Goal:
  
  A : Type
  B : Type
  x : A
  a : A
  l : list A
  proj : A → B
  size : B → nat
  IHl : In x l → size (proj x) < list_size (λ x : A, size (proj x)) l
  H : a = x ∨ In x l
  ============================
   (size (proj x) < S (size (proj a) + list_size (λ x : A, size (proj x)) l))


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 ]