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Proof step 2 from proof is-aligned-align-up-multiple (previous step)

⊦ m = 0, n = 0, is-aligned(align↑(n0, 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)+1 * m)
Proof step 4:
⊦ is-aligned(n, m) ↔ n % m = 0
Proof step 5:
⊦ (n0 % (n * m) = 0 ⊃ n0;(n * n0 / (n * m) + n) * m) % m = 0, m = 0, n = 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-def: ⊦ is-aligned(n, m) ↔ n % m = 0;%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m * (n + 1) = m * n + m; (s)% ⊦ m +1 = m + 1; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m ≠ 0 → (m * n = 0 ↔ n = 0); (s)