Theorem 2wlkdlem2

Description: Lemma 2 for 2wlkd . (Contributed by AV, 14-Feb-2021)

	Ref	Expression
Hypotheses	2wlkd.p	$$⊢P=⟨“ABC”⟩$$
	2wlkd.f	$$⊢F=⟨“JK”⟩$$
Assertion	2wlkdlem2	$$⊢\left(0..^\left|F\right|\right)=\left\{0,1\right\}$$

Proof

Step	Hyp	Ref	Expression
1		2wlkd.p	$$⊢P=⟨“ABC”⟩$$
2		2wlkd.f	$$⊢F=⟨“JK”⟩$$
3	2	fveq2i	$$⊢\left|F\right|=\left|⟨“JK”⟩\right|$$
4		s2len	$$⊢\left|⟨“JK”⟩\right|=2$$
5	3 4	eqtri	$$⊢\left|F\right|=2$$
6	5	oveq2i	$$⊢\left(0..^\left|F\right|\right)=\left(0..^2\right)$$
7		fzo0to2pr	$$⊢\left(0..^2\right)=\left\{0,1\right\}$$
8	6 7	eqtri	$$⊢\left(0..^\left|F\right|\right)=\left\{0,1\right\}$$