`DecEventSpace`

definition

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module: IndisputableMonolith.RecogGeom.Core
domain: RecogGeom
line: 52 · github
papers citing: none yet

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IndisputableMonolith.RecogGeom.Core on GitHub at line 52.

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All declarations in this module, on Recognition.

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depends on

formal source

  49  nontrivial : ∃ e₁ e₂ : E, e₁ ≠ e₂
  50
  51/-- An event space with decidable equality -/
  52class DecEventSpace (E : Type*) extends EventSpace E where
  53  /-- Decidable equality on events -/
  54  decEq : DecidableEq E
  55
  56attribute [instance] DecEventSpace.decEq
  57
  58/-! ## Basic Properties -/
  59
  60/-- **THEOREM**: A configuration space has at least one element.
  61    Replaces the vacuous `∃ c : C, True` with a constructive witness. -/
  62theorem config_exists (C : Type*) [cs : ConfigSpace C] : ∃ c : C, c = ConfigSpace.witness C :=
  63  ⟨ConfigSpace.witness C, rfl⟩
  64
  65/-- An event space has at least two distinct elements -/
  66theorem event_nontrivial (E : Type*) [EventSpace E] : ∃ e₁ e₂ : E, e₁ ≠ e₂ :=
  67  EventSpace.nontrivial
  68
  69/-! ## Recognition Triple -/
  70
  71/-- A recognition triple bundles a configuration space, event space,
  72    and the implicit structure connecting them. This is the basic
  73    object of study in recognition geometry. -/
  74structure RecognitionTriple where
  75  /-- The type of configurations -/
  76  Config : Type*
  77  /-- The type of events -/
  78  Event : Type*
  79  /-- Configurations form a valid configuration space -/
  80  configSpace : ConfigSpace Config
  81  /-- Events form a valid event space -/
  82  eventSpace : EventSpace Event

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