refactor: Spelling and typos

HepLean/AnomalyCancellation/SM/Permutations.lean

@@ -63,7 +63,7 @@ def repCharges {n : ℕ} : Representation ℚ (PermGroup n) (SMCharges n).Charge
     erw [toSMSpecies_toSpecies_inv]
     rfl
 
-/-- The species chages of a set of charges acted on by a family permutation is the permutation
+/-- The species charges of a set of charges acted on by a family permutation is the permutation
   of those species charges with the corresponding part of the family permutation. -/
 lemma repCharges_toSpecies (f : PermGroup n) (S : (SMCharges n).Charges) (j : Fin 5) :
     toSpecies j (repCharges f S) = toSpecies j S ∘ f⁻¹ j := by
@@ -78,7 +78,7 @@ lemma toSpecies_sum_invariant (m : ℕ) (f : PermGroup n) (S : (SMCharges n).Cha
   exact Fintype.sum_equiv (f⁻¹ j) (fun x => ((fun a => a ^ m) ∘ (toSpecies j) S ∘ ⇑(f⁻¹ j)) x)
     (fun x => ((fun a => a ^ m) ∘ (toSpecies j) S) x) (congrFun rfl)
 
-/-- The gravitional anomaly equations is invariant under family permutations. -/
+/-- The gravitational anomaly equations is invariant under family permutations. -/
 lemma accGrav_invariant (f : PermGroup n) (S : (SMCharges n).Charges) :
     accGrav (repCharges f S) = accGrav S := accGrav_ext
   (by simpa using toSpecies_sum_invariant 1 f S)

HepLean/BeyondTheStandardModel/GeorgiGlashow/Basic.lean

@@ -38,7 +38,7 @@ informal_lemma inclSM_ker where
   deps := [``inclSM, ``StandardModel.gaugeGroupℤ₆SubGroup]
 
 /-- The group embedding from `StandardModel.GaugeGroupℤ₆` to `GaugeGroupI` induced by `inclSM` by
-quotienting by the kernal `inclSM_ker`.
+quotienting by the kernel `inclSM_ker`.
 -/
 informal_definition embedSMℤ₆ where
   deps := [``inclSM, ``StandardModel.GaugeGroupℤ₆, ``GaugeGroupI, ``inclSM_ker]

HepLean/BeyondTheStandardModel/PatiSalam/Basic.lean

@@ -43,7 +43,7 @@ informal_lemma inclSM_ker where
   deps := [``inclSM, ``StandardModel.gaugeGroupℤ₃SubGroup]
 
 /-- The group embedding from `StandardModel.GaugeGroupℤ₃` to `GaugeGroupI` induced by `inclSM` by
-quotienting by the kernal `inclSM_ker`.
+quotienting by the kernel `inclSM_ker`.
 -/
 informal_definition embedSMℤ₃ where
   deps := [``inclSM, ``StandardModel.GaugeGroupℤ₃, ``GaugeGroupI, ``inclSM_ker]

HepLean/Lorentz/ComplexTensor/PauliMatrices/Basis.lean

@@ -216,7 +216,7 @@ lemma basis_contr_pauliMatrix_basis_tree_expand' {n : ℕ} {c : Fin n → comple
   rfl
 
 /-- The map to color which appears when contracting a basis vector with
-  puali matrices. -/
+  Pauli matrices. -/
 def pauliMatrixBasisProdMap
     {n : ℕ} {c : Fin n → complexLorentzTensor.C}
     (b : Π k, Fin (complexLorentzTensor.repDim (c k))) (i1 i2 i3 : Fin 4) :

HepLean/Lorentz/Group/Boosts.lean

@@ -43,7 +43,7 @@ def genBoostAux₁ (u v : FuturePointing d) : ContrMod d →ₗ[ℝ] ContrMod d
       smul_tmul, tmul_smul, map_smul, smul_eq_mul, RingHom.id_apply]
     rw [← mul_assoc, mul_comm 2 c, mul_assoc, mul_smul]
 
-/-- An auxiliary linear map used in the definition of a genearlised boost. -/
+/-- An auxiliary linear map used in the definition of a generalised boost. -/
 def genBoostAux₂ (u v : FuturePointing d) : ContrMod d →ₗ[ℝ] ContrMod d where
   toFun x := - (⟪x, u.1.1 + v.1.1⟫ₘ / (1 + ⟪u.1.1, v.1.1⟫ₘ)) • (u.1.1 + v.1.1)
   map_add' x y := by

HepLean/Lorentz/Group/Orthochronous.lean

@@ -113,7 +113,7 @@ lemma orthchroMapReal_minus_one_or_one (Λ : LorentzGroup d) :
 
 local notation "ℤ₂" => Multiplicative (ZMod 2)
 
-/-- A continuous map from `lorentzGroup` to `ℤ₂` whose kernal are the Orthochronous elements. -/
+/-- A continuous map from `lorentzGroup` to `ℤ₂` whose kernel are the Orthochronous elements. -/
 def orthchroMap : C(LorentzGroup d, ℤ₂) :=
   ContinuousMap.comp coeForℤ₂ {
     toFun := fun Λ => ⟨orthchroMapReal Λ, orthchroMapReal_minus_one_or_one Λ⟩,

HepLean/Lorentz/MinkowskiMatrix.lean

@@ -163,7 +163,7 @@ lemma dual_apply (μ ν : Fin 1 ⊕ Fin d) :
     diagonal_mul, transpose_apply, diagonal_apply_eq]
 
 /-- The components of the Minkowski dual of a matrix multiplied by the Minkowski matrix
-  in tems of the original matrix. -/
+  in terms of the original matrix. -/
 lemma dual_apply_minkowskiMatrix (μ ν : Fin 1 ⊕ Fin d) :
     dual Λ μ ν * η ν ν = η μ μ * Λ ν μ := by
   rw [dual_apply, mul_assoc]

HepLean/Lorentz/PauliMatrices/SelfAdjoint.lean

@@ -338,7 +338,7 @@ lemma σSAL_decomp (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
     ring
 
 /-- The component of a self-adjoint matrix in the direction `σ0` under
-  the basis formed by the covaraiant Pauli matrices. -/
+  the basis formed by the covariant Pauli matrices. -/
 @[simp]
 lemma σSAL_repr_inl_0 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
     σSAL.repr M (Sum.inl 0) = 1 / 2 * Matrix.trace (σ0 * M.1) := by
@@ -355,7 +355,7 @@ lemma σSAL_repr_inl_0 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
   simp [σSAL]
 
 /-- The component of a self-adjoint matrix in the direction `-σ1` under
-  the basis formed by the covaraiant Pauli matrices. -/
+  the basis formed by the covariant Pauli matrices. -/
 @[simp]
 lemma σSAL_repr_inr_0 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
     σSAL.repr M (Sum.inr 0) = - 1 / 2 * Matrix.trace (σ1 * M.1) := by
@@ -372,7 +372,7 @@ lemma σSAL_repr_inr_0 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
   simp [σSAL]
 
 /-- The component of a self-adjoint matrix in the direction `-σ2` under
-  the basis formed by the covaraiant Pauli matrices. -/
+  the basis formed by the covariant Pauli matrices. -/
 @[simp]
 lemma σSAL_repr_inr_1 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
     σSAL.repr M (Sum.inr 1) = - 1 / 2 * Matrix.trace (σ2 * M.1) := by
@@ -389,7 +389,7 @@ lemma σSAL_repr_inr_1 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
   simp [σSAL]
 
 /-- The component of a self-adjoint matrix in the direction `-σ3` under
-  the basis formed by the covaraiant Pauli matrices. -/
+  the basis formed by the covariant Pauli matrices. -/
 @[simp]
 lemma σSAL_repr_inr_2 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
     σSAL.repr M (Sum.inr 2) = - 1 / 2 * Matrix.trace (σ3 * M.1) := by

HepLean/Mathematics/List/InsertionSort.lean

@@ -23,7 +23,7 @@ lemma insertionSortMin_lt_length_succ {α : Type} (r : α → α → Prop) [Deci
   rw [eraseIdx_length']
   simp
 
-/-- Given a list `i :: l` the left-most minimial position `a` of `i :: l` wrt `r`
+/-- Given a list `i :: l` the left-most minimal position `a` of `i :: l` wrt `r`
   as an element of `Fin (insertionSortDropMinPos r i l).length.succ`. -/
 def insertionSortMinPosFin {α : Type} (r : α → α → Prop) [DecidableRel r] (i : α) (l : List α) :
     Fin (insertionSortDropMinPos r i l).length.succ :=

HepLean/Meta/Remark/Properties.lean

@@ -25,7 +25,7 @@ def RemarkInfo.toFullName (r : RemarkInfo) : Name :=
   else
     r.name
 
-/-- A Bool which is true if a name correponds to a remark. -/
+/-- A Bool which is true if a name corresponds to a remark. -/
 def RemarkInfo.IsRemark (n : Name) : m Bool := do
   let allRemarks ← allRemarkInfo
   let r := allRemarks.find? fun r => r.toFullName == n

HepLean/PerturbationTheory/CreateAnnihilate.lean

@@ -12,7 +12,7 @@ import Mathlib.Algebra.BigOperators.Group.Finset
 
 /-- The type `CreateAnnihilate` is the type containing two elements `create` and `annihilate`.
   This type is used to specify if an operator is a creation, or annihilation, operator
-  or the sum thereof or intergral thereover etc. -/
+  or the sum thereof or integral thereover etc. -/
 inductive CreateAnnihilate where
   | create : CreateAnnihilate
   | annihilate : CreateAnnihilate

HepLean/PerturbationTheory/FeynmanDiagrams/Momentum.lean

@@ -83,17 +83,17 @@ def euclidInner : F.HalfEdgeMomenta →ₗ[ℝ] F.HalfEdgeMomenta →ₗ[ℝ]
   Corresponding to that spanned by its total outflowing momentum. -/
 def EdgeMomenta : Type := F.𝓔 → ℝ
 
-/-- The edge momenta form an additive commuative group. -/
+/-- The edge momenta form an additive commutative group. -/
 instance : AddCommGroup F.EdgeMomenta := Pi.addCommGroup
 
 /-- The edge momenta form a module over `ℝ`. -/
 instance : Module ℝ F.EdgeMomenta := Pi.module _ _ _
 
-/-- The type which associates to each ege a `1`-dimensional vector space.
+/-- The type which associates to each edge a `1`-dimensional vector space.
   Corresponding to that spanned by its total inflowing momentum. -/
 def VertexMomenta : Type := F.𝓥 → ℝ
 
-/-- The vertex momenta carries the structure of an additive commuative group. -/
+/-- The vertex momenta carries the structure of an additive commutative group. -/
 instance : AddCommGroup F.VertexMomenta := Pi.addCommGroup
 
 /-- The vertex momenta carries the structure of a module over `ℝ`. -/
@@ -106,7 +106,7 @@ def EdgeVertexMomentaMap : Fin 2 → Type := fun i =>
   | 1 => F.VertexMomenta
 
 /-- The target of the map `EdgeVertexMomentaMap` is either the type of edge momenta
-  or vertex momenta and thus carries the structure of an additive commuative group. -/
+  or vertex momenta and thus carries the structure of an additive commutative group. -/
 instance (i : Fin 2) : AddCommGroup (EdgeVertexMomentaMap F i) :=
   match i with
   | 0 => instAddCommGroupEdgeMomenta F

HepLean/PerturbationTheory/FieldOpAlgebra/Basic.lean

@@ -40,7 +40,7 @@ def fieldOpIdealSet : Set (FieldOpFreeAlgebra 𝓕) :=
   This corresponds to the condition that two annihilation operators always super-commute.
 - `[ofCrAnOpF φ, ofCrAnOpF φ']ₛca` for `φ` and `φ'` operators with different statistics.
   This corresponds to the condition that two operators with different statistics always
-  super-commute. In otherwords, fermions and bosons always super-commute.
+  super-commute. In other words, fermions and bosons always super-commute.
 - `[ofCrAnOpF φ1, [ofCrAnOpF φ2, ofCrAnOpF φ3]ₛca]ₛca`. This corresponds to the condition,
   when combined with the conditions above, that the super-commutor is in the center of the
   of the algebra.
@@ -218,7 +218,7 @@ lemma ι_superCommuteF_ofCrAnOpF_ofCrAnOpF_mem_center (φ ψ : 𝓕.CrAnFieldOp)
 
 /-!
 
-## The kernal of ι
+## The kernel of ι
 -/
 
 lemma ι_eq_zero_iff_mem_ideal (x : FieldOpFreeAlgebra 𝓕) :

HepLean/PerturbationTheory/FieldOpAlgebra/NormalOrder/Lemmas.lean

@@ -282,7 +282,7 @@ lemma ofCrAnOp_superCommute_normalOrder_ofFieldOpList_sum (φ : 𝓕.CrAnFieldOp
 
 /--
 The commutor of the annihilation part of a field operator with a normal ordered list of field
-operators can be decomponsed into the sum of the commutators of the annihilation part with each
+operators can be decomposed into the sum of the commutators of the annihilation part with each
 element of the list of field operators, i.e.
 `[anPart φ, 𝓝(φ₀…φₙ)]ₛ= ∑ i, 𝓢(φ, φ₀…φᵢ₋₁) • [anPart φ, φᵢ]ₛ * 𝓝(φ₀…φᵢ₋₁φᵢ₊₁…φₙ)`.
 -/

HepLean/PerturbationTheory/FieldOpAlgebra/WickTerm.lean

@@ -104,7 +104,7 @@ is equal the product of
 - `φsΛ.timeContract`
 - `s • [anPart φ, ofFieldOp φs[k]]ₛ` where `s` is the sign associated with moving `φ` through
   uncontracted fields in `φ₀…φₖ₋₁`
-- the normal ordering `[φsΛ]ᵘᶜ` with the field corresonding to `k` removed.
+- the normal ordering `[φsΛ]ᵘᶜ` with the field corresponding to `k` removed.
 
 The proof of this result relies on
 - `timeContract_insert_some_of_not_lt`

HepLean/PerturbationTheory/FieldOpAlgebra/WicksTheoremNormal.lean

@@ -34,7 +34,7 @@ This result follows from
   those `𝓣(φsΛ.staticWickTerm)` for which `φsΛ` has a contracted pair which are not
   equal time to zero.
 - `staticContract_eq_timeContract_of_eqTimeOnly` to rewrite the static contract
-  in the reminaing `𝓣(φsΛ.staticWickTerm)` as a time contract.
+  in the remaining `𝓣(φsΛ.staticWickTerm)` as a time contract.
 - `timeOrder_timeContract_mul_of_eqTimeOnly_left` to move the time contracts out of the time
   ordering.
 -/

HepLean/PerturbationTheory/FieldSpecification/Basic.lean

@@ -88,7 +88,7 @@ As some intuition, if `f` corresponds to a Weyl-fermion field, then
 - `position f e x`, `e` would correspond to a Lorentz index `α`, and `position f e x` would,
   once represented in the operator algebra, be proportional to the operator
   `∑ s, ∫ d^3p/(…) (x_α(p,s)  a(p, s) e^{-i p x} + y_α(p,s) a^†(p, s) e^{-i p x})`.
-- `outAsymp f e p`, `e` would corresond to a spin `s`, and `outAsymp f e p` would,
+- `outAsymp f e p`, `e` would correspond to a spin `s`, and `outAsymp f e p` would,
   once represented in the operator algebra, be proportional to the
   annihilation operator `a^†(p, s)`.
 

HepLean/PerturbationTheory/FieldSpecification/CrAnFieldOp.lean

@@ -83,7 +83,7 @@ As some intuition, if `f` corresponds to a Weyl-fermion field, it would contribu
 - an element corresponding to the creation parts of position operators for each each Lorentz
   index `α`:
   `∑ s, ∫ d^3p/(…) (x_α(p,s)  a(p, s) e^{-i p x})`.
-- an element corresponding to anihilation parts of position operator,
+- an element corresponding to annihilation parts of position operator,
   for each each Lorentz index `α`:
   `∑ s, ∫ d^3p/(…) (y_α(p,s) a^†(p, s) e^{-i p x})`.
 - an element corresponding to outgoing asymptotic operators for each spin `s`: `a^†(p, s)`.
@@ -98,7 +98,7 @@ def crAnFieldOpToFieldOp : 𝓕.CrAnFieldOp → 𝓕.FieldOp := Sigma.fst
 lemma crAnFieldOpToFieldOp_prod (s : 𝓕.FieldOp) (t : 𝓕.fieldOpToCrAnType s) :
     𝓕.crAnFieldOpToFieldOp ⟨s, t⟩ = s := rfl
 
-/-- For a field specficiation `𝓕`, `𝓕.crAnFieldOpToCreateAnnihilate` is the map from
+/-- For a field specification `𝓕`, `𝓕.crAnFieldOpToCreateAnnihilate` is the map from
   `𝓕.CrAnFieldOp` to `CreateAnnihilate` taking `φ` to `create` if
 - `φ` corresponds to an incoming asymptotic field operator or the creation part of a position based
   field operator.

HepLean/PerturbationTheory/FieldSpecification/CrAnSection.lean

@@ -126,7 +126,7 @@ def singletonEquiv {φ : 𝓕.FieldOp} : CrAnSection [φ] ≃
     simp only [head]
     rfl
 
-/-- An equivalence seperating the head of a creation and annihilation section
+/-- An equivalence separating the head of a creation and annihilation section
   from the tail. -/
 def consEquiv {φ : 𝓕.FieldOp} {φs : List 𝓕.FieldOp} : CrAnSection (φ :: φs) ≃
     𝓕.fieldOpToCrAnType φ × CrAnSection φs where

HepLean/PerturbationTheory/FieldSpecification/TimeOrder.lean

@@ -32,7 +32,7 @@ def timeOrderRel : 𝓕.FieldOp → 𝓕.FieldOp → Prop
   | FieldOp.inAsymp _, FieldOp.position _ => False
   | FieldOp.inAsymp _, FieldOp.inAsymp _ => True
 
-/-- The relation `timeOrderRel` is decidable, but not computablly so due to
+/-- The relation `timeOrderRel` is decidable, but not computable so due to
   `Real.decidableLE`. -/
 noncomputable instance : (φ φ' : 𝓕.FieldOp) → Decidable (timeOrderRel φ φ')
   | FieldOp.outAsymp _, _ => isTrue True.intro
@@ -206,7 +206,7 @@ it is needed that the operator with the greatest time is to the left.
 -/
 def crAnTimeOrderRel (a b : 𝓕.CrAnFieldOp) : Prop := 𝓕.timeOrderRel a.1 b.1
 
-/-- The relation `crAnTimeOrderRel` is decidable, but not computablly so due to
+/-- The relation `crAnTimeOrderRel` is decidable, but not computable so due to
   `Real.decidableLE`. -/
 noncomputable instance (φ φ' : 𝓕.CrAnFieldOp) : Decidable (crAnTimeOrderRel φ φ') :=
   inferInstanceAs (Decidable (𝓕.timeOrderRel φ.1 φ'.1))
@@ -508,7 +508,7 @@ lemma sum_crAnSections_timeOrder {φs : List 𝓕.FieldOp} [AddCommMonoid M]
 def normTimeOrderRel (a b : 𝓕.CrAnFieldOp) : Prop :=
   crAnTimeOrderRel a b ∧ (crAnTimeOrderRel b a → normalOrderRel a b)
 
-/-- The relation `normTimeOrderRel` is decidable, but not computablly so due to
+/-- The relation `normTimeOrderRel` is decidable, but not computable so due to
   `Real.decidableLE`. -/
 noncomputable instance (φ φ' : 𝓕.CrAnFieldOp) : Decidable (normTimeOrderRel φ φ') :=
   instDecidableAnd

HepLean/PerturbationTheory/FieldStatistics/Basic.lean

@@ -26,7 +26,7 @@ namespace FieldStatistic
 
 variable {𝓕 : Type}
 
-/-- The type `FieldStatistic` carries an instance of a commuative group in which
+/-- The type `FieldStatistic` carries an instance of a commutative group in which
 - `bosonic * bosonic = bosonic`
 - `bosonic * fermionic = fermionic`
 - `fermionic * bosonic = fermionic`

HepLean/PerturbationTheory/WickContraction/Sign/Basic.lean

@@ -21,7 +21,7 @@ open FieldStatistic
 
 /-- Given a Wick contraction `c : WickContraction n` and `i1 i2 : Fin n` the finite set
   of elements of `Fin n` between `i1` and `i2` which are either uncontracted
-  or are contracted but are contracted with an element occuring after `i1`.
+  or are contracted but are contracted with an element occurring after `i1`.
   I.e. the elements of `Fin n` between `i1` and `i2` which are not contracted with before `i1`.
   One should assume `i1 < i2` otherwise this finite set is empty. -/
 def signFinset (c : WickContraction n) (i1 i2 : Fin n) : Finset (Fin n) :=

HepLean/PerturbationTheory/WickContraction/TimeCond.lean

@@ -506,7 +506,7 @@ lemma hasEqTimeEquiv_ext_sigma {φs : List 𝓕.FieldOp} {x1 x2 :
     simp only [ne_eq, congr_refl] at h2
     simp [h2]
 
-/-- The equivalence which seperates a Wick contraction which has an equal time contraction
+/-- The equivalence which separates a Wick contraction which has an equal time contraction
 into a non-empty contraction only between equal-time fields and a Wick contraction which
 does not have equal time contractions. -/
 def hasEqTimeEquiv (φs : List 𝓕.FieldOp) :

HepLean/StandardModel/HiggsBoson/GaugeAction.lean

@@ -43,7 +43,7 @@ noncomputable def higgsRepUnitary : GaugeGroupI →* unitaryGroup (Fin 2) ℂ wh
     repeat rw [mul_assoc]
   map_one' := by simp
 
-/-- Using the orthonormal basis of `HiggsVec`, turns a `2×2`-matrix intoa a linear map
+/-- Using the orthonormal basis of `HiggsVec`, turns a `2×2`-matrix into a linear map
   of `HiggsVec`. -/
 noncomputable def matrixToLin : Matrix (Fin 2) (Fin 2) ℂ →* (HiggsVec →L[ℂ] HiggsVec) where
   toFun g := LinearMap.toContinuousLinearMap
@@ -220,7 +220,7 @@ informal_lemma guage_orbit where
   deps := [``rotate_fst_zero_snd_real]
 
 /-- The Higgs boson breaks electroweak symmetry down to the electromagnetic force, i.e., the
-stablity group of the action of `rep` on `![0, Complex.ofReal ‖φ‖]`, for non-zero `‖φ‖`, is the
+stability group of the action of `rep` on `![0, Complex.ofReal ‖φ‖]`, for non-zero `‖φ‖`, is the
 `SU(3) × U(1)` subgroup of `gaugeGroup := SU(3) × SU(2) × U(1)` with the embedding given by
 `(g, e^{i θ}) ↦ (g, diag (e ^ {3 * i θ}, e ^ {- 3 * i θ}), e^{i θ})`.
 -/

HepLean/Tensors/Tree/Elab.lean

@@ -77,7 +77,7 @@ syntax num : indexExpr
 /-- Notation to describe the jiggle of a tensor index. -/
 syntax "τ(" ident ")" : indexExpr
 
-/-- Bool which is ture if an index is a num. -/
+/-- Bool which is true if an index is a num. -/
 def indexExprIsNum (stx : Syntax) : Bool :=
   match stx with
   | `(indexExpr|$_:num) => true