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Proof step 6 from proof max-bigger (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
maxenc(m, n) < m, n ≤ ((m + 2) * m + m) / 2, ∀ n0, m1. n0 - m1 < n - m → maxenc(m1, n0) < m1 → false ⊦

Rule argument

Additional information

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