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Proof step 2 from proof div-not-ls (previous step)

j | i, i < j, 1 < j, 0 < j, 0 < i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i | j ↔ (∃ i0. i * i0 = j)

Rule argument

spec: int-gcd inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [i, j] flags: rewrite, current

Additional information

Used simplifier rules: ls-same: ⊦ 0 < i → (i * j < i ↔ j < 1); from specification int-mult%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: i, j