let E be set ; :: thesis: for A being Subset of (E ^omega )
for n being Nat holds A * = (A |^ 0 ,n) \/ (A |^.. (n + 1))
let A be Subset of (E ^omega ); :: thesis: for n being Nat holds A * = (A |^ 0 ,n) \/ (A |^.. (n + 1))
let n be Nat; :: thesis: A * = (A |^ 0 ,n) \/ (A |^.. (n + 1))
thus A * = A |^.. 0 by Th11
.= (A |^ 0 ,n) \/ (A |^.. (n + 1)) by Th7 ; :: thesis: verum