Goal:
  
  A : Type
  P : nat → A → A → Type
  Q : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  X : ∀ (i : nat) (x y : A), P i x y → Q i x y
  ============================
   (Q i hd hd')


DEBUG:Going to execute:
match goal with
           | |- _ → _ => intro; t_tauto_intuit
           | |- _ => t_reduce; t_solver
           end