docs: Fix typos in docs

HepLean/PerturbationTheory/FieldSpecification/Basic.lean

@@ -43,7 +43,7 @@ The structure `FieldSpecification` is defined to have the following content:
       index of the field and its conjugate.
   - For every field `f` in `Field`, a type `AsymptoticLabel f` whose elements label the different
     types of incoming asymptotic field operators associated with the
-    field `f` (this is also matches the types of outgoing asymptotic field operators).
+    field `f` (this also matches the types of outgoing asymptotic field operators).
     For example,
     - For `f` a *real-scalar field*, `AsymptoticLabel f` will have a unique element.
     - For `f` a *complex-scalar field*, `AsymptoticLabel f` will have two elements, one for the
@@ -81,7 +81,7 @@ variable (𝓕 : FieldSpecification)
   element labelled `outAsymp f e p` corresponding to an outgoing asymptotic field operator of the
   field `f`, of label `e` (e.g. specifying the spin), and momentum `p`.
 
-As some intuition, if `f` corresponds to a Weyl-fermion field, then
+As an example, if `f` corresponds to a Weyl-fermion field, then
 - For `inAsymp f e p`, `e` would correspond to a spin `s`, and `inAsymp f e p` would, once
   represented in the operator algebra,
   be proportional to the creation operator `a(p, s)`.
@@ -120,7 +120,7 @@ def fieldOpToField : 𝓕.FieldOp → 𝓕.Field
 - For `φ` an element of `𝓕.FieldOp`, `𝓕 |>ₛ φ` is `fieldOpStatistic φ`.
 - For `φs` a list of `𝓕.FieldOp`, `𝓕 |>ₛ φs` is the product of `fieldOpStatistic φ` over
   the list `φs`.
-- For a function `f : Fin n → 𝓕.FieldOp` and a finset `a` of `Fin n`, `𝓕 |>ₛ ⟨f, a⟩` is the
+- For a function `f : Fin n → 𝓕.FieldOp` and a finite set `a` of `Fin n`, `𝓕 |>ₛ ⟨f, a⟩` is the
   product of `fieldOpStatistic (f i)` for all `i ∈ a`. -/
 def fieldOpStatistic : 𝓕.FieldOp → FieldStatistic := 𝓕.statistic ∘ 𝓕.fieldOpToField
 

HepLean/PerturbationTheory/FieldSpecification/CrAnFieldOp.lean

@@ -66,18 +66,18 @@ def fieldOpToCreateAnnihilateTypeCongr : {i j : 𝓕.FieldOp} → i = j →
 For a field specification `𝓕`, the (sigma) type `𝓕.CrAnFieldOp`
 corresponds to the type of creation and annihilation parts of field operators.
 It formally defined to consist of the following elements:
-- for each in incoming asymptotic field operator `φ` in `𝓕.FieldOp` an element
+- for each incoming asymptotic field operator `φ` in `𝓕.FieldOp` an element
   written as `⟨φ, ()⟩` in `𝓕.CrAnFieldOp`, corresponding to the creation part of `φ`.
   Here `φ` has no annihilation part. (Here `()` is the unique element of `Unit`.)
 - for each position field operator `φ` in `𝓕.FieldOp` an element of `𝓕.CrAnFieldOp`
   written as `⟨φ, .create⟩`, corresponding to the creation part of `φ`.
 - for each position field operator `φ` in `𝓕.FieldOp` an element of `𝓕.CrAnFieldOp`
   written as `⟨φ, .annihilate⟩`, corresponding to the annihilation part of `φ`.
-- for each out outgoing asymptotic field operator `φ` in `𝓕.FieldOp` an element
+- for each outgoing asymptotic field operator `φ` in `𝓕.FieldOp` an element
   written as `⟨φ, ()⟩` in `𝓕.CrAnFieldOp`, corresponding to the annihilation part of `φ`.
   Here `φ` has no creation part. (Here `()` is the unique element of `Unit`.)
 
-As some intuition, if `f` corresponds to a Weyl-fermion field, it would contribute
+As an example, if `f` corresponds to a Weyl-fermion field, it would contribute
   the following elements to `𝓕.CrAnFieldOp`
 - an element corresponding to incoming asymptotic operators for each spin `s`: `a(p, s)`.
 - an element corresponding to the creation parts of position operators for each each Lorentz

HepLean/PerturbationTheory/FieldSpecification/NormalOrder.lean

@@ -20,7 +20,7 @@ variable {𝓕 : FieldSpecification}
   - `φ₀` is a field creation operator
   - `φ₁` is a field annihilation operator.
 
-  Thus, colloquially `𝓕.normalOrderRel φ₀ φ₁` says the creation operators are 'less then'
+  Thus, colloquially `𝓕.normalOrderRel φ₀ φ₁` says the creation operators are less than
   annihilation operators. -/
 def normalOrderRel : 𝓕.CrAnFieldOp → 𝓕.CrAnFieldOp → Prop :=
   fun a b => CreateAnnihilate.normalOrder (𝓕 |>ᶜ a) (𝓕 |>ᶜ b)

HepLean/PerturbationTheory/FieldSpecification/TimeOrder.lean

@@ -198,10 +198,10 @@ lemma timeOrderList_eq_maxTimeField_timeOrderList (φ : 𝓕.FieldOp) (φs : Lis
 - `φ₀` is an *outgoing* asymptotic operator
 - `φ₁` is an *incoming* asymptotic field operator
 - `φ₀` and `φ₁` are both position field operators where
-  the `SpaceTime` point of `φ₀` has a time *greater* then or equal to that of `φ₁`.
+  the `SpaceTime` point of `φ₀` has a time *greater* than or equal to that of `φ₁`.
 
-Thus, colloquially `𝓕.crAnTimeOrderRel φ₀ φ₁` if `φ₀` has time *greater* then or equal to `φ₁`.
-The use of *greater* then rather then *less* then is because on ordering lists of operators
+Thus, colloquially `𝓕.crAnTimeOrderRel φ₀ φ₁` if `φ₀` has time *greater* than or equal to `φ₁`.
+The use of *greater* than rather then *less* than is because on ordering lists of operators
 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