Research proof index

A charge spectrum is complete if it has all types of fields. -/ def IsComplete (x : ChargeSpectrum 𝓩) : Prop := x.qHd.isSome ∧ x.qHu.isSome ∧ x.Q5 ≠ ∅ ∧ x.Q10 ≠ ∅ instance [DecidableEq 𝓩] (x : ChargeSpectrum 𝓩) : Decidable (IsComplete x) := inferInstanceAs (Decidable (x.qHd.isSome ∧ x.qHu.isSome ∧ x.Q5 ≠ ∅ ∧ x.Q10 ≠ ∅)) /-! ### A.1. The empty spectrum...

The proposition which is true if the addition of a charge q10 to a set of charges x leads x to being phenomenologically constrained. -/ def IsPhenoConstrainedQ10 [DecidableEq 𝓩] (x : ChargeSpectrum 𝓩) (q10 : 𝓩) : Prop := x.AllowsTermQ10 q10 μ ∨ x.AllowsTermQ10 q10 β ∨ x.AllowsTermQ10 q10 Λ ∨ x.AllowsTermQ10 q10 W2 ∨ x.AllowsTermQ10 q10 W4 ∨ x.All...

The proposition which is true if the addition of a charge q5 to a set of charge x leads x to being phenomenologically constrained. -/ def IsPhenoConstrainedQ5 [DecidableEq 𝓩] (x : ChargeSpectrum 𝓩) (q5 : 𝓩) : Prop := x.AllowsTermQ5 q5 μ ∨ x.AllowsTermQ5 q5 β ∨ x.AllowsTermQ5 q5 Λ ∨ x.AllowsTermQ5 q5 W2 ∨ x.AllowsTermQ5 q5 W4 ∨ x.AllowsTermQ5 q5 K...

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...

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...