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Proof step 4 from proof mult (previous step)

∀ n0, n. (n0 + m0 * n) / n = n0 / n + m0 ∨ n = 0 ⊦ (n0 + n * m0) / n = n0 / n + m0, n = 0

User applied rule insert lemma

And obtained the following new goals

Proof step 5:
n ≠ 0 ⊦ (n0 + n) / n = n0 / n + 1
Proof step 6:
((m0 * n + n0) + n) / n = (m0 * n + n0) / n + 1, ∀ n0, n. (n0 + m0 * n) / n = n0 / n + m0 ∨ n = 0 ⊦ (n0 + n * m0) / n = n0 / n + m0, n = 0

Rule argument

spec: <toplevel> name: add seq: n ≠ 0 ⊦ (n0 + n) / n = n0 / n + 1 subst: [n, n0] → [n, m0 * n + n0]

Additional information

Used terms: n, m0 * n + n0