theorem Th48:
  a * vector(LC_Z_Module(V),L) = a * L
  proof
    A1: @@L = L;
    L in the carrier of LC_Z_Module(V) by Def29;
    then L in LC_Z_Module(V);
    hence a * vector(LC_Z_Module(V),L) = LCMult(V). [a,@L] by RLVECT_2:def 1
    .= a * L by A1,Def33;
  end;
