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Proof step 7 from proof square-ls-04 (previous step)

m * m + m0 < n * n, n * n ≤ m * m, n ≤ m, m0 ≤ 2 * m ⊦ n = 0, m * m + m0 < m * m

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

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;% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: m * m + m0, n * n, m * m