Minimally Allows Term iff powerset filter eq
SuperSymmetry.SU5.ChargeSpectrum.minimallyAllowsTerm_iff_powerset_filter_eq
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 𝓩) (T : PotentialTerm) : Prop := ∀ y ∈ x.powerset, y = x ↔ y.AllowsTerm T /-! ### A.1. Decidability of MinimallyAllowsTerm We show that MinimallyAllowsTerm is de...
Exact Lean statement
lemma minimallyAllowsTerm_iff_powerset_filter_eq :
x.MinimallyAllowsTerm T ↔ x.powerset.filter (fun y => y.AllowsTerm T) = {x}Formal artifact
Lean source
lemma minimallyAllowsTerm_iff_powerset_filter_eq : x.MinimallyAllowsTerm T ↔ x.powerset.filter (fun y => y.AllowsTerm T) = {x} := by constructor · intro h ext y simp only [Finset.mem_filter, mem_powerset_iff_subset, Finset.mem_singleton] simp [MinimallyAllowsTerm] at h constructor · exact fun ⟨h1, h2⟩ => (h y h1).mpr h2 · intro h1 subst h1 simp exact (h y (by simp)).mp rfl · intro h simp [MinimallyAllowsTerm] intro y hy rw [Finset.eq_singleton_iff_unique_mem] at h simp at h constructor · intro h1 subst h1 exact h.1 · intro h1 apply h.2 · exact hy · exact h1- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/MinimallyAllowsTerm/Basic.lean:129-154
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