reserve n for Element of NAT,
  a, r for Real,
  x for Point of TOP-REAL n;
reserve n for Element of NAT,
  r for non negative Real,
  s, t, x for Point of TOP-REAL n;
reserve n for non zero Element of NAT,
  s, t, o for Point of TOP-REAL n;

theorem Th6:
  s is Point of Tdisk(o,r) & t is Point of Tdisk(o,r) & s <> t
  implies HC(s,t,o,r) is Point of Tcircle(o,r)
proof
  assume s is Point of Tdisk(o,r) & t is Point of Tdisk(o,r) & s <> t;
  then
  the carrier of Tcircle(o,r) = Sphere(o,r) & HC(s,t,o,r) in halfline(s,t)
  /\ Sphere(o,r) by Def3,TOPREALB:9;
  hence thesis by XBOOLE_0:def 4;
end;
