Research proof index

Ancestor of an action entity should also be an action entity

More well-formedness properties of env.reqty.

Gives a factor of - 1 for every fermion-fermion (q is 1) crossing that occurs when sorting a list of based on r. -/ def koszulSign (q : 𝓕 → FieldStatistic) (le : 𝓕 → 𝓕 → Prop) [DecidableRel le] : List 𝓕 → ℂ | [] => 1 | a :: l => koszulSignInsert q le a l * koszulSign q le l @[simp] lemma koszulSign_singleton (q : 𝓕 → FieldStatistic) (le : 𝓕...

Given a Wick contraction φsΛ for a list φs of 𝓕.FieldOp, an element φ of 𝓕.FieldOp, an i ≤ φs.length and a k in Option φsΛ.uncontracted i.e. is either none or some element of φsΛ.uncontracted, the new Wick contraction φsΛ.insertAndContract φ i k is defined by inserting φ into φs after the first i-elements and moving the value...

For a list φs of 𝓕.FieldOp, a Wick contraction φsΛ of φs, an element φ of 𝓕.FieldOp and a i ≤ φs.length then a sum over 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....

Given a Wick contraction c for n, a position i : Fin n.succ and an optional uncontracted element j : Option (c.uncontracted) of c. The Wick contraction for n.succ formed by 'inserting' i into Fin n and contracting it optionally with j. -/ def insertAndContractNat (c : WickContraction n) (i : Fin n.succ) (j : Option (c.uncontracted)) : Wi...