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Proof step 74 from proof gcd-rec-sub-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 75:
⊦ i - (i - j) = j
Proof step 76:
abs(i) - abs(i0) < abs(i), 0 < abs(i) - abs(i0), abs(i0) < abs(i), 0 < i, i0 < i, i0 < 0 ⊦ gcd(abs(i), abs(i0)) = gcd(abs(i) - abs(i0), abs(i0)), i = 0, i0 = 0

Rule argument

spec: int-abs name: sub-same seq: ⊦ i - (i - j) = j subst: [j, i] → [abs(i0), abs(i)] flags: <all paths>

Additional information

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