Theorems · Theorem · global analysis
ImplicitFunctionData.map_nhds_eq
∀ {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),
Filter.map φ.leftFun (nhds φ.pt) = nhds (φ.leftFun φ.pt)- Defined in
- Mathlib.Analysis.Calculus.Implicit
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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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
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- CompleteSpacestatement and proof · cited by 2,532
- Filter.mapstatement and proof · cited by 819
- Filter.map_mapproof · cited by 80
- ImplicitFunctionDatastatement and proof · cited by 44
- ImplicitFunctionData.ptstatement and proof · cited by 31
- ImplicitFunctionData.leftFunstatement · cited by 24
- ImplicitFunctionData.prodFunproof · cited by 17
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