| import Mathlib | |
| import OAI.Analysis.BiholderTransport.Convexity.UniformEnvelope | |
| namespace OAI | |
| noncomputable section | |
| open Set Filter Manifold Bundle | |
| open scoped Topology ContDiff | |
| namespace WeakMTWTransport | |
| variable {n : ℕ} {M : Type*} [MetricSpace M] | |
| [ChartedSpace (Model n) M] [IsManifold 𝓘(ℝ,Model n) ∞ M] | |
| lemma chartFiberInverse_at_center (a : M) (p : Model n) : | |
| chartFiberInverse a ((extChartAt 𝓘(ℝ,Model n) a) a) p=p := by | |
| dsimp only [chartFiberInverse] | |
| rw [(extChartAt 𝓘(ℝ,Model n) a).left_inv (mem_extChartAt_source a)] | |
| rw [TangentBundle.symmL_trivializationAt_eq_core (mem_chart_source (Model n) a)] | |
| exact tangentCoordChange_self (I := 𝓘(ℝ,Model n)) (mem_extChartAt_source a) | |
| end WeakMTWTransport | |
| end | |
| end OAI | |