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Proof step 54 from proof rg2-sound-main-unfair (previous step)

R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S')), \A ∀ N0, R1, pm, S, Post1, s, G1, Pre1, I, R2, G2, Pre2, Post2, N. N0 < n → R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S')) ∧ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ Pre1(pm, s) ∧ Pre2(pm, s) ∧ I(pm, S) ∧ Post2(pm, s, S) → ((R1(pm, S', S'') ∧ R2(pm, S', S'') ∧ N = N'' + 1) ∧ N0 = N0'' +1) -+-> (last ⊃ Post1(pm, s, S) ∧ Post2(pm, s, S);G1(pm, S, S') ∨ G2(pm, S, S')), n = N0 + 1, R2(pm, s0, S), Post2(pm, s, s1), I(pm, s1), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), I(pm, s0), Post2(pm, s, s0), G1(pm, s0, s1), R1(pm, s1, S), R2(pm, s1, S), R2(pm, s0, s1), I(pm, s), I(pm, S), Post2(pm, s, S), boolvar → s0 = s1 ∧ N0 + 1 = n1 ∧ N + 1 = n2 ⊦ (R1(pm, S', S'') ∧ R2(pm, S', S'') ∧ N = N'' + 1 ∧ N0 = N0'' + 1) -+-> (last ⊃ Post1(pm, s, S) ∧ Post2(pm, s, S);G1(pm, S, S') ∨ G2(pm, S, S'))

User applied rule apply induction

And closed the goal!

Rule argument

subst: [N0, R1, pm, S, Post1, s, G1, Pre1, I, R2, G2, Pre2, Post2, N] → [N0, R1, pm, S, Post1, s, G1, Pre1, I, R2, G2, Pre2, Post2, N]

Additional information

Used simplifier rules: succ: ⊦ m +1 = m + 1; from specification nat-basic2%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: N0, R1, pm, S, Post1, s, G1, Pre1, I, R2, G2, Pre2, Post2, N