Theorem s4len

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

	Ref	Expression
Assertion	s4len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 𝐶 𝐷 ”⟩ ) = 4

Proof

Step	Hyp	Ref	Expression
1		df-s4	⊢ ⟨“ 𝐴 𝐵 𝐶 𝐷 ”⟩ = ( ⟨“ 𝐴 𝐵 𝐶 ”⟩ ++ ⟨“ 𝐷 ”⟩ )
2		s3cli	⊢ ⟨“ 𝐴 𝐵 𝐶 ”⟩ ∈ Word V
3		s3len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 𝐶 ”⟩ ) = 3
4		3p1e4	⊢ ( 3 + 1 ) = 4
5	1 2 3 4	cats1len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 𝐶 𝐷 ”⟩ ) = 4