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refactor: improve docs

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jstoobysmith 2025-01-24 11:09:25 +00:00
parent eeacdef74e
commit 2490535569
6 changed files with 126 additions and 57 deletions
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22
HepLean/PerturbationTheory/WickContraction/InsertAndContract.lean
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@ -268,6 +268,20 @@ 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 =
∑ (φsΛ : WickContraction φs.length), ∑ (k : Option φsΛ.uncontracted), f (φsΛ ↩Λ φ i k) := by
rw [sum_extractEquiv_congr (finCongr (insertIdx_length_fin φ φs i).symm i) f
(insertIdx_length_fin φ φs i)]
rfl
/-!
## Uncontracted list
-/
lemma insertAndContract_uncontractedList_none_map (φ : 𝓕.States) {φs : List 𝓕.States}
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) :
[φsΛ ↩Λ φ i none]ᵘᶜ = List.insertIdx (φsΛ.uncontractedListOrderPos i) φ [φsΛ]ᵘᶜ := by
@ -283,12 +297,4 @@ lemma insertAndContract_uncontractedList_none_map (φ : 𝓕.States) {φs : List
conv_rhs => rw [get_eq_insertIdx_succAbove φ φs i]
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 =
∑ (φsΛ : WickContraction φs.length), ∑ (k : Option φsΛ.uncontracted), f (φsΛ ↩Λ φ i k) := by
rw [sum_extractEquiv_congr (finCongr (insertIdx_length_fin φ φs i).symm i) f
(insertIdx_length_fin φ φs i)]
rfl
end WickContraction