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Project-declaredLean 4.32.0 · mathlib@81a5d257c8e4

Allows Term Q5 or allows Term of allows Term insert Q5

SuperSymmetry.SU5.ChargeSpectrum.allowsTermQ5_or_allowsTerm_of_allowsTerm_insertQ5

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 AllowsTermQ5 (x : ChargeSpectrum 𝓩) (q5 : 𝓩) (T : PotentialTerm) : Prop := match T with | .μ => false | .β => match x with | ⟨_, some qHu, _, _⟩ => q5 = qHu | _ => false | .Λ => (0 : 𝓩) ∈ ((ins...

Exact Lean statement

lemma allowsTermQ5_or_allowsTerm_of_allowsTerm_insertQ5 {qHd qHu : Option 𝓩}
    {Q5 Q10: Finset 𝓩} {q5 : 𝓩} (T : PotentialTerm)
    (h : AllowsTerm ⟨qHd, qHu, insert q5 Q5, Q10⟩ T) :
    AllowsTermQ5 ⟨qHd, qHu, Q5, Q10⟩ q5 T ∨
    AllowsTerm ⟨qHd, qHu, Q5, Q10⟩ T

Formal artifact

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Full Lean sourceLean 4
lemma allowsTermQ5_or_allowsTerm_of_allowsTerm_insertQ5 {qHd qHu : Option 𝓩}    {Q5 Q10: Finset 𝓩} {q5 : 𝓩} (T : PotentialTerm)    (h : AllowsTerm qHd, qHu, insert q5 Q5, Q10 T) :    AllowsTermQ5 qHd, qHu, Q5, Q10 q5 T     AllowsTerm qHd, qHu, Q5, Q10 T := by  rcases T  all_goals    simp [allowsTerm_iff_zero_mem_ofPotentialTerm', ofPotentialTerm', AllowsTermQ5] at h   · exact h  · match qHu with    | some qHu =>      simp at h      simp only [Multiset.mem_map, Finset.mem_val]      convert h using 1      rw [neg_add_eq_zero, eq_comm]    | none => simp at h  · obtain a1, a2, a3, h1, h2, h3, hsum := h    rcases h1 with h1 | h1    · subst h1      refine .inl a2, a3, h2, h3, ?_      rw [ hsum]      abel    · rcases h2 with h2 | h2      · subst h2        exact .inl a1, a3, .inr h1, h3, hsum      · exact .inr a1, a2, a3, h1, h2, h3, hsum  · obtain a1, a2, a3, a4, h1, h2, h3, h4, hsum := h    rcases h1 with h1 | h1    · left      use a2, a3, a4      simp_all    · right      use a1, a2, a3, a4  · simp_all  · match qHu with    | some qHu =>      simp at h      obtain a1, a2, h1, h2, hsum := h      rcases h1 with h1 | h1      · subst h1        left        rcases h2 with h2 | h2        · left          subst h2          rw [ hsum]          abel        · right          use a2          simp_all          rw [ hsum]          abel      · rcases h2 with h2 | h2        · left          right          use a1          simp_all          rw [ hsum]          abel        · right          rw [@Multiset.mem_map]          simp only [Multiset.mem_product, Finset.mem_val, Prod.exists]          use a1, a2    | none => simp at h  · match qHd, qHu with    | some qHd, some qHu =>      simp_all      convert h using 1      constructor      all_goals      · intro h        rw [ h]        abel    | none, _ => simp at h    | some x, none => simp at h  · obtain a1, a2, a3, h1, h2, h3, hsum := h    rcases h1 with h1 | h1    · left      use a2, a3      simp_all    · right      use a1, a2, a3  · simp_all  · simp_all  · match qHd with    | none => simp at h    | some qHd =>      simp_all      obtain a1, a2, h1, h2, hsum := h      rcases h1 with h1 | h1      · subst h1        left        use a2        simp_all        rw [ hsum]        abel      · right        use a1, a2
Project
Physlib
License
Apache-2.0
Commit
dd43e9e65791
Source
Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/AllowsTerm.lean:506-602

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