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Proof step 3 from proof gcd-rec-sub-03 (previous step)

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

Rule argument

spec: <toplevel> name: gcd-rec-sub-02 seq: ⊦ 0 < i ∧ i < j → gcd(i, j) = gcd(j, j - i) subst: [j, i] → [i0 + i, i] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i + j - i = j; (s)%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