Theorems · Theorem · global analysis
ImplicitFunctionData.pt_mem_toOpenPartialHomeomorph_source
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : CompleteSpace E] {F : Type u_3} [inst_4 : NormedAddCommGroup F]
[inst_5 : NormedSpace 𝕜 F] [inst_6 : CompleteSpace F] {G : Type u_4} [inst_7 : NormedAddCommGroup G]
[inst_8 : NormedSpace 𝕜 G] [inst_9 : CompleteSpace G] (φ : ImplicitFunctionData 𝕜 E F G),
φ.pt ∈ φ.toOpenPartialHomeomorph.source- Defined in
- Mathlib.Analysis.Calculus.Implicit
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- CompleteSpacestatement and proof · cited by 2,532
- PartialEquiv.sourcestatement · cited by 964
- PartialHomeomorph.toPartialEquivstatement · cited by 917
- OpenPartialHomeomorph.toPartialHomeomorphstatement · cited by 851
- ImplicitFunctionDatastatement and proof · cited by 44
- ImplicitFunctionData.ptstatement · cited by 31
- ImplicitFunctionData.hasStrictFDerivAtproof · cited by 12
- HasStrictFDerivAt.mem_toOpenPartialHomeomorph_sourceproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- HasStrictFDerivAt.mem_implicitToOpenPartialHomeomorph_sourceproof · cited by 1
- ImplicitFunctionData.map_implicitFunction_nhdsWithin_preimageproof · cited by 0
- ImplicitFunctionData.map_pt_mem_toOpenPartialHomeomorph_targetproof · cited by 0