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 & (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;
