refactor: Remove double empty lines

HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/PlaneWithY3B3.lean

@@ -18,8 +18,6 @@ The plane spanned by Y₃, B₃ and third orthogonal point.
 
 -/
 
-
-
 universe v u
 
 namespace MSSMACC
@@ -93,7 +91,6 @@ lemma planeY₃B₃_val_eq' (R : MSSMACC.AnomalyFreePerp) (a b c : ℚ) (hR' : R
   rw [ha, hb, hc]
   simp
 
-
 lemma planeY₃B₃_quad (R : MSSMACC.AnomalyFreePerp) (a b c : ℚ) :
     accQuad (planeY₃B₃ R a b c).val = c * (2 * a * quadBiLin Y₃.val R.val
     + 2 * b * quadBiLin B₃.val R.val + c * quadBiLin R.val R.val) := by
@@ -184,7 +181,6 @@ def lineCube (R : MSSMACC.AnomalyFreePerp) (a₁ a₂ a₃ : ℚ) :
     (3 * a₃ * cubeTriLin R.val R.val Y₃.val -  a₁ * cubeTriLin R.val R.val R.val)
     (3 * (a₁ * cubeTriLin R.val R.val B₃.val - a₂ * cubeTriLin R.val R.val Y₃.val))
 
-
 lemma lineCube_smul (R : MSSMACC.AnomalyFreePerp) (a b c d : ℚ) :
     lineCube R (d * a) (d * b) (d * c) = d • lineCube R a b c := by
   apply ACCSystemLinear.LinSols.ext
@@ -241,5 +237,4 @@ lemma α₂_proj_zero (T : MSSMACC.Sols) (h1 : α₃ (proj T.1.1) = 0) :
 
 end proj
 
-
 end MSSMACC

HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/ToSols.lean

@@ -18,7 +18,6 @@ To define `toSols` we define a series of other maps from various subtypes of
 `MSSMACC.AnomalyFreePerp × ℚ × ℚ × ℚ` to `MSSMACC.Sols`. And show that these maps form a
 surjection on certain subtypes of `MSSMACC.Sols`.
 
-
 # References
 
 The main reference for the material in this file is:
@@ -78,7 +77,6 @@ lemma linEqPropSol_iff_proj_linEqProp (R : MSSMACC.Sols) :
   rw [h.2.2]
   simp
 
-
 /-- A condition which is satisfied if the plane spanned by `R`, `Y₃` and `B₃` lies
 entirely in the quadratic surface. -/
 def InQuadProp (R : MSSMACC.AnomalyFreePerp) : Prop :=
@@ -237,7 +235,6 @@ not surjective. -/
 def toSolNS : MSSMACC.AnomalyFreePerp × ℚ × ℚ × ℚ → MSSMACC.Sols := fun (R, a, _ , _) =>
   a • AnomalyFreeMk'' (toSolNSQuad R) (toSolNSQuad_cube R)
 
-
 /-- A map from `Sols` to `MSSMACC.AnomalyFreePerp × ℚ × ℚ × ℚ` which on elements of
 `notInLineEqSol` will produce a right inverse to `toSolNS`. -/
 def toSolNSProj (T : MSSMACC.Sols) : MSSMACC.AnomalyFreePerp × ℚ × ℚ × ℚ :=
@@ -457,7 +454,6 @@ theorem toSol_surjective : Function.Surjective toSol := by
   simp at h₃
   exact toSol_inQuadCube ⟨T, And.intro h₁ (And.intro h₂ h₃)⟩
 
-
 end AnomalyFreePerp
 
 end MSSMACC