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Proof step 4 from proof div-le-modzero (previous step)

i % j = 0, i0 ≤ i / j, 0 < j, i < i0 * j ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)

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 simplifier rules: div-mult-03: j ≠ 0 ⊦ (i * j) / j = i;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%ls-pos: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0); from specification int-mult%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: j, i