let E be set ; :: thesis: for A, B being Subset of (E ^omega) st A c= B + holds
A + c= B +
let A, B be Subset of (E ^omega); :: thesis: ( A c= B + implies A + c= B + )
assume A c= B + ; :: thesis: A + c= B +
then A c= B |^.. 1 by Th50;
then A |^.. 1 c= B |^.. 1 by Th29;
then A + c= B |^.. 1 by Th50;
hence A + c= B + by Th50; :: thesis: verum