Mem lift Charge of mem no Exotics has No Zero
FTheory.SU5.TenQuanta.mem_liftCharge_of_mem_noExotics_hasNoZero
Project documentation
Given a finite set of charges c the TenQuanta which do not have exotics, duplicate charges or zero fluxes, which map down to c. This is defined to be as efficient as possible. -/ def liftCharge (c : Finset 𝓩) : Multiset (TenQuanta 𝓩) := /- The {(1, 0), (1, 0), (1, 0)} case. -/ /- The multisets of cardinality 3 containing 3 elements of c. -/ let...
Exact Lean statement
lemma mem_liftCharge_of_mem_noExotics_hasNoZero (c : Finset 𝓩) {x : TenQuanta 𝓩}
(h1 : x.toFluxesTen.NoExotics) (h2 : x.toFluxesTen.HasNoZero)
(h3 : x.toCharges.toFinset = c) (h4 : x.toCharges.Nodup) :
x ∈ liftCharge cFormal artifact
Lean source
lemma mem_liftCharge_of_mem_noExotics_hasNoZero (c : Finset 𝓩) {x : TenQuanta 𝓩} (h1 : x.toFluxesTen.NoExotics) (h2 : x.toFluxesTen.HasNoZero) (h3 : x.toCharges.toFinset = c) (h4 : x.toCharges.Nodup) : x ∈ liftCharge c := by have hf : x.toFluxesTen ∈ FluxesTen.elemsNoExotics := by rw [← FluxesTen.noExotics_iff_mem_elemsNoExotics] exact ⟨h1, h2⟩ rw [mem_liftCharge_iff_exists] refine ⟨x.decompose, ?_, ?_, ?_⟩ · rw [decompose_reduce x hf] exact reduce_eq_self_of_ofCharges_nodup x h4 · trans x.decompose.toCharges.dedup.toFinset · simp · rw [decompose_toCharges_dedup x hf, ← h3] simp · exact decompose_toFluxesTen x hf- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/StringTheory/FTheory/SU5/Quanta/TenQuanta.lean:985-1000
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