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Proof step 2 from proof aligndown-remainder (previous step)

⊦ m = m0 + align↓(m, n) ↔ m0 = m % n, n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
0 ≠ m ⊦ align↓(n, m) = (n % m = 0 ⊃ n;n / m * m)
Proof step 4:
⊦ m = m0 + (m % n = 0 ⊃ m;m / n * n) ↔ m0 = m % n, n = 0

Rule argument

Additional information

Used simplifier rules: aligndown-def: 0 ≠ m ⊦ align↓(n, m) = (n % m = 0 ⊃ n;n / m * m);