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

m0 % n = 0 ⊦ (m + m0) % n = m % n, 0 = n

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:
n ≠ 0, ∃ n0. m0 = n0 * n ⊦ (m + m0) % n = m % n, 0 = n

Rule argument

spec: nat-div inst: name: modex seq: ⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n)) subst: [n, m] → [n, m0] flags: rewrite, current

Additional information

Used terms: n, m0