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refactor: lint

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jstoobysmith 2025-02-03 11:42:56 +00:00
parent 6433259bc4
commit 70f617096b
16 changed files with 103 additions and 87 deletions
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33
HepLean/PerturbationTheory/Algebras/FieldOpFreeAlgebra/NormalOrder.lean
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@ -69,7 +69,8 @@ lemma normalOrderF_normalOrderF_mid (a b c : 𝓕.FieldOpFreeAlgebra) :
obtain ⟨φs', rfl⟩ := hx
simp only [ofListBasis_eq_ofList, pb]
let pa (a : 𝓕.FieldOpFreeAlgebra) (ha : a ∈ Submodule.span ℂ (Set.range ofCrAnListFBasis)) :
Prop := 𝓝ᶠ(a * ofCrAnListF φs' * ofCrAnListF φs) = 𝓝ᶠ(a * 𝓝ᶠ(ofCrAnListF φs') * ofCrAnListF φs)
Prop := 𝓝ᶠ(a * ofCrAnListF φs' * ofCrAnListF φs) =
𝓝ᶠ(a * 𝓝ᶠ(ofCrAnListF φs') * ofCrAnListF φs)
change pa a (Basis.mem_span _ a)
apply Submodule.span_induction
· intro x hx
@ -101,13 +102,15 @@ lemma normalOrderF_normalOrderF_mid (a b c : 𝓕.FieldOpFreeAlgebra) :
· intro x hx h hp
simp_all [pc]
lemma normalOrderF_normalOrderF_right (a b : 𝓕.FieldOpFreeAlgebra) : 𝓝ᶠ(a * b) = 𝓝ᶠ(a * 𝓝ᶠ(b)) := by
lemma normalOrderF_normalOrderF_right (a b : 𝓕.FieldOpFreeAlgebra) :
𝓝ᶠ(a * b) = 𝓝ᶠ(a * 𝓝ᶠ(b)) := by
trans 𝓝ᶠ(a * b * 1)
· simp
· rw [normalOrderF_normalOrderF_mid]
simp
lemma normalOrderF_normalOrderF_left (a b : 𝓕.FieldOpFreeAlgebra) : 𝓝ᶠ(a * b) = 𝓝ᶠ(𝓝ᶠ(a) * b) := by
lemma normalOrderF_normalOrderF_left (a b : 𝓕.FieldOpFreeAlgebra) :
𝓝ᶠ(a * b) = 𝓝ᶠ(𝓝ᶠ(a) * b) := by
trans 𝓝ᶠ(1 * a * b)
· simp
· rw [normalOrderF_normalOrderF_mid]
@ -374,7 +377,8 @@ lemma normalOrderF_ofFieldOpF_mul_ofFieldOpF (φ φ' : 𝓕.FieldOp) :
(crPartF φ' * anPartF φ) +
crPartF φ * anPartF φ' +
anPartF φ * anPartF φ' := by
rw [ofFieldOpF_eq_crPartF_add_anPartF, ofFieldOpF_eq_crPartF_add_anPartF, mul_add, add_mul, add_mul]
rw [ofFieldOpF_eq_crPartF_add_anPartF, ofFieldOpF_eq_crPartF_add_anPartF, mul_add, add_mul,
add_mul]
simp only [map_add, normalOrderF_crPartF_mul_crPartF, normalOrderF_anPartF_mul_crPartF,
instCommGroup.eq_1, normalOrderF_crPartF_mul_anPartF, normalOrderF_anPartF_mul_anPartF]
abel
@ -397,8 +401,8 @@ lemma normalOrderF_superCommuteF_ofCrAnListF_create_create_ofCrAnListF
rw [superCommuteF_ofCrAnOpF_ofCrAnOpF, mul_sub, sub_mul, map_sub]
conv_lhs =>
lhs; rhs
rw [← ofCrAnListF_singleton, ← ofCrAnListF_singleton, ← ofCrAnListF_append, ← ofCrAnListF_append,
← ofCrAnListF_append]
rw [← ofCrAnListF_singleton, ← ofCrAnListF_singleton, ← ofCrAnListF_append,
← ofCrAnListF_append, ← ofCrAnListF_append]
conv_lhs =>
lhs
rw [normalOrderF_ofCrAnListF, normalOrderList_eq_createFilter_append_annihilateFilter]
@ -414,8 +418,8 @@ lemma normalOrderF_superCommuteF_ofCrAnListF_create_create_ofCrAnListF
rhs; rhs
rw [smul_mul_assoc, Algebra.mul_smul_comm, smul_mul_assoc]
rhs
rw [← ofCrAnListF_singleton, ← ofCrAnListF_singleton, ← ofCrAnListF_append, ← ofCrAnListF_append,
← ofCrAnListF_append]
rw [← ofCrAnListF_singleton, ← ofCrAnListF_singleton, ← ofCrAnListF_append,
← ofCrAnListF_append, ← ofCrAnListF_append]
conv_lhs =>
rhs
rw [map_smul]
@ -459,8 +463,8 @@ lemma normalOrderF_superCommuteF_ofCrAnListF_annihilate_annihilate_ofCrAnListF
rw [superCommuteF_ofCrAnOpF_ofCrAnOpF, mul_sub, sub_mul, map_sub]
conv_lhs =>
lhs; rhs
rw [← ofCrAnListF_singleton, ← ofCrAnListF_singleton, ← ofCrAnListF_append, ← ofCrAnListF_append,
← ofCrAnListF_append]
rw [← ofCrAnListF_singleton, ← ofCrAnListF_singleton, ← ofCrAnListF_append,
← ofCrAnListF_append, ← ofCrAnListF_append]
conv_lhs =>
lhs
rw [normalOrderF_ofCrAnListF, normalOrderList_eq_createFilter_append_annihilateFilter]
@ -477,8 +481,8 @@ lemma normalOrderF_superCommuteF_ofCrAnListF_annihilate_annihilate_ofCrAnListF
rw [smul_mul_assoc]
rw [Algebra.mul_smul_comm, smul_mul_assoc]
rhs
rw [← ofCrAnListF_singleton, ← ofCrAnListF_singleton, ← ofCrAnListF_append, ← ofCrAnListF_append,
← ofCrAnListF_append]
rw [← ofCrAnListF_singleton, ← ofCrAnListF_singleton, ← ofCrAnListF_append,
← ofCrAnListF_append, ← ofCrAnListF_append]
conv_lhs =>
rhs
rw [map_smul]
@ -524,8 +528,9 @@ lemma ofCrAnListF_superCommuteF_normalOrderF_ofCrAnListF (φs φs' : List 𝓕.C
[ofCrAnListF φs, 𝓝ᶠ(ofCrAnListF φs')]ₛca =
ofCrAnListF φs * 𝓝ᶠ(ofCrAnListF φs') -
𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • 𝓝ᶠ(ofCrAnListF φs') * ofCrAnListF φs := by
simp [normalOrderF_ofCrAnListF, map_smul, superCommuteF_ofCrAnListF_ofCrAnListF, ofCrAnListF_append,
smul_sub, smul_smul, mul_comm]
simp only [normalOrderF_ofCrAnListF, map_smul, superCommuteF_ofCrAnListF_ofCrAnListF,
ofCrAnListF_append, instCommGroup.eq_1, normalOrderList_statistics, smul_sub, smul_smul,
Algebra.mul_smul_comm, mul_comm, Algebra.smul_mul_assoc]
lemma ofCrAnListF_superCommuteF_normalOrderF_ofFieldOpListF (φs : List 𝓕.CrAnFieldOp)
(φs' : List 𝓕.FieldOp) : [ofCrAnListF φs, 𝓝ᶠ(ofFieldOpListF φs')]ₛca =