reserve MS for non empty MidStr;
reserve a, b for Element of MS;
reserve M for MidSp;
reserve a,b,c,d,a9,b9,c9,d9,x,y,x9 for Element of M;
reserve p,q,r,p9,q9 for Element of [:the carrier of M,the carrier of M:];
reserve u,v,w,u9,w9 for Vector of M;
reserve X for Subset of [:the carrier of M,the carrier of M:];
reserve x for set;

theorem Th48:
  x is Vector of M iff x in setvect(M)
proof
  thus x is Vector of M implies x in setvect(M);
  thus x in setvect(M) implies x is Vector of M
  proof
    assume x in setvect(M);
    then ex X st x = X & X is Vector of M;
    hence thesis;
  end;
end;
