reserve X for set;

theorem
for f being PartFunc of X,ExtREAL, er being ExtReal
 holds great_eq_dom(f,er) misses less_dom(f,er)
proof
    let f be PartFunc of X,ExtREAL, er be ExtReal;
    now let x be object;
     assume x in great_eq_dom(f,er) /\ less_dom(f,er); then
     x in great_eq_dom(f,er) & x in less_dom(f,er) by XBOOLE_0:def 4; then
     f.x >= er & f.x < er by MESFUNC1:def 11,def 14;
     hence contradiction;
    end;
    hence thesis by XBOOLE_0:def 1;
end;
