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Mirrors > Home > MPE Home > Th. List > df-vrmd | Structured version Visualization version GIF version |
Description: Define a free monoid over a set 𝑖 of generators, defined as the set of finite strings on 𝐼 with the operation of concatenation. (Contributed by Mario Carneiro, 27-Sep-2015.) |
Ref | Expression |
---|---|
df-vrmd | ⊢ varFMnd = (𝑖 ∈ V ↦ (𝑗 ∈ 𝑖 ↦ ⟨“𝑗”⟩)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cvrmd 18583 | . 2 class varFMnd | |
2 | vi | . . 3 setvar 𝑖 | |
3 | cvv 3441 | . . 3 class V | |
4 | vj | . . . 4 setvar 𝑗 | |
5 | 2 | cv 1539 | . . . 4 class 𝑖 |
6 | 4 | cv 1539 | . . . . 5 class 𝑗 |
7 | 6 | cs1 14399 | . . . 4 class ⟨“𝑗”⟩ |
8 | 4, 5, 7 | cmpt 5175 | . . 3 class (𝑗 ∈ 𝑖 ↦ ⟨“𝑗”⟩) |
9 | 2, 3, 8 | cmpt 5175 | . 2 class (𝑖 ∈ V ↦ (𝑗 ∈ 𝑖 ↦ ⟨“𝑗”⟩)) |
10 | 1, 9 | wceq 1540 | 1 wff varFMnd = (𝑖 ∈ V ↦ (𝑗 ∈ 𝑖 ↦ ⟨“𝑗”⟩)) |
Colors of variables: wff setvar class |
This definition is referenced by: vrmdfval 18591 |
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