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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-pointsN | Structured version Visualization version GIF version |
Description: Define set of all projective points in a Hilbert lattice (actually in any set at all, for simplicity). A projective point is the singleton of a lattice atom. Definition 15.1 of [MaedaMaeda] p. 61. Note that item 1 in [Holland95] p. 222 defines a point as the atom itself, but this leads to a complicated subspace ordering that may be either membership or inclusion based on its arguments. (Contributed by NM, 2-Oct-2011.) |
Ref | Expression |
---|---|
df-pointsN | β’ Points = (π β V β¦ {π β£ βπ β (Atomsβπ)π = {π}}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cpointsN 37987 | . 2 class Points | |
2 | vk | . . 3 setvar π | |
3 | cvv 3448 | . . 3 class V | |
4 | vq | . . . . . . 7 setvar π | |
5 | 4 | cv 1541 | . . . . . 6 class π |
6 | vp | . . . . . . . 8 setvar π | |
7 | 6 | cv 1541 | . . . . . . 7 class π |
8 | 7 | csn 4591 | . . . . . 6 class {π} |
9 | 5, 8 | wceq 1542 | . . . . 5 wff π = {π} |
10 | 2 | cv 1541 | . . . . . 6 class π |
11 | catm 37754 | . . . . . 6 class Atoms | |
12 | 10, 11 | cfv 6501 | . . . . 5 class (Atomsβπ) |
13 | 9, 6, 12 | wrex 3074 | . . . 4 wff βπ β (Atomsβπ)π = {π} |
14 | 13, 4 | cab 2714 | . . 3 class {π β£ βπ β (Atomsβπ)π = {π}} |
15 | 2, 3, 14 | cmpt 5193 | . 2 class (π β V β¦ {π β£ βπ β (Atomsβπ)π = {π}}) |
16 | 1, 15 | wceq 1542 | 1 wff Points = (π β V β¦ {π β£ βπ β (Atomsβπ)π = {π}}) |
Colors of variables: wff setvar class |
This definition is referenced by: pointsetN 38233 |
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