refactor: Lint

HepLean/PerturbationTheory/WickContraction/InsertAndContract.lean

@@ -32,7 +32,7 @@ open HepLean.Fin
   elements and contracting `φ` optionally with `j`.
 
   The notation `φsΛ ↩Λ φ i j` is used to denote `φsΛ.insertAndContract φ i j`. Thus,
-  `φsΛ ↩Λ φ i none` indicates the case when we insert `φ` into `φs` but do not contract it.  -/
+  `φsΛ ↩Λ φ i none` indicates the case when we insert `φ` into `φs` but do not contract it. -/
 def insertAndContract {φs : List 𝓕.FieldOp} (φ : 𝓕.FieldOp) (φsΛ : WickContraction φs.length)
     (i : Fin φs.length.succ) (j : Option φsΛ.uncontracted) :
     WickContraction (φs.insertIdx i φ).length :=

HepLean/PerturbationTheory/WickContraction/Sign/InsertSome.lean

@@ -856,7 +856,7 @@ lemma signInsertSome_mul_filter_contracted_of_not_lt (φ : 𝓕.FieldOp) (φs :
 
 /--
 For `k < i`, the sign of `φsΛ ↩Λ φ i (some k)` is equal to the product of
-- the sign associated with moving `φ` through the `φsΛ`-uncontracted  fields in `φ₀…φₖ`,
+- the sign associated with moving `φ` through the `φsΛ`-uncontracted fields in `φ₀…φₖ`,
 - the sign associated with moving `φ` through the fields in `φ₀…φᵢ₋₁`,
 - the sign of `φsΛ`.
 
@@ -877,10 +877,9 @@ lemma sign_insert_some_of_lt (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
   rw [mul_comm, ← mul_assoc]
   simp
 
-
 /--
 For `i ≤ k`, the sign of `φsΛ ↩Λ φ i (some k)` is equal to the product of
-- the sign associated with moving `φ` through the `φsΛ`-uncontracted  fields in `φ₀…φₖ₋₁`,
+- the sign associated with moving `φ` through the `φsΛ`-uncontracted fields in `φ₀…φₖ₋₁`,
 - the sign associated with moving `φ` through the fields in `φ₀…φᵢ₋₁`,
 - the sign of `φsΛ`.
 
@@ -903,13 +902,12 @@ lemma sign_insert_some_of_not_lt (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
 
 lemma sign_insert_some_zero (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
     (φsΛ : WickContraction φs.length) (k : φsΛ.uncontracted)
-    (hn : GradingCompliant φs φsΛ ∧ (𝓕|>ₛφ) = 𝓕|>ₛφs[k.1]):
-    (φsΛ ↩Λ φ 0 k).sign =  𝓢(𝓕|>ₛφ, 𝓕 |>ₛ ⟨φs.get, (φsΛ.uncontracted.filter (fun x => x < ↑k))⟩) *
+    (hn : GradingCompliant φs φsΛ ∧ (𝓕|>ₛφ) = 𝓕|>ₛφs[k.1]) :
+    (φsΛ ↩Λ φ 0 k).sign = 𝓢(𝓕|>ₛφ, 𝓕 |>ₛ ⟨φs.get, (φsΛ.uncontracted.filter (fun x => x < ↑k))⟩) *
     φsΛ.sign := by
   rw [sign_insert_some_of_not_lt]
   · simp
   · simp
   · exact hn
 
-
 end WickContraction

HepLean/PerturbationTheory/WickContraction/Sign/Join.lean

@@ -418,7 +418,7 @@ lemma join_sign_induction {φs : List 𝓕.FieldOp} (φsΛ : WickContraction φs
     exact join_uncontractedListGet (singleton hij) φsucΛ'
 
 /-- Let `φsΛ` be a grading compliant Wick contraction for `φs` and
-  `φsucΛ` a Wick contraction for `[φsΛ]ᵘᶜ`. Then  `(join φsΛ φsucΛ).sign = φsΛ.sign * φsucΛ.sign`.
+  `φsucΛ` a Wick contraction for `[φsΛ]ᵘᶜ`. Then `(join φsΛ φsucΛ).sign = φsΛ.sign * φsucΛ.sign`.
 
   This lemma manifests the fact that it does not matter which order contracted pairs are brought
   together when defining the sign of a contraction. -/