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Proof step 2 from proof aligndown-sub-add-sub (previous step)

n1 ≤ n0 ⊦ n0 - n1 + align↓(n0 - n1, n) = (n0 - n1) % 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:
n1 ≤ n0 ⊦ n0 - n1 + ((n0 - n1) % n = 0 ⊃ n0 - n1;(n0 - n1) / n * n) = (n0 - n1) % n, n = 0

Rule argument

Additional information

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