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Proof step 9 from proof no-progress-left-aux0 (previous step)

boolvar ∨ n = N + 1 ∧ N = N'' + 1 until Boolvar, □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), ¬ boolvar ∧ G2(pm, s2, s3) ∧ ¬ R2(pm, s3, s0) ∧ ¬ boolvar1 ∧ [:S | Boolvar ::- [PL □ (¬ P(pm, S) ∧ ¬ last) ∧ R1(pm, S', S'') -+-> G1(pm, S, S')] ∥ false ::- [PL S = s0]] ∨ ¬ boolvar ∧ G2(pm, s2, s3) ∧ R2(pm, s3, s1) ∧ ¬ boolvar1 ∧ [:S | Boolvar ::- [PL □ (¬ P(pm, S) ∧ ¬ last) ∧ R1(pm, S', S'') -+-> G1(pm, S, S')] ∥ false ::- [PL S = s1 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ], \A ∀ N, Boolvar, R1, pm, S, R2, P, G1, Post2, s, G2, Pre1, Post1, I, Pre2. N < n → N = N'' +1 until Boolvar ∧ □ (R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ (P(pm, S) ∨ last) ∧ [:S | Boolvar ::- [PL □ (¬ P(pm, S) ∧ ¬ last) ∧ R1(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) → false, 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 ⊦

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 3

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