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Proof step 8 from proof gcdex-pos (previous step)

gcd(i, j) = i * i0 + j * j0, ∀ i1. gcd(i, j) = i * (i0 - i1 * j) + j * (j0 + i1 * i) ⊦ j = 0, 0 ≤ i0, ∃ i0, j0. gcd(i, j) = i * i0 + j * j0 ∧ 0 ≤ i0

User applied rule cut formula

And obtained the following new goals

Proof step 9:
j < 0, gcd(i, j) = i * i0 + j * j0, ∀ i1. gcd(i, j) = i * (i0 - i1 * j) + j * (j0 + i1 * i) ⊦ j = 0, 0 ≤ i0, ∃ i0, j0. gcd(i, j) = i * i0 + j * j0 ∧ 0 ≤ i0
Proof step 15:
gcd(i, j) = i * i0 + j * j0, ∀ i1. gcd(i, j) = i * (i0 - i1 * j) + j * (j0 + i1 * i) ⊦ j < 0, j = 0, 0 ≤ i0, ∃ i0, j0. gcd(i, j) = i * i0 + j * j0 ∧ 0 ≤ i0

Rule argument

fma: j < 0

Additional information

Used formulas: j < 0