Minimally Allows Term iff powerset count P eq one
SuperSymmetry.SU5.ChargeSpectrum.minimallyAllowsTerm_iff_powerset_countP_eq_one
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_countP_eq_one :
x.MinimallyAllowsTerm T ↔ x.powerset.val.countP (fun y => y.AllowsTerm T) = 1Formal artifact
Lean source
lemma minimallyAllowsTerm_iff_powerset_countP_eq_one : x.MinimallyAllowsTerm T ↔ x.powerset.val.countP (fun y => y.AllowsTerm T) = 1 := by rw [minimallyAllowsTerm_iff_powerset_filter_eq] constructor · intro h trans (Finset.filter (fun y => y.AllowsTerm T) x.powerset).card · change _ = (Multiset.filter (fun y => y.AllowsTerm T) x.powerset.val).card exact Multiset.countP_eq_card_filter (fun y => y.AllowsTerm T) x.powerset.val · rw [h] simp · intro h have h1 : (Multiset.filter (fun y => y.AllowsTerm T) x.powerset.val).card = 1 := by rw [← h] exact Eq.symm (Multiset.countP_eq_card_filter (fun y => y.AllowsTerm T) x.powerset.val) rw [Multiset.card_eq_one] at h1 obtain ⟨a, ha⟩ := h1 have haMem : a ∈ Multiset.filter (fun y => y.AllowsTerm T) x.powerset.val := by simp [ha] simp at haMem have hxMem : x ∈ Multiset.filter (fun y => y.AllowsTerm T) x.powerset.val := by simpa using allowsTerm_mono haMem.1 haMem.2 rw [ha] at hxMem simp at hxMem subst hxMem exact Finset.val_inj.mp ha- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/MinimallyAllowsTerm/Basic.lean:165-189
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