refactor: Lint
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5 changed files with 9 additions and 9 deletions
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@ -87,7 +87,7 @@ lemma toList_get (a : CreateAnnilateSect f l) :
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simp [tail]
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@[simp]
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lemma toList_grade :
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lemma toList_grade :
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FieldStatistic.ofList (fun i => q i.fst) a.toList = fermionic ↔
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FieldStatistic.ofList q l = fermionic := by
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induction l with
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@ -308,7 +308,7 @@ variable {𝓕 : Type} {f : 𝓕 → Type} (q : 𝓕 → FieldStatistic) (le :
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{l : List 𝓕} (a : CreateAnnilateSect f l)
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lemma toList_koszulSignInsert (x : (i : 𝓕) × f i) :
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koszulSignInsert (fun i => q i.fst) (fun i j => le i.fst j.fst) x a.toList =
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koszulSignInsert (fun i => q i.fst) (fun i j => le i.fst j.fst) x a.toList =
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koszulSignInsert q le x.1 l := by
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induction l with
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| nil => simp [koszulSignInsert]
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@ -167,7 +167,7 @@ lemma ofListLift_expand (f : 𝓕 → Type) [∀ i, Fintype (f i)] (x : ℂ) :
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lemma koszulOrder_ofListLift {f : 𝓕 → Type} [∀ i, Fintype (f i)]
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(l : List 𝓕) (x : ℂ) :
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koszulOrder (fun i => q i.fst) (fun i j => le i.1 j.1) (ofListLift f l x) =
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koszulOrder (fun i => q i.fst) (fun i j => le i.1 j.1) (ofListLift f l x) =
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sumFiber f (koszulOrder q le (ofList l x)) := by
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rw [koszulOrder_ofList]
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rw [map_smul]
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@ -24,7 +24,8 @@ open FieldStatistic
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is zero.
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This can be thought as as a condtion on the operator algebra `A` as much as it can
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on `F`. -/
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class OperatorMap {A : Type} [Semiring A] [Algebra ℂ A] (q : I → FieldStatistic) (le1 : I → I → Prop)
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class OperatorMap {A : Type} [Semiring A] [Algebra ℂ A]
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(q : I → FieldStatistic) (le1 : I → I → Prop)
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[DecidableRel le1] (F : FreeAlgebra ℂ I →ₐ[ℂ] A) : Prop where
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superCommute_mem_center : ∀ i j, F (superCommute q (FreeAlgebra.ι ℂ i) (FreeAlgebra.ι ℂ j)) ∈
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Subalgebra.center ℂ A
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@ -255,7 +256,8 @@ lemma le_all_mul_koszulOrder_ofList_expand {I : Type}
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exact fun j => hi j
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lemma le_all_mul_koszulOrder_ofListLift_expand {I : Type} {f : I → Type} [∀ i, Fintype (f i)]
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(q : I → FieldStatistic) (r : List I) (x : ℂ) (le1 : (Σ i, f i) → (Σ i, f i) → Prop) [DecidableRel le1]
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(q : I → FieldStatistic) (r : List I) (x : ℂ)
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(le1 : (Σ i, f i) → (Σ i, f i) → Prop) [DecidableRel le1]
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[IsTotal (Σ i, f i) le1] [IsTrans (Σ i, f i) le1]
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(i : (Σ i, f i)) (hi : ∀ (j : (Σ i, f i)), le1 j i)
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{A : Type} [Semiring A] [Algebra ℂ A]
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@ -103,7 +103,6 @@ lemma insertSign_succ_cons (n : ℕ) (r0 r1 : 𝓕) (r : List 𝓕) : insertSign
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simp only [insertSign, List.take_succ_cons]
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rw [superCommuteCoef_cons]
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lemma insertSign_insert_gt (n m : ℕ) (r0 r1 : 𝓕) (r : List 𝓕) (hn : n < m) :
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insertSign q n r0 (List.insertIdx m r1 r) = insertSign q n r0 r := by
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rw [insertSign, insertSign]
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@ -276,9 +276,8 @@ lemma ofList_ofList_superCommute (la lb : List 𝓕) (xa xb : ℂ) :
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rw [superCommute_ofList_ofList_superCommuteCoef]
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abel
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lemma ofListLift_ofList_superCommute' (l : List 𝓕) (r : List 𝓕) (x y : ℂ) :
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ofList r y * ofList l x = superCommuteCoef q l r • (ofList l x * ofList r y)
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ofList r y * ofList l x = superCommuteCoef q l r • (ofList l x * ofList r y)
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- superCommuteCoef q l r • superCommute q (ofList l x) (ofList r y) := by
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nth_rewrite 2 [ofList_ofList_superCommute q]
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rw [superCommuteCoef]
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@ -340,7 +339,7 @@ lemma ofList_ofListLift_superCommute (l : List (Σ i, f i)) (r : List 𝓕) (x y
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abel
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lemma ofListLift_ofList_superCommute (l : List (Σ i, f i)) (r : List 𝓕) (x y : ℂ) :
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ofListLift f r y * ofList l x = superCommuteLiftCoef q l r • (ofList l x * ofListLift f r y)
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ofListLift f r y * ofList l x = superCommuteLiftCoef q l r • (ofList l x * ofListLift f r y)
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- superCommuteLiftCoef q l r •
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superCommute (fun i => q i.1) (ofList l x) (ofListLift f r y) := by
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rw [ofList_ofListLift_superCommute, superCommuteLiftCoef]
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