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Mirrors > Home > MPE Home > Th. List > df-ana | Structured version Visualization version Unicode version |
Description: Define the set of analytic functions, which are functions such that the Taylor series of the function at each point converges to the function in some neighborhood of the point. (Contributed by Mario Carneiro, 31-Dec-2016.) |
Ref | Expression |
---|---|
df-ana | Ana ℂfld ↾t Tayl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cana 24108 | . 2 Ana | |
2 | vs | . . 3 | |
3 | cr 9935 | . . . 4 | |
4 | cc 9934 | . . . 4 | |
5 | 3, 4 | cpr 4179 | . . 3 |
6 | vx | . . . . . . 7 | |
7 | 6 | cv 1482 | . . . . . 6 |
8 | vf | . . . . . . . . . 10 | |
9 | 8 | cv 1482 | . . . . . . . . 9 |
10 | cpnf 10071 | . . . . . . . . . 10 | |
11 | 2 | cv 1482 | . . . . . . . . . . 11 |
12 | ctayl 24107 | . . . . . . . . . . 11 Tayl | |
13 | 11, 9, 12 | co 6650 | . . . . . . . . . 10 Tayl |
14 | 10, 7, 13 | co 6650 | . . . . . . . . 9 Tayl |
15 | 9, 14 | cin 3573 | . . . . . . . 8 Tayl |
16 | 15 | cdm 5114 | . . . . . . 7 Tayl |
17 | ccnfld 19746 | . . . . . . . . . 10 ℂfld | |
18 | ctopn 16082 | . . . . . . . . . 10 | |
19 | 17, 18 | cfv 5888 | . . . . . . . . 9 ℂfld |
20 | crest 16081 | . . . . . . . . 9 ↾t | |
21 | 19, 11, 20 | co 6650 | . . . . . . . 8 ℂfld ↾t |
22 | cnt 20821 | . . . . . . . 8 | |
23 | 21, 22 | cfv 5888 | . . . . . . 7 ℂfld ↾t |
24 | 16, 23 | cfv 5888 | . . . . . 6 ℂfld ↾t Tayl |
25 | 7, 24 | wcel 1990 | . . . . 5 ℂfld ↾t Tayl |
26 | 9 | cdm 5114 | . . . . 5 |
27 | 25, 6, 26 | wral 2912 | . . . 4 ℂfld ↾t Tayl |
28 | cpm 7858 | . . . . 5 | |
29 | 4, 11, 28 | co 6650 | . . . 4 |
30 | 27, 8, 29 | crab 2916 | . . 3 ℂfld ↾t Tayl |
31 | 2, 5, 30 | cmpt 4729 | . 2 ℂfld ↾t Tayl |
32 | 1, 31 | wceq 1483 | 1 Ana ℂfld ↾t Tayl |
Colors of variables: wff setvar class |
This definition is referenced by: (None) |
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