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Proof step 9 from proof mult-le-01 (previous step)

m ≤ n, n * n ≤ m + 1 ⊦ m * n ≤ m + 1, n ≤ 1 ∧ m ≤ 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat name: le-def seq: ⊦ m ≤ n ↔ ¬ n < m subst: [n, m] → [m + 1, n * n] flags: <all paths>

Additional information

Used simplifier rules: le-succ: ⊦ m * n ≤ m + 1 ↔ m = 0 ∨ m = 1 ∧ n ≤ 2 ∨ 2 ≤ m ∧ n < 2;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%sqls: ⊦ m ≤ n → (m + 1 < n * n ↔ 1 < n);%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ m ≠ 0 → (m ≤ 1 ↔ m = 1); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ 0 ↔ m = 0; (s) Used terms: m + 1, n * n