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;
