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 }