% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/Arrow_Order/prob_291__5189388_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:17:20.068

% Could-be-implicit typings (12)
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Ar809243995le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_Eo_J_J_Mt__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc1094320767le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc518943027le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se2071012361le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Pr367596371le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc16571293le_alt : $tType).
thf(ty_n_t__List__Olist_It__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    list_l1515872562le_alt : $tType).
thf(ty_n_t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    list_A2130511660le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    set_Ar1007576579e_indi : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    arrow_1429744205e_indi : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    arrow_1857593510le_alt : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (47)
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OIIA, type,
    arrow_1821794627le_IIA : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OLin, type,
    arrow_1848678355le_Lin : set_se2071012361le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OProf, type,
    arrow_1951607831e_Prof : set_Ar809243995le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Oabove, type,
    arrow_1726226719_above : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Obelow, type,
    arrow_887341619_below : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_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_Finite__Set_Ocard_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    finite927127589e_indi : set_Ar1007576579e_indi > nat).
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_Hilbert__Choice_Oinv__into_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    hilber700257104e_indi : set_Ar1007576579e_indi > (arrow_1429744205e_indi > arrow_1429744205e_indi) > arrow_1429744205e_indi > arrow_1429744205e_indi).
thf(sy_c_Hilbert__Choice_Oinv__into_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat, type,
    hilber1586975467di_nat : set_Ar1007576579e_indi > (arrow_1429744205e_indi > nat) > nat > arrow_1429744205e_indi).
thf(sy_c_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    if_set550155277le_alt : $o > set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_List_Odistinct_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    distin2037765919le_alt : list_A2130511660le_alt > $o).
thf(sy_c_List_Olist_OCons_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    cons_A1864255580le_alt : arrow_1857593510le_alt > list_A2130511660le_alt > list_A2130511660le_alt).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    cons_l157309922le_alt : list_A2130511660le_alt > list_l1515872562le_alt > list_l1515872562le_alt).
thf(sy_c_List_Olist_ONil_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    nil_Ar277507244le_alt : list_A2130511660le_alt).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    nil_li2110134322le_alt : list_l1515872562le_alt).
thf(sy_c_List_Ounion_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    union_420169888le_alt : list_A2130511660le_alt > list_A2130511660le_alt > list_A2130511660le_alt).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    ord_le1187139159e_indi : set_Ar1007576579e_indi > set_Ar1007576579e_indi > $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_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__Oindi_J, type,
    top_to1799531699e_indi : set_Ar1007576579e_indi).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    top_to224369155le_alt : set_Pr367596371le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    top_to469035705le_alt : set_se2071012361le_alt).
thf(sy_c_Product__Type_OPair_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_Eo_J_J_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc2047839287le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > list_A2130511660le_alt > produc1094320767le_alt).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1494124311le_alt : arrow_1857593510le_alt > arrow_1857593510le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc961395117le_alt : list_A2130511660le_alt > list_A2130511660le_alt > produc518943027le_alt).
thf(sy_c_Set_OCollect_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    collec1559089382le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > $o) > set_Ar809243995le_alt).
thf(sy_c_Set_OCollect_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    collec1169676194e_indi : (arrow_1429744205e_indi > $o) > set_Ar1007576579e_indi).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    collec531981554le_alt : (produc16571293le_alt > $o) > set_Pr367596371le_alt).
thf(sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    collec1399441576le_alt : (set_Pr367596371le_alt > $o) > set_se2071012361le_alt).
thf(sy_c_Wellfounded_Omeasure_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    measur1447705966le_alt : (arrow_1857593510le_alt > nat) > set_Pr367596371le_alt).
thf(sy_c_member_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member684274596le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt > $o).
thf(sy_c_member_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    member1966420836e_indi : arrow_1429744205e_indi > set_Ar1007576579e_indi > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    member2048039092le_alt : produc16571293le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1334244458le_alt : set_Pr367596371le_alt > set_se2071012361le_alt > $o).
thf(sy_v_F, type,
    f : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt).
thf(sy_v_Lab____, type,
    lab : set_Pr367596371le_alt).
thf(sy_v_Lba____, type,
    lba : set_Pr367596371le_alt).
thf(sy_v_P____, type,
    p : arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_v_c____, type,
    c : arrow_1857593510le_alt).
thf(sy_v_d____, type,
    d : arrow_1857593510le_alt).
thf(sy_v_e____, type,
    e : arrow_1857593510le_alt).
thf(sy_v_h____, type,
    h : arrow_1429744205e_indi > nat).
thf(sy_v_n____, type,
    n : nat).

% Relevant facts (137)
thf(fact_0__092_060open_062P_A_092_060in_062_AProf_092_060close_062, axiom,
    ((member684274596le_alt @ p @ arrow_1951607831e_Prof))). % \<open>P \<in> Prof\<close>
thf(fact_1__092_060open_062c_A_092_060noteq_062_Ad_092_060close_062, axiom,
    ((~ ((c = d))))). % \<open>c \<noteq> d\<close>
thf(fact_2_dist, axiom,
    ((distin2037765919le_alt @ (cons_A1864255580le_alt @ c @ (cons_A1864255580le_alt @ d @ (cons_A1864255580le_alt @ e @ nil_Ar277507244le_alt)))))). % dist
thf(fact_3_in__mkbot, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_843587755_mkbot @ L @ Z)) = (((~ ((Y = Z)))) & ((((((X = Z)) => ((~ ((X = Y)))))) & ((((~ ((X = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))). % in_mkbot
thf(fact_4_in__mktop, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_992294841_mktop @ L @ Z)) = (((~ ((X = Z)))) & ((((((Y = Z)) => ((~ ((X = Y)))))) & ((((~ ((Y = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))). % in_mktop
thf(fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062e_O_Adistinct_A_091c_M_Ad_M_Ae_093_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![E : arrow_1857593510le_alt]: (~ ((distin2037765919le_alt @ (cons_A1864255580le_alt @ c @ (cons_A1864255580le_alt @ d @ (cons_A1864255580le_alt @ E @ nil_Ar277507244le_alt))))))))))). % \<open>\<And>thesis. (\<And>e. distinct [c, d, e] \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_6__092_060open_062c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_092_060close_062, axiom,
    ((member2048039092le_alt @ (produc1494124311le_alt @ c @ d) @ (p @ (hilber1586975467di_nat @ top_to1799531699e_indi @ h @ n))))). % \<open>c <\<^bsub>P (inv h n)\<^esub> d\<close>
thf(fact_7__092_060open_062_I_092_060lambda_062i_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_AArrow__Order__Mirabelle__riepwfubkl_Oabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_A_092_060in_062_AProf_092_060close_062, axiom,
    ((member684274596le_alt @ (^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ n) @ (arrow_992294841_mktop @ (p @ I) @ e) @ (if_set550155277le_alt @ ((h @ I) = n) @ (arrow_1726226719_above @ (p @ I) @ c @ e) @ (arrow_843587755_mkbot @ (p @ I) @ e)))) @ arrow_1951607831e_Prof))). % \<open>(\<lambda>i. if h i < n then mktop (P i) e else if h i = n then Arrow_Order_Mirabelle_riepwfubkl.above (P i) c e else mkbot (P i) e) \<in> Prof\<close>
thf(fact_8_prod_Oinject, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X1 @ X2) = (produc1494124311le_alt @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_9_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_10_in__above, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_1726226719_above @ L @ A @ B)) = (((~ ((X = Y)))) & ((((((X = B)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y) @ L)))) & ((((~ ((X = B)))) => ((((((Y = B)) => ((((X = A)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X @ A) @ L)))))) & ((((~ ((Y = B)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))))))))). % in_above
thf(fact_11_n_I1_J, axiom,
    ((ord_less_nat @ n @ (finite927127589e_indi @ top_to1799531699e_indi)))). % n(1)
thf(fact_12_in__measure, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, F : arrow_1857593510le_alt > nat]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (measur1447705966le_alt @ F)) = (ord_less_nat @ (F @ X) @ (F @ Y)))))). % in_measure
thf(fact_13_nat__neq__iff, axiom,
    ((![M : nat, N : nat]: ((~ ((M = N))) = (((ord_less_nat @ M @ N)) | ((ord_less_nat @ N @ M))))))). % nat_neq_iff
thf(fact_14_less__not__refl, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_not_refl
thf(fact_15_less__not__refl2, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ N @ M) => (~ ((M = N))))))). % less_not_refl2
thf(fact_16_less__not__refl3, axiom,
    ((![S : nat, T : nat]: ((ord_less_nat @ S @ T) => (~ ((S = T))))))). % less_not_refl3
thf(fact_17__092_060open_062Lba_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ lba @ arrow_1848678355le_Lin))). % \<open>Lba \<in> Lin\<close>
thf(fact_18__092_060open_062Lab_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ lab @ arrow_1848678355le_Lin))). % \<open>Lab \<in> Lin\<close>
thf(fact_19_injh, axiom,
    ((inj_on528257168di_nat @ h @ top_to1799531699e_indi))). % injh
thf(fact_20_alt3, axiom,
    ((?[A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt, C : arrow_1857593510le_alt]: (distin2037765919le_alt @ (cons_A1864255580le_alt @ A3 @ (cons_A1864255580le_alt @ B3 @ (cons_A1864255580le_alt @ C @ nil_Ar277507244le_alt))))))). % alt3
thf(fact_21_third__alt, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((~ ((A = B))) => (?[C : arrow_1857593510le_alt]: (distin2037765919le_alt @ (cons_A1864255580le_alt @ A @ (cons_A1864255580le_alt @ B @ (cons_A1864255580le_alt @ C @ nil_Ar277507244le_alt))))))))). % third_alt
thf(fact_22_linear__alt, axiom,
    ((?[L2 : set_Pr367596371le_alt]: (member1334244458le_alt @ L2 @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_23_const__Lin__Prof, axiom,
    ((![L : set_Pr367596371le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member684274596le_alt @ (^[P : arrow_1429744205e_indi]: L) @ arrow_1951607831e_Prof))))). % const_Lin_Prof
thf(fact_24_notin__Lin__iff, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((~ ((X = Y))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ L))))))). % notin_Lin_iff
thf(fact_25_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_26_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_27_mktop__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_992294841_mktop @ L @ X) @ arrow_1848678355le_Lin))))). % mktop_Lin
thf(fact_28_mkbot__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_843587755_mkbot @ L @ X) @ arrow_1848678355le_Lin))))). % mkbot_Lin
thf(fact_29_above__Lin, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X = Y))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L @ X @ Y) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_30_old_Oprod_Oinducts, axiom,
    ((![P2 : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_31_old_Oprod_Oexhaust, axiom,
    ((![Y : produc16571293le_alt]: (~ ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (~ ((Y = (produc1494124311le_alt @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_32_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_33_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P2 : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_34_mem__Collect__eq, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((member684274596le_alt @ A @ (collec1559089382le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_35_mem__Collect__eq, axiom,
    ((![A : set_Pr367596371le_alt, P2 : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ A @ (collec1399441576le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_36_Collect__mem__eq, axiom,
    ((![A4 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_37_Collect__mem__eq, axiom,
    ((![A4 : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_38_Collect__mem__eq, axiom,
    ((![A4 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (member1334244458le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_39_prod__cases, axiom,
    ((![P2 : produc16571293le_alt > $o, P3 : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ P3))))). % prod_cases
thf(fact_40_surj__pair, axiom,
    ((![P3 : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P3 = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_41_linorder__neqE__nat, axiom,
    ((![X : nat, Y : nat]: ((~ ((X = Y))) => ((~ ((ord_less_nat @ X @ Y))) => (ord_less_nat @ Y @ X)))))). % linorder_neqE_nat
thf(fact_42_infinite__descent, axiom,
    ((![P2 : nat > $o, N : nat]: ((![N2 : nat]: ((~ ((P2 @ N2))) => (?[M2 : nat]: ((ord_less_nat @ M2 @ N2) & (~ ((P2 @ M2))))))) => (P2 @ N))))). % infinite_descent
thf(fact_43_nat__less__induct, axiom,
    ((![P2 : nat > $o, N : nat]: ((![N2 : nat]: ((![M2 : nat]: ((ord_less_nat @ M2 @ N2) => (P2 @ M2))) => (P2 @ N2))) => (P2 @ N))))). % nat_less_induct
thf(fact_44_less__irrefl__nat, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_irrefl_nat
thf(fact_45_inv__identity, axiom,
    (((hilber700257104e_indi @ top_to1799531699e_indi @ (^[A5 : arrow_1429744205e_indi]: A5)) = (^[A5 : arrow_1429744205e_indi]: A5)))). % inv_identity
thf(fact_46_distinct__singleton, axiom,
    ((![X : arrow_1857593510le_alt]: (distin2037765919le_alt @ (cons_A1864255580le_alt @ X @ nil_Ar277507244le_alt))))). % distinct_singleton
thf(fact_47_unanimity__def, axiom,
    ((arrow_52334694nimity = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => ((![A5 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (X4 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (F2 @ X4))))))))))))). % unanimity_def
thf(fact_48_IIA__def, axiom,
    ((arrow_1821794627le_IIA = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => ((![Y4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ Y4 @ arrow_1951607831e_Prof)) => ((![A5 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (X4 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (Y4 @ I))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (F2 @ X4)) = (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (F2 @ Y4))))))))))))))))). % IIA_def
thf(fact_49_UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % UNIV_I
thf(fact_50_UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % UNIV_I
thf(fact_51_UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % UNIV_I
thf(fact_52_UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % UNIV_I
thf(fact_53_iso__tuple__UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_54_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % iso_tuple_UNIV_I
thf(fact_55_iso__tuple__UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % iso_tuple_UNIV_I
thf(fact_56_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % iso_tuple_UNIV_I
thf(fact_57_list_Oinject, axiom,
    ((![X21 : arrow_1857593510le_alt, X22 : list_A2130511660le_alt, Y21 : arrow_1857593510le_alt, Y22 : list_A2130511660le_alt]: (((cons_A1864255580le_alt @ X21 @ X22) = (cons_A1864255580le_alt @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_58_PiProf, axiom,
    ((![N : nat]: (member684274596le_alt @ (^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ N) @ lab @ lba)) @ arrow_1951607831e_Prof)))). % PiProf
thf(fact_59_inv__into__f__f, axiom,
    ((![F : arrow_1429744205e_indi > nat, A4 : set_Ar1007576579e_indi, X : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ A4) => ((member1966420836e_indi @ X @ A4) => ((hilber1586975467di_nat @ A4 @ F @ (F @ X)) = X)))))). % inv_into_f_f
thf(fact_60_assms_I3_J, axiom,
    ((arrow_1821794627le_IIA @ f))). % assms(3)
thf(fact_61_u, axiom,
    ((arrow_52334694nimity @ f))). % u
thf(fact_62_top__set__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ top_to1473733010indi_o)))). % top_set_def
thf(fact_63_inv__into__f__eq, axiom,
    ((![F : arrow_1429744205e_indi > nat, A4 : set_Ar1007576579e_indi, X : arrow_1429744205e_indi, Y : nat]: ((inj_on528257168di_nat @ F @ A4) => ((member1966420836e_indi @ X @ A4) => (((F @ X) = Y) => ((hilber1586975467di_nat @ A4 @ F @ Y) = X))))))). % inv_into_f_eq
thf(fact_64_inj__imp__inv__eq, axiom,
    ((![F : arrow_1429744205e_indi > nat, G : nat > arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) => ((![X3 : nat]: ((F @ (G @ X3)) = X3)) => ((hilber1586975467di_nat @ top_to1799531699e_indi @ F) = G)))))). % inj_imp_inv_eq
thf(fact_65_inv__f__eq, axiom,
    ((![F : arrow_1429744205e_indi > nat, X : arrow_1429744205e_indi, Y : nat]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) => (((F @ X) = Y) => ((hilber1586975467di_nat @ top_to1799531699e_indi @ F @ Y) = X)))))). % inv_f_eq
thf(fact_66_inv__f__f, axiom,
    ((![F : arrow_1429744205e_indi > nat, X : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) => ((hilber1586975467di_nat @ top_to1799531699e_indi @ F @ (F @ X)) = X))))). % inv_f_f
thf(fact_67_ord__eq__less__subst, axiom,
    ((![A : nat, F : nat > nat, B : nat, C2 : nat]: ((A = (F @ B)) => ((ord_less_nat @ B @ C2) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ A @ (F @ C2)))))))). % ord_eq_less_subst
thf(fact_68_ord__less__eq__subst, axiom,
    ((![A : nat, B : nat, F : nat > nat, C2 : nat]: ((ord_less_nat @ A @ B) => (((F @ B) = C2) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ (F @ A) @ C2))))))). % ord_less_eq_subst
thf(fact_69_order__less__subst1, axiom,
    ((![A : nat, F : nat > nat, B : nat, C2 : nat]: ((ord_less_nat @ A @ (F @ B)) => ((ord_less_nat @ B @ C2) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ A @ (F @ C2)))))))). % order_less_subst1
thf(fact_70_order__less__subst2, axiom,
    ((![A : nat, B : nat, F : nat > nat, C2 : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (F @ B) @ C2) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ (F @ A) @ C2))))))). % order_less_subst2
thf(fact_71_gt__ex, axiom,
    ((![X : nat]: (?[X_1 : nat]: (ord_less_nat @ X @ X_1))))). % gt_ex
thf(fact_72_neqE, axiom,
    ((![X : nat, Y : nat]: ((~ ((X = Y))) => ((~ ((ord_less_nat @ X @ Y))) => (ord_less_nat @ Y @ X)))))). % neqE
thf(fact_73_neq__iff, axiom,
    ((![X : nat, Y : nat]: ((~ ((X = Y))) = (((ord_less_nat @ X @ Y)) | ((ord_less_nat @ Y @ X))))))). % neq_iff
thf(fact_74_order_Oasym, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((ord_less_nat @ B @ A))))))). % order.asym
thf(fact_75_less__imp__neq, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((X = Y))))))). % less_imp_neq
thf(fact_76_less__asym, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((ord_less_nat @ Y @ X))))))). % less_asym
thf(fact_77_less__asym_H, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((ord_less_nat @ B @ A))))))). % less_asym'
thf(fact_78_less__trans, axiom,
    ((![X : nat, Y : nat, Z : nat]: ((ord_less_nat @ X @ Y) => ((ord_less_nat @ Y @ Z) => (ord_less_nat @ X @ Z)))))). % less_trans
thf(fact_79_less__linear, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) | ((X = Y) | (ord_less_nat @ Y @ X)))))). % less_linear
thf(fact_80_less__irrefl, axiom,
    ((![X : nat]: (~ ((ord_less_nat @ X @ X)))))). % less_irrefl
thf(fact_81_ord__eq__less__trans, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((A = B) => ((ord_less_nat @ B @ C2) => (ord_less_nat @ A @ C2)))))). % ord_eq_less_trans
thf(fact_82_ord__less__eq__trans, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_nat @ A @ B) => ((B = C2) => (ord_less_nat @ A @ C2)))))). % ord_less_eq_trans
thf(fact_83_dual__order_Oasym, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ B @ A) => (~ ((ord_less_nat @ A @ B))))))). % dual_order.asym
thf(fact_84_less__imp__not__eq, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((X = Y))))))). % less_imp_not_eq
thf(fact_85_less__not__sym, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((ord_less_nat @ Y @ X))))))). % less_not_sym
thf(fact_86_less__induct, axiom,
    ((![P2 : nat > $o, A : nat]: ((![X3 : nat]: ((![Y5 : nat]: ((ord_less_nat @ Y5 @ X3) => (P2 @ Y5))) => (P2 @ X3))) => (P2 @ A))))). % less_induct
thf(fact_87_antisym__conv3, axiom,
    ((![Y : nat, X : nat]: ((~ ((ord_less_nat @ Y @ X))) => ((~ ((ord_less_nat @ X @ Y))) = (X = Y)))))). % antisym_conv3
thf(fact_88_less__imp__not__eq2, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((Y = X))))))). % less_imp_not_eq2
thf(fact_89_less__imp__triv, axiom,
    ((![X : nat, Y : nat, P2 : $o]: ((ord_less_nat @ X @ Y) => ((ord_less_nat @ Y @ X) => P2))))). % less_imp_triv
thf(fact_90_linorder__cases, axiom,
    ((![X : nat, Y : nat]: ((~ ((ord_less_nat @ X @ Y))) => ((~ ((X = Y))) => (ord_less_nat @ Y @ X)))))). % linorder_cases
thf(fact_91_dual__order_Oirrefl, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ A)))))). % dual_order.irrefl
thf(fact_92_order_Ostrict__trans, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C2) => (ord_less_nat @ A @ C2)))))). % order.strict_trans
thf(fact_93_less__imp__not__less, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((ord_less_nat @ Y @ X))))))). % less_imp_not_less
thf(fact_94_exists__least__iff, axiom,
    (((^[P4 : nat > $o]: (?[X5 : nat]: (P4 @ X5))) = (^[P5 : nat > $o]: (?[N3 : nat]: (((P5 @ N3)) & ((![M3 : nat]: (((ord_less_nat @ M3 @ N3)) => ((~ ((P5 @ M3))))))))))))). % exists_least_iff
thf(fact_95_linorder__less__wlog, axiom,
    ((![P2 : nat > nat > $o, A : nat, B : nat]: ((![A3 : nat, B3 : nat]: ((ord_less_nat @ A3 @ B3) => (P2 @ A3 @ B3))) => ((![A3 : nat]: (P2 @ A3 @ A3)) => ((![A3 : nat, B3 : nat]: ((P2 @ B3 @ A3) => (P2 @ A3 @ B3))) => (P2 @ A @ B))))))). % linorder_less_wlog
thf(fact_96_dual__order_Ostrict__trans, axiom,
    ((![B : nat, A : nat, C2 : nat]: ((ord_less_nat @ B @ A) => ((ord_less_nat @ C2 @ B) => (ord_less_nat @ C2 @ A)))))). % dual_order.strict_trans
thf(fact_97_not__less__iff__gr__or__eq, axiom,
    ((![X : nat, Y : nat]: ((~ ((ord_less_nat @ X @ Y))) = (((ord_less_nat @ Y @ X)) | ((X = Y))))))). % not_less_iff_gr_or_eq
thf(fact_98_order_Ostrict__implies__not__eq, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_99_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_100_not__Cons__self2, axiom,
    ((![X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt]: (~ (((cons_A1864255580le_alt @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_101_UNIV__witness, axiom,
    ((?[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_102_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ top_to685525675le_alt)))). % UNIV_witness
thf(fact_103_UNIV__witness, axiom,
    ((?[X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_104_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ top_to1799531699e_indi)))). % UNIV_witness
thf(fact_105_UNIV__eq__I, axiom,
    ((![A4 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A4)) => (top_to224369155le_alt = A4))))). % UNIV_eq_I
thf(fact_106_UNIV__eq__I, axiom,
    ((![A4 : set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ A4)) => (top_to685525675le_alt = A4))))). % UNIV_eq_I
thf(fact_107_UNIV__eq__I, axiom,
    ((![A4 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ A4)) => (top_to469035705le_alt = A4))))). % UNIV_eq_I
thf(fact_108_UNIV__eq__I, axiom,
    ((![A4 : set_Ar1007576579e_indi]: ((![X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ A4)) => (top_to1799531699e_indi = A4))))). % UNIV_eq_I
thf(fact_109_UNIV__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ (^[X4 : arrow_1429744205e_indi]: $true))))). % UNIV_def
thf(fact_110_top_Oextremum__strict, axiom,
    ((![A : set_Ar1007576579e_indi]: (~ ((ord_le1187139159e_indi @ top_to1799531699e_indi @ A)))))). % top.extremum_strict
thf(fact_111_top_Onot__eq__extremum, axiom,
    ((![A : set_Ar1007576579e_indi]: ((~ ((A = top_to1799531699e_indi))) = (ord_le1187139159e_indi @ A @ top_to1799531699e_indi))))). % top.not_eq_extremum
thf(fact_112_map__tailrec__rev_Oinduct, axiom,
    ((![P2 : (arrow_1857593510le_alt > arrow_1857593510le_alt) > list_A2130511660le_alt > list_A2130511660le_alt > $o, A0 : arrow_1857593510le_alt > arrow_1857593510le_alt, A1 : list_A2130511660le_alt, A22 : list_A2130511660le_alt]: ((![F3 : arrow_1857593510le_alt > arrow_1857593510le_alt, X_1 : list_A2130511660le_alt]: (P2 @ F3 @ nil_Ar277507244le_alt @ X_1)) => ((![F3 : arrow_1857593510le_alt > arrow_1857593510le_alt, A3 : arrow_1857593510le_alt, As : list_A2130511660le_alt, Bs : list_A2130511660le_alt]: ((P2 @ F3 @ As @ (cons_A1864255580le_alt @ (F3 @ A3) @ Bs)) => (P2 @ F3 @ (cons_A1864255580le_alt @ A3 @ As) @ Bs))) => (P2 @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_113_list__nonempty__induct, axiom,
    ((![Xs : list_A2130511660le_alt, P2 : list_A2130511660le_alt > $o]: ((~ ((Xs = nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt]: (P2 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((~ ((Xs2 = nil_Ar277507244le_alt))) => ((P2 @ Xs2) => (P2 @ (cons_A1864255580le_alt @ X3 @ Xs2))))) => (P2 @ Xs))))))). % list_nonempty_induct
thf(fact_114_successively_Oinduct, axiom,
    ((![P2 : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > list_A2130511660le_alt > $o, A0 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A1 : list_A2130511660le_alt]: ((![P6 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (P2 @ P6 @ nil_Ar277507244le_alt)) => ((![P6 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt]: (P2 @ P6 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))) => ((![P6 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((P2 @ P6 @ (cons_A1864255580le_alt @ Y3 @ Xs2)) => (P2 @ P6 @ (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y3 @ Xs2))))) => (P2 @ A0 @ A1))))))). % successively.induct
thf(fact_115_successively_Ocases, axiom,
    ((![X : produc1094320767le_alt]: ((![P6 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (~ ((X = (produc2047839287le_alt @ P6 @ nil_Ar277507244le_alt))))) => ((![P6 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt]: (~ ((X = (produc2047839287le_alt @ P6 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt)))))) => (~ ((![P6 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: (~ ((X = (produc2047839287le_alt @ P6 @ (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y3 @ Xs2)))))))))))))). % successively.cases
thf(fact_116_remdups__adj_Oinduct, axiom,
    ((![P2 : list_A2130511660le_alt > $o, A0 : list_A2130511660le_alt]: ((P2 @ nil_Ar277507244le_alt) => ((![X3 : arrow_1857593510le_alt]: (P2 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: (((X3 = Y3) => (P2 @ (cons_A1864255580le_alt @ X3 @ Xs2))) => (((~ ((X3 = Y3))) => (P2 @ (cons_A1864255580le_alt @ Y3 @ Xs2))) => (P2 @ (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y3 @ Xs2)))))) => (P2 @ A0))))))). % remdups_adj.induct
thf(fact_117_sorted__wrt_Oinduct, axiom,
    ((![P2 : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > list_A2130511660le_alt > $o, A0 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A1 : list_A2130511660le_alt]: ((![P6 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (P2 @ P6 @ nil_Ar277507244le_alt)) => ((![P6 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Ys : list_A2130511660le_alt]: ((P2 @ P6 @ Ys) => (P2 @ P6 @ (cons_A1864255580le_alt @ X3 @ Ys)))) => (P2 @ A0 @ A1)))))). % sorted_wrt.induct
thf(fact_118_remdups__adj_Ocases, axiom,
    ((![X : list_A2130511660le_alt]: ((~ ((X = nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt]: (~ ((X = (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))))) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: (~ ((X = (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y3 @ Xs2))))))))))))). % remdups_adj.cases
thf(fact_119_sorted__wrt_Ocases, axiom,
    ((![X : produc1094320767le_alt]: ((![P6 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (~ ((X = (produc2047839287le_alt @ P6 @ nil_Ar277507244le_alt))))) => (~ ((![P6 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Ys : list_A2130511660le_alt]: (~ ((X = (produc2047839287le_alt @ P6 @ (cons_A1864255580le_alt @ X3 @ Ys)))))))))))). % sorted_wrt.cases
thf(fact_120_transpose_Ocases, axiom,
    ((![X : list_l1515872562le_alt]: ((~ ((X = nil_li2110134322le_alt))) => ((![Xss : list_l1515872562le_alt]: (~ ((X = (cons_l157309922le_alt @ nil_Ar277507244le_alt @ Xss))))) => (~ ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Xss : list_l1515872562le_alt]: (~ ((X = (cons_l157309922le_alt @ (cons_A1864255580le_alt @ X3 @ Xs2) @ Xss)))))))))))). % transpose.cases
thf(fact_121_shuffles_Oinduct, axiom,
    ((![P2 : list_A2130511660le_alt > list_A2130511660le_alt > $o, A0 : list_A2130511660le_alt, A1 : list_A2130511660le_alt]: ((![X_1 : list_A2130511660le_alt]: (P2 @ nil_Ar277507244le_alt @ X_1)) => ((![Xs2 : list_A2130511660le_alt]: (P2 @ Xs2 @ nil_Ar277507244le_alt)) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Y3 : arrow_1857593510le_alt, Ys : list_A2130511660le_alt]: ((P2 @ Xs2 @ (cons_A1864255580le_alt @ Y3 @ Ys)) => ((P2 @ (cons_A1864255580le_alt @ X3 @ Xs2) @ Ys) => (P2 @ (cons_A1864255580le_alt @ X3 @ Xs2) @ (cons_A1864255580le_alt @ Y3 @ Ys))))) => (P2 @ A0 @ A1))))))). % shuffles.induct
thf(fact_122_shuffles_Ocases, axiom,
    ((![X : produc518943027le_alt]: ((![Ys : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ nil_Ar277507244le_alt @ Ys))))) => ((![Xs2 : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ Xs2 @ nil_Ar277507244le_alt))))) => (~ ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Y3 : arrow_1857593510le_alt, Ys : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ (cons_A1864255580le_alt @ X3 @ Xs2) @ (cons_A1864255580le_alt @ Y3 @ Ys))))))))))))). % shuffles.cases
thf(fact_123_induct__list012, axiom,
    ((![P2 : list_A2130511660le_alt > $o, Xs : list_A2130511660le_alt]: ((P2 @ nil_Ar277507244le_alt) => ((![X3 : arrow_1857593510le_alt]: (P2 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Zs : list_A2130511660le_alt]: ((P2 @ Zs) => ((P2 @ (cons_A1864255580le_alt @ Y3 @ Zs)) => (P2 @ (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y3 @ Zs)))))) => (P2 @ Xs))))))). % induct_list012
thf(fact_124_splice_Oinduct, axiom,
    ((![P2 : list_A2130511660le_alt > list_A2130511660le_alt > $o, A0 : list_A2130511660le_alt, A1 : list_A2130511660le_alt]: ((![X_1 : list_A2130511660le_alt]: (P2 @ nil_Ar277507244le_alt @ X_1)) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Ys : list_A2130511660le_alt]: ((P2 @ Ys @ Xs2) => (P2 @ (cons_A1864255580le_alt @ X3 @ Xs2) @ Ys))) => (P2 @ A0 @ A1)))))). % splice.induct
thf(fact_125_list__induct2_H, axiom,
    ((![P2 : list_A2130511660le_alt > list_A2130511660le_alt > $o, Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((P2 @ nil_Ar277507244le_alt @ nil_Ar277507244le_alt) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: (P2 @ (cons_A1864255580le_alt @ X3 @ Xs2) @ nil_Ar277507244le_alt)) => ((![Y3 : arrow_1857593510le_alt, Ys : list_A2130511660le_alt]: (P2 @ nil_Ar277507244le_alt @ (cons_A1864255580le_alt @ Y3 @ Ys))) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Y3 : arrow_1857593510le_alt, Ys : list_A2130511660le_alt]: ((P2 @ Xs2 @ Ys) => (P2 @ (cons_A1864255580le_alt @ X3 @ Xs2) @ (cons_A1864255580le_alt @ Y3 @ Ys)))) => (P2 @ Xs @ Ys2)))))))). % list_induct2'
thf(fact_126_splice_Ocases, axiom,
    ((![X : produc518943027le_alt]: ((![Ys : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ nil_Ar277507244le_alt @ Ys))))) => (~ ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Ys : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ (cons_A1864255580le_alt @ X3 @ Xs2) @ Ys))))))))))). % splice.cases
thf(fact_127_neq__Nil__conv, axiom,
    ((![Xs : list_A2130511660le_alt]: ((~ ((Xs = nil_Ar277507244le_alt))) = (?[Y4 : arrow_1857593510le_alt]: (?[Ys3 : list_A2130511660le_alt]: (Xs = (cons_A1864255580le_alt @ Y4 @ Ys3)))))))). % neq_Nil_conv
thf(fact_128_list_Oinducts, axiom,
    ((![P2 : list_A2130511660le_alt > $o, List : list_A2130511660le_alt]: ((P2 @ nil_Ar277507244le_alt) => ((![X12 : arrow_1857593510le_alt, X23 : list_A2130511660le_alt]: ((P2 @ X23) => (P2 @ (cons_A1864255580le_alt @ X12 @ X23)))) => (P2 @ List)))))). % list.inducts
thf(fact_129_list_Oexhaust, axiom,
    ((![Y : list_A2130511660le_alt]: ((~ ((Y = nil_Ar277507244le_alt))) => (~ ((![X212 : arrow_1857593510le_alt, X222 : list_A2130511660le_alt]: (~ ((Y = (cons_A1864255580le_alt @ X212 @ X222))))))))))). % list.exhaust
thf(fact_130_list_OdiscI, axiom,
    ((![List : list_A2130511660le_alt, X21 : arrow_1857593510le_alt, X22 : list_A2130511660le_alt]: ((List = (cons_A1864255580le_alt @ X21 @ X22)) => (~ ((List = nil_Ar277507244le_alt))))))). % list.discI
thf(fact_131_list_Odistinct_I1_J, axiom,
    ((![X21 : arrow_1857593510le_alt, X22 : list_A2130511660le_alt]: (~ ((nil_Ar277507244le_alt = (cons_A1864255580le_alt @ X21 @ X22))))))). % list.distinct(1)
thf(fact_132_distinct__length__2__or__more, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, Xs : list_A2130511660le_alt]: ((distin2037765919le_alt @ (cons_A1864255580le_alt @ A @ (cons_A1864255580le_alt @ B @ Xs))) = (((~ ((A = B)))) & ((((distin2037765919le_alt @ (cons_A1864255580le_alt @ A @ Xs))) & ((distin2037765919le_alt @ (cons_A1864255580le_alt @ B @ Xs)))))))))). % distinct_length_2_or_more
thf(fact_133_distinct_Osimps_I1_J, axiom,
    ((distin2037765919le_alt @ nil_Ar277507244le_alt))). % distinct.simps(1)
thf(fact_134_inv__equality, axiom,
    ((![G : nat > arrow_1429744205e_indi, F : arrow_1429744205e_indi > nat]: ((![X3 : arrow_1429744205e_indi]: ((G @ (F @ X3)) = X3)) => ((![Y3 : nat]: ((F @ (G @ Y3)) = Y3)) => ((hilber1586975467di_nat @ top_to1799531699e_indi @ F) = G)))))). % inv_equality
thf(fact_135_distinct__union, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((distin2037765919le_alt @ (union_420169888le_alt @ Xs @ Ys2)) = (distin2037765919le_alt @ Ys2))))). % distinct_union
thf(fact_136_in__below, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_887341619_below @ L @ A @ B)) = (((~ ((X = Y)))) & ((((((Y = A)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ B) @ L)))) & ((((~ ((Y = A)))) => ((((((X = A)) => ((((Y = B)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y) @ L)))))) & ((((~ ((X = A)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))))))))). % in_below

% Helper facts (3)
thf(help_If_3_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_T, axiom,
    ((![P2 : $o]: ((P2 = $true) | (P2 = $false))))).
thf(help_If_2_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_T, axiom,
    ((![X : set_Pr367596371le_alt, Y : set_Pr367596371le_alt]: ((if_set550155277le_alt @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_T, axiom,
    ((![X : set_Pr367596371le_alt, Y : set_Pr367596371le_alt]: ((if_set550155277le_alt @ $true @ X @ Y) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((![I2 : arrow_1429744205e_indi]: (~ (((member2048039092le_alt @ (produc1494124311le_alt @ c @ d) @ (p @ I2)) = (~ ((((((ord_less_nat @ (h @ I2) @ n)) => ((member2048039092le_alt @ (produc1494124311le_alt @ c @ d) @ (arrow_992294841_mktop @ (p @ I2) @ e))))) & ((((~ ((ord_less_nat @ (h @ I2) @ n)))) => (((((((h @ I2) = n)) => ((member2048039092le_alt @ (produc1494124311le_alt @ c @ d) @ (arrow_1726226719_above @ (p @ I2) @ c @ e))))) & ((((~ (((h @ I2) = n)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ c @ d) @ (arrow_843587755_mkbot @ (p @ I2) @ e)))))))))))))))))).
