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Proof step 10 from proof aligndown-add-not-smaller (previous step)

n0 % m = 0, (n0 + n1) / m * m < n0 ⊦ (n0 + n1) % m = 0, m = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
n0 % m = 0, (n1 / m + n0 / m) * m < n0 ⊦ n1 % m = 0, m = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m0 % n = 0 ∧ 0 ≠ n → (m + m0) / n = m / n + m0 / 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; (s)