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structure definition def or abbrev

CountLaw

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formal statement (Lean)

  75structure CountLaw (D : ℕ) (Family : Type) [Fintype Family]
  76    (encoding : Family → F2Power D) : Prop where
  77  /-- The encoding is injective on `Family`. -/
  78  injective : Function.Injective encoding
  79  /-- The encoding image avoids the zero vector. -/
  80  nonzero : ∀ x : Family, encoding x ≠ 0
  81  /-- Every non-zero vector is in the image of `encoding`. -/
  82  surjective_on_nonzero :
  83    ∀ v : F2Power D, v ≠ 0 → ∃ x : Family, encoding x = v
  84
  85/-! ## §2. The universal cardinality theorem -/
  86
  87/-- If `CountLaw` holds for some encoding, then the family has
  88    cardinality exactly `2 ^ D - 1`. -/

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