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Proof step 11 from proof square-ls (previous step)

3 * m0 + m0 * m0 < 3 * m + m * m, m ≤ m0, m * m + m ≤ m0 * m0 + m0, 3 * m + m * m ≤ 3 * m0 + m * m ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 12:
3 * m0 + m0 * m0 < 3 * m + m * m, 3 * m + m * m ≤ 3 * m0 + m * m, m * m + m ≤ m0 * m0 + m0, m ≤ m0 ⊦ 3 * m0 + m0 * m0 < 3 * m0 + m * m

Rule argument

fma: 3 * m0 + m0 * m0 < 3 * m0 + m * m

Additional information

Used simplifier rules: square-less: ⊦ m * m < n * n ↔ m < n;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used formulas: 3 * m0 + m0 * m0 < 3 * m0 + m * m