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Metamath Proof Explorer

Definition df-s7

Description: Define the length 7 word constructor. (Contributed by Mario Carneiro, 26-Feb-2016)

Ref Expression
Assertion df-s7 ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 𝐺 ”⟩ = ( ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 ”⟩ ++ ⟨“ 𝐺 ”⟩ )

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 cG ⊢ 𝐺
7 0 1 2 3 4 5 6 cs7 ⊢ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 𝐺 ”⟩
8 0 1 2 3 4 5 cs6 ⊢ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 ”⟩
9 cconcat ⊢ ++
10 6 cs1 ⊢ ⟨“ 𝐺 ”⟩
11 8 10 9 co ⊢ ( ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 ”⟩ ++ ⟨“ 𝐺 ”⟩ )
12 7 11 wceq ⊢ ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 𝐺 ”⟩ = ( ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 ”⟩ ++ ⟨“ 𝐺 ”⟩ )