Theorem s2len

Description: The length of a doubleton word. (Contributed by Stefan O'Rear, 23-Aug-2015) (Revised by Mario Carneiro, 26-Feb-2016)

	Ref	Expression
Assertion	s2len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 ”⟩ ) = 2

Proof

Step	Hyp	Ref	Expression
1		df-s2	⊢ ⟨“ 𝐴 𝐵 ”⟩ = ( ⟨“ 𝐴 ”⟩ ++ ⟨“ 𝐵 ”⟩ )
2		s1cli	⊢ ⟨“ 𝐴 ”⟩ ∈ Word V
3		s1len	⊢ ( ♯ ‘ ⟨“ 𝐴 ”⟩ ) = 1
4		1p1e2	⊢ ( 1 + 1 ) = 2
5	1 2 3 4	cats1len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 ”⟩ ) = 2