theorem Th12:
  ex a,b being Element of N st c = <%a,b%>
  proof
    set C = Cayley-Dickson(N);
    the carrier of C = product <% the carrier of N,the carrier of N %> by Def9;
    then ex a,b being set st a in the carrier of N & b in the carrier of N
    & c = <%a,b%> by Th7;
    hence thesis;
  end;
