Map subset
SuperSymmetry.SU5.ChargeSpectrum.map_subset
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.qHu Q5 := x.Q5.image f Q10 := x.Q10.image f /- ### A.1. Mapping the e...
Exact Lean statement
lemma map_subset {f : 𝓩 →+ 𝓩1} {x y : ChargeSpectrum 𝓩} (h : x ⊆ y) :
map f x ⊆ map f yFormal artifact
Lean source
lemma map_subset {f : 𝓩 →+ 𝓩1} {x y : ChargeSpectrum 𝓩} (h : x ⊆ y) : map f x ⊆ map f y := by simp [map, subset_def] at * obtain ⟨hHd, hHu, hQ5, hQ10⟩ := h refine ⟨?_, ?_, ?_, ?_⟩ · match x, y with | ⟨a, _, _, _⟩, ⟨b, _, _, _⟩ => cases a all_goals cases b all_goals simp all_goals simp at hHd subst hHd rfl · match x, y with | ⟨_, a, _, _⟩, ⟨_, b, _, _⟩ => cases a all_goals cases b all_goals simp all_goals simp at hHu subst hHu rfl · exact Finset.image_subset_image hQ5 · exact Finset.image_subset_image hQ10- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/Map.lean:167-189
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