refactor: pass at removing double spaces

HepLean/SpaceTime/LorentzGroup/Basic.lean

@@ -44,7 +44,7 @@ scoped[LorentzGroup] notation (name := lorentzGroup_notation) "𝓛" => LorentzG
 
 open minkowskiMetric
 
-variable  {Λ Λ' : Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ}
+variable {Λ Λ' : Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ}
 
 /-!
 
@@ -52,7 +52,7 @@ variable  {Λ Λ' : Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ}
 
 -/
 
-lemma mem_iff_norm :  Λ ∈ LorentzGroup d ↔
+lemma mem_iff_norm : Λ ∈ LorentzGroup d ↔
     ∀ (x : LorentzVector d), ⟪Λ *ᵥ x, Λ *ᵥ x⟫ₘ = ⟪x, x⟫ₘ := by
   refine Iff.intro (fun h x => h x x) (fun h x y => ?_)
   have hp := h (x + y)
@@ -78,7 +78,7 @@ lemma mem_iff_dual_mul_self : Λ ∈ LorentzGroup d ↔ dual Λ * Λ = 1  := by
   rw [mem_iff_on_right, matrix_eq_id_iff]
   exact forall_comm
 
-lemma mem_iff_self_mul_dual :  Λ ∈ LorentzGroup d ↔ Λ * dual Λ = 1  := by
+lemma mem_iff_self_mul_dual : Λ ∈ LorentzGroup d ↔ Λ * dual Λ = 1 := by
   rw [mem_iff_dual_mul_self]
   exact mul_eq_one_comm
 
@@ -147,7 +147,7 @@ open minkowskiMetric
 
 variable  {Λ Λ' : LorentzGroup d}
 
-lemma coe_inv  : (Λ⁻¹).1 = Λ.1⁻¹:= by
+lemma coe_inv : (Λ⁻¹).1 = Λ.1⁻¹:= by
   refine (inv_eq_left_inv ?h).symm
   exact mem_iff_dual_mul_self.mp Λ.2
 
@@ -190,7 +190,7 @@ def toProd : LorentzGroup d →* (Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ
     (Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ)ᵐᵒᵖ :=
   MonoidHom.comp (Units.embedProduct _) toGL
 
-lemma toProd_eq_transpose_η  : toProd Λ = (Λ.1, MulOpposite.op $ minkowskiMetric.dual Λ.1) := rfl
+lemma toProd_eq_transpose_η : toProd Λ = (Λ.1, MulOpposite.op $ minkowskiMetric.dual Λ.1) := rfl
 
 lemma toProd_injective : Function.Injective (@toProd d) := by
   intro A B h

HepLean/SpaceTime/LorentzGroup/Boosts.lean

@@ -100,7 +100,7 @@ lemma toMatrix_mulVec (u v : FuturePointing d) (x : LorentzVector d) :
 open minkowskiMatrix LorentzVector in
 @[simp]
 lemma toMatrix_apply (u v : FuturePointing d) (μ ν  : Fin 1 ⊕ Fin d) :
-    (toMatrix u v) μ ν = η μ μ  * (⟪e μ, e ν⟫ₘ + 2 * ⟪e ν, u⟫ₘ * ⟪e μ, v⟫ₘ
+    (toMatrix u v) μ ν = η μ μ * (⟪e μ, e ν⟫ₘ + 2 * ⟪e ν, u⟫ₘ * ⟪e μ, v⟫ₘ
     - ⟪e μ, u + v⟫ₘ * ⟪e ν, u + v⟫ₘ / (1 + ⟪u, v.1.1⟫ₘ)) := by
   rw [matrix_apply_stdBasis (toMatrix u v) μ ν, toMatrix_mulVec]
   simp only [genBoost, genBoostAux₁, genBoostAux₂, map_add, smul_add, neg_smul, LinearMap.add_apply,

HepLean/SpaceTime/LorentzGroup/Orthochronous.lean

@@ -39,7 +39,7 @@ lemma IsOrthochronous_iff_transpose :
     IsOrthochronous Λ ↔ IsOrthochronous (transpose Λ) := by rfl
 
 lemma IsOrthochronous_iff_ge_one :
-    IsOrthochronous Λ ↔ 1 ≤ timeComp Λ  := by
+    IsOrthochronous Λ ↔ 1 ≤ timeComp Λ := by
   rw [IsOrthochronous_iff_futurePointing, NormOneLorentzVector.FuturePointing.mem_iff,
     NormOneLorentzVector.time_pos_iff]
   simp only [time, toNormOneLorentzVector, timeVec, Fin.isValue]
@@ -68,7 +68,7 @@ def timeCompCont : C(LorentzGroup d, ℝ) := ⟨fun Λ => timeComp Λ  ,
 /-- An auxillary function used in the definition of `orthchroMapReal`. -/
 def stepFunction : ℝ → ℝ := fun t =>
   if t ≤ -1 then -1 else
-    if 1 ≤  t then 1 else t
+    if 1 ≤ t then 1 else t
 
 lemma stepFunction_continuous : Continuous stepFunction := by
   apply Continuous.if ?_ continuous_const (Continuous.if ?_ continuous_const continuous_id)
@@ -105,20 +105,20 @@ lemma orthchroMapReal_minus_one_or_one (Λ : LorentzGroup d) :
   apply Or.inr $ orthchroMapReal_on_IsOrthochronous h
   apply Or.inl $ orthchroMapReal_on_not_IsOrthochronous h
 
-local notation  "ℤ₂" => Multiplicative (ZMod 2)
+local notation "ℤ₂" => Multiplicative (ZMod 2)
 
 /-- A continuous map from `lorentzGroup` to `ℤ₂` whose kernal are the Orthochronous elements. -/
 def orthchroMap : C(LorentzGroup d, ℤ₂) :=
   ContinuousMap.comp coeForℤ₂ {
     toFun := fun Λ => ⟨orthchroMapReal Λ, orthchroMapReal_minus_one_or_one Λ⟩,
-    continuous_toFun :=  Continuous.subtype_mk (ContinuousMap.continuous orthchroMapReal) _}
+    continuous_toFun := Continuous.subtype_mk (ContinuousMap.continuous orthchroMapReal) _}
 
 lemma orthchroMap_IsOrthochronous {Λ : LorentzGroup d} (h : IsOrthochronous Λ) :
     orthchroMap Λ = 1 := by
   simp [orthchroMap, orthchroMapReal_on_IsOrthochronous h]
 
 lemma orthchroMap_not_IsOrthochronous {Λ : LorentzGroup d} (h : ¬ IsOrthochronous Λ) :
-    orthchroMap Λ =  Additive.toMul (1 : ZMod 2) := by
+    orthchroMap Λ = Additive.toMul (1 : ZMod 2) := by
   simp [orthchroMap, orthchroMapReal_on_not_IsOrthochronous h]
   rfl
 
@@ -136,7 +136,7 @@ lemma mul_othchron_of_not_othchron_not_othchron {Λ Λ' : LorentzGroup d} (h :
   rw [IsOrthochronous, timeComp_mul]
   exact NormOneLorentzVector.FuturePointing.metric_reflect_not_mem_not_mem h h'
 
-lemma mul_not_othchron_of_othchron_not_othchron {Λ Λ' : LorentzGroup d} (h :  IsOrthochronous Λ)
+lemma mul_not_othchron_of_othchron_not_othchron {Λ Λ' : LorentzGroup d} (h : IsOrthochronous Λ)
     (h' : ¬ IsOrthochronous Λ') : ¬ IsOrthochronous (Λ * Λ') := by
   rw [not_orthochronous_iff_le_zero, timeComp_mul]
   rw [IsOrthochronous_iff_transpose] at h

HepLean/SpaceTime/LorentzGroup/Proper.lean

@@ -42,7 +42,7 @@ instance : TopologicalGroup ℤ₂ := TopologicalGroup.mk
 
 /-- A continuous function from `({-1, 1} : Set ℝ)` to `ℤ₂`. -/
 @[simps!]
-def coeForℤ₂ :  C(({-1, 1} : Set ℝ), ℤ₂) where
+def coeForℤ₂ : C(({-1, 1} : Set ℝ), ℤ₂) where
   toFun x := if x = ⟨1, Set.mem_insert_of_mem (-1) rfl⟩
     then (Additive.toMul 0) else (Additive.toMul (1 : ZMod 2))
   continuous_toFun := by
@@ -50,7 +50,7 @@ def coeForℤ₂ :  C(({-1, 1} : Set ℝ), ℤ₂) where
     exact continuous_of_discreteTopology
 
 /-- The continuous map taking a Lorentz matrix to its determinant. -/
-def detContinuous :  C(𝓛 d, ℤ₂) :=
+def detContinuous : C(𝓛 d, ℤ₂) :=
   ContinuousMap.comp  coeForℤ₂ {
     toFun := fun Λ => ⟨Λ.1.det, Or.symm (LorentzGroup.det_eq_one_or_neg_one _)⟩,
     continuous_toFun := by
@@ -64,7 +64,7 @@ lemma detContinuous_eq_iff_det_eq (Λ Λ' : LorentzGroup d) :
   apply Iff.intro
   intro h
   simp [detContinuous] at h
-  cases'  det_eq_one_or_neg_one Λ with h1 h1
+  cases' det_eq_one_or_neg_one Λ with h1 h1
     <;> cases'  det_eq_one_or_neg_one Λ' with h2 h2
     <;> simp_all [h1, h2, h]
   rw [← toMul_zero, @Equiv.apply_eq_iff_eq] at h
@@ -92,16 +92,16 @@ def detRep : 𝓛 d →* ℤ₂ where
 
 lemma detRep_continuous : Continuous (@detRep d) := detContinuous.2
 
-lemma det_on_connected_component {Λ Λ'  : LorentzGroup d} (h : Λ' ∈ connectedComponent Λ) :
+lemma det_on_connected_component {Λ Λ' : LorentzGroup d} (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
   haveI : PreconnectedSpace s := isPreconnected_iff_preconnectedSpace.mp hs.1
   simpa [f, detContinuous_eq_iff_det_eq] using
     (@IsPreconnected.subsingleton ℤ₂ _ _ _ (isPreconnected_range f.2))
-    (Set.mem_range_self ⟨Λ, hs.2⟩)  (Set.mem_range_self ⟨Λ', hΛ'⟩)
+    (Set.mem_range_self ⟨Λ, hs.2⟩) (Set.mem_range_self ⟨Λ', hΛ'⟩)
 
-lemma detRep_on_connected_component {Λ Λ'  : LorentzGroup d} (h : Λ' ∈ connectedComponent Λ) :
+lemma detRep_on_connected_component {Λ Λ' : LorentzGroup d} (h : Λ' ∈ connectedComponent Λ) :
     detRep Λ = detRep Λ' := by
   simp [detRep_apply, detRep_apply, detContinuous]
   rw [det_on_connected_component h]
@@ -125,7 +125,7 @@ lemma IsProper_iff (Λ : LorentzGroup d) : IsProper Λ ↔ detRep Λ = 1 := by
 lemma id_IsProper : (@IsProper d) 1 := by
   simp [IsProper]
 
-lemma isProper_on_connected_component {Λ Λ'  : LorentzGroup d} (h : Λ' ∈ connectedComponent Λ) :
+lemma isProper_on_connected_component {Λ Λ' : LorentzGroup d} (h : Λ' ∈ connectedComponent Λ) :
     IsProper Λ ↔ IsProper Λ' := by
   simp [detRep_apply, detRep_apply, detContinuous]
   rw [det_on_connected_component h]