Theorem 2wlkdlem2

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

	Ref	Expression
Hypotheses	2wlkd.p	|- P = <" A B C ">
	2wlkd.f	|- F = <" J K ">
Assertion	2wlkdlem2	|- ( 0 ..^ ( # ` F ) ) = { 0 , 1 }

Proof

Step	Hyp	Ref	Expression
1		2wlkd.p	|- P = <" A B C ">
2		2wlkd.f	|- F = <" J K ">
3	2	fveq2i	|- ( # ` F ) = ( # ` <" J K "> )
4		s2len	|- ( # ` <" J K "> ) = 2
5	3 4	eqtri	|- ( # ` F ) = 2
6	5	oveq2i	|- ( 0 ..^ ( # ` F ) ) = ( 0 ..^ 2 )
7		fzo0to2pr	|- ( 0 ..^ 2 ) = { 0 , 1 }
8	6 7	eqtri	|- ( 0 ..^ ( # ` F ) ) = { 0 , 1 }