Yukawa Generates Dangerous At Level of subset
SuperSymmetry.SU5.ChargeSpectrum.yukawaGeneratesDangerousAtLevel_of_subset
Plain-language statement
For charges x : Charges, the proposition which states that the singlets needed to regenerate the Yukawa couplings regenerate a dangerous coupling (in the superpotential) with up-to n insertions of the scalars. Note: If defined as (x.ofYukawaTermsNSum n).toFinset ∩ x.phenoConstrainingChargesSP.toFinset ≠ ∅ the execution time is greatly increased. -/ de...
Exact Lean statement
lemma yukawaGeneratesDangerousAtLevel_of_subset {x y : ChargeSpectrum 𝓩} {n : ℕ} (h : x ⊆ y)
(hx : x.YukawaGeneratesDangerousAtLevel n) :
y.YukawaGeneratesDangerousAtLevel nFormal artifact
Lean source
lemma yukawaGeneratesDangerousAtLevel_of_subset {x y : ChargeSpectrum 𝓩} {n : ℕ} (h : x ⊆ y) (hx : x.YukawaGeneratesDangerousAtLevel n) : y.YukawaGeneratesDangerousAtLevel n := by simp [yukawaGeneratesDangerousAtLevel_iff_toFinset] at * have h1 : (x.ofYukawaTermsNSum n).toFinset ∩ x.phenoConstrainingChargesSP.toFinset ⊆ (y.ofYukawaTermsNSum n).toFinset ∩ y.phenoConstrainingChargesSP.toFinset := by trans (x.ofYukawaTermsNSum n).toFinset ∩ y.phenoConstrainingChargesSP.toFinset · apply Finset.inter_subset_inter_left simp only [Multiset.toFinset_subset] exact phenoConstrainingChargesSP_mono h · apply Finset.inter_subset_inter_right simp only [Multiset.toFinset_subset] exact ofYukawaTermsNSum_subset_of_subset h n by_contra hn rw [hn] at h1 simp at h1 rw [h1] at hx simp at hx- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/Yukawa.lean:218-235
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
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.
Source project: Physlib
Person-level attribution pending.
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.
Source project: Physlib
Person-level attribution pending.
Deriv Within mean Energy Beta eq neg variance
CanonicalEnsemble.derivWithin_meanEnergy_Beta_eq_neg_variance
Plain-language statement
(∂U/∂β) = -Var(E) for finite systems.
Source project: Physlib
Person-level attribution pending.