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

theorem Th1:
  for VS being strict VectSp of F for H being non empty Subset of
  Subspaces VS holds (carr VS).:H is non empty
proof
  let VS be strict VectSp of F;
  let H be non empty Subset of Subspaces VS;
  consider x being Element of Subspaces VS such that
A1: x in H by SUBSET_1:4;
  (carr VS).x in ((carr VS).:H) by A1,FUNCT_2:35;
  hence thesis;
end;
