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refactor: Slight adjustments to doc-strings

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jstoobysmith 2025-02-12 06:14:11 +00:00
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12
HepLean/PerturbationTheory/WickContraction/InsertAndContract.lean
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@ -291,9 +291,15 @@ lemma insert_fin_eq_self (φ : 𝓕.FieldOp) {φs : List 𝓕.FieldOp}
Wick contractions of `φs` with `φ` inserted at `i` is equal to the sum over Wick contractions
`φsΛ` of just `φs` and the sum over optional uncontracted elements of the `φsΛ`.
In other words, `∑ (φsΛ : WickContraction (φs.insertIdx i φ).length), f φsΛ` is equal to
`∑ (φsΛ : WickContraction φs.length), ∑ (k : Option φsΛ.uncontracted), f (φsΛ ↩Λ φ i k) `.
where `(φs.insertIdx i φ)` is `φs` with `φ` inserted at position `i`. -/
In other words,
`∑ (φsΛ : WickContraction (φs.insertIdx i φ).length), f φsΛ`
where `(φs.insertIdx i φ)` is `φs` with `φ` inserted at position `i`. is equal to
`∑ (φsΛ : WickContraction φs.length), ∑ k, f (φsΛ ↩Λ φ i k) `.
where the sum over `k` is over all `k` in `Option φsΛ.uncontracted`. -/
lemma insertLift_sum (φ : 𝓕.FieldOp) {φs : List 𝓕.FieldOp}
(i : Fin φs.length.succ) [AddCommMonoid M] (f : WickContraction (φs.insertIdx i φ).length → M) :
∑ c, f c =