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Proof step 6 from proof no-progress-left-aux (previous step)

[:S | [PL □ (¬ P(pm, S) ∧ ¬ last) ∧ R1(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'')), N = N'' +1 until (P(pm, S) ∨ last), \A ∀ N, R1, pm, S, R2, P, G1, Post2, s, G2, Pre1, Post1, I, Pre2. N < m → □ (R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ [:S | [PL □ (¬ P(pm, S) ∧ ¬ last) ∧ R1(pm, S', S'') -+-> G1(pm, S, S')] ∥ [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) ∧ 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) ∨ last), m = N, 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) ⊦ [:S | [PL □ (¬ P(pm, S) ∧ ¬ last) ∧ 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'))] ] ∧ (P(pm, S) ∨ last)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
[:S | [PL □ (¬ P(pm, S) ∧ ¬ last) ∧ R1(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'')), N = N'' + 1 until (P(pm, S) ∨ last), \A ∀ N, R1, pm, S, R2, P, G1, Post2, s, G2, Pre1, Post1, I, Pre2. N < m → □ (R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ [:S | [PL □ (¬ P(pm, S) ∧ ¬ last) ∧ R1(pm, S', S'') -+-> G1(pm, S, S')] ∥ [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) ∧ 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) ∨ last), m = N, 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) ⊦ [:S | [PL □ (¬ P(pm, S) ∧ ¬ last) ∧ R1(pm, S', S'') -+-> G1(pm, S, S')] ∥ [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]] ∧ (P(pm, S) ∨ last)

Rule argument

Additional information

Used simplifier rules: succ: ⊦ m +1 = m + 1; from specification nat-basic2