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59d1c80 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | import Mathlib
namespace OAI
/-! Convex bodies and exact coverings by a single lattice in real coordinate space. -/
namespace SingleLatticeCovering
open MeasureTheory
open scoped Pointwise
abbrev Space (n : ℕ) := Fin n → ℝ
def IsConvexBody {n : ℕ} (K : Set (Space n)) : Prop :=
IsCompact K ∧ Convex ℝ K ∧ (interior K).Nonempty
def LatticeCovers {n : ℕ} (K : Set (Space n)) (L : Submodule ℤ (Space n)) : Prop :=
K + (L : Set (Space n)) = Set.univ
end SingleLatticeCovering
end OAI
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