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 ‘ ≤ ) ) |