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Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-xlim | Structured version Visualization version GIF version |
Description: Define the convergence relation for extended real sequences. (Contributed by Glauco Siliprandi, 5-Feb-2022.) |
Ref | Expression |
---|---|
df-xlim | ⊢ ~~>* = (⇝𝑡‘(ordTop‘ ≤ )) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clsxlim 40783 | . 2 class ~~>* | |
2 | cle 10365 | . . . 4 class ≤ | |
3 | cordt 16473 | . . . 4 class ordTop | |
4 | 2, 3 | cfv 6102 | . . 3 class (ordTop‘ ≤ ) |
5 | clm 21358 | . . 3 class ⇝𝑡 | |
6 | 4, 5 | cfv 6102 | . 2 class (⇝𝑡‘(ordTop‘ ≤ )) |
7 | 1, 6 | wceq 1653 | 1 wff ~~>* = (⇝𝑡‘(ordTop‘ ≤ )) |
Colors of variables: wff setvar class |
This definition is referenced by: xlimrel 40785 xlimres 40786 xlimcl 40787 xlimclim 40789 xlimconst 40790 xlimbr 40792 xlimmnfvlem1 40797 xlimmnfvlem2 40798 xlimpnfvlem1 40801 xlimpnfvlem2 40802 |
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