Project-declaredLean 4.32.0 · mathlib@81a5d257c8e4

Is Viable iff charges mem viable Charges mem lift Charges

FTheory.SU5.Quanta.isViable_iff_charges_mem_viableCharges_mem_liftCharges

physics quantum field theory relativity is viable

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The quanta satisfy the linear anomaly cancellation conditions. -/ linear_anomalies : x.LinearAnomalyCancellation lemma isViable_iff_def (x : Quanta) : IsViable x ↔ x.toCharges.IsComplete ∧ ¬ x.toCharges.IsPhenoConstrained ∧ ¬ x.toCharges.YukawaGeneratesDangerousAtLevel 1 ∧ (∃ I : CodimensionOneConfig, x.toCharges ∈ ofFinset I.allowedBarFiveCharges I.allow...

Exact Lean statement

lemma isViable_iff_charges_mem_viableCharges_mem_liftCharges (x : Quanta) :
    IsViable x ↔ (∃ I, x.toCharges ∈ viableCharges I) ∧
      x ∈ Quanta.liftCharge x.toCharges ∧
      x.LinearAnomalyCancellation

Formal artifact

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lemma isViable_iff_charges_mem_viableCharges_mem_liftCharges (x : Quanta) :    IsViable x ↔ (∃ I, x.toCharges ∈ viableCharges I) ∧      x ∈ Quanta.liftCharge x.toCharges ∧      x.LinearAnomalyCancellation := by  simp [Quanta.mem_liftCharge_iff, toCharges_qHd, toCharges_qHu]  rw [FiveQuanta.mem_liftCharge_iff, TenQuanta.mem_liftCharge_iff,    isViable_iff_charges_mem_viableCharges, ← FluxesFive.noExotics_iff_mem_elemsNoExotics,    ← FluxesTen.noExotics_iff_mem_elemsNoExotics]  aesop

Project: Physlib
License: Apache-2.0
Commit: dd43e9e65791
Source: Physlib/StringTheory/FTheory/SU5/Quanta/IsViable.lean:157-165

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