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Mirrors > Home > MPE Home > Th. List > df-reps | Structured version Visualization version GIF version |
Description: Definition to construct a word consisting of one repeated symbol, often called "repeated symbol word" for short in the following. (Contributed by Alexander van der Vekens, 4-Nov-2018.) |
Ref | Expression |
---|---|
df-reps | ⊢ repeatS = (𝑠 ∈ V, 𝑛 ∈ ℕ0 ↦ (𝑥 ∈ (0..^𝑛) ↦ 𝑠)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | creps 14479 | . 2 class repeatS | |
2 | vs | . . 3 setvar 𝑠 | |
3 | vn | . . 3 setvar 𝑛 | |
4 | cvv 3431 | . . 3 class V | |
5 | cn0 12233 | . . 3 class ℕ0 | |
6 | vx | . . . 4 setvar 𝑥 | |
7 | cc0 10872 | . . . . 5 class 0 | |
8 | 3 | cv 1541 | . . . . 5 class 𝑛 |
9 | cfzo 13381 | . . . . 5 class ..^ | |
10 | 7, 8, 9 | co 7271 | . . . 4 class (0..^𝑛) |
11 | 2 | cv 1541 | . . . 4 class 𝑠 |
12 | 6, 10, 11 | cmpt 5162 | . . 3 class (𝑥 ∈ (0..^𝑛) ↦ 𝑠) |
13 | 2, 3, 4, 5, 12 | cmpo 7273 | . 2 class (𝑠 ∈ V, 𝑛 ∈ ℕ0 ↦ (𝑥 ∈ (0..^𝑛) ↦ 𝑠)) |
14 | 1, 13 | wceq 1542 | 1 wff repeatS = (𝑠 ∈ V, 𝑛 ∈ ℕ0 ↦ (𝑥 ∈ (0..^𝑛) ↦ 𝑠)) |
Colors of variables: wff setvar class |
This definition is referenced by: reps 14481 repsundef 14482 |
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