Theorem gpgprismgr4cycllem4

Description: Lemma 4 for gpgprismgr4cycl0 : the cycle <. P , F >. consists of 5 vertices (the first and the last vertex are identical, see gpgprismgr4cycllem6 . (Contributed by AV, 1-Nov-2025)

	Ref	Expression
Hypothesis	gpgprismgr4cycl.p	|- P = <" <. 0 , 0 >. <. 0 , 1 >. <. 1 , 1 >. <. 1 , 0 >. <. 0 , 0 >. ">
Assertion	gpgprismgr4cycllem4	|- ( # ` P ) = 5

Proof

Step	Hyp	Ref	Expression
1		gpgprismgr4cycl.p	|- P = <" <. 0 , 0 >. <. 0 , 1 >. <. 1 , 1 >. <. 1 , 0 >. <. 0 , 0 >. ">
2	1	fveq2i	|- ( # ` P ) = ( # ` <" <. 0 , 0 >. <. 0 , 1 >. <. 1 , 1 >. <. 1 , 0 >. <. 0 , 0 >. "> )
3		s5len	|- ( # ` <" <. 0 , 0 >. <. 0 , 1 >. <. 1 , 1 >. <. 1 , 0 >. <. 0 , 0 >. "> ) = 5
4	2 3	eqtri	|- ( # ` P ) = 5