Theorem s4len

Description: The length of a length 4 string. (Contributed by Mario Carneiro, 26-Feb-2016)

	Ref	Expression
Assertion	s4len	$$⊢\left|⟨“ABCD”⟩\right|=4$$

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		3p1e4	$$⊢3+1=4$$
5	1 2 3 4	cats1len	$$⊢\left|⟨“ABCD”⟩\right|=4$$