Theorem s5len

Description: The length of a length 5 string. (Contributed by Mario Carneiro, 26-Feb-2016)

	Ref	Expression
Assertion	s5len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ ) = 5

Proof

Step	Hyp	Ref	Expression
1		df-s5	⊢ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ = ( ⟨“ 𝐴 𝐵 𝐶 𝐷 ”⟩ ++ ⟨“ 𝐸 ”⟩ )
2		s4cli	⊢ ⟨“ 𝐴 𝐵 𝐶 𝐷 ”⟩ ∈ Word V
3		s4len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 𝐶 𝐷 ”⟩ ) = 4
4		4p1e5	⊢ ( 4 + 1 ) = 5
5	1 2 3 4	cats1len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ ) = 5