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Proof step 7 from proof is-aligned-still-space (previous step)

n0 % n1 = 0, n0 < (n2 * n1) % n0 + n1 ⊦ (n2 * n1) % n0 = 0, n0 = 0, n1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n))
Proof step 9:
n0 < (n2 * n1) % n0 + n1, ∃ n2. n0 = n2 * n1 ⊦ (n2 * n1) % n0 = 0, n0 = 0, n1 = 0

Rule argument

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

Additional information

Used terms: n1, n0