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refactor: Lint

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jstoobysmith 2025-01-24 11:25:22 +00:00
parent 2490535569
commit c7bd59c981
10 changed files with 120 additions and 90 deletions
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31
HepLean/PerturbationTheory/WickContraction/InsertAndContract.lean
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@ -29,12 +29,13 @@ open HepLean.Fin
`j : Option (c.uncontracted)` of `c`.
The Wick contraction associated with `(φs.insertIdx i φ).length` formed by 'inserting' `φ`
into `φs` after the first `i` elements and contracting it optionally with j. -/
def insertAndContract {φs : List 𝓕.States} (φ : 𝓕.States) (φsΛ : WickContraction φs.length)
def insertAndContract {φs : List 𝓕.States} (φ : 𝓕.States) (φsΛ : WickContraction φs.length)
(i : Fin φs.length.succ) (j : Option φsΛ.uncontracted) :
WickContraction (φs.insertIdx i φ).length :=
congr (by simp) (φsΛ.insertAndContractNat i j)
scoped[WickContraction] notation φs "↩Λ" φ:max i:max j => insertAndContract φ φs i j
@[inherit_doc insertAndContract]
scoped[WickContraction] notation φs "↩Λ" φ:max i:max j => insertAndContract φ φs i j
@[simp]
lemma insertAndContract_fstFieldOfContract (φ : 𝓕.States) (φs : List 𝓕.States)
@ -56,14 +57,16 @@ lemma insertAndContract_sndFieldOfContract (φ : 𝓕.States) (φs : List 𝓕.S
lemma insertAndContract_fstFieldOfContract_some_incl (φ : 𝓕.States) (φs : List 𝓕.States)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : φsΛ.uncontracted) :
(insertAndContract φ φsΛ i (some j)).fstFieldOfContract
(congrLift (insertIdx_length_fin φ φs i).symm ⟨{i, i.succAbove j}, by simp [insertAndContractNat]⟩) =
(congrLift (insertIdx_length_fin φ φs i).symm ⟨{i, i.succAbove j}, by
simp [insertAndContractNat]⟩) =
if i < i.succAbove j.1 then
finCongr (insertIdx_length_fin φ φs i).symm i else
finCongr (insertIdx_length_fin φ φs i).symm (i.succAbove j.1) := by
split
· rename_i h
refine (insertAndContract φ φsΛ i (some j)).eq_fstFieldOfContract_of_mem
(a := congrLift (insertIdx_length_fin φ φs i).symm ⟨{i, i.succAbove j}, by simp [insertAndContractNat]⟩)
(a := congrLift (insertIdx_length_fin φ φs i).symm ⟨{i, i.succAbove j}, by
simp [insertAndContractNat]⟩)
(i := finCongr (insertIdx_length_fin φ φs i).symm i) (j :=
finCongr (insertIdx_length_fin φ φs i).symm (i.succAbove j)) ?_ ?_ ?_
· simp [congrLift]
@ -72,7 +75,8 @@ lemma insertAndContract_fstFieldOfContract_some_incl (φ : 𝓕.States) (φs : L
simp_all
· rename_i h
refine (insertAndContract φ φsΛ i (some j)).eq_fstFieldOfContract_of_mem
(a := congrLift (insertIdx_length_fin φ φs i).symm ⟨{i, i.succAbove j}, by simp [insertAndContractNat]⟩)
(a := congrLift (insertIdx_length_fin φ φs i).symm ⟨{i, i.succAbove j}, by
simp [insertAndContractNat]⟩)
(i := finCongr (insertIdx_length_fin φ φs i).symm (i.succAbove j))
(j := finCongr (insertIdx_length_fin φ φs i).symm i) ?_ ?_ ?_
· simp [congrLift]
@ -141,7 +145,8 @@ lemma insertAndContract_some_succAbove_getDual?_eq_option (φ : 𝓕.States) (φ
(i.succAbove j)) = Option.map (Fin.cast (insertIdx_length_fin φ φs i).symm ∘ i.succAbove)
(φsΛ.getDual? j) := by
simp only [Nat.succ_eq_add_one, insertAndContract, getDual?_congr, finCongr_apply, Fin.cast_trans,
Fin.cast_eq_self, ne_eq, hkj, not_false_eq_true, insertAndContractNat_some_getDual?_of_neq, Option.map_map]
Fin.cast_eq_self, ne_eq, hkj, not_false_eq_true, insertAndContractNat_some_getDual?_of_neq,
Option.map_map]
rfl
@[simp]
@ -167,14 +172,16 @@ lemma insertAndContract_none_getDual?_get_eq (φ : 𝓕.States) (φs : List 𝓕
lemma insertAndContract_sndFieldOfContract_some_incl (φ : 𝓕.States) (φs : List 𝓕.States)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : φsΛ.uncontracted) :
(φsΛ ↩Λ φ i (some j)).sndFieldOfContract
(congrLift (insertIdx_length_fin φ φs i).symm ⟨{i, i.succAbove j}, by simp [insertAndContractNat]⟩) =
(congrLift (insertIdx_length_fin φ φs i).symm ⟨{i, i.succAbove j}, by
simp [insertAndContractNat]⟩) =
if i < i.succAbove j.1 then
finCongr (insertIdx_length_fin φ φs i).symm (i.succAbove j.1) else
finCongr (insertIdx_length_fin φ φs i).symm i := by
split
· rename_i h
refine (φsΛ ↩Λ φ i (some j)).eq_sndFieldOfContract_of_mem
(a := congrLift (insertIdx_length_fin φ φs i).symm ⟨{i, i.succAbove j}, by simp [insertAndContractNat]⟩)
(a := congrLift (insertIdx_length_fin φ φs i).symm ⟨{i, i.succAbove j}, by
simp [insertAndContractNat]⟩)
(i := finCongr (insertIdx_length_fin φ φs i).symm i) (j :=
finCongr (insertIdx_length_fin φ φs i).symm (i.succAbove j)) ?_ ?_ ?_
· simp [congrLift]
@ -183,7 +190,8 @@ lemma insertAndContract_sndFieldOfContract_some_incl (φ : 𝓕.States) (φs : L
simp_all
· rename_i h
refine (φsΛ ↩Λ φ i (some j)).eq_sndFieldOfContract_of_mem
(a := congrLift (insertIdx_length_fin φ φs i).symm ⟨{i, i.succAbove j}, by simp [insertAndContractNat]⟩)
(a := congrLift (insertIdx_length_fin φ φs i).symm ⟨{i, i.succAbove j}, by
simp [insertAndContractNat]⟩)
(i := finCongr (insertIdx_length_fin φ φs i).symm (i.succAbove j))
(j := finCongr (insertIdx_length_fin φ φs i).symm i) ?_ ?_ ?_
· simp [congrLift]
@ -240,8 +248,8 @@ lemma self_not_mem_insertAndContractLiftFinset (φ : 𝓕.States) {φs : List
lemma succAbove_mem_insertAndContractLiftFinset (φ : 𝓕.States) {φs : List 𝓕.States}
(i : Fin φs.length.succ) (a : Finset (Fin φs.length)) (j : Fin φs.length) :
Fin.cast (insertIdx_length_fin φ φs i).symm (i.succAbove j) ∈ insertAndContractLiftFinset φ i a ↔
j ∈ a := by
Fin.cast (insertIdx_length_fin φ φs i).symm (i.succAbove j)
∈ insertAndContractLiftFinset φ i a ↔ j ∈ a := by
simp only [insertAndContractLiftFinset, Finset.mem_map_equiv, finCongr_symm, finCongr_apply,
Fin.cast_trans, Fin.cast_eq_self]
simp only [Finset.mem_map, Fin.succAboveEmb_apply]
@ -268,7 +276,6 @@ lemma insert_fin_eq_self (φ : 𝓕.States) {φs : List 𝓕.States}
use z
rfl
lemma insertLift_sum (φ : 𝓕.States) {φs : List 𝓕.States}
(i : Fin φs.length.succ) [AddCommMonoid M] (f : WickContraction (φs.insertIdx i φ).length → M) :
∑ c, f c =