theorem
  the carrier of Tunit_circle(2) = circle(0,0,1)
  proof
A1: the carrier of Tunit_circle(2) c= circle(0,0,1)
    proof
      let u be object;
      assume u in the carrier of Tunit_circle(2);
      then u in the carrier of Tcircle(0.TOP-REAL 2,1) by TOPREALB:def 7;
      then u in Sphere(0.TOP-REAL 2,1) by TOPREALB:9;
      hence thesis by EUCLID:54,TOPREAL9:52;
    end;
    circle(0,0,1) c= the carrier of Tunit_circle(2)
    proof
      let u be object;
      assume u in circle(0,0,1);
      then u in Sphere(0.TOP-REAL 2,1) by TOPREAL9:52,EUCLID:54;
      then u in the carrier of Tcircle(0.TOP-REAL 2,1) by TOPREALB:9;
      hence thesis by TOPREALB:def 7;
    end;
    hence thesis by A1;
  end;
