Goal:
  
  A : Type
  B : Type
  k : nat
  Q : nat → A → Type
  R : nat → A → B → Type
  l : list A
  l' : list B
  n : nat
  x : A
  y : B
  xs : list A
  ys : list B
  r : R n x y
  rs : All2i R (S n) xs ys
  ih : Alli Q (S n) xs
       → All2i (λ (i : nat) (x : A) (y : B), Q i x × R i x y) (S n) xs ys
  q : Q n x
  q0 : Alli Q (S n) xs
  ============================
   (Q n x × R n x y)


DEBUG:Going to execute:
solve
[ do
![ solve
 [ trivial | apply : eq_sym ; trivial ]
 | discriminate
 | contradiction
 | Ltac.split ]
| case not_locked_false_eq_true; Ltac.assumption
| match goal with
  | H:¬ _ |- _ => solve [ case H; trivial ]
  end ]