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Proof step 2 from proof mult (previous step)

⊦ (n0 + m * n) / n = n0 / n + m, n = 0

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ n0, n. (n0 + m0 * n) / n = n0 / n + m0 ∨ n = 0 ⊦ (n0 + m0 +1 * n) / n = n0 / n + m0 +1, n = 0

Rule argument

term: m

Additional information

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