let L be RelStr ; :: thesis: for x being set holds
( x is directed Subset of (L opp) iff x is filtered Subset of L )
let x be set ; :: thesis: ( x is directed Subset of (L opp) iff x is filtered Subset of L )
( x is filtered Subset of L iff x is filtered Subset of ((L opp) ~) ) by WAYBEL_0:4;
hence ( x is directed Subset of (L opp) iff x is filtered Subset of L ) by Th26; :: thesis: verum