openAI-math-dataset / lean /OAI /Analysis /IrrationalRotation /Operators /ConcreteTracialDirectFiniteness.lean
| import OAI.Analysis.IrrationalRotation.Operators.TracialDirectFiniteness | |
| import OAI.Analysis.IrrationalRotation.Rotation.RotationTrace | |
| import OAI.Analysis.IrrationalRotation.Product.ProductTracialVector | |
| namespace OAI | |
| noncomputable section | |
| namespace Invariant233 | |
| theorem Rotation.algebra_isDedekindFiniteMonoid (θ : ℝ) : | |
| IsDedekindFiniteMonoid (Rotation.algebra θ) := | |
| (Rotation.vacuum_faithfulTracial θ).isDedekindFiniteMonoid | |
| theorem ProductModel.factor_isDedekindFiniteMonoid (θ : ℕ → ℝ) : | |
| IsDedekindFiniteMonoid (ProductModel.factor θ) := | |
| (ProductModel.traceVector_faithfulTracial θ).isDedekindFiniteMonoid | |
| end Invariant233 | |
| end | |
| end OAI | |