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Proof step 6 from proof alignup-lower-bound (previous step)

m0 % n = 0, (m % n = 0 ⊃ m;n * m / n + n) < m, n * m / n + n < m0, m0 ≤ m ⊦ m % n = 0, n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
m0 % n = 0, n * m / n + n < m0, n * m / n + n < m, m0 ≤ m ⊦ m % n = 0, n = 0

Rule argument

Additional information

Used simplifier rules: fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat