refactor: LInt

HepLean/Lorentz/ComplexVector/Basic.lean

@@ -138,7 +138,7 @@ lemma inclCongrRealLorentz_ρ (M : SL(2, ℂ)) (v : ContrMod 3) :
   change _ = ContrMod.toFin1dℝ ((SL2C.toLorentzGroup M) *ᵥ v)
   simp only [SL2C.toLorentzGroup_apply_coe, ContrMod.mulVec_toFin1dℝ]
 
-/-! TODO: Rename.-/
+/-! TODO: Rename. -/
 lemma SL2CRep_ρ_basis (M : SL(2, ℂ)) (i : Fin 1 ⊕ Fin 3) :
     (complexContr.ρ M) (complexContrBasis i) =
     ∑ j, (SL2C.toLorentzGroup M).1 j i •
@@ -150,6 +150,6 @@ lemma SL2CRep_ρ_basis (M : SL(2, ℂ)) (i : Fin 1 ⊕ Fin 3) :
   simp only [LinearMap.map_smulₛₗ, ofRealHom_eq_coe, coe_smul]
   rw [complexContrBasis_of_real]
 
-/-! TODO: Include relation to real Lorentz vectors.-/
+/-! TODO: Include relation to real Lorentz vectors. -/
 end Lorentz
 end

HepLean/Lorentz/Group/Basic.lean

@@ -85,7 +85,6 @@ lemma dual_mem (h : Λ ∈ LorentzGroup d) : dual Λ ∈ LorentzGroup d := by
   rw [mem_iff_dual_mul_self, dual_dual]
   exact mem_iff_self_mul_dual.mp h
 
-
 end LorentzGroup
 
 /-!
@@ -187,7 +186,7 @@ lemma comm_minkowskiMatrix : Λ.1 * minkowskiMatrix = minkowskiMatrix * (transpo
   rw [h1]
   simp
 
-lemma minkowskiMatrix_comm : minkowskiMatrix *  Λ.1  = (transpose Λ⁻¹).1 * minkowskiMatrix := by
+lemma minkowskiMatrix_comm : minkowskiMatrix * Λ.1 = (transpose Λ⁻¹).1 * minkowskiMatrix := by
   conv_rhs => rw [← @transpose_mul_minkowskiMatrix_mul_self d Λ]
   rw [← transpose_inv, coe_inv, transpose_val]
   rw [← mul_assoc, ← mul_assoc]

HepLean/Lorentz/Group/Boosts.lean

@@ -39,7 +39,7 @@ def genBoostAux₁ (u v : FuturePointing d) : ContrMod d →ₗ[ℝ] ContrMod d
   map_add' x y := by
     simp [map_add, LinearMap.add_apply, tmul_add, add_tmul, mul_add, add_smul]
   map_smul' c x := by
-    simp only [ Action.instMonoidalCategory_tensorObj_V,
+    simp only [Action.instMonoidalCategory_tensorObj_V,
       Action.instMonoidalCategory_tensorUnit_V, CategoryTheory.Equivalence.symm_inverse,
       Action.functorCategoryEquivalence_functor, Action.FunctorCategoryEquivalence.functor_obj_obj,
       smul_tmul, tmul_smul, map_smul, smul_eq_mul, RingHom.id_apply]
@@ -74,7 +74,7 @@ lemma genBoostAux₂_self (u : FuturePointing d) : genBoostAux₂ u u = - genBoo
   congr 1
   rw [u.1.2]
   conv => lhs; lhs; rhs; rhs; change 1
-  rw [show 1 + (1 : ℝ) = (2 : ℝ ) by ring]
+  rw [show 1 + (1 : ℝ) = (2 : ℝ) by ring]
   simp only [isUnit_iff_ne_zero, ne_eq, OfNat.ofNat_ne_zero, not_false_eq_true,
     IsUnit.div_mul_cancel]
   rw [← (two_smul ℝ u.val.val)]
@@ -137,15 +137,15 @@ lemma toMatrix_mulVec (u v : FuturePointing d) (x : Contr d) :
 open minkowskiMatrix in
 @[simp]
 lemma toMatrix_apply (u v : FuturePointing d) (μ ν : Fin 1 ⊕ Fin d) :
-    (toMatrix u v) μ ν = η μ μ * (toField d ⟪ContrMod.stdBasis μ, ContrMod.stdBasis ν⟫ₘ + 2 *
+    (toMatrix u v) μ ν = η μ μ * (⟪ContrMod.stdBasis μ, ContrMod.stdBasis ν⟫ₘ + 2 *
-     toField d ⟪ContrMod.stdBasis ν, u.val.val⟫ₘ * toField d  ⟪ContrMod.stdBasis μ, v.val.val⟫ₘ
+    ⟪ContrMod.stdBasis ν, u.val.val⟫ₘ * ⟪ContrMod.stdBasis μ, v.val.val⟫ₘ
-    - toField d  ⟪ContrMod.stdBasis μ, u.val.val + v.val.val⟫ₘ *
+    - ⟪ContrMod.stdBasis μ, u.val.val + v.val.val⟫ₘ *
-    toField d  ⟪ContrMod.stdBasis ν, u.val.val + v.val.val⟫ₘ /
+    ⟪ContrMod.stdBasis ν, u.val.val + v.val.val⟫ₘ /
-    (1 + toField d  ⟪u.val.val, v.val.val⟫ₘ)) := by
+    (1 + ⟪u.val.val, v.val.val⟫ₘ)) := by
   rw [contrContrContractField.matrix_apply_stdBasis (Λ := toMatrix u v) μ ν, toMatrix_mulVec]
-  simp only [genBoost, genBoostAux₁, genBoostAux₂, map_add, smul_add, neg_smul, LinearMap.add_apply,
+  simp only [genBoost, genBoostAux₁, genBoostAux₂, smul_add, neg_smul, LinearMap.add_apply,
-    LinearMap.id_apply, LinearMap.coe_mk, AddHom.coe_mk, contrContrContractField.basis_left, map_smul, smul_eq_mul, map_neg,
+    LinearMap.id_apply, LinearMap.coe_mk, AddHom.coe_mk, contrContrContractField.basis_left,
-    mul_eq_mul_left_iff, toField_apply]
+    map_add, map_smul, map_neg, toField_apply, mul_eq_mul_left_iff]
   ring_nf
   simp only [Pi.add_apply, Action.instMonoidalCategory_tensorObj_V,
     Action.instMonoidalCategory_tensorUnit_V, CategoryTheory.Equivalence.symm_inverse,
@@ -186,9 +186,9 @@ lemma toMatrix_in_lorentzGroup (u v : FuturePointing d) : (toMatrix u v) ∈ Lor
   rw [LorentzGroup.mem_iff_invariant]
   intro x y
   rw [toMatrix_mulVec, toMatrix_mulVec]
-  have h1 : (((1 +  ⟪u.1.1, v.1.1⟫ₘ)) * (1 +  ⟪u.1.1, v.1.1⟫ₘ)) •
+  have h1 : (((1 + ⟪u.1.1, v.1.1⟫ₘ)) * (1 + ⟪u.1.1, v.1.1⟫ₘ)) •
-       (contrContrContractField ((genBoost u v) y ⊗ₜ[ℝ] (genBoost u v) x))
+      (contrContrContractField ((genBoost u v) y ⊗ₜ[ℝ] (genBoost u v) x))
-    = (((1 +  ⟪u.1.1, v.1.1⟫ₘ)) * (1 +  ⟪u.1.1, v.1.1⟫ₘ)) • ⟪y, x⟫ₘ := by
+      = (((1 + ⟪u.1.1, v.1.1⟫ₘ)) * (1 + ⟪u.1.1, v.1.1⟫ₘ)) • ⟪y, x⟫ₘ := by
     conv_lhs =>
       erw [← map_smul]
       rw [← smul_smul]
@@ -200,7 +200,7 @@ lemma toMatrix_in_lorentzGroup (u v : FuturePointing d) : (toMatrix u v) ∈ Lor
         contrContrContractField.symm u.1.1 x]
     simp only [smul_eq_mul]
     ring
-  have hn (a  : ℝ ) {b c : ℝ} (h : a ≠ 0) (hab : a * b = a * c ) : b =  c := by
+  have hn (a : ℝ) {b c : ℝ} (h : a ≠ 0) (hab : a * b = a * c) : b = c := by
     simp_all only [smul_eq_mul, ne_eq, mul_eq_mul_left_iff, or_false]
   refine hn _ ?_ h1
   simpa using (FuturePointing.one_add_metric_non_zero u v)

HepLean/Lorentz/Group/Orthochronous.lean

@@ -86,7 +86,7 @@ lemma orthchroMapReal_on_IsOrthochronous {Λ : LorentzGroup d} (h : IsOrthochron
 lemma orthchroMapReal_on_not_IsOrthochronous {Λ : LorentzGroup d} (h : ¬ IsOrthochronous Λ) :
     orthchroMapReal Λ = - 1 := by
   rw [not_orthochronous_iff_le_neg_one] at h
-  change stepFunction (_)= - 1
+  change stepFunction _ = - 1
   rw [stepFunction, if_pos]
   exact h
 

HepLean/Lorentz/MinkowskiMatrix.lean

@@ -10,7 +10,6 @@ import Mathlib.Algebra.Lie.Classical
 
 # The Minkowski matrix
 
-
 -/
 
 open Matrix
@@ -98,7 +97,6 @@ lemma mulVec_inr_i (v : (Fin 1 ⊕ Fin d) → ℝ) (i : Fin d) :
   simp only [mulVec, minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal, mulVec_diagonal]
   simp only [diagonal_dotProduct, Sum.elim_inr, neg_mul, one_mul]
 
-
 variable (Λ Λ' : Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ)
 
 /-- The dual of a matrix with respect to the Minkowski metric. -/

HepLean/Lorentz/PauliMatrices/Basic.lean

@@ -19,7 +19,7 @@ open Complex
 open Matrix
 
 /-- The zeroth Pauli-matrix as a `2 x 2` complex matrix.
-  That is the matrix `!![1, 0; 0, 1]`.  -/
+  That is the matrix `!![1, 0; 0, 1]`. -/
 def σ0 : Matrix (Fin 2) (Fin 2) ℂ := !![1, 0; 0, 1]
 
 /-- The first Pauli-matrix as a `2 x 2` complex matrix.

HepLean/Lorentz/RealVector/Basic.lean

@@ -49,7 +49,7 @@ lemma continuous_contr {T : Type} [TopologicalSpace T] (f : T → Contr d)
   exact continuous_induced_rng.mpr h
 
 lemma contr_continuous {T : Type} [TopologicalSpace T] (f : Contr d → T)
-    (h : Continuous (f ∘ (@ContrMod.toFin1dℝEquiv d).symm)): Continuous f := by
+    (h : Continuous (f ∘ (@ContrMod.toFin1dℝEquiv d).symm)) : Continuous f := by
   let x := Equiv.toHomeomorphOfIsInducing (@ContrMod.toFin1dℝEquiv d).toEquiv
     toFin1dℝEquiv_isInducing
   rw [← Homeomorph.comp_continuous_iff' x.symm]

HepLean/Lorentz/RealVector/Contraction.lean

@@ -78,7 +78,7 @@ def coModContrModBi (d : ℕ) : CoMod d →ₗ[ℝ] ContrMod d →ₗ[ℝ] ℝ w
 def contrCoContract : Contr d ⊗ Co d ⟶ 𝟙_ (Rep ℝ (LorentzGroup d)) where
   hom := TensorProduct.lift (contrModCoModBi d)
   comm M := TensorProduct.ext' fun ψ φ => by
-    change (M.1 *ᵥ ψ.toFin1dℝ)  ⬝ᵥ ((LorentzGroup.transpose M⁻¹).1 *ᵥ φ.toFin1dℝ) = _
+    change (M.1 *ᵥ ψ.toFin1dℝ) ⬝ᵥ ((LorentzGroup.transpose M⁻¹).1 *ᵥ φ.toFin1dℝ) = _
     rw [dotProduct_mulVec, LorentzGroup.transpose_val,
       vecMul_transpose, mulVec_mulVec, LorentzGroup.coe_inv, inv_mul_of_invertible M.1]
     simp only [one_mulVec, CategoryTheory.Equivalence.symm_inverse,
@@ -101,7 +101,7 @@ lemma contrCoContract_hom_tmul (ψ : Contr d) (φ : Co d) : ⟪ψ, φ⟫ₘ = ψ
 def coContrContract : Co d ⊗ Contr d ⟶ 𝟙_ (Rep ℝ (LorentzGroup d)) where
   hom := TensorProduct.lift (coModContrModBi d)
   comm M := TensorProduct.ext' fun ψ φ => by
-    change ((LorentzGroup.transpose M⁻¹).1 *ᵥ ψ.toFin1dℝ) ⬝ᵥ (M.1 *ᵥ φ.toFin1dℝ)  = _
+    change ((LorentzGroup.transpose M⁻¹).1 *ᵥ ψ.toFin1dℝ) ⬝ᵥ (M.1 *ᵥ φ.toFin1dℝ) = _
     rw [dotProduct_mulVec, LorentzGroup.transpose_val, mulVec_transpose, vecMul_vecMul,
       LorentzGroup.coe_inv, inv_mul_of_invertible M.1]
     simp only [vecMul_one, CategoryTheory.Equivalence.symm_inverse,
@@ -143,7 +143,7 @@ def contrContrContract : Contr d ⊗ Contr d ⟶ 𝟙_ (Rep ℝ (LorentzGroup d)
 
 /-- The linear map from Contr d ⊗ Contr d to ℝ induced by the homomorphism
   `Contr.toCo` and the contraction `contrCoContract`. -/
-def contrContrContractField : (Contr d).V ⊗[ℝ] (Contr d).V →ₗ[ℝ] ℝ  :=
+def contrContrContractField : (Contr d).V ⊗[ℝ] (Contr d).V →ₗ[ℝ] ℝ :=
   contrContrContract.hom
 
 /-- Notation for `contrContrContractField` acting on a tmul. -/
@@ -200,7 +200,7 @@ lemma action_tmul (g : LorentzGroup d) : ⟪(Contr d).ρ g x, (Contr d).ρ g y
   rfl
 
 lemma as_sum : ⟪x, y⟫ₘ = x.val (Sum.inl 0) * y.val (Sum.inl 0) -
-      ∑ i, x.val (Sum.inr i) * y.val (Sum.inr i)  := by
+      ∑ i, x.val (Sum.inr i) * y.val (Sum.inr i) := by
   rw [contrContrContract_hom_tmul]
   simp only [dotProduct, minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal, mulVec_diagonal,
     Fintype.sum_sum_type, Finset.univ_unique, Fin.default_eq_zero, Fin.isValue, Sum.elim_inl,
@@ -244,7 +244,7 @@ lemma dual_mulVec_right : ⟪x, dual Λ *ᵥ y⟫ₘ = ⟪Λ *ᵥ x, y⟫ₘ :=
 lemma dual_mulVec_left : ⟪dual Λ *ᵥ x, y⟫ₘ = ⟪x, Λ *ᵥ y⟫ₘ := by
   rw [symm, dual_mulVec_right, symm]
 
-lemma right_parity : ⟪x, (Contr d).ρ LorentzGroup.parity y⟫ₘ =  ∑ i, x.val i * y.val i := by
+lemma right_parity : ⟪x, (Contr d).ρ LorentzGroup.parity y⟫ₘ = ∑ i, x.val i * y.val i := by
   rw [as_sum]
   simp only [Action.instMonoidalCategory_tensorUnit_V, Fin.isValue, Fintype.sum_sum_type,
     Finset.univ_unique, Fin.default_eq_zero, Finset.sum_singleton]
@@ -258,7 +258,7 @@ lemma right_parity : ⟪x, (Contr d).ρ LorentzGroup.parity y⟫ₘ =  ∑ i, x.
     exact mul_eq_mul_left_iff.mp rfl
   · congr
     funext i
-    change - (x.val (Sum.inr i) * ((η *ᵥ y.toFin1dℝ) (Sum.inr i)))  = _
+    change - (x.val (Sum.inr i) * ((η *ᵥ y.toFin1dℝ) (Sum.inr i))) = _
     simp only [mulVec_inr_i, mul_neg, neg_neg, mul_eq_mul_left_iff]
     exact mul_eq_mul_left_iff.mp rfl
 
@@ -338,7 +338,7 @@ lemma _root_.LorentzGroup.mem_iff_norm : Λ ∈ LorentzGroup d ↔
   rw [ContrMod.mulVec_sub, tmul_sub, sub_tmul, sub_tmul, tmul_sub, sub_tmul, sub_tmul] at hn
   simp only [map_add, LinearMap.add_apply, map_sub, LinearMap.sub_apply] at hp hn
   rw [symm (Λ *ᵥ y) (Λ *ᵥ x), symm y x] at hp hn
-  let e :  𝟙_ (Rep ℝ ↑(LorentzGroup d)) ≃ₗ[ℝ] ℝ :=
+  let e : 𝟙_ (Rep ℝ ↑(LorentzGroup d)) ≃ₗ[ℝ] ℝ :=
     LinearEquiv.refl ℝ (CoeSort.coe (𝟙_ (Rep ℝ ↑(LorentzGroup d))))
   apply e.injective
   have hp' := e.injective.eq_iff.mpr hp
@@ -346,7 +346,7 @@ lemma _root_.LorentzGroup.mem_iff_norm : Λ ∈ LorentzGroup d ↔
   simp only [Action.instMonoidalCategory_tensorUnit_V, Action.instMonoidalCategory_tensorObj_V,
     Equivalence.symm_inverse, Action.functorCategoryEquivalence_functor,
     Action.FunctorCategoryEquivalence.functor_obj_obj, map_add, map_sub] at hp' hn'
-  linear_combination  (norm := ring_nf) (1 / 4) * hp' + (-1/ 4) * hn'
+  linear_combination (norm := ring_nf) (1 / 4) * hp' + (-1/ 4) * hn'
   rw [symm (Λ *ᵥ y) (Λ *ᵥ x), symm y x]
   simp only [Action.instMonoidalCategory_tensorUnit_V, Action.instMonoidalCategory_tensorObj_V,
     Equivalence.symm_inverse, Action.functorCategoryEquivalence_functor,
@@ -373,19 +373,17 @@ lemma le_inl_sq (v : Contr d) : ⟪v, v⟫ₘ ≤ v.val (Sum.inl 0) ^ 2 := by
   refine Fintype.sum_nonneg ?hf
   exact fun i => pow_two_nonneg (v.val (Sum.inr i))
 
-
+lemma ge_abs_inner_product (v w : Contr d) : v.val (Sum.inl 0) * w.val (Sum.inl 0) -
-lemma ge_abs_inner_product (v w : Contr d) : v.val (Sum.inl 0)  * w.val (Sum.inl 0)  -
     ‖⟪v.toSpace, w.toSpace⟫_ℝ‖ ≤ ⟪v, w⟫ₘ := by
   rw [as_sum_toSpace, sub_le_sub_iff_left]
   exact Real.le_norm_self ⟪v.toSpace, w.toSpace⟫_ℝ
 
-lemma ge_sub_norm  (v w : Contr d) : v.val (Sum.inl 0)  * w.val (Sum.inl 0) -
+lemma ge_sub_norm (v w : Contr d) : v.val (Sum.inl 0) * w.val (Sum.inl 0) -
     ‖v.toSpace‖ * ‖w.toSpace‖ ≤ ⟪v, w⟫ₘ := by
   apply le_trans _ (ge_abs_inner_product v w)
   rw [sub_le_sub_iff_left]
   exact norm_inner_le_norm v.toSpace w.toSpace
 
-
 /-!
 
 # The Minkowski metric and the standard basis
@@ -413,7 +411,6 @@ lemma on_basis_mulVec (μ ν : Fin 1 ⊕ Fin d) :
   rw [basis_left, ContrMod.mulVec_toFin1dℝ]
   simp [basis_left, mulVec, dotProduct, ContrMod.stdBasis_apply, ContrMod.toFin1dℝ_eq_val]
 
-
 lemma on_basis (μ ν : Fin 1 ⊕ Fin d) : ⟪ContrMod.stdBasis μ, ContrMod.stdBasis ν⟫ₘ = η μ ν := by
   trans ⟪ContrMod.stdBasis μ, 1 *ᵥ ContrMod.stdBasis ν⟫ₘ
   · rw [ContrMod.one_mulVec]
@@ -424,10 +421,9 @@ lemma on_basis (μ ν : Fin 1 ⊕ Fin d) : ⟪ContrMod.stdBasis μ, ContrMod.std
   · simp only [Action.instMonoidalCategory_tensorUnit_V, ne_eq, h, not_false_eq_true, one_apply_ne,
     mul_zero, off_diag_zero]
 
-
 lemma matrix_apply_stdBasis (ν μ : Fin 1 ⊕ Fin d) :
-    Λ ν μ = η ν ν * ⟪ ContrMod.stdBasis ν, Λ *ᵥ  ContrMod.stdBasis μ⟫ₘ := by
+    Λ ν μ = η ν ν * ⟪ ContrMod.stdBasis ν, Λ *ᵥ ContrMod.stdBasis μ⟫ₘ := by
-  rw [on_basis_mulVec,  ← mul_assoc]
+  rw [on_basis_mulVec, ← mul_assoc]
   simp [η_apply_mul_η_apply_diag ν]
 
 /-!
@@ -437,7 +433,7 @@ lemma matrix_apply_stdBasis (ν μ : Fin 1 ⊕ Fin d) :
 -/
 
 lemma same_eq_det_toSelfAdjoint (x : ContrMod 3) :
-    ⟪x, x⟫ₘ = det (ContrMod.toSelfAdjoint x).1  := by
+    ⟪x, x⟫ₘ = det (ContrMod.toSelfAdjoint x).1 := by
   rw [ContrMod.toSelfAdjoint_apply_coe]
   simp only [Fin.isValue, as_sum_toSpace,
     PiLp.inner_apply, Function.comp_apply, RCLike.inner_apply, conj_trivial, Fin.sum_univ_three,

HepLean/Lorentz/RealVector/Modules.lean

@@ -86,7 +86,6 @@ lemma toFin1dℝ_eq_val (ψ : ContrMod d) : ψ.toFin1dℝ = ψ.val := by rfl
 @[simps!]
 def stdBasis : Basis (Fin 1 ⊕ Fin d) ℝ (ContrMod d) := Basis.ofEquivFun toFin1dℝEquiv
 
-
 @[simp]
 lemma stdBasis_toFin1dℝEquiv_apply_same (μ : Fin 1 ⊕ Fin d) :
     toFin1dℝEquiv (stdBasis μ) μ = 1 := by
@@ -121,7 +120,7 @@ lemma stdBasis_apply (μ ν : Fin 1 ⊕ Fin d) : (stdBasis μ).val ν = if μ =
 /-- Decomposition of a contrvariant Lorentz vector into the standard basis. -/
 lemma stdBasis_decomp (v : ContrMod d) : v = ∑ i, v.toFin1dℝ i • stdBasis i := by
   apply toFin1dℝEquiv.injective
-  simp only  [map_sum, _root_.map_smul]
+  simp only [map_sum, _root_.map_smul]
   funext μ
   rw [Fintype.sum_apply μ fun c => toFin1dℝEquiv v c • toFin1dℝEquiv (stdBasis c)]
   change _ = ∑ x : Fin 1 ⊕ Fin d, toFin1dℝEquiv v x • (toFin1dℝEquiv (stdBasis x) μ)
@@ -189,7 +188,6 @@ def toSpace (v : ContrMod d) : EuclideanSpace ℝ (Fin d) := v.val ∘ Sum.inr
 
 -/
 
-
 /-- The representation of the Lorentz group acting on `ContrℝModule d`. -/
 def rep : Representation ℝ (LorentzGroup d) (ContrMod d) where
   toFun g := Matrix.toLinAlgEquiv stdBasis g
@@ -237,7 +235,6 @@ lemma toSelfAdjoint_apply_coe (x : ContrMod 3) : (toSelfAdjoint x).1 =
   rw [toSelfAdjoint_apply]
   rfl
 
-
 lemma toSelfAdjoint_stdBasis (i : Fin 1 ⊕ Fin 3) :
     toSelfAdjoint (stdBasis i) = PauliMatrix.σSAL i := by
   rw [toSelfAdjoint_apply]
@@ -352,11 +349,10 @@ lemma stdBasis_apply (μ ν : Fin 1 ⊕ Fin d) : (stdBasis μ).val ν = if μ =
   refine ite_congr ?h₁ (congrFun rfl) (congrFun rfl)
   exact Eq.propIntro (fun a => id (Eq.symm a)) fun a => id (Eq.symm a)
 
-
 /-- Decomposition of a covariant Lorentz vector into the standard basis. -/
 lemma stdBasis_decomp (v : CoMod d) : v = ∑ i, v.toFin1dℝ i • stdBasis i := by
   apply toFin1dℝEquiv.injective
-  simp only  [map_sum, _root_.map_smul]
+  simp only [map_sum, _root_.map_smul]
   funext μ
   rw [Fintype.sum_apply μ fun c => toFin1dℝEquiv v c • toFin1dℝEquiv (stdBasis c)]
   change _ = ∑ x : Fin 1 ⊕ Fin d, toFin1dℝEquiv v x • (toFin1dℝEquiv (stdBasis x) μ)

HepLean/Lorentz/SL2C/Basic.lean

@@ -103,8 +103,8 @@ lemma toMatrix_apply_contrMod (M : SL(2, ℂ)) (v : ContrMod 3) :
   rw [LinearEquiv.apply_symm_apply]
   simp only [ContrMod.toSelfAdjoint, LinearEquiv.trans_symm, LinearEquiv.symm_symm,
     LinearEquiv.trans_apply]
-  change ContrMod.toFin1dℝEquiv.symm ((
+  change ContrMod.toFin1dℝEquiv.symm
-    ((LinearMap.toMatrix PauliMatrix.σSAL PauliMatrix.σSAL) (toLinearMapSelfAdjointMatrix M)))
+    ((((LinearMap.toMatrix PauliMatrix.σSAL PauliMatrix.σSAL) (toLinearMapSelfAdjointMatrix M)))
     *ᵥ (((Finsupp.linearEquivFunOnFinite ℝ ℝ (Fin 1 ⊕ Fin 3)) (PauliMatrix.σSAL.repr a)))) = _
   apply congrArg
   erw [LinearMap.toMatrix_mulVec_repr]
@@ -131,7 +131,6 @@ def toLorentzGroup : SL(2, ℂ) →* LorentzGroup 3 where
     ext1
     simp only [_root_.map_mul, lorentzGroupIsGroup_mul_coe]
 
-
 lemma toLorentzGroup_eq_σSAL (M : SL(2, ℂ)) :
     toLorentzGroup M = LinearMap.toMatrix
     PauliMatrix.σSAL PauliMatrix.σSAL (toLinearMapSelfAdjointMatrix M) := by

HepLean/Lorentz/Weyl/Two.lean

@@ -722,7 +722,7 @@ lemma altLeftAltRightToMatrix_ρ_symm_selfAdjoint (v : Matrix (Fin 2) (Fin 2)
     (SL2C.toLinearMapSelfAdjointMatrix (M.transpose⁻¹) ⟨v, hv⟩) := by
   rw [altLeftAltRightToMatrix_ρ_symm]
   apply congrArg
-  simp only [ MonoidHom.coe_mk, OneHom.coe_mk,
+  simp only [MonoidHom.coe_mk, OneHom.coe_mk,
     SL2C.toLinearMapSelfAdjointMatrix_apply_coe, SpecialLinearGroup.coe_inv,
     SpecialLinearGroup.coe_transpose]
   congr