Mathlib Map

Theorems · Definition · global analysis

ImplicitFunctionData.leftFun

{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] → ImplicitFunctionData 𝕜 E F G → E → F

Left function

Defined in
Mathlib.Analysis.Calculus.Implicit
Cited by
24 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceCompleteSpaceNormedAddCommGroupNormedSpaceCompleteSpaceNormedAddCommGroupNormedSpaceCompleteSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ImplicitFunctionData.prodFun · cited by 17ImplicitFunctionData.prod…ImplicitFunctionData.prodFun_apply · cited by 5ImplicitFunctionData.prod…HasStrictFDerivAt.eventually_apply_eq_iff_implicitFunctionOfProdDomain · cited by 4HasStrictFDerivAt.eventua…ImplicitFunctionData.fderiv_implicitFunction_apply_eq_iff · cited by 3ImplicitFunctionData.fder…ImplicitFunctionData.hasStrictFDerivAt_implicitFunction · cited by 3ImplicitFunctionData.hasS…ImplicitFunctionData.hasStrictFDerivAt_implicitFunction_fderiv · cited by 2ImplicitFunctionData.hasS…HasStrictFDerivAt.leftFun_implicitFunctionDataOfProdDomain · cited by 2HasStrictFDerivAt.leftFun…ImplicitFunctionData.implicitFunction_apply_image · cited by 2ImplicitFunctionData.impl…ImplicitFunctionData.leftFun_implicitFunction · cited by 2ImplicitFunctionData.left…HasStrictFDerivAt.to_implicitFunctionOfComplemented · cited by 1HasStrictFDerivAt.to_impl…ImplicitFunctionData.contDiffAt_implicitFunction · cited by 1ImplicitFunctionData.cont…ImplicitFunctionData.hasStrictFDerivAt_leftFun · cited by 1ImplicitFunctionData.hasS…ImplicitFunctionData.leftFun_eq_iff_implicitFunction · cited by 1ImplicitFunctionData.left…ImplicitFunctionData.leftFun_implicitFunction_eq_leftFun · cited by 1ImplicitFunctionData.left…ImplicitFunctionData.rightFun_implicitFunction_eq_rightFun · cited by 1ImplicitFunctionData.righ…NormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldCompleteSpace · cited by 2532CompleteSpaceImplicitFunctionData · cited by 44ImplicitFunctionDataImplicitFunctionData.leftFunCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by25

Results whose statement or proof uses this declaration.