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Proof step 5 from proof gcd-rec (previous step)

abs(i) = i0 * abs(j) + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j) ∧ 0 ≤ i0 ∧ 0 < abs(j) ∧ 0 ≤ abs(i) ⊦ gcd(abs(i), abs(j)) = gcd(abs(j), j0), j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
abs(i) = i0 * abs(j) + j0, 0 ≤ i0, 0 ≤ j0, j0 < abs(j) ⊦ j = 0, gcd(abs(i), abs(j)) = gcd(abs(j), j0)

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%abs-03: ⊦ 0 ≤ abs(i); from specification int-abs%abs-06: ⊦ 0 < abs(i) ↔ i ≠ 0; from specification int-abs