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Proof step 7 from proof is-aligned-is-aligned-mod (previous step)

n0 % n = 0, (m0 * n0 + n1) % n = 0, n1 = m1 * n + n2, n1 < n0, n2 < n ⊦ n = 0, n2 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
(m0 * n0 + n2) % n = 0, n0 % n = 0, m1 * n + n2 < n0, n2 < n ⊦ n2 = 0

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (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)