Theorem releupth

Description: The set ( EulerPathsG ) of all Eulerian paths on G is a set of pairs by our definition of an Eulerian path, and so is a relation. (Contributed by Mario Carneiro, 12-Mar-2015) (Revised by AV, 18-Feb-2021)

	Ref	Expression
Assertion	releupth	$$⊢\mathrm{Rel}\mathrm{EulerPaths}\left(G\right)$$

Proof

Step	Hyp	Ref	Expression
1		df-eupth	$$⊢\mathrm{EulerPaths}=\left(g\in \mathrm{V}⟼\left\{⟨f,p⟩|\left(f\mathrm{Trails}\left(g\right)p\wedge f:\left(0..^\left|f\right|\right)\underset{onto}{⟶}\mathrm{dom}\mathrm{iEdg}\left(g\right)\right)\right\}\right)$$
2	1	relmptopab	$$⊢\mathrm{Rel}\mathrm{EulerPaths}\left(G\right)$$