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Proof step 2 from proof alignup-same0 (previous step)

is-aligned(m, n) ⊦ align↑(m, n) = m, 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)+1 * m)
Proof step 4:
m ≠ 0 ⊦ is-aligned(n, m) → n % m = 0

Rule argument

Additional information

Used simplifier rules: alignup-def: 0 ≠ m ⊦ align↑(n, m) = (n % m = 0 ⊃ n;(n / m)+1 * m);%is-aligned-mod: m ≠ 0 ⊦ is-aligned(n, m) → n % m = 0;