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Proof step 6 from proof aligndown-add-not-smaller (previous step)

(n0 + n1) % m = 0, n0 + n1 < n0 / m * m ⊦ n0 % m = 0, m = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
(n0 + n1) % m = 0, n0 + n1 < n0 / m * m ⊦ n0 % m = 0, n0 / m = 0, m = 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% ⊦ m ≠ 0 → (m * n = 0 ↔ n = 0); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic