src/HOL/Quot/PER.ML

new theory PPROD

(*  Title:      HOL/Quot/PER.ML
    ID:         $Id$
    Author:     Oscar Slotosch
    Copyright   1997 Technische Universitaet Muenchen

*)
open PER;

Goalw [fun_per_def,per_def] "f===g=(!x y. x:D&y:D&x===y-->f x===g y)";
by (rtac refl 1);
qed "inst_fun_per";

(* Witness that quot is not empty *)
Goal "?z:{s.? r.!y. y:s=y===r}";
br CollectI 1;
by (res_inst_tac [("x","x")] exI 1);
by (rtac allI 1);
by (rtac mem_Collect_eq 1);
qed "quotNE";