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refactor: Lint

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jstoobysmith 2025-01-29 16:06:28 +00:00
parent a329661c24
commit e5c85ac109
11 changed files with 179 additions and 182 deletions
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24
HepLean/PerturbationTheory/Algebras/FieldOpAlgebra/TimeOrder.lean
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@ -20,7 +20,7 @@ namespace FieldOpAlgebra
variable {𝓕 : FieldSpecification}
lemma ι_timeOrder_superCommute_superCommute_eq_time_ofCrAnList {φ1 φ2 φ3 : 𝓕.CrAnStates}
(φs1 φs2 : List 𝓕.CrAnStates) (h :
(φs1 φs2 : List 𝓕.CrAnStates) (h :
crAnTimeOrderRel φ1 φ2 ∧ crAnTimeOrderRel φ1 φ3 ∧
crAnTimeOrderRel φ2 φ1 ∧ crAnTimeOrderRel φ2 φ3 ∧
crAnTimeOrderRel φ3 φ1 ∧ crAnTimeOrderRel φ3 φ2):
@ -115,12 +115,12 @@ lemma ι_timeOrder_superCommute_superCommute_eq_time_ofCrAnList {φ1 φ2 φ3 :
rw [← smul_sub, ← smul_sub, smul_smul, mul_comm, ← smul_smul, ← smul_sub]
simp
right
rw [← smul_mul_assoc, ← mul_smul_comm, mul_assoc]
rw [← smul_mul_assoc, ← mul_smul_comm, mul_assoc]
rw [← smul_mul_assoc, ← mul_smul_comm]
rw [← smul_mul_assoc, ← mul_smul_comm]
rw [smul_sub]
rw [← smul_mul_assoc, ← mul_smul_comm]
rw [← smul_mul_assoc, ← mul_smul_comm]
rw [← smul_mul_assoc, ← mul_smul_comm]
rw [← smul_mul_assoc, ← mul_smul_comm]
repeat rw [mul_assoc]
rw [← mul_sub, ← mul_sub, ← mul_sub]
rw [← sub_mul, ← sub_mul, ← sub_mul]
@ -181,7 +181,7 @@ lemma ι_timeOrder_superCommute_eq_time {φ ψ : 𝓕.CrAnStates}
ι 𝓣ᶠ(a * [ofCrAnState φ, ofCrAnState ψ]ₛca * b) =
ι ([ofCrAnState φ, ofCrAnState ψ]ₛca * 𝓣ᶠ(a * b)) := by
let pb (b : 𝓕.CrAnAlgebra) (hc : b ∈ Submodule.span ℂ (Set.range ofCrAnListBasis)) :
Prop := ι 𝓣ᶠ(a * [ofCrAnState φ, ofCrAnState ψ]ₛca * b) =
Prop := ι 𝓣ᶠ(a * [ofCrAnState φ, ofCrAnState ψ]ₛca * b) =
ι ([ofCrAnState φ, ofCrAnState ψ]ₛca * 𝓣ᶠ(a * b))
change pb b (Basis.mem_span _ b)
apply Submodule.span_induction
@ -201,7 +201,7 @@ lemma ι_timeOrder_superCommute_eq_time {φ ψ : 𝓕.CrAnStates}
simp [mul_sub, sub_mul, ← ofCrAnList_append]
rw [timeOrder_ofCrAnList, timeOrder_ofCrAnList]
have h1 : crAnTimeOrderSign (φs' ++ φ :: ψ :: φs) = crAnTimeOrderSign (φs' ++ ψ :: φ :: φs) := by
trans crAnTimeOrderSign (φs' ++ [φ, ψ] ++ φs)
trans crAnTimeOrderSign (φs' ++ [φ, ψ] ++ φs)
simp
rw [crAnTimeOrderSign]
have hp : List.Perm [φ,ψ] [ψ,φ] := by exact List.Perm.swap ψ φ []
@ -244,7 +244,7 @@ lemma ι_timeOrder_superCommute_eq_time {φ ψ : 𝓕.CrAnStates}
rw [← map_mul, ← map_mul, ← map_mul, ← map_mul]
rw [← ofCrAnList_append, ← ofCrAnList_append, ← ofCrAnList_append, ← ofCrAnList_append]
have h1 := insertionSort_of_takeWhile_filter 𝓕.crAnTimeOrderRel φ φs' φs
simp at h1 ⊢
simp at h1 ⊢
rw [← h1]
rw [← crAnTimeOrderList]
by_cases hq : (𝓕 |>ₛ φ) ≠ (𝓕 |>ₛ ψ)
@ -269,7 +269,7 @@ lemma ι_timeOrder_superCommute_eq_time {φ ψ : 𝓕.CrAnStates}
lemma ι_timeOrder_superCommute_neq_time {φ ψ : 𝓕.CrAnStates}
(hφψ : ¬ (crAnTimeOrderRel φ ψ ∧ crAnTimeOrderRel ψ φ)) (a b : 𝓕.CrAnAlgebra) :
(hφψ : ¬ (crAnTimeOrderRel φ ψ ∧ crAnTimeOrderRel ψ φ)) (a b : 𝓕.CrAnAlgebra) :
ι 𝓣ᶠ(a * [ofCrAnState φ, ofCrAnState ψ]ₛca * b) = 0 := by
rw [timeOrder_timeOrder_mid]
have hφψ : ¬ (crAnTimeOrderRel φ ψ) ∨ ¬ (crAnTimeOrderRel ψ φ) := by
@ -309,7 +309,7 @@ lemma ι_timeOrder_zero_of_mem_ideal (a : 𝓕.CrAnAlgebra)
simp
| Or.inr (Or.inl hc) =>
obtain ⟨φa, hφa, φb, hφb, rfl⟩ := hc
by_cases heqt : (crAnTimeOrderRel φa φb ∧ crAnTimeOrderRel φb φa)
by_cases heqt : (crAnTimeOrderRel φa φb ∧ crAnTimeOrderRel φb φa)
· rw [ι_timeOrder_superCommute_eq_time]
simp
rw [ι_superCommute_of_create_create]
@ -321,7 +321,7 @@ lemma ι_timeOrder_zero_of_mem_ideal (a : 𝓕.CrAnAlgebra)
· rw [ι_timeOrder_superCommute_neq_time heqt]
| Or.inr (Or.inr (Or.inl hc)) =>
obtain ⟨φa, hφa, φb, hφb, rfl⟩ := hc
by_cases heqt : (crAnTimeOrderRel φa φb ∧ crAnTimeOrderRel φb φa)
by_cases heqt : (crAnTimeOrderRel φa φb ∧ crAnTimeOrderRel φb φa)
· rw [ι_timeOrder_superCommute_eq_time]
simp
rw [ι_superCommute_of_annihilate_annihilate]
@ -333,7 +333,7 @@ lemma ι_timeOrder_zero_of_mem_ideal (a : 𝓕.CrAnAlgebra)
· rw [ι_timeOrder_superCommute_neq_time heqt]
| Or.inr (Or.inr (Or.inr hc)) =>
obtain ⟨φa, φb, hdiff, rfl⟩ := hc
by_cases heqt : (crAnTimeOrderRel φa φb ∧ crAnTimeOrderRel φb φa)
by_cases heqt : (crAnTimeOrderRel φa φb ∧ crAnTimeOrderRel φb φa)
· rw [ι_timeOrder_superCommute_eq_time]
simp
rw [ι_superCommute_of_diff_statistic]