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Proof step 16 from proof alignup-le-is-aligned (previous step)

m - m / n * n = 0, m0 = n0 + m0 / n * n, m0 < n * m0 / n + n, m < n * m0 / n + n, n0 < n, m0 ≤ m ⊦ n = 0, n0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
m - m / n * n = 0, m0 = n0 + m0 / n * n, n0 < n, m < n * m0 / n + n, m0 < n * m0 / n + n, m0 ≤ m ⊦ n0 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)