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Proof step 4 from proof is-aligned-is-aligned-mod (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
m % n = 0, n0 % n = 0, m = m0 * n0 + n1, n1 < n0 ⊦ n1 % n = 0, n = 0, n0 = 0

Rule argument

spec: nat-div name: div-elim seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [m, n, m0, n0] → [m, n0, m0, n1]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: m, n0, m0, n1