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Proof step 8 from proof mod-mult (previous step)

(n + n1 * m) % m = n % m ∨ m = 0, ∀ m, n. (m + n1 * n) % n = m % n ∨ n = 0 ⊦ n = 0, (m + n * n1) % n = m % n

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 2 terms: m, n

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: m, n