let E be set ; :: thesis: for A being Subset of (E ^omega ) holds (A + ) ^^ (A + ) = A |^.. 2
let A be Subset of (E ^omega ); :: thesis: (A + ) ^^ (A + ) = A |^.. 2
thus (A + ) ^^ (A + ) = (A |^.. 1) ^^ (A + ) by Th50
.= (A |^.. 1) ^^ (A |^.. 1) by Th50
.= A |^.. (1 + 1) by Th18
.= A |^.. 2 ; :: thesis: verum