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 |^.. 1 c= B |^.. 1 by Th13;
then A + c= B |^.. 1 by Th50;
hence A + c= B + by Th50; :: thesis: verum