refactor: Lint
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jstoobysmith
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8 changed files with 229 additions and 194 deletions
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@ -8,7 +8,7 @@ import HepLean.PerturbationTheory.WickContraction.StaticContract
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import HepLean.PerturbationTheory.Algebras.FieldOpAlgebra.TimeContraction
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/-!
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# Sub contractions
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# Sub contractions
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-/
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@ -20,7 +20,10 @@ variable {n : ℕ} {φs : List 𝓕.States} {φsΛ : WickContraction φs.length}
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open HepLean.List
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open FieldOpAlgebra
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def subContraction (S : Finset (Finset (Fin φs.length))) (ha : S ⊆ φsΛ.1) : WickContraction φs.length :=
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/-- Given a Wick contraction `φsΛ`, and a subset of `φsΛ.1`, the Wick contraction
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conisting of contracted pairs within that subset. -/
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def subContraction (S : Finset (Finset (Fin φs.length))) (ha : S ⊆ φsΛ.1) :
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WickContraction φs.length :=
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⟨S, by
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intro i hi
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exact φsΛ.2.1 i (ha hi),
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@ -32,13 +35,16 @@ lemma mem_of_mem_subContraction {S : Finset (Finset (Fin φs.length))} {hs : S
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{a : Finset (Fin φs.length)} (ha : a ∈ (φsΛ.subContraction S hs).1) : a ∈ φsΛ.1 := by
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exact hs ha
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/-- Given a Wick contraction `φsΛ`, and a subset `S` of `φsΛ.1`, the Wick contraction
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on the uncontracted list `[φsΛ.subContraction S ha]ᵘᶜ`
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consisting of the remaining contracted pairs of `φsΛ` not in `S`. -/
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def quotContraction (S : Finset (Finset (Fin φs.length))) (ha : S ⊆ φsΛ.1) :
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WickContraction [φsΛ.subContraction S ha]ᵘᶜ.length :=
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⟨Finset.filter (fun a => Finset.map uncontractedListEmd a ∈ φsΛ.1) Finset.univ,
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by
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intro a ha'
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simp only [Finset.mem_filter, Finset.mem_univ, true_and] at ha'
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simpa using φsΛ.2.1 (Finset.map uncontractedListEmd a) ha' , by
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simpa using φsΛ.2.1 (Finset.map uncontractedListEmd a) ha', by
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intro a ha b hb
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simp only [Finset.mem_filter, Finset.mem_univ, true_and] at ha hb
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by_cases hab : a = b
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@ -103,13 +109,16 @@ lemma subContraction_fstFieldOfContract {S : Finset (Finset (Fin φs.length))} {
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(a : (subContraction S hs).1) :
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(subContraction S hs).fstFieldOfContract a =
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φsΛ.fstFieldOfContract ⟨a.1, mem_of_mem_subContraction a.2⟩:= by
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apply eq_fstFieldOfContract_of_mem _ _ _ (φsΛ.sndFieldOfContract ⟨a.1, mem_of_mem_subContraction a.2⟩)
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· have ha := finset_eq_fstFieldOfContract_sndFieldOfContract _ ⟨a.1, mem_of_mem_subContraction a.2⟩
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apply eq_fstFieldOfContract_of_mem _ _ _
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(φsΛ.sndFieldOfContract ⟨a.1, mem_of_mem_subContraction a.2⟩)
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· have ha := finset_eq_fstFieldOfContract_sndFieldOfContract _
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⟨a.1, mem_of_mem_subContraction a.2⟩
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simp only at ha
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conv_lhs =>
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rw [ha]
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simp
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· have ha := finset_eq_fstFieldOfContract_sndFieldOfContract _ ⟨a.1, mem_of_mem_subContraction a.2⟩
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· have ha := finset_eq_fstFieldOfContract_sndFieldOfContract _
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⟨a.1, mem_of_mem_subContraction a.2⟩
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simp only at ha
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conv_lhs =>
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rw [ha]
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@ -121,27 +130,31 @@ lemma subContraction_sndFieldOfContract {S : Finset (Finset (Fin φs.length))} {
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(a : (subContraction S hs).1) :
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(subContraction S hs).sndFieldOfContract a =
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φsΛ.sndFieldOfContract ⟨a.1, mem_of_mem_subContraction a.2⟩:= by
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apply eq_sndFieldOfContract_of_mem _ _ (φsΛ.fstFieldOfContract ⟨a.1, mem_of_mem_subContraction a.2⟩)
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· have ha := finset_eq_fstFieldOfContract_sndFieldOfContract _ ⟨a.1, mem_of_mem_subContraction a.2⟩
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apply eq_sndFieldOfContract_of_mem _ _
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(φsΛ.fstFieldOfContract ⟨a.1, mem_of_mem_subContraction a.2⟩)
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· have ha := finset_eq_fstFieldOfContract_sndFieldOfContract _
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⟨a.1, mem_of_mem_subContraction a.2⟩
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simp only at ha
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conv_lhs =>
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rw [ha]
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simp
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· have ha := finset_eq_fstFieldOfContract_sndFieldOfContract _ ⟨a.1, mem_of_mem_subContraction a.2⟩
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· have ha := finset_eq_fstFieldOfContract_sndFieldOfContract _
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⟨a.1, mem_of_mem_subContraction a.2⟩
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simp only at ha
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conv_lhs =>
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rw [ha]
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simp
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· exact fstFieldOfContract_lt_sndFieldOfContract φsΛ ⟨↑a, mem_of_mem_subContraction a.property⟩
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@[simp]
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lemma quotContraction_fstFieldOfContract_uncontractedListEmd {S : Finset (Finset (Fin φs.length))}
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{hs : S ⊆ φsΛ.1} (a : (quotContraction S hs).1) :
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uncontractedListEmd ((quotContraction S hs).fstFieldOfContract a) =
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(φsΛ.fstFieldOfContract ⟨Finset.map uncontractedListEmd a.1, mem_of_mem_quotContraction a.2⟩) := by
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(φsΛ.fstFieldOfContract
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⟨Finset.map uncontractedListEmd a.1, mem_of_mem_quotContraction a.2⟩) := by
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symm
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apply eq_fstFieldOfContract_of_mem _ _ _ (uncontractedListEmd ((quotContraction S hs).sndFieldOfContract a) )
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apply eq_fstFieldOfContract_of_mem _ _ _
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(uncontractedListEmd ((quotContraction S hs).sndFieldOfContract a))
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· simp only [Finset.mem_map', fstFieldOfContract_mem]
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· simp
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· apply uncontractedListEmd_strictMono
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@ -151,9 +164,11 @@ lemma quotContraction_fstFieldOfContract_uncontractedListEmd {S : Finset (Finset
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lemma quotContraction_sndFieldOfContract_uncontractedListEmd {S : Finset (Finset (Fin φs.length))}
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{hs : S ⊆ φsΛ.1} (a : (quotContraction S hs).1) :
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uncontractedListEmd ((quotContraction S hs).sndFieldOfContract a) =
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(φsΛ.sndFieldOfContract ⟨Finset.map uncontractedListEmd a.1, mem_of_mem_quotContraction a.2⟩) := by
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(φsΛ.sndFieldOfContract
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⟨Finset.map uncontractedListEmd a.1, mem_of_mem_quotContraction a.2⟩) := by
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symm
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apply eq_sndFieldOfContract_of_mem _ _ (uncontractedListEmd ((quotContraction S hs).fstFieldOfContract a) )
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apply eq_sndFieldOfContract_of_mem _ _
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(uncontractedListEmd ((quotContraction S hs).fstFieldOfContract a))
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· simp only [Finset.mem_map', fstFieldOfContract_mem]
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· simp
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· apply uncontractedListEmd_strictMono
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@ -164,7 +179,6 @@ lemma quotContraction_gradingCompliant {S : Finset (Finset (Fin φs.length))} {h
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GradingCompliant [φsΛ.subContraction S hs]ᵘᶜ (quotContraction S hs) := by
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simp only [GradingCompliant, Fin.getElem_fin, Subtype.forall]
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intro a ha
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have h1' := mem_of_mem_quotContraction ha
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erw [subContraction_uncontractedList_get]
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erw [subContraction_uncontractedList_get]
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simp only [quotContraction_fstFieldOfContract_uncontractedListEmd, Fin.getElem_fin,
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@ -173,7 +187,7 @@ lemma quotContraction_gradingCompliant {S : Finset (Finset (Fin φs.length))} {h
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lemma mem_quotContraction_iff {S : Finset (Finset (Fin φs.length))} {hs : S ⊆ φsΛ.1}
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{a : Finset (Fin [φsΛ.subContraction S hs]ᵘᶜ.length)} :
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a ∈ (quotContraction S hs).1 ↔ a.map uncontractedListEmd ∈ φsΛ.1
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a ∈ (quotContraction S hs).1 ↔ a.map uncontractedListEmd ∈ φsΛ.1
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∧ a.map uncontractedListEmd ∉ (subContraction S hs).1 := by
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apply Iff.intro
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· intro h
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@ -184,5 +198,4 @@ lemma mem_quotContraction_iff {S : Finset (Finset (Fin φs.length))} {hs : S ⊆
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have h2 := mem_subContraction_or_quotContraction (S := S) (hs := hs) h.1
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simp_all
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end WickContraction
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