theorem Th39:
  a * vector(LC_CLSpace V,L) = a * L
proof
  L in the carrier of LC_CLSpace V by Def12;
  then L in LC_CLSpace V;
  then
A1: (C_LCMult V).[a,vector(LC_CLSpace V,L)] = (C_LCMult V).[a,@L] by
RLVECT_2:def 1;
  @@L = L;
  hence thesis by A1,Def16;
end;
