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:
let rec t_tauto_intuit :=
            <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
           in
           t_tauto_intuit