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Proof step 2 from proof mod-eq (previous step)

m < n ⊦ m % n = m, n = 0

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ n ≠ 0 → m = m / n * n + m % n

Rule argument

spec: inst: name: Moddef seq: ⊦ n ≠ 0 → m = m / n * n + m % n subst: [n, m] → [n, m] flags: current, []

Additional information

Used simplifier rules: zero-01: ⊦ m < n → m / n = 0;%zero: ⊦ 0 * n = 0; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: n, m