let E be set ; :: thesis: for A being Subset of (E ^omega)
for k being Nat holds (A +) ^^ (A |^ k) = A |^.. (k + 1)
let A be Subset of (E ^omega); :: thesis: for k being Nat holds (A +) ^^ (A |^ k) = A |^.. (k + 1)
let k be Nat; :: thesis: (A +) ^^ (A |^ k) = A |^.. (k + 1)
thus (A +) ^^ (A |^ k) = (A |^.. 1) ^^ (A |^ k) by Th50
.= A |^.. (k + 1) by Th22 ; :: thesis: verum