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	$$⊢F=⟨“\left\{⟨0,0⟩,⟨0,1⟩\right\}\left\{⟨0,1⟩,⟨1,1⟩\right\}\left\{⟨1,1⟩,⟨1,0⟩\right\}\left\{⟨1,0⟩,⟨0,0⟩\right\}”⟩$$
Assertion	gpgprismgr4cycllem1	$$⊢\left|F\right|=4$$

Proof

Step	Hyp	Ref	Expression
1		gpgprismgr4cycllem1.f	$$⊢F=⟨“\left\{⟨0,0⟩,⟨0,1⟩\right\}\left\{⟨0,1⟩,⟨1,1⟩\right\}\left\{⟨1,1⟩,⟨1,0⟩\right\}\left\{⟨1,0⟩,⟨0,0⟩\right\}”⟩$$
2	1	fveq2i	$$⊢\left|F\right|=\left|⟨“\left\{⟨0,0⟩,⟨0,1⟩\right\}\left\{⟨0,1⟩,⟨1,1⟩\right\}\left\{⟨1,1⟩,⟨1,0⟩\right\}\left\{⟨1,0⟩,⟨0,0⟩\right\}”⟩\right|$$
3		s4len	$$⊢\left|⟨“\left\{⟨0,0⟩,⟨0,1⟩\right\}\left\{⟨0,1⟩,⟨1,1⟩\right\}\left\{⟨1,1⟩,⟨1,0⟩\right\}\left\{⟨1,0⟩,⟨0,0⟩\right\}”⟩\right|=4$$
4	2 3	eqtri	$$⊢\left|F\right|=4$$