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Proof step 3 from proof rax (previous step)

m = n0 + m / n * n, m / n * n ≤ m ⊦ m % n = n0, n = 0

User applied rule insert lemma

And obtained the following new goals

Proof step 4:
⊦ 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: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic2 Used terms: n, m