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Proof step 5 from proof div-add-both (previous step)

i % j = 0 ⊦ j = 0, (i + j0 * j) / j = i / j + j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)
Proof step 7:
j ≠ 0, ∃ j0. i = j0 * j ⊦ j = 0, (i + j0 * j) / j = i / j + j0

Rule argument

spec: int-div inst: name: modex seq: j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j) subst: [j, i] → [j, i] flags: rewrite, current

Additional information

Used terms: j, i