let S, T be non empty up-complete Poset; :: thesis: for f being Function of S,T holds
( f is isomorphic iff Sigma f is isomorphic )
let f be Function of S,T; :: thesis: ( f is isomorphic iff Sigma f is isomorphic )
( RelStr(# the carrier of (Sigma S),the InternalRel of (Sigma S) #) = RelStr(# the carrier of S,the InternalRel of S #) & RelStr(# the carrier of (Sigma T),the InternalRel of (Sigma T) #) = RelStr(# the carrier of T,the InternalRel of T #) ) by YELLOW_9:def 4;
hence ( f is isomorphic iff Sigma f is isomorphic ) by Th6; :: thesis: verum