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Proof step 2 from proof mod-mod-01 (previous step)

m % (n + 1) = 0, (n + 1) % n0 = 0 ⊦ m % n0 = 0, n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n))
Proof step 4:
n0 ≠ 0, m % (n + 1) = 0, ∃ n1. n + 1 = n1 * n0 ⊦ m % n0 = 0, n0 = 0

Rule argument

spec: nat-div inst: name: modex seq: ⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n)) subst: [n, m] → [n0, n + 1] flags: rewrite, current

Additional information

Used terms: n0, n + 1