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Proof step 9 from proof alignup-le-is-aligned (previous step)

m % n = 0, m < n * m0 / n + n, m0 < n * m0 / n + n, m0 ≤ m ⊦ m0 % n = 0, n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ n ≠ 0 → m % n = m - m / n * n
Proof step 11:
m % n = 0, m0 < n * m0 / n + n, m < n * m0 / n + n, m0 ≤ m ⊦ m0 - m0 / n * n = 0, n = 0

Rule argument

spec: nat-div name: mod-rew seq: ⊦ n ≠ 0 → m % n = m - m / n * n subst: [n, m] → [n, m0] flags: <all paths>

Additional information

Used terms: n, m0