Mem minimally Allows Term Of Finset of minimally Allows Term
SuperSymmetry.SU5.ChargeSpectrum.mem_minimallyAllowsTermOfFinset_of_minimallyAllowsTerm
Project documentation
The multiset of all charges within ofFinset S5 S10 which minimally allow the potential term T. -/ def minimallyAllowsTermsOfFinset (S5 S10 : Finset 𝓩) : (T : PotentialTerm) → Multiset (ChargeSpectrum 𝓩) | μ => let SqHd := S5.val let SqHu := S5.val let prod := SqHd ×ˢ (SqHu) let Filt := prod.filter (fun x => - x.1 + x.2 = 0) (Filt.map (fun x => ⟨x.1,...
Exact Lean statement
lemma mem_minimallyAllowsTermOfFinset_of_minimallyAllowsTerm {S5 S10 : Finset 𝓩}
{T : PotentialTerm} (x : ChargeSpectrum 𝓩) (h : x.MinimallyAllowsTerm T)
(hx : x ∈ ofFinset S5 S10) :
x ∈ minimallyAllowsTermsOfFinset S5 S10 TFormal artifact
Lean source
lemma mem_minimallyAllowsTermOfFinset_of_minimallyAllowsTerm {S5 S10 : Finset 𝓩} {T : PotentialTerm} (x : ChargeSpectrum 𝓩) (h : x.MinimallyAllowsTerm T) (hx : x ∈ ofFinset S5 S10) : x ∈ minimallyAllowsTermsOfFinset S5 S10 T := by obtain ⟨a, b, c, rfl⟩ := eq_allowsTermForm_of_minimallyAllowsTerm h cases T all_goals simp [allowsTermForm, minimallyAllowsTermsOfFinset] rw [mem_ofFinset_iff] at hx case μ => simp_all [allowsTermForm] case β => exact ⟨{a}, by simp_all [allowsTermForm]⟩ case Λ => exact ⟨{a, b}, {- a - b}, by simp_all [allowsTermForm]⟩ case W1 => refine ⟨⟨{- a - b - c}, {a, b, c}, ?_⟩, h⟩ simp_all [allowsTermForm] abel case W2 => refine ⟨⟨{a, b, c}, ?_⟩, h⟩ simp_all [allowsTermForm] abel case W3 => use {b, - b - 2 • a} simp_all [allowsTermForm] abel case W4 => exact ⟨{c}, by simp_all [allowsTermForm]⟩ case K1 => exact ⟨{-a}, {b, - a - b}, by simp_all [allowsTermForm]⟩ case K2 => exact ⟨{- a - b}, by simp_all [allowsTermForm]⟩ case topYukawa => exact ⟨{b, - a - b}, by simp_all [allowsTermForm]⟩ case bottomYukawa => exact ⟨{b}, {- a - b}, by simp_all [allowsTermForm]⟩- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/MinimallyAllowsTerm/OfFinset.lean:470-506
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