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Mirrors > Home > MPE Home > Th. List > df-glb | Structured version Visualization version Unicode version |
Description: Define the greatest lower bound (GLB) of a set of (poset) elements. The domain is restricted to exclude sets for which the GLB doesn't exist uniquely. (Contributed by NM, 12-Sep-2011.) (Revised by NM, 6-Sep-2018.) |
Ref | Expression |
---|---|
df-glb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cglb 16943 | . 2 | |
2 | vp | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | vs | . . . . 5 | |
5 | 2 | cv 1482 | . . . . . . 7 |
6 | cbs 15857 | . . . . . . 7 | |
7 | 5, 6 | cfv 5888 | . . . . . 6 |
8 | 7 | cpw 4158 | . . . . 5 |
9 | vx | . . . . . . . . . 10 | |
10 | 9 | cv 1482 | . . . . . . . . 9 |
11 | vy | . . . . . . . . . 10 | |
12 | 11 | cv 1482 | . . . . . . . . 9 |
13 | cple 15948 | . . . . . . . . . 10 | |
14 | 5, 13 | cfv 5888 | . . . . . . . . 9 |
15 | 10, 12, 14 | wbr 4653 | . . . . . . . 8 |
16 | 4 | cv 1482 | . . . . . . . 8 |
17 | 15, 11, 16 | wral 2912 | . . . . . . 7 |
18 | vz | . . . . . . . . . . . 12 | |
19 | 18 | cv 1482 | . . . . . . . . . . 11 |
20 | 19, 12, 14 | wbr 4653 | . . . . . . . . . 10 |
21 | 20, 11, 16 | wral 2912 | . . . . . . . . 9 |
22 | 19, 10, 14 | wbr 4653 | . . . . . . . . 9 |
23 | 21, 22 | wi 4 | . . . . . . . 8 |
24 | 23, 18, 7 | wral 2912 | . . . . . . 7 |
25 | 17, 24 | wa 384 | . . . . . 6 |
26 | 25, 9, 7 | crio 6610 | . . . . 5 |
27 | 4, 8, 26 | cmpt 4729 | . . . 4 |
28 | 25, 9, 7 | wreu 2914 | . . . . 5 |
29 | 28, 4 | cab 2608 | . . . 4 |
30 | 27, 29 | cres 5116 | . . 3 |
31 | 2, 3, 30 | cmpt 4729 | . 2 |
32 | 1, 31 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: glbfval 16991 |
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