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

N = N'' + 1 until ¬ ◇ P(pm, S), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), □ (last ⊃ Post2(pm, s, S);G2(pm, S, S')), \A ∀ N, P, pm, S, Post2, s, G2, R1, R2, I, Pre2, Pre1, G1, Post1. N < n → 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, n = N + 1, I(pm, S), P(pm, s1), R1(pm, s0, s1), G2(pm, s0, s1), R2(pm, s1, S), R1(pm, s1, S), P(pm, s0), 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), I(pm, s0), R1(pm, s0, S), I(pm, s1), P(pm, S), boolvar → s0 = s1 ∧ N + 1 = n0 ⊦

User applied rule apply induction

And closed the goal!

Rule argument

subst: [N, P, pm, S, Post2, s, G2, R1, R2, I, Pre2, Pre1, G1, Post1] → [N, P, pm, S, Post2, s, G2, R1, R2, I, Pre2, Pre1, G1, Post1]

Additional information

Used simplifier rules: s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: N, P, pm, S, Post2, s, G2, R1, R2, I, Pre2, Pre1, G1, Post1