`DiffGeoStructure`

definition

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module: IndisputableMonolith.Mathematics.DifferentialGeometryFromRS
domain: Mathematics
line: 22 · github
papers citing: none yet

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IndisputableMonolith.Mathematics.DifferentialGeometryFromRS on GitHub at line 22.

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formal source

  19
  20namespace IndisputableMonolith.Mathematics.DifferentialGeometryFromRS
  21
  22inductive DiffGeoStructure where
  23  | smoothManifold | riemannian | pseudoRiemannian | kahler | symplectic
  24  deriving DecidableEq, Repr, BEq, Fintype
  25
  26theorem diffGeoStructureCount : Fintype.card DiffGeoStructure = 5 := by decide
  27
  28def rsDimension : ℕ := 3
  29def rsSpacetimeDim : ℕ := rsDimension + 1
  30
  31theorem rsSpacetimeDim_eq_4 : rsSpacetimeDim = 4 := by decide
  32theorem rsSpacetimeDim_lorentzian : rsSpacetimeDim = 4 := rsSpacetimeDim_eq_4
  33
  34structure DiffGeoCert where
  35  five_structures : Fintype.card DiffGeoStructure = 5
  36  spacetime_4 : rsSpacetimeDim = 4
  37
  38def diffGeoCert : DiffGeoCert where
  39  five_structures := diffGeoStructureCount
  40  spacetime_4 := rsSpacetimeDim_eq_4
  41
  42end IndisputableMonolith.Mathematics.DifferentialGeometryFromRS

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