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;
reserve v,u for VECTOR of RLSp_LpFunct(M,k);
reserve v,u for VECTOR of RLSp_AlmostZeroLpFunct(M,k);

theorem
f=u implies a(#)f=a*u
proof
   reconsider u2=u as VECTOR of RLSp_LpFunct(M,k) by TARSKI:def 3;
   assume A1: f=u;
   a*u=a*u2 by LPSPACE1:5;
   hence a*u = a(#)f by Th30,A1;
end;
