theorem Th63:
  a * vector(LC_RLSpace(V),L) = a * L
proof
A1: @@L = L;
  L in the carrier of LC_RLSpace(V) by Def14;
  then L in LC_RLSpace(V);
  hence a * vector(LC_RLSpace(V),L) = LCMult(V).[a,@L] by Def1
    .= a * L by A1,Def18;
end;
