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Proof step 2 from proof mod-neq-02 (previous step)

m * n = m0 * n + n0, n0 < n ⊦ n0 = 0

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: nat-mult inst: name: numeral-07 seq: m1 < m2 ⊦ (* m2) * m = (* m1) * m + n0 ↔ (m2 - m1) * m = n0 subst: [m1, m2, m, n0] → [m0, m, n, n0] flags: current, []

Additional information

Used simplifier rules: coef-04: ⊦ m * n + m0 * n = m1 * n ↔ ¬ ¬(m + m0 = m1 ∨ n = 0);%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%zero-01: ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0;%ls-01: ⊦ m0 * m < m ↔ m0 = 0 ∧ m ≠ 0;%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic1%f: ⊦ m < n → n ≠ 0; from specification nat-basic1%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: m0, m, n, n0