Goal:
    A : Type  B : Type  f : A -> B  a : A  x : B  H : Some (f a) = Some x
  ============================
   (∑ y : A, Some a = Some y /\ x = f y)


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