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Proof step 7 from proof progress-left (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), □ (last ⊃ Post2(pm, s, S);G2(pm, S, S')), ¬ P(pm, s2) ∧ ¬ ◇ P(pm, S) ∨ n = N + 1 ∧ N = N'' + 1 until ¬ ◇ P(pm, S), \A ∀ N, P, pm, S, Post1, s, G1, R1, Post2, G2, R2, Pre1, I, Pre2. N < n → [:S | [PL □ ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ∧ □ (R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ stable(pm, I, R1) ∧ stable(pm, I, R2) ∧ I(pm, S) ∧ Pre1(pm, s) ∧ Pre2(pm, s) ∧ P-restr(pm, P, I, R1) → ¬ N = N'' +1 until ¬ ◇ P(pm, S), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, s2), Pre1(pm, s), Pre2(pm, s), P-restr(pm, P, I, R1), R1(pm, s3, S), R2(pm, s3, S), boolvar → s2 = s3 ∧ n = n0, P(pm, s2), Post1(pm, s, s2), R1(pm, s2, s2), G2(pm, s2, s3) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
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, Post1, s, G1, R1, Post2, G2, R2, Pre1, I, Pre2. N < n → [:S | [PL □ ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ∧ □ (R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ stable(pm, I, R1) ∧ stable(pm, I, R2) ∧ I(pm, S) ∧ Pre1(pm, s) ∧ Pre2(pm, s) ∧ P-restr(pm, P, I, R1) → ¬ N = N'' +1 until ¬ ◇ P(pm, S), n = N + 1, P(pm, s3), I(pm, S), P(pm, s2), I(pm, s2), R1(pm, s2, s2), R1(pm, s2, s3), G2(pm, s2, s3), Post1(pm, s, s2), R2(pm, s3, S), R1(pm, s3, 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), I(pm, s3), R1(pm, s2, S), P(pm, S), boolvar → s2 = s3 ∧ N + 1 = n0 ⊦

Rule argument

Additional information

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