theorem
  rng f c= dom (g|S) & S c= T implies (g|S)/*f = (g|T)/*f
proof
  assume
A1: rng f c= dom (g|S);
  assume S c= T;
  then g|S c= g|T by RELAT_1:75;
  then
A2: dom (g|S) c= dom (g|T) by RELAT_1:11;
  thus (g|S)/*f = g/*f by A1,Th116
    .= (g|T)/*f by A1,A2,Th116,XBOOLE_1:1;
end;
