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Proof step 4 from proof gcd-div-mult-shift (previous step)

¬(gcd(i, j) | i ∧ gcd(i, j) ≠ 0) ⊦ i / gcd(i, j) * j0 = (i * j0) / gcd(i, j), i = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: gcd-zero-zero: ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;