Theorems · Theorem · global analysis
ImplicitFunctionData.hasStrictFDerivAt
∀ {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),
HasStrictFDerivAt φ.prodFun (↑(φ.leftDeriv.equivProdOfSurjectiveOfIsCompl φ.rightDeriv ⋯ ⋯ ⋯)) φ.pt- Defined in
- Mathlib.Analysis.Calculus.Implicit
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- 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
- ContinuousLinearEquiv.toContinuousLinearMapstatement · cited by 448
- HasStrictFDerivAtstatement · cited by 261
- ImplicitFunctionDatastatement and proof · cited by 44
- ImplicitFunctionData.ptstatement · cited by 31
- ImplicitFunctionData.prodFunstatement · cited by 17
- HasStrictFDerivAt.prodMkproof · cited by 16
- ImplicitFunctionData.leftDerivstatement · cited by 12
Cited by13
Results whose statement or proof uses this declaration.
- ImplicitFunctionData.toOpenPartialHomeomorphproof · cited by 6
- ImplicitFunctionData.pt_mem_toOpenPartialHomeomorph_sourceproof · cited by 4
- ImplicitFunctionData.prodFun_implicitFunctionproof · cited by 3
- ImplicitFunctionData.fderiv_implicitFunction_apply_eq_iffproof · cited by 3
- ImplicitFunctionData.hasStrictFDerivAt_implicitFunction_fderivproof · cited by 2
- ImplicitFunctionData.implicitFunction_apply_imageproof · cited by 2
- ImplicitFunctionData.contDiffAt_implicitFunctionproof · cited by 1
- ImplicitFunctionData.implicitFunction_defstatement · cited by 1
- ImplicitFunctionData.rightFun_implicitFunction_eq_rightFunproof · cited by 1
- ImplicitFunctionData.leftFun_implicitFunction_eq_leftFunproof · cited by 1
- ImplicitFunctionData.eventuallyEq_implicitFunctionproof · cited by 0
- ImplicitFunctionData.isInvertible_fderiv_prodFunproof · cited by 0