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Proof step 2 from proof coef-05 (previous step)

⊦ m * n + m0 * n ≤ m1 * n ↔ m + m0 ≤ m1 ∨ n = 0

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: nat-mult inst: name: le seq: ⊦ m0 ≠ 0 → (m0 * m ≤ m0 * n ↔ m ≤ n) subst: [m0, m, n] → [n, m + m0, m1] flags: current, []

Additional information

Used simplifier rules: dist: ⊦ m0 * (m + n) = m0 * m + m0 * n;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%zero: ⊦ 0 * n = 0;%coef-08: ⊦ m * n < m1 * n + m2 * n ↔ ¬ ¬(m < m1 + m2 ∧ n ≠ 0);%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat Used terms: n, m + m0, m1