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
  V is finite-dimensional implies for A being Subset of V st
    A is linearly-independent holds A is finite
proof
  assume
A1: V is finite-dimensional;
  let A be Subset of V;
  assume A is linearly-independent;
  then consider B being Basis of V such that
A2: A c= B by VECTSP_7:19;
  B is finite by A1;
  hence thesis by A2;
end;
