TSTP Solution File: SWW884+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW884+1 : TPTP v8.1.2. Released v7.3.0.
% 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 : n027.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 : Fri Sep 1 00:56:13 EDT 2023
% Result : Theorem 72.28s 9.67s
% Output : Proof 73.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW884+1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % 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 : n027.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 : Sun Aug 27 18:51:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 72.28/9.67 Command-line arguments: --no-flatten-goal
% 72.28/9.67
% 72.28/9.67 % SZS status Theorem
% 72.28/9.67
% 72.28/9.70 % SZS output start Proof
% 72.28/9.70 Take the following subset of the input axioms:
% 72.80/9.71 fof('HL_EXT', axiom, ![V_3f2384, V_3f2380, Vf, Vg]: (![Vx]: s__02(V_3f2380, chapp__02(s__02(cfun__02(V_3f2384, V_3f2380), Vf), s__02(V_3f2384, Vx)))=s__02(V_3f2380, chapp__02(s__02(cfun__02(V_3f2384, V_3f2380), Vg), s__02(V_3f2384, Vx))) => s__02(cfun__02(V_3f2384, V_3f2380), Vf)=s__02(cfun__02(V_3f2384, V_3f2380), Vg))).
% 72.80/9.71 fof('thm.ml_translator.Eval_def', axiom, ![V_27P_27, V_27env_27, V_27exp_27]: (p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), V_27env_27), s__02(c_27type_2east_2eexp_27__00, V_27exp_27), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), V_27P_27)))) <=> ![V_27refs_27]: ?[V_27res_27, V_27refs_7c39_7c_27]: (p__01(s__02(cbool__00, c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00, cF__00), s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), V_27env_27), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), V_27refs_27))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2east_2eexp_27__00, V_27exp_27), s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), V_27refs_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), V_27refs_7c39_7c_27))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00), c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00, V_27res_27)))))))) & p__01(s__02(cbool__00, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), V_27P_27), s__02(c_27type_2esemanticPrimitives_2ev_27__00, V_27res_27))))))).
% 72.80/9.71 fof('thm.ml_translator.FUN_FORALL', axiom, ![V_27A_27, V_27B_27, Vx0, Vx1, Vx2]: (p__01(s__02(cbool__00, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(V_27A_27, cfun__02(V_27B_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), Vx2), s__02(V_27B_27, Vx0))), s__02(c_27type_2esemanticPrimitives_2ev_27__00, Vx1)))) <=> ![V_27y_27]: p__01(s__02(cbool__00, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(V_27B_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(V_27A_27, cfun__02(V_27B_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), Vx2), s__02(V_27A_27, V_27y_27))), s__02(V_27B_27, Vx0))), s__02(c_27type_2esemanticPrimitives_2ev_27__00, Vx1)))))).
% 72.80/9.71 fof('thm.ml_translator.evaluate_11_Rval', axiom, ![V_27s2_27, V_27s1_27, V_27s_27, V_27res2_27, V_27res1_27, V_27b_27, V_27env_27_2, V_27exp_27_2, V_27A_27_2]: (p__01(s__02(cbool__00, c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00, V_27b_27), s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), V_27env_27_2), s__02(c_27type_2esemanticPrimitives_2estate_27__01(V_27A_27_2), V_27s_27), s__02(c_27type_2east_2eexp_27__00, V_27exp_27_2), s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(V_27A_27_2), c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(V_27A_27_2), V_27s1_27), s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00), c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00, V_27res1_27)))))))) => (p__01(s__02(cbool__00, c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00, V_27b_27), s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), V_27env_27_2), s__02(c_27type_2esemanticPrimitives_2estate_27__01(V_27A_27_2), V_27s_27), s__02(c_27type_2east_2eexp_27__00, V_27exp_27_2), s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(V_27A_27_2), c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(V_27A_27_2), V_27s2_27), s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00), c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00, V_27res2_27)))))))) => s__02(c_27type_2esemanticPrimitives_2ev_27__00, V_27res1_27)=s__02(c_27type_2esemanticPrimitives_2ev_27__00, V_27res2_27)))).
% 72.80/9.71 fof(conjecture, conjecture, ![V__0, V_27A_27_2, V_27B_27_2]: (![V_27x_27, V_27p_27]: s__02(cfun__02(V_27B_27_2, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(V_27A_27_2, cfun__02(V_27B_27_2, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), chapp__02(s__02(cfun__02(cfun__02(V_27A_27_2, cfun__02(V_27B_27_2, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), cfun__02(V_27A_27_2, cfun__02(V_27B_27_2, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)))), V__0), s__02(cfun__02(V_27A_27_2, cfun__02(V_27B_27_2, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), V_27p_27))), s__02(V_27A_27_2, V_27x_27)))=s__02(cfun__02(V_27B_27_2, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(V_27A_27_2, cfun__02(V_27B_27_2, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), V_27p_27), s__02(V_27A_27_2, V_27x_27))) => ![V_27f_27, V_27p_27_2, V_27env_27_2, V_27exp_27_2]: (![V_27x_27_2]: p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), V_27env_27_2), s__02(c_27type_2east_2eexp_27__00, V_27exp_27_2), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(V_27B_27_2, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(V_27A_27_2, cfun__02(V_27B_27_2, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), V_27p_27_2), s__02(V_27A_27_2, V_27x_27_2))), s__02(V_27B_27_2, V_27f_27)))))) => p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), V_27env_27_2), s__02(c_27type_2east_2eexp_27__00, V_27exp_27_2), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(V_27A_27_2, cfun__02(V_27B_27_2, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), chapp__02(s__02(cfun__02(cfun__02(V_27A_27_2, cfun__02(V_27B_27_2, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), cfun__02(V_27A_27_2, cfun__02(V_27B_27_2, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)))), V__0), s__02(cfun__02(V_27A_27_2, cfun__02(V_27B_27_2, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), V_27p_27_2))), s__02(V_27B_27_2, V_27f_27))))))))).
% 72.80/9.71
% 72.80/9.71 Now clausify the problem and encode Horn clauses using encoding 3 of
% 72.80/9.71 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 72.80/9.71 We repeatedly replace C & s=t => u=v by the two clauses:
% 72.80/9.71 fresh(y, y, x1...xn) = u
% 72.80/9.71 C => fresh(s, t, x1...xn) = v
% 72.80/9.71 where fresh is a fresh function symbol and x1..xn are the free
% 72.80/9.71 variables of u and v.
% 72.80/9.71 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 72.80/9.71 input problem has no model of domain size 1).
% 72.80/9.71
% 72.80/9.71 The encoding turns the above axioms into the following unit equations and goals:
% 72.80/9.71
% 72.80/9.71 Axiom 1 (thm.bool.IMP_CLAUSES_7): fresh51(X, X, Y) = p__01(s__02(cbool__00, Y)).
% 72.80/9.71 Axiom 2 (thm.ml_translator.evaluate_11_Rval): fresh42(X, X, Y, Z) = s__02(c_27type_2esemanticPrimitives_2ev_27__00, Y).
% 72.80/9.71 Axiom 3 (thm.ml_translator.Eval_def): fresh47(X, X, Y, Z, W) = true2.
% 72.80/9.71 Axiom 4 (HL_EXT): fresh59(X, X, Y, Z, W, V) = s__02(cfun__02(Y, Z), V).
% 72.80/9.71 Axiom 5 (thm.ml_translator.Eval_def_1): fresh46(X, X, Y, Z, W, V) = true2.
% 72.80/9.71 Axiom 6 (thm.ml_translator.Eval_def_2): fresh45(X, X, Y, Z, W, V) = true2.
% 72.80/9.71 Axiom 7 (thm.ml_translator.FUN_FORALL): fresh44(X, X, Y, Z, W, V, U) = true2.
% 72.80/9.71 Axiom 8 (thm.ml_translator.evaluate_11_Rval): fresh41(X, X, Y, Z, W, V, U, T, S, X2) = s__02(c_27type_2esemanticPrimitives_2ev_27__00, U).
% 72.80/9.71 Axiom 9 (thm.ml_translator.Eval_def): fresh48(X, X, Y, Z, W, V) = p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), Y), s__02(c_27type_2east_2eexp_27__00, Z), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), W)))).
% 72.80/9.72 Axiom 10 (thm.ml_translator.Eval_def_1): fresh46(p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), X), s__02(c_27type_2east_2eexp_27__00, Y), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), Z)))), true2, X, Y, Z, W) = p__01(s__02(cbool__00, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), Z), s__02(c_27type_2esemanticPrimitives_2ev_27__00, v_27res_27(X, Y, Z, W))))).
% 72.80/9.72 Axiom 11 (HL_EXT): fresh59(s__02(X, chapp__02(s__02(cfun__02(Y, X), Z), s__02(Y, vx(Y, X, Z, W)))), s__02(X, chapp__02(s__02(cfun__02(Y, X), W), s__02(Y, vx(Y, X, Z, W)))), Y, X, Z, W) = s__02(cfun__02(Y, X), Z).
% 72.80/9.72 Axiom 12 (conjecture_1): p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), v_27env_27), s__02(c_27type_2east_2eexp_27__00, v_27exp_27), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)))))) = true2.
% 72.80/9.72 Axiom 13 (conjecture): s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), chapp__02(s__02(cfun__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)))), v__0), s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), X))), s__02(v_27a_27, Y))) = s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), X), s__02(v_27a_27, Y))).
% 72.80/9.72 Axiom 14 (thm.ml_translator.FUN_FORALL): fresh44(p__01(s__02(cbool__00, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(X, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(Y, cfun__02(X, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), Z), s__02(Y, v_27y_27(Y, X, Z, W, V)))), s__02(X, W))), s__02(c_27type_2esemanticPrimitives_2ev_27__00, V)))), true2, Y, X, Z, W, V) = p__01(s__02(cbool__00, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(Y, cfun__02(X, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), Z), s__02(X, W))), s__02(c_27type_2esemanticPrimitives_2ev_27__00, V)))).
% 72.80/9.72 Axiom 15 (thm.ml_translator.evaluate_11_Rval): fresh41(p__01(s__02(cbool__00, c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00, X), s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), Y), s__02(c_27type_2esemanticPrimitives_2estate_27__01(Z), W), s__02(c_27type_2east_2eexp_27__00, V), s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(Z), c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(Z), U), s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00), c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00, T)))))))), true2, Z, S, W, X2, T, V, Y, X) = fresh42(p__01(s__02(cbool__00, c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00, X), s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), Y), s__02(c_27type_2esemanticPrimitives_2estate_27__01(Z), W), s__02(c_27type_2east_2eexp_27__00, V), s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(Z), c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(Z), S), s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00), c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00, X2)))))))), true2, X2, T).
% 72.80/9.72 Axiom 16 (thm.ml_translator.Eval_def_2): fresh45(p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), X), s__02(c_27type_2east_2eexp_27__00, Y), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), Z)))), true2, X, Y, Z, W) = p__01(s__02(cbool__00, c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00, cF__00), s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), X), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), W))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2east_2eexp_27__00, Y), s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), W), s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_7c39_7c_27(X, Y, Z, W)))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00), c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00, v_27res_27(X, Y, Z, W))))))))).
% 72.80/9.72 Axiom 17 (thm.ml_translator.Eval_def): fresh48(p__01(s__02(cbool__00, c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00, cF__00), s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), X), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_27(X, Y, Z)))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2east_2eexp_27__00, Y), s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_27(X, Y, Z)), s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), W))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00), c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00, V)))))))), true2, X, Y, Z, V) = fresh47(p__01(s__02(cbool__00, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), Z), s__02(c_27type_2esemanticPrimitives_2ev_27__00, V)))), true2, X, Y, Z).
% 72.80/9.72
% 72.80/9.72 Lemma 18: fresh51(X, X, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), Y), s__02(c_27type_2east_2eexp_27__00, Z), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), W))) = fresh48(V, V, Y, Z, W, U).
% 72.80/9.72 Proof:
% 72.80/9.72 fresh51(X, X, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), Y), s__02(c_27type_2east_2eexp_27__00, Z), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), W)))
% 72.80/9.72 = { by axiom 1 (thm.bool.IMP_CLAUSES_7) }
% 72.80/9.72 p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), Y), s__02(c_27type_2east_2eexp_27__00, Z), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), W))))
% 72.80/9.72 = { by axiom 9 (thm.ml_translator.Eval_def) R->L }
% 72.80/9.72 fresh48(V, V, Y, Z, W, U)
% 72.80/9.72
% 72.80/9.72 Lemma 19: fresh48(X, X, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, Y))), s__02(v_27b_27, v_27f_27)), Z) = true2.
% 72.80/9.72 Proof:
% 72.80/9.72 fresh48(X, X, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, Y))), s__02(v_27b_27, v_27f_27)), Z)
% 72.80/9.72 = { by lemma 18 R->L }
% 72.80/9.72 fresh51(W, W, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), v_27env_27), s__02(c_27type_2east_2eexp_27__00, v_27exp_27), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, Y))), s__02(v_27b_27, v_27f_27)))))
% 72.80/9.72 = { by axiom 1 (thm.bool.IMP_CLAUSES_7) }
% 72.80/9.72 p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), v_27env_27), s__02(c_27type_2east_2eexp_27__00, v_27exp_27), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, Y))), s__02(v_27b_27, v_27f_27))))))
% 72.80/9.72 = { by axiom 12 (conjecture_1) }
% 72.80/9.72 true2
% 72.80/9.72
% 72.80/9.72 Lemma 20: fresh51(X, X, c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00, cF__00), s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), Y), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), Z))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2east_2eexp_27__00, W), s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), Z), s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_7c39_7c_27(Y, W, V, Z)))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00), c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00, v_27res_27(Y, W, V, Z)))))))) = fresh45(fresh48(U, U, Y, W, V, T), true2, Y, W, V, Z).
% 72.80/9.72 Proof:
% 72.80/9.72 fresh51(X, X, c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00, cF__00), s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), Y), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), Z))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2east_2eexp_27__00, W), s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), Z), s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_7c39_7c_27(Y, W, V, Z)))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00), c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00, v_27res_27(Y, W, V, Z))))))))
% 72.80/9.72 = { by axiom 1 (thm.bool.IMP_CLAUSES_7) }
% 72.80/9.72 p__01(s__02(cbool__00, c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00, cF__00), s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), Y), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), Z))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2east_2eexp_27__00, W), s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), Z), s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_7c39_7c_27(Y, W, V, Z)))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00), c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00, v_27res_27(Y, W, V, Z)))))))))
% 72.80/9.72 = { by axiom 16 (thm.ml_translator.Eval_def_2) R->L }
% 72.80/9.72 fresh45(p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), Y), s__02(c_27type_2east_2eexp_27__00, W), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), V)))), true2, Y, W, V, Z)
% 72.80/9.72 = { by axiom 1 (thm.bool.IMP_CLAUSES_7) R->L }
% 72.80/9.72 fresh45(fresh51(S, S, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), Y), s__02(c_27type_2east_2eexp_27__00, W), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), V))), true2, Y, W, V, Z)
% 72.80/9.72 = { by lemma 18 }
% 72.80/9.72 fresh45(fresh48(U, U, Y, W, V, T), true2, Y, W, V, Z)
% 72.80/9.72
% 72.80/9.72 Goal 1 (conjecture_2): p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), v_27env_27), s__02(c_27type_2east_2eexp_27__00, v_27exp_27), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), chapp__02(s__02(cfun__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)))), v__0), s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27))), s__02(v_27b_27, v_27f_27)))))) = true2.
% 72.80/9.72 Proof:
% 72.80/9.73 p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), v_27env_27), s__02(c_27type_2east_2eexp_27__00, v_27exp_27), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), chapp__02(s__02(cfun__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)))), v__0), s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27))), s__02(v_27b_27, v_27f_27))))))
% 72.80/9.73 = { by axiom 4 (HL_EXT) R->L }
% 72.80/9.73 p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), v_27env_27), s__02(c_27type_2east_2eexp_27__00, v_27exp_27), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), c_27const_2eml__translator_2eFUN__FORALL_27__02(fresh59(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, vx(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), v_27p_27, chapp__02(s__02(cfun__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)))), v__0), s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27)))))), s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, vx(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), v_27p_27, chapp__02(s__02(cfun__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)))), v__0), s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27)))))), v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), v_27p_27, chapp__02(s__02(cfun__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)))), v__0), s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27))), s__02(v_27b_27, v_27f_27))))))
% 72.80/9.73 = { by axiom 13 (conjecture) R->L }
% 72.80/9.73 p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), v_27env_27), s__02(c_27type_2east_2eexp_27__00, v_27exp_27), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), c_27const_2eml__translator_2eFUN__FORALL_27__02(fresh59(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, vx(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), v_27p_27, chapp__02(s__02(cfun__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)))), v__0), s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27)))))), s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), chapp__02(s__02(cfun__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)))), v__0), s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27))), s__02(v_27a_27, vx(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), v_27p_27, chapp__02(s__02(cfun__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)))), v__0), s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27)))))), v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), v_27p_27, chapp__02(s__02(cfun__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)))), v__0), s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27))), s__02(v_27b_27, v_27f_27))))))
% 72.80/9.73 = { by axiom 11 (HL_EXT) }
% 72.80/9.73 p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), v_27env_27), s__02(c_27type_2east_2eexp_27__00, v_27exp_27), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))
% 72.80/9.73 = { by axiom 9 (thm.ml_translator.Eval_def) R->L }
% 72.80/9.73 fresh48(true2, true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))
% 72.80/9.73 = { by axiom 6 (thm.ml_translator.Eval_def_2) R->L }
% 72.80/9.73 fresh48(fresh45(true2, true2, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))
% 72.80/9.73 = { by lemma 19 R->L }
% 72.80/9.73 fresh48(fresh45(fresh48(Y, Y, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), Z), true2, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))
% 72.80/9.73 = { by lemma 20 R->L }
% 72.80/9.73 fresh48(fresh51(W, W, c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00, cF__00), s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), v_27env_27), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2east_2eexp_27__00, v_27exp_27), s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_7c39_7c_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00), c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))
% 72.80/9.73 = { by axiom 1 (thm.bool.IMP_CLAUSES_7) }
% 72.80/9.73 fresh48(p__01(s__02(cbool__00, c_27const_2ebigStep_2eevaluate_27__05(s__02(cbool__00, cF__00), s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), v_27env_27), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2east_2eexp_27__00, v_27exp_27), s__02(c_27type_2epair_2eprod_27__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2epair_2e_2c_27__02(s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_7c39_7c_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00))), s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00), c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))
% 72.80/9.73 = { by axiom 17 (thm.ml_translator.Eval_def) }
% 72.80/9.73 fresh47(p__01(s__02(cbool__00, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))), s__02(c_27type_2esemanticPrimitives_2ev_27__00, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 72.80/9.74 = { by axiom 14 (thm.ml_translator.FUN_FORALL) R->L }
% 72.80/9.74 fresh47(fresh44(p__01(s__02(cbool__00, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27))), s__02(c_27type_2esemanticPrimitives_2ev_27__00, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 72.80/9.74 = { by axiom 1 (thm.bool.IMP_CLAUSES_7) R->L }
% 72.80/9.74 fresh47(fresh44(fresh51(V, V, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27))), s__02(c_27type_2esemanticPrimitives_2ev_27__00, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 72.80/9.74 = { by axiom 2 (thm.ml_translator.evaluate_11_Rval) R->L }
% 72.80/9.74 fresh47(fresh44(fresh51(V, V, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27))), fresh42(true2, true2, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 72.80/9.75 = { by axiom 6 (thm.ml_translator.Eval_def_2) R->L }
% 72.80/9.75 fresh47(fresh44(fresh51(V, V, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27))), fresh42(fresh45(true2, true2, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), true2, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 72.80/9.75 = { by lemma 19 R->L }
% 72.80/9.75 fresh47(fresh44(fresh51(V, V, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27))), fresh42(fresh45(fresh48(U, U, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), T), true2, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), true2, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 72.80/9.75 = { by lemma 20 R->L }
% 72.80/9.76 fresh47(fresh44(fresh51(V, V, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27))), 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chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 72.80/9.76 = { by axiom 1 (thm.bool.IMP_CLAUSES_7) }
% 72.80/9.76 fresh47(fresh44(fresh51(V, V, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27))), 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cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, 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% 72.80/9.77 = { by axiom 15 (thm.ml_translator.evaluate_11_Rval) R->L }
% 73.24/9.77 fresh47(fresh44(fresh51(V, V, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27))), 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% 73.24/9.78 = { by axiom 1 (thm.bool.IMP_CLAUSES_7) R->L }
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s__02(c_27type_2esemanticPrimitives_2eresult_27__02(c_27type_2esemanticPrimitives_2ev_27__00, c_27type_2esemanticPrimitives_2ev_27__00), c_27const_2esemanticPrimitives_2eRval_27__01(s__02(c_27type_2esemanticPrimitives_2ev_27__00, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))))))), true2, c_27type_2eone_2eone_27__00, c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_7c39_7c_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00)), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00)), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), v_27exp_27, v_27env_27, cF__00))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 73.24/9.79 = { by lemma 20 }
% 73.24/9.79 fresh47(fresh44(fresh51(V, V, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27))), fresh41(fresh45(fresh48(Y2, Y2, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), Z2), true2, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), true2, c_27type_2eone_2eone_27__00, c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_7c39_7c_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00)), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00)), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), v_27exp_27, v_27env_27, cF__00))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 73.24/9.79 = { by lemma 19 }
% 73.24/9.79 fresh47(fresh44(fresh51(V, V, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27))), fresh41(fresh45(true2, true2, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), true2, c_27type_2eone_2eone_27__00, c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_7c39_7c_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00)), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00)), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), v_27exp_27, v_27env_27, cF__00))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 73.24/9.79 = { by axiom 6 (thm.ml_translator.Eval_def_2) }
% 73.24/9.80 fresh47(fresh44(fresh51(V, V, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27))), fresh41(true2, true2, c_27type_2eone_2eone_27__00, c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_7c39_7c_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00)), c_27const_2esemanticPrimitives_2estate__refs__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2esemanticPrimitives_2estore__v_27__01(c_27type_2esemanticPrimitives_2ev_27__00)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))), s__02(c_27type_2esemanticPrimitives_2estate_27__01(c_27type_2eone_2eone_27__00), c_27const_2eml__translator_2eempty__state_27__00)), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), v_27exp_27, v_27env_27, cF__00))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 73.24/9.80 = { by axiom 8 (thm.ml_translator.evaluate_11_Rval) }
% 73.24/9.80 fresh47(fresh44(fresh51(V, V, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27))), s__02(c_27type_2esemanticPrimitives_2ev_27__00, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 73.24/9.80 = { by axiom 1 (thm.bool.IMP_CLAUSES_7) }
% 73.24/9.80 fresh47(fresh44(p__01(s__02(cbool__00, chapp__02(s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27))), s__02(c_27type_2esemanticPrimitives_2ev_27__00, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 73.24/9.80 = { by axiom 10 (thm.ml_translator.Eval_def_1) R->L }
% 73.24/9.81 fresh47(fresh44(fresh46(p__01(s__02(cbool__00, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), v_27env_27), s__02(c_27type_2east_2eexp_27__00, v_27exp_27), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)))))), true2, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 73.24/9.81 = { by axiom 1 (thm.bool.IMP_CLAUSES_7) R->L }
% 73.24/9.81 fresh47(fresh44(fresh46(fresh51(W2, W2, c_27const_2eml__translator_2eEval_27__03(s__02(c_27type_2esemanticPrimitives_2esem__env_27__01(c_27type_2esemanticPrimitives_2ev_27__00), v_27env_27), s__02(c_27type_2east_2eexp_27__00, v_27exp_27), s__02(cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00), chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 73.24/9.81 = { by lemma 18 }
% 73.24/9.81 fresh47(fresh44(fresh46(fresh48(V2, V2, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), U2), true2, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 73.24/9.81 = { by lemma 19 }
% 73.24/9.81 fresh47(fresh44(fresh46(true2, true2, v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, v_27y_27(v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))))))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))), true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 73.24/9.81 = { by axiom 5 (thm.ml_translator.Eval_def_1) }
% 73.24/9.81 fresh47(fresh44(true2, true2, v_27a_27, v_27b_27, v_27p_27, v_27f_27, v_27res_27(v_27env_27, v_27exp_27, chapp__02(s__02(cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00)), chapp__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27a_27, X))), s__02(v_27b_27, v_27f_27)), v_27refs_27(v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27))))), true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 73.24/9.81 = { by axiom 7 (thm.ml_translator.FUN_FORALL) }
% 73.24/9.81 fresh47(true2, true2, v_27env_27, v_27exp_27, c_27const_2eml__translator_2eFUN__FORALL_27__02(s__02(cfun__02(v_27a_27, cfun__02(v_27b_27, cfun__02(c_27type_2esemanticPrimitives_2ev_27__00, cbool__00))), v_27p_27), s__02(v_27b_27, v_27f_27)))
% 73.24/9.81 = { by axiom 3 (thm.ml_translator.Eval_def) }
% 73.24/9.81 true2
% 73.24/9.81 % SZS output end Proof
% 73.24/9.81
% 73.24/9.81 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------