Goal:
  
  A : Type
  B : Type
  C : Type
  P : A → B → Type
  Q : B → C → Type
  R : A → C → Type
  l'' : list C
  x : A
  y : B
  l : list A
  l' : list B
  r : P x y
  X : All2 P l l'
  IHX : ∀ l'' : list C,
          All2 Q l' l''
          → (∀ (x : A) (y : B) (z : C), P x y → Q y z → R x z) → All2 R l l''
  a : All2 Q (y :: l') l''
  ============================
   ((∀ (x : A) (y : B) (z : C), P x y → Q y z → R x z) → All2 R (x :: l) l'')


DEBUG:Going to execute:
intros until H
Level 0: Backtrace:

No quantified hypothesis named a in current goal even after head-reduction.
Level 0: Backtrace:

No quantified hypothesis named a in current goal even after head-reduction.