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Proof step 12 from proof progress-left-aux (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL S = s1 ∧ ¬ Boolvar until P(pm, S)] ∥ false ::- [PL S = s4]], boolvar ∨ n = N + 1 ∧ N = N'' + 1 until Boolvar, \A ∀ N, R1, pm, S, R2, Boolvar, P, Post1, s, G1, Post2, G2, Pre1, I, Pre2. N < n → □ (R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ N = N'' +1 until Boolvar ∧ [:S | Boolvar ::- [PL ¬ Boolvar until P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ false ::- [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) → ◇ 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), ¬ P(pm, s2), boolvar1 → s2 = s3 ∧ (boolvar ↔ boolvar0) ∧ n = n0, G1(pm, s2, s2), G2(pm, s2, s3), ¬ boolvar, ¬ R1(pm, s2, s1), ¬ R2(pm, s3, s4) ⊦ ◇ P(pm, S)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL S = s1 ∧ ¬ Boolvar until P(pm, S)] ∥ false ::- [PL S = s4]], N = N'' + 1 until Boolvar, \A ∀ N, R1, pm, S, R2, Boolvar, P, Post1, s, G1, Post2, G2, Pre1, I, Pre2. N < n → □ (R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ N = N'' +1 until Boolvar ∧ [:S | Boolvar ::- [PL ¬ Boolvar until P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ false ::- [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) → ◇ P(pm, S), n = N + 1, R1(pm, s2, S), I(pm, s3), I(pm, s2), 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), R1(pm, s3, S), R2(pm, s3, S), G1(pm, s2, s2), G2(pm, s2, s3), R2(pm, s2, s2), R1(pm, s2, s3), I(pm, S), ¬ P(pm, s2), ¬ R1(pm, s2, s1), ¬ R2(pm, s3, s4), boolvar1 → s2 = s3 ∧ ¬ boolvar0 ∧ N + 1 = n0 ⊦ ◇ P(pm, S)

Rule argument

Additional information

Used simplifier rules: stable-fw: ⊦ stable(pm, I, R) ∧ I(pm, s) ∧ R(pm, s, s0) → I(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%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); (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