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Proof step 8 from proof is-aligned-multiple (previous step)

n = n1 + n / m * m, n1 = 0, n / m * m ≤ n ⊦ m = 0, ∃ n0. n = n0 * m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
n = n / m * m ⊦ m = 0, ∃ n0. n = n0 * m

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%n ≠ 0 ⊦ m / n * n ≤ m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)