Goal:
  
  A : Type
  B : Type
  C : Type
  R : A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ l' : list B,
         #|xs| = #|l'|
         → All2 R xs (map2 g xs l')
           → All2 (λ (x : A) (y : B), R x (g x y)) xs l'
  y : B
  ys : list B
  H : S #|xs| = S #|ys|
  X : All2 R (x :: xs) (g x y :: map2 g xs ys)
  ============================
   (All2 (λ (x : A) (y : B), R x (g x y)) (x :: xs) (y :: ys))


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 ]