reserve X,Y for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,h for Function;

theorem
  x in dom h & h = f \/ g implies h.x = f.x or h.x = g.x
proof
  assume x in dom h;
  then [x,h.x] in h by FUNCT_1:def 2;
  then h = f \/ g implies [x,h.x] in f or [x,h.x] in g by XBOOLE_0:def 3;
  hence thesis by FUNCT_1:1;
end;
