Research proof index

For a given S5 S10 : Finset 𝓩, the minimal multiset of charges which satisfies the condition ContainsPhenoCompletionsOfMinimallyAllows. That is to say, every multiset of charges which satisfies ContainsPhenoCompletionsOfMinimallyAllows has completeMinSubset as a subset. -/ def completeMinSubset (S5 S10 : Finset 𝓩) : Multiset (ChargeSpectrum 𝓩)...

The multisets completions S5 S10 x and completionsTopYukawa S5 x are equivalent if x minimally allows the top Yukawa.

The proposition that for multiset set of charges charges contains all viable completions of charges which allow the top Yukawa, given allowed values of 5d and 10d charges S5 and S10. -/ def ContainsPhenoCompletionsOfMinimallyAllows (S5 S10 : Finset 𝓩) (charges : Multiset (ChargeSpectrum 𝓩)) : Prop := ∀ x ∈ (minimallyAllowsTermsOfFinset S5 S10...

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,...

If x is a subset of y and y is complete, then there is a completion of x which is also a subset of y.

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...