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Proof step 18 from proof gcdex-pos (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 19:
gcd(i, j) = i * i0 + j * j0, 0 < j, i0 < 0, gcd(i, j) = i * (i0 - i0 * j) + j * (j0 + i0 * i), ∀ i1. gcd(i, j) = i * (i0 - i1 * j) + j * (j0 + i1 * i) ⊦ j = 0, ∃ i0, j0. gcd(i, j) = i * i0 + j * j0 ∧ 0 ≤ i0

Rule argument

pos: left 4 terms: i0 abort: F discard: F computed: F

Additional information

Used terms: i0