Goal:
  
  A : Type
  B : Type
  P : A → B → B → Type
  b : A
  bs : list A
  hd : B
  hd' : B
  tl : list B
  p : P b hd hd'
  e : #|bs| = #|tl|
  ============================
   ((∑ ni : nat, nth_error (b :: bs) ni = Some b) × P b hd hd')


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 ])