refactor: Change case of type and props

2024-06-26 11:54:02 -04:00 · 2024-06-26 11:54:02 -04:00 · f7a638d32e
commit f7a638d32e
parent 18b83f582e
58 changed files with 695 additions and 696 deletions
--- a/HepLean/SpaceTime/LorentzGroup/Basic.lean
+++ b/HepLean/SpaceTime/LorentzGroup/Basic.lean
@ -26,7 +26,7 @@ identity.

 noncomputable section

-namespace spaceTime
+namespace SpaceTime

 open Manifold
 open Matrix
@ -44,14 +44,14 @@ These matrices form the Lorentz group, which we will define in the next section
 /-- We say a matrix `Λ` preserves `ηLin` if for all `x` and `y`,
  `ηLin (Λ *ᵥ x) (Λ *ᵥ y) = ηLin x y`.  -/
 def PreservesηLin (Λ : Matrix (Fin 4) (Fin 4) ℝ) : Prop :=
-  ∀ (x y : spaceTime), ηLin (Λ *ᵥ x) (Λ *ᵥ y) = ηLin x y
+  ∀ (x y : SpaceTime), ηLin (Λ *ᵥ x) (Λ *ᵥ y) = ηLin x y

 namespace PreservesηLin

 variable  (Λ : Matrix (Fin 4) (Fin 4) ℝ)

 lemma iff_norm : PreservesηLin Λ ↔
-    ∀ (x : spaceTime), ηLin (Λ *ᵥ x) (Λ *ᵥ x) = ηLin x x := by
+    ∀ (x : SpaceTime), ηLin (Λ *ᵥ x) (Λ *ᵥ x) = ηLin x x := by
  refine Iff.intro (fun h x => h x x) (fun h x y => ?_)
  have hp := h (x + y)
  have hn := h (x - y)
@ -75,7 +75,7 @@ lemma iff_det_selfAdjoint : PreservesηLin Λ ↔
  simpa [det_eq_ηLin] using h1

 lemma iff_on_right : PreservesηLin Λ ↔
-    ∀ (x y : spaceTime), ηLin x ((η * Λᵀ * η * Λ) *ᵥ y) = ηLin x y := by
+    ∀ (x y : SpaceTime), ηLin x ((η * Λᵀ * η * Λ) *ᵥ y) = ηLin x y := by
  apply Iff.intro
  intro h x y
  have h1 := h x y
@ -138,10 +138,10 @@ We show that the Lorentz group is indeed a group.
 -/

 /-- The Lorentz group is the subset of matrices which preserve ηLin. -/
-def lorentzGroup : Type := {Λ : Matrix (Fin 4) (Fin 4) ℝ // PreservesηLin Λ}
+def LorentzGroup : Type := {Λ : Matrix (Fin 4) (Fin 4) ℝ // PreservesηLin Λ}

@[simps mul_coe one_coe inv div]
-instance lorentzGroupIsGroup : Group lorentzGroup where
+instance lorentzGroupIsGroup : Group LorentzGroup where
  mul A B := ⟨A.1 * B.1, PreservesηLin.mul A.2 B.2⟩
  mul_assoc A B C := by
    apply Subtype.eq
@ -160,20 +160,20 @@ instance lorentzGroupIsGroup : Group lorentzGroup where
    exact (PreservesηLin.iff_matrix A.1).mp A.2

 /-- Notation for the Lorentz group. -/
-scoped[spaceTime] notation (name := lorentzGroup_notation) "𝓛" => lorentzGroup
+scoped[SpaceTime] notation (name := lorentzGroup_notation) "𝓛" => LorentzGroup


 /-- `lorentzGroup` has the subtype topology. -/
-instance : TopologicalSpace lorentzGroup := instTopologicalSpaceSubtype
+instance : TopologicalSpace LorentzGroup := instTopologicalSpaceSubtype

-namespace lorentzGroup
+namespace LorentzGroup

-lemma coe_inv (A : 𝓛) : (A⁻¹).1 = A.1⁻¹:= by
+lemma coe_inv (A : LorentzGroup) : (A⁻¹).1 = A.1⁻¹:= by
  refine (inv_eq_left_inv ?h).symm
  exact (PreservesηLin.iff_matrix A.1).mp A.2

 /-- The transpose of an matrix in the Lorentz group is an element of the Lorentz group. -/
-def transpose (Λ : lorentzGroup) : lorentzGroup := ⟨Λ.1ᵀ, (PreservesηLin.iff_transpose Λ.1).mp Λ.2⟩
+def transpose (Λ : LorentzGroup) : LorentzGroup := ⟨Λ.1ᵀ, (PreservesηLin.iff_transpose Λ.1).mp Λ.2⟩

 /-!

@ -186,7 +186,7 @@ embedding.
 -/

 /-- The homomorphism of the Lorentz group into `GL (Fin 4) ℝ`. -/
-def toGL : 𝓛 →* GL (Fin 4) ℝ where
+def toGL : LorentzGroup →* GL (Fin 4) ℝ where
  toFun A := ⟨A.1, (A⁻¹).1, mul_eq_one_comm.mpr $ (PreservesηLin.iff_matrix A.1).mp A.2,
    (PreservesηLin.iff_matrix A.1).mp A.2⟩
  map_one' := by
@ -206,7 +206,7 @@ lemma toGL_injective : Function.Injective toGL := by
 /-- The homomorphism from the Lorentz Group into the monoid of matrices times the opposite of
  the monoid of matrices. -/
@[simps!]
-def toProd : 𝓛 →* (Matrix (Fin 4) (Fin 4) ℝ) × (Matrix (Fin 4) (Fin 4) ℝ)ᵐᵒᵖ :=
+def toProd : LorentzGroup →* (Matrix (Fin 4) (Fin 4) ℝ) × (Matrix (Fin 4) (Fin 4) ℝ)ᵐᵒᵖ :=
  MonoidHom.comp (Units.embedProduct _) toGL

 lemma toProd_eq_transpose_η  : toProd A = (A.1, ⟨η * A.1ᵀ * η⟩) := rfl
@ -248,11 +248,11 @@ lemma toGL_embedding : Embedding toGL.toFun where
    exact exists_exists_and_eq_and


-instance : TopologicalGroup 𝓛 := Inducing.topologicalGroup toGL toGL_embedding.toInducing
+instance : TopologicalGroup LorentzGroup := Inducing.topologicalGroup toGL toGL_embedding.toInducing



-end lorentzGroup
+end LorentzGroup


-end spaceTime
+end SpaceTime
--- a/HepLean/SpaceTime/LorentzGroup/Boosts.lean
+++ b/HepLean/SpaceTime/LorentzGroup/Boosts.lean
@ -28,14 +28,14 @@ A boost is the special case of a generalised boost when `u = stdBasis 0`.

 -/
 noncomputable section
-namespace spaceTime
+namespace SpaceTime

-namespace lorentzGroup
+namespace LorentzGroup

 open FourVelocity

 /-- An auxillary linear map used in the definition of a generalised boost. -/
-def genBoostAux₁ (u v : FourVelocity) : spaceTime →ₗ[ℝ] spaceTime where
+def genBoostAux₁ (u v : FourVelocity) : SpaceTime →ₗ[ℝ] SpaceTime where
  toFun x := (2 * ηLin x u) • v.1.1
  map_add' x y := by
    simp only [map_add, LinearMap.add_apply]
@ -46,7 +46,7 @@ def genBoostAux₁ (u v : FourVelocity) : spaceTime →ₗ[ℝ] spaceTime where
    rw [← mul_assoc, mul_comm 2 c, mul_assoc, mul_smul]

 /-- An auxillary linear map used in the definition of a genearlised boost. -/
-def genBoostAux₂ (u v : FourVelocity) : spaceTime →ₗ[ℝ] spaceTime where
+def genBoostAux₂ (u v : FourVelocity) : SpaceTime →ₗ[ℝ] SpaceTime where
  toFun x := - (ηLin x (u + v) / (1 + ηLin u v)) • (u + v)
  map_add' x y := by
    simp only
@ -62,7 +62,7 @@ def genBoostAux₂ (u v : FourVelocity) : spaceTime →ₗ[ℝ] spaceTime where

 /-- An generalised boost. This is a Lorentz transformation which takes the four velocity `u`
 to `v`. -/
-def genBoost (u v : FourVelocity) : spaceTime →ₗ[ℝ] spaceTime :=
+def genBoost (u v : FourVelocity) : SpaceTime →ₗ[ℝ] SpaceTime :=
  LinearMap.id + genBoostAux₁ u v + genBoostAux₂ u v

 namespace genBoost
@ -91,7 +91,7 @@ lemma self (u : FourVelocity) : genBoost u u = LinearMap.id := by
 def toMatrix (u v : FourVelocity) : Matrix (Fin 4) (Fin 4) ℝ :=
  LinearMap.toMatrix stdBasis stdBasis (genBoost u v)

-lemma toMatrix_mulVec (u v : FourVelocity) (x : spaceTime) :
+lemma toMatrix_mulVec (u v : FourVelocity) (x : SpaceTime) :
    (toMatrix u v).mulVec x = genBoost u v x :=
  LinearMap.toMatrix_mulVec_repr stdBasis stdBasis (genBoost u v) x

@ -143,7 +143,7 @@ lemma toMatrix_PreservesηLin (u v : FourVelocity) : PreservesηLin (toMatrix u
  ring

 /-- A generalised boost as an element of the Lorentz Group. -/
-def toLorentz (u v : FourVelocity) : lorentzGroup :=
+def toLorentz (u v : FourVelocity) : LorentzGroup :=
  ⟨toMatrix u v, toMatrix_PreservesηLin u v⟩

 lemma toLorentz_continuous (u : FourVelocity) : Continuous (toLorentz u) := by
@ -171,8 +171,8 @@ lemma isProper (u v : FourVelocity) : IsProper (toLorentz u v) :=
 end genBoost


-end lorentzGroup
+end LorentzGroup


-end spaceTime
+end SpaceTime
 end
--- a/HepLean/SpaceTime/LorentzGroup/Orthochronous.lean
+++ b/HepLean/SpaceTime/LorentzGroup/Orthochronous.lean
@ -20,19 +20,19 @@ matrices.

 noncomputable section

-namespace spaceTime
+namespace SpaceTime

 open Manifold
 open Matrix
 open Complex
 open ComplexConjugate

-namespace lorentzGroup
+namespace LorentzGroup
 open PreFourVelocity

 /-- The first column of a lorentz matrix as a `PreFourVelocity`. -/
@[simp]
-def fstCol (Λ : lorentzGroup) : PreFourVelocity := ⟨Λ.1 *ᵥ stdBasis 0, by
+def fstCol (Λ : LorentzGroup) : PreFourVelocity := ⟨Λ.1 *ᵥ stdBasis 0, by
  rw [mem_PreFourVelocity_iff, ηLin_expand]
  simp only [Fin.isValue, stdBasis_mulVec]
  have h00 := congrFun (congrFun ((PreservesηLin.iff_matrix Λ.1).mp  Λ.2) 0) 0
@ -46,18 +46,18 @@ def fstCol (Λ : lorentzGroup) : PreFourVelocity := ⟨Λ.1 *ᵥ stdBasis 0, by
  exact h00⟩

 /-- A Lorentz transformation is  `orthochronous` if its `0 0` element is non-negative. -/
-def IsOrthochronous (Λ : lorentzGroup) : Prop := 0 ≤ Λ.1 0 0
+def IsOrthochronous (Λ : LorentzGroup) : Prop := 0 ≤ Λ.1 0 0

-lemma IsOrthochronous_iff_transpose (Λ : lorentzGroup) :
+lemma IsOrthochronous_iff_transpose (Λ : LorentzGroup) :
    IsOrthochronous Λ ↔ IsOrthochronous (transpose Λ) := by rfl

-lemma IsOrthochronous_iff_fstCol_IsFourVelocity (Λ : lorentzGroup) :
+lemma IsOrthochronous_iff_fstCol_IsFourVelocity (Λ : LorentzGroup) :
    IsOrthochronous Λ ↔ IsFourVelocity (fstCol Λ) := by
  simp [IsOrthochronous, IsFourVelocity]
  rw [stdBasis_mulVec]

 /-- The continuous map taking a Lorentz transformation to its `0 0` element. -/
-def mapZeroZeroComp : C(lorentzGroup, ℝ) := ⟨fun Λ => Λ.1 0 0,
+def mapZeroZeroComp : C(LorentzGroup, ℝ) := ⟨fun Λ => Λ.1 0 0,
   Continuous.matrix_elem (continuous_iff_le_induced.mpr fun _ a => a) 0 0⟩

 /-- An auxillary function used in the definition of `orthchroMapReal`. -/
@ -78,10 +78,10 @@ lemma stepFunction_continuous : Continuous stepFunction := by

 /-- The continuous map from `lorentzGroup` to `ℝ` wh
 taking Orthochronous elements to `1` and non-orthochronous to `-1`. -/
-def orthchroMapReal : C(lorentzGroup, ℝ) := ContinuousMap.comp
+def orthchroMapReal : C(LorentzGroup, ℝ) := ContinuousMap.comp
  ⟨stepFunction, stepFunction_continuous⟩ mapZeroZeroComp

-lemma orthchroMapReal_on_IsOrthochronous {Λ : lorentzGroup} (h : IsOrthochronous Λ) :
+lemma orthchroMapReal_on_IsOrthochronous {Λ : LorentzGroup} (h : IsOrthochronous Λ) :
    orthchroMapReal Λ = 1 := by
  rw [IsOrthochronous_iff_fstCol_IsFourVelocity] at h
  simp only [IsFourVelocity] at h
@ -92,7 +92,7 @@ lemma orthchroMapReal_on_IsOrthochronous {Λ : lorentzGroup} (h : IsOrthochronou
  rw [stepFunction, if_neg h1, if_pos h]


-lemma orthchroMapReal_on_not_IsOrthochronous {Λ : lorentzGroup} (h : ¬ IsOrthochronous Λ) :
+lemma orthchroMapReal_on_not_IsOrthochronous {Λ : LorentzGroup} (h : ¬ IsOrthochronous Λ) :
    orthchroMapReal Λ = - 1 := by
  rw [IsOrthochronous_iff_fstCol_IsFourVelocity] at h
  rw [not_IsFourVelocity_iff, zero_nonpos_iff] at h
@ -100,7 +100,7 @@ lemma orthchroMapReal_on_not_IsOrthochronous {Λ : lorentzGroup} (h : ¬ IsOrtho
  change stepFunction (Λ.1 0 0) = - 1
  rw [stepFunction, if_pos h]

-lemma orthchroMapReal_minus_one_or_one (Λ : lorentzGroup) :
+lemma orthchroMapReal_minus_one_or_one (Λ : LorentzGroup) :
    orthchroMapReal Λ = -1 ∨ orthchroMapReal Λ = 1 := by
  by_cases h : IsOrthochronous Λ
  apply Or.inr $ orthchroMapReal_on_IsOrthochronous h
@ -109,21 +109,21 @@ lemma orthchroMapReal_minus_one_or_one (Λ : lorentzGroup) :
 local notation  "ℤ₂" => Multiplicative (ZMod 2)

 /-- A continuous map from `lorentzGroup` to `ℤ₂` whose kernal are the Orthochronous elements. -/
-def orthchroMap : C(lorentzGroup, ℤ₂) :=
+def orthchroMap : C(LorentzGroup, ℤ₂) :=
  ContinuousMap.comp coeForℤ₂ {
    toFun := fun Λ => ⟨orthchroMapReal Λ, orthchroMapReal_minus_one_or_one Λ⟩,
    continuous_toFun :=  Continuous.subtype_mk (ContinuousMap.continuous orthchroMapReal) _}

-lemma orthchroMap_IsOrthochronous {Λ : lorentzGroup} (h : IsOrthochronous Λ) :
+lemma orthchroMap_IsOrthochronous {Λ : LorentzGroup} (h : IsOrthochronous Λ) :
    orthchroMap Λ = 1 := by
  simp [orthchroMap, orthchroMapReal_on_IsOrthochronous h]

-lemma orthchroMap_not_IsOrthochronous {Λ : lorentzGroup} (h : ¬ IsOrthochronous Λ) :
+lemma orthchroMap_not_IsOrthochronous {Λ : LorentzGroup} (h : ¬ IsOrthochronous Λ) :
    orthchroMap Λ =  Additive.toMul (1 : ZMod 2) := by
  simp [orthchroMap, orthchroMapReal_on_not_IsOrthochronous h]
  rfl

-lemma zero_zero_mul (Λ Λ' : lorentzGroup) :
+lemma zero_zero_mul (Λ Λ' : LorentzGroup) :
    (Λ * Λ').1 0 0 =  (fstCol (transpose Λ)).1 0 * (fstCol Λ').1 0 +
    ⟪(fstCol (transpose Λ)).1.space, (fstCol Λ').1.space⟫_ℝ := by
  simp only [Fin.isValue, lorentzGroupIsGroup_mul_coe, mul_apply, Fin.sum_univ_four, fstCol,
@ -132,21 +132,21 @@ lemma zero_zero_mul (Λ Λ' : lorentzGroup) :
    cons_val_one, head_cons, cons_val_two, tail_cons]
  ring

-lemma mul_othchron_of_othchron_othchron {Λ Λ' : lorentzGroup} (h : IsOrthochronous Λ)
+lemma mul_othchron_of_othchron_othchron {Λ Λ' : LorentzGroup} (h : IsOrthochronous Λ)
    (h' : IsOrthochronous Λ') : IsOrthochronous (Λ * Λ') := by
  rw [IsOrthochronous_iff_transpose] at h
  rw [IsOrthochronous_iff_fstCol_IsFourVelocity] at h h'
  rw [IsOrthochronous, zero_zero_mul]
  exact euclid_norm_IsFourVelocity_IsFourVelocity h h'

-lemma mul_othchron_of_not_othchron_not_othchron {Λ Λ' : lorentzGroup} (h : ¬  IsOrthochronous Λ)
+lemma mul_othchron_of_not_othchron_not_othchron {Λ Λ' : LorentzGroup} (h : ¬  IsOrthochronous Λ)
    (h' : ¬ IsOrthochronous Λ') : IsOrthochronous (Λ * Λ') := by
  rw [IsOrthochronous_iff_transpose] at h
  rw [IsOrthochronous_iff_fstCol_IsFourVelocity] at h h'
  rw [IsOrthochronous, zero_zero_mul]
  exact euclid_norm_not_IsFourVelocity_not_IsFourVelocity h h'

-lemma mul_not_othchron_of_othchron_not_othchron {Λ Λ' : lorentzGroup} (h :  IsOrthochronous Λ)
+lemma mul_not_othchron_of_othchron_not_othchron {Λ Λ' : LorentzGroup} (h :  IsOrthochronous Λ)
    (h' : ¬ IsOrthochronous Λ') : ¬ IsOrthochronous (Λ * Λ') := by
  rw [IsOrthochronous_iff_transpose] at h
  rw [IsOrthochronous_iff_fstCol_IsFourVelocity] at h h'
@ -156,7 +156,7 @@ lemma mul_not_othchron_of_othchron_not_othchron {Λ Λ' : lorentzGroup} (h :  Is
  rw [zero_zero_mul]
  exact euclid_norm_IsFourVelocity_not_IsFourVelocity h h'

-lemma mul_not_othchron_of_not_othchron_othchron {Λ Λ' : lorentzGroup} (h : ¬ IsOrthochronous Λ)
+lemma mul_not_othchron_of_not_othchron_othchron {Λ Λ' : LorentzGroup} (h : ¬ IsOrthochronous Λ)
    (h' : IsOrthochronous Λ') : ¬ IsOrthochronous (Λ * Λ') := by
  rw [IsOrthochronous_iff_transpose] at h
  rw [IsOrthochronous_iff_fstCol_IsFourVelocity] at h h'
@ -167,7 +167,7 @@ lemma mul_not_othchron_of_not_othchron_othchron {Λ Λ' : lorentzGroup} (h : ¬
  exact euclid_norm_not_IsFourVelocity_IsFourVelocity h h'

 /-- The homomorphism from `lorentzGroup` to `ℤ₂` whose kernel are the Orthochronous elements. -/
-def orthchroRep : lorentzGroup →* ℤ₂ where
+def orthchroRep : LorentzGroup →* ℤ₂ where
  toFun := orthchroMap
  map_one' := orthchroMap_IsOrthochronous (by simp [IsOrthochronous])
  map_mul' Λ Λ' := by
@ -187,7 +187,7 @@ def orthchroRep : lorentzGroup →* ℤ₂ where
      orthchroMap_IsOrthochronous (mul_othchron_of_not_othchron_not_othchron h h')]
    rfl

-end lorentzGroup
+end LorentzGroup

-end spaceTime
+end SpaceTime
 end
--- a/HepLean/SpaceTime/LorentzGroup/Proper.lean
+++ b/HepLean/SpaceTime/LorentzGroup/Proper.lean
@ -14,14 +14,14 @@ We define the give a series of lemmas related to the determinant of the lorentz

 noncomputable section

-namespace spaceTime
+namespace SpaceTime

 open Manifold
 open Matrix
 open Complex
 open ComplexConjugate

-namespace lorentzGroup
+namespace LorentzGroup

 /-- The determinant of a member of the lorentz group is `1` or `-1`. -/
 lemma det_eq_one_or_neg_one (Λ : 𝓛) : Λ.1.det = 1 ∨ Λ.1.det = -1 := by
@ -49,14 +49,14 @@ def coeForℤ₂ :  C(({-1, 1} : Set ℝ), ℤ₂) where
 /-- The continuous map taking a lorentz matrix to its determinant. -/
 def detContinuous :  C(𝓛, ℤ₂) :=
  ContinuousMap.comp  coeForℤ₂ {
-    toFun := fun Λ => ⟨Λ.1.det, Or.symm (lorentzGroup.det_eq_one_or_neg_one _)⟩,
+    toFun := fun Λ => ⟨Λ.1.det, Or.symm (LorentzGroup.det_eq_one_or_neg_one _)⟩,
    continuous_toFun := by
      refine Continuous.subtype_mk ?_ _
      apply Continuous.matrix_det $
        Continuous.comp' (continuous_iff_le_induced.mpr fun U a => a) continuous_id'
      }

-lemma detContinuous_eq_iff_det_eq (Λ Λ' : lorentzGroup) :
+lemma detContinuous_eq_iff_det_eq (Λ Λ' : LorentzGroup) :
    detContinuous Λ = detContinuous Λ' ↔ Λ.1.det = Λ'.1.det := by
  apply Iff.intro
  intro h
@ -90,7 +90,7 @@ def detRep : 𝓛 →* ℤ₂ where

 lemma detRep_continuous : Continuous detRep := detContinuous.2

-lemma det_on_connected_component {Λ Λ'  : lorentzGroup} (h : Λ' ∈ connectedComponent Λ) :
+lemma det_on_connected_component {Λ Λ'  : LorentzGroup} (h : Λ' ∈ connectedComponent Λ) :
    Λ.1.det = Λ'.1.det := by
  obtain ⟨s, hs, hΛ'⟩ := h
  let f : ContinuousMap s ℤ₂ := ContinuousMap.restrict s detContinuous
@ -99,23 +99,23 @@ lemma det_on_connected_component {Λ Λ'  : lorentzGroup} (h : Λ' ∈ connected
    (@IsPreconnected.subsingleton ℤ₂ _ _ _ (isPreconnected_range f.2))
    (Set.mem_range_self ⟨Λ, hs.2⟩)  (Set.mem_range_self ⟨Λ', hΛ'⟩)

-lemma detRep_on_connected_component {Λ Λ'  : lorentzGroup} (h : Λ' ∈ connectedComponent Λ) :
+lemma detRep_on_connected_component {Λ Λ'  : LorentzGroup} (h : Λ' ∈ connectedComponent Λ) :
    detRep Λ = detRep Λ' := by
  simp [detRep_apply, detRep_apply, detContinuous]
  rw [det_on_connected_component h]

-lemma det_of_joined {Λ Λ' : lorentzGroup} (h : Joined Λ Λ') : Λ.1.det = Λ'.1.det :=
+lemma det_of_joined {Λ Λ' : LorentzGroup} (h : Joined Λ Λ') : Λ.1.det = Λ'.1.det :=
  det_on_connected_component $ pathComponent_subset_component _ h

 /-- A Lorentz Matrix is proper if its determinant is 1. -/
@[simp]
-def IsProper (Λ : lorentzGroup) : Prop := Λ.1.det = 1
+def IsProper (Λ : LorentzGroup) : Prop := Λ.1.det = 1

 instance : DecidablePred IsProper := by
  intro Λ
  apply Real.decidableEq

-lemma IsProper_iff (Λ : lorentzGroup) : IsProper Λ ↔ detRep Λ = 1 := by
+lemma IsProper_iff (Λ : LorentzGroup) : IsProper Λ ↔ detRep Λ = 1 := by
  rw [show 1 = detRep 1 from Eq.symm (MonoidHom.map_one detRep)]
  rw [detRep_apply, detRep_apply, detContinuous_eq_iff_det_eq]
  simp only [IsProper, lorentzGroupIsGroup_one_coe, det_one]
@ -123,12 +123,12 @@ lemma IsProper_iff (Λ : lorentzGroup) : IsProper Λ ↔ detRep Λ = 1 := by
 lemma id_IsProper : IsProper 1 := by
  simp [IsProper]

-lemma isProper_on_connected_component {Λ Λ'  : lorentzGroup} (h : Λ' ∈ connectedComponent Λ) :
+lemma isProper_on_connected_component {Λ Λ'  : LorentzGroup} (h : Λ' ∈ connectedComponent Λ) :
    IsProper Λ ↔ IsProper Λ' := by
  simp [detRep_apply, detRep_apply, detContinuous]
  rw [det_on_connected_component h]

-end lorentzGroup
+end LorentzGroup

-end spaceTime
+end SpaceTime
 end
--- a/HepLean/SpaceTime/LorentzGroup/Rotations.lean
+++ b/HepLean/SpaceTime/LorentzGroup/Rotations.lean
@ -11,7 +11,7 @@ import Mathlib.Topology.Constructions

 -/
 noncomputable section
-namespace spaceTime
+namespace SpaceTime

 namespace lorentzGroup
 open GroupTheory
@ -54,5 +54,5 @@ def SO3ToLorentz : SO(3) →* 𝓛 where
 end lorentzGroup


-end spaceTime
+end SpaceTime
 end