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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ m0 * (m + n) = m0 * m + m0 * n
Proof step 8:
¬((m0 * (m0 + 1)) / 2 ≤ m ∧ m < ((m0 + 1) * m0 + (m0 + 1) * 2) / 2 ∧ (m0 * (m0 + 1)) / 2 ≤ m), ¬ ((m0 + 1) * m0 + (m0 + 1) * 2) / 2 ≤ m, true, ∀ m2, m3, n. m2 - m3 < m - m0 → true → maxenc(m3, m2) = n ∧ (m3 * (m3 + 1)) / 2 ≤ m2 → (n * (n + 1)) / 2 ≤ m2 ∧ m2 < ((n + 1) * (n + 2)) / 2 ⊦ maxenc(m0, m) = n ∧ (m0 * (m0 + 1)) / 2 ≤ m → (n * (n + 1)) / 2 ≤ m ∧ m < ((n + 1) * (n + 2)) / 2

Rule argument

spec: nat-mult inst: name: dist seq: ⊦ m0 * (m + n) = m0 * m + m0 * n subst: [n, m, m0] → [2, m0, m0 + 1] flags: rewrite

Additional information

Used terms: 2, m0, m0 + 1