Theorem cyclispth

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

	Ref	Expression
Assertion	cyclispth	$$⊢F\mathrm{Cycles}\left(G\right)P\to F\mathrm{Paths}\left(G\right)P$$

Proof

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