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Proof step 11 from proof aligndown-aligndown-add (previous step)

n0 % n = 0 ⊦ (n0 + n1) % n = 0, ((n0 % n = 0 ⊃ n0;n0 / n * n) + n1) / n * n = (n0 % n = 0 ⊃ n0;n0 / n * n) + (n1 % n = 0 ⊃ n1;n1 / n * n), n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
n0 % n = 0 ⊦ n1 % n = 0, (n1 / n + n0 / n) * n = n0 + n1 / n * n, n = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m0 % n = 0 ∧ 0 ≠ n → (m + m0) % n = m % n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m0 % n = 0 ∧ 0 ≠ n → (m + m0) / n = m / n + m0 / n; (s)