Subset minimally Allows Term of allows Term
SuperSymmetry.SU5.ChargeSpectrum.subset_minimallyAllowsTerm_of_allowsTerm
Project documentation
A collection of charges x : Charges is said to minimally allow the potential term T if it allows T and no strict subset of it allows T. -/ def MinimallyAllowsTerm (x : ChargeSpectrum ๐ฉ) (T : PotentialTerm) : Prop := โ y โ x.powerset, y = x โ y.AllowsTerm T /-! ### A.1. Decidability of MinimallyAllowsTerm We show that MinimallyAllowsTerm is de...
Exact Lean statement
lemma subset_minimallyAllowsTerm_of_allowsTerm
(hx : x.AllowsTerm T) : โ y โ powerset x, y.MinimallyAllowsTerm TFormal artifact
Lean source
lemma subset_minimallyAllowsTerm_of_allowsTerm (hx : x.AllowsTerm T) : โ y โ powerset x, y.MinimallyAllowsTerm T := by have hPresent : (x.powerset.filter (fun y => y.AllowsTerm T)) โ โ
:= by rw [โ @Finset.nonempty_iff_ne_empty] use x simp [hx] obtain โจy, h1, h2โฉ := min_exists (x.powerset.filter (fun y => y.AllowsTerm T)) hPresent use y simp at h1 simp_all rw [minimallyAllowsTerm_iff_powerset_filter_eq] rw [โ h2] ext z simp only [Finset.mem_filter, mem_powerset_iff_subset, Finset.mem_inter, and_congr_right_iff, iff_and_self] intro hzy hzpres exact subset_trans hzy h1.1- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/MinimallyAllowsTerm/Basic.lean:199-215
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