reserve X for non empty set,
        x for Element of X,
        S for SigmaField of X,
        M for sigma_Measure of S,
        f,g,f1,g1 for PartFunc of X,REAL,
        l,m,n,n1,n2 for Nat,
        a,b,c for Real;
reserve k for positive Real;

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;
