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Proof step 3 from proof gcd-div-mult-shift (previous step)

⊦ i / gcd(i, j) * j0 = (i * j0) / gcd(i, j), i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ j | i ∧ j ≠ 0 → i / j * j0 = (i * j0) / j
Proof step 5:
⊦ i / gcd(i, j) * j0 = (i * j0) / gcd(i, j), i = 0, gcd(i, j) | i ∧ gcd(i, j) ≠ 0

Rule argument

spec: <toplevel> name: div-mult-shift seq: ⊦ j | i ∧ j ≠ 0 → i / j * j0 = (i * j0) / j subst: [j0, j, i] → [j0, gcd(i, j), i] flags: <all paths>

Additional information

Used terms: j0, gcd(i, j), i