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

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

Rule argument

Additional information

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