TSTP Solution File: SCT071-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SCT071-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:22:02 EDT 2023
% Result : Unsatisfiable 241.17s 31.22s
% Output : Proof 241.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT071-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 15:13:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 241.17/31.22 Command-line arguments: --flatten
% 241.17/31.22
% 241.17/31.22 % SZS status Unsatisfiable
% 241.17/31.22
% 241.20/31.25 % SZS output start Proof
% 241.20/31.25 Take the following subset of the input axioms:
% 241.20/31.25 fof(cls_Int__UNIV__left_0, axiom, ![T_a, V_B]: c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(T_a, tc_bool)), V_B, tc_fun(T_a, tc_bool))=V_B).
% 241.20/31.25 fof(cls_bij__betw__def_0, axiom, ![V_f, T_b, V_A, T_a2, V_B2]: (c_Fun_Oinj__on(V_f, V_A, T_a2, T_b) | ~c_Fun_Obij__betw(V_f, V_A, V_B2, T_a2, T_b))).
% 241.20/31.25 fof(cls_bij__betw__def_1, axiom, ![V_f2, T_a2, T_b2, V_A2, V_B2]: (c_Set_Oimage(V_f2, V_A2, T_a2, T_b2)=V_B2 | ~c_Fun_Obij__betw(V_f2, V_A2, V_B2, T_a2, T_b2))).
% 241.20/31.25 fof(cls_conjecture_0, negated_conjecture, ~v_thesis____).
% 241.20/31.25 fof(cls_ex__bij__betw__finite__nat_0, axiom, ![V_M, T_a2]: (c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(V_M, T_a2), V_M, c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(V_M, T_a2), tc_nat), T_a2, tc_nat) | ~c_Finite__Set_Ofinite(V_M, T_a2))).
% 241.20/31.25 fof(cls_finite__Int_0, axiom, ![V_F, V_G, T_a2]: (c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(V_F, V_G, tc_fun(T_a2, tc_bool)), T_a2) | ~c_Finite__Set_Ofinite(V_F, T_a2))).
% 241.20/31.25 fof(cls_finite__indi_0, axiom, c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi)).
% 241.20/31.25 fof(cls_le0_0, axiom, ![V_n]: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat)).
% 241.20/31.25 fof(cls_subset__UNIV_0, axiom, ![T_a2, V_A2]: c_lessequals(V_A2, c_Orderings_Otop__class_Otop(tc_fun(T_a2, tc_bool)), tc_fun(T_a2, tc_bool))).
% 241.20/31.25 fof(cls_subset__inj__on_0, axiom, ![V_f2, T_a2, T_b2, V_A2, V_B2]: (c_Fun_Oinj__on(V_f2, V_A2, T_a2, T_b2) | (~c_lessequals(V_A2, V_B2, tc_fun(T_a2, tc_bool)) | ~c_Fun_Oinj__on(V_f2, V_B2, T_a2, T_b2)))).
% 241.20/31.25 fof(cls_that_0, axiom, ![V_h]: (c_Set_Oimage(V_h, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat)!=c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat) | (~c_Fun_Oinj__on(V_h, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat) | v_thesis____))).
% 241.20/31.25 fof(cls_zero__less__Suc_0, axiom, ![V_n2]: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(V_n2), tc_nat)).
% 241.20/31.25 fof(clsarity_nat__Lattices_Odistrib__lattice, axiom, class_Lattices_Odistrib__lattice(tc_nat)).
% 241.20/31.25 fof(clsarity_nat__Orderings_Obot, axiom, class_Orderings_Obot(tc_nat)).
% 241.20/31.25 fof(clsarity_nat__Ring__and__Field_Osemiring__0, axiom, class_Ring__and__Field_Osemiring__0(tc_nat)).
% 241.20/31.25
% 241.20/31.25 Now clausify the problem and encode Horn clauses using encoding 3 of
% 241.20/31.25 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 241.20/31.25 We repeatedly replace C & s=t => u=v by the two clauses:
% 241.20/31.25 fresh(y, y, x1...xn) = u
% 241.20/31.25 C => fresh(s, t, x1...xn) = v
% 241.20/31.26 where fresh is a fresh function symbol and x1..xn are the free
% 241.20/31.26 variables of u and v.
% 241.20/31.26 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 241.20/31.26 input problem has no model of domain size 1).
% 241.20/31.26
% 241.20/31.26 The encoding turns the above axioms into the following unit equations and goals:
% 241.20/31.26
% 241.20/31.26 Axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0): class_Ring__and__Field_Osemiring__0(tc_nat) = true2.
% 241.20/31.26 Axiom 2 (clsarity_nat__Orderings_Obot): class_Orderings_Obot(tc_nat) = true2.
% 241.20/31.26 Axiom 3 (clsarity_nat__Lattices_Odistrib__lattice): class_Lattices_Odistrib__lattice(tc_nat) = true2.
% 241.20/31.26 Axiom 4 (cls_that_0): fresh177(X, X) = true2.
% 241.20/31.26 Axiom 5 (cls_that_0): fresh178(X, X, Y) = v_thesis____.
% 241.20/31.26 Axiom 6 (cls_ex__bij__betw__finite__nat_0): fresh569(X, X, Y, Z) = true2.
% 241.20/31.26 Axiom 7 (cls_le0_0): c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), X, tc_nat) = true2.
% 241.20/31.26 Axiom 8 (cls_finite__Int_0): fresh553(X, X, Y, Z, W) = true2.
% 241.20/31.26 Axiom 9 (cls_finite__indi_0): c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi) = true2.
% 241.20/31.26 Axiom 10 (cls_zero__less__Suc_0): c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat) = true2.
% 241.20/31.26 Axiom 11 (cls_bij__betw__def_0): fresh631(X, X, Y, Z, W, V) = true2.
% 241.20/31.26 Axiom 12 (cls_subset__inj__on_0): fresh213(X, X, Y, Z, W, V) = true2.
% 241.20/31.26 Axiom 13 (cls_subset__inj__on_0): fresh214(X, X, Y, Z, W, V, U) = c_Fun_Oinj__on(Y, Z, W, V).
% 241.20/31.26 Axiom 14 (cls_bij__betw__def_1): fresh46(X, X, Y, Z, W, V, U) = U.
% 241.20/31.26 Axiom 15 (cls_finite__Int_0): fresh553(c_Finite__Set_Ofinite(X, Y), true2, X, Z, Y) = c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X, Z, tc_fun(Y, tc_bool)), Y).
% 241.20/31.26 Axiom 16 (cls_Int__UNIV__left_0): c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X, tc_bool)), Y, tc_fun(X, tc_bool)) = Y.
% 241.20/31.26 Axiom 17 (cls_subset__UNIV_0): c_lessequals(X, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_bool)), tc_fun(Y, tc_bool)) = true2.
% 241.20/31.26 Axiom 18 (cls_bij__betw__def_0): fresh631(c_Fun_Obij__betw(X, Y, Z, W, V), true2, X, Y, W, V) = c_Fun_Oinj__on(X, Y, W, V).
% 241.20/31.26 Axiom 19 (cls_subset__inj__on_0): fresh214(c_Fun_Oinj__on(X, Y, Z, W), true2, X, V, Z, W, Y) = fresh213(c_lessequals(V, Y, tc_fun(Z, tc_bool)), true2, X, V, Z, W).
% 241.20/31.26 Axiom 20 (cls_bij__betw__def_1): fresh46(c_Fun_Obij__betw(X, Y, Z, W, V), true2, X, Y, W, V, Z) = c_Set_Oimage(X, Y, W, V).
% 241.20/31.26 Axiom 21 (cls_ex__bij__betw__finite__nat_0): fresh569(c_Finite__Set_Ofinite(X, Y), true2, X, Y) = c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(X, Y), X, c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(X, Y), tc_nat), Y, tc_nat).
% 241.20/31.26 Axiom 22 (cls_that_0): fresh178(c_Fun_Oinj__on(X, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), true2, X) = fresh177(c_Set_Oimage(X, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat)).
% 241.20/31.26
% 241.20/31.26 Lemma 23: class_Orderings_Obot(tc_nat) = class_Ring__and__Field_Osemiring__0(tc_nat).
% 241.20/31.26 Proof:
% 241.20/31.26 class_Orderings_Obot(tc_nat)
% 241.20/31.26 = { by axiom 2 (clsarity_nat__Orderings_Obot) }
% 241.20/31.26 true2
% 241.20/31.26 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) R->L }
% 241.20/31.26 class_Ring__and__Field_Osemiring__0(tc_nat)
% 241.20/31.26
% 241.20/31.26 Lemma 24: class_Lattices_Odistrib__lattice(tc_nat) = class_Orderings_Obot(tc_nat).
% 241.20/31.26 Proof:
% 241.20/31.26 class_Lattices_Odistrib__lattice(tc_nat)
% 241.20/31.26 = { by axiom 3 (clsarity_nat__Lattices_Odistrib__lattice) }
% 241.20/31.26 true2
% 241.20/31.26 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) R->L }
% 241.20/31.26 class_Ring__and__Field_Osemiring__0(tc_nat)
% 241.20/31.26 = { by lemma 23 R->L }
% 241.20/31.26 class_Orderings_Obot(tc_nat)
% 241.20/31.26
% 241.20/31.26 Lemma 25: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), X, tc_nat) = class_Lattices_Odistrib__lattice(tc_nat).
% 241.20/31.26 Proof:
% 241.20/31.26 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), X, tc_nat)
% 241.20/31.26 = { by axiom 7 (cls_le0_0) }
% 241.20/31.26 true2
% 241.20/31.26 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) R->L }
% 241.20/31.26 class_Ring__and__Field_Osemiring__0(tc_nat)
% 241.20/31.26 = { by lemma 23 R->L }
% 241.20/31.26 class_Orderings_Obot(tc_nat)
% 241.20/31.26 = { by lemma 24 R->L }
% 241.20/31.26 class_Lattices_Odistrib__lattice(tc_nat)
% 241.20/31.26
% 241.20/31.26 Lemma 26: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(Y), tc_nat) = c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), X, tc_nat).
% 241.20/31.26 Proof:
% 241.20/31.26 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(Y), tc_nat)
% 241.20/31.26 = { by axiom 10 (cls_zero__less__Suc_0) }
% 241.20/31.26 true2
% 241.20/31.26 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) R->L }
% 241.20/31.26 class_Ring__and__Field_Osemiring__0(tc_nat)
% 241.20/31.26 = { by lemma 23 R->L }
% 241.20/31.26 class_Orderings_Obot(tc_nat)
% 241.20/31.26 = { by lemma 24 R->L }
% 241.20/31.26 class_Lattices_Odistrib__lattice(tc_nat)
% 241.20/31.26 = { by lemma 25 R->L }
% 241.20/31.26 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), X, tc_nat)
% 241.20/31.26
% 241.20/31.26 Lemma 27: c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(X, tc_Arrow__Order__Mirabelle_Oindi), X, c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(X, tc_Arrow__Order__Mirabelle_Oindi), tc_nat), tc_Arrow__Order__Mirabelle_Oindi, tc_nat) = c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(Y), tc_nat).
% 241.20/31.26 Proof:
% 241.20/31.26 c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(X, tc_Arrow__Order__Mirabelle_Oindi), X, c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(X, tc_Arrow__Order__Mirabelle_Oindi), tc_nat), tc_Arrow__Order__Mirabelle_Oindi, tc_nat)
% 241.20/31.26 = { by axiom 21 (cls_ex__bij__betw__finite__nat_0) R->L }
% 241.20/31.26 fresh569(c_Finite__Set_Ofinite(X, tc_Arrow__Order__Mirabelle_Oindi), true2, X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) R->L }
% 241.20/31.26 fresh569(c_Finite__Set_Ofinite(X, tc_Arrow__Order__Mirabelle_Oindi), class_Ring__and__Field_Osemiring__0(tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 23 R->L }
% 241.20/31.26 fresh569(c_Finite__Set_Ofinite(X, tc_Arrow__Order__Mirabelle_Oindi), class_Orderings_Obot(tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 24 R->L }
% 241.20/31.26 fresh569(c_Finite__Set_Ofinite(X, tc_Arrow__Order__Mirabelle_Oindi), class_Lattices_Odistrib__lattice(tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 25 R->L }
% 241.20/31.26 fresh569(c_Finite__Set_Ofinite(X, tc_Arrow__Order__Mirabelle_Oindi), c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), Z, tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 26 R->L }
% 241.20/31.26 fresh569(c_Finite__Set_Ofinite(X, tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by axiom 16 (cls_Int__UNIV__left_0) R->L }
% 241.20/31.26 fresh569(c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), X, tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by axiom 15 (cls_finite__Int_0) R->L }
% 241.20/31.26 fresh569(fresh553(c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), true2, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), X, tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) R->L }
% 241.20/31.26 fresh569(fresh553(c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), class_Ring__and__Field_Osemiring__0(tc_nat), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), X, tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 23 R->L }
% 241.20/31.26 fresh569(fresh553(c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), class_Orderings_Obot(tc_nat), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), X, tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 24 R->L }
% 241.20/31.26 fresh569(fresh553(c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), class_Lattices_Odistrib__lattice(tc_nat), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), X, tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 25 R->L }
% 241.20/31.26 fresh569(fresh553(c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), V, tc_nat), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), X, tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 26 R->L }
% 241.20/31.26 fresh569(fresh553(c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(U), tc_nat), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), X, tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by axiom 9 (cls_finite__indi_0) }
% 241.20/31.26 fresh569(fresh553(true2, c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(U), tc_nat), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), X, tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) R->L }
% 241.20/31.26 fresh569(fresh553(class_Ring__and__Field_Osemiring__0(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(U), tc_nat), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), X, tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 23 R->L }
% 241.20/31.26 fresh569(fresh553(class_Orderings_Obot(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(U), tc_nat), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), X, tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 24 R->L }
% 241.20/31.26 fresh569(fresh553(class_Lattices_Odistrib__lattice(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(U), tc_nat), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), X, tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 25 R->L }
% 241.20/31.26 fresh569(fresh553(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), T, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(U), tc_nat), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), X, tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 26 R->L }
% 241.20/31.26 fresh569(fresh553(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(U), tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(U), tc_nat), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), X, tc_Arrow__Order__Mirabelle_Oindi), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by axiom 8 (cls_finite__Int_0) }
% 241.20/31.26 fresh569(true2, c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) R->L }
% 241.20/31.26 fresh569(class_Ring__and__Field_Osemiring__0(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 23 R->L }
% 241.20/31.26 fresh569(class_Orderings_Obot(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 24 R->L }
% 241.20/31.26 fresh569(class_Lattices_Odistrib__lattice(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 25 R->L }
% 241.20/31.26 fresh569(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), S, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by lemma 26 R->L }
% 241.20/31.26 fresh569(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(W), tc_nat), X, tc_Arrow__Order__Mirabelle_Oindi)
% 241.20/31.26 = { by axiom 6 (cls_ex__bij__betw__finite__nat_0) }
% 241.20/31.26 true2
% 241.20/31.26 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) R->L }
% 241.20/31.26 class_Ring__and__Field_Osemiring__0(tc_nat)
% 241.20/31.26 = { by lemma 23 R->L }
% 241.20/31.26 class_Orderings_Obot(tc_nat)
% 241.20/31.26 = { by lemma 24 R->L }
% 241.20/31.26 class_Lattices_Odistrib__lattice(tc_nat)
% 241.20/31.26 = { by lemma 25 R->L }
% 241.20/31.26 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), X2, tc_nat)
% 241.20/31.26 = { by lemma 26 R->L }
% 241.20/31.26 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(Y), tc_nat)
% 241.20/31.26
% 241.20/31.26 Goal 1 (cls_conjecture_0): v_thesis____ = true2.
% 241.20/31.26 Proof:
% 241.20/31.26 v_thesis____
% 241.20/31.26 = { by axiom 5 (cls_that_0) R->L }
% 241.20/31.26 fresh178(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by lemma 26 }
% 241.20/31.26 fresh178(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), Y, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by lemma 25 }
% 241.20/31.26 fresh178(class_Lattices_Odistrib__lattice(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by lemma 24 }
% 241.20/31.26 fresh178(class_Orderings_Obot(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by lemma 23 }
% 241.20/31.26 fresh178(class_Ring__and__Field_Osemiring__0(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) }
% 241.20/31.26 fresh178(true2, c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by axiom 12 (cls_subset__inj__on_0) R->L }
% 241.20/31.26 fresh178(fresh213(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(Z), tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(Z), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by lemma 26 }
% 241.20/31.26 fresh178(fresh213(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), W, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(Z), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by lemma 25 }
% 241.20/31.26 fresh178(fresh213(class_Lattices_Odistrib__lattice(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(Z), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by lemma 24 }
% 241.20/31.26 fresh178(fresh213(class_Orderings_Obot(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(Z), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by lemma 23 }
% 241.20/31.26 fresh178(fresh213(class_Ring__and__Field_Osemiring__0(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(Z), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) }
% 241.20/31.26 fresh178(fresh213(true2, c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(Z), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by axiom 17 (cls_subset__UNIV_0) R->L }
% 241.20/31.26 fresh178(fresh213(c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(Z), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by lemma 26 }
% 241.20/31.26 fresh178(fresh213(c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), V, tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by lemma 25 }
% 241.20/31.26 fresh178(fresh213(c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), class_Lattices_Odistrib__lattice(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by lemma 24 }
% 241.20/31.26 fresh178(fresh213(c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), class_Orderings_Obot(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by lemma 23 }
% 241.20/31.26 fresh178(fresh213(c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), class_Ring__and__Field_Osemiring__0(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.26 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) }
% 241.20/31.27 fresh178(fresh213(c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), true2, c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by axiom 19 (cls_subset__inj__on_0) R->L }
% 241.20/31.27 fresh178(fresh214(c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), true2, c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) R->L }
% 241.20/31.27 fresh178(fresh214(c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), class_Ring__and__Field_Osemiring__0(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 23 R->L }
% 241.20/31.27 fresh178(fresh214(c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), class_Orderings_Obot(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 24 R->L }
% 241.20/31.27 fresh178(fresh214(c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), class_Lattices_Odistrib__lattice(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 25 R->L }
% 241.20/31.27 fresh178(fresh214(c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), U, tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 26 R->L }
% 241.20/31.27 fresh178(fresh214(c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by axiom 18 (cls_bij__betw__def_0) R->L }
% 241.20/31.27 fresh178(fresh214(fresh631(c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), true2, c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) R->L }
% 241.20/31.27 fresh178(fresh214(fresh631(c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), class_Ring__and__Field_Osemiring__0(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 23 R->L }
% 241.20/31.27 fresh178(fresh214(fresh631(c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), class_Orderings_Obot(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 24 R->L }
% 241.20/31.27 fresh178(fresh214(fresh631(c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), class_Lattices_Odistrib__lattice(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 25 R->L }
% 241.20/31.27 fresh178(fresh214(fresh631(c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), S, tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 26 R->L }
% 241.20/31.27 fresh178(fresh214(fresh631(c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X2), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 27 }
% 241.20/31.27 fresh178(fresh214(fresh631(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X2), tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X2), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by axiom 11 (cls_bij__betw__def_0) }
% 241.20/31.27 fresh178(fresh214(true2, c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) R->L }
% 241.20/31.27 fresh178(fresh214(class_Ring__and__Field_Osemiring__0(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 23 R->L }
% 241.20/31.27 fresh178(fresh214(class_Orderings_Obot(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 24 R->L }
% 241.20/31.27 fresh178(fresh214(class_Lattices_Odistrib__lattice(tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 25 R->L }
% 241.20/31.27 fresh178(fresh214(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), Y2, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 26 R->L }
% 241.20/31.27 fresh178(fresh214(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(T), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool))), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by axiom 13 (cls_subset__inj__on_0) }
% 241.20/31.27 fresh178(c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 26 }
% 241.20/31.27 fresh178(c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), Z2, tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 25 }
% 241.20/31.27 fresh178(c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), class_Lattices_Odistrib__lattice(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 24 }
% 241.20/31.27 fresh178(c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), class_Orderings_Obot(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by lemma 23 }
% 241.20/31.27 fresh178(c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), class_Ring__and__Field_Osemiring__0(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) }
% 241.20/31.27 fresh178(c_Fun_Oinj__on(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), true2, c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi))
% 241.20/31.27 = { by axiom 22 (cls_that_0) }
% 241.20/31.27 fresh177(c_Set_Oimage(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat))
% 241.20/31.27 = { by axiom 20 (cls_bij__betw__def_1) R->L }
% 241.20/31.27 fresh177(fresh46(c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), true2, c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat))
% 241.20/31.27 = { by axiom 1 (clsarity_nat__Ring__and__Field_Osemiring__0) R->L }
% 241.20/31.27 fresh177(fresh46(c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), class_Ring__and__Field_Osemiring__0(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat))
% 241.20/31.27 = { by lemma 23 R->L }
% 241.20/31.27 fresh177(fresh46(c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), class_Orderings_Obot(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat))
% 241.20/31.27 = { by lemma 24 R->L }
% 241.20/31.27 fresh177(fresh46(c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), class_Lattices_Odistrib__lattice(tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat))
% 241.20/31.27 = { by lemma 25 R->L }
% 241.20/31.27 fresh177(fresh46(c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), W2, tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat))
% 241.20/31.27 = { by lemma 26 R->L }
% 241.20/31.27 fresh177(fresh46(c_Fun_Obij__betw(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat), tc_Arrow__Order__Mirabelle_Oindi, tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(V2), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat))
% 241.20/31.27 = { by lemma 27 }
% 241.20/31.27 fresh177(fresh46(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(V2), tc_nat), c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(V2), tc_nat), c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi, tc_nat, c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat)), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat))
% 241.20/31.27 = { by axiom 14 (cls_bij__betw__def_1) }
% 241.20/31.27 fresh177(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat), c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat), c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_bool)), tc_Arrow__Order__Mirabelle_Oindi), tc_nat))
% 241.20/31.27 = { by axiom 4 (cls_that_0) }
% 241.20/31.27 true2
% 241.20/31.27 % SZS output end Proof
% 241.20/31.27
% 241.20/31.27 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------