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Proof step 13 from proof gcd-rec-sub-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ 0 < i ∧ i < j → gcd(i, j) = gcd(i, j - i)
Proof step 15:
i < 0, i0 < 0 ⊦ gcd(abs(i), abs(i0 + i)) = gcd(i, i0), i = 0, i0 = 0, 0 < i ∧ i < i0 + i, 0 < abs(i) ∧ abs(i) < abs(i0 + i)
Proof step 18:
i < 0, i0 < 0, 0 < abs(i), abs(i) < abs(i0 + i) ⊦ gcd(abs(i), abs(i0 + i) - abs(i)) = gcd(i, i0), i = 0, i0 = 0, 0 < i ∧ i < i0 + i

Rule argument

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

Additional information

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