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Proof step 5 from proof mod-mod (previous step)

m % (n1 * n0) = 0 ⊦ n0 = 0, m % n0 = 0, n1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat-div inst: name: modex seq: ⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n)) subst: [n, m] → [n1 * n0, m] flags: rewrite, current

Additional information

Used simplifier rules: mod-mult-01: n ≠ 0 ⊦ (m * n) % n = 0;%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%zero-06: ⊦ m ≠ 0 → (m * n = 0 ↔ n = 0); from specification nat-mult Used terms: n1 * n0, m