Decompose to Charge Map
FTheory.SU5.TenQuanta.decompose_toChargeMap
Project documentation
The decomposition of a TenQuanta into a TenQuanta which has the same reduce by has fluxes {⟨1, 0⟩, ⟨1, 0⟩, ⟨1, 0⟩} or {⟨1, 1⟩, ⟨1, -1⟩, ⟨1, 0⟩} only. This only works for fluxes which have no exotics or zeros. -/ def decompose (x : TenQuanta 𝓩) : TenQuanta 𝓩 := x.bind fun p => (decomposeFluxes p.2).map fun f => (p.1, f) /-! #### C.2.1. Decompos...
Exact Lean statement
lemma decompose_toChargeMap [DecidableEq 𝓩] (x : TenQuanta 𝓩)
(hx : x.toFluxesTen ∈ FluxesTen.elemsNoExotics) :
x.decompose.toChargeMap = x.toChargeMapFormal artifact
Lean source
lemma decompose_toChargeMap [DecidableEq 𝓩] (x : TenQuanta 𝓩) (hx : x.toFluxesTen ∈ FluxesTen.elemsNoExotics) : x.decompose.toChargeMap = x.toChargeMap := by ext q rw [toChargeMap, decompose_filter_charge] simp [decompose] rw [Multiset.map_bind] simp only [Multiset.map_map, Function.comp_apply, Multiset.map_id', Multiset.sum_bind] rw [toChargeMap] congr 1 refine Multiset.map_congr rfl fun a ha => ?_ apply decomposeFluxes_sum_of_noExotics use x.toFluxesTen simp_all [toFluxesTen] use a.1 exact ha.1- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/StringTheory/FTheory/SU5/Quanta/TenQuanta.lean:649-664
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