theorem
  (for n holds F.n = Y /\ less_dom(f,(r+1/(n+1)))) implies Y /\
  less_eq_dom(f,r) = meet rng F
proof
  assume for n holds F.n = Y /\ less_dom(f,r+1/(n+1));
  then
  for n be Element of NAT holds F.n =Y /\ less_dom(R_EAL f,(r+1/(n+1) ));
  then Y /\ less_eq_dom(f,r) = meet rng F by MESFUNC1:20;
  hence thesis;
end;
