Map lift Charge
FTheory.SU5.FiveQuanta.map_liftCharge
Project documentation
Given a finite set of charges c the FiveQuanta which do not have exotics, duplicate charges or zero fluxes, which map down to c. -/ def liftCharge (c : Finset ๐ฉ) : Multiset (FiveQuanta ๐ฉ) := /- The multisets of cardinality 3 containing 3 elements of c. -/ let S53 : Multiset (Multiset ๐ฉ) := toMultisetsThree c /- Pairs of multisets (s1, s2) such...
Exact Lean statement
lemma map_liftCharge {๐ฉ ๐ฉ1 : Type}[DecidableEq ๐ฉ] [DecidableEq ๐ฉ1] [CommRing ๐ฉ] [CommRing ๐ฉ1]
(f : ๐ฉ โ+* ๐ฉ1) (c : Finset ๐ฉ) (F : FiveQuanta ๐ฉ) (h : F โ liftCharge c) :
FiveQuanta.reduce (F.map fun y => (f y.1, y.2)) โ liftCharge (c.image f)Formal artifact
Lean source
lemma map_liftCharge {๐ฉ ๐ฉ1 : Type}[DecidableEq ๐ฉ] [DecidableEq ๐ฉ1] [CommRing ๐ฉ] [CommRing ๐ฉ1] (f : ๐ฉ โ+* ๐ฉ1) (c : Finset ๐ฉ) (F : FiveQuanta ๐ฉ) (h : F โ liftCharge c) : FiveQuanta.reduce (F.map fun y => (f y.1, y.2)) โ liftCharge (c.image f) := by rw [mem_liftCharge_iff] at h โข refine โจ?_, ?_, ?_โฉ ยท apply reduce_mem_elemsNoExotics simpa [toFluxesFive, Multiset.map_map] using h.1 ยท rw [reduce_toCharges] simp [โ h.2.1, โ Multiset.toFinset_map, toCharges] ยท simp [reduce_toCharges]- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/StringTheory/FTheory/SU5/Quanta/FiveQuanta.lean:880-889
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