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Proof step 8 from proof alignup-le (previous step)

m0 % n = 0, m1 < n * m1 / n + n, m0 < n * m1 / n + n, m1 ≤ m0 ⊦ m1 % n = 0, n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ n ≠ 0 → m % n = m - m / n * n
Proof step 10:
m0 - m0 / n * n = 0, m0 < n * m1 / n + n, m1 < n * m1 / n + n, m1 ≤ m0 ⊦ m1 % 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