theorem
  f=u implies a(#)f=a*u
proof
  assume
A1: f=u;
  reconsider u2=u as VECTOR of RLSp_L1Funct M by TARSKI:def 3;
  thus a*u=a*u2 by Th5
    .=a(#)f by A1,Th26;
end;
