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Proof step 21 from proof gcdex (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 22:
gcd(abs(i), abs(j)) = abs(i) * i0 + abs(j) * j0, j < 0, abs(j) ≤ abs(i) ⊦ i < 0, ∃ i0, j0. gcd(abs(i), abs(j)) = i * i0 + j * j0
Proof step 23:
gcd(abs(i), abs(j)) = abs(i) * i0 + abs(j) * j0, abs(j) ≤ abs(i) ⊦ i < 0, j < 0, ∃ i0, j0. gcd(abs(i), abs(j)) = i * i0 + j * j0

Rule argument

fma: j < 0

Additional information

Used formulas: j < 0