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Proof step 85 from proof rg2-lem1-term-unfair (previous step)

N0 = N0'' + 1 until Boolvar0, □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar0 ∨ Boolvar ::- [PL N = n16 ∧ N' = N'' + 1 until ¬ R1(pm, S', S'') ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s5 ∧ N = n3 ∧ □ ¬ 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(n16 + 1) ∧ INDHYP-nat0(n16 + 1)) ∧ INDHYP-nat1(N0 + 1), N = n16 + 1, R2(pm, s3, S), R1(pm, s3, S), I(pm, s2), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), I(pm, s3), R1(pm, s2, S), I(pm, s5), I(pm, S), R1(pm, s2, s3), n3 ≤ n16 + 1, R2(pm, s3, s5), G2(pm, s2, s3), I(pm, s) ⊦ ◇ last

User applied rule apply VD induction

And obtained the following new goals

Rule argument

subst: [R1, pm, Post1, s, G1, Post2, G2, R2, Pre2, Pre1, I, n] → [R1, pm, Post1, s, G1, Post2, G2, R2, Pre2, Pre1, I, n16] path: 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 13, 5, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1

Additional information

Used simplifier rules: l: ⊦ m + n < m + n0 ↔ n < n0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1 Used terms: R1, pm, Post1, s, G1, Post2, G2, R2, Pre2, Pre1, I, n16