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Proof step 2 from proof div-ls-modnotzero (previous step)

0 ≤ i, 0 < j ⊦ i0 < i / j ↔ i0 * j ≤ i ∧ i0 ≠ i / j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i * j = j * i
Proof step 4:
0 ≤ i, 0 < j ⊦ i0 < i / j ↔ j * i0 ≤ i ∧ i0 ≠ i / j

Rule argument

spec: int-mult inst: name: commutativity seq: ⊦ i * j = j * i subst: [j, i] → [j, i0] flags: rewrite

Additional information

Used terms: j, i0