reserve u,v,x,y,z,X,Y for set;
reserve r,s for Real;
reserve N for non empty ConjNormAlgStr;
reserve a,a1,a2,b,b1,b2 for Element of N;
reserve c,c1,c2 for Element of Cayley-Dickson(N);

theorem Th28:
  N is add-associative right_zeroed right_complementable implies
  <% a1,b1 %> - <% a2,b2 %> = <% a1-a2,b1-b2 %>
  proof
    assume N is add-associative right_zeroed right_complementable;
    hence <%a1,b1%> - <%a2,b2%> = <%a1,b1%>+<%-a2,-b2%> by Th27
    .= <%a1-a2,b1-b2%> by Def9;
  end;
