TSTP Solution File: SWV926-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV926-1 : 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 : n029.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 23:06:47 EDT 2023
% Result : Unsatisfiable 47.66s 6.42s
% Output : Proof 51.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV926-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.13 % 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 : n029.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 : Tue Aug 29 04:34:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 47.66/6.42 Command-line arguments: --flatten
% 47.66/6.42
% 47.66/6.42 % SZS status Unsatisfiable
% 47.66/6.42
% 49.41/6.66 % SZS output start Proof
% 49.41/6.66 Take the following subset of the input axioms:
% 49.41/6.66 fof(cls_Un__assoc_0, axiom, ![T_a, V_A, V_C, V_B]: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool))=c_Lattices_Oupper__semilattice__class_Osup(V_A, c_Lattices_Oupper__semilattice__class_Osup(V_B, V_C, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool))).
% 49.41/6.66 fof(cls_Un__commute_0, axiom, ![T_a2, V_A2, V_B2]: c_Lattices_Oupper__semilattice__class_Osup(V_A2, V_B2, tc_fun(T_a2, tc_bool))=c_Lattices_Oupper__semilattice__class_Osup(V_B2, V_A2, tc_fun(T_a2, tc_bool))).
% 49.41/6.66 fof(cls_Un__left__commute_0, axiom, ![T_a2, V_A2, V_C2, V_B2]: c_Lattices_Oupper__semilattice__class_Osup(V_A2, c_Lattices_Oupper__semilattice__class_Osup(V_B2, V_C2, tc_fun(T_a2, tc_bool)), tc_fun(T_a2, tc_bool))=c_Lattices_Oupper__semilattice__class_Osup(V_B2, c_Lattices_Oupper__semilattice__class_Osup(V_A2, V_C2, tc_fun(T_a2, tc_bool)), tc_fun(T_a2, tc_bool))).
% 49.41/6.66 fof(cls_conjecture_0, negated_conjecture, c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))).
% 49.41/6.67 fof(cls_conjecture_1, negated_conjecture, hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))).
% 49.41/6.67 fof(cls_conjecture_3, negated_conjecture, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))=v_ab).
% 49.41/6.67 fof(cls_conjecture_5, negated_conjecture, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))=v_ad).
% 49.41/6.67 fof(cls_conjecture_7, negated_conjecture, ~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | ~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))).
% 49.41/6.67 fof(cls_inf__sup__ord_I3_J_0, axiom, ![V_x, V_y, T_a2]: (~class_Lattices_Olattice(T_a2) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a2), T_a2))).
% 49.41/6.67 fof(cls_inf__sup__ord_I4_J_0, axiom, ![T_a2, V_x2, V_y2]: (~class_Lattices_Olattice(T_a2) | c_lessequals(V_y2, c_Lattices_Oupper__semilattice__class_Osup(V_x2, V_y2, T_a2), T_a2))).
% 49.41/6.67 fof(cls_le__supI1_0, axiom, ![V_b, V_a, T_a2, V_x2]: (~class_Lattices_Oupper__semilattice(T_a2) | (c_lessequals(V_x2, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a2), T_a2) | ~c_lessequals(V_x2, V_a, T_a2)))).
% 49.41/6.67 fof(cls_le__supI2_0, axiom, ![T_a2, V_x2, V_b2, V_a2]: (~class_Lattices_Oupper__semilattice(T_a2) | (c_lessequals(V_x2, c_Lattices_Oupper__semilattice__class_Osup(V_a2, V_b2, T_a2), T_a2) | ~c_lessequals(V_x2, V_b2, T_a2)))).
% 49.41/6.67 fof(cls_order__trans_0, axiom, ![V_z, T_a2, V_x2, V_y2]: (~class_Orderings_Opreorder(T_a2) | (c_lessequals(V_x2, V_z, T_a2) | (~c_lessequals(V_y2, V_z, T_a2) | ~c_lessequals(V_x2, V_y2, T_a2))))).
% 49.41/6.67 fof(clsarity_bool__Lattices_Obounded__lattice, axiom, class_Lattices_Obounded__lattice(tc_bool)).
% 49.41/6.67 fof(clsarity_bool__Lattices_Olattice, axiom, class_Lattices_Olattice(tc_bool)).
% 49.41/6.67 fof(clsarity_bool__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_bool)).
% 49.41/6.67 fof(clsarity_fun__Lattices_Olattice, axiom, ![T_2, T_1]: (class_Lattices_Olattice(tc_fun(T_2, T_1)) | ~class_Lattices_Olattice(T_1))).
% 49.41/6.67 fof(clsarity_fun__Lattices_Oupper__semilattice, axiom, ![T_2_2, T_1_2]: (class_Lattices_Oupper__semilattice(tc_fun(T_2_2, T_1_2)) | ~class_Lattices_Olattice(T_1_2))).
% 49.41/6.67 fof(clsarity_fun__Orderings_Opreorder, axiom, ![T_2_2, T_1_2]: (class_Orderings_Opreorder(tc_fun(T_2_2, T_1_2)) | ~class_Orderings_Opreorder(T_1_2))).
% 49.41/6.67 fof(clsarity_nat__Orderings_Olinorder, axiom, class_Orderings_Olinorder(tc_nat)).
% 49.41/6.67
% 49.41/6.67 Now clausify the problem and encode Horn clauses using encoding 3 of
% 49.41/6.67 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 49.41/6.67 We repeatedly replace C & s=t => u=v by the two clauses:
% 49.41/6.67 fresh(y, y, x1...xn) = u
% 49.41/6.67 C => fresh(s, t, x1...xn) = v
% 49.41/6.67 where fresh is a fresh function symbol and x1..xn are the free
% 49.41/6.67 variables of u and v.
% 49.41/6.67 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 49.41/6.67 input problem has no model of domain size 1).
% 49.41/6.67
% 49.41/6.67 The encoding turns the above axioms into the following unit equations and goals:
% 49.41/6.67
% 49.41/6.67 Axiom 1 (clsarity_nat__Orderings_Olinorder): class_Orderings_Olinorder(tc_nat) = true2.
% 49.41/6.67 Axiom 2 (clsarity_bool__Lattices_Obounded__lattice): class_Lattices_Obounded__lattice(tc_bool) = true2.
% 49.41/6.67 Axiom 3 (clsarity_bool__Orderings_Opreorder): class_Orderings_Opreorder(tc_bool) = true2.
% 49.41/6.67 Axiom 4 (clsarity_bool__Lattices_Olattice): class_Lattices_Olattice(tc_bool) = true2.
% 49.41/6.67 Axiom 5 (clsarity_fun__Lattices_Olattice): fresh73(X, X, Y, Z) = true2.
% 49.41/6.67 Axiom 6 (clsarity_fun__Lattices_Oupper__semilattice): fresh72(X, X, Y, Z) = true2.
% 49.41/6.67 Axiom 7 (clsarity_fun__Orderings_Opreorder): fresh69(X, X, Y, Z) = true2.
% 49.41/6.67 Axiom 8 (cls_order__trans_0): fresh273(X, X, Y, Z, W) = true2.
% 49.41/6.67 Axiom 9 (cls_inf__sup__ord_I3_J_0): fresh163(X, X, Y, Z, W) = true2.
% 49.41/6.67 Axiom 10 (cls_inf__sup__ord_I4_J_0): fresh162(X, X, Y, Z, W) = true2.
% 49.41/6.67 Axiom 11 (clsarity_fun__Lattices_Olattice): fresh73(class_Lattices_Olattice(X), true2, Y, X) = class_Lattices_Olattice(tc_fun(Y, X)).
% 49.41/6.67 Axiom 12 (clsarity_fun__Lattices_Oupper__semilattice): fresh72(class_Lattices_Olattice(X), true2, Y, X) = class_Lattices_Oupper__semilattice(tc_fun(Y, X)).
% 49.41/6.67 Axiom 13 (clsarity_fun__Orderings_Opreorder): fresh69(class_Orderings_Opreorder(X), true2, Y, X) = class_Orderings_Opreorder(tc_fun(Y, X)).
% 49.41/6.67 Axiom 14 (cls_Un__commute_0): c_Lattices_Oupper__semilattice__class_Osup(X, Y, tc_fun(Z, tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(Y, X, tc_fun(Z, tc_bool)).
% 49.41/6.67 Axiom 15 (cls_le__supI1_0): fresh151(X, X, Y, Z, W, V) = true2.
% 49.41/6.67 Axiom 16 (cls_le__supI2_0): fresh149(X, X, Y, Z, W, V) = true2.
% 49.41/6.67 Axiom 17 (cls_order__trans_0): fresh133(X, X, Y, Z, W, V) = c_lessequals(Z, W, Y).
% 49.41/6.67 Axiom 18 (cls_inf__sup__ord_I3_J_0): fresh163(class_Lattices_Olattice(X), true2, X, Y, Z) = c_lessequals(Y, c_Lattices_Oupper__semilattice__class_Osup(Y, Z, X), X).
% 49.41/6.67 Axiom 19 (cls_inf__sup__ord_I4_J_0): fresh162(class_Lattices_Olattice(X), true2, X, Y, Z) = c_lessequals(Y, c_Lattices_Oupper__semilattice__class_Osup(Z, Y, X), X).
% 49.41/6.67 Axiom 20 (cls_le__supI1_0): fresh152(X, X, Y, Z, W, V) = c_lessequals(Z, c_Lattices_Oupper__semilattice__class_Osup(W, V, Y), Y).
% 49.41/6.67 Axiom 21 (cls_le__supI2_0): fresh150(X, X, Y, Z, W, V) = c_lessequals(Z, c_Lattices_Oupper__semilattice__class_Osup(W, V, Y), Y).
% 49.41/6.67 Axiom 22 (cls_conjecture_0): c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = true2.
% 49.41/6.67 Axiom 23 (cls_inf__sup__aci_I6_J_0): fresh166(X, X, Y, Z, W, V) = c_Lattices_Oupper__semilattice__class_Osup(Z, c_Lattices_Oupper__semilattice__class_Osup(W, V, Y), Y).
% 49.41/6.67 Axiom 24 (cls_order__trans_0): fresh272(X, X, Y, Z, W, V) = fresh273(c_lessequals(Z, V, Y), true2, Y, Z, W).
% 49.41/6.67 Axiom 25 (cls_le__supI1_0): fresh152(class_Lattices_Oupper__semilattice(X), true2, X, Y, Z, W) = fresh151(c_lessequals(Y, Z, X), true2, X, Y, Z, W).
% 49.41/6.67 Axiom 26 (cls_le__supI2_0): fresh150(class_Lattices_Oupper__semilattice(X), true2, X, Y, Z, W) = fresh149(c_lessequals(Y, W, X), true2, X, Y, Z, W).
% 49.41/6.67 Axiom 27 (cls_order__trans_0): fresh272(class_Orderings_Opreorder(X), true2, X, Y, Z, W) = fresh133(c_lessequals(W, Z, X), true2, X, Y, Z, W).
% 49.41/6.67 Axiom 28 (cls_Un__left__commute_0): c_Lattices_Oupper__semilattice__class_Osup(X, c_Lattices_Oupper__semilattice__class_Osup(Y, Z, tc_fun(W, tc_bool)), tc_fun(W, tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(Y, c_Lattices_Oupper__semilattice__class_Osup(X, Z, tc_fun(W, tc_bool)), tc_fun(W, tc_bool)).
% 49.41/6.67 Axiom 29 (cls_conjecture_5): c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ad.
% 49.41/6.67 Axiom 30 (cls_conjecture_3): c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab.
% 49.41/6.67 Axiom 31 (cls_Un__assoc_0): c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X, Y, tc_fun(Z, tc_bool)), W, tc_fun(Z, tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X, c_Lattices_Oupper__semilattice__class_Osup(Y, W, tc_fun(Z, tc_bool)), tc_fun(Z, tc_bool)).
% 49.41/6.67 Axiom 32 (cls_conjecture_1): hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))) = true2.
% 49.41/6.67
% 49.41/6.67 Lemma 33: class_Lattices_Obounded__lattice(tc_bool) = class_Orderings_Olinorder(tc_nat).
% 49.41/6.67 Proof:
% 49.41/6.67 class_Lattices_Obounded__lattice(tc_bool)
% 49.41/6.67 = { by axiom 2 (clsarity_bool__Lattices_Obounded__lattice) }
% 49.41/6.67 true2
% 49.41/6.67 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 49.41/6.67 class_Orderings_Olinorder(tc_nat)
% 49.41/6.67
% 49.41/6.67 Lemma 34: class_Lattices_Olattice(tc_bool) = class_Lattices_Obounded__lattice(tc_bool).
% 49.41/6.67 Proof:
% 49.41/6.67 class_Lattices_Olattice(tc_bool)
% 49.41/6.67 = { by axiom 4 (clsarity_bool__Lattices_Olattice) }
% 49.41/6.67 true2
% 49.41/6.67 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 49.41/6.67 class_Orderings_Olinorder(tc_nat)
% 49.41/6.67 = { by lemma 33 R->L }
% 49.41/6.67 class_Lattices_Obounded__lattice(tc_bool)
% 49.41/6.67
% 49.41/6.67 Lemma 35: c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = class_Lattices_Obounded__lattice(tc_bool).
% 49.41/6.67 Proof:
% 49.41/6.67 c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))
% 49.41/6.67 = { by axiom 22 (cls_conjecture_0) }
% 49.41/6.67 true2
% 49.41/6.67 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 49.41/6.67 class_Orderings_Olinorder(tc_nat)
% 49.41/6.67 = { by lemma 33 R->L }
% 49.41/6.67 class_Lattices_Obounded__lattice(tc_bool)
% 49.41/6.67
% 49.41/6.67 Lemma 36: fresh152(U, U, tc_fun(Y, tc_bool), Z, V, W) = fresh152(X, X, tc_fun(Y, tc_bool), Z, W, V).
% 49.41/6.67 Proof:
% 49.41/6.67 fresh152(U, U, tc_fun(Y, tc_bool), Z, V, W)
% 49.41/6.67 = { by axiom 20 (cls_le__supI1_0) }
% 49.41/6.67 c_lessequals(Z, c_Lattices_Oupper__semilattice__class_Osup(V, W, tc_fun(Y, tc_bool)), tc_fun(Y, tc_bool))
% 49.41/6.67 = { by axiom 14 (cls_Un__commute_0) }
% 49.41/6.67 c_lessequals(Z, c_Lattices_Oupper__semilattice__class_Osup(W, V, tc_fun(Y, tc_bool)), tc_fun(Y, tc_bool))
% 49.41/6.67 = { by axiom 20 (cls_le__supI1_0) R->L }
% 49.41/6.67 fresh152(X, X, tc_fun(Y, tc_bool), Z, W, V)
% 49.41/6.67
% 49.41/6.67 Lemma 37: fresh166(U, U, tc_fun(Y, tc_bool), W, Z, V) = fresh166(X, X, tc_fun(Y, tc_bool), Z, W, V).
% 49.41/6.67 Proof:
% 49.41/6.67 fresh166(U, U, tc_fun(Y, tc_bool), W, Z, V)
% 49.41/6.67 = { by axiom 23 (cls_inf__sup__aci_I6_J_0) }
% 49.41/6.67 c_Lattices_Oupper__semilattice__class_Osup(W, c_Lattices_Oupper__semilattice__class_Osup(Z, V, tc_fun(Y, tc_bool)), tc_fun(Y, tc_bool))
% 49.41/6.67 = { by axiom 28 (cls_Un__left__commute_0) R->L }
% 49.41/6.67 c_Lattices_Oupper__semilattice__class_Osup(Z, c_Lattices_Oupper__semilattice__class_Osup(W, V, tc_fun(Y, tc_bool)), tc_fun(Y, tc_bool))
% 49.41/6.67 = { by axiom 23 (cls_inf__sup__aci_I6_J_0) R->L }
% 49.41/6.67 fresh166(X, X, tc_fun(Y, tc_bool), Z, W, V)
% 49.41/6.67
% 49.41/6.67 Lemma 38: c_Lattices_Oupper__semilattice__class_Osup(V, c_Lattices_Oupper__semilattice__class_Osup(Z, W, tc_fun(Y, tc_bool)), tc_fun(Y, tc_bool)) = fresh166(X, X, tc_fun(Y, tc_bool), Z, W, V).
% 49.41/6.67 Proof:
% 49.41/6.68 c_Lattices_Oupper__semilattice__class_Osup(V, c_Lattices_Oupper__semilattice__class_Osup(Z, W, tc_fun(Y, tc_bool)), tc_fun(Y, tc_bool))
% 49.41/6.68 = { by axiom 23 (cls_inf__sup__aci_I6_J_0) R->L }
% 49.41/6.68 fresh166(S, S, tc_fun(Y, tc_bool), V, Z, W)
% 49.41/6.68 = { by lemma 37 }
% 49.41/6.68 fresh166(T, T, tc_fun(Y, tc_bool), Z, V, W)
% 49.41/6.68 = { by axiom 23 (cls_inf__sup__aci_I6_J_0) }
% 49.41/6.68 c_Lattices_Oupper__semilattice__class_Osup(Z, c_Lattices_Oupper__semilattice__class_Osup(V, W, tc_fun(Y, tc_bool)), tc_fun(Y, tc_bool))
% 49.41/6.68 = { by axiom 31 (cls_Un__assoc_0) R->L }
% 49.41/6.68 c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(Z, V, tc_fun(Y, tc_bool)), W, tc_fun(Y, tc_bool))
% 49.41/6.68 = { by axiom 14 (cls_Un__commute_0) R->L }
% 49.41/6.68 c_Lattices_Oupper__semilattice__class_Osup(W, c_Lattices_Oupper__semilattice__class_Osup(Z, V, tc_fun(Y, tc_bool)), tc_fun(Y, tc_bool))
% 49.41/6.68 = { by axiom 23 (cls_inf__sup__aci_I6_J_0) R->L }
% 49.41/6.68 fresh166(U, U, tc_fun(Y, tc_bool), W, Z, V)
% 49.41/6.68 = { by lemma 37 }
% 49.41/6.68 fresh166(X, X, tc_fun(Y, tc_bool), Z, W, V)
% 49.41/6.68
% 49.41/6.68 Lemma 39: hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))) = c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)).
% 49.41/6.68 Proof:
% 49.41/6.68 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))
% 49.41/6.68 = { by axiom 32 (cls_conjecture_1) }
% 49.41/6.68 true2
% 49.41/6.68 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 49.41/6.68 class_Orderings_Olinorder(tc_nat)
% 49.41/6.68 = { by lemma 33 R->L }
% 49.41/6.68 class_Lattices_Obounded__lattice(tc_bool)
% 49.41/6.68 = { by lemma 35 R->L }
% 49.41/6.68 c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))
% 49.41/6.68
% 49.41/6.68 Lemma 40: fresh272(X, X, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) = c_lessequals(Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)).
% 49.41/6.68 Proof:
% 49.41/6.68 fresh272(X, X, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 49.41/6.68 = { by axiom 24 (cls_order__trans_0) }
% 49.41/6.68 fresh273(c_lessequals(Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), true2, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 49.41/6.69 = { by axiom 24 (cls_order__trans_0) R->L }
% 49.41/6.69 fresh272(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.69 = { by lemma 39 }
% 50.06/6.69 fresh272(c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.69 = { by lemma 35 }
% 50.06/6.69 fresh272(class_Lattices_Obounded__lattice(tc_bool), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.69 = { by lemma 33 }
% 50.06/6.69 fresh272(class_Orderings_Olinorder(tc_nat), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.69 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.69 fresh272(true2, hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.69 = { by axiom 7 (clsarity_fun__Orderings_Opreorder) R->L }
% 50.06/6.69 fresh272(fresh69(class_Lattices_Obounded__lattice(tc_bool), class_Lattices_Obounded__lattice(tc_bool), tc_List_Olist(tc_String_Ochar), tc_bool), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by lemma 33 }
% 50.06/6.70 fresh272(fresh69(class_Orderings_Olinorder(tc_nat), class_Lattices_Obounded__lattice(tc_bool), tc_List_Olist(tc_String_Ochar), tc_bool), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.70 fresh272(fresh69(true2, class_Lattices_Obounded__lattice(tc_bool), tc_List_Olist(tc_String_Ochar), tc_bool), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by axiom 3 (clsarity_bool__Orderings_Opreorder) R->L }
% 50.06/6.70 fresh272(fresh69(class_Orderings_Opreorder(tc_bool), class_Lattices_Obounded__lattice(tc_bool), tc_List_Olist(tc_String_Ochar), tc_bool), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by lemma 33 }
% 50.06/6.70 fresh272(fresh69(class_Orderings_Opreorder(tc_bool), class_Orderings_Olinorder(tc_nat), tc_List_Olist(tc_String_Ochar), tc_bool), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.70 fresh272(fresh69(class_Orderings_Opreorder(tc_bool), true2, tc_List_Olist(tc_String_Ochar), tc_bool), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by axiom 13 (clsarity_fun__Orderings_Opreorder) }
% 50.06/6.70 fresh272(class_Orderings_Opreorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by lemma 39 }
% 50.06/6.70 fresh272(class_Orderings_Opreorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by lemma 35 }
% 50.06/6.70 fresh272(class_Orderings_Opreorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), class_Lattices_Obounded__lattice(tc_bool), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by lemma 33 }
% 50.06/6.70 fresh272(class_Orderings_Opreorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), class_Orderings_Olinorder(tc_nat), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.70 fresh272(class_Orderings_Opreorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), true2, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by axiom 27 (cls_order__trans_0) }
% 50.06/6.70 fresh133(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), true2, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 50.06/6.70 fresh133(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), class_Orderings_Olinorder(tc_nat), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by lemma 33 R->L }
% 50.06/6.70 fresh133(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), class_Lattices_Obounded__lattice(tc_bool), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by lemma 35 R->L }
% 50.06/6.70 fresh133(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.70 = { by lemma 39 R->L }
% 50.06/6.70 fresh133(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.71 = { by axiom 30 (cls_conjecture_3) }
% 50.06/6.71 fresh133(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.71 = { by axiom 29 (cls_conjecture_5) }
% 50.06/6.71 fresh133(c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.71 = { by lemma 39 R->L }
% 50.06/6.71 fresh133(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.71 = { by axiom 17 (cls_order__trans_0) }
% 50.06/6.71 c_lessequals(Y, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))
% 50.06/6.71
% 50.06/6.71 Lemma 41: hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))) = true2.
% 50.06/6.71 Proof:
% 50.06/6.71 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))
% 50.06/6.71 = { by lemma 39 }
% 50.06/6.71 c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))
% 50.06/6.71 = { by lemma 35 }
% 50.06/6.71 class_Lattices_Obounded__lattice(tc_bool)
% 50.06/6.71 = { by lemma 33 }
% 50.06/6.71 class_Orderings_Olinorder(tc_nat)
% 50.06/6.71 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.71 true2
% 50.06/6.71
% 50.06/6.71 Lemma 42: hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))) = class_Lattices_Oupper__semilattice(tc_fun(X, tc_bool)).
% 50.06/6.71 Proof:
% 50.06/6.71 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))
% 50.06/6.71 = { by lemma 39 }
% 50.06/6.71 c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))
% 50.06/6.71 = { by lemma 35 }
% 50.06/6.71 class_Lattices_Obounded__lattice(tc_bool)
% 50.06/6.71 = { by lemma 33 }
% 50.06/6.71 class_Orderings_Olinorder(tc_nat)
% 50.06/6.71 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.71 true2
% 50.06/6.71 = { by axiom 6 (clsarity_fun__Lattices_Oupper__semilattice) R->L }
% 50.06/6.71 fresh72(class_Lattices_Obounded__lattice(tc_bool), class_Lattices_Obounded__lattice(tc_bool), X, tc_bool)
% 50.06/6.71 = { by lemma 34 R->L }
% 50.06/6.71 fresh72(class_Lattices_Olattice(tc_bool), class_Lattices_Obounded__lattice(tc_bool), X, tc_bool)
% 50.06/6.71 = { by lemma 33 }
% 50.06/6.71 fresh72(class_Lattices_Olattice(tc_bool), class_Orderings_Olinorder(tc_nat), X, tc_bool)
% 50.06/6.71 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.71 fresh72(class_Lattices_Olattice(tc_bool), true2, X, tc_bool)
% 50.06/6.71 = { by axiom 12 (clsarity_fun__Lattices_Oupper__semilattice) }
% 50.06/6.71 class_Lattices_Oupper__semilattice(tc_fun(X, tc_bool))
% 50.06/6.71
% 50.06/6.71 Lemma 43: hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))) = class_Lattices_Olattice(tc_fun(X, tc_bool)).
% 50.06/6.71 Proof:
% 50.06/6.71 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))
% 50.06/6.71 = { by lemma 39 }
% 50.06/6.71 c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))
% 50.06/6.71 = { by lemma 35 }
% 50.06/6.71 class_Lattices_Obounded__lattice(tc_bool)
% 50.06/6.71 = { by lemma 33 }
% 50.06/6.71 class_Orderings_Olinorder(tc_nat)
% 50.06/6.71 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.71 true2
% 50.06/6.71 = { by axiom 5 (clsarity_fun__Lattices_Olattice) R->L }
% 50.06/6.71 fresh73(class_Lattices_Obounded__lattice(tc_bool), class_Lattices_Obounded__lattice(tc_bool), X, tc_bool)
% 50.06/6.71 = { by lemma 34 R->L }
% 50.06/6.71 fresh73(class_Lattices_Olattice(tc_bool), class_Lattices_Obounded__lattice(tc_bool), X, tc_bool)
% 50.06/6.71 = { by lemma 33 }
% 50.06/6.71 fresh73(class_Lattices_Olattice(tc_bool), class_Orderings_Olinorder(tc_nat), X, tc_bool)
% 50.06/6.71 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.71 fresh73(class_Lattices_Olattice(tc_bool), true2, X, tc_bool)
% 50.06/6.71 = { by axiom 11 (clsarity_fun__Lattices_Olattice) }
% 50.06/6.71 class_Lattices_Olattice(tc_fun(X, tc_bool))
% 50.06/6.71
% 50.06/6.72 Lemma 44: hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))) = fresh273(X, X, Y, Z, W).
% 50.06/6.72 Proof:
% 50.06/6.72 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))
% 50.06/6.72 = { by lemma 39 }
% 50.06/6.72 c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))
% 50.06/6.72 = { by lemma 35 }
% 50.06/6.72 class_Lattices_Obounded__lattice(tc_bool)
% 50.06/6.72 = { by lemma 33 }
% 50.06/6.72 class_Orderings_Olinorder(tc_nat)
% 50.06/6.72 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.72 true2
% 50.06/6.72 = { by axiom 8 (cls_order__trans_0) R->L }
% 50.06/6.72 fresh273(X, X, Y, Z, W)
% 50.06/6.72
% 50.06/6.72 Lemma 45: hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))) = fresh151(X, X, Y, Z, W, V).
% 50.06/6.72 Proof:
% 50.06/6.72 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))
% 50.06/6.72 = { by lemma 39 }
% 50.06/6.72 c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))
% 50.06/6.72 = { by lemma 35 }
% 50.06/6.72 class_Lattices_Obounded__lattice(tc_bool)
% 50.06/6.72 = { by lemma 33 }
% 50.06/6.72 class_Orderings_Olinorder(tc_nat)
% 50.06/6.72 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.72 true2
% 50.06/6.72 = { by axiom 15 (cls_le__supI1_0) R->L }
% 50.06/6.72 fresh151(X, X, Y, Z, W, V)
% 50.06/6.72
% 50.06/6.72 Lemma 46: hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))) = c_lessequals(X, c_Lattices_Oupper__semilattice__class_Osup(Y, X, tc_fun(Z, tc_bool)), tc_fun(Z, tc_bool)).
% 50.06/6.72 Proof:
% 50.06/6.72 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))
% 50.06/6.72 = { by lemma 39 }
% 50.06/6.72 c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))
% 50.06/6.72 = { by lemma 35 }
% 50.06/6.72 class_Lattices_Obounded__lattice(tc_bool)
% 50.06/6.72 = { by lemma 33 }
% 50.06/6.72 class_Orderings_Olinorder(tc_nat)
% 50.06/6.72 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.72 true2
% 50.06/6.72 = { by axiom 10 (cls_inf__sup__ord_I4_J_0) R->L }
% 50.06/6.72 fresh162(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(Z, tc_bool), X, Y)
% 50.06/6.72 = { by lemma 43 }
% 50.06/6.72 fresh162(class_Lattices_Olattice(tc_fun(Z, tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(Z, tc_bool), X, Y)
% 50.06/6.72 = { by lemma 39 }
% 50.06/6.72 fresh162(class_Lattices_Olattice(tc_fun(Z, tc_bool)), c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(Z, tc_bool), X, Y)
% 50.06/6.72 = { by lemma 35 }
% 50.06/6.72 fresh162(class_Lattices_Olattice(tc_fun(Z, tc_bool)), class_Lattices_Obounded__lattice(tc_bool), tc_fun(Z, tc_bool), X, Y)
% 50.06/6.72 = { by lemma 33 }
% 50.06/6.72 fresh162(class_Lattices_Olattice(tc_fun(Z, tc_bool)), class_Orderings_Olinorder(tc_nat), tc_fun(Z, tc_bool), X, Y)
% 50.06/6.72 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.72 fresh162(class_Lattices_Olattice(tc_fun(Z, tc_bool)), true2, tc_fun(Z, tc_bool), X, Y)
% 50.06/6.72 = { by axiom 19 (cls_inf__sup__ord_I4_J_0) }
% 50.06/6.72 c_lessequals(X, c_Lattices_Oupper__semilattice__class_Osup(Y, X, tc_fun(Z, tc_bool)), tc_fun(Z, tc_bool))
% 50.06/6.72
% 50.06/6.73 Lemma 47: fresh273(c_lessequals(X, Y, Z), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), Z, X, W) = fresh272(V, V, Z, X, W, Y).
% 50.06/6.73 Proof:
% 50.06/6.73 fresh273(c_lessequals(X, Y, Z), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), Z, X, W)
% 50.06/6.73 = { by lemma 39 }
% 50.06/6.73 fresh273(c_lessequals(X, Y, Z), c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), Z, X, W)
% 50.06/6.73 = { by lemma 35 }
% 50.06/6.73 fresh273(c_lessequals(X, Y, Z), class_Lattices_Obounded__lattice(tc_bool), Z, X, W)
% 50.06/6.73 = { by lemma 33 }
% 50.06/6.73 fresh273(c_lessequals(X, Y, Z), class_Orderings_Olinorder(tc_nat), Z, X, W)
% 50.06/6.73 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.73 fresh273(c_lessequals(X, Y, Z), true2, Z, X, W)
% 50.06/6.73 = { by axiom 24 (cls_order__trans_0) R->L }
% 50.06/6.73 fresh272(V, V, Z, X, W, Y)
% 50.06/6.73
% 50.06/6.73 Lemma 48: fresh151(c_lessequals(X, Y, Z), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), Z, X, Y, W) = fresh152(class_Lattices_Oupper__semilattice(Z), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), Z, X, Y, W).
% 50.06/6.73 Proof:
% 50.06/6.73 fresh151(c_lessequals(X, Y, Z), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), Z, X, Y, W)
% 50.06/6.73 = { by lemma 39 }
% 50.06/6.73 fresh151(c_lessequals(X, Y, Z), c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), Z, X, Y, W)
% 50.06/6.73 = { by lemma 35 }
% 50.06/6.73 fresh151(c_lessequals(X, Y, Z), class_Lattices_Obounded__lattice(tc_bool), Z, X, Y, W)
% 50.06/6.73 = { by lemma 33 }
% 50.06/6.73 fresh151(c_lessequals(X, Y, Z), class_Orderings_Olinorder(tc_nat), Z, X, Y, W)
% 50.06/6.73 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 50.06/6.73 fresh151(c_lessequals(X, Y, Z), true2, Z, X, Y, W)
% 50.06/6.73 = { by axiom 25 (cls_le__supI1_0) R->L }
% 50.06/6.73 fresh152(class_Lattices_Oupper__semilattice(Z), true2, Z, X, Y, W)
% 50.06/6.73 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 50.06/6.73 fresh152(class_Lattices_Oupper__semilattice(Z), class_Orderings_Olinorder(tc_nat), Z, X, Y, W)
% 50.06/6.73 = { by lemma 33 R->L }
% 50.06/6.73 fresh152(class_Lattices_Oupper__semilattice(Z), class_Lattices_Obounded__lattice(tc_bool), Z, X, Y, W)
% 50.06/6.73 = { by lemma 35 R->L }
% 50.06/6.73 fresh152(class_Lattices_Oupper__semilattice(Z), c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), Z, X, Y, W)
% 50.06/6.73 = { by lemma 39 R->L }
% 50.06/6.73 fresh152(class_Lattices_Oupper__semilattice(Z), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), Z, X, Y, W)
% 50.06/6.73
% 50.06/6.73 Goal 1 (cls_conjecture_7): tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) = tuple(true2, true2, true2).
% 50.06/6.73 Proof:
% 50.06/6.73 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.73 = { by axiom 20 (cls_le__supI1_0) R->L }
% 50.06/6.73 tuple(fresh152(X, X, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.73 = { by axiom 23 (cls_inf__sup__aci_I6_J_0) R->L }
% 50.06/6.73 tuple(fresh152(X, X, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), fresh166(Y, Y, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, v_x), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.73 = { by axiom 23 (cls_inf__sup__aci_I6_J_0) R->L }
% 50.06/6.73 tuple(fresh152(X, X, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), fresh166(Y, Y, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, v_x), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(v_ae, fresh166(Z, Z, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, v_x), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.73 = { by lemma 38 R->L }
% 50.06/6.73 tuple(fresh152(X, X, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(v_ae, fresh166(Z, Z, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, v_x), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.74 = { by lemma 38 R->L }
% 50.06/6.74 tuple(fresh152(X, X, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.74 = { by axiom 20 (cls_le__supI1_0) }
% 50.06/6.74 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.74 = { by axiom 20 (cls_le__supI1_0) R->L }
% 50.06/6.74 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh152(W, W, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.74 = { by lemma 36 }
% 50.06/6.74 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh152(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.74 = { by lemma 42 }
% 50.06/6.74 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh152(class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.74 = { by lemma 48 R->L }
% 50.06/6.74 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.75 = { by lemma 40 R->L }
% 50.06/6.75 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(fresh272(V, V, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.75 = { by lemma 47 R->L }
% 50.06/6.75 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(fresh273(c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.75 = { by axiom 18 (cls_inf__sup__ord_I3_J_0) R->L }
% 50.06/6.75 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(fresh273(fresh163(class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), true2, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.76 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 50.06/6.76 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(fresh273(fresh163(class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), class_Orderings_Olinorder(tc_nat), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.76 = { by lemma 33 R->L }
% 50.06/6.76 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(fresh273(fresh163(class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), class_Lattices_Obounded__lattice(tc_bool), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.76 = { by lemma 35 R->L }
% 50.06/6.77 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(fresh273(fresh163(class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.77 = { by lemma 39 R->L }
% 50.06/6.77 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(fresh273(fresh163(class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.77 = { by lemma 43 R->L }
% 50.06/6.78 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(fresh273(fresh163(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.78 = { by axiom 9 (cls_inf__sup__ord_I3_J_0) }
% 50.06/6.78 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(fresh273(true2, hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.78 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 50.06/6.78 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(fresh273(class_Orderings_Olinorder(tc_nat), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.79 = { by lemma 33 R->L }
% 50.06/6.79 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(fresh273(class_Lattices_Obounded__lattice(tc_bool), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.06/6.79 = { by lemma 35 R->L }
% 50.84/6.79 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(fresh273(c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.84/6.79 = { by lemma 39 R->L }
% 50.84/6.80 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(fresh273(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.90/6.80 = { by lemma 44 R->L }
% 50.90/6.80 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), fresh151(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.90/6.80 = { by lemma 45 R->L }
% 50.90/6.80 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))
% 50.90/6.80 = { by axiom 20 (cls_le__supI1_0) R->L }
% 50.90/6.81 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), fresh152(U, U, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_ae, v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))
% 50.90/6.81 = { by lemma 36 }
% 50.90/6.81 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), fresh152(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x))
% 50.90/6.81 = { by lemma 42 }
% 51.02/6.81 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), fresh152(class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x))
% 51.02/6.82 = { by lemma 48 R->L }
% 51.02/6.82 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), fresh151(c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x))
% 51.02/6.82 = { by lemma 40 R->L }
% 51.02/6.83 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), fresh151(fresh272(T, T, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x))
% 51.02/6.83 = { by lemma 47 R->L }
% 51.02/6.83 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), fresh151(fresh273(c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x))
% 51.02/6.83 = { by lemma 46 R->L }
% 51.02/6.84 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), fresh151(fresh273(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x))
% 51.02/6.84 = { by lemma 44 R->L }
% 51.02/6.84 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), fresh151(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_x))
% 51.02/6.84 = { by lemma 45 R->L }
% 51.02/6.85 tuple(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.85 = { by axiom 21 (cls_le__supI2_0) R->L }
% 51.02/6.85 tuple(fresh150(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.85 = { by lemma 42 }
% 51.02/6.85 tuple(fresh150(class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.85 = { by lemma 39 }
% 51.02/6.86 tuple(fresh150(class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.86 = { by lemma 35 }
% 51.02/6.86 tuple(fresh150(class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), class_Lattices_Obounded__lattice(tc_bool), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.86 = { by lemma 33 }
% 51.02/6.86 tuple(fresh150(class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), class_Orderings_Olinorder(tc_nat), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.86 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) }
% 51.02/6.86 tuple(fresh150(class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), true2, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.86 = { by axiom 26 (cls_le__supI2_0) }
% 51.02/6.87 tuple(fresh149(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), true2, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.87 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 51.02/6.87 tuple(fresh149(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), class_Orderings_Olinorder(tc_nat), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.87 = { by lemma 33 R->L }
% 51.02/6.87 tuple(fresh149(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), class_Lattices_Obounded__lattice(tc_bool), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.87 = { by lemma 35 R->L }
% 51.02/6.88 tuple(fresh149(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.88 = { by lemma 39 R->L }
% 51.02/6.88 tuple(fresh149(c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.88 = { by lemma 46 R->L }
% 51.02/6.88 tuple(fresh149(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool), v_x, c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.88 = { by axiom 16 (cls_le__supI2_0) }
% 51.02/6.88 tuple(true2, hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))), hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.88 = { by lemma 41 }
% 51.02/6.89 tuple(true2, true2, hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))
% 51.02/6.89 = { by lemma 41 }
% 51.02/6.89 tuple(true2, true2, true2)
% 51.02/6.89 % SZS output end Proof
% 51.02/6.89
% 51.02/6.89 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------