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

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

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 1

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