Metamath Proof Explorer


Definition df-s5

Description: Define the length 5 word constructor. (Contributed by Mario Carneiro, 26-Feb-2016)

Ref Expression
Assertion df-s5 ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ = ( ⟨“ 𝐴 𝐵 𝐶 𝐷 ”⟩ ++ ⟨“ 𝐸 ”⟩ )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA ⊢ 𝐴
1 cB ⊢ 𝐵
2 cC ⊢ 𝐶
3 cD ⊢ 𝐷
4 cE ⊢ 𝐸
5 0 1 2 3 4 cs5 ⊢ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩
6 0 1 2 3 cs4 ⊢ ⟨“ 𝐴 𝐵 𝐶 𝐷 ”⟩
7 cconcat ⊢ ++
8 4 cs1 ⊢ ⟨“ 𝐸 ”⟩
9 6 8 7 co ⊢ ( ⟨“ 𝐴 𝐵 𝐶 𝐷 ”⟩ ++ ⟨“ 𝐸 ”⟩ )
10 5 9 wceq ⊢ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ = ( ⟨“ 𝐴 𝐵 𝐶 𝐷 ”⟩ ++ ⟨“ 𝐸 ”⟩ )