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Proof step 11 from proof progress-left (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
N = N'' + 1 until ¬ ◇ P(pm, S), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), □ (last ⊃ Post2(pm, s, S);G2(pm, S, S')), \A ∀ N, P, pm, S, Post2, s, G2, R1, R2, I, Pre2, Pre1, G1, Post1. N < n → N = N'' + 1 until ¬ ◇ P(pm, S) ∧ □ (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ □ (R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ I(pm, S) ∧ P-restr(pm, P, I, R1) ∧ Pre2(pm, s) ∧ Pre1(pm, s) ∧ stable(pm, I, R2) ∧ stable(pm, I, R1) ∧ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ P(pm, S) → false, n = N + 1, I(pm, S), P(pm, s1), R1(pm, s0, s1), G2(pm, s0, s1), R2(pm, s1, S), R1(pm, s1, S), P(pm, s0), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), Pre1(pm, s), Pre2(pm, s), P-restr(pm, P, I, R1), I(pm, s0), R1(pm, s0, S), I(pm, s1), P(pm, S), boolvar → s0 = s1 ∧ N + 1 = n0 ⊦

Rule argument

Additional information

Used simplifier rules: stable-fw: ⊦ stable(pm, I, R) ∧ I(pm, s) ∧ R(pm, s, s0) → I(pm, s0);%progress-fw: ⊦ P-restr(pm, P, I, R) ∧ P(pm, s) ∧ R(pm, s, s0) ∧ I(pm, s) ∧ I(pm, s0) → P(pm, s0);%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); (forward) from specification RG-I-2-Theory%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); (forward) from specification RG-I-2-Theory