Theorem 3wlkdlem2

Description: Lemma 2 for 3wlkd . (Contributed by AV, 7-Feb-2021)

	Ref	Expression
Hypotheses	3wlkd.p	|- P = <" A B C D ">
	3wlkd.f	|- F = <" J K L ">
Assertion	3wlkdlem2	|- ( 0 ..^ ( # ` F ) ) = { 0 , 1 , 2 }

Proof

Step	Hyp	Ref	Expression
1		3wlkd.p	|- P = <" A B C D ">
2		3wlkd.f	|- F = <" J K L ">
3	2	fveq2i	|- ( # ` F ) = ( # ` <" J K L "> )
4		s3len	|- ( # ` <" J K L "> ) = 3
5	3 4	eqtri	|- ( # ` F ) = 3
6	5	oveq2i	|- ( 0 ..^ ( # ` F ) ) = ( 0 ..^ 3 )
7		fzo0to3tp	|- ( 0 ..^ 3 ) = { 0 , 1 , 2 }
8	6 7	eqtri	|- ( 0 ..^ ( # ` F ) ) = { 0 , 1 , 2 }