| 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 | |