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Metamath Proof Explorer

Definition df-s6

Description: Define the length 6 word constructor. (Contributed by Mario Carneiro, 26-Feb-2016)

Ref Expression
Assertion df-s6 ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 ”⟩ = ( ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ ++ ⟨“ 𝐹 ”⟩ )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA ⊢ 𝐴
1 cB ⊢ 𝐵
2 cC ⊢ 𝐶
3 cD ⊢ 𝐷
4 cE ⊢ 𝐸
5 cF ⊢ 𝐹
6 0 1 2 3 4 5 cs6 ⊢ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 ”⟩
7 0 1 2 3 4 cs5 ⊢ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩
8 cconcat ⊢ ++
9 5 cs1 ⊢ ⟨“ 𝐹 ”⟩
10 7 9 8 co ⊢ ( ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ ++ ⟨“ 𝐹 ”⟩ )
11 6 10 wceq ⊢ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 ”⟩ = ( ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ ++ ⟨“ 𝐹 ”⟩ )