let E be set ; :: thesis: for A being Subset of (E ^omega ) holds (A + ) ^^ (A * ) = A +
let A be Subset of (E ^omega ); :: thesis: (A + ) ^^ (A * ) = A +
thus (A + ) ^^ (A * ) = (A |^.. 1) ^^ (A * ) by Th50
.= A |^.. 1 by Th17
.= A + by Th50 ; :: thesis: verum