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Proof step 2 from proof aligndown-is-aligned (previous step)

⊦ m = 0, is-aligned(align↓(n, m), m)

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:
⊦ is-aligned(n, m) ↔ n % m = 0
Proof step 5:
⊦ (n % m = 0 ⊃ n;n / m * m) % m = 0, m = 0

Rule argument

Additional information

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