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	$$⊢\left|P\right|=5$$

Proof

Step	Hyp	Ref	Expression
1		gpgprismgr4cycl.p	$$⊢P=⟨“⟨0,0⟩⟨0,1⟩⟨1,1⟩⟨1,0⟩⟨0,0⟩”⟩$$
2	1	fveq2i	$$⊢\left|P\right|=\left|⟨“⟨0,0⟩⟨0,1⟩⟨1,1⟩⟨1,0⟩⟨0,0⟩”⟩\right|$$
3		s5len	$$⊢\left|⟨“⟨0,0⟩⟨0,1⟩⟨1,1⟩⟨1,0⟩⟨0,0⟩”⟩\right|=5$$
4	2 3	eqtri	$$⊢\left|P\right|=5$$