Reduce num Anti Chiral D of mem elems No Exotics
FTheory.SU5.FiveQuanta.reduce_numAntiChiralD_of_mem_elemsNoExotics
Project documentation
The reduce of FiveQuanta is a new FiveQuanta with all the fluxes corresponding to the same charge (i.e. representation) added together. -/ def reduce (x : FiveQuanta ๐ฉ) : FiveQuanta ๐ฉ := x.toCharges.dedup.map fun q5 => (q5, ((x.filter (fun f => f.1 = q5)).map (fun y => y.2)).sum) /-! ### B.1. The reduced FiveQuanta has no duplicate elements -/ l...
Exact Lean statement
lemma reduce_numAntiChiralD_of_mem_elemsNoExotics {F : FiveQuanta ๐ฉ}
(hx : F.toFluxesFive โ FluxesFive.elemsNoExotics) :
F.reduce.toFluxesFive.numAntiChiralD = 0Formal artifact
Lean source
lemma reduce_numAntiChiralD_of_mem_elemsNoExotics {F : FiveQuanta ๐ฉ} (hx : F.toFluxesFive โ FluxesFive.elemsNoExotics) : F.reduce.toFluxesFive.numAntiChiralD = 0 := by rw [FluxesFive.numAntiChiralD, FluxesFive.chiralIndicesOfD, Multiset.filter_eq_nil.mpr ?_, Multiset.sum_zero] intro a ha obtain โจf, hf, rflโฉ := Multiset.mem_map.mp ha replace hf := mem_powerset_sum_of_mem_reduce_toFluxesFive hf clear ha generalize F.toFluxesFive = G at * revert f revert G decide- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/StringTheory/FTheory/SU5/Quanta/FiveQuanta.lean:453-465
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