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

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