refactor: Text based Lint

HepLean/Tensors/ComplexLorentz/Basic.lean

@@ -209,10 +209,10 @@ lemma basis_contr (c : complexLorentzTensor.C) (i : Fin (complexLorentzTensor.re
   | Color.up => Lorentz.contrCoContraction_basis _ _
   | Color.down => Lorentz.coContrContraction_basis _ _
 
-instance  {n : ℕ} {c : Fin n → complexLorentzTensor.C} :
+instance {n : ℕ} {c : Fin n → complexLorentzTensor.C} :
     DecidableEq (OverColor.mk c).left := instDecidableEqFin n
 
-instance  {n : ℕ} {c : Fin n → complexLorentzTensor.C} :
+instance {n : ℕ} {c : Fin n → complexLorentzTensor.C} :
     Fintype (OverColor.mk c).left := Fin.fintype n
 
 instance {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
@@ -220,6 +220,5 @@ instance {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
     Decidable (σ = σ') :=
   decidable_of_iff _ (OverColor.Hom.ext_iff σ σ')
 
-
 end complexLorentzTensor
 end

HepLean/Tensors/ComplexLorentz/Bispinors/Basic.lean

@@ -76,7 +76,7 @@ lemma tensorNode_contrBispinorDown (p : complexContr) :
   rw [contrBispinorDown, tensorNode_tensor]
 
 /-- The definitional tensor node relation for `coBispinorUp`. -/
-lemma tensorNode_coBispinorUp  (p : complexCo) :
+lemma tensorNode_coBispinorUp (p : complexCo) :
     {coBispinorUp p | α β}ᵀ.tensor = {pauliContr | μ α β ⊗ p | μ}ᵀ.tensor := by
   rw [coBispinorUp, tensorNode_tensor]
 
@@ -94,23 +94,26 @@ lemma tensorNode_coBispinorDown (p : complexCo) :
 -/
 
 lemma contrBispinorDown_expand (p : complexContr) :
-    {contrBispinorDown p | α β}ᵀ.tensor = {Fermion.altLeftMetric | α α' ⊗ Fermion.altRightMetric | β β' ⊗
+    {contrBispinorDown p | α β}ᵀ.tensor =
+    {Fermion.altLeftMetric | α α' ⊗ Fermion.altRightMetric | β β' ⊗
     (pauliCo | μ α β ⊗ p | μ)}ᵀ.tensor := by
   rw [tensorNode_contrBispinorDown p]
   rw [contr_tensor_eq <| contr_tensor_eq <| prod_tensor_eq_snd <| tensorNode_contrBispinorUp p]
 
 lemma coBispinorDown_expand (p : complexCo) :
-    {coBispinorDown p | α β}ᵀ.tensor = {Fermion.altLeftMetric | α α' ⊗ Fermion.altRightMetric | β β' ⊗
+    {coBispinorDown p | α β}ᵀ.tensor =
+    {Fermion.altLeftMetric | α α' ⊗ Fermion.altRightMetric | β β' ⊗
     (pauliContr | μ α β ⊗ p | μ)}ᵀ.tensor := by
   rw [tensorNode_coBispinorDown p]
   rw [contr_tensor_eq <| contr_tensor_eq <| prod_tensor_eq_snd <| tensorNode_coBispinorUp p]
 
 set_option maxRecDepth 5000 in
 lemma contrBispinorDown_eq_pauliCoDown_contr (p : complexContr) :
-    {contrBispinorDown p | α β = pauliCoDown | μ α β ⊗ p | μ}ᵀ  := by
+    {contrBispinorDown p | α β = pauliCoDown | μ α β ⊗ p | μ}ᵀ := by
   conv =>
     rhs
-    rw [perm_tensor_eq <| contr_tensor_eq <| prod_tensor_eq_fst <| pauliCoDown_eq_metric_mul_pauliCo]
+    rw [perm_tensor_eq <| contr_tensor_eq <| prod_tensor_eq_fst <|
+      pauliCoDown_eq_metric_mul_pauliCo]
     rw [perm_tensor_eq <| contr_tensor_eq <| prod_perm_left _ _ _ _]
     rw [perm_tensor_eq <| perm_contr_congr 2 2]
     rw [perm_perm]
@@ -118,12 +121,14 @@ lemma contrBispinorDown_eq_pauliCoDown_contr (p : complexContr) :
     rw [perm_tensor_eq <| perm_contr_congr 2 2]
     rw [perm_perm]
     apply (perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| perm_eq_id _ rfl _).trans
-    rw [perm_tensor_eq <| contr_tensor_eq <|  contr_tensor_eq <| contr_prod _ _ _]
+    rw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| contr_prod _ _ _]
     rw [perm_tensor_eq <| contr_tensor_eq <| perm_contr_congr 1 3]
     rw [perm_tensor_eq <| perm_contr_congr 2 2]
     rw [perm_perm]
-    erw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| perm_eq_id _ rfl _]
-    rw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| prod_assoc' _ _ _ _ _ _]
+    erw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <|
+      perm_eq_id _ rfl _]
+    rw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <|
+      prod_assoc' _ _ _ _ _ _]
     rw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| perm_contr_congr 0 4]
     rw [perm_tensor_eq <| contr_tensor_eq <| perm_contr_congr 1 3]
     rw [perm_tensor_eq <| perm_contr_congr 2 2]
@@ -144,10 +149,11 @@ lemma contrBispinorDown_eq_pauliCoDown_contr (p : complexContr) :
 
 set_option maxRecDepth 5000 in
 lemma coBispinorDown_eq_pauliContrDown_contr (p : complexCo) :
-    {coBispinorDown p | α β = pauliContrDown | μ α β ⊗ p | μ}ᵀ  := by
+    {coBispinorDown p | α β = pauliContrDown | μ α β ⊗ p | μ}ᵀs := by
   conv =>
     rhs
-    rw [perm_tensor_eq <| contr_tensor_eq <| prod_tensor_eq_fst <| pauliContrDown_eq_metric_mul_pauliContr]
+    rw [perm_tensor_eq <| contr_tensor_eq <| prod_tensor_eq_fst <|
+      pauliContrDown_eq_metric_mul_pauliContr]
     rw [perm_tensor_eq <| contr_tensor_eq <| prod_perm_left _ _ _ _]
     rw [perm_tensor_eq <| perm_contr_congr 2 2]
     rw [perm_perm]
@@ -155,12 +161,14 @@ lemma coBispinorDown_eq_pauliContrDown_contr (p : complexCo) :
     rw [perm_tensor_eq <| perm_contr_congr 2 2]
     rw [perm_perm]
     apply (perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| perm_eq_id _ rfl _).trans
-    rw [perm_tensor_eq <| contr_tensor_eq <|  contr_tensor_eq <| contr_prod _ _ _]
+    rw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| contr_prod _ _ _]
     rw [perm_tensor_eq <| contr_tensor_eq <| perm_contr_congr 1 3]
     rw [perm_tensor_eq <| perm_contr_congr 2 2]
     rw [perm_perm]
-    erw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| perm_eq_id _ rfl _]
-    rw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| prod_assoc' _ _ _ _ _ _]
+    erw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <|
+      perm_eq_id _ rfl _]
+    rw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <|
+      prod_assoc' _ _ _ _ _ _]
     rw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| perm_contr_congr 0 4]
     rw [perm_tensor_eq <| contr_tensor_eq <| perm_contr_congr 1 3]
     rw [perm_tensor_eq <| perm_contr_congr 2 2]

HepLean/Tensors/ComplexLorentz/PauliMatrices/Basic.lean

@@ -63,7 +63,7 @@ lemma tensorNode_pauliContr : {pauliContr | μ α β}ᵀ.tensor =
   rfl
 
 /-- The definitional tensor node relation for `pauliCo`. -/
-lemma tensorNode_pauliCo : {pauliCo | μ α β}ᵀ.tensor  =
+lemma tensorNode_pauliCo : {pauliCo | μ α β}ᵀ.tensor =
     {Lorentz.coMetric | μ ν ⊗ PauliMatrix.asConsTensor | ν α β}ᵀ.tensor := by
   rfl
 
@@ -111,7 +111,7 @@ lemma pauliCoDown_eq_metric_mul_pauliCo :
     rw [perm_perm]
     rw [perm_tensor_eq <| contr_congr 1 2]
     rw [perm_perm]
-    rw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| prod_comm  _ _ _ _]
+    rw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| prod_comm _ _ _ _]
     rw [perm_tensor_eq <| contr_tensor_eq <| perm_contr _ _]
     rw [perm_tensor_eq <| contr_tensor_eq <| perm_tensor_eq <| contr_congr 5 0]
     rw [perm_tensor_eq <| contr_tensor_eq <| perm_perm _ _ _]
@@ -138,7 +138,7 @@ lemma pauliCoDown_eq_metric_mul_pauliCo :
 set_option maxRecDepth 5000 in
 /-- A rearanging of `pauliContrDown` to place the pauli matrices on the right. -/
 lemma pauliContrDown_eq_metric_mul_pauliContr :
-   {pauliContrDown | μ α' β' = Fermion.altLeftMetric | α α' ⊗
+    {pauliContrDown | μ α' β' = Fermion.altLeftMetric | α α' ⊗
     Fermion.altRightMetric | β β' ⊗ pauliContr | μ α β}ᵀ := by
   conv =>
     lhs
@@ -161,7 +161,7 @@ lemma pauliContrDown_eq_metric_mul_pauliContr :
     rw [perm_perm]
     rw [perm_tensor_eq <| contr_congr 1 2]
     rw [perm_perm]
-    rw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| prod_comm  _ _ _ _]
+    rw [perm_tensor_eq <| contr_tensor_eq <| contr_tensor_eq <| prod_comm _ _ _ _]
     rw [perm_tensor_eq <| contr_tensor_eq <| perm_contr _ _]
     rw [perm_tensor_eq <| contr_tensor_eq <| perm_tensor_eq <| contr_congr 5 0]
     rw [perm_tensor_eq <| contr_tensor_eq <| perm_perm _ _ _]

HepLean/Tensors/ComplexLorentz/PauliMatrices/Basis.lean

@@ -26,7 +26,6 @@ noncomputable section
 namespace complexLorentzTensor
 open Fermion
 
-
 /-!
 
 ## Expanding pauliContr in a basis.
@@ -94,7 +93,6 @@ lemma pauliContr_basis_expand_tree : {pauliContr | μ α β}ᵀ.tensor =
     smul_tensor, neg_smul, one_smul]
   rfl
 
-
 /-- The map to colors one gets when contracting with Pauli matrices on the right. -/
 abbrev pauliMatrixContrMap {n : ℕ} (c : Fin n → complexLorentzTensor.C) :=
   (Sum.elim c ![Color.up, Color.upL, Color.upR] ∘ ⇑finSumFinEquiv.symm)
@@ -325,14 +323,12 @@ lemma basis_contr_pauliMatrix_basis_tree_expand_tensor {n : ℕ} {c : Fin n →
   simp_all only [Function.comp_apply, Nat.succ_eq_add_one, Nat.reduceAdd, Fin.isValue]
   rfl
 
-
 /-!
 
 ## Expanding pauliCo in a basis.
 
 -/
 
-
 /-- The map to color one gets when lowering the indices of pauli matrices. -/
 def pauliCoMap := ((Sum.elim ![Color.down, Color.down] ![Color.up, Color.upL, Color.upR] ∘
   ⇑finSumFinEquiv.symm) ∘ Fin.succAbove 1 ∘ Fin.succAbove 1)