reserve x,y for object,X for set,
  f for Function,
  R,S for Relation;

theorem
  for f being non empty constant ext-real-valued Function ex r being
  ExtReal st for x being object st x in dom f holds f.x = r
proof
  let f be non empty constant ext-real-valued Function;
  consider r being object such that
A1: for x being object st x in dom f holds f.x = r by FUNCOP_1:78;
  consider x being object such that
A2: x in dom f by XBOOLE_0:def 1;
  r = f.x by A1,A2;
  hence thesis by A1;
end;
