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Proof step 38 from proof gcd-rec-sub-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ 0 < i ∧ i < j → gcd(i, j) = gcd(j, j - i)
Proof step 40:
i < 0 ⊦ gcd(abs(i) - abs(i0), abs(i)) = gcd(abs(i) - abs(i0), abs(i0)), abs(i) < i0, i0 < 0, 0 < i ∧ i < i0 + i, 0 < abs(i) - abs(i0) ∧ abs(i) - abs(i0) < abs(i)
Proof step 44:
i < 0, 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)), abs(i) < i0, i0 < 0, 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] → [abs(i), abs(i) - abs(i0)] flags: <all paths>

Additional information

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