reserve F for Field;
reserve VS for strict VectSp of F;
reserve u,e for set;

theorem
  for VS being strict VectSp of F for H being strict Subspace of VS
  holds 0.VS in (carr VS).H
proof
  let VS be strict VectSp of F;
  let H be strict Subspace of VS;
  H in Subspaces VS by VECTSP_5:def 3;
  then
A1: (carr VS).H = the carrier of H by Def4;
  0.H = 0.VS by VECTSP_4:11;
  hence thesis by A1;
end;
