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Proof step 19 from proof is-aligned-still-space (previous step)

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

User applied rule insert elim lemma

And closed the goal!

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] → [n2, n, m, n0]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: n2, n, m, n0