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Proof step 16 from proof square-ls (previous step)

3 * m0 + m0 * m0 < 3 * m + m0 * m0, m0 < m, m0 * m0 + m0 < m * m + m, 3 * m + m * m ≤ 3 * m0 + m0 * m0 ⊦ m = 0, m * m + m = 0

User applied rule cut formula

And obtained the following new goals

Proof step 17:
3 * m0 + m0 * m0 < 3 * m + m0 * m0, m0 < m, m0 * m0 + m0 < m * m + m, 3 * m + m * m ≤ 3 * m0 + m0 * m0 ⊦ 3 * m + m * m < 3 * m + m0 * m0, m = 0, m * m + m = 0

Rule argument

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

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;%l: ⊦ m + n < m + n0 ↔ n < n0; from specification nat-basic2%ls-02: ⊦ m < n → ¬ n < m; from specification nat-basic1%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used formulas: 3 * m + m * m < 3 * m + m0 * m0