refactor: Lint

HepLean/SpaceTime/LorentzVector/Complex/Metric.lean

@@ -130,7 +130,6 @@ lemma coMetric_apply_one : coMetric.hom (1 : ℂ) = coMetricVal := by
   simp only [Action.instMonoidalCategory_tensorObj_V, Action.instMonoidalCategory_tensorUnit_V,
     coMetric, AddHom.toFun_eq_coe, AddHom.coe_mk, one_smul]
 
-
 /-!
 
 ## Contraction of metrics

HepLean/SpaceTime/LorentzVector/Complex/Unit.lean

@@ -145,10 +145,11 @@ lemma contr_contrCoUnit (x : complexCo) :
     Fintype.sum_sum_type, Finset.univ_unique, Fin.default_eq_zero, Fin.isValue,
     Finset.sum_singleton, Fin.sum_univ_three, tmul_add, add_tmul, smul_tmul, tmul_smul, map_add,
     _root_.map_smul]
-  have h1'  (x y :  CoeSort.coe complexCo) (z :  CoeSort.coe complexContr) :
+  have h1' (x y : CoeSort.coe complexCo) (z : CoeSort.coe complexContr) :
     (α_ complexCo.V complexContr.V complexCo.V).inv (x ⊗ₜ[ℂ] z ⊗ₜ[ℂ] y) = (x ⊗ₜ[ℂ] z) ⊗ₜ[ℂ] y := rfl
   repeat rw [h1']
-  have h1'' ( y :  CoeSort.coe complexCo) (z :  CoeSort.coe complexCo ⊗[ℂ] CoeSort.coe complexContr) :
+  have h1'' (y : CoeSort.coe complexCo)
+    (z : CoeSort.coe complexCo ⊗[ℂ] CoeSort.coe complexContr) :
     (coContrContraction.hom ▷ complexCo.V) (z ⊗ₜ[ℂ] y) = (coContrContraction.hom z) ⊗ₜ[ℂ] y := rfl
   repeat rw (config := { transparency := .instances }) [h1'']
   repeat rw [coContrContraction_basis']
@@ -178,11 +179,14 @@ lemma contr_coContrUnit (x : complexContr) :
     Fintype.sum_sum_type, Finset.univ_unique, Fin.default_eq_zero, Fin.isValue,
     Finset.sum_singleton, Fin.sum_univ_three, tmul_add, add_tmul, smul_tmul, tmul_smul, map_add,
     _root_.map_smul]
-  have h1' (x y :  CoeSort.coe complexContr) (z :  CoeSort.coe complexCo) :
+  have h1' (x y : CoeSort.coe complexContr) (z : CoeSort.coe complexCo) :
-    (α_ complexContr.V complexCo.V complexContr.V).inv (x ⊗ₜ[ℂ] z ⊗ₜ[ℂ] y) = (x ⊗ₜ[ℂ] z) ⊗ₜ[ℂ] y := rfl
+    (α_ complexContr.V complexCo.V complexContr.V).inv
+    (x ⊗ₜ[ℂ] z ⊗ₜ[ℂ] y) = (x ⊗ₜ[ℂ] z) ⊗ₜ[ℂ] y := rfl
   repeat rw [h1']
-  have h1'' ( y :  CoeSort.coe complexContr) (z :  CoeSort.coe complexContr ⊗[ℂ] CoeSort.coe complexCo) :
+  have h1'' (y : CoeSort.coe complexContr)
-    (contrCoContraction.hom ▷ complexContr.V) (z ⊗ₜ[ℂ] y) = (contrCoContraction.hom z) ⊗ₜ[ℂ] y := rfl
+    (z : CoeSort.coe complexContr ⊗[ℂ] CoeSort.coe complexCo) :
+    (contrCoContraction.hom ▷ complexContr.V) (z ⊗ₜ[ℂ] y) =
+    (contrCoContraction.hom z) ⊗ₜ[ℂ] y := rfl
   repeat rw (config := { transparency := .instances }) [h1'']
   repeat rw [contrCoContraction_basis']
   simp only [Fin.isValue, Action.instMonoidalCategory_tensorUnit_V, ↓reduceIte, reduceCtorEq,
@@ -199,7 +203,6 @@ lemma contr_coContrUnit (x : complexContr) :
 
 -/
 
-
 open CategoryTheory
 
 lemma contrCoUnit_symm :

HepLean/SpaceTime/WeylFermion/Metric.lean

@@ -352,8 +352,8 @@ lemma rightAltContraction_apply_metric : (β_ rightHanded altRightHanded).hom.ho
     ((rightHanded.V ◁ rightAltContraction.hom ▷ altRightHanded.V) (((rightHanded.V ◁
     (α_ rightHanded.V altRightHanded.V altRightHanded.V).inv)
     ((α_ rightHanded.V rightHanded.V (altRightHanded.V ⊗ altRightHanded.V)).hom
-    ((x1 ⊗ₜ[ℂ] x2) ⊗ₜ[ℂ] y1 ⊗ₜ[ℂ] y2)))))
+    ((x1 ⊗ₜ[ℂ] x2) ⊗ₜ[ℂ] y1 ⊗ₜ[ℂ] y2))))) = x1 ⊗ₜ[ℂ] ((λ_ altRightHanded.V).hom
-      = x1 ⊗ₜ[ℂ] ((λ_ altRightHanded.V).hom ((rightAltContraction.hom (x2 ⊗ₜ[ℂ] y1)) ⊗ₜ[ℂ] y2)) := rfl
+    ((rightAltContraction.hom (x2 ⊗ₜ[ℂ] y1)) ⊗ₜ[ℂ] y2)) := rfl
   repeat rw (config := { transparency := .instances }) [h1]
   repeat rw [rightAltContraction_basis]
   simp only [Fin.isValue, Fin.val_one, Fin.val_zero, one_ne_zero, ↓reduceIte, zero_tmul, map_zero,
@@ -374,7 +374,8 @@ lemma altRightContraction_apply_metric : (β_ altRightHanded rightHanded).hom.ho
   rw [rightMetricVal_expand_tmul, altRightMetricVal_expand_tmul]
   simp only [Action.instMonoidalCategory_tensorObj_V, Action.instMonoidalCategory_tensorUnit_V,
     Fin.isValue, tmul_add, tmul_neg, sub_tmul, map_add, map_neg, map_sub]
-  have h1 (x1 x2 : altRightHanded) (y1 y2 : rightHanded) : (altRightHanded.V ◁ (λ_ rightHanded.V).hom)
+  have h1 (x1 x2 : altRightHanded) (y1 y2 : rightHanded) :
+    (altRightHanded.V ◁ (λ_ rightHanded.V).hom)
     ((altRightHanded.V ◁ altRightContraction.hom ▷ rightHanded.V) (((altRightHanded.V ◁
     (α_ altRightHanded.V rightHanded.V rightHanded.V).inv)
     ((α_ altRightHanded.V altRightHanded.V (rightHanded.V ⊗ rightHanded.V)).hom

HepLean/SpaceTime/WeylFermion/Unit.lean

@@ -251,7 +251,7 @@ lemma contr_altLeftLeftUnit (x : leftHanded) :
   simp only [Fin.isValue, one_smul]
 
 /-- Contraction on the right with `leftAltLeftUnit` does nothing. -/
-lemma contr_leftAltLeftUnit  (x : altLeftHanded) :
+lemma contr_leftAltLeftUnit (x : altLeftHanded) :
     (λ_ altLeftHanded).hom.hom
     (((altLeftContraction) ▷ altLeftHanded).hom
     ((α_ _ _ altLeftHanded).inv.hom
@@ -333,29 +333,29 @@ lemma contr_rightAltRightUnit (x : altRightHanded) :
 open CategoryTheory
 
 lemma altLeftLeftUnit_symm :
-    (altLeftLeftUnit.hom (1 : ℂ)) = (altLeftHanded ◁ 𝟙 _).hom ((β_ leftHanded altLeftHanded ).hom.hom
+    (altLeftLeftUnit.hom (1 : ℂ)) = (altLeftHanded ◁ 𝟙 _).hom
-    (leftAltLeftUnit.hom (1 : ℂ))) := by
+    ((β_ leftHanded altLeftHanded).hom.hom (leftAltLeftUnit.hom (1 : ℂ))) := by
   rw [altLeftLeftUnit_apply_one, altLeftLeftUnitVal_expand_tmul]
   rw [leftAltLeftUnit_apply_one, leftAltLeftUnitVal_expand_tmul]
   rfl
 
 lemma leftAltLeftUnit_symm :
-    (leftAltLeftUnit.hom (1 : ℂ)) = (leftHanded ◁ 𝟙 _).hom ((β_ altLeftHanded leftHanded ).hom.hom
+    (leftAltLeftUnit.hom (1 : ℂ)) = (leftHanded ◁ 𝟙 _).hom ((β_ altLeftHanded leftHanded).hom.hom
     (altLeftLeftUnit.hom (1 : ℂ))) := by
   rw [altLeftLeftUnit_apply_one, altLeftLeftUnitVal_expand_tmul]
   rw [leftAltLeftUnit_apply_one, leftAltLeftUnitVal_expand_tmul]
   rfl
 
 lemma altRightRightUnit_symm :
-    (altRightRightUnit.hom (1 : ℂ)) = (altRightHanded ◁ 𝟙 _).hom ((β_ rightHanded altRightHanded ).hom.hom
+    (altRightRightUnit.hom (1 : ℂ)) = (altRightHanded ◁ 𝟙 _).hom
-    (rightAltRightUnit.hom (1 : ℂ))) := by
+    ((β_ rightHanded altRightHanded).hom.hom (rightAltRightUnit.hom (1 : ℂ))) := by
   rw [altRightRightUnit_apply_one, altRightRightUnitVal_expand_tmul]
   rw [rightAltRightUnit_apply_one, rightAltRightUnitVal_expand_tmul]
   rfl
 
 lemma rightAltRightUnit_symm :
-    (rightAltRightUnit.hom (1 : ℂ)) = (rightHanded ◁ 𝟙 _).hom ((β_ altRightHanded rightHanded ).hom.hom
+    (rightAltRightUnit.hom (1 : ℂ)) = (rightHanded ◁ 𝟙 _).hom
-    (altRightRightUnit.hom (1 : ℂ))) := by
+    ((β_ altRightHanded rightHanded).hom.hom (altRightRightUnit.hom (1 : ℂ))) := by
   rw [altRightRightUnit_apply_one, altRightRightUnitVal_expand_tmul]
   rw [rightAltRightUnit_apply_one, rightAltRightUnitVal_expand_tmul]
   rfl

HepLean/Tensors/ComplexLorentz/Basic.lean

@@ -183,7 +183,7 @@ def complexLorentzTensor : TensorSpecies where
     | Color.downR => Fermion.rightAltRightUnit_symm
     | Color.up => Lorentz.coContrUnit_symm
     | Color.down => Lorentz.contrCoUnit_symm
-  contr_metric :=  fun c =>
+  contr_metric := fun c =>
     match c with
     | Color.upL => by simpa using Fermion.leftAltContraction_apply_metric
     | Color.downL => by simpa using Fermion.altLeftContraction_apply_metric