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Proof step 109 from proof rg2-lem2-term-unfair (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), N0 = N0'' + 1 until Boolvar, [:S | Boolvar ::- [PL N = n20 ∧ S = s20 ∧ N' = N'' + 1 until last ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s21 ∧ N = n21 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ¬ □ R2(pm, S', S'')] ], □ (N = N' ∧ ¬ N' < N''), INDHYP-nat(n20 + 1) ∧ INDHYP-nat0(N0 + 1), R1(pm, s2, S), I(pm, s2), I(pm, s3), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), R1(pm, s3, S), R2(pm, s3, S), N ≤ n20 + 1, I(pm, s), G1(pm, s2, s2), R1(pm, s2, s20), G2(pm, s2, s3), R2(pm, s3, s21), n21 ≤ n20 + 1, R2(pm, s2, s2), R1(pm, s2, s3), I(pm, s20), I(pm, S), I(pm, s21), boolvar1 → s2 = s3 ∧ (boolvar ↔ boolvar0) ∧ N0 + 1 = n4 ⊦ ◇ last

User applied rule apply VD induction

And obtained the following new goals

Rule argument

subst: [Post1, pm, s, G1, R1, Post2, G2, R2, Pre1, I, Pre2] → [Post1, pm, s, G1, R1, Post2, G2, R2, Pre1, I, Pre2] path: 1, 2, 1, 1, 1, 1, 1, 1

Additional information

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