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Proof step 4 from proof max-bigger (previous step)

maxenc(m, n) < m, ∀ n0, m1. n0 - m1 < n - m → maxenc(m1, n0) < m1 → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ((m + 1) * (m + 2)) / 2 ≤ n → maxenc(m, n) = maxenc(m + 1, n)
Proof step 6:
¬ ((m + 1) * (m + 2)) / 2 ≤ n, maxenc(m, n) < m, ∀ n0, m1. n0 - m1 < n - m → maxenc(m1, n0) < m1 → false ⊦
Proof step 9:
((m + 1) * (m + 2)) / 2 ≤ n, maxenc(m + 1, n) < m, ∀ n0, m1. n0 - m1 < n - m → maxenc(m1, n0) < m1 → false ⊦

Rule argument

spec: nat-pair inst: name: maxi-rec seq: ⊦ ((m + 1) * (m + 2)) / 2 ≤ n → maxenc(m, n) = maxenc(m + 1, n) subst: [n, m] → [n, m] flags: rewrite, current

Additional information

Used terms: n, m