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Proof step 3 from proof gcd-rec-sub-01 (previous step)

⊦ gcd(i, i0 + i) = gcd(i, i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 0 < i ∧ i < j → gcd(i, j) = gcd(i, j - i)
Proof step 5:
¬(0 < i ∧ i < i0 + i) ⊦ gcd(i, i0 + i) = gcd(i, i0)

Rule argument

spec: int-gcd inst: name: gcd-rec-sub seq: ⊦ 0 < i ∧ i < j → gcd(i, j) = gcd(i, j - i) subst: [j, i] → [i0 + i, i] flags: rewrite, current

Additional information

Used simplifier rules: sub-add: ⊦ i + j - i = j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i0 + i, i