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Proof step 4 from proof gcd-div-eq (previous step)

¬(gcd(i, j) | i ∧ gcd(i, j) ≠ 0) ⊦ i / gcd(i, j) = i0 ↔ i = i0 * gcd(i, j), i = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
i = i0 * gcd(i, j) ⊦ gcd(i, j) = 0, i = 0, i / gcd(i, j) = i0, gcd(i, j) | i

Rule argument

Additional information

Used simplifier rules: gcd-zero-zero: ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;%mod-gcd: ⊦ i ≠ 0 → i % gcd(i, j) = 0;%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%div-eq-same: ⊦ 0 ≠ j → (j * i / j = i ↔ i % j = 0); from specification int-div