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Proof step 18 from proof square-ls-03 (previous step)

((m * m + m) + 2 * m0) % 2 = 0, ((n + 2) * n + n) / 2 < (m * m + m) / 2 + m0, m0 ≤ n, (m + 2) * m + 2 ≤ m * m + 2 * m0, ((m + 2) * m + m) / 2 * 2 ≤ (n + 2) * n + n, m ≤ n, m0 ≤ m ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat-mult name: dist seq: ⊦ m0 * (m + n) = m0 * m + m0 * n subst: [m0, n, m] → [m, 2, m] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m * n + n ≤ m1 * n ↔ m + 1 ≤ m1 ∨ n = 0; (s)% ⊦ m + 1 ≤ n ↔ m < n; (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%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: m, 2, m