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

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