reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;

theorem Th24:
  ((f +* g)|(dom f \ dom g)) c= f
proof
A1: for x being object
   st x in dom((f +* g)|(dom f \ dom g)) holds ((f +* g)|(dom f \ dom
  g)).x = f.x
  proof
    let x be object such that
A2: x in dom((f +* g)|(dom f \ dom g));
    dom((f +* g)|(dom f \ dom g)) c= dom f \ dom g by RELAT_1:58;
    then not x in dom g by A2,XBOOLE_0:def 5;
    then (f +* g).x = f.x by Th11;
    hence thesis by A2,FUNCT_1:47;
  end;
  dom((f +* g)|(dom f \ dom g)) c= dom f \ dom g by RELAT_1:58;
  then dom((f +* g)|(dom f \ dom g)) c= dom f by XBOOLE_1:1;
  hence thesis by A1,GRFUNC_1:2;
end;
