Decompose filter charge
FTheory.SU5.FiveQuanta.decompose_filter_charge
Project documentation
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...
Exact Lean statement
lemma decompose_filter_charge [DecidableEq 𝓩] (x : FiveQuanta 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 : FiveQuanta 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 match a with | (q', f) => simp [decomposeFluxes] by_cases h : q' = q · subst h simp [decompose, decomposeFluxes] congr all_goals · refine Multiset.filter_eq_self.mpr ?_ intro a ha simp [Multiset.mem_replicate] at ha rw [ha.2] · simp [h, decompose] apply And.intro all_goals · intro a b h simp [Multiset.mem_replicate] at h simp_all- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/StringTheory/FTheory/SU5/Quanta/FiveQuanta.lean:548-576
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