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Mathbox for Norm Megill |
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| 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) |
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