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Theorem gcd-zero-zero

⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0

Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp, simp,
Comment:
Used by: div-gcd-is-neg, div-gcd-not-neg, div-gcd-zero, exgcd-div, gcd-div-eq, gcd-div-gcd, gcd-div-gcd-pos, gcd-div-mult, gcd-div-mult-shift, gcd-ge-one, gcd-less-eq-zero, gcd-negone-eq, gcd-nls-zero, gcd-one, gcd-one-eq, gcd-one-eq-01, gcd-one-eq-02, gcd-zero-05, square-neq-any-pos-02,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 2
Used lemmas: gcd-com, gcd-zero-03, div-zero-zero, gcd-div1, gcd-zero,
Used spec theorems:
- Used simplifier rules:
  - int-abs/abs-07