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    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_Oinj__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    inj_on207902653le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > set_Ar1665529862le_alt > $o).
thf(sy_c_Fun_Oinj__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    inj_on1502689526e_indi : (arrow_1857593510le_alt > arrow_1429744205e_indi) > set_Ar1665529862le_alt > $o).
thf(sy_c_Fun_Oinj__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    inj_on1409615164le_alt : (arrow_1857593510le_alt > produc16571293le_alt) > set_Ar1665529862le_alt > $o).
thf(sy_c_Fun_Oinj__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    inj_on23696648le_alt : (arrow_1429744205e_indi > arrow_1857593510le_alt) > set_Ar1007576579e_indi > $o).
thf(sy_c_Fun_Oinj__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    inj_on1663454827e_indi : (arrow_1429744205e_indi > arrow_1429744205e_indi) > set_Ar1007576579e_indi > $o).
thf(sy_c_Fun_Oinj__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat, type,
    inj_on528257168di_nat : (arrow_1429744205e_indi > nat) > set_Ar1007576579e_indi > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Nat__Onat_J, type,
    inj_on1530862398lt_nat : (produc1873242156e_indi > produc1720672805lt_nat) > set_Pr1205120524e_indi > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    inj_on1711456116le_alt : (produc1831632630le_alt > produc171651403le_alt) > set_Pr195493846le_alt > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Nat__Onat_J, type,
    inj_on1832254384di_nat : (produc851024659e_indi > produc1399759614di_nat) > set_Pr773120585e_indi > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    inj_on1612178390e_indi : (produc851024659e_indi > produc195853822e_indi) > set_Pr773120585e_indi > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J, type,
    inj_on2118364411at_nat : (produc851024659e_indi > product_prod_nat_nat) > set_Pr773120585e_indi > $o).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    piE_Ar1187035700le_alt : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar1665529862le_alt) > set_Ar1380421567le_alt).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    piE_Ar415527999e_indi : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar1007576579e_indi) > set_Ar528567456e_indi).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    piE_Ar1084018769le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar1665529862le_alt) > set_Ar1666424426le_alt).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    piE_Ar738911586e_indi : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar1007576579e_indi) > set_Ar1612966069e_indi).
thf(sy_c_FuncSet_OPi_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__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,
    pi_Arr1849985851le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt) > set_Ar1108837783le_alt).
thf(sy_c_FuncSet_OPi_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_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_Arr1114944513le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar3481041le_alt).
thf(sy_c_FuncSet_OPi_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_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Arr479247969le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt) > set_Ar182050865le_alt).
thf(sy_c_FuncSet_OPi_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,
    pi_Arr1981691447le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_se2071012361le_alt) > set_Ar809243995le_alt).
thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_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, type,
    pi_Pro1164444725le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Ar809243995le_alt) > set_Pr1911398973le_alt).
thf(sy_c_FuncSet_OPi_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,
    pi_Pro1847889543le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr665675179le_alt).
thf(sy_c_FuncSet_OPi_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,
    pi_Pro1122205927le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_se2071012361le_alt) > set_Pr720748555le_alt).
thf(sy_c_FuncSet_OPi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_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, type,
    pi_set1343364587le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Ar809243995le_alt) > set_se1538189555le_alt).
thf(sy_c_FuncSet_OPi_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,
    pi_set365323601le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se791007093le_alt).
thf(sy_c_FuncSet_OPi_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,
    pi_set1240805297le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_se2071012361le_alt) > set_se370278869le_alt).
thf(sy_c_FuncSet_Oextensional_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_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    extens951643470le_alt : set_Ar809243995le_alt > set_Ar182050865le_alt).
thf(sy_c_FuncSet_Oextensional_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,
    extens1528283402le_alt : set_Ar1007576579e_indi > set_Ar809243995le_alt).
thf(sy_c_Order__Relation_Ostrict__linear__order__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    order_257197092le_alt : set_Ar1665529862le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_062_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_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    bot_bo13098693le_alt : set_Ar182050865le_alt).
thf(sy_c_Orderings_Obot__class_Obot_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,
    bot_bo365569479le_alt : set_Ar809243995le_alt).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    bot_bo1127707250le_alt : set_Ar1665529862le_alt).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    bot_bo1390904983e_indi : set_Ar1007576579e_indi).
thf(sy_c_Orderings_Obot__class_Obot_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,
    bot_bo1518363805le_alt : set_se2071012361le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_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_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_M_Eo_J, type,
    top_to1892800228_alt_o : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_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_M_Eo_J, type,
    top_to1344581618_alt_o : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_Eo_J_J, type,
    top_to701951606_alt_o : arrow_1857593510le_alt > arrow_1857593510le_alt > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_Eo_J, type,
    top_to516240647_alt_o : arrow_1857593510le_alt > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_M_Eo_J, type,
    top_to1473733010indi_o : arrow_1429744205e_indi > $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_I_062_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_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    top_to803745505le_alt : set_Ar182050865le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    top_to290516239le_alt : set_Ar1380421567le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    top_to2048848e_indi : set_Ar528567456e_indi).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    top_to1139905818le_alt : set_Ar1666424426le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    top_to498310661e_indi : set_Ar1612966069e_indi).
thf(sy_c_Orderings_Otop__class_Otop_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,
    top_to685525675le_alt : set_Ar809243995le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    top_to958727510le_alt : set_Ar1665529862le_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__Nat__Onat_J, type,
    top_top_set_nat : set_nat).
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__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    top_to883938140e_indi : set_Pr1205120524e_indi).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    top_to2021795110le_alt : set_Pr195493846le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    top_to491983097e_indi : set_Pr773120585e_indi).
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_001_062_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_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001_062_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_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc1102161897le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc46079031le_alt).
thf(sy_c_Product__Type_OPair_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__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,
    produc1825994351le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc1638831733le_alt).
thf(sy_c_Product__Type_OPair_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_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc233791437le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt > produc1751271773le_alt).
thf(sy_c_Product__Type_OPair_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_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc806763053le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt > produc1766186941le_alt).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
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thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_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, type,
    produc283291649le_alt : produc16571293le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc1556693961le_alt).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc41061307le_alt : produc16571293le_alt > produc16571293le_alt > produc1556433673le_alt).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc268611099le_alt : produc16571293le_alt > set_Pr367596371le_alt > produc1114386793le_alt).
thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_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,
    produc1670879671le_alt : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc552053119le_alt).
thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc1659212421le_alt : set_Pr367596371le_alt > produc16571293le_alt > produc670815699le_alt).
thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc1931840741le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > produc541234227le_alt).
thf(sy_c_Product__Type_OSigma_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__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,
    produc783065342le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt) > set_Pr1877138731le_alt).
thf(sy_c_Product__Type_OSigma_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_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc1711776894le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr319694141le_alt).
thf(sy_c_Product__Type_OSigma_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_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc712719070le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt) > set_Pr696203165le_alt).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc2062971558le_alt : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar1665529862le_alt) > set_Pr367596371le_alt).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc711907405e_indi : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar1007576579e_indi) > set_Pr1205120524e_indi).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1380398175le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar1665529862le_alt) > set_Pr195493846le_alt).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc1762100436e_indi : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar1007576579e_indi) > set_Pr773120585e_indi).
thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_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, type,
    produc1761277106le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Ar809243995le_alt) > set_Pr80128425le_alt).
thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc1360152522le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr448479039le_alt).
thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc1173532202le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_se2071012361le_alt) > set_Pr1043548575le_alt).
thf(sy_c_Product__Type_OSigma_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_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,
    produc1576835688le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Ar809243995le_alt) > set_Pr2052341855le_alt).
thf(sy_c_Product__Type_OSigma_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc416649876le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_Pr1113807113le_alt).
thf(sy_c_Product__Type_OSigma_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc223727860le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_se2071012361le_alt) > set_Pr851393385le_alt).
thf(sy_c_Product__Type_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_Oapfst_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1985979043le_alt : (arrow_1429744205e_indi > nat) > produc1831632630le_alt > produc171651403le_alt).
thf(sy_c_Product__Type_Oapfst_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc961456016e_indi : (arrow_1429744205e_indi > nat) > produc851024659e_indi > produc195853822e_indi).
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_Oapsnd_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc86521573le_alt : (arrow_1429744205e_indi > nat) > produc1873242156e_indi > produc1720672805lt_nat).
thf(sy_c_Product__Type_Oapsnd_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc1894589390e_indi : (arrow_1429744205e_indi > nat) > produc851024659e_indi > produc1399759614di_nat).
thf(sy_c_Product__Type_Ocurry_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001_Eo, type,
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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__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat, type,
    produc1669992998di_nat : (arrow_1429744205e_indi > nat) > (arrow_1429744205e_indi > nat) > produc851024659e_indi > product_prod_nat_nat).
thf(sy_c_Product__Type_Oproduct_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc961482780le_alt : set_Ar1665529862le_alt > set_Ar1665529862le_alt > set_Pr367596371le_alt).
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thf(sy_c_Relation_Oinv__image_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
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thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
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    total_535758719le_alt : set_Ar809243995le_alt > set_Pr1877138731le_alt > $o).
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thf(sy_c_Relation_Ototal__on_001t__Nat__Onat, type,
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thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
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thf(sy_c_Relation_Ototal__on_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
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thf(sy_c_member_001_062_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_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
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thf(sy_c_member_001t__Product____Type__Oprod_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_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
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thf(sy_c_member_001t__Product____Type__Oprod_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_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
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thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
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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_M_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,
    member1263449330le_alt : produc1556693961le_alt > set_Pr80128425le_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,
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thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
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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_M_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,
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thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
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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,
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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_h____, type,
    h : arrow_1429744205e_indi > nat).
thf(sy_v_thesis____, type,
    thesis : $o).

% Relevant facts (249)
thf(fact_0_assms_I3_J, axiom,
    ((arrow_1821794627le_IIA @ f))). % assms(3)
thf(fact_1_u, axiom,
    ((arrow_52334694nimity @ f))). % u
thf(fact_2__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) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P2 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) => (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P2))))))))))))). % "1"
thf(fact_3__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) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P2 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P2))))))))))))). % "2"
thf(fact_4__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) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (P2 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (f @ P2)))))))))). % "3"
thf(fact_5__C4_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, C : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((B = C))) => ((~ ((A = C))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (P2 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (f @ P2)))))))))))). % "4"
thf(fact_6_pairwise__neutrality, 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))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P2 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P2))))))))))). % pairwise_neutrality
thf(fact_7_IIA__def, axiom,
    ((arrow_1821794627le_IIA = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ arrow_1951607831e_Prof)) => ((![Y : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ Y @ arrow_1951607831e_Prof)) => ((![A3 : arrow_1857593510le_alt]: (![B3 : arrow_1857593510le_alt]: (((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (Y @ I2))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F @ X)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F @ Y))))))))))))))))). % IIA_def
thf(fact_8_unanimity__def, axiom,
    ((arrow_52334694nimity = (^[F : (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]: (((![I2 : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F @ X))))))))))))). % unanimity_def
thf(fact_9_assms_I1_J, axiom,
    ((member183760530le_alt @ f @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))))). % assms(1)
thf(fact_10_const__Lin__Prof, axiom,
    ((![L : set_Pr367596371le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member684274596le_alt @ (^[P3 : arrow_1429744205e_indi]: L) @ arrow_1951607831e_Prof))))). % const_Lin_Prof
thf(fact_11_notin__Lin__iff, axiom,
    ((![L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((~ ((X2 = Y2))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ L))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y2 @ X2) @ L))))))). % notin_Lin_iff
thf(fact_12_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_13_linear__alt, axiom,
    ((?[L2 : set_Pr367596371le_alt]: (member1334244458le_alt @ L2 @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_14_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_15_dictatorI, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I3 : arrow_1429744205e_indi]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))) => ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ arrow_1951607831e_Prof) => (![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: ((~ ((A4 = B4))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (X3 @ I3)) => (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F2 @ X3))))))) => (arrow_960434986ctator @ F2 @ I3)))))). % dictatorI
thf(fact_16_Pi__I, axiom,
    ((![A5 : set_Ar1007576579e_indi, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_17_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_18_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_19_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_20_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_21_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_22_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_23_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_24_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_25_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_26_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_27_prod_Oinject, axiom,
    ((![X1 : arrow_1857593510le_alt, X22 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y22 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X1 @ X22) = (produc1494124311le_alt @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_28_in__below, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ (arrow_887341619_below @ L @ A @ B)) = (((~ ((X2 = Y2)))) & ((((((Y2 = A)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ B) @ L)))) & ((((~ ((Y2 = A)))) => ((((((X2 = A)) => ((((Y2 = B)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y2) @ L)))))) & ((((~ ((X2 = A)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ L))))))))))))))))). % in_below
thf(fact_29_in__above, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ (arrow_1726226719_above @ L @ A @ B)) = (((~ ((X2 = Y2)))) & ((((((X2 = B)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y2) @ L)))) & ((((~ ((X2 = B)))) => ((((((Y2 = B)) => ((((X2 = A)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ A) @ L)))))) & ((((~ ((Y2 = B)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ L))))))))))))))))). % in_above
thf(fact_30_dictator__def, axiom,
    ((arrow_960434986ctator = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (^[I2 : arrow_1429744205e_indi]: (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ arrow_1951607831e_Prof)) => (((F @ X) = (X @ I2)))))))))). % dictator_def
thf(fact_31_funcset__mem, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : set_se2071012361le_alt, X2 : arrow_1429744205e_indi]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))) => ((member1966420836e_indi @ X2 @ A5) => (member1334244458le_alt @ (F3 @ X2) @ B5)))))). % funcset_mem
thf(fact_32_funcset__mem, axiom,
    ((![F3 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt, X2 : produc16571293le_alt]: ((member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X2 @ A5) => (member2048039092le_alt @ (F3 @ X2) @ B5)))))). % funcset_mem
thf(fact_33_funcset__mem, axiom,
    ((![F3 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : set_se2071012361le_alt, X2 : produc16571293le_alt]: ((member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X2 @ A5) => (member1334244458le_alt @ (F3 @ X2) @ B5)))))). % funcset_mem
thf(fact_34_funcset__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt, X2 : set_Pr367596371le_alt]: ((member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X2 @ A5) => (member2048039092le_alt @ (F3 @ X2) @ B5)))))). % funcset_mem
thf(fact_35_funcset__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_se2071012361le_alt, X2 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X2 @ A5) => (member1334244458le_alt @ (F3 @ X2) @ B5)))))). % funcset_mem
thf(fact_36_funcset__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : set_Pr367596371le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X2 @ A5) => (member2048039092le_alt @ (F3 @ X2) @ B5)))))). % funcset_mem
thf(fact_37_funcset__mem, axiom,
    ((![F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : set_Ar809243995le_alt, X2 : produc16571293le_alt]: ((member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X2 @ A5) => (member684274596le_alt @ (F3 @ X2) @ B5)))))). % funcset_mem
thf(fact_38_funcset__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Ar809243995le_alt, X2 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X2 @ A5) => (member684274596le_alt @ (F3 @ X2) @ B5)))))). % funcset_mem
thf(fact_39_funcset__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : set_se2071012361le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X2 @ A5) => (member1334244458le_alt @ (F3 @ X2) @ B5)))))). % funcset_mem
thf(fact_40_funcset__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : set_Ar809243995le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X2 @ A5) => (member684274596le_alt @ (F3 @ X2) @ B5)))))). % funcset_mem
thf(fact_41_funcsetI, axiom,
    ((![A5 : set_Ar1007576579e_indi, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ B5))) => (member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))))))). % funcsetI
thf(fact_42_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ B5))) => (member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_43_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ B5))) => (member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_44_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ B5))) => (member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_45_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ B5))) => (member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_46_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ B5))) => (member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_47_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ B5))) => (member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_48_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ B5))) => (member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_49_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ B5))) => (member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_50_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ B5))) => (member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_51_surj__pair, axiom,
    ((![P4 : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P4 = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_52_prod__cases, axiom,
    ((![P : produc16571293le_alt > $o, P4 : produc16571293le_alt]: ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A4 @ B4))) => (P @ P4))))). % prod_cases
thf(fact_53_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_54_old_Oprod_Oexhaust, axiom,
    ((![Y2 : produc16571293le_alt]: (~ ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (~ ((Y2 = (produc1494124311le_alt @ A4 @ B4)))))))))). % old.prod.exhaust
thf(fact_55_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_56_PiE, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt, X2 : arrow_1429744205e_indi]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F3 @ X2) @ (B5 @ X2)))) => (~ ((member1966420836e_indi @ X2 @ A5)))))))). % PiE
thf(fact_57_PiE, axiom,
    ((![F3 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt, X2 : produc16571293le_alt]: ((member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F3 @ X2) @ (B5 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A5)))))))). % PiE
thf(fact_58_PiE, axiom,
    ((![F3 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt, X2 : set_Pr367596371le_alt]: ((member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F3 @ X2) @ (B5 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A5)))))))). % PiE
thf(fact_59_PiE, axiom,
    ((![F3 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt, X2 : produc16571293le_alt]: ((member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F3 @ X2) @ (B5 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A5)))))))). % PiE
thf(fact_60_PiE, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt, X2 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F3 @ X2) @ (B5 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A5)))))))). % PiE
thf(fact_61_PiE, axiom,
    ((![F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt, X2 : produc16571293le_alt]: ((member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F3 @ X2) @ (B5 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A5)))))))). % PiE
thf(fact_62_PiE, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F3 @ X2) @ (B5 @ X2)))) => (~ ((member684274596le_alt @ X2 @ A5)))))))). % PiE
thf(fact_63_PiE, axiom,
    ((![F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt, X2 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F3 @ X2) @ (B5 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A5)))))))). % PiE
thf(fact_64_PiE, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F3 @ X2) @ (B5 @ X2)))) => (~ ((member684274596le_alt @ X2 @ A5)))))))). % PiE
thf(fact_65_PiE, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F3 @ X2) @ (B5 @ X2)))) => (~ ((member684274596le_alt @ X2 @ A5)))))))). % PiE
thf(fact_66_Pi__I_H, axiom,
    ((![A5 : set_Ar1007576579e_indi, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_67_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_68_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_69_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_70_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_71_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_72_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_73_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_74_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_75_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_76_Pi__iff, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, I4 : set_Ar1007576579e_indi, X4 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ I4 @ X4)) = (![X : arrow_1429744205e_indi]: (((member1966420836e_indi @ X @ I4)) => ((member1334244458le_alt @ (F3 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_77_Pi__iff, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I4 : set_Ar809243995le_alt, X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ I4 @ X4)) = (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ I4)) => ((member1334244458le_alt @ (F3 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_78_Pi__mem, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt, X2 : arrow_1429744205e_indi]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)) => ((member1966420836e_indi @ X2 @ A5) => (member1334244458le_alt @ (F3 @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_79_Pi__mem, axiom,
    ((![F3 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt, X2 : produc16571293le_alt]: ((member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X2 @ A5) => (member2048039092le_alt @ (F3 @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_80_Pi__mem, axiom,
    ((![F3 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt, X2 : produc16571293le_alt]: ((member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X2 @ A5) => (member1334244458le_alt @ (F3 @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_81_Pi__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt, X2 : set_Pr367596371le_alt]: ((member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X2 @ A5) => (member2048039092le_alt @ (F3 @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_82_Pi__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt, X2 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X2 @ A5) => (member1334244458le_alt @ (F3 @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_83_Pi__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ B5)) => ((member684274596le_alt @ X2 @ A5) => (member2048039092le_alt @ (F3 @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_84_Pi__mem, axiom,
    ((![F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt, X2 : produc16571293le_alt]: ((member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X2 @ A5) => (member684274596le_alt @ (F3 @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_85_Pi__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt, X2 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X2 @ A5) => (member684274596le_alt @ (F3 @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_86_Pi__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)) => ((member684274596le_alt @ X2 @ A5) => (member1334244458le_alt @ (F3 @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_87_Pi__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ B5)) => ((member684274596le_alt @ X2 @ A5) => (member684274596le_alt @ (F3 @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_88_Pi__cong, axiom,
    ((![A5 : set_Ar1007576579e_indi, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, G : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi]: ((member1966420836e_indi @ W @ A5) => ((F3 @ W) = (G @ W)))) => ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)) = (member684274596le_alt @ G @ (pi_Arr1981691447le_alt @ A5 @ B5))))))). % Pi_cong
thf(fact_89_Pi__cong, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ W @ A5) => ((F3 @ W) = (G @ W)))) => ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)) = (member183760530le_alt @ G @ (pi_Arr479247969le_alt @ A5 @ B5))))))). % Pi_cong
thf(fact_90_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_91_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_92_mem__Collect__eq, axiom,
    ((![A : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, P : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member183760530le_alt @ A @ (collec1382217680le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_93_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_94_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_95_Collect__mem__eq, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X : produc16571293le_alt]: (member2048039092le_alt @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_96_Collect__mem__eq, axiom,
    ((![A5 : set_Ar182050865le_alt]: ((collec1382217680le_alt @ (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_97_Collect__mem__eq, axiom,
    ((![A5 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_98_Collect__cong, axiom,
    ((![P : set_Pr367596371le_alt > $o, Q : set_Pr367596371le_alt > $o]: ((![X3 : set_Pr367596371le_alt]: ((P @ X3) = (Q @ X3))) => ((collec1399441576le_alt @ P) = (collec1399441576le_alt @ Q)))))). % Collect_cong
thf(fact_99_above__Lin, axiom,
    ((![X2 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X2 = Y2))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L @ X2 @ Y2) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_100_below__Lin, axiom,
    ((![X2 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X2 = Y2))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_887341619_below @ L @ X2 @ Y2) @ arrow_1848678355le_Lin)))))). % below_Lin
thf(fact_101_mkbot__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_843587755_mkbot @ L @ X2) @ arrow_1848678355le_Lin))))). % mkbot_Lin
thf(fact_102_mktop__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_992294841_mktop @ L @ X2) @ arrow_1848678355le_Lin))))). % mktop_Lin
thf(fact_103_pred__equals__eq2, axiom,
    ((![R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: (((^[X : arrow_1857593510le_alt]: (^[Y : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R))) = (^[X : arrow_1857593510le_alt]: (^[Y : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_104_in__mkbot, axiom,
    ((![X2 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ (arrow_843587755_mkbot @ L @ Z)) = (((~ ((Y2 = Z)))) & ((((((X2 = Z)) => ((~ ((X2 = Y2)))))) & ((((~ ((X2 = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ L))))))))))). % in_mkbot
thf(fact_105_in__mktop, axiom,
    ((![X2 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ (arrow_992294841_mktop @ L @ Z)) = (((~ ((X2 = Z)))) & ((((((Y2 = Z)) => ((~ ((X2 = Y2)))))) & ((((~ ((Y2 = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ L))))))))))). % in_mktop
thf(fact_106_ssubst__Pair__rhs, axiom,
    ((![R2 : arrow_1857593510le_alt, S2 : arrow_1857593510le_alt, R : set_Pr367596371le_alt, S3 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ R2 @ S2) @ R) => ((S3 = S2) => (member2048039092le_alt @ (produc1494124311le_alt @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_107_Prof__def, axiom,
    ((arrow_1951607831e_Prof = (pi_Arr1981691447le_alt @ top_to1799531699e_indi @ (^[Uu : arrow_1429744205e_indi]: arrow_1848678355le_Lin))))). % Prof_def
thf(fact_108_in__inv__image, axiom,
    ((![X2 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt, R2 : set_Pr367596371le_alt, F3 : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ (inv_im155136540le_alt @ R2 @ F3)) = (member2048039092le_alt @ (produc1494124311le_alt @ (F3 @ X2) @ (F3 @ Y2)) @ R2))))). % in_inv_image
thf(fact_109_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_110_Pi__UNIV, axiom,
    ((![A5 : set_Ar809243995le_alt]: ((pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: top_to469035705le_alt)) = top_to803745505le_alt)))). % Pi_UNIV
thf(fact_111_Pi__UNIV, axiom,
    ((![A5 : set_Ar1007576579e_indi]: ((pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: top_to469035705le_alt)) = top_to685525675le_alt)))). % Pi_UNIV
thf(fact_112_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_113_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_114_UNIV__I, axiom,
    ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X2 @ top_to685525675le_alt)))). % UNIV_I
thf(fact_115_UNIV__I, axiom,
    ((![X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ top_to224369155le_alt)))). % UNIV_I
thf(fact_116_UNIV__I, axiom,
    ((![X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X2 @ top_to803745505le_alt)))). % UNIV_I
thf(fact_117_UNIV__I, axiom,
    ((![X2 : set_Pr367596371le_alt]: (member1334244458le_alt @ X2 @ top_to469035705le_alt)))). % UNIV_I
thf(fact_118_UNIV__I, axiom,
    ((![X2 : arrow_1429744205e_indi]: (member1966420836e_indi @ X2 @ top_to1799531699e_indi)))). % UNIV_I
thf(fact_119_UNIV__I, axiom,
    ((![X2 : arrow_1857593510le_alt]: (member519365071le_alt @ X2 @ top_to958727510le_alt)))). % UNIV_I
thf(fact_120_iso__tuple__UNIV__I, axiom,
    ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X2 @ top_to685525675le_alt)))). % iso_tuple_UNIV_I
thf(fact_121_iso__tuple__UNIV__I, axiom,
    ((![X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_122_iso__tuple__UNIV__I, axiom,
    ((![X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X2 @ top_to803745505le_alt)))). % iso_tuple_UNIV_I
thf(fact_123_iso__tuple__UNIV__I, axiom,
    ((![X2 : set_Pr367596371le_alt]: (member1334244458le_alt @ X2 @ top_to469035705le_alt)))). % iso_tuple_UNIV_I
thf(fact_124_iso__tuple__UNIV__I, axiom,
    ((![X2 : arrow_1429744205e_indi]: (member1966420836e_indi @ X2 @ top_to1799531699e_indi)))). % iso_tuple_UNIV_I
thf(fact_125_iso__tuple__UNIV__I, axiom,
    ((![X2 : arrow_1857593510le_alt]: (member519365071le_alt @ X2 @ top_to958727510le_alt)))). % iso_tuple_UNIV_I
thf(fact_126_injh, axiom,
    ((inj_on528257168di_nat @ h @ top_to1799531699e_indi))). % injh
thf(fact_127_UNIV__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: $true))))). % UNIV_def
thf(fact_128_UNIV__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ (^[X : arrow_1429744205e_indi]: $true))))). % UNIV_def
thf(fact_129_UNIV__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: $true))))). % UNIV_def
thf(fact_130_top__empty__eq2, axiom,
    ((top_to701951606_alt_o = (^[X : arrow_1857593510le_alt]: (^[Y : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ top_to224369155le_alt)))))). % top_empty_eq2
thf(fact_131_top__empty__eq, axiom,
    ((top_to1344581618_alt_o = (^[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt))))). % top_empty_eq
thf(fact_132_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_133_top__empty__eq, axiom,
    ((top_to1892800228_alt_o = (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ top_to803745505le_alt))))). % top_empty_eq
thf(fact_134_top__empty__eq, axiom,
    ((top_to1900088076_alt_o = (^[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt))))). % top_empty_eq
thf(fact_135_top__empty__eq, axiom,
    ((top_to1473733010indi_o = (^[X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi))))). % top_empty_eq
thf(fact_136_top__empty__eq, axiom,
    ((top_to516240647_alt_o = (^[X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt))))). % top_empty_eq
thf(fact_137_top__set__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ top_to1900088076_alt_o)))). % top_set_def
thf(fact_138_top__set__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ top_to1473733010indi_o)))). % top_set_def
thf(fact_139_top__set__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ top_to516240647_alt_o)))). % top_set_def
thf(fact_140_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ top_to685525675le_alt)))). % UNIV_witness
thf(fact_141_UNIV__witness, axiom,
    ((?[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_142_UNIV__witness, axiom,
    ((?[X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X3 @ top_to803745505le_alt)))). % UNIV_witness
thf(fact_143_UNIV__witness, axiom,
    ((?[X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_144_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ top_to1799531699e_indi)))). % UNIV_witness
thf(fact_145_UNIV__witness, axiom,
    ((?[X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ top_to958727510le_alt)))). % UNIV_witness
thf(fact_146_UNIV__eq__I, axiom,
    ((![A5 : set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ A5)) => (top_to685525675le_alt = A5))))). % UNIV_eq_I
thf(fact_147_UNIV__eq__I, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A5)) => (top_to224369155le_alt = A5))))). % UNIV_eq_I
thf(fact_148_UNIV__eq__I, axiom,
    ((![A5 : set_Ar182050865le_alt]: ((![X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X3 @ A5)) => (top_to803745505le_alt = A5))))). % UNIV_eq_I
thf(fact_149_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_150_UNIV__eq__I, axiom,
    ((![A5 : set_Ar1007576579e_indi]: ((![X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ A5)) => (top_to1799531699e_indi = A5))))). % UNIV_eq_I
thf(fact_151_UNIV__eq__I, axiom,
    ((![A5 : set_Ar1665529862le_alt]: ((![X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ A5)) => (top_to958727510le_alt = A5))))). % UNIV_eq_I
thf(fact_152_injD, axiom,
    ((![F3 : arrow_1429744205e_indi > nat, X2 : arrow_1429744205e_indi, Y2 : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F3 @ top_to1799531699e_indi) => (((F3 @ X2) = (F3 @ Y2)) => (X2 = Y2)))))). % injD
thf(fact_153_injI, axiom,
    ((![F3 : arrow_1429744205e_indi > nat]: ((![X3 : arrow_1429744205e_indi, Y3 : arrow_1429744205e_indi]: (((F3 @ X3) = (F3 @ Y3)) => (X3 = Y3))) => (inj_on528257168di_nat @ F3 @ top_to1799531699e_indi))))). % injI
thf(fact_154_inj__eq, axiom,
    ((![F3 : arrow_1429744205e_indi > nat, X2 : arrow_1429744205e_indi, Y2 : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F3 @ top_to1799531699e_indi) => (((F3 @ X2) = (F3 @ Y2)) = (X2 = Y2)))))). % inj_eq
thf(fact_155_inj__def, axiom,
    ((![F3 : arrow_1429744205e_indi > nat]: ((inj_on528257168di_nat @ F3 @ top_to1799531699e_indi) = (![X : arrow_1429744205e_indi]: (![Y : arrow_1429744205e_indi]: ((((F3 @ X) = (F3 @ Y))) => ((X = Y))))))))). % inj_def
thf(fact_156_Lin__def, axiom,
    ((arrow_1848678355le_Lin = (collec1399441576le_alt @ (order_257197092le_alt @ top_to958727510le_alt))))). % Lin_def
thf(fact_157_apfst__conv, axiom,
    ((![F3 : arrow_1857593510le_alt > arrow_1857593510le_alt, X2 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: ((produc1245692284le_alt @ F3 @ (produc1494124311le_alt @ X2 @ Y2)) = (produc1494124311le_alt @ (F3 @ X2) @ Y2))))). % apfst_conv
thf(fact_158_apsnd__conv, axiom,
    ((![F3 : arrow_1857593510le_alt > arrow_1857593510le_alt, X2 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: ((produc1710313402le_alt @ F3 @ (produc1494124311le_alt @ X2 @ Y2)) = (produc1494124311le_alt @ X2 @ (F3 @ Y2)))))). % apsnd_conv
thf(fact_159_inj__on__convol__ident, axiom,
    ((![F3 : arrow_1857593510le_alt > arrow_1857593510le_alt, X4 : set_Ar1665529862le_alt]: (inj_on1409615164le_alt @ (^[X : arrow_1857593510le_alt]: (produc1494124311le_alt @ X @ (F3 @ X))) @ X4)))). % inj_on_convol_ident
thf(fact_160_inj__on__apsnd, axiom,
    ((![F3 : arrow_1429744205e_indi > nat, A5 : set_Ar1007576579e_indi]: ((inj_on1832254384di_nat @ (produc1894589390e_indi @ F3) @ (produc1762100436e_indi @ top_to1799531699e_indi @ (^[Uu : arrow_1429744205e_indi]: A5))) = (inj_on528257168di_nat @ F3 @ A5))))). % inj_on_apsnd
thf(fact_161_inj__on__apsnd, axiom,
    ((![F3 : arrow_1429744205e_indi > nat, A5 : set_Ar1007576579e_indi]: ((inj_on1530862398lt_nat @ (produc86521573le_alt @ F3) @ (produc711907405e_indi @ top_to958727510le_alt @ (^[Uu : arrow_1857593510le_alt]: A5))) = (inj_on528257168di_nat @ F3 @ A5))))). % inj_on_apsnd
thf(fact_162_inj__on__apfst, axiom,
    ((![F3 : arrow_1429744205e_indi > nat, A5 : set_Ar1007576579e_indi]: ((inj_on1612178390e_indi @ (produc961456016e_indi @ F3) @ (produc1762100436e_indi @ A5 @ (^[Uu : arrow_1429744205e_indi]: top_to1799531699e_indi))) = (inj_on528257168di_nat @ F3 @ A5))))). % inj_on_apfst
thf(fact_163_inj__on__apfst, axiom,
    ((![F3 : arrow_1429744205e_indi > nat, A5 : set_Ar1007576579e_indi]: ((inj_on1711456116le_alt @ (produc1985979043le_alt @ F3) @ (produc1380398175le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: top_to958727510le_alt))) = (inj_on528257168di_nat @ F3 @ A5))))). % inj_on_apfst
thf(fact_164_total__inv__image, axiom,
    ((![F3 : arrow_1429744205e_indi > nat, R2 : set_Pr1986765409at_nat]: ((inj_on528257168di_nat @ F3 @ top_to1799531699e_indi) => ((total_on_nat @ top_top_set_nat @ R2) => (total_2071657417e_indi @ top_to1799531699e_indi @ (inv_im1106624241e_indi @ R2 @ F3))))))). % total_inv_image
thf(fact_165_total__inv__image, axiom,
    ((![F3 : arrow_1429744205e_indi > arrow_1429744205e_indi, R2 : set_Pr773120585e_indi]: ((inj_on1663454827e_indi @ F3 @ top_to1799531699e_indi) => ((total_2071657417e_indi @ top_to1799531699e_indi @ R2) => (total_2071657417e_indi @ top_to1799531699e_indi @ (inv_im452716874e_indi @ R2 @ F3))))))). % total_inv_image
thf(fact_166_total__inv__image, axiom,
    ((![F3 : arrow_1429744205e_indi > arrow_1857593510le_alt, R2 : set_Pr367596371le_alt]: ((inj_on23696648le_alt @ F3 @ top_to1799531699e_indi) => ((total_2034085930le_alt @ top_to958727510le_alt @ R2) => (total_2071657417e_indi @ top_to1799531699e_indi @ (inv_im1842083415e_indi @ R2 @ F3))))))). % total_inv_image
thf(fact_167_total__inv__image, axiom,
    ((![F3 : arrow_1857593510le_alt > arrow_1429744205e_indi, R2 : set_Pr773120585e_indi]: ((inj_on1502689526e_indi @ F3 @ top_to958727510le_alt) => ((total_2071657417e_indi @ top_to1799531699e_indi @ R2) => (total_2034085930le_alt @ top_to958727510le_alt @ (inv_im363090537le_alt @ R2 @ F3))))))). % total_inv_image
thf(fact_168_total__inv__image, axiom,
    ((![F3 : arrow_1857593510le_alt > arrow_1857593510le_alt, R2 : set_Pr367596371le_alt]: ((inj_on207902653le_alt @ F3 @ top_to958727510le_alt) => ((total_2034085930le_alt @ top_to958727510le_alt @ R2) => (total_2034085930le_alt @ top_to958727510le_alt @ (inv_im155136540le_alt @ R2 @ F3))))))). % total_inv_image
thf(fact_169_mem__Sigma__iff, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A5 @ B5)) = (((member519365071le_alt @ A @ A5)) & ((member519365071le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_170_mem__Sigma__iff, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (produc1360152522le_alt @ A5 @ B5)) = (((member2048039092le_alt @ A @ A5)) & ((member2048039092le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_171_mem__Sigma__iff, axiom,
    ((![A : produc16571293le_alt, B : set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member1923768064le_alt @ (produc268611099le_alt @ A @ B) @ (produc1173532202le_alt @ A5 @ B5)) = (((member2048039092le_alt @ A @ A5)) & ((member1334244458le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_172_mem__Sigma__iff, axiom,
    ((![A : set_Pr367596371le_alt, B : produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1480196970le_alt @ (produc1659212421le_alt @ A @ B) @ (produc416649876le_alt @ A5 @ B5)) = (((member1334244458le_alt @ A @ A5)) & ((member2048039092le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_173_mem__Sigma__iff, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ (produc223727860le_alt @ A5 @ B5)) = (((member1334244458le_alt @ A @ A5)) & ((member1334244458le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_174_mem__Sigma__iff, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member1458027142le_alt @ (produc233791437le_alt @ A @ B) @ (produc1711776894le_alt @ A5 @ B5)) = (((member684274596le_alt @ A @ A5)) & ((member2048039092le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_175_mem__Sigma__iff, axiom,
    ((![A : produc16571293le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((member1263449330le_alt @ (produc283291649le_alt @ A @ B) @ (produc1761277106le_alt @ A5 @ B5)) = (((member2048039092le_alt @ A @ A5)) & ((member684274596le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_176_mem__Sigma__iff, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member1902783718le_alt @ (produc806763053le_alt @ A @ B) @ (produc712719070le_alt @ A5 @ B5)) = (((member684274596le_alt @ A @ A5)) & ((member1334244458le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_177_mem__Sigma__iff, axiom,
    ((![A : set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((member688649896le_alt @ (produc1670879671le_alt @ A @ B) @ (produc1576835688le_alt @ A5 @ B5)) = (((member1334244458le_alt @ A @ A5)) & ((member684274596le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_178_mem__Sigma__iff, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((member1926142604le_alt @ (produc1825994351le_alt @ A @ B) @ (produc783065342le_alt @ A5 @ B5)) = (((member684274596le_alt @ A @ A5)) & ((member684274596le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_179_SigmaI, axiom,
    ((![A : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member519365071le_alt @ A @ A5) => ((member519365071le_alt @ B @ (B5 @ A)) => (member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_180_SigmaI, axiom,
    ((![A : produc16571293le_alt, A5 : set_Pr367596371le_alt, B : produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ A @ A5) => ((member2048039092le_alt @ B @ (B5 @ A)) => (member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (produc1360152522le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_181_SigmaI, axiom,
    ((![A : produc16571293le_alt, A5 : set_Pr367596371le_alt, B : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member2048039092le_alt @ A @ A5) => ((member1334244458le_alt @ B @ (B5 @ A)) => (member1923768064le_alt @ (produc268611099le_alt @ A @ B) @ (produc1173532202le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_182_SigmaI, axiom,
    ((![A : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B : produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ A @ A5) => ((member2048039092le_alt @ B @ (B5 @ A)) => (member1480196970le_alt @ (produc1659212421le_alt @ A @ B) @ (produc416649876le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_183_SigmaI, axiom,
    ((![A : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1334244458le_alt @ A @ A5) => ((member1334244458le_alt @ B @ (B5 @ A)) => (member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ (produc223727860le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_184_SigmaI, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B : produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member684274596le_alt @ A @ A5) => ((member2048039092le_alt @ B @ (B5 @ A)) => (member1458027142le_alt @ (produc233791437le_alt @ A @ B) @ (produc1711776894le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_185_SigmaI, axiom,
    ((![A : produc16571293le_alt, A5 : set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((member2048039092le_alt @ A @ A5) => ((member684274596le_alt @ B @ (B5 @ A)) => (member1263449330le_alt @ (produc283291649le_alt @ A @ B) @ (produc1761277106le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_186_SigmaI, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B : set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member684274596le_alt @ A @ A5) => ((member1334244458le_alt @ B @ (B5 @ A)) => (member1902783718le_alt @ (produc806763053le_alt @ A @ B) @ (produc712719070le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_187_SigmaI, axiom,
    ((![A : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((member1334244458le_alt @ A @ A5) => ((member684274596le_alt @ B @ (B5 @ A)) => (member688649896le_alt @ (produc1670879671le_alt @ A @ B) @ (produc1576835688le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_188_SigmaI, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((member684274596le_alt @ A @ A5) => ((member684274596le_alt @ B @ (B5 @ A)) => (member1926142604le_alt @ (produc1825994351le_alt @ A @ B) @ (produc783065342le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_189_UNIV__Times__UNIV, axiom,
    (((produc1762100436e_indi @ top_to1799531699e_indi @ (^[Uu : arrow_1429744205e_indi]: top_to1799531699e_indi)) = top_to491983097e_indi))). % UNIV_Times_UNIV
thf(fact_190_UNIV__Times__UNIV, axiom,
    (((produc1380398175le_alt @ top_to1799531699e_indi @ (^[Uu : arrow_1429744205e_indi]: top_to958727510le_alt)) = top_to2021795110le_alt))). % UNIV_Times_UNIV
thf(fact_191_UNIV__Times__UNIV, axiom,
    (((produc711907405e_indi @ top_to958727510le_alt @ (^[Uu : arrow_1857593510le_alt]: top_to1799531699e_indi)) = top_to883938140e_indi))). % UNIV_Times_UNIV
thf(fact_192_UNIV__Times__UNIV, axiom,
    (((produc2062971558le_alt @ top_to958727510le_alt @ (^[Uu : arrow_1857593510le_alt]: top_to958727510le_alt)) = top_to224369155le_alt))). % UNIV_Times_UNIV
thf(fact_193_total__on__def, axiom,
    ((total_2034085930le_alt = (^[A6 : set_Ar1665529862le_alt]: (^[R3 : set_Pr367596371le_alt]: (![X : arrow_1857593510le_alt]: (((member519365071le_alt @ X @ A6)) => ((![Y : arrow_1857593510le_alt]: (((member519365071le_alt @ Y @ A6)) => ((((~ ((X = Y)))) => ((((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R3)) | ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ R3)))))))))))))))). % total_on_def
thf(fact_194_total__onI, axiom,
    ((![A5 : set_Ar809243995le_alt, R2 : set_Pr1877138731le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt, Y3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => ((member684274596le_alt @ Y3 @ A5) => ((~ ((X3 = Y3))) => ((member1926142604le_alt @ (produc1825994351le_alt @ X3 @ Y3) @ R2) | (member1926142604le_alt @ (produc1825994351le_alt @ Y3 @ X3) @ R2)))))) => (total_535758719le_alt @ A5 @ R2))))). % total_onI
thf(fact_195_total__onI, axiom,
    ((![A5 : set_Pr367596371le_alt, R2 : set_Pr448479039le_alt]: ((![X3 : produc16571293le_alt, Y3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => ((member2048039092le_alt @ Y3 @ A5) => ((~ ((X3 = Y3))) => ((member2146260128le_alt @ (produc41061307le_alt @ X3 @ Y3) @ R2) | (member2146260128le_alt @ (produc41061307le_alt @ Y3 @ X3) @ R2)))))) => (total_608959769le_alt @ A5 @ R2))))). % total_onI
thf(fact_196_total__onI, axiom,
    ((![A5 : set_Ar182050865le_alt, R2 : set_Pr1665528429le_alt]: ((![X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, Y3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ X3 @ A5) => ((member183760530le_alt @ Y3 @ A5) => ((~ ((X3 = Y3))) => ((member775439054le_alt @ (produc1102161897le_alt @ X3 @ Y3) @ R2) | (member775439054le_alt @ (produc1102161897le_alt @ Y3 @ X3) @ R2)))))) => (total_159340151le_alt @ A5 @ R2))))). % total_onI
thf(fact_197_total__onI, axiom,
    ((![A5 : set_se2071012361le_alt, R2 : set_Pr851393385le_alt]: ((![X3 : set_Pr367596371le_alt, Y3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => ((member1334244458le_alt @ Y3 @ A5) => ((~ ((X3 = Y3))) => ((member1392960970le_alt @ (produc1931840741le_alt @ X3 @ Y3) @ R2) | (member1392960970le_alt @ (produc1931840741le_alt @ Y3 @ X3) @ R2)))))) => (total_51659983le_alt @ A5 @ R2))))). % total_onI
thf(fact_198_total__onI, axiom,
    ((![A5 : set_Ar1665529862le_alt, R2 : set_Pr367596371le_alt]: ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((member519365071le_alt @ X3 @ A5) => ((member519365071le_alt @ Y3 @ A5) => ((~ ((X3 = Y3))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R2) | (member2048039092le_alt @ (produc1494124311le_alt @ Y3 @ X3) @ R2)))))) => (total_2034085930le_alt @ A5 @ R2))))). % total_onI
thf(fact_199_SigmaE2, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A5 @ B5)) => (~ (((member519365071le_alt @ A @ A5) => (~ ((member519365071le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_200_SigmaE2, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (produc1360152522le_alt @ A5 @ B5)) => (~ (((member2048039092le_alt @ A @ A5) => (~ ((member2048039092le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_201_SigmaE2, axiom,
    ((![A : produc16571293le_alt, B : set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member1923768064le_alt @ (produc268611099le_alt @ A @ B) @ (produc1173532202le_alt @ A5 @ B5)) => (~ (((member2048039092le_alt @ A @ A5) => (~ ((member1334244458le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_202_SigmaE2, axiom,
    ((![A : set_Pr367596371le_alt, B : produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1480196970le_alt @ (produc1659212421le_alt @ A @ B) @ (produc416649876le_alt @ A5 @ B5)) => (~ (((member1334244458le_alt @ A @ A5) => (~ ((member2048039092le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_203_SigmaE2, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ (produc223727860le_alt @ A5 @ B5)) => (~ (((member1334244458le_alt @ A @ A5) => (~ ((member1334244458le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_204_SigmaE2, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member1458027142le_alt @ (produc233791437le_alt @ A @ B) @ (produc1711776894le_alt @ A5 @ B5)) => (~ (((member684274596le_alt @ A @ A5) => (~ ((member2048039092le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_205_SigmaE2, axiom,
    ((![A : produc16571293le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((member1263449330le_alt @ (produc283291649le_alt @ A @ B) @ (produc1761277106le_alt @ A5 @ B5)) => (~ (((member2048039092le_alt @ A @ A5) => (~ ((member684274596le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_206_SigmaE2, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member1902783718le_alt @ (produc806763053le_alt @ A @ B) @ (produc712719070le_alt @ A5 @ B5)) => (~ (((member684274596le_alt @ A @ A5) => (~ ((member1334244458le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_207_SigmaE2, axiom,
    ((![A : set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((member688649896le_alt @ (produc1670879671le_alt @ A @ B) @ (produc1576835688le_alt @ A5 @ B5)) => (~ (((member1334244458le_alt @ A @ A5) => (~ ((member684274596le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_208_SigmaE2, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((member1926142604le_alt @ (produc1825994351le_alt @ A @ B) @ (produc783065342le_alt @ A5 @ B5)) => (~ (((member684274596le_alt @ A @ A5) => (~ ((member684274596le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_209_SigmaD2, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A5 @ B5)) => (member519365071le_alt @ B @ (B5 @ A)))))). % SigmaD2
thf(fact_210_SigmaD1, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A5 @ B5)) => (member519365071le_alt @ A @ A5))))). % SigmaD1
thf(fact_211_SigmaE, axiom,
    ((![C : produc16571293le_alt, A5 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ C @ (produc2062971558le_alt @ A5 @ B5)) => (~ ((![X3 : arrow_1857593510le_alt]: ((member519365071le_alt @ X3 @ A5) => (![Y3 : arrow_1857593510le_alt]: ((member519365071le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc1494124311le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_212_SigmaE, axiom,
    ((![C : produc1556433673le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2146260128le_alt @ C @ (produc1360152522le_alt @ A5 @ B5)) => (~ ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (![Y3 : produc16571293le_alt]: ((member2048039092le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc41061307le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_213_SigmaE, axiom,
    ((![C : produc1114386793le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member1923768064le_alt @ C @ (produc1173532202le_alt @ A5 @ B5)) => (~ ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (![Y3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc268611099le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_214_SigmaE, axiom,
    ((![C : produc670815699le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1480196970le_alt @ C @ (produc416649876le_alt @ A5 @ B5)) => (~ ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (![Y3 : produc16571293le_alt]: ((member2048039092le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc1659212421le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_215_SigmaE, axiom,
    ((![C : produc541234227le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1392960970le_alt @ C @ (produc223727860le_alt @ A5 @ B5)) => (~ ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (![Y3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc1931840741le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_216_SigmaE, axiom,
    ((![C : produc1751271773le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member1458027142le_alt @ C @ (produc1711776894le_alt @ A5 @ B5)) => (~ ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (![Y3 : produc16571293le_alt]: ((member2048039092le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc233791437le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_217_SigmaE, axiom,
    ((![C : produc1556693961le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((member1263449330le_alt @ C @ (produc1761277106le_alt @ A5 @ B5)) => (~ ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (![Y3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc283291649le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_218_SigmaE, axiom,
    ((![C : produc1766186941le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member1902783718le_alt @ C @ (produc712719070le_alt @ A5 @ B5)) => (~ ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (![Y3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc806763053le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_219_SigmaE, axiom,
    ((![C : produc552053119le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((member688649896le_alt @ C @ (produc1576835688le_alt @ A5 @ B5)) => (~ ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (![Y3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc1670879671le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_220_SigmaE, axiom,
    ((![C : produc1638831733le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((member1926142604le_alt @ C @ (produc783065342le_alt @ A5 @ B5)) => (~ ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (![Y3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc1825994351le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_221_member__product, axiom,
    ((![X2 : produc16571293le_alt, A5 : set_Ar1665529862le_alt, B5 : set_Ar1665529862le_alt]: ((member2048039092le_alt @ X2 @ (produc961482780le_alt @ A5 @ B5)) = (member2048039092le_alt @ X2 @ (produc2062971558le_alt @ A5 @ (^[Uu : arrow_1857593510le_alt]: B5))))))). % member_product
thf(fact_222_total__lex__prod, axiom,
    ((![R2 : set_Pr773120585e_indi, S2 : set_Pr773120585e_indi]: ((total_2071657417e_indi @ top_to1799531699e_indi @ R2) => ((total_2071657417e_indi @ top_to1799531699e_indi @ S2) => (total_462929551e_indi @ top_to491983097e_indi @ (lex_pr357123757e_indi @ R2 @ S2))))))). % total_lex_prod
thf(fact_223_total__lex__prod, axiom,
    ((![R2 : set_Pr773120585e_indi, S2 : set_Pr367596371le_alt]: ((total_2071657417e_indi @ top_to1799531699e_indi @ R2) => ((total_2034085930le_alt @ top_to958727510le_alt @ S2) => (total_1059175546le_alt @ top_to2021795110le_alt @ (lex_pr2059037766le_alt @ R2 @ S2))))))). % total_lex_prod
thf(fact_224_total__lex__prod, axiom,
    ((![R2 : set_Pr367596371le_alt, S2 : set_Pr773120585e_indi]: ((total_2034085930le_alt @ top_to958727510le_alt @ R2) => ((total_2071657417e_indi @ top_to1799531699e_indi @ S2) => (total_1100785072e_indi @ top_to883938140e_indi @ (lex_pr1390546996e_indi @ R2 @ S2))))))). % total_lex_prod
thf(fact_225_total__lex__prod, axiom,
    ((![R2 : set_Pr367596371le_alt, S2 : set_Pr367596371le_alt]: ((total_2034085930le_alt @ top_to958727510le_alt @ R2) => ((total_2034085930le_alt @ top_to958727510le_alt @ S2) => (total_608959769le_alt @ top_to224369155le_alt @ (lex_pr3395839le_alt @ R2 @ S2))))))). % total_lex_prod
thf(fact_226_in__lex__prod, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, R2 : set_Pr367596371le_alt, S2 : set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ (produc1494124311le_alt @ A @ B) @ (produc1494124311le_alt @ A2 @ B2)) @ (lex_pr3395839le_alt @ R2 @ S2)) = (((member2048039092le_alt @ (produc1494124311le_alt @ A @ A2) @ R2)) | ((((A = A2)) & ((member2048039092le_alt @ (produc1494124311le_alt @ B @ B2) @ S2))))))))). % in_lex_prod
thf(fact_227_map__prod__inj__on, axiom,
    ((![F3 : arrow_1429744205e_indi > nat, A5 : set_Ar1007576579e_indi, G : arrow_1429744205e_indi > nat, B5 : set_Ar1007576579e_indi]: ((inj_on528257168di_nat @ F3 @ A5) => ((inj_on528257168di_nat @ G @ B5) => (inj_on2118364411at_nat @ (produc1669992998di_nat @ F3 @ G) @ (produc1762100436e_indi @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5)))))))). % map_prod_inj_on
thf(fact_228_map__prod__simp, axiom,
    ((![F3 : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc1074667658le_alt @ F3 @ G @ (produc1494124311le_alt @ A @ B)) = (produc1494124311le_alt @ (F3 @ A) @ (G @ B)))))). % map_prod_simp
thf(fact_229_extensionalityI, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, G : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ F3 @ (extens1528283402le_alt @ A5)) => ((member684274596le_alt @ G @ (extens1528283402le_alt @ A5)) => ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => ((F3 @ X3) = (G @ X3)))) => (F3 = G))))))). % extensionalityI
thf(fact_230_extensionalityI, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ F3 @ (extens951643470le_alt @ A5)) => ((member183760530le_alt @ G @ (extens951643470le_alt @ A5)) => ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => ((F3 @ X3) = (G @ X3)))) => (F3 = G))))))). % extensionalityI
thf(fact_231_prod_Oinj__map, axiom,
    ((![F1 : arrow_1429744205e_indi > nat, F22 : arrow_1429744205e_indi > nat]: ((inj_on528257168di_nat @ F1 @ top_to1799531699e_indi) => ((inj_on528257168di_nat @ F22 @ top_to1799531699e_indi) => (inj_on2118364411at_nat @ (produc1669992998di_nat @ F1 @ F22) @ top_to491983097e_indi)))))). % prod.inj_map
thf(fact_232_same__fstI, axiom,
    ((![P : arrow_1857593510le_alt > $o, X2 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt, R : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((P @ X2) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y4 @ Y2) @ (R @ X2)) => (member2146260128le_alt @ (produc41061307le_alt @ (produc1494124311le_alt @ X2 @ Y4) @ (produc1494124311le_alt @ X2 @ Y2)) @ (same_f554660482le_alt @ P @ R))))))). % same_fstI
thf(fact_233_Pi__empty, axiom,
    ((![B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((pi_Arr479247969le_alt @ bot_bo365569479le_alt @ B5) = top_to803745505le_alt)))). % Pi_empty
thf(fact_234_Pi__empty, axiom,
    ((![B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((pi_Arr1981691447le_alt @ bot_bo1390904983e_indi @ B5) = top_to685525675le_alt)))). % Pi_empty
thf(fact_235_Collect__const, axiom,
    ((![P : $o]: ((P => ((collec1399441576le_alt @ (^[S4 : set_Pr367596371le_alt]: P)) = top_to469035705le_alt)) & ((~ (P)) => ((collec1399441576le_alt @ (^[S4 : set_Pr367596371le_alt]: P)) = bot_bo1518363805le_alt)))))). % Collect_const
thf(fact_236_Collect__const, axiom,
    ((![P : $o]: ((P => ((collec1169676194e_indi @ (^[S4 : arrow_1429744205e_indi]: P)) = top_to1799531699e_indi)) & ((~ (P)) => ((collec1169676194e_indi @ (^[S4 : arrow_1429744205e_indi]: P)) = bot_bo1390904983e_indi)))))). % Collect_const
thf(fact_237_Collect__const, axiom,
    ((![P : $o]: ((P => ((collec1364151825le_alt @ (^[S4 : arrow_1857593510le_alt]: P)) = top_to958727510le_alt)) & ((~ (P)) => ((collec1364151825le_alt @ (^[S4 : arrow_1857593510le_alt]: P)) = bot_bo1127707250le_alt)))))). % Collect_const
thf(fact_238_Pi__eq__empty, axiom,
    ((![A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: (((pi_Arr479247969le_alt @ A5 @ B5) = bot_bo13098693le_alt) = (?[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ A5)) & (((B5 @ X) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_239_Pi__eq__empty, axiom,
    ((![A5 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: (((pi_Arr1981691447le_alt @ A5 @ B5) = bot_bo365569479le_alt) = (?[X : arrow_1429744205e_indi]: (((member1966420836e_indi @ X @ A5)) & (((B5 @ X) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_240_empty__not__UNIV, axiom,
    ((~ ((bot_bo1390904983e_indi = top_to1799531699e_indi))))). % empty_not_UNIV
thf(fact_241_empty__not__UNIV, axiom,
    ((~ ((bot_bo1127707250le_alt = top_to958727510le_alt))))). % empty_not_UNIV
thf(fact_242_funcset__to__empty__iff, axiom,
    ((![A5 : set_Ar809243995le_alt]: (((A5 = bot_bo365569479le_alt) => ((pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: bot_bo1518363805le_alt)) = top_to803745505le_alt)) & ((~ ((A5 = bot_bo365569479le_alt))) => ((pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: bot_bo1518363805le_alt)) = bot_bo13098693le_alt)))))). % funcset_to_empty_iff
thf(fact_243_funcset__to__empty__iff, axiom,
    ((![A5 : set_Ar1007576579e_indi]: (((A5 = bot_bo1390904983e_indi) => ((pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: bot_bo1518363805le_alt)) = top_to685525675le_alt)) & ((~ ((A5 = bot_bo1390904983e_indi))) => ((pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: bot_bo1518363805le_alt)) = bot_bo365569479le_alt)))))). % funcset_to_empty_iff
thf(fact_244_empty__def, axiom,
    ((bot_bo1518363805le_alt = (collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: $false))))). % empty_def
thf(fact_245_PiE__UNIV, axiom,
    (((piE_Ar738911586e_indi @ top_to1799531699e_indi @ (^[I2 : arrow_1429744205e_indi]: top_to1799531699e_indi)) = top_to498310661e_indi))). % PiE_UNIV
thf(fact_246_PiE__UNIV, axiom,
    (((piE_Ar1084018769le_alt @ top_to1799531699e_indi @ (^[I2 : arrow_1429744205e_indi]: top_to958727510le_alt)) = top_to1139905818le_alt))). % PiE_UNIV
thf(fact_247_PiE__UNIV, axiom,
    (((piE_Ar415527999e_indi @ top_to958727510le_alt @ (^[I2 : arrow_1857593510le_alt]: top_to1799531699e_indi)) = top_to2048848e_indi))). % PiE_UNIV
thf(fact_248_PiE__UNIV, axiom,
    (((piE_Ar1187035700le_alt @ top_to958727510le_alt @ (^[I2 : arrow_1857593510le_alt]: top_to958727510le_alt)) = top_to290516239le_alt))). % PiE_UNIV

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![A7 : arrow_1857593510le_alt, B6 : arrow_1857593510le_alt]: ((~ ((A7 = B6))) => thesis)))).
thf(conj_1, conjecture,
    (thesis)).
