Metamath Proof Explorer


Definition df-s3

Description: Define the length 3 word constructor. (Contributed by Mario Carneiro, 26-Feb-2016)

Ref Expression
Assertion df-s3 ⟨“ 𝐴 𝐵 𝐶 ”⟩ = ( ⟨“ 𝐴 𝐵 ”⟩ ++ ⟨“ 𝐶 ”⟩ )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA 𝐴
1 cB 𝐵
2 cC 𝐶
3 0 1 2 cs3 ⟨“ 𝐴 𝐵 𝐶 ”⟩
4 0 1 cs2 ⟨“ 𝐴 𝐵 ”⟩
5 cconcat ++
6 2 cs1 ⟨“ 𝐶 ”⟩
7 4 6 5 co ( ⟨“ 𝐴 𝐵 ”⟩ ++ ⟨“ 𝐶 ”⟩ )
8 3 7 wceq ⟨“ 𝐴 𝐵 𝐶 ”⟩ = ( ⟨“ 𝐴 𝐵 ”⟩ ++ ⟨“ 𝐶 ”⟩ )