Research proof index

The decomposition of a FiveQuanta into a FiveQuanta which has the same reduce by has fluxes ⟨1, -1⟩ and ⟨0,1⟩ only. -/ def decompose (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.bind fun p => (decomposeFluxes p.2).map fun f => (p.1, f) /-! #### C.2.1. Decomposition distributes over addition -/ lemma decompose_add (x y : FiveQuanta 𝓩) : (x + y).deco...

Given a finite set of charges c the FiveQuanta which do not have exotics, duplicate charges or zero fluxes, which map down to c. -/ def liftCharge (c : Finset 𝓩) : Multiset (FiveQuanta 𝓩) := /- The multisets of cardinality 3 containing 3 elements of c. -/ let S53 : Multiset (Multiset 𝓩) := toMultisetsThree c /- Pairs of multisets (s1, s2) such...

Given a finite set of charges c the FiveQuanta which do not have exotics, duplicate charges or zero fluxes, which map down to c. -/ def liftCharge (c : Finset 𝓩) : Multiset (FiveQuanta 𝓩) := /- The multisets of cardinality 3 containing 3 elements of c. -/ let S53 : Multiset (Multiset 𝓩) := toMultisetsThree c /- Pairs of multisets (s1, s2) such...

Given a finite set of charges c the FiveQuanta which do not have exotics, duplicate charges or zero fluxes, which map down to c. -/ def liftCharge (c : Finset 𝓩) : Multiset (FiveQuanta 𝓩) := /- The multisets of cardinality 3 containing 3 elements of c. -/ let S53 : Multiset (Multiset 𝓩) := toMultisetsThree c /- Pairs of multisets (s1, s2) such...

The reduce of FiveQuanta is a new FiveQuanta with all the fluxes corresponding to the same charge (i.e. representation) added together. -/ def reduce (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.toCharges.dedup.map fun q5 => (q5, ((x.filter (fun f => f.1 = q5)).map (fun y => y.2)).sum) /-! ### B.1. The reduced FiveQuanta has no duplicate elements -/ l...

The reduce of FiveQuanta is a new FiveQuanta with all the fluxes corresponding to the same charge (i.e. representation) added together. -/ def reduce (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.toCharges.dedup.map fun q5 => (q5, ((x.filter (fun f => f.1 = q5)).map (fun y => y.2)).sum) /-! ### B.1. The reduced FiveQuanta has no duplicate elements -/ l...