Research proof index

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...

The charge spectrum allowsTermForm a b c T allows the potential term T.

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) |...