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Proof step 5 from proof square-ls-05 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 6:
m * m + m * m0 < n * n + n * m0, n * n + n * m0 ≤ m * m + n * m0, m * m + n * m0 ≤ m * m + m * m0 ⊦ m < n

Rule argument

fma: m * m + n * m0 ≤ m * m + m * m0

Additional information

Used simplifier rules: square-le-02: ⊦ m * m ≤ n * n ↔ m ≤ n;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%ls: ⊦ m0 * m < m0 * n ↔ m0 ≠ 0 ∧ m < n;% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss) Used formulas: m * m + n * m0 ≤ m * m + m * m0