theorem Th27:
f in Lp_Functions(M,k) & g in Lp_Functions(M,k) implies
  f - g in Lp_Functions(M,k)
proof
   assume A1: f in Lp_Functions(M,k) & g in Lp_Functions(M,k); then
   (-1)(#)g in Lp_Functions(M,k) by Th26;
   hence thesis by Th25,A1;
end;
