Goal:
  
  P : elt -> elt -> Prop
  s : t
  H : forall v1 v2 : elt, In v1 s -> In v2 s -> P v1 v2
  x : elt
  H0 : In x s
  ============================
   (forall x0 : elt, In x0 s -> P x x0)


DEBUG:Going to execute:
<Coq.Init.Tauto.axioms> flags ||
             match reverse goal with
             | id:(?X1 -> ?X2) -> ?X3
               |- _ =>
                   cut X3;
                    [ intro; clear id; t_tauto_intuit
                    | cut (X1 -> X2);
                       [ exact
                       id
                       | generalize (fun y : X2 => id (fun x : X1 => y));
                          intro; clear id; (solve 
                          [ t_tauto_intuit ]) ] ]
             | id:~ ?X1 -> ?X3
               |- _ =>
                   cut X3;
                    [ intro; clear id; t_tauto_intuit
                    | cut (~ X1);
                       [ exact
                       id
                       | clear id; intro; (solve [ t_tauto_intuit ]) ] ]
             | |- ?X1 =>
                   <Coq.Init.Tauto.is_disj> flags X1; (solve
                    [ left; t_tauto_intuit | right; t_tauto_intuit ])
             end ||
               match goal with
               | |- _ -> _ => intro; t_tauto_intuit
               | |- _ => t_reduce; t_solver
               end || t_solver
Level 3: evaluation returns
<coq-core.plugins.tauto::is_conj@0>
where
tauto_flags := 
of type
tauto_flags
X1 := forall x0 : elt, In x0 s -> P x x0
of type
constr of type tacvalue

Level 3: Backtrace:

Tactic failure.
Level 3: Backtrace:

Tactic failure.
Level 2: Backtrace:

Tactic failure.
Level 2: Backtrace:

Tactic failure.
Level 1: Backtrace:

No matching clauses for match.
Level 1: Backtrace:

No matching clauses for match.