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;
