Theorems · Theorem · global analysis

Manifold.IsSubmersionAtOfComplement.congr_F

∀ {𝕜 : Type u_1} {E'' : Type u_3} {F : Type u_5} {F' : Type u_6} {H : Type u_7} {G : Type u_9} {E : Type u}
  [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E]
  [inst_3 : NormedAddCommGroup E''] [inst_4 : NormedSpace 𝕜 E''] [inst_5 : NormedAddCommGroup F]
  [inst_6 : NormedSpace 𝕜 F] [inst_7 : NormedAddCommGroup F'] [inst_8 : NormedSpace 𝕜 F'] [inst_9 : TopologicalSpace H]
  [inst_10 : TopologicalSpace G] {I : ModelWithCorners 𝕜 E H} {J : ModelWithCorners 𝕜 E'' G} {M : Type u_11}
  {N : Type u_13} [inst_11 : TopologicalSpace M] [inst_12 : ChartedSpace H M] [inst_13 : TopologicalSpace N]
  [inst_14 : ChartedSpace G N] {n : WithTop ℕ∞} {f : M → N} {x : M} (e : F ≃L[𝕜] F'),
  Manifold.IsSubmersionAtOfComplement F I J n f x ↔ Manifold.IsSubmersionAtOfComplement F' I J n f x

Being a submersion at x w.r.t. F is stable under replacing F by an isomorphic copy.

Defined in

Mathlib.Geometry.Manifold.Submersion

Cited by

3 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpace