Project-declaredLean 4.32.0 · mathlib@81a5d257c8e4

Minimally Allows Term Of Finset subset of subset

SuperSymmetry.SU5.ChargeSpectrum.minimallyAllowsTermOfFinset_subset_of_subset

physics quantum field theory relativity of finset

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 minimallyAllowsTermOfFinset_subset_of_subset {S5 S5' S10 S10' : Finset 𝓩} {T : PotentialTerm}
    (h5 : S5' ⊆ S5) (h10 : S10' ⊆ S10) :
    minimallyAllowsTermsOfFinset S5' S10' T ⊆ minimallyAllowsTermsOfFinset S5 S10 T

Formal artifact

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Canonical source

Full Lean sourceLean 4

lemma minimallyAllowsTermOfFinset_subset_of_subset {S5 S5' S10 S10' : Finset 𝓩} {T : PotentialTerm}    (h5 : S5' ⊆ S5) (h10 : S10' ⊆ S10) :    minimallyAllowsTermsOfFinset S5' S10' T ⊆ minimallyAllowsTermsOfFinset S5 S10 T := by  intro x hx  have h1 : x ∈ ofFinset S5' S10' := mem_ofFinset_of_mem_minimallyAllowsTermOfFinset hx  rw [← minimallyAllowsTerm_iff_mem_minimallyAllowsTermOfFinset    (ofFinset_subset_of_subset h5 h10 h1)]  exact (minimallyAllowsTerm_iff_mem_minimallyAllowsTermOfFinset h1).mpr hx

Project: Physlib
License: Apache-2.0
Commit: dd43e9e65791
Source: Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/MinimallyAllowsTerm/OfFinset.lean:539-546

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