theorem Th14:
  a is left_complementable & b is left_complementable implies
  <%a,b%> is left_complementable
  proof
    given x being Element of N such that
A1: x+a = 0.N;
    given y being Element of N such that
A2: y+b = 0.N;
    take <%x,y%>;
    thus <%x,y%>+<%a,b%> = <%x+a,y+b%> by Def9
    .= 0.Cayley-Dickson(N) by A1,A2,Def9;
  end;
