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