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Proof step 2 from proof coef-03 (previous step)

⊦ m * n + m0 * n < m1 * n + m2 * n ↔ m + m0 < m1 + m2 ∧ n ≠ 0

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: nat-mult inst: name: ls-02 seq: ⊦ m0 ≠ 0 → (m0 * m < m0 * n ↔ m < n) subst: [m0, m, n] → [n, m + m0, m1 + m2] 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-02: ⊦ m * n + m0 * n ≤ m1 * n + m2 * n ↔ ¬ ¬(m + m0 ≤ m1 + m2 ∨ n = 0);%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%l-04: ⊦ m + m0 < n + n0 → (¬ m + m0 < n + n0 ↔ false); from specification nat-basic2%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat Used terms: n, m + m0, m1 + m2