Theorem s4fv0

Description: Extract the first symbol from a length 4 string. (Contributed by Thierry Arnoux, 8-Oct-2020)

	Ref	Expression
Assertion	s4fv0	$$⊢A\in V\to ⟨“ABCD”⟩\left(0\right)=A$$

Proof

Step	Hyp	Ref	Expression
1		df-s4	$$⊢⟨“ABCD”⟩=⟨“ABC”⟩\mathrm{++}⟨“D”⟩$$
2		s3cli	$$⊢⟨“ABC”⟩\in \mathrm{Word}\mathrm{V}$$
3		s3len	$$⊢\left|⟨“ABC”⟩\right|=3$$
4		s3fv0	$$⊢A\in V\to ⟨“ABC”⟩\left(0\right)=A$$
5		0nn0	$$⊢0\in {\mathbb{N}}_0$$
6		3pos	$$⊢0<3$$
7	1 2 3 4 5 6	cats1fv	$$⊢A\in V\to ⟨“ABCD”⟩\left(0\right)=A$$