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 Th29:
  f +* g c= f \/ g
proof
  let p be object;
  assume
A1: p in f +* g;
  then consider x,y being object such that
A2: p = [x,y] by RELAT_1:def 1;
  x in dom(f +* g) by A1,A2,FUNCT_1:1;
  then x in dom f & not x in dom g or x in dom g by Th12;
  then
A3: x in dom f & (f +* g).x = f.x or x in dom g & (f +* g).x = g.x by Th11,Th13
;
  y = (f +* g).x by A1,A2,FUNCT_1:1;
  then p in f or p in g by A2,A3,FUNCT_1:1;
  hence thesis by XBOOLE_0:def 3;
end;
