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Proof step 3 from proof max-square (previous step)

⊦ maxenc(((m + n) * (m + n + 1)) / 2 + n) = m + n, ((m + n) * ((m + n) + 1)) / 2 ≤ ((m + n) * (m + n + 1)) / 2 + n ∧ ((m + n) * (m + n + 1)) / 2 + n < (((m + n) + 1) * ((m + n) + 2)) / 2

User applied rule case distinction

And obtained the following new goals

Proof step 4:
⊦ maxenc(((m + n) * (m + n + 1)) / 2 + n) = m + n, ((m + n) * (m + n + 1)) / 2 + n < (((m + n) + 1) * ((m + n) + 2)) / 2

Rule argument

pos: right 2

Additional information

Used simplifier rules: ⊦ m * (n + 1) = m * n + m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ m + n < m; (s)