`LinguisticRole`

definition

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module: IndisputableMonolith.CrossDomain.ConfigDimUniversality
domain: CrossDomain
line: 42 · github
papers citing: none yet

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IndisputableMonolith.CrossDomain.ConfigDimUniversality on GitHub at line 42.

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formal source

  39  | recession | recovery | expansion | peak | contraction
  40  deriving DecidableEq, Repr, BEq, Fintype
  41
  42inductive LinguisticRole where
  43  | subject | verb | object | modifier | complement
  44  deriving DecidableEq, Repr, BEq, Fintype
  45
  46theorem sensory_hasConfigDim5 : HasConfigDim5 SensoryModality := by
  47  unfold HasConfigDim5; decide
  48theorem emotion_hasConfigDim5 : HasConfigDim5 PrimaryEmotion := by
  49  unfold HasConfigDim5; decide
  50theorem biological_hasConfigDim5 : HasConfigDim5 BiologicalState := by
  51  unfold HasConfigDim5; decide
  52theorem economic_hasConfigDim5 : HasConfigDim5 EconomicCycle := by
  53  unfold HasConfigDim5; decide
  54theorem linguistic_hasConfigDim5 : HasConfigDim5 LinguisticRole := by
  55  unfold HasConfigDim5; decide
  56
  57/-! ## Cross-domain product theorems. -/
  58
  59/-- Any triple of D=5 types has a product of size 125. -/
  60theorem triple_product_125
  61    {A B C : Type} [Fintype A] [Fintype B] [Fintype C]
  62    (hA : HasConfigDim5 A) (hB : HasConfigDim5 B) (hC : HasConfigDim5 C) :
  63    Fintype.card (A × B × C) = 125 := by
  64  unfold HasConfigDim5 at hA hB hC
  65  simp [Fintype.card_prod, hA, hB, hC]
  66
  67/-- Any pair of D=5 types has a product of size 25. -/
  68theorem pair_product_25
  69    {A B : Type} [Fintype A] [Fintype B]
  70    (hA : HasConfigDim5 A) (hB : HasConfigDim5 B) :
  71    Fintype.card (A × B) = 25 := by
  72  unfold HasConfigDim5 at hA hB

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