reserve GF for Field,
  V for VectSp of GF,
  W for Subspace of V,
  x, y, y1, y2 for set,
  i, n, m for Nat;

theorem Th24:
  V is finite-dimensional implies W is finite-dimensional
proof
  set A = the Basis of W;
  consider I being Basis of V such that
A1: A c= I by Th13;
  assume V is finite-dimensional;
  then I is finite;
  hence thesis by A1,MATRLIN:def 1;
end;
