openAI-math-dataset / lean /OAI /Analysis /JiangSu /DimensionDrop /SequentialCStarInductiveLimit.lean
| import Mathlib | |
| import OAI.Analysis.TracialSplitting.PreparedBlocks | |
| import OAI.Analysis.JiangSu.Model | |
| namespace OAI | |
| section | |
| noncomputable section | |
| open Filter | |
| open scoped ENNReal Topology CStarAlgebra | |
| namespace SequentialCStar | |
| variable (C : ℕ → Type*) [∀ n, CStarAlgebra (C n)] [∀ n, Nontrivial (C n)] | |
| open TraceCone | |
| namespace System | |
| variable {C} (S : System C) | |
| lemma stage_isometry (n : ℕ) : Isometry (S.stage n) := | |
| AddMonoidHomClass.isometry_of_norm _ (S.stage_norm n) | |
| @[simp] lemma inclusion_compatible {n m} (h : n≤ m) (a : C n) : | |
| S.inclusion m (S.map h a)=S.inclusion n a := Subtype.ext (S.stage_compatible h a) | |
| end System | |
| end SequentialCStar | |
| end | |
| end | |
| end OAI | |