Goal:
  
  A : Type
  B : Type
  P : A → B → Type
  x : A
  x0 : A
  l : list A
  H : x0 = x ∨ In x l
  y : B
  l' : list B
  r : P x0 y
  X : All2 P l l'
  IHX : In x l → ∥ ∑ x' : B, P x x' ∥
  ============================
   (∥ ∑ x' : B, P x x' ∥)


DEBUG:Going to execute:
trivial; hnf; intros; (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 ])