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Proof step 2 from proof gcd-div-eq (previous step)

⊦ i / gcd(i, j) = i0 ↔ i = i0 * gcd(i, j), i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ j | i ∧ j ≠ 0 → (i / j = i0 ↔ i = i0 * j)
Proof step 4:
¬(gcd(i, j) | i ∧ gcd(i, j) ≠ 0) ⊦ i / gcd(i, j) = i0 ↔ i = i0 * gcd(i, j), i = 0

Rule argument

spec: int-gcd inst: name: div-eq seq: ⊦ j | i ∧ j ≠ 0 → (i / j = i0 ↔ i = i0 * j) subst: [i0, j, i] → [i0, gcd(i, j), i] flags: rewrite, current

Additional information

Used terms: i0, gcd(i, j), i