theorem Th22:
  r < s implies Sphere(x,r) c= Ball(x,s)
proof
  assume r < s;
  then
A1: cl_Ball(x,r) c= Ball(x,s) by Th21;
  Sphere(x,r) c= cl_Ball(x,r) by TOPREAL9:17;
  hence thesis by A1;
end;
