Decompose to Charges dedup
FTheory.SU5.FiveQuanta.decompose_toCharges_dedup
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_toCharges_dedup [DecidableEq 𝓩] (x : FiveQuanta 𝓩)
(hx : x.toFluxesFive ∈ FluxesFive.elemsNoExotics) :
x.decompose.toCharges.dedup = x.toCharges.dedupFormal artifact
Lean source
lemma decompose_toCharges_dedup [DecidableEq 𝓩] (x : FiveQuanta 𝓩) (hx : x.toFluxesFive ∈ FluxesFive.elemsNoExotics) : x.decompose.toCharges.dedup = x.toCharges.dedup := by refine Multiset.dedup_ext.mpr ?_ intro q simp [decompose, toCharges, -existsAndEq] constructor · rintro ⟨a, b, c, h1, h2, rfl⟩ exact ⟨c, h1⟩ · rintro ⟨c, h1⟩ have hn : (decomposeFluxes c) ≠ 0 := by have c_mem_f : c ∈ x.toFluxesFive := by simp [toFluxesFive] use q generalize x.toFluxesFive = F at * clear h1 revert c revert F decide apply Multiset.exists_mem_of_ne_zero at hn obtain ⟨c', h⟩ := hn use c', q, c- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/StringTheory/FTheory/SU5/Quanta/FiveQuanta.lean:606-627
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