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Proof step 10 from proof aligndown-sub-add-sub (previous step)

n2 = n0 + n2 / n * n ⊦ n2 % n = 0, n = 0, n0 = n2 % n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ n ≠ 0 → m / n * n = m - m % n

Rule argument

spec: <toplevel> name: div-mult-to-diff-mod seq: ⊦ n ≠ 0 → m / n * n = m - m % n subst: [n, m] → [n, n2] flags: <all paths>

Additional information

Used simplifier rules: n ≠ 0 ⊦ m % n ≤ m; (s)%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: n, n2