Theorems · Theorem · global analysis

UniqueMDiffOn.uniqueDiffWithinAt_range_inter

∀ {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} [IsManifold I 1 M],
  UniqueMDiff[s] →
    ∀ (x : M),
      ∀ y ∈ (extChartAt I x).target ∩ ↑(extChartAt I x).symm ⁻¹' s,
        UniqueDiffWithinAt 𝕜 (Set.range ↑I ∩ ↑(extChartAt I x).symm ⁻¹' s) y

Defined in

Mathlib.Geometry.Manifold.MFDeriv.UniqueDifferential

Cited by

0 results in Mathlib

Foundations

Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifold