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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 44534 | . 2 class ~~>* | |
2 | cle 11249 | . . . 4 class ≤ | |
3 | cordt 17445 | . . . 4 class ordTop | |
4 | 2, 3 | cfv 6544 | . . 3 class (ordTop‘ ≤ ) |
5 | clm 22730 | . . 3 class ⇝𝑡 | |
6 | 4, 5 | cfv 6544 | . 2 class (⇝𝑡‘(ordTop‘ ≤ )) |
7 | 1, 6 | wceq 1542 | 1 wff ~~>* = (⇝𝑡‘(ordTop‘ ≤ )) |
Colors of variables: wff setvar class |
This definition is referenced by: xlimrel 44536 xlimres 44537 xlimcl 44538 xlimclim 44540 xlimconst 44541 xlimbr 44543 xlimmnfvlem1 44548 xlimmnfvlem2 44549 xlimpnfvlem1 44552 xlimpnfvlem2 44553 xlimuni 44569 xlimfun 44571 |
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