structure
definition
def or abbrev
RecognitionChart
show as:
view Lean formalization →
formal statement (Lean)
57structure RecognitionChart (L : LocalConfigSpace C) (r : Recognizer C E) (n : ℕ) where
58 /-- The domain: a neighborhood in the local structure -/
59 domain : Set C
60 /-- The domain is a valid neighborhood of some point -/
61 domain_is_nbhd : ∃ c, domain ∈ L.N c
62 /-- The coordinate map -/
63 toFun : domain → Fin n → ℝ
64 /-- Indistinguishable configurations map to the same coordinates -/
65 respects_indistinguishable : ∀ c₁ c₂ : domain,
66 Indistinguishable r c₁.val c₂.val → toFun c₁ = toFun c₂
67 /-- The map is injective on resolution classes -/
68 injective_on_classes : ∀ c₁ c₂ : domain,
69 toFun c₁ = toFun c₂ → Indistinguishable r c₁.val c₂.val
70
71/-! ## Chart Properties -/
72
73variable {n : ℕ} (L : LocalConfigSpace C) (r : Recognizer C E)
74
75/-- A chart maps equivalent configurations to the same coordinates -/
used by (14)
-
ChartCompatible -
chartCompatible_refl -
chartCompatible_symm -
chart_exists_implies -
chartOnQuotient -
chartOnQuotient_well_defined -
chart_respects_equiv -
charts_status -
finite_resolution_no_chart -
finite_resolution_no_chart_hypothesis -
hasRecognitionDimension -
RecognitionAtlas -
recognition_dimension_unique -
recognition_dimension_unique_hypothesis