Is Complete mono
SuperSymmetry.SU5.ChargeSpectrum.isComplete_mono
Project documentation
A charge spectrum is complete if it has all types of fields. -/ def IsComplete (x : ChargeSpectrum 𝓩) : Prop := x.qHd.isSome ∧ x.qHu.isSome ∧ x.Q5 ≠ ∅ ∧ x.Q10 ≠ ∅ instance [DecidableEq 𝓩] (x : ChargeSpectrum 𝓩) : Decidable (IsComplete x) := inferInstanceAs (Decidable (x.qHd.isSome ∧ x.qHu.isSome ∧ x.Q5 ≠ ∅ ∧ x.Q10 ≠ ∅)) /-! ### A.1. The empty spectrum...
Exact Lean statement
lemma isComplete_mono {x y : ChargeSpectrum 𝓩} (h : x ⊆ y) (hx : IsComplete x) :
IsComplete yFormal artifact
Lean source
lemma isComplete_mono {x y : ChargeSpectrum 𝓩} (h : x ⊆ y) (hx : IsComplete x) : IsComplete y := by rw [subset_def] at h obtain ⟨hd, hu, h5, h10⟩ := h obtain ⟨hxd, hxu, hx5, hx10⟩ := hx refine ⟨?_, ?_, ?_, ?_⟩ · obtain ⟨a, ha⟩ := Option.isSome_iff_exists.mp hxd rw [ha, Option.toFinset_some, Finset.singleton_subset_iff, Option.mem_toFinset] at hd exact Option.isSome_of_mem hd · obtain ⟨a, ha⟩ := Option.isSome_iff_exists.mp hxu rw [ha, Option.toFinset_some, Finset.singleton_subset_iff, Option.mem_toFinset] at hu exact Option.isSome_of_mem hu · exact fun hy => hx5 (Finset.subset_empty.mp (hy ▸ h5)) · exact fun hy => hx10 (Finset.subset_empty.mp (hy ▸ h10))- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/Completions.lean:102-115
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