theorem Th30:
  X common_on_dom H1 & X common_on_dom H2 implies for x st x in X
  holds H1#x + H2#x = (H1+H2)#x & H1#x - H2#x = (H1-H2)#x 
  proof
    assume
    A1: X common_on_dom H1 & X common_on_dom H2;
    let x;
    assume x in X;
    then {x} common_on_dom H1 & {x} common_on_dom H2 by A1, Th25;
    hence thesis by Th27;
  end;
