Theorem trliswlk

Description: A trail is a walk. (Contributed by Alexander van der Vekens, 20-Oct-2017) (Revised by AV, 7-Jan-2021) (Proof shortened by AV, 29-Oct-2021)

	Ref	Expression
Assertion	trliswlk	$$⊢F\mathrm{Trails}\left(G\right)P\to F\mathrm{Walks}\left(G\right)P$$

Proof

Step	Hyp	Ref	Expression
1		istrl	$$⊢F\mathrm{Trails}\left(G\right)P\leftrightarrow \left(F\mathrm{Walks}\left(G\right)P\wedge \mathrm{Fun}{F}^{-1}\right)$$
2	1	simplbi	$$⊢F\mathrm{Trails}\left(G\right)P\to F\mathrm{Walks}\left(G\right)P$$