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

⊦ gcd(abs(i), abs(j)) = gcd(abs(j), abs(i) % abs(j)), j = 0

User applied rule insert elim lemma

And obtained the following new goals

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

Rule argument

spec: int-div name: div-elim-pospos seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0) subst: [i, j, i0, j0] → [abs(i), abs(j), i0, j0]

Additional information

Used simplifier rules: ⊦ 0 < abs(i) ↔ i ≠ 0; (s)% ⊦ 0 ≤ abs(i); (s)%⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0); (elim) Used terms: abs(i), abs(j), i0, j0