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Theorem gcd-one

⊦ gcd(i, j) = 1 ↔ ¬(∃ i1. i1 > 1 ∧ i1 | i ∧ i1 | j)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: gcd-div-gcd-pos, gcd-one-01, gcd-one-prime, gcd-prime, gcd-primes,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 7
Proof steps: 16
Used lemmas: gcd-div2, gcd-div1, gcd-zero, gcd-zero-zero, gcd-less-eq-zero, div-one-neg-pos, div-one-pos, div-zero-01, gcd-com, gcd-zero-04, div-one, gcd-less,
Used spec theorems:
- int-abs/Abs-neg
Used simplifier rules: