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Proof step 8 from proof mult-le-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

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-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%one: ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); from specification nat-basic1%one-02: ⊦ m ≠ 0 → (m ≤ 1 ↔ m = 1); from specification nat%anti: ⊦ m ≤ n → (n ≤ m ↔ m = n); from specification nat%lez-01: ⊦ m ≤ 0 ↔ m = 0; from specification nat%twols-02: ⊦ m ≠ 0 → (m < 2 ↔ m = 1); from specification nat-basic1%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat Used terms: m + 1, n * n