Theorems · Theorem · manifolds

SmoothBumpCovering.toSmoothPartitionOfUnity.congr_simp

∀ {ι : Type uι} {E : Type uE} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {H : Type uH}
  [inst_2 : TopologicalSpace H] {I : ModelWithCorners ℝ E H} {M : Type uM} [inst_3 : TopologicalSpace M]
  [inst_4 : ChartedSpace H M] [inst_5 : FiniteDimensional ℝ E] {s : Set M} (fs fs_1 : SmoothBumpCovering ι I M s),
  fs = fs_1 →
    ∀ [inst_6 : T2Space M] [inst_7 : IsManifold I (↑⊤) M], fs.toSmoothPartitionOfUnity = fs_1.toSmoothPartitionOfUnity

Defined in

Mathlib.Geometry.Manifold.PartitionOfUnity

Cited by

0 results in Mathlib

Foundations

Depth 295 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceFiniteDimensionalT2SpaceIsManifold