let equivalent $f\;g$ = 
  let $f',g'$ be such that
    $f \semeq \sigma_{j}(f')$ and $g \semeq \pi_{i}(g')$
  in if $f'$,$g'$ do not exist then 
         false
     elseif $X_{1-i}$ is copointed then 
	 equal $\sigma_{j}(f')\;\sigma_{j}(g')$
     else (*$A_{1-j}$ is pointed*) 
         equal $\pi_{i}(f')\;\pi_{i}(g')$