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

⊦ align↓(n, m) = n + n0 ↔ n0 = 0 ∧ is-aligned(n, 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 * m)
Proof step 4:
⊦ is-aligned(n, m) ↔ n % m = 0
Proof step 5:
(n % m = 0 ⊃ n;n / m * m) = n + n0 ⊦ m = 0, n0 = 0 ∧ n % m = 0

Rule argument

Additional information

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