Research proof index

Given an additive monoid homomorphisms f : 𝓩 →+ 𝓩1, for a charge x : Charges 𝓩, x.map f is the charge of Charges 𝓩1 obtained by mapping the elements of x by f. -/ def map (f : 𝓩 →+ 𝓩1) (x : ChargeSpectrum 𝓩) : ChargeSpectrum 𝓩1 where qHd := f <$> x.qHd qHu := f <$> x.qHu Q5 := x.Q5.image f Q10 := x.Q10.image f /- ### A.1. Mapping the e...

Given an additive monoid homomorphisms f : 𝓩 →+ 𝓩1, for a charge x : Charges 𝓩, x.map f is the charge of Charges 𝓩1 obtained by mapping the elements of x by f. -/ def map (f : 𝓩 →+ 𝓩1) (x : ChargeSpectrum 𝓩) : ChargeSpectrum 𝓩1 where qHd := f <$> x.qHd qHu := f <$> x.qHu Q5 := x.Q5.image f Q10 := x.Q10.image f /- ### A.1. Mapping the e...

A charge spectrum which is a member of the completions of another charge spectrum is complete.

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 set of charges of the form (qHd, qHu, {q5}, {-qHd-q5, q10, qHu - q10}) This includes every charge which minimally allows for the top and bottom Yukawas. -/ def minTopBottom (S5 S10 : Finset 𝓩) : Multiset (ChargeSpectrum 𝓩) := Multiset.dedup <| (S5.val ×ˢ S5.val ×ˢ S5.val ×ˢ S10.val).map (fun x => ⟨x.1, x.2.1, {x.2.2.1}, {- x.1 - x.2.2.1, x.2.2.2,...

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,...