reserve m,n for non zero Element of NAT;
reserve i,j,k for Element of NAT;
reserve Z for set;

theorem
for f be PartFunc of REAL i,REAL st Z c= dom f holds dom ((<>*f) |Z) = Z
proof
   let f be PartFunc of REAL i,REAL;
   assume Z c= dom f; then
   Z c= dom (<>*f) by Th3;
   hence thesis by RELAT_1:62;
end;
