Allows Term insert Q10 of allows Term Q10
SuperSymmetry.SU5.ChargeSpectrum.allowsTerm_insertQ10_of_allowsTermQ10
Project documentation
The proposition for which says, given a charge x adding a charge q5 permits the existence of a potential term T due to the addition of that charge. -/ def AllowsTermQ10 (x : ChargeSpectrum 𝓩) (q10 : 𝓩) (T : PotentialTerm) : Prop := match T with | .μ => false | .β => false | .Λ => (0 : 𝓩) ∈ (x.Q5.product x.Q5).val.map (fun (y, z) => y + z + q10) |...
Exact Lean statement
lemma allowsTerm_insertQ10_of_allowsTermQ10 {qHd qHu : Option 𝓩}
{Q5 Q10: Finset 𝓩} {q10 : 𝓩} (T : PotentialTerm)
(h : AllowsTermQ10 ⟨qHd, qHu, Q5, Q10⟩ q10 T) :
AllowsTerm ⟨qHd, qHu, Q5, insert q10 Q10⟩ TFormal artifact
Lean source
lemma allowsTerm_insertQ10_of_allowsTermQ10 {qHd qHu : Option 𝓩} {Q5 Q10: Finset 𝓩} {q10 : 𝓩} (T : PotentialTerm) (h : AllowsTermQ10 ⟨qHd, qHu, Q5, Q10⟩ q10 T) : AllowsTerm ⟨qHd, qHu, Q5, insert q10 Q10⟩ T := by rcases T all_goals simp [AllowsTermQ10] at h all_goals simp [allowsTerm_iff_zero_mem_ofPotentialTerm', ofPotentialTerm'] · obtain ⟨a1, a2, ⟨h1, h2⟩, hsum⟩ := h use a1, a2, q10 simp_all · obtain ⟨a1, a2, a3, ⟨h1, h2, h3⟩, hsum⟩ := h use a1, a2, a3, q10 simp_all · match qHd with | none => simp at h | some qHd => simp at h ⊢ obtain ⟨a1, a2, ⟨h1, h2⟩, hsum⟩ := h use a1, a2, q10 simp_all · obtain ⟨a1, a2, ⟨h1, h2⟩, hsum⟩ := h use a1, a2, q10 simp_all · match qHd, qHu with | none, _ => simp at h | some x, none => simp at h | some qHd, some qHu => simp_all · match qHu with | none => simp at h | some qHu => simp at h ⊢ rcases h with h | h · use q10, q10 rw [← h] simp only [true_or, and_self, true_and] abel · obtain ⟨a1, h1, hsum⟩ := h use a1, q10 simp_all rw [← hsum] abel · match qHd with | none => simp at h | some qHd => simp at h ⊢ obtain ⟨a1, h1, hsum⟩ := h use a1, q10 simp_all rw [← hsum] abel- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/AllowsTerm.lean:946-997
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