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Proof step 10 from proof gcdex-pos (previous step)

gcd(i, j) = i * i0 + j * j0, j < 0, 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 11:
gcd(i, j) = i * i0 + j * j0, j < 0, i0 < 0, gcd(i, j) = i * (i0 - abs(i0) * j) + j * (j0 + abs(i0) * i) ⊦ j = 0, ∃ i0, j0. gcd(i, j) = i * i0 + j * j0 ∧ 0 ≤ i0

Rule argument

pos: left 4 terms: abs(i0) abort: F discard: T computed: F

Additional information

Used terms: abs(i0)