Theorems · Theorem · global analysis
ImplicitFunctionData.leftFun_eq_iff_implicitFunction
∀ {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),
∀ᶠ (x : E) in nhds φ.pt, φ.leftFun x = φ.leftFun φ.pt ↔ φ.implicitFunction (φ.leftFun φ.pt) (φ.rightFun x) = x- Defined in
- Mathlib.Analysis.Calculus.Implicit
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsstatement · cited by 5,554
- Filter.Eventuallystatement · cited by 3,134
- CompleteSpacestatement and proof · cited by 2,532
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- ImplicitFunctionDatastatement and proof · cited by 44
- ImplicitFunctionData.ptstatement and proof · cited by 31
- ImplicitFunctionData.implicitFunctionstatement and proof · cited by 26
- ImplicitFunctionData.leftFunstatement and proof · cited by 24
Cited by1
Results whose statement or proof uses this declaration.
- HasStrictFDerivAt.eventually_apply_eq_iff_implicitFunctionOfProdDomainproof · cited by 4