Theorem crctistrl

Description: A circuit is a trail. (Contributed by Alexander van der Vekens, 30-Oct-2017) (Revised by AV, 31-Jan-2021)

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

Proof

Step	Hyp	Ref	Expression
1		crctprop	$$⊢F\mathrm{Circuits}\left(G\right)P\to \left(F\mathrm{Trails}\left(G\right)P\wedge P\left(0\right)=P\left(\left|F\right|\right)\right)$$
2	1	simpld	$$⊢F\mathrm{Circuits}\left(G\right)P\to F\mathrm{Trails}\left(G\right)P$$