therefore
Sign up
Open navigation
All proofs
Project-declaredLean 4.32.0 · mathlib@81a5d257c8e4

Mem lift Charge of mem no Exotics has No Zero

FTheory.SU5.FiveQuanta.mem_liftCharge_of_mem_noExotics_hasNoZero

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 mem_liftCharge_of_mem_noExotics_hasNoZero (c : Finset 𝓩) {x : FiveQuanta 𝓩}
    (h1 : x.toFluxesFive.NoExotics) (h2 : x.toFluxesFive.HasNoZero)
    (h3 : x.toCharges.toFinset = c) (h4 : x.toCharges.Nodup) :
    x ∈ liftCharge c

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
lemma mem_liftCharge_of_mem_noExotics_hasNoZero (c : Finset 𝓩) {x : FiveQuanta 𝓩}    (h1 : x.toFluxesFive.NoExotics) (h2 : x.toFluxesFive.HasNoZero)    (h3 : x.toCharges.toFinset = c) (h4 : x.toCharges.Nodup) :    x ∈ liftCharge c := by  have hf : x.toFluxesFive ∈ FluxesFive.elemsNoExotics :=    (FluxesFive.noExotics_iff_mem_elemsNoExotics _).mp ⟨h1, h2⟩  rw [mem_liftCharge_iff_exists]  use x.decompose  apply And.intro  · rw [decompose_reduce x hf]    exact reduce_eq_self_of_ofCharges_nodup x h4  · constructor    · trans x.decompose.toCharges.dedup.toFinset      · simp      · rw [decompose_toCharges_dedup x hf, ← h3]        simp    · rw [decompose_toFluxesFive x hf]
Project
Physlib
License
Apache-2.0
Commit
dd43e9e65791
Source
Physlib/StringTheory/FTheory/SU5/Quanta/FiveQuanta.lean:842-858

Reuse this declaration

Bring the exact result into your workflow

The import identifies the source module. Your project still needs the pinned package dependency shown on this page.

What this badge means

This completion status comes from the project or community source. It has not yet been represented here as an independent rebuild and axiom audit.

Continue in this project

Related declarations

Project-declaredLean 4.32.0

Adiabatic relation log

adiabatic_relation_log

Plain-language statement

Adiabatic relation in logarithmic form: If S(Ua,Va,N) = S(Ub,Vb,N) with N fixed, then c * log (Ua/Ub) + log (Va/Vb) = 0.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Adiabatic relation Ua Ub Va Vb

adiabatic_relation_UaUbVaVb

Plain-language statement

Adiabatic relation in product form: If S(Ua,Va,N) = S(Ub,Vb,N) with N fixed, then (Ua/Ub)^c * (Va/Vb) = 1.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record