% 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/StrongNorm/prob_58__5209810_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:37:08.834

% Could-be-implicit typings (6)
thf(ty_n_t__List__Olist_It__Lambda__OdB_J, type,
    list_dB : $tType).
thf(ty_n_t__Set__Oset_It__Lambda__OdB_J, type,
    set_dB : $tType).
thf(ty_n_t__List__Olist_It__Nat__Onat_J, type,
    list_nat : $tType).
thf(ty_n_t__Set__Oset_It__Nat__Onat_J, type,
    set_nat : $tType).
thf(ty_n_t__Lambda__OdB, type,
    dB : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (38)
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat, type,
    one_one_nat : nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_InductTermi_OIT, type,
    it : dB > $o).
thf(sy_c_Lambda_OdB_OAbs, type,
    abs : dB > dB).
thf(sy_c_Lambda_OdB_OApp, type,
    app : dB > dB > dB).
thf(sy_c_Lambda_OdB_OVar, type,
    var : nat > dB).
thf(sy_c_Lambda_OdB_Osize__dB, type,
    size_dB : dB > nat).
thf(sy_c_Lambda_Olift, type,
    lift : dB > nat > dB).
thf(sy_c_Lambda_Oliftn, type,
    liftn : nat > dB > nat > dB).
thf(sy_c_Lambda_Osubst, type,
    subst : dB > dB > nat > dB).
thf(sy_c_Lambda_Osubstn, type,
    substn : dB > dB > nat > dB).
thf(sy_c_List_Ocount__list_001t__Lambda__OdB, type,
    count_list_dB : list_dB > dB > nat).
thf(sy_c_List_Ofoldl_001t__Lambda__OdB_001t__Lambda__OdB, type,
    foldl_dB_dB : (dB > dB > dB) > dB > list_dB > dB).
thf(sy_c_List_Ofoldl_001t__Lambda__OdB_001t__Nat__Onat, type,
    foldl_dB_nat : (dB > nat > dB) > dB > list_nat > dB).
thf(sy_c_List_Ofoldl_001t__Nat__Onat_001t__Lambda__OdB, type,
    foldl_nat_dB : (nat > dB > nat) > nat > list_dB > nat).
thf(sy_c_List_Ofoldl_001t__Nat__Onat_001t__Nat__Onat, type,
    foldl_nat_nat : (nat > nat > nat) > nat > list_nat > nat).
thf(sy_c_List_Ogen__length_001t__Lambda__OdB, type,
    gen_length_dB : nat > list_dB > nat).
thf(sy_c_List_Olist_Omap_001t__Lambda__OdB_001t__Lambda__OdB, type,
    map_dB_dB : (dB > dB) > list_dB > list_dB).
thf(sy_c_List_Olist_Omap_001t__Lambda__OdB_001t__Nat__Onat, type,
    map_dB_nat : (dB > nat) > list_dB > list_nat).
thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat, type,
    map_nat_nat : (nat > nat) > list_nat > list_nat).
thf(sy_c_List_Olist_Oset_001t__Lambda__OdB, type,
    set_dB2 : list_dB > set_dB).
thf(sy_c_List_Olist_Oset_001t__Nat__Onat, type,
    set_nat2 : list_nat > set_nat).
thf(sy_c_List_Olistsp_001t__Lambda__OdB, type,
    listsp_dB : (dB > $o) > list_dB > $o).
thf(sy_c_List_Omap__tailrec_001t__Lambda__OdB_001t__Lambda__OdB, type,
    map_tailrec_dB_dB : (dB > dB) > list_dB > list_dB).
thf(sy_c_List_Omap__tailrec_001t__Lambda__OdB_001t__Nat__Onat, type,
    map_tailrec_dB_nat : (dB > nat) > list_dB > list_nat).
thf(sy_c_Nat_OSuc, type,
    suc : nat > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__Lambda__OdB, type,
    size_size_dB : dB > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Lambda__OdB_J, type,
    size_size_list_dB : list_dB > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J, type,
    size_size_list_nat : list_nat > nat).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_member_001t__Lambda__OdB, type,
    member_dB : dB > set_dB > $o).
thf(sy_c_member_001t__Nat__Onat, type,
    member_nat : nat > set_nat > $o).
thf(sy_v_ia, type,
    ia : nat).
thf(sy_v_ja, type,
    ja : nat).
thf(sy_v_ra, type,
    ra : dB).
thf(sy_v_s, type,
    s : dB).
thf(sy_v_ss, type,
    ss : list_dB).

% Relevant facts (150)
thf(fact_0_subst__map, axiom,
    ((![T : dB, Ts : list_dB, U : dB, I : nat]: ((subst @ (foldl_dB_dB @ app @ T @ Ts) @ U @ I) = (foldl_dB_dB @ app @ (subst @ T @ U @ I) @ (map_dB_dB @ (^[T2 : dB]: (subst @ T2 @ U @ I)) @ Ts)))))). % subst_map
thf(fact_1_Var__apps__eq__Var__apps__conv, axiom,
    ((![M : nat, Rs : list_dB, N : nat, Ss : list_dB]: (((foldl_dB_dB @ app @ (var @ M) @ Rs) = (foldl_dB_dB @ app @ (var @ N) @ Ss)) = (((M = N)) & ((Rs = Ss))))))). % Var_apps_eq_Var_apps_conv
thf(fact_2_Abs__apps__eq__Abs__apps__conv, axiom,
    ((![R : dB, Rs : list_dB, S : dB, Ss : list_dB]: (((foldl_dB_dB @ app @ (abs @ R) @ Rs) = (foldl_dB_dB @ app @ (abs @ S) @ Ss)) = (((R = S)) & ((Rs = Ss))))))). % Abs_apps_eq_Abs_apps_conv
thf(fact_3_Beta, axiom,
    ((![R : dB, S : dB, Ss : list_dB]: ((it @ (foldl_dB_dB @ app @ (subst @ R @ S @ zero_zero_nat) @ Ss)) => ((it @ S) => (it @ (foldl_dB_dB @ app @ (app @ (abs @ R) @ S) @ Ss))))))). % Beta
thf(fact_4_subst__eq, axiom,
    ((![K : nat, U : dB]: ((subst @ (var @ K) @ U @ K) = U)))). % subst_eq
thf(fact_5_apps__eq__tail__conv, axiom,
    ((![R : dB, Ts : list_dB, S : dB]: (((foldl_dB_dB @ app @ R @ Ts) = (foldl_dB_dB @ app @ S @ Ts)) = (R = S))))). % apps_eq_tail_conv
thf(fact_6_ex__head__tail, axiom,
    ((![T : dB]: (?[Ts2 : list_dB, H : dB]: ((T = (foldl_dB_dB @ app @ H @ Ts2)) & ((?[N2 : nat]: (H = (var @ N2))) | (?[U2 : dB]: (H = (abs @ U2))))))))). % ex_head_tail
thf(fact_7_Abs__App__neq__Var__apps, axiom,
    ((![S : dB, T : dB, N : nat, Ss : list_dB]: (~ (((app @ (abs @ S) @ T) = (foldl_dB_dB @ app @ (var @ N) @ Ss))))))). % Abs_App_neq_Var_apps
thf(fact_8_Var__apps__neq__Abs__apps, axiom,
    ((![N : nat, Ts : list_dB, R : dB, Ss : list_dB]: (~ (((foldl_dB_dB @ app @ (var @ N) @ Ts) = (foldl_dB_dB @ app @ (abs @ R) @ Ss))))))). % Var_apps_neq_Abs_apps
thf(fact_9_map__ident, axiom,
    (((map_dB_dB @ (^[X : dB]: X)) = (^[Xs : list_dB]: Xs)))). % map_ident
thf(fact_10_dB_Oinduct, axiom,
    ((![P : dB > $o, DB : dB]: ((![X2 : nat]: (P @ (var @ X2))) => ((![X1a : dB, X22 : dB]: ((P @ X1a) => ((P @ X22) => (P @ (app @ X1a @ X22))))) => ((![X2 : dB]: ((P @ X2) => (P @ (abs @ X2)))) => (P @ DB))))))). % dB.induct
thf(fact_11_dB_Oexhaust, axiom,
    ((![Y : dB]: ((![X1 : nat]: (~ ((Y = (var @ X1))))) => ((![X21 : dB, X222 : dB]: (~ ((Y = (app @ X21 @ X222))))) => (~ ((![X3 : dB]: (~ ((Y = (abs @ X3)))))))))))). % dB.exhaust
thf(fact_12_dB_Oinject_I2_J, axiom,
    ((![X212 : dB, X223 : dB, Y21 : dB, Y22 : dB]: (((app @ X212 @ X223) = (app @ Y21 @ Y22)) = (((X212 = Y21)) & ((X223 = Y22))))))). % dB.inject(2)
thf(fact_13_dB_Oinject_I3_J, axiom,
    ((![X32 : dB, Y3 : dB]: (((abs @ X32) = (abs @ Y3)) = (X32 = Y3))))). % dB.inject(3)
thf(fact_14_dB_Oinject_I1_J, axiom,
    ((![X12 : nat, Y1 : nat]: (((var @ X12) = (var @ Y1)) = (X12 = Y1))))). % dB.inject(1)
thf(fact_15_list_Omap__ident, axiom,
    ((![T : list_dB]: ((map_dB_dB @ (^[X : dB]: X) @ T) = T)))). % list.map_ident
thf(fact_16_dB_Odistinct_I5_J, axiom,
    ((![X212 : dB, X223 : dB, X32 : dB]: (~ (((app @ X212 @ X223) = (abs @ X32))))))). % dB.distinct(5)
thf(fact_17_dB_Odistinct_I1_J, axiom,
    ((![X12 : nat, X212 : dB, X223 : dB]: (~ (((var @ X12) = (app @ X212 @ X223))))))). % dB.distinct(1)
thf(fact_18_subst__App, axiom,
    ((![T : dB, U : dB, S : dB, K : nat]: ((subst @ (app @ T @ U) @ S @ K) = (app @ (subst @ T @ S @ K) @ (subst @ U @ S @ K)))))). % subst_App
thf(fact_19_dB_Odistinct_I3_J, axiom,
    ((![X12 : nat, X32 : dB]: (~ (((var @ X12) = (abs @ X32))))))). % dB.distinct(3)
thf(fact_20_Lambda, axiom,
    ((![R : dB]: ((it @ R) => (it @ (abs @ R)))))). % Lambda
thf(fact_21_foldl__map, axiom,
    ((![G : nat > nat > nat, A : nat, F : nat > nat, Xs2 : list_nat]: ((foldl_nat_nat @ G @ A @ (map_nat_nat @ F @ Xs2)) = (foldl_nat_nat @ (^[A2 : nat]: (^[X : nat]: (G @ A2 @ (F @ X)))) @ A @ Xs2))))). % foldl_map
thf(fact_22_foldl__map, axiom,
    ((![G : dB > dB > dB, A : dB, F : dB > dB, Xs2 : list_dB]: ((foldl_dB_dB @ G @ A @ (map_dB_dB @ F @ Xs2)) = (foldl_dB_dB @ (^[A2 : dB]: (^[X : dB]: (G @ A2 @ (F @ X)))) @ A @ Xs2))))). % foldl_map
thf(fact_23_foldl__map, axiom,
    ((![G : dB > nat > dB, A : dB, F : dB > nat, Xs2 : list_dB]: ((foldl_dB_nat @ G @ A @ (map_dB_nat @ F @ Xs2)) = (foldl_dB_dB @ (^[A2 : dB]: (^[X : dB]: (G @ A2 @ (F @ X)))) @ A @ Xs2))))). % foldl_map
thf(fact_24_foldl__map, axiom,
    ((![G : nat > nat > nat, A : nat, F : dB > nat, Xs2 : list_dB]: ((foldl_nat_nat @ G @ A @ (map_dB_nat @ F @ Xs2)) = (foldl_nat_dB @ (^[A2 : nat]: (^[X : dB]: (G @ A2 @ (F @ X)))) @ A @ Xs2))))). % foldl_map
thf(fact_25_IT_Oinducts, axiom,
    ((![X4 : dB, P : dB > $o]: ((it @ X4) => ((![Rs2 : list_dB, N2 : nat]: ((listsp_dB @ (^[X : dB]: (((it @ X)) & ((P @ X)))) @ Rs2) => (P @ (foldl_dB_dB @ app @ (var @ N2) @ Rs2)))) => ((![R2 : dB]: ((it @ R2) => ((P @ R2) => (P @ (abs @ R2))))) => ((![R2 : dB, S2 : dB, Ss2 : list_dB]: ((it @ (foldl_dB_dB @ app @ (subst @ R2 @ S2 @ zero_zero_nat) @ Ss2)) => ((P @ (foldl_dB_dB @ app @ (subst @ R2 @ S2 @ zero_zero_nat) @ Ss2)) => ((it @ S2) => ((P @ S2) => (P @ (foldl_dB_dB @ app @ (app @ (abs @ R2) @ S2) @ Ss2))))))) => (P @ X4)))))))). % IT.inducts
thf(fact_26_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_27_nat_Oinject, axiom,
    ((![X23 : nat, Y2 : nat]: (((suc @ X23) = (suc @ Y2)) = (X23 = Y2))))). % nat.inject
thf(fact_28_IT_Osimps, axiom,
    ((it = (^[A2 : dB]: (((?[Rs3 : list_dB]: (?[N3 : nat]: (((A2 = (foldl_dB_dB @ app @ (var @ N3) @ Rs3))) & ((listsp_dB @ it @ Rs3)))))) | ((((?[R3 : dB]: (((A2 = (abs @ R3))) & ((it @ R3))))) | ((?[R3 : dB]: (?[S3 : dB]: (?[Ss3 : list_dB]: (((A2 = (foldl_dB_dB @ app @ (app @ (abs @ R3) @ S3) @ Ss3))) & ((((it @ (foldl_dB_dB @ app @ (subst @ R3 @ S3 @ zero_zero_nat) @ Ss3))) & ((it @ S3)))))))))))))))). % IT.simps
thf(fact_29_IT_Ocases, axiom,
    ((![A : dB]: ((it @ A) => ((![Rs2 : list_dB]: ((?[N2 : nat]: (A = (foldl_dB_dB @ app @ (var @ N2) @ Rs2))) => (~ ((listsp_dB @ it @ Rs2))))) => ((![R2 : dB]: ((A = (abs @ R2)) => (~ ((it @ R2))))) => (~ ((![R2 : dB, S2 : dB, Ss2 : list_dB]: ((A = (foldl_dB_dB @ app @ (app @ (abs @ R2) @ S2) @ Ss2)) => ((it @ (foldl_dB_dB @ app @ (subst @ R2 @ S2 @ zero_zero_nat) @ Ss2)) => (~ ((it @ S2)))))))))))))). % IT.cases
thf(fact_30_not0__implies__Suc, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (?[M2 : nat]: (N = (suc @ M2))))))). % not0_implies_Suc
thf(fact_31_old_Onat_Oinducts, axiom,
    ((![P : nat > $o, Nat : nat]: ((P @ zero_zero_nat) => ((![Nat3 : nat]: ((P @ Nat3) => (P @ (suc @ Nat3)))) => (P @ Nat)))))). % old.nat.inducts
thf(fact_32_listsp__conj__eq, axiom,
    ((![A3 : dB > $o, B : dB > $o]: ((listsp_dB @ (^[X : dB]: (((A3 @ X)) & ((B @ X))))) = (^[X : list_dB]: (((listsp_dB @ A3 @ X)) & ((listsp_dB @ B @ X)))))))). % listsp_conj_eq
thf(fact_33_zero__reorient, axiom,
    ((![X4 : nat]: ((zero_zero_nat = X4) = (X4 = zero_zero_nat))))). % zero_reorient
thf(fact_34_Suc__inject, axiom,
    ((![X4 : nat, Y : nat]: (((suc @ X4) = (suc @ Y)) => (X4 = Y))))). % Suc_inject
thf(fact_35_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_36_IT_OVar, axiom,
    ((![Rs : list_dB, N : nat]: ((listsp_dB @ it @ Rs) => (it @ (foldl_dB_dB @ app @ (var @ N) @ Rs)))))). % IT.Var
thf(fact_37_nat_Odistinct_I1_J, axiom,
    ((![X23 : nat]: (~ ((zero_zero_nat = (suc @ X23))))))). % nat.distinct(1)
thf(fact_38_old_Onat_Odistinct_I2_J, axiom,
    ((![Nat2 : nat]: (~ (((suc @ Nat2) = zero_zero_nat)))))). % old.nat.distinct(2)
thf(fact_39_old_Onat_Odistinct_I1_J, axiom,
    ((![Nat2 : nat]: (~ ((zero_zero_nat = (suc @ Nat2))))))). % old.nat.distinct(1)
thf(fact_40_nat_OdiscI, axiom,
    ((![Nat : nat, X23 : nat]: ((Nat = (suc @ X23)) => (~ ((Nat = zero_zero_nat))))))). % nat.discI
thf(fact_41_nat__induct, axiom,
    ((![P : nat > $o, N : nat]: ((P @ zero_zero_nat) => ((![N2 : nat]: ((P @ N2) => (P @ (suc @ N2)))) => (P @ N)))))). % nat_induct
thf(fact_42_diff__induct, axiom,
    ((![P : nat > nat > $o, M : nat, N : nat]: ((![X2 : nat]: (P @ X2 @ zero_zero_nat)) => ((![Y4 : nat]: (P @ zero_zero_nat @ (suc @ Y4))) => ((![X2 : nat, Y4 : nat]: ((P @ X2 @ Y4) => (P @ (suc @ X2) @ (suc @ Y4)))) => (P @ M @ N))))))). % diff_induct
thf(fact_43_zero__induct, axiom,
    ((![P : nat > $o, K : nat]: ((P @ K) => ((![N2 : nat]: ((P @ (suc @ N2)) => (P @ N2))) => (P @ zero_zero_nat)))))). % zero_induct
thf(fact_44_Suc__neq__Zero, axiom,
    ((![M : nat]: (~ (((suc @ M) = zero_zero_nat)))))). % Suc_neq_Zero
thf(fact_45_Zero__neq__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_neq_Suc
thf(fact_46_Zero__not__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_not_Suc
thf(fact_47_old_Onat_Oexhaust, axiom,
    ((![Y : nat]: ((~ ((Y = zero_zero_nat))) => (~ ((![Nat3 : nat]: (~ ((Y = (suc @ Nat3))))))))))). % old.nat.exhaust
thf(fact_48_lifts__IT, axiom,
    ((![Ts : list_dB]: ((listsp_dB @ it @ Ts) => (listsp_dB @ it @ (map_dB_dB @ (^[T2 : dB]: (lift @ T2 @ zero_zero_nat)) @ Ts)))))). % lifts_IT
thf(fact_49_lift__map, axiom,
    ((![T : dB, Ts : list_dB, I : nat]: ((lift @ (foldl_dB_dB @ app @ T @ Ts) @ I) = (foldl_dB_dB @ app @ (lift @ T @ I) @ (map_dB_dB @ (^[T2 : dB]: (lift @ T2 @ I)) @ Ts)))))). % lift_map
thf(fact_50_dB_Osize__gen_I1_J, axiom,
    ((![X12 : nat]: ((size_dB @ (var @ X12)) = zero_zero_nat)))). % dB.size_gen(1)
thf(fact_51_map__eq__map__tailrec, axiom,
    ((map_dB_dB = map_tailrec_dB_dB))). % map_eq_map_tailrec
thf(fact_52_map__eq__map__tailrec, axiom,
    ((map_dB_nat = map_tailrec_dB_nat))). % map_eq_map_tailrec
thf(fact_53_substn__subst__0, axiom,
    ((![T : dB, S : dB]: ((substn @ T @ S @ zero_zero_nat) = (subst @ T @ S @ zero_zero_nat))))). % substn_subst_0
thf(fact_54_Apps__dB__induct, axiom,
    ((![P : dB > $o, T : dB]: ((![N2 : nat, Ts2 : list_dB]: ((![X5 : dB]: ((member_dB @ X5 @ (set_dB2 @ Ts2)) => (P @ X5))) => (P @ (foldl_dB_dB @ app @ (var @ N2) @ Ts2)))) => ((![U2 : dB]: ((P @ U2) => (![Ts2 : list_dB]: ((![X5 : dB]: ((member_dB @ X5 @ (set_dB2 @ Ts2)) => (P @ X5))) => (P @ (foldl_dB_dB @ app @ (abs @ U2) @ Ts2)))))) => (P @ T)))))). % Apps_dB_induct
thf(fact_55_map__eq__conv, axiom,
    ((![F : dB > dB, Xs2 : list_dB, G : dB > dB]: (((map_dB_dB @ F @ Xs2) = (map_dB_dB @ G @ Xs2)) = (![X : dB]: (((member_dB @ X @ (set_dB2 @ Xs2))) => (((F @ X) = (G @ X))))))))). % map_eq_conv
thf(fact_56_map__eq__conv, axiom,
    ((![F : dB > nat, Xs2 : list_dB, G : dB > nat]: (((map_dB_nat @ F @ Xs2) = (map_dB_nat @ G @ Xs2)) = (![X : dB]: (((member_dB @ X @ (set_dB2 @ Xs2))) => (((F @ X) = (G @ X))))))))). % map_eq_conv
thf(fact_57_in__listspI, axiom,
    ((![Xs2 : list_dB, A3 : dB > $o]: ((![X2 : dB]: ((member_dB @ X2 @ (set_dB2 @ Xs2)) => (A3 @ X2))) => (listsp_dB @ A3 @ Xs2))))). % in_listspI
thf(fact_58_subst__lift, axiom,
    ((![T : dB, K : nat, S : dB]: ((subst @ (lift @ T @ K) @ S @ K) = T)))). % subst_lift
thf(fact_59_lift__IT, axiom,
    ((![T : dB, I : nat]: ((it @ T) => (it @ (lift @ T @ I)))))). % lift_IT
thf(fact_60_list_Oinj__map__strong, axiom,
    ((![X4 : list_dB, Xa : list_dB, F : dB > dB, Fa : dB > dB]: ((![Z : dB, Za : dB]: ((member_dB @ Z @ (set_dB2 @ X4)) => ((member_dB @ Za @ (set_dB2 @ Xa)) => (((F @ Z) = (Fa @ Za)) => (Z = Za))))) => (((map_dB_dB @ F @ X4) = (map_dB_dB @ Fa @ Xa)) => (X4 = Xa)))))). % list.inj_map_strong
thf(fact_61_list_Oinj__map__strong, axiom,
    ((![X4 : list_dB, Xa : list_dB, F : dB > nat, Fa : dB > nat]: ((![Z : dB, Za : dB]: ((member_dB @ Z @ (set_dB2 @ X4)) => ((member_dB @ Za @ (set_dB2 @ Xa)) => (((F @ Z) = (Fa @ Za)) => (Z = Za))))) => (((map_dB_nat @ F @ X4) = (map_dB_nat @ Fa @ Xa)) => (X4 = Xa)))))). % list.inj_map_strong
thf(fact_62_list_Omap__cong0, axiom,
    ((![X4 : list_dB, F : dB > dB, G : dB > dB]: ((![Z : dB]: ((member_dB @ Z @ (set_dB2 @ X4)) => ((F @ Z) = (G @ Z)))) => ((map_dB_dB @ F @ X4) = (map_dB_dB @ G @ X4)))))). % list.map_cong0
thf(fact_63_list_Omap__cong0, axiom,
    ((![X4 : list_dB, F : dB > nat, G : dB > nat]: ((![Z : dB]: ((member_dB @ Z @ (set_dB2 @ X4)) => ((F @ Z) = (G @ Z)))) => ((map_dB_nat @ F @ X4) = (map_dB_nat @ G @ X4)))))). % list.map_cong0
thf(fact_64_list_Omap__cong, axiom,
    ((![X4 : list_dB, Ya : list_dB, F : dB > dB, G : dB > dB]: ((X4 = Ya) => ((![Z : dB]: ((member_dB @ Z @ (set_dB2 @ Ya)) => ((F @ Z) = (G @ Z)))) => ((map_dB_dB @ F @ X4) = (map_dB_dB @ G @ Ya))))))). % list.map_cong
thf(fact_65_list_Omap__cong, axiom,
    ((![X4 : list_dB, Ya : list_dB, F : dB > nat, G : dB > nat]: ((X4 = Ya) => ((![Z : dB]: ((member_dB @ Z @ (set_dB2 @ Ya)) => ((F @ Z) = (G @ Z)))) => ((map_dB_nat @ F @ X4) = (map_dB_nat @ G @ Ya))))))). % list.map_cong
thf(fact_66_ex__map__conv, axiom,
    ((![Ys : list_nat, F : dB > nat]: ((?[Xs : list_dB]: (Ys = (map_dB_nat @ F @ Xs))) = (![X : nat]: (((member_nat @ X @ (set_nat2 @ Ys))) => ((?[Y5 : dB]: (X = (F @ Y5)))))))))). % ex_map_conv
thf(fact_67_ex__map__conv, axiom,
    ((![Ys : list_dB, F : dB > dB]: ((?[Xs : list_dB]: (Ys = (map_dB_dB @ F @ Xs))) = (![X : dB]: (((member_dB @ X @ (set_dB2 @ Ys))) => ((?[Y5 : dB]: (X = (F @ Y5)))))))))). % ex_map_conv
thf(fact_68_map__cong, axiom,
    ((![Xs2 : list_dB, Ys : list_dB, F : dB > dB, G : dB > dB]: ((Xs2 = Ys) => ((![X2 : dB]: ((member_dB @ X2 @ (set_dB2 @ Ys)) => ((F @ X2) = (G @ X2)))) => ((map_dB_dB @ F @ Xs2) = (map_dB_dB @ G @ Ys))))))). % map_cong
thf(fact_69_map__cong, axiom,
    ((![Xs2 : list_dB, Ys : list_dB, F : dB > nat, G : dB > nat]: ((Xs2 = Ys) => ((![X2 : dB]: ((member_dB @ X2 @ (set_dB2 @ Ys)) => ((F @ X2) = (G @ X2)))) => ((map_dB_nat @ F @ Xs2) = (map_dB_nat @ G @ Ys))))))). % map_cong
thf(fact_70_map__idI, axiom,
    ((![Xs2 : list_dB, F : dB > dB]: ((![X2 : dB]: ((member_dB @ X2 @ (set_dB2 @ Xs2)) => ((F @ X2) = X2))) => ((map_dB_dB @ F @ Xs2) = Xs2))))). % map_idI
thf(fact_71_map__ext, axiom,
    ((![Xs2 : list_dB, F : dB > dB, G : dB > dB]: ((![X2 : dB]: ((member_dB @ X2 @ (set_dB2 @ Xs2)) => ((F @ X2) = (G @ X2)))) => ((map_dB_dB @ F @ Xs2) = (map_dB_dB @ G @ Xs2)))))). % map_ext
thf(fact_72_map__ext, axiom,
    ((![Xs2 : list_dB, F : dB > nat, G : dB > nat]: ((![X2 : dB]: ((member_dB @ X2 @ (set_dB2 @ Xs2)) => ((F @ X2) = (G @ X2)))) => ((map_dB_nat @ F @ Xs2) = (map_dB_nat @ G @ Xs2)))))). % map_ext
thf(fact_73_foldl__cong, axiom,
    ((![A : nat, B2 : nat, L : list_nat, K : list_nat, F : nat > nat > nat, G : nat > nat > nat]: ((A = B2) => ((L = K) => ((![A4 : nat, X2 : nat]: ((member_nat @ X2 @ (set_nat2 @ L)) => ((F @ A4 @ X2) = (G @ A4 @ X2)))) => ((foldl_nat_nat @ F @ A @ L) = (foldl_nat_nat @ G @ B2 @ K)))))))). % foldl_cong
thf(fact_74_foldl__cong, axiom,
    ((![A : dB, B2 : dB, L : list_dB, K : list_dB, F : dB > dB > dB, G : dB > dB > dB]: ((A = B2) => ((L = K) => ((![A4 : dB, X2 : dB]: ((member_dB @ X2 @ (set_dB2 @ L)) => ((F @ A4 @ X2) = (G @ A4 @ X2)))) => ((foldl_dB_dB @ F @ A @ L) = (foldl_dB_dB @ G @ B2 @ K)))))))). % foldl_cong
thf(fact_75_in__listsp__conv__set, axiom,
    ((listsp_dB = (^[A5 : dB > $o]: (^[Xs : list_dB]: (![X : dB]: (((member_dB @ X @ (set_dB2 @ Xs))) => ((A5 @ X))))))))). % in_listsp_conv_set
thf(fact_76_in__listspD, axiom,
    ((![A3 : dB > $o, Xs2 : list_dB]: ((listsp_dB @ A3 @ Xs2) => (![X5 : dB]: ((member_dB @ X5 @ (set_dB2 @ Xs2)) => (A3 @ X5))))))). % in_listspD
thf(fact_77_lift_Osimps_I2_J, axiom,
    ((![S : dB, T : dB, K : nat]: ((lift @ (app @ S @ T) @ K) = (app @ (lift @ S @ K) @ (lift @ T @ K)))))). % lift.simps(2)
thf(fact_78_substn_Osimps_I2_J, axiom,
    ((![T : dB, U : dB, S : dB, K : nat]: ((substn @ (app @ T @ U) @ S @ K) = (app @ (substn @ T @ S @ K) @ (substn @ U @ S @ K)))))). % substn.simps(2)
thf(fact_79_lem, axiom,
    ((![P : dB > $o, T : dB, N : nat]: ((![N2 : nat, Ts2 : list_dB]: ((![X5 : dB]: ((member_dB @ X5 @ (set_dB2 @ Ts2)) => (P @ X5))) => (P @ (foldl_dB_dB @ app @ (var @ N2) @ Ts2)))) => ((![U2 : dB]: ((P @ U2) => (![Ts2 : list_dB]: ((![X5 : dB]: ((member_dB @ X5 @ (set_dB2 @ Ts2)) => (P @ X5))) => (P @ (foldl_dB_dB @ app @ (abs @ U2) @ Ts2)))))) => (((size_size_dB @ T) = N) => (P @ T))))))). % lem
thf(fact_80_substn__subst__n, axiom,
    ((substn = (^[T2 : dB]: (^[S3 : dB]: (^[N3 : nat]: (subst @ T2 @ (liftn @ N3 @ S3 @ zero_zero_nat) @ N3))))))). % substn_subst_n
thf(fact_81_count__notin, axiom,
    ((![X4 : dB, Xs2 : list_dB]: ((~ ((member_dB @ X4 @ (set_dB2 @ Xs2)))) => ((count_list_dB @ Xs2 @ X4) = zero_zero_nat))))). % count_notin
thf(fact_82_liftn__lift, axiom,
    ((![N : nat, T : dB, K : nat]: ((liftn @ (suc @ N) @ T @ K) = (lift @ (liftn @ N @ T @ K) @ K))))). % liftn_lift
thf(fact_83_dB_Osize__gen_I3_J, axiom,
    ((![X32 : dB]: ((size_dB @ (abs @ X32)) = (plus_plus_nat @ (size_dB @ X32) @ (suc @ zero_zero_nat)))))). % dB.size_gen(3)
thf(fact_84_add__left__cancel, axiom,
    ((![A : nat, B2 : nat, C : nat]: (((plus_plus_nat @ A @ B2) = (plus_plus_nat @ A @ C)) = (B2 = C))))). % add_left_cancel
thf(fact_85_add__right__cancel, axiom,
    ((![B2 : nat, A : nat, C : nat]: (((plus_plus_nat @ B2 @ A) = (plus_plus_nat @ C @ A)) = (B2 = C))))). % add_right_cancel
thf(fact_86_add_Oleft__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A)))). % add.left_neutral
thf(fact_87_add_Oright__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % add.right_neutral
thf(fact_88_add__cancel__left__left, axiom,
    ((![B2 : nat, A : nat]: (((plus_plus_nat @ B2 @ A) = A) = (B2 = zero_zero_nat))))). % add_cancel_left_left
thf(fact_89_add__cancel__left__right, axiom,
    ((![A : nat, B2 : nat]: (((plus_plus_nat @ A @ B2) = A) = (B2 = zero_zero_nat))))). % add_cancel_left_right
thf(fact_90_add__cancel__right__left, axiom,
    ((![A : nat, B2 : nat]: ((A = (plus_plus_nat @ B2 @ A)) = (B2 = zero_zero_nat))))). % add_cancel_right_left
thf(fact_91_add__cancel__right__right, axiom,
    ((![A : nat, B2 : nat]: ((A = (plus_plus_nat @ A @ B2)) = (B2 = zero_zero_nat))))). % add_cancel_right_right
thf(fact_92_add__eq__0__iff__both__eq__0, axiom,
    ((![X4 : nat, Y : nat]: (((plus_plus_nat @ X4 @ Y) = zero_zero_nat) = (((X4 = zero_zero_nat)) & ((Y = zero_zero_nat))))))). % add_eq_0_iff_both_eq_0
thf(fact_93_zero__eq__add__iff__both__eq__0, axiom,
    ((![X4 : nat, Y : nat]: ((zero_zero_nat = (plus_plus_nat @ X4 @ Y)) = (((X4 = zero_zero_nat)) & ((Y = zero_zero_nat))))))). % zero_eq_add_iff_both_eq_0
thf(fact_94_add__is__0, axiom,
    ((![M : nat, N : nat]: (((plus_plus_nat @ M @ N) = zero_zero_nat) = (((M = zero_zero_nat)) & ((N = zero_zero_nat))))))). % add_is_0
thf(fact_95_Nat_Oadd__0__right, axiom,
    ((![M : nat]: ((plus_plus_nat @ M @ zero_zero_nat) = M)))). % Nat.add_0_right
thf(fact_96_add__Suc__right, axiom,
    ((![M : nat, N : nat]: ((plus_plus_nat @ M @ (suc @ N)) = (suc @ (plus_plus_nat @ M @ N)))))). % add_Suc_right
thf(fact_97_liftn__0, axiom,
    ((![T : dB, K : nat]: ((liftn @ zero_zero_nat @ T @ K) = T)))). % liftn_0
thf(fact_98_size__neq__size__imp__neq, axiom,
    ((![X4 : dB, Y : dB]: ((~ (((size_size_dB @ X4) = (size_size_dB @ Y)))) => (~ ((X4 = Y))))))). % size_neq_size_imp_neq
thf(fact_99_size__neq__size__imp__neq, axiom,
    ((![X4 : list_dB, Y : list_dB]: ((~ (((size_size_list_dB @ X4) = (size_size_list_dB @ Y)))) => (~ ((X4 = Y))))))). % size_neq_size_imp_neq
thf(fact_100_add_Ocomm__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % add.comm_neutral
thf(fact_101_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_102_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : nat, B2 : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B2) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B2 @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_103_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (K = L)) => ((plus_plus_nat @ I @ K) = (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_104_group__cancel_Oadd1, axiom,
    ((![A3 : nat, K : nat, A : nat, B2 : nat]: ((A3 = (plus_plus_nat @ K @ A)) => ((plus_plus_nat @ A3 @ B2) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B2))))))). % group_cancel.add1
thf(fact_105_group__cancel_Oadd2, axiom,
    ((![B : nat, K : nat, B2 : nat, A : nat]: ((B = (plus_plus_nat @ K @ B2)) => ((plus_plus_nat @ A @ B) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B2))))))). % group_cancel.add2
thf(fact_106_add_Oassoc, axiom,
    ((![A : nat, B2 : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B2) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B2 @ C)))))). % add.assoc
thf(fact_107_add_Ocommute, axiom,
    ((plus_plus_nat = (^[A2 : nat]: (^[B3 : nat]: (plus_plus_nat @ B3 @ A2)))))). % add.commute
thf(fact_108_add_Oleft__commute, axiom,
    ((![B2 : nat, A : nat, C : nat]: ((plus_plus_nat @ B2 @ (plus_plus_nat @ A @ C)) = (plus_plus_nat @ A @ (plus_plus_nat @ B2 @ C)))))). % add.left_commute
thf(fact_109_add__left__imp__eq, axiom,
    ((![A : nat, B2 : nat, C : nat]: (((plus_plus_nat @ A @ B2) = (plus_plus_nat @ A @ C)) => (B2 = C))))). % add_left_imp_eq
thf(fact_110_add__right__imp__eq, axiom,
    ((![B2 : nat, A : nat, C : nat]: (((plus_plus_nat @ B2 @ A) = (plus_plus_nat @ C @ A)) => (B2 = C))))). % add_right_imp_eq
thf(fact_111_plus__nat_Oadd__0, axiom,
    ((![N : nat]: ((plus_plus_nat @ zero_zero_nat @ N) = N)))). % plus_nat.add_0
thf(fact_112_add__eq__self__zero, axiom,
    ((![M : nat, N : nat]: (((plus_plus_nat @ M @ N) = M) => (N = zero_zero_nat))))). % add_eq_self_zero
thf(fact_113_add__Suc__shift, axiom,
    ((![M : nat, N : nat]: ((plus_plus_nat @ (suc @ M) @ N) = (plus_plus_nat @ M @ (suc @ N)))))). % add_Suc_shift
thf(fact_114_nat__arith_Osuc1, axiom,
    ((![A3 : nat, K : nat, A : nat]: ((A3 = (plus_plus_nat @ K @ A)) => ((suc @ A3) = (plus_plus_nat @ K @ (suc @ A))))))). % nat_arith.suc1
thf(fact_115_add__Suc, axiom,
    ((![M : nat, N : nat]: ((plus_plus_nat @ (suc @ M) @ N) = (suc @ (plus_plus_nat @ M @ N)))))). % add_Suc
thf(fact_116_dB_Osize_I5_J, axiom,
    ((![X212 : dB, X223 : dB]: ((size_size_dB @ (app @ X212 @ X223)) = (plus_plus_nat @ (plus_plus_nat @ (size_size_dB @ X212) @ (size_size_dB @ X223)) @ (suc @ zero_zero_nat)))))). % dB.size(5)
thf(fact_117_dB_Osize_I6_J, axiom,
    ((![X32 : dB]: ((size_size_dB @ (abs @ X32)) = (plus_plus_nat @ (size_size_dB @ X32) @ (suc @ zero_zero_nat)))))). % dB.size(6)
thf(fact_118_add__is__1, axiom,
    ((![M : nat, N : nat]: (((plus_plus_nat @ M @ N) = (suc @ zero_zero_nat)) = (((((M = (suc @ zero_zero_nat))) & ((N = zero_zero_nat)))) | ((((M = zero_zero_nat)) & ((N = (suc @ zero_zero_nat)))))))))). % add_is_1
thf(fact_119_one__is__add, axiom,
    ((![M : nat, N : nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ M @ N)) = (((((M = (suc @ zero_zero_nat))) & ((N = zero_zero_nat)))) | ((((M = zero_zero_nat)) & ((N = (suc @ zero_zero_nat)))))))))). % one_is_add
thf(fact_120_liftn_Osimps_I2_J, axiom,
    ((![N : nat, S : dB, T : dB, K : nat]: ((liftn @ N @ (app @ S @ T) @ K) = (app @ (liftn @ N @ S @ K) @ (liftn @ N @ T @ K)))))). % liftn.simps(2)
thf(fact_121_dB_Osize_I4_J, axiom,
    ((![X12 : nat]: ((size_size_dB @ (var @ X12)) = zero_zero_nat)))). % dB.size(4)
thf(fact_122_dB_Osize__gen_I2_J, axiom,
    ((![X212 : dB, X223 : dB]: ((size_dB @ (app @ X212 @ X223)) = (plus_plus_nat @ (plus_plus_nat @ (size_dB @ X212) @ (size_dB @ X223)) @ (suc @ zero_zero_nat)))))). % dB.size_gen(2)
thf(fact_123_Euclid__induct, axiom,
    ((![P : nat > nat > $o, A : nat, B2 : nat]: ((![A4 : nat, B4 : nat]: ((P @ A4 @ B4) = (P @ B4 @ A4))) => ((![A4 : nat]: (P @ A4 @ zero_zero_nat)) => ((![A4 : nat, B4 : nat]: ((P @ A4 @ B4) => (P @ A4 @ (plus_plus_nat @ A4 @ B4)))) => (P @ A @ B2))))))). % Euclid_induct
thf(fact_124_size__apps, axiom,
    ((![R : dB, Rs : list_dB]: ((size_size_dB @ (foldl_dB_dB @ app @ R @ Rs)) = (plus_plus_nat @ (plus_plus_nat @ (size_size_dB @ R) @ (foldl_nat_nat @ plus_plus_nat @ zero_zero_nat @ (map_dB_nat @ size_size_dB @ Rs))) @ (size_size_list_dB @ Rs)))))). % size_apps
thf(fact_125_add__0__iff, axiom,
    ((![B2 : nat, A : nat]: ((B2 = (plus_plus_nat @ B2 @ A)) = (A = zero_zero_nat))))). % add_0_iff
thf(fact_126_verit__sum__simplify, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % verit_sum_simplify
thf(fact_127_length__map, axiom,
    ((![F : dB > nat, Xs2 : list_dB]: ((size_size_list_nat @ (map_dB_nat @ F @ Xs2)) = (size_size_list_dB @ Xs2))))). % length_map
thf(fact_128_length__map, axiom,
    ((![F : dB > dB, Xs2 : list_dB]: ((size_size_list_dB @ (map_dB_dB @ F @ Xs2)) = (size_size_list_dB @ Xs2))))). % length_map
thf(fact_129_Ex__list__of__length, axiom,
    ((![N : nat]: (?[Xs3 : list_dB]: ((size_size_list_dB @ Xs3) = N))))). % Ex_list_of_length
thf(fact_130_neq__if__length__neq, axiom,
    ((![Xs2 : list_dB, Ys : list_dB]: ((~ (((size_size_list_dB @ Xs2) = (size_size_list_dB @ Ys)))) => (~ ((Xs2 = Ys))))))). % neq_if_length_neq
thf(fact_131_map__eq__imp__length__eq, axiom,
    ((![F : dB > dB, Xs2 : list_dB, G : dB > dB, Ys : list_dB]: (((map_dB_dB @ F @ Xs2) = (map_dB_dB @ G @ Ys)) => ((size_size_list_dB @ Xs2) = (size_size_list_dB @ Ys)))))). % map_eq_imp_length_eq
thf(fact_132_map__eq__imp__length__eq, axiom,
    ((![F : dB > nat, Xs2 : list_dB, G : dB > nat, Ys : list_dB]: (((map_dB_nat @ F @ Xs2) = (map_dB_nat @ G @ Ys)) => ((size_size_list_dB @ Xs2) = (size_size_list_dB @ Ys)))))). % map_eq_imp_length_eq
thf(fact_133_subst__Abs, axiom,
    ((![T : dB, S : dB, K : nat]: ((subst @ (abs @ T) @ S @ K) = (abs @ (subst @ T @ (lift @ S @ zero_zero_nat) @ (plus_plus_nat @ K @ one_one_nat))))))). % subst_Abs
thf(fact_134_gen__length__def, axiom,
    ((gen_length_dB = (^[N3 : nat]: (^[Xs : list_dB]: (plus_plus_nat @ N3 @ (size_size_list_dB @ Xs))))))). % gen_length_def
thf(fact_135_One__nat__def, axiom,
    ((one_one_nat = (suc @ zero_zero_nat)))). % One_nat_def
thf(fact_136_Suc__eq__plus1__left, axiom,
    ((suc = (plus_plus_nat @ one_one_nat)))). % Suc_eq_plus1_left
thf(fact_137_plus__1__eq__Suc, axiom,
    (((plus_plus_nat @ one_one_nat) = suc))). % plus_1_eq_Suc
thf(fact_138_Suc__eq__plus1, axiom,
    ((suc = (^[N3 : nat]: (plus_plus_nat @ N3 @ one_one_nat))))). % Suc_eq_plus1
thf(fact_139_one__reorient, axiom,
    ((![X4 : nat]: ((one_one_nat = X4) = (X4 = one_one_nat))))). % one_reorient
thf(fact_140_lift_Osimps_I3_J, axiom,
    ((![S : dB, K : nat]: ((lift @ (abs @ S) @ K) = (abs @ (lift @ S @ (plus_plus_nat @ K @ one_one_nat))))))). % lift.simps(3)
thf(fact_141_liftn_Osimps_I3_J, axiom,
    ((![N : nat, S : dB, K : nat]: ((liftn @ N @ (abs @ S) @ K) = (abs @ (liftn @ N @ S @ (plus_plus_nat @ K @ one_one_nat))))))). % liftn.simps(3)
thf(fact_142_substn_Osimps_I3_J, axiom,
    ((![T : dB, S : dB, K : nat]: ((substn @ (abs @ T) @ S @ K) = (abs @ (substn @ T @ S @ (plus_plus_nat @ K @ one_one_nat))))))). % substn.simps(3)
thf(fact_143_length__code, axiom,
    ((size_size_list_dB = (gen_length_dB @ zero_zero_nat)))). % length_code
thf(fact_144_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_145_subst__subst, axiom,
    ((![I : nat, J : nat, T : dB, V : dB, U : dB]: ((ord_less_nat @ I @ (plus_plus_nat @ J @ one_one_nat)) => ((subst @ (subst @ T @ (lift @ V @ I) @ (suc @ J)) @ (subst @ U @ V @ J) @ I) = (subst @ (subst @ T @ U @ I) @ V @ J)))))). % subst_subst
thf(fact_146_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_147_add__less__cancel__right, axiom,
    ((![A : nat, C : nat, B2 : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B2 @ C)) = (ord_less_nat @ A @ B2))))). % add_less_cancel_right
thf(fact_148_add__less__cancel__left, axiom,
    ((![C : nat, A : nat, B2 : nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B2)) = (ord_less_nat @ A @ B2))))). % add_less_cancel_left
thf(fact_149_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv

% Conjectures (5)
thf(conj_0, hypothesis,
    ((it @ (foldl_dB_dB @ app @ (subst @ ra @ s @ zero_zero_nat) @ ss)))).
thf(conj_1, hypothesis,
    ((![I2 : nat, J2 : nat]: (it @ (foldl_dB_dB @ app @ (subst @ (subst @ ra @ (var @ (suc @ I2)) @ (suc @ J2)) @ (subst @ s @ (var @ I2) @ J2) @ zero_zero_nat) @ (map_dB_dB @ (^[T2 : dB]: (subst @ T2 @ (var @ I2) @ J2)) @ ss)))))).
thf(conj_2, hypothesis,
    ((it @ s))).
thf(conj_3, hypothesis,
    ((![I2 : nat, J2 : nat]: (it @ (subst @ s @ (var @ I2) @ J2))))).
thf(conj_4, conjecture,
    ((it @ (foldl_dB_dB @ app @ (app @ (abs @ (subst @ ra @ (var @ (suc @ ia)) @ (suc @ ja))) @ (subst @ s @ (var @ ia) @ ja)) @ (map_dB_dB @ (^[T2 : dB]: (subst @ T2 @ (var @ ia) @ ja)) @ ss))))).
