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Proof step 53 from proof rg2-sound-main-unfair (previous step)

R1(pm, s1, S) → R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S')), \A ∀ N0, R1, pm, S, Post1, s, G1, Pre1, I, R2, G2, Pre2, Post2, N. N0 < m → R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S')) ∧ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ Pre1(pm, s) ∧ Pre2(pm, s) ∧ I(pm, S) ∧ Post2(pm, s, S) → ((R1(pm, S', S'') ∧ R2(pm, S', S'') ∧ N = N'' + 1) ∧ N0 = N0'' +1) -+-> (last ⊃ Post1(pm, s, S) ∧ Post2(pm, s, S);G1(pm, S, S') ∨ G2(pm, S, S')), m = n, RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), I(pm, s0), Post2(pm, s, s0), ¬ false, boolvar → s0 = s1 ∧ n = n1 ∧ n0 = n2, (false ⊃ Post1(pm, s, s0);G1(pm, s0, s1)) ⊦ (false ⊃ Post1(pm, s, s0) ∧ Post2(pm, s, s0);G1(pm, s0, s1) ∨ G2(pm, s0, s1)) ∧ ( (R1(pm, s1, S) ∧ R2(pm, s1, S) ∧ n0 = N + 1) ∧ n = N0 +1 → ((R1(pm, S', S'') ∧ R2(pm, S', S'') ∧ N = N'' + 1) ∧ N0 = N0'' +1) -+-> (last ⊃ Post1(pm, s, S) ∧ Post2(pm, s, S);G1(pm, S, S') ∨ G2(pm, S, S')))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S')), \A ∀ N0, R1, pm, S, Post1, s, G1, Pre1, I, R2, G2, Pre2, Post2, N. N0 < n → R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S')) ∧ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ Pre1(pm, s) ∧ Pre2(pm, s) ∧ I(pm, S) ∧ Post2(pm, s, S) → ((R1(pm, S', S'') ∧ R2(pm, S', S'') ∧ N = N'' + 1) ∧ N0 = N0'' +1) -+-> (last ⊃ Post1(pm, s, S) ∧ Post2(pm, s, S);G1(pm, S, S') ∨ G2(pm, S, S')), n = N0 + 1, R2(pm, s0, S), Post2(pm, s, s1), I(pm, s1), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), I(pm, s0), Post2(pm, s, s0), G1(pm, s0, s1), R1(pm, s1, S), R2(pm, s1, S), R2(pm, s0, s1), I(pm, s), I(pm, S), Post2(pm, s, S), boolvar → s0 = s1 ∧ N0 + 1 = n1 ∧ N + 1 = n2 ⊦ (R1(pm, S', S'') ∧ R2(pm, S', S'') ∧ N = N'' + 1 ∧ N0 = N0'' + 1) -+-> (last ⊃ Post1(pm, s, S) ∧ Post2(pm, s, S);G1(pm, S, S') ∨ G2(pm, S, S'))

Rule argument

Additional information

Used simplifier rules: pre2-i: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ Pre2(pm, s) → I(pm, s);%g1-r2: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ G1(pm, s, s0) ∧ I(pm, s) → R2(pm, s, s0);%r2-trans: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R2(pm, s, s0) ∧ R2(pm, s0, s1) ∧ I(pm, s) → R2(pm, s, s1);%post2-r2: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R2(pm, s0, s1) ∧ Post2(pm, s, s0) ∧ Pre2(pm, s) ∧ I(pm, s0) → Post2(pm, s, s1);%i-r2-i: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R2(pm, s, s0) ∧ I(pm, s) → I(pm, s0);%succ: ⊦ m +1 = m + 1; from specification nat-basic2