reserve m,n,s for non zero Element of NAT;

theorem Th14:
  n-BinaryVectSp is finite-dimensional & dim (n-BinaryVectSp) = n
proof
  set V = n-BinaryVectSp;
  consider B be finite Subset of n-BinaryVectSp such that
A1: B is Basis of n-BinaryVectSp & card B = n &
  ex A be FinSequence of n-tuples_on BOOLEAN
  st len A = n & A is one-to-one & card (rng A) = n & rng A = B &
  for i,j be Nat st i in Seg n & j in Seg n
  holds (i = j implies (A.i).j = TRUE) & (i <> j implies (A.i).j = FALSE)
  by Th13;
  thus V is finite-dimensional by A1,MATRLIN:def 1;
  hence dim V = n by A1,VECTSP_9:def 1;
end;
