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Proof step 19 from proof rg2-sound-main-unfair (previous step)

R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')), \A ∀ N, Post1, pm, s, S, G1, R1, Post2, G2, R2, Pre1, I, Pre2. N < n → [:S | [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]] ∧ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ Pre1(pm, s) ∧ Pre2(pm, s) ∧ I(pm, S) → ((R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ N = N'' +1) -+-> (last ⊃ Post1(pm, s, S) ∧ Post2(pm, s, S);G1(pm, S, S') ∨ G2(pm, S, S')), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), I(pm, s2), I(pm, s), boolvar → s2 = s3 ∧ n = n0, Post1(pm, s, s2), R1(pm, s2, s2), G2(pm, s2, s3), R2(pm, s3, S) ⊦ (G1(pm, s2, s3) ∨ G2(pm, s2, s3)) ∧ ( R1(pm, s3, S) ∧ R2(pm, s3, S) ∧ n = N + 1 → (R1(pm, S', S'') ∧ R2(pm, S', S'') ∧ N = N'' + 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 20:
R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')), \A ∀ N, Post1, pm, s, S, G1, R1, Post2, G2, R2, Pre1, I, Pre2. N < n → [:S | [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]] ∧ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ Pre1(pm, s) ∧ Pre2(pm, s) ∧ I(pm, S) → ((R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ N = N'' +1) -+-> (last ⊃ Post1(pm, s, S) ∧ Post2(pm, s, S);G1(pm, S, S') ∨ G2(pm, S, S')), n = N + 1, R1(pm, s2, s2), R1(pm, s2, S), Post1(pm, s, s2), I(pm, s2), R1(pm, s2, s3), R1(pm, s3, S), R2(pm, s3, S), G2(pm, s2, s3), I(pm, s), Pre2(pm, s), Pre1(pm, s), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), I(pm, S), I(pm, s3), Post1(pm, s, S), Post1(pm, s, s3), boolvar → s2 = s3 ∧ N + 1 = n0 ⊦ (R1(pm, S', S'') ∧ R2(pm, S', S'') ∧ N = N'' + 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: r1-trans: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R1(pm, s, s0) ∧ R1(pm, s0, s1) ∧ I(pm, s) → R1(pm, s, s1);%r-g-r: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R1(pm, s, s0) ∧ G2(pm, s0, s1) ∧ R1(pm, s1, s2) ∧ I(pm, s) → R1(pm, s, s2);%post1-r1: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R1(pm, s0, s1) ∧ Post1(pm, s, s0) ∧ Pre1(pm, s) ∧ I(pm, s0) → Post1(pm, s, s1);%i-r1-i: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R1(pm, s, s0) ∧ I(pm, s) → I(pm, s0);%g2-r1: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ G2(pm, s, s0) ∧ I(pm, s) → R1(pm, s, s0);