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Proof step 15 from proof max-def (previous step)

m < ((m0 + 1) * (m0 + 2)) / 2, m < ((m0 + 1) * (m0 + 2)) / 2, 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 ⊦ ¬ (m0 * (m0 + 1)) / 2 < (n * (n + 1)) / 2, (n * (n + 1)) / 2 ≤ m ∧ m < ((n + 1) * (n + 2)) / 2 ∧ (m0 * (m0 + 1)) / 2 ≤ m → m0 = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ (m * (m + 1)) / 2 < (n * (n + 1)) / 2 ↔ m < n
Proof step 17:
m < ((m0 + 1) * (m0 + 2)) / 2, m < ((m0 + 1) * (m0 + 2)) / 2, 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 ⊦ ¬ m0 < n, (n * (n + 1)) / 2 ≤ m ∧ m < ((n + 1) * (n + 2)) / 2 ∧ (m0 * (m0 + 1)) / 2 ≤ m → m0 = n

Rule argument

spec: nat-div inst: name: square-ls-02 seq: ⊦ (m * (m + 1)) / 2 < (n * (n + 1)) / 2 ↔ m < n subst: [n, m] → [n, m0] flags: rewrite

Additional information

Used terms: n, m0