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Proof step 2 from proof cond-01 (previous step)

m < m / n * n ⊦ n = 0, m / n = 0

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
n ≠ 0 ⊦ m / n * n ≤ m

Rule argument

spec: nat-div inst: name: cond seq: n ≠ 0 ⊦ m / n * n ≤ m subst: [n, m] → [n, m] flags: current, []

Additional information

Used simplifier rules: ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat Used terms: n, m