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Project-declaredLean 4.32.0 Β· mathlib@81a5d257c8e4

To Charges to Finset of mem lift Charge

FTheory.SU5.FiveQuanta.toCharges_toFinset_of_mem_liftCharge

physicsquantum field theoryrelativityfive quanta

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 𝓩) : Multiset (FiveQuanta 𝓩) := /- The multisets of cardinality 3 containing 3 elements of c. -/ let S53 : Multiset (Multiset 𝓩) := toMultisetsThree c /- Pairs of multisets (s1, s2) such...

Exact Lean statement

lemma toCharges_toFinset_of_mem_liftCharge (c : Finset 𝓩) {x : FiveQuanta 𝓩}
    (h : x ∈ liftCharge c) : x.toCharges.toFinset = c

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
lemma toCharges_toFinset_of_mem_liftCharge (c : Finset 𝓩) {x : FiveQuanta 𝓩}    (h : x ∈ liftCharge c) : x.toCharges.toFinset = c := by  simp [liftCharge] at h  obtain ⟨s1, s2, ⟨⟨⟨s1_subset, s1_card⟩, ⟨s2_subset, s2_card⟩⟩, hsum⟩, rfl⟩ := h  rw [← Multiset.toFinset_dedup, reduce_toCharges]  simp only [Int.reduceNeg, Multiset.dedup_idem, Multiset.toFinset_dedup]  simp [toCharges]  refine Finset.Subset.antisymm (Finset.union_subset s1_subset s2_subset) fun a ha => ?_  simpa using Multiset.mem_of_le hsum ha
Project
Physlib
License
Apache-2.0
Commit
dd43e9e65791
Source
Physlib/StringTheory/FTheory/SU5/Quanta/FiveQuanta.lean:703-711

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