Research proof index

A collection of charges x : Charges is said to minimally allow the potential term T if it allows T and no strict subset of it allows T. -/ def MinimallyAllowsTerm (x : ChargeSpectrum 𝓩) (T : PotentialTerm) : Prop := ∀ y ∈ x.powerset, y = x ↔ y.AllowsTerm T /-! ### A.1. Decidability of MinimallyAllowsTerm We show that MinimallyAllowsTerm is de...

A collection of charges x : Charges is said to minimally allow the potential term T if it allows T and no strict subset of it allows T. -/ def MinimallyAllowsTerm (x : ChargeSpectrum 𝓩) (T : PotentialTerm) : Prop := ∀ y ∈ x.powerset, y = x ↔ y.AllowsTerm T /-! ### A.1. Decidability of MinimallyAllowsTerm We show that MinimallyAllowsTerm is de...

The multiset of all charges within ofFinset S5 S10 which minimally allow the potential term T. -/ def minimallyAllowsTermsOfFinset (S5 S10 : Finset 𝓩) : (T : PotentialTerm) → Multiset (ChargeSpectrum 𝓩) | μ => let SqHd := S5.val let SqHu := S5.val let prod := SqHd ×ˢ (SqHu) let Filt := prod.filter (fun x => - x.1 + x.2 = 0) (Filt.map (fun x => ⟨x.1,...

The multiset of all charges within ofFinset S5 S10 which minimally allow the potential term T. -/ def minimallyAllowsTermsOfFinset (S5 S10 : Finset 𝓩) : (T : PotentialTerm) → Multiset (ChargeSpectrum 𝓩) | μ => let SqHd := S5.val let SqHu := S5.val let prod := SqHd ×ˢ (SqHu) let Filt := prod.filter (fun x => - x.1 + x.2 = 0) (Filt.map (fun x => ⟨x.1,...

Given a collection of charges x in ofFinset S5 S10, the minimal charges y in ofFinset S5 S10 which are a super sets of x. -/ def minimalSuperSet (S5 S10 : Finset 𝓩) (x : ChargeSpectrum 𝓩) : Finset (ChargeSpectrum 𝓩) := let SqHd := if x.qHd.isSome then ∅ else S5.map ⟨fun y => ⟨some y, x.qHu, x.Q5, x.Q10⟩, by intro y1 y2; simp⟩ let SqHu := if x...

Given a charges x : Charges associated to the representations, and a potential term T, the charges associated with instances of that potential term. -/ def ofPotentialTerm (x : ChargeSpectrum 𝓩) (T : PotentialTerm) : Multiset 𝓩 := let add : Multiset 𝓩 → Multiset 𝓩 → Multiset 𝓩 := fun a b => (a ×ˢ b).map fun (x, y) => x + y (T.toFieldLabel.map fun...