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Proof step 30 from proof gcd-mult-pos (previous step)

j ≤ i, 0 ≤ i, 0 < i1, 0 < i, 0 < j, ∀ j0, i0, i2. i→n(j0 * i0 + i2 * i0) < i→n(j * i1 + i * i1) → 0 < i0 ∧ 0 < i2 ∧ 0 ≤ j0 → gcd(i2 * i0, j0 * i0) = gcd(i2, j0) * i0 ⊦ gcd(j * i1, i % j * i1) = gcd(i, j) * i1, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ j ≠ 0 → gcd(i, j) = gcd(abs(j), abs(i) % abs(j))
Proof step 32:
j ≠ 0, j ≤ i, 0 ≤ i, 0 < i1, 0 < i, 0 < j, ∀ j0, i0, i2. i→n(j0 * i0 + i2 * i0) < i→n(j * i1 + i * i1) → 0 < i0 ∧ 0 < i2 ∧ 0 ≤ j0 → gcd(i2 * i0, j0 * i0) = gcd(i2, j0) * i0 ⊦ gcd(j * i1, i % j * i1) = gcd(abs(j), abs(i) % abs(j)) * i1, j = 0

Rule argument

spec: int-gcd inst: name: gcd-rec seq: ⊦ j ≠ 0 → gcd(i, j) = gcd(abs(j), abs(i) % abs(j)) subst: [j, i] → [j, i] flags: rewrite, current

Additional information

Used terms: j, i