Of Potential Term mono
SuperSymmetry.SU5.ChargeSpectrum.ofPotentialTerm_mono
Project documentation
Given a charges x : Charges associated to the representations, and a potential term T, the charges associated with instances of that potential term. -/ def ofPotentialTerm (x : ChargeSpectrum ๐ฉ) (T : PotentialTerm) : Multiset ๐ฉ := let add : Multiset ๐ฉ โ Multiset ๐ฉ โ Multiset ๐ฉ := fun a b => (a รหข b).map fun (x, y) => x + y (T.toFieldLabel.map fun...
Exact Lean statement
lemma ofPotentialTerm_mono {x y : ChargeSpectrum ๐ฉ} (h : x โ y) (T : PotentialTerm) :
x.ofPotentialTerm T โ y.ofPotentialTerm TFormal artifact
Lean source
lemma ofPotentialTerm_mono {x y : ChargeSpectrum ๐ฉ} (h : x โ y) (T : PotentialTerm) : x.ofPotentialTerm T โ y.ofPotentialTerm T := by have h1 {S1 S2 T1 T2 : Multiset ๐ฉ} (h1 : S1 โ S2) (h2 : T1 โ T2) : (S1 รหข T1) โ S2 รหข T2 := Multiset.subset_iff.mpr (fun x => by simpa only [Multiset.mem_product, and_imp] using fun h1' h2' => โจh1 h1', h2 h2'โฉ) rw [subset_def] at h cases T all_goals simp [ofPotentialTerm, PotentialTerm.toFieldLabel] repeat' apply Multiset.map_subset_map <| Multiset.subset_iff.mpr <| h1 _ (Finset.subset_def.mp (ofFieldLabel_mono h _)) simp- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/OfPotentialTerm.lean:88-101
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