Research proof index

The charge spectrum allowsTermForm a b c T allows the potential term T. -/ lemma allowsTermForm_allowsTerm {a b c : 𝓩} {T : PotentialTerm} : (allowsTermForm a b c T).AllowsTerm T := by simp [AllowsTerm, ofPotentialTerm, allowsTermForm] cases T all_goals simp [PotentialTerm.toFieldLabel, ofFieldLabel] case Λ => exact ⟨a, b, by simp⟩ case K1 | topYukaw...

The charge spectrum allowsTermForm a b c T allows the potential term T. -/ lemma allowsTermForm_allowsTerm {a b c : 𝓩} {T : PotentialTerm} : (allowsTermForm a b c T).AllowsTerm T := by simp [AllowsTerm, ofPotentialTerm, allowsTermForm] cases T all_goals simp [PotentialTerm.toFieldLabel, ofFieldLabel] case Λ => exact ⟨a, b, by simp⟩ case K1 | topYukaw...

The proposition for which says, given a charge x adding a charge q5 permits the existence of a potential term T due to the addition of that charge. -/ def AllowsTermQ10 (x : ChargeSpectrum 𝓩) (q10 : 𝓩) (T : PotentialTerm) : Prop := match T with | .μ => false | .β => false | .Λ => (0 : 𝓩) ∈ (x.Q5.product x.Q5).val.map (fun (y, z) => y + z + q10) |...

The proposition for which says, given a charge x adding a charge q5 permits the existence of a potential term T due to the addition of that charge. -/ def AllowsTermQ5 (x : ChargeSpectrum 𝓩) (q5 : 𝓩) (T : PotentialTerm) : Prop := match T with | .μ => false | .β => match x with | ⟨_, some qHu, _, _⟩ => q5 = qHu | _ => false | .Λ => (0 : 𝓩) ∈ ((ins...

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...

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)...