Goal:
  
  A : Type
  P : list A → A → Type
  a : A
  Γ : list A
  Δ : list A
  IHΓ : All_fold P (Γ ++ Δ)
        → All_fold P Δ × All_fold (λ Γ : list A, P (Γ ++ Δ)) Γ
  X : All_fold P (Γ ++ Δ)
  p : P (Γ ++ Δ) a
  ============================
   (All_fold P Δ)


DEBUG:Going to execute:
fun => <coq-core.plugins.tauto::reduction_not_iff@0>