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


DEBUG:Going to execute:
<Coq.Init.Tauto.simplif> flags;
            <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