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chore: rename misnamed lemmas involving isOpenMap (#11607)
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- open_map_of_strict_deriv -> isOpenMap_of_hasStrictDerivAt
- open_map_of_strict_fderiv_equiv -> isOpenMap_of_hasStrictFderivAt_equiv
These lemmas have conclusion `isOpenMap`, hence should be named accordingly.
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grunweg committed Mar 23, 2024
1 parent f2373e0 commit 853378f
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Showing 3 changed files with 8 additions and 5 deletions.
5 changes: 3 additions & 2 deletions Mathlib/Analysis/Calculus/InverseFunctionTheorem/Deriv.lean
Expand Up @@ -50,7 +50,8 @@ end HasStrictDerivAt
variable {f}

/-- If a function has a non-zero strict derivative at all points, then it is an open map. -/
theorem open_map_of_strict_deriv {f' : π•œ β†’ π•œ}
theorem isOpenMap_of_hasStrictDerivAt {f' : π•œ β†’ π•œ}
(hf : βˆ€ x, HasStrictDerivAt f (f' x) x) (h0 : βˆ€ x, f' x β‰  0) : IsOpenMap f :=
isOpenMap_iff_nhds_le.2 fun x => ((hf x).map_nhds_eq (h0 x)).ge
#align open_map_of_strict_deriv open_map_of_strict_deriv
#align open_map_of_strict_deriv isOpenMap_of_hasStrictDerivAt
@[deprecated] alias open_map_of_strict_deriv := isOpenMap_of_hasStrictDerivAt -- 2024-03-23
6 changes: 4 additions & 2 deletions Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean
Expand Up @@ -213,7 +213,9 @@ theorem to_local_left_inverse (hf : HasStrictFDerivAt f (f' : E β†’L[π•œ] F) a)
end HasStrictFDerivAt

/-- If a function has an invertible strict derivative at all points, then it is an open map. -/
theorem open_map_of_strict_fderiv_equiv [CompleteSpace E] {f : E β†’ F} {f' : E β†’ E ≃L[π•œ] F}
theorem isOpenMap_of_hasStrictFDerivAt_equiv [CompleteSpace E] {f : E β†’ F} {f' : E β†’ E ≃L[π•œ] F}
(hf : βˆ€ x, HasStrictFDerivAt f (f' x : E β†’L[π•œ] F) x) : IsOpenMap f :=
isOpenMap_iff_nhds_le.2 fun x => (hf x).map_nhds_eq_of_equiv.ge
#align open_map_of_strict_fderiv_equiv open_map_of_strict_fderiv_equiv
#align open_map_of_strict_fderiv_equiv isOpenMap_of_hasStrictFDerivAt_equiv
@[deprecated] alias open_map_of_strict_fderiv_equiv :=
isOpenMap_of_hasStrictFDerivAt_equiv -- 2024-03-23
2 changes: 1 addition & 1 deletion Mathlib/Analysis/SpecialFunctions/Complex/LogDeriv.lean
Expand Up @@ -22,7 +22,7 @@ open scoped Real Topology
namespace Complex

theorem isOpenMap_exp : IsOpenMap exp :=
open_map_of_strict_deriv hasStrictDerivAt_exp exp_ne_zero
isOpenMap_of_hasStrictDerivAt hasStrictDerivAt_exp exp_ne_zero
#align complex.is_open_map_exp Complex.isOpenMap_exp

/-- `Complex.exp` as a `PartialHomeomorph` with `source = {z | -Ο€ < im z < Ο€}` and
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