Decompose filter charge
FTheory.SU5.TenQuanta.decompose_filter_charge
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_filter_charge [DecidableEq 𝓩] (x : TenQuanta 𝓩) (q : 𝓩) :
(x.decompose).filter (fun p => p.1 = q) =
decompose (x.filter (fun p => p.1 = q))Formal artifact
Lean source
lemma decompose_filter_charge [DecidableEq 𝓩] (x : TenQuanta 𝓩) (q : 𝓩) : (x.decompose).filter (fun p => p.1 = q) = decompose (x.filter (fun p => p.1 = q)) := by rw [decompose] revert x apply Multiset.induction · simp [decompose] · intro a x ih simp only [Multiset.cons_bind, Multiset.filter_add] rw [Multiset.filter_cons, decompose_add, ih] congr obtain ⟨q', f⟩ := a simp [decomposeFluxes] by_cases h : q' = q · subst h simp [decompose, decomposeFluxes] · simp [h, decompose]- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/StringTheory/FTheory/SU5/Quanta/TenQuanta.lean:625-641
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