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Proof step 2 from proof alignup-add-mult (previous step)

⊦ align↑(n * m + n0, m) = n * m + align↑(n0, 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)+1 * m)
Proof step 4:
⊦ (n0 % m = 0 ⊃ n * m + n0;m * (n0 / m + n) + m) = n * m + (n0 % m = 0 ⊃ n0;m * n0 / m + m), m = 0

Rule argument

Additional information

Used simplifier rules: alignup-def: 0 ≠ m ⊦ align↑(n, m) = (n % m = 0 ⊃ n;(n / m)+1 * m);% ⊦ m * (n + 1) = m * n + m; (s)% ⊦ m +1 = m + 1; (s)%n ≠ 0 ⊦ (n0 + m * n) / n = n0 / n + m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%n ≠ 0 ⊦ (m + n0 * n) % n = m % n; (s)