refactor: Linting substrings

HepLean/AnomalyCancellation/MSSMNu/Basic.lean

@@ -76,7 +76,7 @@ def toSMSpecies (i : Fin 6) : MSSMCharges.Charges →ₗ[ℚ] MSSMSpecies.Charge
 
 lemma toSMSpecies_toSpecies_inv (i : Fin 6) (f : (Fin 6 → Fin 3 → ℚ) × (Fin 2 → ℚ)) :
     (toSMSpecies i) (toSpecies.symm f) = f.1 i := by
-  change (Prod.fst ∘ toSpecies ∘ toSpecies.symm ) _ i= f.1 i
+  change (Prod.fst ∘ toSpecies ∘ toSpecies.symm) _ i= f.1 i
   simp
 
 /-- The `Q` charges as a map `Fin 3 → ℚ`. -/

HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/Basic.lean

@@ -56,7 +56,7 @@ def proj (T : MSSMACC.LinSols) : MSSMACC.AnomalyFreePerp :=
 
 lemma proj_val (T : MSSMACC.LinSols) :
     (proj T).val = (dot B₃.val T.val - dot Y₃.val T.val) • Y₃.val +
-    ( (dot Y₃.val T.val - 2 * dot B₃.val T.val)) • B₃.val +
+    (dot Y₃.val T.val - 2 * dot B₃.val T.val) • B₃.val +
     dot Y₃.val B₃.val • T.val := by
   rfl
 
@@ -110,7 +110,7 @@ lemma quad_self_proj (T : MSSMACC.Sols) :
 lemma quad_proj (T : MSSMACC.Sols) :
     quadBiLin (proj T.1.1).val (proj T.1.1).val = 2 * dot Y₃.val B₃.val *
      ((dot B₃.val T.val - dot Y₃.val T.val) * quadBiLin Y₃.val T.val +
-   (dot Y₃.val T.val - 2 * dot B₃.val T.val) * quadBiLin B₃.val T.val ) := by
+   (dot Y₃.val T.val - 2 * dot B₃.val T.val) * quadBiLin B₃.val T.val) := by
   nth_rewrite 1 [proj_val]
   repeat rw [quadBiLin.map_add₁]
   repeat rw [quadBiLin.map_smul₁]
@@ -159,7 +159,7 @@ lemma cube_proj_proj_self (T : MSSMACC.Sols) :
     cubeTriLin (proj T.1.1).val (proj T.1.1).val T.val =
     2 * dot Y₃.val B₃.val *
     ((dot B₃.val T.val - dot Y₃.val T.val) * cubeTriLin T.val T.val Y₃.val +
-    ( dot Y₃.val T.val- 2 * dot B₃.val T.val) * cubeTriLin T.val T.val B₃.val) := by
+    (dot Y₃.val T.val - 2 * dot B₃.val T.val) * cubeTriLin T.val T.val B₃.val) := by
   rw [proj_val]
   rw [cubeTriLin.map_add₁, cubeTriLin.map_add₂]
   erw [lineY₃B₃_doublePoint]

HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/PlaneWithY3B3.lean

@@ -155,23 +155,23 @@ def α₁ (T : MSSMACC.AnomalyFreePerp) : ℚ :=
   (3 * cubeTriLin T.val T.val B₃.val * quadBiLin T.val T.val -
     2 * cubeTriLin T.val T.val T.val * quadBiLin B₃.val T.val)
 
-  /-- A helper function to simplify following expressions. -/
-  def α₂ (T : MSSMACC.AnomalyFreePerp) : ℚ :=
-    (2 * cubeTriLin T.val T.val T.val * quadBiLin Y₃.val T.val -
-    3 * cubeTriLin T.val T.val Y₃.val * quadBiLin T.val T.val)
+/-- A helper function to simplify following expressions. -/
+def α₂ (T : MSSMACC.AnomalyFreePerp) : ℚ :=
+  (2 * cubeTriLin T.val T.val T.val * quadBiLin Y₃.val T.val -
+  3 * cubeTriLin T.val T.val Y₃.val * quadBiLin T.val T.val)
 
-  /-- A helper function to simplify following expressions. -/
-  def α₃ (T : MSSMACC.AnomalyFreePerp) : ℚ :=
-    6 * ((cubeTriLin T.val T.val Y₃.val) * quadBiLin B₃.val T.val -
-        (cubeTriLin T.val T.val B₃.val) * quadBiLin Y₃.val T.val)
+/-- A helper function to simplify following expressions. -/
+def α₃ (T : MSSMACC.AnomalyFreePerp) : ℚ :=
+  6 * ((cubeTriLin T.val T.val Y₃.val) * quadBiLin B₃.val T.val -
+      (cubeTriLin T.val T.val B₃.val) * quadBiLin Y₃.val T.val)
 
-  lemma lineQuad_cube (R : MSSMACC.AnomalyFreePerp) (c₁ c₂ c₃ : ℚ) :
-      accCube (lineQuad R c₁ c₂ c₃).val =
-      - 4 * ( c₁ * quadBiLin B₃.val R.val - c₂ * quadBiLin Y₃.val R.val) ^ 2 *
-      ( α₁ R * c₁ + α₂ R * c₂ + α₃ R * c₃ ) := by
-    rw [lineQuad_val]
-    rw [planeY₃B₃_cubic, α₁, α₂, α₃]
-    ring
+lemma lineQuad_cube (R : MSSMACC.AnomalyFreePerp) (c₁ c₂ c₃ : ℚ) :
+    accCube (lineQuad R c₁ c₂ c₃).val =
+    - 4 * (c₁ * quadBiLin B₃.val R.val - c₂ * quadBiLin Y₃.val R.val) ^ 2 *
+    (α₁ R * c₁ + α₂ R * c₂ + α₃ R * c₃) := by
+  rw [lineQuad_val]
+  rw [planeY₃B₃_cubic, α₁, α₂, α₃]
+  ring
 
 /-- The line in the plane spanned by `Y₃`, `B₃` and `R` which is in the cubic. -/
 def lineCube (R : MSSMACC.AnomalyFreePerp) (a₁ a₂ a₃ : ℚ) :

HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/ToSols.lean

@@ -147,7 +147,7 @@ def InCubeSolProp (R : MSSMACC.Sols) : Prop :=
 that solution satisfies `inCubeSolProp`. It appears in the definition of `inLineEqProj`. -/
 def cubicCoeff (T : MSSMACC.Sols) : ℚ :=
     3 * (dot Y₃.val B₃.val) ^ 3 * (cubeTriLin T.val T.val Y₃.val ^ 2 +
-    cubeTriLin T.val T.val B₃.val ^ 2 )
+    cubeTriLin T.val T.val B₃.val ^ 2)
 
 lemma inCubeSolProp_iff_cubicCoeff_zero (T : MSSMACC.Sols) :
     InCubeSolProp T ↔ cubicCoeff T = 0 := by

HepLean/AnomalyCancellation/MSSMNu/Permutations.lean

@@ -60,7 +60,7 @@ lemma chargeMap_toSpecies (f : PermGroup) (S : MSSMCharges.Charges) (j : Fin 6)
 @[simp]
 def repCharges : Representation ℚ PermGroup (MSSMCharges).Charges where
   toFun f := chargeMap f⁻¹
-  map_mul' f g :=by
+  map_mul' f g := by
     simp only [PermGroup, mul_inv_rev]
     apply LinearMap.ext
     intro S

HepLean/AnomalyCancellation/PureU1/Basic.lean

@@ -51,22 +51,19 @@ def accCubeTriLinSymm {n : ℕ} : TriLinearSymm (PureU1Charges n).Charges := Tri
     rw [← Finset.sum_add_distrib]
     apply Fintype.sum_congr
     intro i
-    ring
-    )
+    ring)
   (by
     intro S L T
     simp only [PureU1Charges_numberCharges]
     apply Fintype.sum_congr
     intro i
-    ring
-  )
+    ring)
   (by
     intro S L T
     simp only [PureU1Charges_numberCharges]
     apply Fintype.sum_congr
     intro i
-    ring
-  )
+    ring)
 
 /-- The cubic anomaly equation. -/
 @[simp]

HepLean/AnomalyCancellation/PureU1/BasisLinear.lean

@@ -117,7 +117,7 @@ def coordinateMap : ((PureU1 n.succ).LinSols) ≃ₗ[ℚ] Fin n →₀ ℚ where
     exact Rat.mul_zero (f k)
     simp
 
-/-- The basis of `LinSols`.-/
+/-- The basis of `LinSols`. -/
 noncomputable
 def asBasis : Basis (Fin n) ℚ ((PureU1 n.succ).LinSols) where
   repr := coordinateMap

HepLean/AnomalyCancellation/PureU1/ConstAbs.lean

@@ -191,7 +191,7 @@ lemma AFL_odd_noBoundary {A : (PureU1 (2 * n + 1)).LinSols} (h : ConstAbsSorted
 lemma AFL_odd_zero {A : (PureU1 (2 * n + 1)).LinSols} (h : ConstAbsSorted A.val) :
     A.val (0 : Fin (2 * n + 1)) = 0 := by
   by_contra hn
-  exact (AFL_odd_noBoundary h hn ) (AFL_hasBoundary h hn)
+  exact (AFL_odd_noBoundary h hn) (AFL_hasBoundary h hn)
 
 theorem AFL_odd (A : (PureU1 (2 * n + 1)).LinSols) (h : ConstAbsSorted A.val) :
     A = 0 := by

HepLean/AnomalyCancellation/PureU1/Even/BasisLinear.lean

@@ -689,7 +689,7 @@ lemma P!_in_span (f : Fin n → ℚ) : P! f ∈ Submodule.span ℚ (Set.range ba
      use f
      rfl
 
-lemma smul_basis!AsCharges_in_span (S : (PureU1 (2 * n.succ )).LinSols) (j : Fin n) :
+lemma smul_basis!AsCharges_in_span (S : (PureU1 (2 * n.succ)).LinSols) (j : Fin n) :
     (S.val (δ!₂ j) - S.val (δ!₁ j)) • basis!AsCharges j ∈
     Submodule.span ℚ (Set.range basis!AsCharges) := by
   apply Submodule.smul_mem

HepLean/AnomalyCancellation/PureU1/Even/LineInCubic.lean

@@ -69,7 +69,7 @@ lemma line_in_cubic_P_P_P! {S : (PureU1 (2 * n.succ)).LinSols} (h : LineInCubic
 
 /-- We say a `LinSol` satisfies `lineInCubicPerm` if all its permutations satisfy `lineInCubic`. -/
 def LineInCubicPerm (S : (PureU1 (2 * n.succ)).LinSols) : Prop :=
-  ∀ (M : (FamilyPermutations (2 * n.succ)).group ),
+  ∀ (M : (FamilyPermutations (2 * n.succ)).group),
   LineInCubic ((FamilyPermutations (2 * n.succ)).linSolRep M S)
 
 /-- If `lineInCubicPerm S` then `lineInCubic S`. -/
@@ -104,7 +104,7 @@ lemma lineInCubicPerm_swap {S : (PureU1 (2 * n.succ)).LinSols}
   rw [accCubeTriLinSymm.map_add₃, h1, accCubeTriLinSymm.map_smul₃] at h2
   simpa using h2
 
-lemma P_P_P!_accCube' {S : (PureU1 (2 * n.succ.succ )).LinSols}
+lemma P_P_P!_accCube' {S : (PureU1 (2 * n.succ.succ)).LinSols}
     (f : Fin n.succ.succ → ℚ) (g : Fin n.succ → ℚ) (hS : S.val = Pa f g) :
     accCubeTriLinSymm (P f) (P f) (basis!AsCharges (Fin.last n)) =
     - (S.val (δ!₂ (Fin.last n)) + S.val (δ!₁ (Fin.last n))) * (2 * S.val δ!₄ +
@@ -114,12 +114,12 @@ lemma P_P_P!_accCube' {S : (PureU1 (2 * n.succ.succ )).LinSols}
   have h2 := Pa_δ!₁ f g (Fin.last n)
   have h3 := Pa_δ!₂ f g (Fin.last n)
   simp at h1 h2 h3
-  have hl : f (Fin.succ (Fin.last (n ))) = - Pa f g δ!₄ := by
+  have hl : f (Fin.succ (Fin.last n)) = - Pa f g δ!₄ := by
     simp_all only [Fin.succ_last, neg_neg]
   erw [hl] at h2
   have hg : g (Fin.last n) = Pa f g (δ!₁ (Fin.last n)) + Pa f g δ!₄ := by
     linear_combination -(1 * h2)
-  have hll : f (Fin.castSucc (Fin.last (n ))) =
+  have hll : f (Fin.castSucc (Fin.last n)) =
       - (Pa f g (δ!₂ (Fin.last n)) + Pa f g (δ!₁ (Fin.last n)) + Pa f g δ!₄) := by
     linear_combination h3 - 1 * hg
   rw [← hS] at hl hll

HepLean/AnomalyCancellation/PureU1/Even/Parameterization.lean

@@ -93,7 +93,7 @@ lemma genericCase_exists (S : (PureU1 (2 * n.succ)).Sols)
   rw [hS'.1, hS'.2] at hC
   exact hC' hC
 
-/-- A proposition on a solution which is true if `accCubeTriLinSymm (P g, P g, P! f) = 0`.-/
+/-- A proposition on a solution which is true if `accCubeTriLinSymm (P g, P g, P! f) = 0`. -/
 def SpecialCase (S : (PureU1 (2 * n.succ)).Sols) : Prop :=
   ∀ (g : Fin n.succ → ℚ) (f : Fin n → ℚ) (_ : S.val = P g + P! f) ,
   accCubeTriLinSymm (P g) (P g) (P! f) = 0
@@ -125,7 +125,7 @@ theorem generic_case {S : (PureU1 (2 * n.succ)).Sols} (h : GenericCase S) :
   rw [parameterization]
   apply ACCSystem.Sols.ext
   rw [parameterizationAsLinear_val]
-  change S.val = _ • ( _ • P g + _• P! f)
+  change S.val = _ • (_ • P g + _• P! f)
   rw [anomalyFree_param _ _ hS]
   rw [neg_neg, ← smul_add, smul_smul, inv_mul_cancel, one_smul]
   exact hS

HepLean/AnomalyCancellation/PureU1/LineInPlaneCond.lean

@@ -52,7 +52,7 @@ lemma lineInPlaneCond_perm {S : (PureU1 (n)).LinSols} (hS : LineInPlaneCond S)
     not_false_eq_true]
 
 lemma lineInPlaneCond_eq_last' {S : (PureU1 (n.succ.succ)).LinSols} (hS : LineInPlaneCond S)
-    (h : ¬ (S.val ((Fin.last n).castSucc))^2 = (S.val ((Fin.last n).succ))^2 ) :
+    (h : ¬ (S.val ((Fin.last n).castSucc))^2 = (S.val ((Fin.last n).succ))^2) :
     (2 - n) * S.val (Fin.last (n + 1)) =
     - (2 - n)* S.val (Fin.castSucc (Fin.last n)) := by
   erw [sq_eq_sq_iff_eq_or_eq_neg] at h

HepLean/AnomalyCancellation/PureU1/LowDim/Three.lean

@@ -43,7 +43,7 @@ lemma cube_for_linSol (S : (PureU1 3).LinSols) :
 lemma three_sol_zero (S : (PureU1 3).Sols) : S.val (0 : Fin 3) = 0 ∨ S.val (1 : Fin 3) = 0
     ∨ S.val (2 : Fin 3) = 0 := (cube_for_linSol S.1.1).mpr S.cubicSol
 
-/-- Given a `LinSol` with a charge equal to zero a `Sol`.-/
+/-- Given a `LinSol` with a charge equal to zero a `Sol`. -/
 def solOfLinear (S : (PureU1 3).LinSols)
     (hS : S.val (0 : Fin 3) = 0 ∨ S.val (1 : Fin 3) = 0 ∨ S.val (2 : Fin 3) = 0) :
     (PureU1 3).Sols :=

HepLean/AnomalyCancellation/PureU1/Odd/LineInCubic.lean

@@ -58,12 +58,12 @@ lemma line_in_cubic_P_P_P! {S : (PureU1 (2 * n + 1)).LinSols} (h : LineInCubic S
     ∀ (g : Fin n → ℚ) (f : Fin n → ℚ) (_ : S.val = P g + P! f),
     accCubeTriLinSymm (P g) (P g) (P! f) = 0 := by
   intro g f hS
-  linear_combination 2 / 3 * (lineInCubic_expand h g f hS 1 1 ) -
-     (lineInCubic_expand h g f hS 1 2 ) / 6
+  linear_combination 2 / 3 * (lineInCubic_expand h g f hS 1 1) -
+     (lineInCubic_expand h g f hS 1 2) / 6
 
 /-- We say a `LinSol` satisfies `lineInCubicPerm` if all its permutations satisfy `lineInCubic`. -/
 def LineInCubicPerm (S : (PureU1 (2 * n + 1)).LinSols) : Prop :=
-  ∀ (M : (FamilyPermutations (2 * n + 1)).group ),
+  ∀ (M : (FamilyPermutations (2 * n + 1)).group),
     LineInCubic ((FamilyPermutations (2 * n + 1)).linSolRep M S)
 
 /-- If `lineInCubicPerm S` then `lineInCubic S`. -/

HepLean/AnomalyCancellation/PureU1/Odd/Parameterization.lean

@@ -124,7 +124,7 @@ theorem generic_case {S : (PureU1 (2 * n.succ + 1)).Sols} (h : GenericCase S) :
   rw [parameterization]
   apply ACCSystem.Sols.ext
   rw [parameterizationAsLinear_val]
-  change S.val = _ • ( _ • P g + _• P! f)
+  change S.val = _ • (_ • P g + _• P! f)
   rw [anomalyFree_param _ _ hS]
   rw [neg_neg, ← smul_add, smul_smul, inv_mul_cancel, one_smul]
   exact hS

HepLean/AnomalyCancellation/PureU1/Permutations.lean

@@ -51,7 +51,7 @@ open PureU1Charges in
 @[simp]
 def permCharges {n : ℕ} : Representation ℚ (PermGroup n) (PureU1 n).Charges where
   toFun f := chargeMap f⁻¹
-  map_mul' f g :=by
+  map_mul' f g := by
     simp only [PermGroup, mul_inv_rev]
     apply LinearMap.ext
     intro S
@@ -214,7 +214,7 @@ lemma permTwo_fst : (permTwo hij hij').toFun i' = i := by
 lemma permTwo_snd : (permTwo hij hij').toFun j' = j := by
   rw [permTwo, permOfInjection]
   have ht := Equiv.extendSubtype_apply_of_mem
-    ((permTwoInj hij' ).toEquivRange.symm.trans
+    ((permTwoInj hij').toEquivRange.symm.trans
     (permTwoInj hij).toEquivRange) j' (permTwoInj_snd hij')
   simp at ht
   simp [ht, permTwoInj_snd_apply]
@@ -303,16 +303,15 @@ lemma Prop_two (P : ℚ × ℚ → Prop) {S : (PureU1 n).LinSols}
     {a b : Fin n} (hab : a ≠ b)
     (h : ∀ (f : (FamilyPermutations n).group),
     P ((((FamilyPermutations n).linSolRep f S).val a),
-      (((FamilyPermutations n).linSolRep f S).val b)
-    )) : ∀ (i j : Fin n) (_ : i ≠ j),
+      (((FamilyPermutations n).linSolRep f S).val b))) : ∀ (i j : Fin n) (_ : i ≠ j),
     P (S.val i, S.val j) := by
   intro i j hij
-  have h1 := h (permTwo hij hab ).symm
+  have h1 := h (permTwo hij hab).symm
   rw [FamilyPermutations_anomalyFreeLinear_apply, FamilyPermutations_anomalyFreeLinear_apply] at h1
   simp at h1
   change P
-   (S.val ((permTwo hij hab ).toFun a),
-   S.val ((permTwo hij hab ).toFun b)) at h1
+   (S.val ((permTwo hij hab).toFun a),
+   S.val ((permTwo hij hab).toFun b)) at h1
   erw [permTwo_fst,permTwo_snd] at h1
   exact h1
 
@@ -321,9 +320,8 @@ lemma Prop_three (P : ℚ × ℚ × ℚ → Prop) {S : (PureU1 n).LinSols}
     (h : ∀ (f : (FamilyPermutations n).group),
     P ((((FamilyPermutations n).linSolRep f S).val a),(
       (((FamilyPermutations n).linSolRep f S).val b),
-      (((FamilyPermutations n).linSolRep f S).val c)
-    ))) : ∀ (i j k : Fin n) (_ : i ≠ j) (_ : j ≠ k) (_ : i ≠ k),
-    P (S.val i, (S.val j, S.val k)) := by
+      (((FamilyPermutations n).linSolRep f S).val c)))) : ∀ (i j k : Fin n)
+      (_ : i ≠ j) (_ : j ≠ k) (_ : i ≠ k), P (S.val i, (S.val j, S.val k)) := by
   intro i j k hij hjk hik
   have h1 := h (permThree hij hjk hik hab hbc hac).symm
   rw [FamilyPermutations_anomalyFreeLinear_apply, FamilyPermutations_anomalyFreeLinear_apply,

HepLean/AnomalyCancellation/SM/Basic.lean

@@ -54,9 +54,9 @@ lemma charges_eq_toSpecies_eq (S T : (SMCharges n).Charges) :
   apply toSpeciesEquiv.injective
   exact (Set.eqOn_univ (toSpeciesEquiv S) (toSpeciesEquiv T)).mp fun ⦃x⦄ _ => h x
 
-lemma toSMSpecies_toSpecies_inv (i : Fin 5) (f : (Fin 5 → Fin n → ℚ) ) :
+lemma toSMSpecies_toSpecies_inv (i : Fin 5) (f : Fin 5 → Fin n → ℚ) :
     (toSpecies i) (toSpeciesEquiv.symm f) = f i := by
-  change (toSpeciesEquiv ∘ toSpeciesEquiv.symm ) _ i= f i
+  change (toSpeciesEquiv ∘ toSpeciesEquiv.symm) _ i= f i
   simp
 
 /-- The `Q` charges as a map `Fin n → ℚ`. -/
@@ -272,8 +272,7 @@ def cubeTriLin : TriLinearSymm (SMCharges n).Charges := TriLinearSymm.mk₃
     intro i
     repeat erw [map_smul]
     simp [HSMul.hSMul, SMul.smul]
-    ring
-  )
+    ring)
   (by
     intro S T R L
     simp only
@@ -282,22 +281,19 @@ def cubeTriLin : TriLinearSymm (SMCharges n).Charges := TriLinearSymm.mk₃
     intro i
     repeat erw [map_add]
     simp only [ACCSystemCharges.chargesAddCommMonoid_add, toSpecies_apply, Fin.isValue]
-    ring
-  )
+    ring)
   (by
     intro S T L
     simp only [SMSpecies_numberCharges, toSpecies_apply, Fin.isValue]
     apply Fintype.sum_congr
     intro i
-    ring
-  )
+    ring)
   (by
     intro S T L
     simp only [SMSpecies_numberCharges, toSpecies_apply, Fin.isValue]
     apply Fintype.sum_congr
     intro i
-    ring
-  )
+    ring)
 
 /-- The cubic acc. -/
 @[simp]

HepLean/AnomalyCancellation/SM/FamilyMaps.lean

@@ -100,7 +100,7 @@ def speciesFamilyUniversial (n : ℕ) :
 
 /-- The embedding of the `1`-family charges into the `n`-family charges in
 a universal manor. -/
-def familyUniversal ( n : ℕ) : (SMCharges 1).Charges →ₗ[ℚ] (SMCharges n).Charges :=
+def familyUniversal (n : ℕ) : (SMCharges 1).Charges →ₗ[ℚ] (SMCharges n).Charges :=
   chargesMapOfSpeciesMap (speciesFamilyUniversial n)
 
 end SM

HepLean/AnomalyCancellation/SM/NoGrav/One/LinearParameterization.lean

@@ -183,7 +183,8 @@ lemma grav (S : linearParameters) :
 
 end linearParameters
 
-/-- The parameters for solutions to the linear ACCs with the condition that Q and E are non-zero.-/
+/-- The parameters for solutions to the linear ACCs with the condition that Q and E are
+  non-zero. -/
 structure linearParametersQENeqZero where
   /-- The parameter `x`. -/
   x : ℚ
@@ -291,7 +292,7 @@ lemma cubic_v_or_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection
   exact h2 h
 
 lemma cubic_v_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
-    (hv : S.v = 0 ) : S.w = -1 := by
+    (hv : S.v = 0) : S.w = -1 := by
   rw [S.cubic, hv] at h
   simp at h
   have h' : (S.w + 1) * (1 * S.w * S.w + (-1) * S.w + 1) = 0 := by
@@ -309,7 +310,7 @@ lemma cubic_v_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.
   exact eq_neg_of_add_eq_zero_left h'
 
 lemma cube_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
-    (hw : S.w = 0 ) : S.v = -1 := by
+    (hw : S.w = 0) : S.v = -1 := by
   rw [S.cubic, hw] at h
   simp at h
   have h' : (S.v + 1) * (1 * S.v * S.v + (-1) * S.v + 1) = 0 := by

HepLean/AnomalyCancellation/SM/Permutations.lean

@@ -36,7 +36,7 @@ instance : Group (PermGroup n) := Pi.group
 /-- The image of an element of `permGroup n` under the representation on charges. -/
 @[simps!]
 def chargeMap (f : PermGroup n) : (SMCharges n).Charges →ₗ[ℚ] (SMCharges n).Charges where
-  toFun S := toSpeciesEquiv.symm (fun i => toSpecies i S ∘ f i )
+  toFun S := toSpeciesEquiv.symm (fun i => toSpecies i S ∘ f i)
   map_add' _ _ := rfl
   map_smul' _ _ := rfl
 
@@ -44,7 +44,7 @@ def chargeMap (f : PermGroup n) : (SMCharges n).Charges →ₗ[ℚ] (SMCharges n
 @[simp]
 def repCharges {n : ℕ} : Representation ℚ (PermGroup n) (SMCharges n).Charges where
   toFun f := chargeMap f⁻¹
-  map_mul' f g :=by
+  map_mul' f g := by
     simp only [PermGroup, mul_inv_rev]
     apply LinearMap.ext
     intro S

HepLean/AnomalyCancellation/SMNu/Basic.lean

@@ -31,7 +31,7 @@ namespace SMνCharges
 variable {n : ℕ}
 
 /-- An equivalence between `(SMνCharges n).charges` and `(Fin 6 → Fin n → ℚ)`
-splitting the charges into species.-/
+splitting the charges into species. -/
 @[simps!]
 def toSpeciesEquiv : (SMνCharges n).Charges ≃ (Fin 6 → Fin n → ℚ) :=
   ((Equiv.curry _ _ _).symm.trans ((@finProdFinEquiv 6 n).arrowCongr (Equiv.refl ℚ))).symm
@@ -54,9 +54,9 @@ lemma charges_eq_toSpecies_eq (S T : (SMνCharges n).Charges) :
   funext i
   exact h i
 
-lemma toSMSpecies_toSpecies_inv (i : Fin 6) (f : (Fin 6 → Fin n → ℚ) ) :
+lemma toSMSpecies_toSpecies_inv (i : Fin 6) (f : Fin 6 → Fin n → ℚ) :
     (toSpecies i) (toSpeciesEquiv.symm f) = f i := by
-  change (toSpeciesEquiv ∘ toSpeciesEquiv.symm ) _ i = f i
+  change (toSpeciesEquiv ∘ toSpeciesEquiv.symm) _ i = f i
   simp
 
 lemma toSpecies_one (S : (SMνCharges 1).Charges) (j : Fin 6) :

HepLean/AnomalyCancellation/SMNu/Ordinary/DimSevenPlane.lean

@@ -24,12 +24,11 @@ open BigOperators
 namespace PlaneSeven
 
 /-- A charge assignment forming one of the basis elements of the plane. -/
-def B₀ : (SM 3).Charges := toSpeciesEquiv.invFun ( fun s => fun i =>
+def B₀ : (SM 3).Charges := toSpeciesEquiv.invFun (fun s => fun i =>
   match s, i with
   | 0, 0 => 1
   | 0, 1 => - 1
-  | _, _ => 0
-  )
+  | _, _ => 0)
 
 lemma B₀_cubic (S T : (SM 3).Charges) : cubeTriLin B₀ S T =
     6 * (S (0 : Fin 18) * T (0 : Fin 18) - S (1 : Fin 18) * T (1 : Fin 18)) := by
@@ -37,12 +36,11 @@ lemma B₀_cubic (S T : (SM 3).Charges) : cubeTriLin B₀ S T =
   ring
 
 /-- A charge assignment forming one of the basis elements of the plane. -/
-def B₁ : (SM 3).Charges := toSpeciesEquiv.invFun ( fun s => fun i =>
+def B₁ : (SM 3).Charges := toSpeciesEquiv.invFun (fun s => fun i =>
   match s, i with
   | 1, 0 => 1
   | 1, 1 => - 1
-  | _, _ => 0
-  )
+  | _, _ => 0)
 
 lemma B₁_cubic (S T : (SM 3).Charges) : cubeTriLin B₁ S T =
     3 * (S (3 : Fin 18) * T (3 : Fin 18) - S (4 : Fin 18) * T (4 : Fin 18)) := by
@@ -50,12 +48,11 @@ lemma B₁_cubic (S T : (SM 3).Charges) : cubeTriLin B₁ S T =
   ring
 
 /-- A charge assignment forming one of the basis elements of the plane. -/
-def B₂ : (SM 3).Charges := toSpeciesEquiv.invFun ( fun s => fun i =>
+def B₂ : (SM 3).Charges := toSpeciesEquiv.invFun (fun s => fun i =>
   match s, i with
   | 2, 0 => 1
   | 2, 1 => - 1
-  | _, _ => 0
-  )
+  | _, _ => 0)
 
 lemma B₂_cubic (S T : (SM 3).Charges) : cubeTriLin B₂ S T =
     3 * (S (6 : Fin 18) * T (6 : Fin 18) - S (7 : Fin 18) * T (7 : Fin 18)) := by
@@ -63,12 +60,11 @@ lemma B₂_cubic (S T : (SM 3).Charges) : cubeTriLin B₂ S T =
   ring
 
 /-- A charge assignment forming one of the basis elements of the plane. -/
-def B₃ : (SM 3).Charges := toSpeciesEquiv.invFun ( fun s => fun i =>
+def B₃ : (SM 3).Charges := toSpeciesEquiv.invFun (fun s => fun i =>
   match s, i with
   | 3, 0 => 1
   | 3, 1 => - 1
-  | _, _ => 0
-  )
+  | _, _ => 0)
 
 lemma B₃_cubic (S T : (SM 3).Charges) : cubeTriLin B₃ S T =
     2 * (S (9 : Fin 18) * T (9 : Fin 18) - S (10 : Fin 18) * T (10 : Fin 18)) := by
@@ -77,12 +73,11 @@ lemma B₃_cubic (S T : (SM 3).Charges) : cubeTriLin B₃ S T =
   rfl
 
 /-- A charge assignment forming one of the basis elements of the plane. -/
-def B₄ : (SM 3).Charges := toSpeciesEquiv.invFun ( fun s => fun i =>
+def B₄ : (SM 3).Charges := toSpeciesEquiv.invFun (fun s => fun i =>
   match s, i with
   | 4, 0 => 1
   | 4, 1 => - 1
-  | _, _ => 0
-  )
+  | _, _ => 0)
 
 lemma B₄_cubic (S T : (SM 3).Charges) : cubeTriLin B₄ S T =
     (S (12 : Fin 18) * T (12 : Fin 18) - S (13 : Fin 18) * T (13 : Fin 18)) := by
@@ -91,12 +86,11 @@ lemma B₄_cubic (S T : (SM 3).Charges) : cubeTriLin B₄ S T =
   rfl
 
 /-- A charge assignment forming one of the basis elements of the plane. -/
-def B₅ : (SM 3).Charges := toSpeciesEquiv.invFun ( fun s => fun i =>
+def B₅ : (SM 3).Charges := toSpeciesEquiv.invFun (fun s => fun i =>
   match s, i with
   | 5, 0 => 1
   | 5, 1 => - 1
-  | _, _ => 0
-  )
+  | _, _ => 0)
 
 lemma B₅_cubic (S T : (SM 3).Charges) : cubeTriLin B₅ S T =
     (S (15 : Fin 18) * T (15 : Fin 18) - S (16 : Fin 18) * T (16 : Fin 18)) := by
@@ -105,12 +99,11 @@ lemma B₅_cubic (S T : (SM 3).Charges) : cubeTriLin B₅ S T =
   rfl
 
 /-- A charge assignment forming one of the basis elements of the plane. -/
-def B₆ : (SM 3).Charges := toSpeciesEquiv.invFun ( fun s => fun i =>
+def B₆ : (SM 3).Charges := toSpeciesEquiv.invFun (fun s => fun i =>
   match s, i with
   | 1, 2 => 1
   | 2, 2 => -1
-  | _, _ => 0
-  )
+  | _, _ => 0)
 
 lemma B₆_cubic (S T : (SM 3).Charges) : cubeTriLin B₆ S T =
     3 * (S (5 : Fin 18) * T (5 : Fin 18) - S (8 : Fin 18) * T (8 : Fin 18)) := by

HepLean/AnomalyCancellation/SMNu/Permutations.lean

@@ -36,7 +36,7 @@ instance : Group (PermGroup n) := Pi.group
 /-- The image of an element of `permGroup n` under the representation on charges. -/
 @[simps!]
 def chargeMap (f : PermGroup n) : (SMνCharges n).Charges →ₗ[ℚ] (SMνCharges n).Charges where
-  toFun S := toSpeciesEquiv.symm (fun i => toSpecies i S ∘ f i )
+  toFun S := toSpeciesEquiv.symm (fun i => toSpecies i S ∘ f i)
   map_add' _ _ := rfl
   map_smul' _ _ := rfl
 

HepLean/FeynmanDiagrams/Basic.lean

@@ -289,7 +289,7 @@ instance diagramVertexPropDecidable
   @decidable_of_decidable_of_iff _ _
     (@Fintype.decidableForallFintype _ _ (fun _ => @Fintype.decidableExistsFintype _ _
     (fun _ => @And.decidable _ _ _ (@Fintype.decidablePiFintype _ _
-    (fun _ => P.preFeynmanRuleDecEq𝓱𝓔) _ _ _)) _ ) _)
+    (fun _ => P.preFeynmanRuleDecEq𝓱𝓔) _ _ _)) _) _)
     (P.diagramVertexProp_iff F f).symm
 
 instance diagramEdgePropDecidable
@@ -299,7 +299,7 @@ instance diagramEdgePropDecidable
   @decidable_of_decidable_of_iff _ _
     (@Fintype.decidableForallFintype _ _ (fun _ => @Fintype.decidableExistsFintype _ _
     (fun _ => @And.decidable _ _ _ (@Fintype.decidablePiFintype _ _
-    (fun _ => P.preFeynmanRuleDecEq𝓱𝓔) _ _ _)) _ ) _)
+    (fun _ => P.preFeynmanRuleDecEq𝓱𝓔) _ _ _)) _) _)
     (P.diagramEdgeProp_iff F f).symm
 
 end PreFeynmanRule
@@ -717,7 +717,7 @@ instance [IsFiniteDiagram F] : DecidableRel F.AdjRelation := fun _ _ =>
   @Fintype.decidableExistsFintype _ _ (fun _ => @Fintype.decidableExistsFintype _ _ (
   fun _ => @And.decidable _ _ (instDecidableEq𝓔OfIsFiniteDiagram _ _) $
     @And.decidable _ _ (instDecidableEq𝓥OfIsFiniteDiagram _ _)
-    (instDecidableEq𝓥OfIsFiniteDiagram _ _)) _ ) _
+    (instDecidableEq𝓥OfIsFiniteDiagram _ _)) _) _
 
 /-- From a Feynman diagram the simple graph showing those vertices which are connected. -/
 def toSimpleGraph : SimpleGraph F.𝓥 where

HepLean/FeynmanDiagrams/Momentum.lean

@@ -109,7 +109,7 @@ instance (i : Fin 2) : Module ℝ (EdgeVertexMomentaMap F i) :=
   | 0 => instModuleRealEdgeMomenta F
   | 1 => instModuleRealVertexMomenta F
 
-/-- The direct sum of `EdgeMomenta` and `VertexMomenta`.-/
+/-- The direct sum of `EdgeMomenta` and `VertexMomenta`. -/
 def EdgeVertexMomenta : Type := DirectSum (Fin 2) (EdgeVertexMomentaMap F)
 
 instance : AddCommGroup F.EdgeVertexMomenta := DirectSum.instAddCommGroup _

HepLean/FlavorPhysics/CKMMatrix/Basic.lean

@@ -236,7 +236,7 @@ lemma td (V : CKMMatrix) (a b c d e f : ℝ) :
   simp only [Fin.isValue, cons_val', cons_val_zero, empty_val', cons_val_fin_one, vecCons_const,
     cons_val_two, tail_val', head_val', cons_val_one, head_cons, tail_cons, head_fin_const,
     zero_mul, add_zero, mul_zero]
-  change (0 * _ + _ ) * _ + (0 * _ + _ ) * 0 = _
+  change (0 * _ + _) * _ + (0 * _ + _) * 0 = _
   simp only [Fin.isValue, zero_mul, zero_add, mul_zero, add_zero]
   rw [exp_add]
   ring_nf

HepLean/FlavorPhysics/CKMMatrix/PhaseFreedom.lean

@@ -227,9 +227,9 @@ lemma fstRowThdColRealCond_holds_up_to_equiv (V : CKMMatrix) :
   obtain ⟨τ, hτ⟩ := V.uRow_cross_cRow_eq_tRow
   let U : CKMMatrix := phaseShiftApply V
     0
-    (- τ + arg [V]ud + arg [V]us + arg [V]tb )
-    (- τ + arg [V]cb + arg [V]ud + arg [V]us )
-    (- arg [V]ud )
+    (- τ + arg [V]ud + arg [V]us + arg [V]tb)
+    (- τ + arg [V]cb + arg [V]ud + arg [V]us)
+    (- arg [V]ud)
     (- arg [V]us)
     (τ - arg [V]ud - arg [V]us - arg [V]cb - arg [V]tb)
   have hUV : Quotient.mk CKMMatrixSetoid U = ⟦V⟧ := by
@@ -262,7 +262,7 @@ lemma ubOnePhaseCond_hold_up_to_equiv_of_ub_one {V : CKMMatrix} (hb : ¬ ([V]ud
     (hV : FstRowThdColRealCond V) :
     ∃ (U : CKMMatrix), V ≈ U ∧ ubOnePhaseCond U:= by
   let U : CKMMatrix := phaseShiftApply V 0 0 (- Real.pi + arg [V]cd + arg [V]cs + arg [V]ub)
-    (Real.pi - arg [V]cd ) (- arg [V]cs) (- arg [V]ub )
+    (Real.pi - arg [V]cd) (- arg [V]cs) (- arg [V]ub)
   use U
   have hUV : Quotient.mk CKMMatrixSetoid U= ⟦V⟧ := by
     simp only [Quotient.eq]
@@ -318,7 +318,7 @@ lemma ubOnePhaseCond_hold_up_to_equiv_of_ub_one {V : CKMMatrix} (hb : ¬ ([V]ud
 lemma cd_of_fstRowThdColRealCond {V : CKMMatrix} (hb : [V]ud ≠ 0 ∨ [V]us ≠ 0)
     (hV : FstRowThdColRealCond V) :
     [V]cd = (- VtbAbs ⟦V⟧ * VusAbs ⟦V⟧ / (VudAbs ⟦V⟧ ^2 + VusAbs ⟦V⟧ ^2)) +
-    (- VubAbs ⟦V⟧ * VudAbs ⟦V⟧ * VcbAbs ⟦V⟧ / (VudAbs ⟦V⟧ ^2 + VusAbs ⟦V⟧ ^2 ))
+    (- VubAbs ⟦V⟧ * VudAbs ⟦V⟧ * VcbAbs ⟦V⟧ / (VudAbs ⟦V⟧ ^2 + VusAbs ⟦V⟧ ^2))
     * cexp (- arg [V]ub * I) := by
   have hτ : [V]t = cexp ((0 : ℝ) * I) • (conj ([V]u) ×₃ conj ([V]c)) := by
     simp only [ofReal_zero, zero_mul, exp_zero, one_smul]

HepLean/FlavorPhysics/CKMMatrix/Relations.lean

@@ -84,7 +84,7 @@ lemma ud_us_neq_zero_iff_ub_neq_one (V : CKMMatrix) :
   simp_all
   have h1 := Complex.abs.nonneg [V]ub
   rw [h2] at h1
-  have h2 : ¬ 0 ≤ ( -1 : ℝ) := by simp
+  have h2 : ¬ 0 ≤ (-1 : ℝ) := by simp
   exact h2 h1
 
 lemma normSq_Vud_plus_normSq_Vus_neq_zero_ℝ {V : CKMMatrix} (hb : [V]ud ≠ 0 ∨ [V]us ≠ 0) :
@@ -100,7 +100,7 @@ lemma normSq_Vud_plus_normSq_Vus_neq_zero_ℝ {V : CKMMatrix} (hb : [V]ud ≠ 0
   exact hb h2
   have h3 := Complex.abs.nonneg [V]ub
   rw [h2] at h3
-  have h2 : ¬ 0 ≤ ( -1 : ℝ) := by simp
+  have h2 : ¬ 0 ≤ (-1 : ℝ) := by simp
   exact h2 h3
 
 lemma VAbsub_neq_zero_Vud_Vus_neq_zero {V : Quotient CKMMatrixSetoid}
@@ -154,11 +154,11 @@ lemma fst_row_orthog_thd_row (V : CKMMatrix) :
 
 lemma Vcd_mul_conj_Vud (V : CKMMatrix) :
     [V]cd * conj [V]ud = -[V]cs * conj [V]us - [V]cb * conj [V]ub := by
-  linear_combination (V.fst_row_orthog_snd_row )
+  linear_combination (V.fst_row_orthog_snd_row)
 
 lemma Vcs_mul_conj_Vus (V : CKMMatrix) :
     [V]cs * conj [V]us = - [V]cd * conj [V]ud - [V]cb * conj [V]ub := by
-  linear_combination (V.fst_row_orthog_snd_row )
+  linear_combination V.fst_row_orthog_snd_row
 
 end orthogonal
 
@@ -344,7 +344,7 @@ lemma cb_tb_neq_zero_iff_ub_neq_one (V : CKMMatrix) :
   simp_all
   have h1 := Complex.abs.nonneg [V]ub
   rw [h2] at h1
-  have h2 : ¬ 0 ≤ ( -1 : ℝ) := by simp
+  have h2 : ¬ 0 ≤ (-1 : ℝ) := by simp
   exact h2 h1
 
 lemma VAbs_fst_col_eq_one_snd_eq_zero {V : Quotient CKMMatrixSetoid} {i : Fin 3}

HepLean/FlavorPhysics/CKMMatrix/Rows.lean

@@ -240,7 +240,7 @@ lemma cRow_cross_tRow_eq_uRow (V : CKMMatrix) :
 lemma uRow_cross_cRow_eq_tRow (V : CKMMatrix) :
     ∃ (τ : ℝ), [V]t = cexp (τ * I) • (conj ([V]u) ×₃ conj ([V]c)) := by
   obtain ⟨g, hg⟩ := (mem_span_range_iff_exists_fun ℂ).mp (Basis.mem_span (rowBasis V)
-    (conj ([V]u) ×₃ conj ([V]c)) )
+    (conj ([V]u) ×₃ conj ([V]c)))
   rw [Fin.sum_univ_three, rowBasis] at hg
   simp at hg
   have h0 := congrArg (fun X => conj [V]u ⬝ᵥ X) hg
@@ -307,20 +307,20 @@ def ucCross : Fin 3 → ℂ :=
   conj [phaseShiftApply V a b c d e f]u ×₃ conj [phaseShiftApply V a b c d e f]c
 
 lemma ucCross_fst (V : CKMMatrix) : (ucCross V a b c d e f) 0 =
-    cexp ((- a * I) + (- b * I) + ( - e * I) + (- f * I)) * (conj [V]u ×₃ conj [V]c) 0 := by
+    cexp ((- a * I) + (- b * I) + (- e * I) + (- f * I)) * (conj [V]u ×₃ conj [V]c) 0 := by
   simp [ucCross, crossProduct, Nat.succ_eq_add_one, Nat.reduceAdd, Fin.isValue,
     LinearMap.mk₂_apply, Pi.conj_apply, cons_val_zero, neg_mul, uRow, us, ub, cRow, cs, cb,
     exp_add, exp_sub, ← exp_conj, conj_ofReal]
   ring
 
 lemma ucCross_snd (V : CKMMatrix) : (ucCross V a b c d e f) 1 =
-    cexp ((- a * I) + (- b * I) + ( - d * I) + (- f * I)) * (conj [V]u ×₃ conj [V]c) 1 := by
+    cexp ((- a * I) + (- b * I) + (- d * I) + (- f * I)) * (conj [V]u ×₃ conj [V]c) 1 := by
   simp [ucCross, crossProduct, uRow, us, ub, cRow, cs, cb, ud, cd, exp_add,
     exp_sub, ← exp_conj, conj_ofReal]
   ring
 
 lemma ucCross_thd (V : CKMMatrix) : (ucCross V a b c d e f) 2 =
-    cexp ((- a * I) + (- b * I) + ( - d * I) + (- e * I)) * (conj [V]u ×₃ conj [V]c) 2 := by
+    cexp ((- a * I) + (- b * I) + (- d * I) + (- e * I)) * (conj [V]u ×₃ conj [V]c) 2 := by
   simp [ucCross, crossProduct, uRow, us, ub, cRow, cs, cb, ud, cd, exp_add, exp_sub,
     ← exp_conj, conj_ofReal]
   ring

HepLean/FlavorPhysics/CKMMatrix/StandardParameterization/StandardParameters.lean

@@ -373,8 +373,8 @@ lemma mulExpδ₁₃_on_param_abs (V : CKMMatrix) (δ₁₃ : ℝ) :
     complexAbs_sin_θ₂₃, complexAbs_cos_θ₂₃]
 
 lemma mulExpδ₁₃_on_param_neq_zero_arg (V : CKMMatrix) (δ₁₃ : ℝ)
-    (h1 : mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧ ≠ 0 ) :
-    cexp (arg ( mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧ ) * I) =
+    (h1 : mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧ ≠ 0) :
+    cexp (arg (mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧) * I) =
     cexp (δ₁₃ * I) := by
   have h1a := mulExpδ₁₃_on_param_δ₁₃ V δ₁₃
   have habs := mulExpδ₁₃_on_param_abs V δ₁₃
@@ -383,7 +383,7 @@ lemma mulExpδ₁₃_on_param_neq_zero_arg (V : CKMMatrix) (δ₁₃ : ℝ)
     rw [habs, h1a]
     ring_nf
   nth_rewrite 1 [← abs_mul_exp_arg_mul_I (mulExpδ₁₃
-    ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧ )] at h2
+    ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧)] at h2
   have habs_neq_zero :
       (Complex.abs (mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧) : ℂ) ≠ 0 := by
     simp only [ne_eq, ofReal_eq_zero, map_eq_zero]
@@ -505,7 +505,7 @@ lemma eq_standParam_of_fstRowThdColRealCond {V : CKMMatrix} (hb : [V]ud ≠ 0
     rw [ud_us_neq_zero_iff_ub_neq_one] at hb
     simp [VAbs, hb]
   have h1 : ofReal (√(VAbs 0 0 ⟦V⟧ ^ 2 + VAbs 0 1 ⟦V⟧ ^ 2) *
-    ↑√(VAbs 0 0 ⟦V⟧ ^ 2 + VAbs 0 1 ⟦V⟧ ^ 2)) = ofReal ((VAbs 0 0 ⟦V⟧ ^ 2 + VAbs 0 1 ⟦V⟧ ^ 2) ) := by
+    ↑√(VAbs 0 0 ⟦V⟧ ^ 2 + VAbs 0 1 ⟦V⟧ ^ 2)) = ofReal (VAbs 0 0 ⟦V⟧ ^ 2 + VAbs 0 1 ⟦V⟧ ^ 2) := by
     rw [Real.mul_self_sqrt ]
     apply add_nonneg (sq_nonneg _) (sq_nonneg _)
   simp at h1

HepLean/Mathematics/LinearMaps.lean

@@ -70,7 +70,7 @@ def mk₂ (f : V × V → ℚ) (map_smul : ∀ a S T, f (a • S, T) = a * f (S,
       simp only
       rw [swap, map_add]
       exact Mathlib.Tactic.LinearCombination.add_pf (swap T1 S) (swap T2 S)
-    map_smul' :=by
+    map_smul' := by
       intro a T
       simp only [eq_ratCast, Rat.cast_eq_id, id_eq, smul_eq_mul]
       rw [swap, map_smul]
@@ -173,7 +173,7 @@ namespace TriLinearSymm
 open BigOperators
 variable {V : Type} [AddCommMonoid V] [Module ℚ V]
 
-instance instFun : FunLike (TriLinearSymm V) V (V →ₗ[ℚ] V →ₗ[ℚ] ℚ ) where
+instance instFun : FunLike (TriLinearSymm V) V (V →ₗ[ℚ] V →ₗ[ℚ] ℚ) where
   coe f := f.toFun
   coe_injective' f g h := by
     cases f

HepLean/Mathematics/SO3/Basic.lean

@@ -183,12 +183,12 @@ def toEnd (A : SO(3)) : End ℝ (EuclideanSpace ℝ (Fin 3)) :=
 
 lemma one_is_eigenvalue (A : SO(3)) : A.toEnd.HasEigenvalue 1 := by
   rw [End.hasEigenvalue_iff_mem_spectrum]
-  erw [AlgEquiv.spectrum_eq (Matrix.toLinAlgEquiv (EuclideanSpace.basisFun (Fin 3) ℝ).toBasis ) A.1]
+  erw [AlgEquiv.spectrum_eq (Matrix.toLinAlgEquiv (EuclideanSpace.basisFun (Fin 3) ℝ).toBasis) A.1]
   exact one_in_spectrum A
 
 lemma exists_stationary_vec (A : SO(3)) :
     ∃ (v : EuclideanSpace ℝ (Fin 3)),
-    Orthonormal ℝ (({0} : Set (Fin 3)).restrict (fun _ => v ))
+    Orthonormal ℝ (({0} : Set (Fin 3)).restrict (fun _ => v))
     ∧ A.toEnd v = v := by
   obtain ⟨v, hv⟩ := End.HasEigenvalue.exists_hasEigenvector $ one_is_eigenvalue A
   have hvn : ‖v‖ ≠ 0 := norm_ne_zero_iff.mpr hv.2

HepLean/SpaceTime/LorentzGroup/Basic.lean

@@ -239,7 +239,7 @@ open LorentzVector
 
 -/
 
-/-- The first column of a lorentz matrix as a `NormOneLorentzVector`. -/
+/-- The first column of a Lorentz matrix as a `NormOneLorentzVector`. -/
 @[simps!]
 def toNormOneLorentzVector (Λ : LorentzGroup d) : NormOneLorentzVector d :=
   ⟨Λ.1 *ᵥ timeVec, by rw [NormOneLorentzVector.mem_iff, Λ.2, minkowskiMetric.on_timeVec]⟩

HepLean/SpaceTime/LorentzGroup/Orthochronous.lean

@@ -150,7 +150,7 @@ lemma mul_not_othchron_of_not_othchron_othchron {Λ Λ' : LorentzGroup d} (h :
   rw [IsOrthochronous_iff_futurePointing] at h h'
   exact NormOneLorentzVector.FuturePointing.metric_reflect_not_mem_mem h h'
 
-/-- The homomorphism from `lorentzGroup` to `ℤ₂` whose kernel are the Orthochronous elements. -/
+/-- The homomorphism from `LorentzGroup` to `ℤ₂` whose kernel are the Orthochronous elements. -/
 def orthchroRep : LorentzGroup d →* ℤ₂ where
   toFun := orthchroMap
   map_one' := orthchroMap_IsOrthochronous (by simp [IsOrthochronous])

HepLean/SpaceTime/LorentzGroup/Proper.lean

@@ -122,7 +122,7 @@ lemma IsProper_iff (Λ : LorentzGroup d) : IsProper Λ ↔ detRep Λ = 1 := by
   rw [detRep_apply, detRep_apply, detContinuous_eq_iff_det_eq]
   simp only [IsProper, lorentzGroupIsGroup_one_coe, det_one]
 
-lemma id_IsProper : (@IsProper d) 1 := by
+lemma id_IsProper : @IsProper d 1 := by
   simp [IsProper]
 
 lemma isProper_on_connected_component {Λ Λ' : LorentzGroup d} (h : Λ' ∈ connectedComponent Λ) :

HepLean/SpaceTime/LorentzVector/AsSelfAdjointMatrix.lean

@@ -75,12 +75,12 @@ noncomputable def toSelfAdjointMatrix :
     ext i j
     fin_cases i <;> fin_cases j <;>
       field_simp [fromSelfAdjointMatrix', toMatrix, conj_ofReal]
-    exact conj_eq_iff_re.mp (congrArg (fun M => M 0 0) $ selfAdjoint.mem_iff.mp x.2 )
+    exact conj_eq_iff_re.mp (congrArg (fun M => M 0 0) $ selfAdjoint.mem_iff.mp x.2)
     have h01 := congrArg (fun M => M 0 1) $ selfAdjoint.mem_iff.mp x.2
     simp only [Fin.isValue, star_apply, RCLike.star_def] at h01
     rw [← h01, RCLike.conj_eq_re_sub_im]
     rfl
-    exact conj_eq_iff_re.mp (congrArg (fun M => M 1 1) $ selfAdjoint.mem_iff.mp x.2 )
+    exact conj_eq_iff_re.mp (congrArg (fun M => M 1 1) $ selfAdjoint.mem_iff.mp x.2)
   map_add' x y := by
     ext i j : 2
     simp only [toSelfAdjointMatrix'_coe, add_apply, ofReal_add, of_apply, cons_val', empty_val',

HepLean/SpaceTime/MinkowskiMetric.lean

@@ -190,7 +190,7 @@ lemma self_spaceReflection_eq_zero_iff : ⟪v, v.spaceReflection⟫ₘ = 0 ↔ v
 /-- The metric tensor is non-degenerate. -/
 lemma nondegenerate : (∀ w, ⟪w, v⟫ₘ = 0) ↔ v = 0 := by
   refine Iff.intro (fun h => ?_) (fun h => ?_)
-  · exact (self_spaceReflection_eq_zero_iff _ ).mp ((symm _ _).trans $ h v.spaceReflection)
+  · exact (self_spaceReflection_eq_zero_iff _).mp ((symm _ _).trans $ h v.spaceReflection)
   · simp [h]
 
 /-!

HepLean/StandardModel/HiggsBoson/PointwiseInnerProd.lean

@@ -95,7 +95,7 @@ lemma smooth_innerProd (φ1 φ2 : HiggsField) : Smooth 𝓘(ℝ, SpaceTime) 𝓘
 /-- Given a `HiggsField`, the map `SpaceTime → ℝ` obtained by taking the square norm of the
   pointwise Higgs vector. -/
 @[simp]
-def normSq (φ : HiggsField) : SpaceTime → ℝ := fun x => ( ‖φ x‖ ^ 2)
+def normSq (φ : HiggsField) : SpaceTime → ℝ := fun x => ‖φ x‖ ^ 2
 
 /-- Notation for the norm squared of a Higgs field. -/
 scoped[StandardModel.HiggsField] notation "‖" φ1 "‖_H ^ 2" => normSq φ1

HepLean/StandardModel/HiggsBoson/Potential.lean

@@ -34,7 +34,7 @@ open SpaceTime
 
 /-- The Higgs potential of the form `- μ² * |φ|² + 𝓵 * |φ|⁴`. -/
 @[simp]
-def potential (μ2 𝓵 : ℝ ) (φ : HiggsField) (x : SpaceTime) : ℝ :=
+def potential (μ2 𝓵 : ℝ) (φ : HiggsField) (x : SpaceTime) : ℝ :=
   - μ2 * ‖φ‖_H ^ 2 x + 𝓵 * ‖φ‖_H ^ 2 x * ‖φ‖_H ^ 2 x
 
 /-!
@@ -94,7 +94,7 @@ lemma snd_term_nonneg (φ : HiggsField) (x : SpaceTime) :
     and_self]
 
 lemma as_quad (μ2 𝓵 : ℝ) (φ : HiggsField) (x : SpaceTime) :
-    𝓵 * ‖φ‖_H ^ 2 x * ‖φ‖_H ^ 2 x + (- μ2 ) * ‖φ‖_H ^ 2 x + (- potential μ2 𝓵 φ x) = 0 := by
+    𝓵 * ‖φ‖_H ^ 2 x * ‖φ‖_H ^ 2 x + (- μ2) * ‖φ‖_H ^ 2 x + (- potential μ2 𝓵 φ x) = 0 := by
   simp only [normSq, neg_mul, potential, neg_add_rev, neg_neg]
   ring
 
@@ -237,7 +237,7 @@ lemma IsMinOn_iff_of_μSq_nonpos {μ2 : ℝ} (hμ2 : μ2 ≤ 0) :
     have h0 := isMinOn_univ_iff.mp h 0
     have h1 := bounded_below_of_μSq_nonpos h𝓵 hμ2 φ x
     simp only at h0
-    rw [(eq_bound_iff_of_μSq_nonpos h𝓵 hμ2 0 0 ).mpr (by rfl)] at h0
+    rw [(eq_bound_iff_of_μSq_nonpos h𝓵 hμ2 0 0).mpr (by rfl)] at h0
     exact (Real.partialOrder.le_antisymm _ _ h1 h0).symm
   · exact eq_bound_IsMinOn_of_μSq_nonpos h𝓵 hμ2 φ x
 

scripts/hepLean_style_lint.lean

@@ -46,6 +46,19 @@ def doubleSpaceLinter : HepLeanTextLinter := fun lines ↦ Id.run do
     else none)
   errors.toArray
 
+/-- Substring linter. -/
+def substringLinter (s : String) : HepLeanTextLinter := fun lines ↦ Id.run do
+  let enumLines := (lines.toList.enumFrom 1)
+  let errors := enumLines.filterMap (fun (lno, l) ↦
+    if String.containsSubstr l s then
+      let k := (Substring.findAllSubstr l s).toList.getLast?
+      let col := match k with
+        | none => 1
+        | some k => String.offsetOfPos l k.stopPos
+      some (s!" Found instance of substring {s}.", lno, col)
+    else none)
+  errors.toArray
+
 structure HepLeanErrorContext where
   /-- The underlying `message`. -/
   error : String
@@ -64,7 +77,8 @@ def hepLeanLintFile (path : FilePath) : IO Bool := do
   let lines ← IO.FS.lines path
   let allOutput := (Array.map (fun lint ↦
     (Array.map (fun (e, n, c) ↦ HepLeanErrorContext.mk e n c path)) (lint lines)))
-    #[doubleEmptyLineLinter, doubleSpaceLinter]
+    #[doubleEmptyLineLinter, doubleSpaceLinter, substringLinter ".-/", substringLinter " )",
+    substringLinter "( ", substringLinter "=by", substringLinter "  def "]
   let errors := allOutput.flatten
   printErrors errors
   return errors.size > 0
@@ -72,7 +86,7 @@ def hepLeanLintFile (path : FilePath) : IO Bool := do
 def main (_ : List String) : IO UInt32 := do
   initSearchPath (← findSysroot)
   let mods : Name :=  `HepLean
-  let imp :  Import := {module := mods}
+  let imp : Import := {module := mods}
   let mFile ← findOLean imp.module
   unless (← mFile.pathExists) do
         throw <| IO.userError s!"object file '{mFile}' of module {imp.module} does not exist"
@@ -85,4 +99,6 @@ def main (_ : List String) : IO UInt32 := do
       warned := true
   if warned then
     throw <| IO.userError s!"Errors found."
+  else
+    IO.println "No linting issues found."
   return 0