Project-declaredLean 4.32.0 · mathlib@81a5d257c8e4

Map of Field Label

SuperSymmetry.SU5.ChargeSpectrum.map_ofFieldLabel

physics quantum field theory relativity map

Project documentation

Given an additive monoid homomorphisms f : 𝓩 →+ 𝓩1, for a charge x : Charges 𝓩, x.map f is the charge of Charges 𝓩1 obtained by mapping the elements of x by f. -/ def map (f : 𝓩 →+ 𝓩1) (x : ChargeSpectrum 𝓩) : ChargeSpectrum 𝓩1 where qHd := f < $> x.qHd qHu := f <$ > x.qHu Q5 := x.Q5.image f Q10 := x.Q10.image f /- ### A.1. Mapping the e...

Exact Lean statement

lemma map_ofFieldLabel (f : 𝓩 →+ 𝓩1) (x : ChargeSpectrum 𝓩) (F : FieldLabel) :
    ofFieldLabel (map f x) F = (ofFieldLabel x F).image f

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

lemma map_ofFieldLabel (f : 𝓩 →+ 𝓩1) (x : ChargeSpectrum 𝓩) (F : FieldLabel) :    ofFieldLabel (map f x) F = (ofFieldLabel x F).image f := by  simp [ofFieldLabel, map]  match x with  | ⟨qHd, qHu, Q5, Q10⟩ =>  fin_cases F  all_goals simp  case «0» | «1» =>    match qHu with    | some a => simp    | none => simp  case «2» | «3» =>    match qHd with    | some a => simp    | none => simp  · trans (Finset.image (⇑f) Q5).image Neg.neg    · ext a      simp    · rw [Finset.image_image]      symm      trans Finset.image (⇑f ∘ Neg.neg) (Q5)      · ext a        simp      congr 1      funext a      simp

Project: Physlib
License: Apache-2.0
Commit: dd43e9e65791
Source: Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/Map.lean:135-160

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