Ar1007576579e_indi, G1 : set_Pr367596371le_alt > set_Pr367596371le_alt, G22 : set_Pr367596371le_alt > set_Pr367596371le_alt]: (((image_444707709le_alt @ F3 @ X6) = top_to469035705le_alt) => ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ X6) => ((comp_s941199056e_indi @ G1 @ F3 @ X3) = (comp_s941199056e_indi @ G22 @ F3 @ X3)))) => (G1 = G22)))))). % surj_fun_eq
thf(fact_103_type__copy__set__map0, axiom,
    ((![Rep : arrow_1429744205e_indi > set_Pr367596371le_alt, Abs : set_Pr367596371le_alt > arrow_1429744205e_indi, S3 : set_Pr367596371le_alt > set_Pr367596371le_alt, M : set_Pr367596371le_alt > set_Pr367596371le_alt, F3 : produc16571293le_alt > produc16571293le_alt, S4 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((type_d1784961046le_alt @ Rep @ Abs @ top_to469035705le_alt) => (((comp_s966035830le_alt @ S3 @ M) = (comp_s966035830le_alt @ (image_1873259469le_alt @ F3) @ S4)) => ((comp_A1383563978e_indi @ (comp_s941199056e_indi @ S3 @ Rep) @ (comp_s1104322294e_indi @ (comp_s1389889948le_alt @ Abs @ M) @ G2)) = (comp_s941199056e_indi @ (image_1873259469le_alt @ F3) @ (comp_s941199056e_indi @ S4 @ G2)))))))). % type_copy_set_map0
thf(fact_104_type__copy__set__map0, axiom,
    ((![Rep : arrow_1429744205e_indi > set_Pr367596371le_alt, Abs : set_Pr367596371le_alt > arrow_1429744205e_indi, S3 : set_Pr367596371le_alt > set_Pr367596371le_alt, M : arrow_1429744205e_indi > set_Pr367596371le_alt, F3 : produc16571293le_alt > produc16571293le_alt, S4 : arrow_1429744205e_indi > set_Pr367596371le_alt, G2 : arrow_1429744205e_indi > arrow_1429744205e_indi]: ((type_d1784961046le_alt @ Rep @ Abs @ top_to469035705le_alt) => (((comp_s941199056e_indi @ S3 @ M) = (comp_s941199056e_indi @ (image_1873259469le_alt @ F3) @ S4)) => ((comp_A1383563978e_indi @ (comp_s941199056e_indi @ S3 @ Rep) @ (comp_A721289968e_indi @ (comp_s1104322294e_indi @ Abs @ M) @ G2)) = (comp_s941199056e_indi @ (image_1873259469le_alt @ F3) @ (comp_A1383563978e_indi @ S4 @ G2)))))))). % type_copy_set_map0
thf(fact_105_type__copy__set__map0, axiom,
    ((![Rep : set_Pr367596371le_alt > set_Pr367596371le_alt, Abs : set_Pr367596371le_alt > set_Pr367596371le_alt, S3 : set_Pr367596371le_alt > set_Pr367596371le_alt, M : arrow_1429744205e_indi > set_Pr367596371le_alt, F3 : produc16571293le_alt > produc16571293le_alt, S4 : arrow_1429744205e_indi > set_Pr367596371le_alt, G2 : arrow_1429744205e_indi > arrow_1429744205e_indi]: ((type_d623995280le_alt @ Rep @ Abs @ top_to469035705le_alt) => (((comp_s941199056e_indi @ S3 @ M) = (comp_s941199056e_indi @ (image_1873259469le_alt @ F3) @ S4)) => ((comp_s941199056e_indi @ (comp_s966035830le_alt @ S3 @ Rep) @ (comp_A1383563978e_indi @ (comp_s941199056e_indi @ Abs @ M) @ G2)) = (comp_s941199056e_indi @ (image_1873259469le_alt @ F3) @ (comp_A1383563978e_indi @ S4 @ G2)))))))). % type_copy_set_map0
thf(fact_106_map__prod__simp, axiom,
    ((![F3 : arrow_1857593510le_alt > arrow_1857593510le_alt, G2 : arrow_1857593510le_alt > arrow_1857593510le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc1074667658le_alt @ F3 @ G2 @ (produc1494124311le_alt @ A @ B)) = (produc1494124311le_alt @ (F3 @ A) @ (G2 @ B)))))). % map_prod_simp
thf(fact_107_map__prod__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R3 : set_Pr367596371le_alt, F3 : arrow_1857593510le_alt > arrow_1857593510le_alt, G2 : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R3) => (member2048039092le_alt @ (produc1494124311le_alt @ (F3 @ A) @ (G2 @ B)) @ (image_1873259469le_alt @ (produc1074667658le_alt @ F3 @ G2) @ R3)))))). % map_prod_imageI
thf(fact_108_fst__eqD, axiom,
    ((![X4 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, A : arrow_1857593510le_alt]: (((produc2071652395le_alt @ (produc1494124311le_alt @ X4 @ Y4)) = A) => (X4 = A))))). % fst_eqD
thf(fact_109_fst__conv, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt]: ((produc2071652395le_alt @ (produc1494124311le_alt @ X1 @ X2)) = X1)))). % fst_conv
thf(fact_110_fstI, axiom,
    ((![X4 : produc16571293le_alt, Y4 : arrow_1857593510le_alt, Z : arrow_1857593510le_alt]: ((X4 = (produc1494124311le_alt @ Y4 @ Z)) => ((produc2071652395le_alt @ X4) = Y4))))). % fstI
thf(fact_111_prod_Omap__comp, axiom,
    ((![G1 : set_Pr367596371le_alt > set_Pr367596371le_alt, G22 : set_Pr367596371le_alt > set_Pr367596371le_alt, F1 : arrow_1429744205e_indi > set_Pr367596371le_alt, F22 : arrow_1429744205e_indi > set_Pr367596371le_alt, V : produc851024659e_indi]: ((produc804913030le_alt @ G1 @ G22 @ (produc662251826le_alt @ F1 @ F22 @ V)) = (produc662251826le_alt @ (comp_s941199056e_indi @ G1 @ F1) @ (comp_s941199056e_indi @ G22 @ F22) @ V))))). % prod.map_comp
thf(fact_112_map__prod_Ocomp, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, H : arrow_1429744205e_indi > set_Pr367596371le_alt, I4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((comp_P2102120662e_indi @ (produc804913030le_alt @ F3 @ G2) @ (produc662251826le_alt @ H @ I4)) = (produc662251826le_alt @ (comp_s941199056e_indi @ F3 @ H) @ (comp_s941199056e_indi @ G2 @ I4)))))). % map_prod.comp
thf(fact_113_map__prod__compose, axiom,
    ((![F1 : set_Pr367596371le_alt > set_Pr367596371le_alt, F22 : arrow_1429744205e_indi > set_Pr367596371le_alt, G1 : set_Pr367596371le_alt > set_Pr367596371le_alt, G22 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((produc662251826le_alt @ (comp_s941199056e_indi @ F1 @ F22) @ (comp_s941199056e_indi @ G1 @ G22)) = (comp_P2102120662e_indi @ (produc804913030le_alt @ F1 @ G1) @ (produc662251826le_alt @ F22 @ G22)))))). % map_prod_compose
thf(fact_114_map__prod_Ocompositionality, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : set_Pr367596371le_alt > set_Pr367596371le_alt, H : arrow_1429744205e_indi > set_Pr367596371le_alt, I4 : arrow_1429744205e_indi > set_Pr367596371le_alt, Prod : produc851024659e_indi]: ((produc804913030le_alt @ F3 @ G2 @ (produc662251826le_alt @ H @ I4 @ Prod)) = (produc662251826le_alt @ (comp_s941199056e_indi @ F3 @ H) @ (comp_s941199056e_indi @ G2 @ I4) @ Prod))))). % map_prod.compositionality
thf(fact_115_type__copy__map__comp0, axiom,
    ((![Rep : set_Pr367596371le_alt > arrow_1429744205e_indi, Abs : arrow_1429744205e_indi > set_Pr367596371le_alt, M : arrow_1429744205e_indi > set_Pr367596371le_alt, M1 : arrow_1429744205e_indi > set_Pr367596371le_alt, M2 : arrow_1429744205e_indi > arrow_1429744205e_indi, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : arrow_1429744205e_indi > arrow_1429744205e_indi]: ((type_d1560731370e_indi @ Rep @ Abs @ top_to1799531699e_indi) => ((M = (comp_A1383563978e_indi @ M1 @ M2)) => ((comp_A1383563978e_indi @ (comp_s941199056e_indi @ F3 @ M) @ G2) = (comp_s941199056e_indi @ (comp_A396692848le_alt @ (comp_s941199056e_indi @ F3 @ M1) @ Rep) @ (comp_A1383563978e_indi @ (comp_A1383563978e_indi @ Abs @ M2) @ G2)))))))). % type_copy_map_comp0
thf(fact_116_type__copy__map__comp0, axiom,
    ((![Rep : set_Pr367596371le_alt > arrow_1429744205e_indi, Abs : arrow_1429744205e_indi > set_Pr367596371le_alt, M : set_Pr367596371le_alt > set_Pr367596371le_alt, M1 : arrow_1429744205e_indi > set_Pr367596371le_alt, M2 : set_Pr367596371le_alt > arrow_1429744205e_indi, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((type_d1560731370e_indi @ Rep @ Abs @ top_to1799531699e_indi) => ((M = (comp_A396692848le_alt @ M1 @ M2)) => ((comp_s941199056e_indi @ (comp_s966035830le_alt @ F3 @ M) @ G2) = (comp_s941199056e_indi @ (comp_A396692848le_alt @ (comp_s941199056e_indi @ F3 @ M1) @ Rep) @ (comp_s941199056e_indi @ (comp_A396692848le_alt @ Abs @ M2) @ G2)))))))). % type_copy_map_comp0
thf(fact_117_type__copy__map__comp0, axiom,
    ((![Rep : set_Pr367596371le_alt > set_Pr367596371le_alt, Abs : set_Pr367596371le_alt > set_Pr367596371le_alt, M : arrow_1429744205e_indi > set_Pr367596371le_alt, M1 : set_Pr367596371le_alt > set_Pr367596371le_alt, M2 : arrow_1429744205e_indi > set_Pr367596371le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, G2 : arrow_1429744205e_indi > arrow_1429744205e_indi]: ((type_d623995280le_alt @ Rep @ Abs @ top_to469035705le_alt) => ((M = (comp_s941199056e_indi @ M1 @ M2)) => ((comp_A1383563978e_indi @ (comp_s941199056e_indi @ F3 @ M) @ G2) = (comp_s941199056e_indi @ (comp_s966035830le_alt @ (comp_s966035830le_alt @ F3 @ M1) @ Rep) @ (comp_A1383563978e_indi @ (comp_s941199056e_indi @ Abs @ M2) @ G2)))))))). % type_copy_map_comp0
thf(fact_118_type__copy__map__comp0__undo, axiom,
    ((![Rep : set_Pr367596371le_alt > set_Pr367596371le_alt, Abs : set_Pr367596371le_alt > set_Pr367596371le_alt, Rep2 : set_Pr367596371le_alt > set_Pr367596371le_alt, Abs2 : set_Pr367596371le_alt > set_Pr367596371le_alt, Rep3 : arrow_1429744205e_indi > arrow_1429744205e_indi, Abs3 : arrow_1429744205e_indi > arrow_1429744205e_indi, M : arrow_1429744205e_indi > set_Pr367596371le_alt, M1 : set_Pr367596371le_alt > set_Pr367596371le_alt, M2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((type_d623995280le_alt @ Rep @ Abs @ top_to469035705le_alt) => ((type_d623995280le_alt @ Rep2 @ Abs2 @ top_to469035705le_alt) => ((type_d271080816e_indi @ Rep3 @ Abs3 @ top_to1799531699e_indi) => (((comp_A1383563978e_indi @ (comp_s941199056e_indi @ Abs2 @ M) @ Rep3) = (comp_s941199056e_indi @ (comp_s966035830le_alt @ (comp_s966035830le_alt @ Abs2 @ M1) @ Rep) @ (comp_A1383563978e_indi @ (comp_s941199056e_indi @ Abs @ M2) @ Rep3))) => ((comp_s941199056e_indi @ M1 @ M2) = M)))))))). % type_copy_map_comp0_undo
thf(fact_119_type__copy__map__comp0__undo, axiom,
    ((![Rep : set_Pr367596371le_alt > arrow_1429744205e_indi, Abs : arrow_1429744205e_indi > set_Pr367596371le_alt, Rep2 : set_Pr367596371le_alt > set_Pr367596371le_alt, Abs2 : set_Pr367596371le_alt > set_Pr367596371le_alt, Rep3 : arrow_1429744205e_indi > arrow_1429744205e_indi, Abs3 : arrow_1429744205e_indi > arrow_1429744205e_indi, M : arrow_1429744205e_indi > set_Pr367596371le_alt, M1 : arrow_1429744205e_indi > set_Pr367596371le_alt, M2 : arrow_1429744205e_indi > arrow_1429744205e_indi]: ((type_d1560731370e_indi @ Rep @ Abs @ top_to1799531699e_indi) => ((type_d623995280le_alt @ Rep2 @ Abs2 @ top_to469035705le_alt) => ((type_d271080816e_indi @ Rep3 @ Abs3 @ top_to1799531699e_indi) => (((comp_A1383563978e_indi @ (comp_s941199056e_indi @ Abs2 @ M) @ Rep3) = (comp_s941199056e_indi @ (comp_A396692848le_alt @ (comp_s941199056e_indi @ Abs2 @ M1) @ Rep) @ (comp_A1383563978e_indi @ (comp_A1383563978e_indi @ Abs @ M2) @ Rep3))) => ((comp_A1383563978e_indi @ M1 @ M2) = M)))))))). % type_copy_map_comp0_undo
thf(fact_120_type__copy__map__comp0__undo, axiom,
    ((![Rep : set_Pr367596371le_alt > arrow_1429744205e_indi, Abs : arrow_1429744205e_indi > set_Pr367596371le_alt, Rep2 : set_Pr367596371le_alt > set_Pr367596371le_alt, Abs2 : set_Pr367596371le_alt > set_Pr367596371le_alt, Rep3 : arrow_1429744205e_indi > set_Pr367596371le_alt, Abs3 : set_Pr367596371le_alt > arrow_1429744205e_indi, M : set_Pr367596371le_alt > set_Pr367596371le_alt, M1 : arrow_1429744205e_indi > set_Pr367596371le_alt, M2 : set_Pr367596371le_alt > arrow_1429744205e_indi]: ((type_d1560731370e_indi @ Rep @ Abs @ top_to1799531699e_indi) => ((type_d623995280le_alt @ Rep2 @ Abs2 @ top_to469035705le_alt) => ((type_d1784961046le_alt @ Rep3 @ Abs3 @ top_to469035705le_alt) => (((comp_s941199056e_indi @ (comp_s966035830le_alt @ Abs2 @ M) @ Rep3) = (comp_s941199056e_indi @ (comp_A396692848le_alt @ (comp_s941199056e_indi @ Abs2 @ M1) @ Rep) @ (comp_s941199056e_indi @ (comp_A396692848le_alt @ Abs @ M2) @ Rep3))) => ((comp_A396692848le_alt @ M1 @ M2) = M)))))))). % type_copy_map_comp0_undo
thf(fact_121_prod__fun__imageE, axiom,
    ((![C : produc16571293le_alt, F3 : arrow_1857593510le_alt > arrow_1857593510le_alt, G2 : arrow_1857593510le_alt > arrow_1857593510le_alt, R3 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (image_1873259469le_alt @ (produc1074667658le_alt @ F3 @ G2) @ R3)) => (~ ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((C = (produc1494124311le_alt @ (F3 @ X3) @ (G2 @ Y))) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ R3))))))))))). % prod_fun_imageE
thf(fact_122_type__copy__wit, axiom,
    ((![Rep : arrow_1429744205e_indi > set_Pr367596371le_alt, Abs : set_Pr367596371le_alt > arrow_1429744205e_indi, X4 : produc16571293le_alt, S3 : set_Pr367596371le_alt > set_Pr367596371le_alt, Y4 : set_Pr367596371le_alt]: ((type_d1784961046le_alt @ Rep @ Abs @ top_to469035705le_alt) => ((member2048039092le_alt @ X4 @ (comp_s941199056e_indi @ S3 @ Rep @ (Abs @ Y4))) => (member2048039092le_alt @ X4 @ (S3 @ Y4))))))). % type_copy_wit
thf(fact_123_eq__fst__iff, axiom,
    ((![A : arrow_1857593510le_alt, P3 : produc16571293le_alt]: ((A = (produc2071652395le_alt @ P3)) = (?[B3 : arrow_1857593510le_alt]: (P3 = (produc1494124311le_alt @ A @ B3))))))). % eq_fst_iff
thf(fact_124_prod_Ocollapse, axiom,
    ((![Prod : produc16571293le_alt]: ((produc1494124311le_alt @ (produc2071652395le_alt @ Prod) @ (produc1272650601le_alt @ Prod)) = Prod)))). % prod.collapse
thf(fact_125_Product__Type_OCollect__case__prodD, axiom,
    ((![X4 : produc16571293le_alt, A5 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((member2048039092le_alt @ X4 @ (collec531981554le_alt @ (produc624247124_alt_o @ A5))) => (A5 @ (produc2071652395le_alt @ X4) @ (produc1272650601le_alt @ X4)))))). % Product_Type.Collect_case_prodD

% Conjectures (1)
thf(conj_0, conjecture,
    ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ (comp_s941199056e_indi @ conver1781819635le_alt @ p2 @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ b @ c) @ (p @ I2)))))).
