Contains Pheno Completions Of Minimally Allows iff completions Top Yukawa
SuperSymmetry.SU5.ChargeSpectrum.containsPhenoCompletionsOfMinimallyAllows_iff_completionsTopYukawa
Project documentation
The proposition that for multiset set of charges charges contains all viable completions of charges which allow the top Yukawa, given allowed values of 5d and 10d charges S5 and S10. -/ def ContainsPhenoCompletionsOfMinimallyAllows (S5 S10 : Finset ๐ฉ) (charges : Multiset (ChargeSpectrum ๐ฉ)) : Prop := โ x โ (minimallyAllowsTermsOfFinset S5 S10...
Exact Lean statement
lemma containsPhenoCompletionsOfMinimallyAllows_iff_completionsTopYukawa {S5 S10 : Finset ๐ฉ}
{charges : Multiset (ChargeSpectrum ๐ฉ)} :
ContainsPhenoCompletionsOfMinimallyAllows S5 S10 charges โ
โ x โ (minimallyAllowsTermsOfFinset S5 S10 topYukawa),
โ y โ completionsTopYukawa S5 x, ยฌ y.IsPhenoConstrained
โง ยฌ y.YukawaGeneratesDangerousAtLevel 1 โ y โ chargesFormal artifact
Lean source
lemma containsPhenoCompletionsOfMinimallyAllows_iff_completionsTopYukawa {S5 S10 : Finset ๐ฉ} {charges : Multiset (ChargeSpectrum ๐ฉ)} : ContainsPhenoCompletionsOfMinimallyAllows S5 S10 charges โ โ x โ (minimallyAllowsTermsOfFinset S5 S10 topYukawa), โ y โ completionsTopYukawa S5 x, ยฌ y.IsPhenoConstrained โง ยฌ y.YukawaGeneratesDangerousAtLevel 1 โ y โ charges := by rw [ContainsPhenoCompletionsOfMinimallyAllows] have h1 (x : ChargeSpectrum ๐ฉ) (hx : x โ (minimallyAllowsTermsOfFinset S5 S10 topYukawa)) : ยฌ x.IsPhenoConstrained โ True := by simp only [iff_true] exact not_isPhenoConstrained_of_minimallyAllowsTermsOfFinset_topYukawa hx conv_lhs => enter [x, hx] rw [completions_eq_completionsTopYukawa_of_mem_minimallyAllowsTermsOfFinset x hx] rw [h1 x hx] simp- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/PhenoClosed.lean:170-185
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