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Proof step 9 from proof aligndown-sub-add-sub (previous step)

n2 = n0 + n2 / n * n, n2 / n * n ≤ n2 ⊦ n2 % n = 0, n = 0, n0 = n2 % n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
n2 = n0 + n2 / n * n ⊦ n2 % n = 0, n = 0, n0 = n2 % n

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)