Theorems · Theorem · global analysis

mfderivWithin_id

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {s : Set M} {x : M},
  UniqueMDiffAt[s] x → mfderiv[s] id x = ContinuousLinearMap.id 𝕜 (TangentSpace I x)

Defined in

Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions

Cited by

4 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace