Research proof index

Double contraction. Contracting the last k of k+2 index pairs leaves two free pairs, with value a 2×2 generalized Kronecker delta times the factorial factor.

Symbol-level double contraction, two free pairs.

Full contraction. Iterating the snoc contraction over all four indices: ∑_f δ^{f}_{f} = 4!. Here f ranges over all maps Fin 4 → Fin 4.

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.