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Proof step 2 from proof mod-mult (previous step)

⊦ (m + n0 * n) % n = m % n, n = 0

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ m, n. (m + n1 * n) % n = m % n ∨ n = 0 ⊦ (m + n1 +1 * n) % n = m % n, n = 0

Rule argument

term: n0

Additional information

Used simplifier rules: nat freely generated by 0, +1;;%zero: ⊦ 0 * n = 0; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2