Theorems · Theorem · global analysis
ImplicitFunctionData.prodFun_apply
∀ {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) (x : E),
φ.prodFun x = (φ.leftFun x, φ.rightFun x)- Defined in
- Mathlib.Analysis.Calculus.Implicit
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- CompleteSpacestatement and proof · cited by 2,532
- ImplicitFunctionDatastatement and proof · cited by 44
- ImplicitFunctionData.leftFunstatement · cited by 24
- ImplicitFunctionData.rightFunstatement · cited by 23
- ImplicitFunctionData.prodFunstatement and proof · cited by 17
Cited by5
Results whose statement or proof uses this declaration.
- ContDiffAt.contDiffAt_implicitFunctionproof · cited by 1
- ImplicitFunctionData.contDiffAt_implicitFunctionproof · cited by 1
- ImplicitFunctionData.leftFun_implicitFunction_eq_leftFunproof · cited by 1
- ImplicitFunctionData.rightFun_implicitFunction_eq_rightFunproof · cited by 1
- ImplicitFunctionData.map_implicitFunction_nhdsWithin_preimageproof · cited by 0