reactor: Removal of double spaces

HepLean/SpaceTime/LorentzGroup/Basic.lean

@@ -30,7 +30,7 @@ We start studying the properties of matrices which preserve `ηLin`.
 These matrices form the Lorentz group, which we will define in the next section at `lorentzGroup`.
 
 -/
-variable  {d : ℕ}
+variable {d : ℕ}
 
 open minkowskiMetric in
 /-- The Lorentz group is the subset of matrices which preserve the minkowski metric. -/
@@ -74,7 +74,7 @@ lemma mem_iff_on_right : Λ ∈ LorentzGroup d ↔
   rw [← dual_mulVec_right, mulVec_mulVec]
   exact h x y
 
-lemma mem_iff_dual_mul_self : Λ ∈ LorentzGroup d ↔ dual Λ * Λ = 1  := by
+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
 
@@ -145,7 +145,7 @@ namespace LorentzGroup
 
 open minkowskiMetric
 
-variable  {Λ Λ' : LorentzGroup d}
+variable {Λ Λ' : LorentzGroup d}
 
 lemma coe_inv : (Λ⁻¹).1 = Λ.1⁻¹:= by
   refine (inv_eq_left_inv ?h).symm
@@ -172,7 +172,7 @@ def toGL : LorentzGroup d →* GL (Fin 1 ⊕ Fin d) ℝ where
   map_one' := by
     simp
     rfl
-  map_mul' x y  := by
+  map_mul' x y := by
     simp only [lorentzGroupIsGroup, _root_.mul_inv_rev, coe_inv]
     ext
     rfl

HepLean/SpaceTime/LorentzGroup/Boosts.lean

@@ -99,7 +99,7 @@ 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) :
+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
     - ⟪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]

HepLean/SpaceTime/LorentzGroup/Orthochronous.lean

@@ -27,7 +27,7 @@ variable (Λ : LorentzGroup d)
 open LorentzVector
 open minkowskiMetric
 
-/-- A Lorentz transformation is  `orthochronous` if its `0 0` element is non-negative. -/
+/-- A Lorentz transformation is `orthochronous` if its `0 0` element is non-negative. -/
 def IsOrthochronous : Prop := 0 ≤ timeComp Λ
 
 lemma IsOrthochronous_iff_futurePointing :
@@ -62,7 +62,7 @@ lemma not_orthochronous_iff_le_zero :
   linarith
 
 /-- The continuous map taking a Lorentz transformation to its `0 0` element. -/
-def timeCompCont : C(LorentzGroup d, ℝ) := ⟨fun Λ => timeComp Λ  ,
+def timeCompCont : C(LorentzGroup d, ℝ) := ⟨fun Λ => timeComp Λ,
    Continuous.matrix_elem (continuous_iff_le_induced.mpr fun _ a => a) (Sum.inl 0) (Sum.inl 0)⟩
 
 /-- An auxillary function used in the definition of `orthchroMapReal`. -/
@@ -75,7 +75,7 @@ lemma stepFunction_continuous : Continuous stepFunction := by
    <;> intro a ha
   rw [@Set.Iic_def, @frontier_Iic, @Set.mem_singleton_iff] at ha
   rw [ha]
-  simp  [neg_lt_self_iff, zero_lt_one, ↓reduceIte]
+  simp [neg_lt_self_iff, zero_lt_one, ↓reduceIte]
   have h1 : ¬ (1 : ℝ) ≤ 0 := by simp
   exact Eq.symm (if_neg h1)
   rw [Set.Ici_def, @frontier_Ici, @Set.mem_singleton_iff] at ha

HepLean/SpaceTime/LorentzGroup/Proper.lean

@@ -31,7 +31,7 @@ lemma det_eq_one_or_neg_one (Λ : 𝓛 d) : Λ.1.det = 1 ∨ Λ.1.det = -1 := by
   simp [det_mul, det_dual] at h1
   exact mul_self_eq_one_iff.mp h1
 
-local notation  "ℤ₂" => Multiplicative (ZMod 2)
+local notation "ℤ₂" => Multiplicative (ZMod 2)
 
 instance : TopologicalSpace ℤ₂ := instTopologicalSpaceFin
 
@@ -51,7 +51,7 @@ def coeForℤ₂ : C(({-1, 1} : Set ℝ), ℤ₂) where
 
 /-- The continuous map taking a Lorentz matrix to its determinant. -/
 def detContinuous : C(𝓛 d, ℤ₂) :=
-  ContinuousMap.comp  coeForℤ₂ {
+  ContinuousMap.comp coeForℤ₂ {
     toFun := fun Λ => ⟨Λ.1.det, Or.symm (LorentzGroup.det_eq_one_or_neg_one _)⟩,
     continuous_toFun := by
       refine Continuous.subtype_mk ?_ _
@@ -65,7 +65,7 @@ lemma detContinuous_eq_iff_det_eq (Λ Λ' : LorentzGroup d) :
   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 h2 h2
+    <;> 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
   · change (0 : Fin 2) = (1 : Fin 2) at h