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
  [[x,x9],[y,y9]] in dom |:f,g:| implies |:f,g:|.([x,x9],[y,y9]) = [f.(x
  ,y),g.(x9,y9)]
proof
  assume [[x,x9],[y,y9]] in dom |:f,g:|;
  then [x,y] in dom f & [x9,y9] in dom g by Th54;
  hence thesis by Def3;
end;
