
theorem
  for F being Field for V being finite-dimensional VectSp of F for m
  being Nat st 1 <= m & m+1 < dim V holds GrassmannSpace(V,m,m+1) is PLS
proof
  let F be Field;
  let V be finite-dimensional VectSp of F;
  let m be Nat;
  assume that
A1: 1 <= m and
A2: m+1 < dim V;
A3: m < m+1 by NAT_1:13;
  m <= dim V by A2,NAT_1:13;
  hence thesis by A1,A2,A3,Th25,Th26,Th27,Th28,VECTSP_9:36;
end;
