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;
reserve V for finite-dimensional VectSp of GF,
  W, W1, W2 for Subspace of V,
  u, v for Vector of V;

theorem
  dim(W1 /\ W2) >= dim W1 + dim W2 - dim V
proof
A1: dim(W1 + W2) <= dim V & dim V + (dim(W1 /\ W2) - dim V) = dim(W1 /\ W2)
  by Th25;
  dim W1 + dim W2 - dim V = dim(W1 + W2) + dim(W1 /\ W2) - dim V by Th32
    .= dim(W1 + W2) + (dim(W1 /\ W2) - dim V);
  hence thesis by A1,XREAL_1:6;
end;
