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Proof step 17 from proof square-ls (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat name: fle-01 seq: ⊦ m ≤ n ∧ n < n0 → m < n0 subst: [m, n, n0] → [3 * m + m * m, 3 * m0 + m0 * m0, 3 * m + m0 * m0] flags: <all paths>

Additional information

Used simplifier rules: ls: ⊦ m0 * m < m0 * n ↔ m0 ≠ 0 ∧ m < n;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%square-less: ⊦ m * m < n * n ↔ 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; (s) Used terms: 3 * m + m * m, 3 * m0 + m0 * m0, 3 * m + m0 * m0