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Theorem gcdex-pos

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

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment: if j = 0: gcd(i, 0) = abs(i) = i * i0 + 0, hence i0 = -1 is the only solution if i < 0.
Used by: gcdex-smallest-pos,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 9
Proof steps: 17
Used lemmas: gcd-zero-04, gcdex-not-unique, gcdex,
Used spec theorems:
- Used simplifier rules: