![]() |
Mathbox for Norm Megill |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > dvhlmod | Structured version Visualization version GIF version |
Description: The full vector space π constructed from a Hilbert lattice πΎ (given a fiducial hyperplane π) is a left module. (Contributed by NM, 23-May-2015.) |
Ref | Expression |
---|---|
dvhlvec.h | β’ π» = (LHypβπΎ) |
dvhlvec.u | β’ π = ((DVecHβπΎ)βπ) |
dvhlvec.k | β’ (π β (πΎ β HL β§ π β π»)) |
Ref | Expression |
---|---|
dvhlmod | β’ (π β π β LMod) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dvhlvec.h | . . 3 β’ π» = (LHypβπΎ) | |
2 | dvhlvec.u | . . 3 β’ π = ((DVecHβπΎ)βπ) | |
3 | dvhlvec.k | . . 3 β’ (π β (πΎ β HL β§ π β π»)) | |
4 | 1, 2, 3 | dvhlvec 39968 | . 2 β’ (π β π β LVec) |
5 | lveclmod 20709 | . 2 β’ (π β LVec β π β LMod) | |
6 | 4, 5 | syl 17 | 1 β’ (π β π β LMod) |
Copyright terms: Public domain | W3C validator |