Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  Γ' : list A
  a : A
  Δ : list A
  a0 : A
  Δ' : list A
  H : #|Γ| = #|Γ'|
  IHΔ : All2_fold P (Δ ++ Γ) (Δ' ++ Γ')
        → All2_fold P Γ Γ'
          × All2_fold (λ Δ Δ' : list A, P (Δ ++ Γ) (Δ' ++ Γ')) Δ Δ'
  ============================
   ({| pr1 := a :: Δ ++ Γ; pr2 := a0 :: Δ' ++ Γ' |} =
    {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold P Γ Γ'
      × All2_fold (λ Δ Δ' : list A, P (Δ ++ Γ) (Δ' ++ Γ')) 
          (a :: Δ) (a0 :: Δ'))


DEBUG:Going to execute:
<coq-equations.plugin::simplify@0> $1

Goals:

DEBUG:Going to execute:
cbv beta