Theorems · Theorem · global analysis
ImplicitFunctionData.range_rightDeriv
∀ {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] (self : ImplicitFunctionData 𝕜 E F G),
(↑self.rightDeriv).range = ⊤- Defined in
- Mathlib.Analysis.Calculus.Implicit
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Top.topstatement · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Submodulestatement · cited by 7,192
- CompleteSpacestatement and proof · cited by 2,532
- LinearMap.rangestatement · cited by 893
- ContinuousLinearMap.toLinearMapstatement · cited by 528
- ImplicitFunctionDatastatement and proof · cited by 44
- ImplicitFunctionData.rightDerivstatement · cited by 11
Cited by5
Results whose statement or proof uses this declaration.
- ImplicitFunctionData.hasStrictFDerivAtstatement · cited by 12
- ImplicitFunctionData.prodFun_implicitFunctionproof · cited by 3
- ImplicitFunctionData.fderiv_implicitFunction_apply_eq_iffproof · cited by 3
- ImplicitFunctionData.hasStrictFDerivAt_implicitFunction_fderivproof · cited by 2
- ImplicitFunctionData.implicitFunction_defstatement · cited by 1