Goal:
  
  A : Type
  B : Type
  P : B → B → Type
  Q : A → B → Type
  R : A → B → Type
  x : A
  l : list A
  p : ∀ y z : B, Q x y → R x z → ∑ v : B, P y v × P z v
  H : All (λ x : A, ∀ y z : B, Q x y → R x z → ∑ v : B, P y v × P z v) l
  IHAll : ∀ l' l'' : list B,
            All2 Q l l'
            → All2 R l l''
              → ∑ l''' : list B, All2 P l' l''' × All2 P l'' l'''
  y : B
  l'0 : list B
  H' : All2 Q (x :: l) (y :: l'0)
  y0 : B
  l'1 : list B
  H'' : All2 R (x :: l) (y0 :: l'1)
  X : Q x y
  X0 : All2 Q l l'0
  X1 : R x y0
  X2 : All2 R l l'1
  x0 : list B
  a : All2 P l'0 x0
  a0 : All2 P l'1 x0
  x1 : B
  p0 : P y x1
  p1 : P y0 x1
  ============================
   (All2 P l'0 x0)


DEBUG:Going to execute:
<Coq.Init.Tauto.is_unit_or_eq> flags X1; Ltac.cut X2;
            [ intro; clear id
            | Ltac.cut X1; [ exact id | constructor 1; fail ] ]
Level 0: Backtrace:

P is used in conclusion.
Level 0: Backtrace:

P is used in conclusion.
Level 0: Backtrace:

P is used in conclusion.
Level 0: Backtrace:

P is used in conclusion.
Level 0: Backtrace:

P is used in conclusion.
Level 1: Backtrace:

P is used in conclusion.
Level 0: Backtrace:

P is used in conclusion.
Level 2: Backtrace:

Not convertible.
Level 2: Backtrace:

Not convertible.
Level 2: Backtrace:

Not convertible.
Level 1: Backtrace:

Not convertible.