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Proof step 4 from proof mod-mod (previous step)

n0 ≠ 0, m % n = 0, ∃ n1. n = n1 * n0 ⊦ m % n0 = 0, n0 = 0, n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
m % (n1 * n0) = 0 ⊦ n0 = 0, m % n0 = 0, n1 = 0

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%zero-06: ⊦ m ≠ 0 → (m * n = 0 ↔ n = 0); from specification nat-mult