Theorem gpgprismgr4cycllem1

Description: Lemma 1 for gpgprismgr4cycl0 : the cycle <. P , F >. consists of 4 edges (i.e., has length 4). (Contributed by AV, 1-Nov-2025)

	Ref	Expression
Hypothesis	gpgprismgr4cycllem1.f	|- F = <" { <. 0 , 0 >. , <. 0 , 1 >. } { <. 0 , 1 >. , <. 1 , 1 >. } { <. 1 , 1 >. , <. 1 , 0 >. } { <. 1 , 0 >. , <. 0 , 0 >. } ">
Assertion	gpgprismgr4cycllem1	|- ( # ` F ) = 4

Proof

Step	Hyp	Ref	Expression
1		gpgprismgr4cycllem1.f	|- F = <" { <. 0 , 0 >. , <. 0 , 1 >. } { <. 0 , 1 >. , <. 1 , 1 >. } { <. 1 , 1 >. , <. 1 , 0 >. } { <. 1 , 0 >. , <. 0 , 0 >. } ">
2	1	fveq2i	|- ( # ` F ) = ( # ` <" { <. 0 , 0 >. , <. 0 , 1 >. } { <. 0 , 1 >. , <. 1 , 1 >. } { <. 1 , 1 >. , <. 1 , 0 >. } { <. 1 , 0 >. , <. 0 , 0 >. } "> )
3		s4len	|- ( # ` <" { <. 0 , 0 >. , <. 0 , 1 >. } { <. 0 , 1 >. , <. 1 , 1 >. } { <. 1 , 1 >. , <. 1 , 0 >. } { <. 1 , 0 >. , <. 0 , 0 >. } "> ) = 4
4	2 3	eqtri	|- ( # ` F ) = 4