refactor: Remove double empty lines

HepLean/AnomalyCancellation/PureU1/Even/BasisLinear.lean

@@ -190,7 +190,6 @@ lemma basis!_on_other {k : Fin n} {j : Fin (2 * n.succ)} (h1 : j ≠ δ!₁ k)
   simp [basis!AsCharges]
   simp_all only [ne_eq, ↓reduceIte]
 
-
 lemma basis!_on_δ!₁_other {k j : Fin n} (h : k ≠ j) :
     basis!AsCharges k (δ!₁ j) = 0 := by
   simp [basis!AsCharges]
@@ -310,7 +309,6 @@ lemma basis!_accCube (j : Fin n) :
   simp [basis!_δ!₂_eq_minus_δ!₁]
   ring
 
-
 /-- The first part of the basis as `LinSols`. -/
 @[simps!]
 def basis (j : Fin n.succ) : (PureU1 (2 * n.succ)).LinSols :=
@@ -587,7 +585,6 @@ theorem basis!_linear_independent : LinearIndependent ℚ (@basis! n) := by
   rw [P!'_val] at h1
   exact P!_zero f h1
 
-
 theorem basisa_linear_independent : LinearIndependent ℚ (@basisa n) := by
   apply Fintype.linearIndependent_iff.mpr
   intro f h
@@ -663,7 +660,6 @@ lemma Pa_eq (g g' : Fin n.succ → ℚ) (f f' : Fin n → ℚ) :
   rw [← join_ext]
   exact Pa'_eq _ _
 
-
 lemma basisa_card :  Fintype.card ((Fin n.succ) ⊕ (Fin n)) =
     FiniteDimensional.finrank ℚ (PureU1 (2 * n.succ)).LinSols := by
   erw [BasisLinear.finrank_AnomalyFreeLinear]
@@ -675,7 +671,6 @@ noncomputable def basisaAsBasis :
     Basis (Fin (succ n) ⊕ Fin n) ℚ (PureU1 (2 * succ n)).LinSols :=
   basisOfLinearIndependentOfCardEqFinrank (@basisa_linear_independent n) basisa_card
 
-
 lemma span_basis (S : (PureU1 (2 * n.succ)).LinSols) :
     ∃ (g : Fin n.succ → ℚ) (f : Fin n → ℚ), S.val = P g + P! f  := by
   have h := (mem_span_range_iff_exists_fun ℚ).mp (Basis.mem_span basisaAsBasis S)

HepLean/AnomalyCancellation/PureU1/Even/Parameterization.lean

@@ -134,7 +134,6 @@ theorem generic_case {S : (PureU1 (2 * n.succ)).Sols} (h : GenericCase S) :
   simp at h
   exact h
 
-
 lemma special_case_lineInCubic {S : (PureU1 (2 * n.succ)).Sols}
     (h : SpecialCase S) : LineInCubic S.1.1 := by
   intro g f hS a b
@@ -152,7 +151,6 @@ lemma special_case_lineInCubic {S : (PureU1 (2 * n.succ)).Sols}
   erw [h]
   simp
 
-
 lemma special_case_lineInCubic_perm {S : (PureU1 (2 * n.succ)).Sols}
     (h : ∀ (M : (FamilyPermutations (2 * n.succ)).group),
     SpecialCase ((FamilyPermutations (2 * n.succ)).solAction.toFun S M)) :
@@ -160,7 +158,6 @@ lemma special_case_lineInCubic_perm {S : (PureU1 (2 * n.succ)).Sols}
   intro M
   exact special_case_lineInCubic (h M)
 
-
 theorem special_case {S : (PureU1 (2 * n.succ.succ)).Sols}
     (h : ∀ (M : (FamilyPermutations (2 * n.succ.succ)).group),
     SpecialCase ((FamilyPermutations (2 * n.succ.succ)).solAction.toFun S M)) :