Goal:
  
  X : Type
  Y : Type
  R : nat → X → Y → Type
  n : nat
  l : list X
  a0 : Y
  ys : list Y
  ys' : list Y
  a : All2i R n l ((a0 :: ys) ++ ys')
  IHys : ∀ (n : nat) (l : list X) (ys' : list Y),
           All2i R n l (ys ++ ys')
           → ∑ xs xs' : list X,
               l = xs ++ xs' × All2i R n xs ys × All2i R (n + #|xs|) xs' ys'
  ============================
   (∑ xs xs' : list X,
      l = xs ++ xs' × All2i R n xs (a0 :: ys) × All2i R (n + #|xs|) xs' ys')


DEBUG:Going to execute:
DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H