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Proof step 86 from proof gcd-rec-sub-03 (previous step)

abs(i0) - abs(i) < abs(i0), 0 < abs(i0) - abs(i), i0 < 0, i0 < i, 0 < i ⊦ gcd(abs(i), abs(i0) - abs(i)) = gcd(abs(i0), abs(i)), i = 0, i0 = 0, abs(i0) < abs(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 87:
⊦ gcd(i, j) = gcd(j, i)
Proof step 88:
0 < i, i0 < i, i0 < 0, 0 < abs(i0) - abs(i), abs(i0) - abs(i) < abs(i0) ⊦ gcd(abs(i), abs(i0) - abs(i)) = gcd(abs(i), abs(i0)), i = 0, i0 = 0, abs(i0) < abs(i)

Rule argument

spec: <toplevel> name: gcd-com seq: ⊦ gcd(i, j) = gcd(j, i) subst: [j, i] → [abs(i), abs(i0)] flags: <all paths>

Additional information

Used terms: abs(i), abs(i0)