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Proof step 5 from proof mult (previous step)

((m0 * n + n0) + n) / n = (m0 * n + n0) / n + 1, ∀ n, n0. n ≠ 0 → (n0 + m0 * n) / n = n0 / n + m0 ⊦ n = 0, (n0 + n * m0) / n = n0 / n + m0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
∀ n, n0. n ≠ 0 → (n0 + m0 * n) / n = n0 / n + m0 ⊦ n = 0, (n0 + n * m0) / n = n0 / n + m0

Rule argument

Additional information

Used simplifier rules: add: n ≠ 0 ⊦ (n0 + n) / n = n0 / n + 1;%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2