reserve X for non empty set,
  Y for set,
  S for SigmaField of X,
  F for sequence of S,
  f,g for PartFunc of X,REAL,
  A,B for Element of S,
  r,s for Real,
  a for Real,
  n for Nat;

theorem
  for x be set holds x in less_eq_dom(f,a) iff x in dom f &
   ex y being Real st y=f.x & y <= a
proof
  let x be set;
  (ex y being Real st y=f.x & y <= a) iff f.x <= a;
  hence thesis by MESFUNC1:def 12;
end;
