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110f4f3 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | 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
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