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Proof step 8 from proof gcdex (previous step)

i < 0, gcd(abs(j), abs(i)) = abs(j) * i0 + abs(i) * j0, abs(i) < abs(j) ⊦ ∃ i0, j0. gcd(abs(i), abs(j)) = i * i0 + j * j0

User applied rule cut formula

And obtained the following new goals

Proof step 9:
j < 0, i < 0, gcd(abs(j), abs(i)) = abs(j) * i0 + abs(i) * j0, abs(i) < abs(j) ⊦ ∃ i0, j0. gcd(abs(i), abs(j)) = i * i0 + j * j0
Proof step 10:
i < 0, gcd(abs(j), abs(i)) = abs(j) * i0 + abs(i) * j0, abs(i) < abs(j) ⊦ j < 0, ∃ i0, j0. gcd(abs(i), abs(j)) = i * i0 + j * j0

Rule argument

fma: j < 0

Additional information

Used formulas: j < 0