Decompose to Fluxes Ten
FTheory.SU5.TenQuanta.decompose_toFluxesTen
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_toFluxesTen (x : TenQuanta 𝓩)
(hx : x.toFluxesTen ∈ FluxesTen.elemsNoExotics) :
x.decompose.toFluxesTen = {⟨1, 0⟩, ⟨1, 0⟩, ⟨1, 0⟩} ∨
x.decompose.toFluxesTen = {⟨1, 1⟩, ⟨1, -1⟩, ⟨1, 0⟩}Formal artifact
Lean source
lemma decompose_toFluxesTen (x : TenQuanta 𝓩) (hx : x.toFluxesTen ∈ FluxesTen.elemsNoExotics) : x.decompose.toFluxesTen = {⟨1, 0⟩, ⟨1, 0⟩, ⟨1, 0⟩} ∨ x.decompose.toFluxesTen = {⟨1, 1⟩, ⟨1, -1⟩, ⟨1, 0⟩} := by rw [toFluxesTen, decompose] rw [Multiset.map_bind] simp only [Multiset.map_map, Function.comp_apply, Multiset.map_id', Multiset.insert_eq_cons, Int.reduceNeg] have hx : (Multiset.bind x fun a => decomposeFluxes a.2) = (Multiset.bind x.toFluxesTen fun a => decomposeFluxes a) := by rw [toFluxesTen, Multiset.bind_map] rw [hx] clear hx generalize x.toFluxesTen = F at * revert F decide- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/StringTheory/FTheory/SU5/Quanta/TenQuanta.lean:716-731
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