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Proof step 9 from proof progress-left (previous step)

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) ⊦

User applied rule induction

And obtained the following new goals

Proof step 10:
□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), □ (last ⊃ Post2(pm, s, S);G2(pm, S, S')), N = N'' + 1 until ¬ ◇ P(pm, 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, 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) ⊦

Rule argument

indvar: N wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: N