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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ m ≤ n ↔ ¬ n < m
Proof step 14:
(m0 * (m0 + 1)) / 2 < (n * (n + 1)) / 2, m < ((n + 1) * (n + 2)) / 2, (n * (n + 1)) / 2 ≤ m, (m0 * (m0 + 1)) / 2 ≤ m, ∀ m2, m3, n. m2 - m3 < m - m0 → m2 < ((n + 1) * (n + 2)) / 2 ∧ (n * (n + 1)) / 2 ≤ m2 ∧ (m3 * (m3 + 1)) / 2 ≤ m2 → maxenc(m3, m2) = n ⊦ m0 = n, ((m0 + 1) * (m0 + 2)) / 2 ≤ m

Rule argument

spec: nat name: le-def seq: ⊦ m ≤ n ↔ ¬ n < m subst: [n, m] → [(m0 * (m0 + 1)) / 2, (n * (n + 1)) / 2] flags: <all paths>

Additional information

Used terms: (m0 * (m0 + 1)) / 2, (n * (n + 1)) / 2