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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 44145 | . 2 class ~~>* | |
2 | cle 11195 | . . . 4 class ≤ | |
3 | cordt 17386 | . . . 4 class ordTop | |
4 | 2, 3 | cfv 6497 | . . 3 class (ordTop‘ ≤ ) |
5 | clm 22593 | . . 3 class ⇝𝑡 | |
6 | 4, 5 | cfv 6497 | . 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 44147 xlimres 44148 xlimcl 44149 xlimclim 44151 xlimconst 44152 xlimbr 44154 xlimmnfvlem1 44159 xlimmnfvlem2 44160 xlimpnfvlem1 44163 xlimpnfvlem2 44164 xlimuni 44180 xlimfun 44182 |
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