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	$$⊢\mathrm{Rel}\mathrm{Trails}\left(G\right)$$

Proof

Step	Hyp	Ref	Expression
1		df-trls	$$⊢\mathrm{Trails}=\left(g\in \mathrm{V}⟼\left\{⟨f,p⟩|\left(f\mathrm{Walks}\left(g\right)p\wedge \mathrm{Fun}{f}^{-1}\right)\right\}\right)$$
2	1	relmptopab	$$⊢\mathrm{Rel}\mathrm{Trails}\left(G\right)$$