Theorem s6len

Description: The length of a length 6 string. (Contributed by Mario Carneiro, 26-Feb-2016)

	Ref	Expression
Assertion	s6len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 ”⟩ ) = 6

Proof

Step	Hyp	Ref	Expression
1		df-s6	⊢ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 ”⟩ = ( ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ ++ ⟨“ 𝐹 ”⟩ )
2		s5cli	⊢ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ ∈ Word V
3		s5len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ ) = 5
4		5p1e6	⊢ ( 5 + 1 ) = 6
5	1 2 3 4	cats1len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 ”⟩ ) = 6