theorem Th83:
  f1 <##> f2 = f2 <##> f1
proof
  dom(f1<##>f2) = dom f1 /\ dom f2 by Def47;
  hence
A1: dom(f1<##>f2) = dom(f2<##>f1) by Def47;
  let x be object;
  assume
A2: x in dom(f1<##>f2);
  hence (f1<##>f2).x = f1.x (#) f2.x by Def47
    .= (f2<##>f1).x by A1,A2,Def47;
end;
