Metamath Proof Explorer
Description: Define the convergence relation for extended real sequences. (Contributed by Glauco Siliprandi, 5-Feb-2022)
|
|
Ref |
Expression |
|
Assertion |
df-xlim |
⊢ ~~>* = ( ⇝𝑡 ‘ ( ordTop ‘ ≤ ) ) |
Detailed syntax breakdown
| Step |
Hyp |
Ref |
Expression |
| 0 |
|
clsxlim |
⊢ ~~>* |
| 1 |
|
clm |
⊢ ⇝𝑡 |
| 2 |
|
cordt |
⊢ ordTop |
| 3 |
|
cle |
⊢ ≤ |
| 4 |
3 2
|
cfv |
⊢ ( ordTop ‘ ≤ ) |
| 5 |
4 1
|
cfv |
⊢ ( ⇝𝑡 ‘ ( ordTop ‘ ≤ ) ) |
| 6 |
0 5
|
wceq |
⊢ ~~>* = ( ⇝𝑡 ‘ ( ordTop ‘ ≤ ) ) |