refactor: Lint

HepLean.lean

@@ -124,6 +124,7 @@ import HepLean.Meta.TransverseTactics
 import HepLean.PerturbationTheory.Algebras.CrAnAlgebra.Basic
 import HepLean.PerturbationTheory.Algebras.CrAnAlgebra.NormalOrder
 import HepLean.PerturbationTheory.Algebras.CrAnAlgebra.SuperCommute
+import HepLean.PerturbationTheory.Algebras.CrAnAlgebra.TimeOrder
 import HepLean.PerturbationTheory.Algebras.FieldOpAlgebra.Basic
 import HepLean.PerturbationTheory.Algebras.FieldOpAlgebra.NormalOrder
 import HepLean.PerturbationTheory.Algebras.ProtoOperatorAlgebra.Basic

HepLean/PerturbationTheory/Algebras/CrAnAlgebra/Basic.lean

@@ -113,7 +113,7 @@ lemma ofStateList_sum (φs : List 𝓕.States) :
 /-- The algebra map taking an element of the free-state algbra to
   the part of it in the creation and annihlation free algebra
   spanned by creation operators. -/
-def crPart : 𝓕.States →  𝓕.CrAnAlgebra := fun φ =>
+def crPart : 𝓕.States → 𝓕.CrAnAlgebra := fun φ =>
   match φ with
   | States.inAsymp φ => ofCrAnState ⟨States.inAsymp φ, ()⟩
   | States.position φ => ofCrAnState ⟨States.position φ, CreateAnnihilate.create⟩

HepLean/PerturbationTheory/Algebras/CrAnAlgebra/SuperCommute.lean

@@ -14,7 +14,6 @@ variable {𝓕 : FieldSpecification}
 
 namespace CrAnAlgebra
 
-
 /-!
 
 ## The super commutor on the CrAnAlgebra.

HepLean/PerturbationTheory/Algebras/CrAnAlgebra/TimeOrder.lean

@@ -46,7 +46,7 @@ lemma timeOrder_ofStateList (φs : List 𝓕.States) :
     rw [ofStateList_sum, map_sum]
     enter [2, x]
     rw [timeOrder_ofCrAnList]
-  simp
+  simp only [crAnTimeOrderSign_crAnSection]
   rw [← Finset.smul_sum]
   congr
   rw [ofStateList_sum, sum_crAnSections_timeOrder]
@@ -155,6 +155,7 @@ lemma timeOrder_eq_maxTimeField_mul_finset (φ : 𝓕.States) (φs : List 𝓕.S
 ## Norm-time order
 
 -/
+/-- The normal-time ordering on `CrAnAlgebra`. -/
 def normTimeOrder : CrAnAlgebra 𝓕 →ₗ[ℂ] CrAnAlgebra 𝓕 :=
   Basis.constr ofCrAnListBasis ℂ fun φs =>
   normTimeOrderSign φs • ofCrAnList (normTimeOrderList φs)

HepLean/PerturbationTheory/Algebras/FieldOpAlgebra/Basic.lean

@@ -42,6 +42,7 @@ abbrev FieldOpAlgebra : Type := (TwoSidedIdeal.span 𝓕.fieldOpIdealSet).ringCo
 namespace FieldOpAlgebra
 variable {𝓕 : FieldSpecification}
 
+/-- The instance of a setoid on `CrAnAlgebra` from the ideal `TwoSidedIdeal`. -/
 instance : Setoid (CrAnAlgebra 𝓕) := (TwoSidedIdeal.span 𝓕.fieldOpIdealSet).ringCon.toSetoid
 
 lemma equiv_iff_sub_mem_ideal (x y : CrAnAlgebra 𝓕) :

HepLean/PerturbationTheory/FieldSpecification/Basic.lean

@@ -66,9 +66,11 @@ def statesToField : 𝓕.States → 𝓕.Fields
   | States.position φ => φ.1
   | States.outAsymp φ => φ.1
 
+/-- The bool on `States` which is true only for position states. -/
 def statesIsPosition : 𝓕.States → Bool
   | States.position _ => true
   | _ => false
+
 /-- The statistics associated to a state. -/
 def statesStatistic : 𝓕.States → FieldStatistic := 𝓕.statistics ∘ 𝓕.statesToField
 

HepLean/PerturbationTheory/FieldSpecification/CrAnSection.lean

@@ -160,23 +160,23 @@ lemma card_cons_eq {φ : 𝓕.States} {φs : List 𝓕.States} :
   rw [Fintype.ofEquiv_card consEquiv.symm]
   simp
 
-lemma card_eq_mul : {φs : List 𝓕.States} →  Fintype.card (CrAnSection φs) =
+lemma card_eq_mul : {φs : List 𝓕.States} → Fintype.card (CrAnSection φs) =
     2 ^ (List.countP 𝓕.statesIsPosition φs)
   | [] => by
     simp
   | States.position _ :: φs => by
-      simp [statesIsPosition]
+      simp only [statesIsPosition, List.countP_cons_of_pos]
       rw [card_cons_eq]
       rw [card_eq_mul]
-      simp [statesToCrAnType]
+      simp only [statesToCrAnType, CreateAnnihilate.CreateAnnihilate_card_eq_two]
       ring
   | States.inAsymp x_ :: φs => by
-      simp [statesIsPosition]
+      simp only [statesIsPosition, Bool.false_eq_true, not_false_eq_true, List.countP_cons_of_neg]
       rw [card_cons_eq]
       rw [card_eq_mul]
       simp [statesToCrAnType]
   | States.outAsymp _ :: φs => by
-      simp [statesIsPosition]
+      simp only [statesIsPosition, Bool.false_eq_true, not_false_eq_true, List.countP_cons_of_neg]
       rw [card_cons_eq]
       rw [card_eq_mul]
       simp [statesToCrAnType]

HepLean/PerturbationTheory/FieldSpecification/TimeOrder.lean

@@ -203,7 +203,7 @@ noncomputable instance (φ φ' : 𝓕.CrAnStates) : Decidable (crAnTimeOrderRel
 instance : IsTotal 𝓕.CrAnStates 𝓕.crAnTimeOrderRel where
   total a b := IsTotal.total (r := 𝓕.timeOrderRel) a.1 b.1
 
-/-- Time ordering of `CrAnStates`  is transitive. -/
+/-- Time ordering of `CrAnStates` is transitive. -/
 instance : IsTrans 𝓕.CrAnStates 𝓕.crAnTimeOrderRel where
   trans a b c := IsTrans.trans (r := 𝓕.timeOrderRel) a.1 b.1 c.1
 
@@ -231,7 +231,6 @@ lemma crAnTimeOrderList_nil : crAnTimeOrderList (𝓕 := 𝓕) [] = [] := by
 ## Relationship to sections
 -/
 
-
 lemma koszulSignInsert_crAnTimeOrderRel_crAnSection {φ : 𝓕.States} {ψ : 𝓕.CrAnStates}
     (h : ψ.1 = φ) : {φs : List 𝓕.States} → (ψs : CrAnSection φs) →
     Wick.koszulSignInsert 𝓕.crAnStatistics 𝓕.crAnTimeOrderRel ψ ψs.1 =
@@ -239,15 +238,15 @@ lemma koszulSignInsert_crAnTimeOrderRel_crAnSection {φ : 𝓕.States} {ψ :
   | [], ⟨[], h⟩ => by
     simp [Wick.koszulSignInsert]
   | φ' :: φs, ⟨ψ' :: ψs, h1⟩ => by
-    simp [Wick.koszulSignInsert, crAnTimeOrderRel, h]
+    simp only [Wick.koszulSignInsert, crAnTimeOrderRel, h]
-    simp at h1
+    simp only [List.map_cons, List.cons.injEq] at h1
     have hi := koszulSignInsert_crAnTimeOrderRel_crAnSection h (φs := φs) ⟨ψs, h1.2⟩
     rw [hi]
     congr
     · exact h1.1
-    · simp [crAnStatistics, crAnStatesToStates, h1.1 ]
+    · simp only [crAnStatistics, crAnStatesToStates, Function.comp_apply]
       congr
-    · simp [crAnStatistics, crAnStatesToStates, h1.1 ]
+    · simp only [crAnStatistics, crAnStatesToStates, Function.comp_apply]
       congr
       exact h1.1
 
@@ -265,24 +264,24 @@ lemma crAnTimeOrderSign_crAnSection : {φs : List 𝓕.States} → (ψs : CrAnSe
 
 lemma orderedInsert_crAnTimeOrderRel_crAnSection {φ : 𝓕.States} {ψ : 𝓕.CrAnStates}
     (h : ψ.1 = φ) : {φs : List 𝓕.States} → (ψs : CrAnSection φs) →
-    (List.orderedInsert 𝓕.crAnTimeOrderRel ψ ψs.1).map  𝓕.crAnStatesToStates  =
+    (List.orderedInsert 𝓕.crAnTimeOrderRel ψ ψs.1).map 𝓕.crAnStatesToStates =
     List.orderedInsert 𝓕.timeOrderRel φ φs
   | [], ⟨[], _⟩ => by
-    simp [Wick.koszulSignInsert]
+    simp only [List.orderedInsert, List.map_cons, List.map_nil, List.cons.injEq, and_true]
     exact h
   | φ' :: φs, ⟨ψ' :: ψs, h1⟩ => by
-    simp [Wick.koszulSignInsert, crAnTimeOrderRel, h]
+    simp only [List.orderedInsert, crAnTimeOrderRel, h]
-    simp at h1
+    simp only [List.map_cons, List.cons.injEq] at h1
     by_cases hr : timeOrderRel φ φ'
-    · simp [hr]
+    · simp only [hr, ↓reduceIte]
       rw [← h1.1] at hr
-      simp [crAnStatesToStates] at hr
+      simp only [crAnStatesToStates] at hr
-      simp [hr]
+      simp only [hr, ↓reduceIte, List.map_cons, List.cons.injEq]
       exact And.intro h (And.intro h1.1 h1.2)
-    · simp [hr]
+    · simp only [hr, ↓reduceIte]
       rw [← h1.1] at hr
-      simp [crAnStatesToStates] at hr
+      simp only [crAnStatesToStates] at hr
-      simp [hr]
+      simp only [hr, ↓reduceIte, List.map_cons, List.cons.injEq]
       apply And.intro h1.1
       exact orderedInsert_crAnTimeOrderRel_crAnSection h ⟨ψs, h1.2⟩
 
@@ -291,65 +290,65 @@ lemma crAnTimeOrderList_crAnSection_is_crAnSection : {φs : List 𝓕.States}
   | [], ⟨[], h⟩ => by
     simp
   | φ :: φs, ⟨ψ :: ψs, h⟩ => by
-    simp [timeOrderList, crAnTimeOrderList]
+    simp only [crAnTimeOrderList, List.insertionSort, timeOrderList]
-    simp at h
+    simp only [List.map_cons, List.cons.injEq] at h
     exact orderedInsert_crAnTimeOrderRel_crAnSection h.1 ⟨(List.insertionSort crAnTimeOrderRel ψs),
       crAnTimeOrderList_crAnSection_is_crAnSection ⟨ψs, h.2⟩⟩
 
+/-- Time ordering of sections of a list of states. -/
 def crAnSectionTimeOrder (φs : List 𝓕.States) (ψs : CrAnSection φs) :
     CrAnSection (timeOrderList φs) :=
   ⟨crAnTimeOrderList ψs.1, crAnTimeOrderList_crAnSection_is_crAnSection ψs⟩
 
 lemma orderedInsert_crAnTimeOrderRel_injective {ψ ψ' : 𝓕.CrAnStates} (h : ψ.1 = ψ'.1) :
-    {φs : List 𝓕.States} →  (ψs ψs' : 𝓕.CrAnSection φs) →
+    {φs : List 𝓕.States} → (ψs ψs' : 𝓕.CrAnSection φs) →
-    (ho : List.orderedInsert crAnTimeOrderRel ψ ψs.1 =  List.orderedInsert crAnTimeOrderRel ψ' ψs'.1) →
+    (ho : List.orderedInsert crAnTimeOrderRel ψ ψs.1 =
-    ψ = ψ' ∧ ψs = ψs'
+    List.orderedInsert crAnTimeOrderRel ψ' ψs'.1) → ψ = ψ' ∧ ψs = ψs'
   | [], ⟨[], _⟩, ⟨[], _⟩, h => by
-    simp at h
+    simp only [List.orderedInsert, List.cons.injEq, and_true] at h
     simpa using h
   | φ :: φs, ⟨ψ1 :: ψs, h1⟩, ⟨ψ1' :: ψs', h1'⟩, ho => by
-    simp at h1 h1'
+    simp only [List.map_cons, List.cons.injEq] at h1 h1'
     have ih := orderedInsert_crAnTimeOrderRel_injective h ⟨ψs, h1.2⟩ ⟨ψs', h1'.2⟩
-    simp at ho
+    simp only [List.orderedInsert] at ho
     by_cases hr : crAnTimeOrderRel ψ ψ1
-    · simp_all
+    · simp_all only [ite_true]
       by_cases hr2 : crAnTimeOrderRel ψ' ψ1'
       · simp_all
-      · simp [crAnTimeOrderRel] at hr hr2
+      · simp only [crAnTimeOrderRel] at hr hr2
-        simp_all
+        simp_all only
         rw [crAnStatesToStates] at h1 h1'
         rw [h1.1] at hr
         rw [h1'.1] at hr2
         exact False.elim (hr2 hr)
-    · simp_all
+    · simp_all only [ite_false]
       by_cases hr2 : crAnTimeOrderRel ψ' ψ1'
-      · simp [crAnTimeOrderRel] at hr hr2
+      · simp only [crAnTimeOrderRel] at hr hr2
-        simp_all
+        simp_all only
         rw [crAnStatesToStates] at h1 h1'
         rw [h1.1] at hr
         rw [h1'.1] at hr2
         exact False.elim (hr hr2)
-      · simp [hr2] at ho
+      · simp only [hr2, ↓reduceIte, List.cons.injEq] at ho
         have ih' := ih ho.2
-        simp_all
+        simp_all only [and_self, implies_true, not_false_eq_true, true_and]
         apply Subtype.ext
-        simp
+        simp only [List.cons.injEq, true_and]
         rw [Subtype.eq_iff] at ih'
         exact ih'.2
 
-lemma crAnSectionTimeOrder_injective : {φs : List 𝓕.States}  →
+lemma crAnSectionTimeOrder_injective : {φs : List 𝓕.States} →
     Function.Injective (𝓕.crAnSectionTimeOrder φs)
   | [], ⟨[], _⟩, ⟨[], _⟩ => by
     simp
   | φ :: φs, ⟨ψ :: ψs, h⟩, ⟨ψ' :: ψs', h'⟩ => by
     intro h1
     apply Subtype.ext
-    simp
+    simp only [List.cons.injEq]
-    simp [crAnSectionTimeOrder] at h1
+    simp only [crAnSectionTimeOrder] at h1
     rw [Subtype.eq_iff] at h1
-    simp [crAnTimeOrderList] at h1
+    simp only [crAnTimeOrderList, List.insertionSort] at h1
-    simp at h h'
+    simp only [List.map_cons, List.cons.injEq] at h h'
-    have hi := crAnSectionTimeOrder_injective (φs := φs) (a₁ := ⟨ψs, h.2⟩) (a₂ := ⟨ψs', h'.2⟩)
     rw [crAnStatesToStates] at h h'
     have hin := orderedInsert_crAnTimeOrderRel_injective (by rw [h.1, h'.1])
       (𝓕.crAnSectionTimeOrder φs ⟨ψs, h.2⟩)
@@ -364,7 +363,7 @@ lemma crAnSectionTimeOrder_bijective (φs : List 𝓕.States) :
   rw [Fintype.bijective_iff_injective_and_card]
   apply And.intro crAnSectionTimeOrder_injective
   apply CrAnSection.card_perm_eq
-  simp [timeOrderList]
+  simp only [timeOrderList]
   exact List.Perm.symm (List.perm_insertionSort timeOrderRel φs)
 
 lemma sum_crAnSections_timeOrder {φs : List 𝓕.States} [AddCommMonoid M]
@@ -392,15 +391,15 @@ instance : IsTotal 𝓕.CrAnStates 𝓕.normTimeOrderRel where
   total a b := by
     simp only [normTimeOrderRel]
     match IsTotal.total (r := 𝓕.crAnTimeOrderRel) a b,
-      IsTotal.total (r := 𝓕.normalOrderRel) a b  with
+      IsTotal.total (r := 𝓕.normalOrderRel) a b with
     | Or.inl h1, Or.inl h2 => simp [h1, h2]
-    | Or.inr h1, Or.inl h2  =>
+    | Or.inr h1, Or.inl h2 =>
-      simp [h1, h2]
+      simp only [h1, h2, imp_self, and_true, true_and]
       by_cases hn : crAnTimeOrderRel a b
       · simp [hn]
       · simp [hn]
     | Or.inl h1, Or.inr h2 =>
-      simp [h1, h2]
+      simp only [h1, true_and, h2, imp_self, and_true]
       by_cases hn : crAnTimeOrderRel b a
       · simp [hn]
       · simp [hn]
@@ -410,7 +409,7 @@ instance : IsTotal 𝓕.CrAnStates 𝓕.normTimeOrderRel where
 instance : IsTrans 𝓕.CrAnStates 𝓕.normTimeOrderRel where
   trans a b c := by
     intro h1 h2
-    simp_all [normTimeOrderRel]
+    simp_all only [normTimeOrderRel]
     apply And.intro
     · exact IsTrans.trans _ _ _ h1.1 h2.1
     · intro hc

scripts/MetaPrograms/notes.lean

@@ -144,12 +144,9 @@ def perturbationTheory : Note where
     .p "We will want to consider all three of these types of states simultanously so we define
       and inductive type `States` which is the disjoint union of these three types of states.",
     .name `FieldSpecification.States,
-    .name `FieldSpecification.StateAlgebra,
     .h2 "Time ordering",
     .name `FieldSpecification.timeOrderRel,
     .name `FieldSpecification.timeOrderSign,
-    .name `FieldSpecification.StateAlgebra.timeOrder,
-    .name `FieldSpecification.StateAlgebra.timeOrder_eq_maxTimeField_mul_finset,
     .h2 "Creation and annihilation states",
     .h2 "Normal ordering",
     .h2 "Proto-operator algebra",