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

¬ ((m0 + 1) * (m0 + 2)) / 2 ≤ m, true, ∀ m2, m3, n. m2 - m3 < m - m0 → true → (n * (n + 1)) / 2 ≤ m2 ∧ m2 < ((n + 1) * (n + 2)) / 2 ∧ (m3 * (m3 + 1)) / 2 ≤ m2 → maxenc(m3, m2) = n ⊦ (n * (n + 1)) / 2 ≤ m ∧ m < ((n + 1) * (n + 2)) / 2 ∧ (m0 * (m0 + 1)) / 2 ≤ m → maxenc(m0, m) = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ¬ ((m + 1) * (m + 2)) / 2 ≤ n → maxenc(m, n) = m
Proof step 6:
¬ ((m0 + 1) * (m0 + 2)) / 2 ≤ m, ¬ ((m0 + 1) * (m0 + 2)) / 2 ≤ m, true, ∀ m2, m3, n. m2 - m3 < m - m0 → true → (n * (n + 1)) / 2 ≤ m2 ∧ m2 < ((n + 1) * (n + 2)) / 2 ∧ (m3 * (m3 + 1)) / 2 ≤ m2 → maxenc(m3, m2) = n ⊦ (n * (n + 1)) / 2 ≤ m ∧ m < ((n + 1) * (n + 2)) / 2 ∧ (m0 * (m0 + 1)) / 2 ≤ m → m0 = n

Rule argument

spec: nat-pair inst: name: maxi-found seq: ⊦ ¬ ((m + 1) * (m + 2)) / 2 ≤ n → maxenc(m, n) = m subst: [n, m] → [m, m0] flags: rewrite, current

Additional information

Used terms: m, m0