OAI/MeasureTheory/Falconer/Geometry/PlanarScalarGrid.lean

GitHub source file

13 declarations, 0 contain sorry, 0 declared as axioms

Actual scalar grid coordinates for a planar finite set. Rounding is injective below the separation scale and coordinate counts are exactly the original scalar cell counts.

  1. def OAI.Falconer.scalarGridFloor line 11
  2. theorem OAI.Falconer.scalarGridFloor_error line 13
  3. theorem OAI.Falconer.scalarGridFloor_injective line 21
  4. theorem OAI.Falconer.scalarGridFloor_card line 26
  5. theorem OAI.Falconer.scalarGridFloor_separated line 33
  6. def OAI.Falconer.planarGridFloor line 50
  7. theorem OAI.Falconer.planarGridFloor_apply line 53
  8. theorem OAI.Falconer.planarGridFloor_error line 57
  9. theorem OAI.Falconer.planarGridFloor_injOn line 64
  10. theorem OAI.Falconer.planarGridFloor_card line 78
  11. theorem OAI.Falconer.planarGridFloor_coordinate_card line 83
  12. theorem OAI.Falconer.planarGridFloor_coordinate_separated line 92
  13. theorem OAI.Falconer.planarGridFloor_separated line 102