(*#* #stop file *)

Require Export pr0_defs.

      Inductive pr1 : T -> T -> Prop :=
         | pr1_r : (t:?) (pr1 t t)
         | pr1_u : (t2,t1:?) (pr0 t1 t2) -> (t3:?) (pr1 t2 t3) -> (pr1 t1 t3).

      Hint pr1 : ltlc := Constructors pr1.

   Section pr1_props. (******************************************************)

      Theorem pr1_pr0 : (t1,t2:?) (pr0 t1 t2) -> (pr1 t1 t2).
      XEAuto.
      Qed.

      Theorem pr1_t : (t2,t1:?) (pr1 t1 t2) ->
                      (t3:?) (pr1 t2 t3) -> (pr1 t1 t3).
      Intros t2 t1 H; XElim H; XEAuto.
      Qed.

   End pr1_props.

      Hints Resolve pr1_pr0 pr1_t : ltlc.