let E be set ; :: thesis: for A being Subset of (E ^omega ) holds (A * ) ^^ (A + ) = (A + ) ^^ (A * )
let A be Subset of (E ^omega ); :: thesis: (A * ) ^^ (A + ) = (A + ) ^^ (A * )
thus (A * ) ^^ (A + ) = (A * ) ^^ (A |^.. 1) by Th50
.= (A |^.. 1) ^^ (A * ) by Th32
.= (A + ) ^^ (A * ) by Th50 ; :: thesis: verum