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Proof step 12 from proof max-bigger (previous step)

maxenc(m + 1, n1 + m) < m, ((m + 2) * m + m) / 2 < n1 + m, ∀ n0, m1. n0 - m1 < n1 → maxenc(m1, n0) < m1 → false ⊦

User applied rule apply induction

And closed the goal!

Rule argument

subst: [n0, m1] → [n1 + m, m + 1]

Additional information

Used simplifier rules: ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m < n → ¬ n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n - n + n1 = m - n1; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ 0 + m = m; (s)% ⊦ (m + n) / 2 < n ↔ m < n; (s)% ⊦ m0 * m < m ↔ m0 = 0 ∧ m ≠ 0; (ws)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0; (s)% ⊦ ¬ n < n; (s) Used terms: n1 + m, m + 1