theorem
  (for n holds F.n = Y /\ great_dom(f,r-1/(n+1))) implies Y /\
  great_eq_dom(f,r) = meet rng F
proof
  assume for n holds F.n = Y /\ great_dom(f,r-1/(n+1));
  then
  for n be Element of NAT holds F.n = Y /\ great_dom(R_EAL f,(r-1/(n+
  1)));
  then Y /\ great_eq_dom(f,r) = meet rng F by MESFUNC1:19;
  hence thesis;
end;
