Theorem reltrls

Description: The set ( TrailsG ) of all trails on G is a set of pairs by our definition of a trail, and so is a relation. (Contributed by AV, 29-Oct-2021)

	Ref	Expression
Assertion	reltrls	⊢ Rel ( Trails ‘ 𝐺 )

Proof

Step	Hyp	Ref	Expression
1		df-trls	⊢ Trails = ( 𝑔 ∈ V ↦ { ⟨ 𝑓 , 𝑝 ⟩ ∣ ( 𝑓 ( Walks ‘ 𝑔 ) 𝑝 ∧ Fun ◡ 𝑓 ) } )
2	1	relmptopab	⊢ Rel ( Trails ‘ 𝐺 )