let E be set ; :: thesis: for A being Subset of (E ^omega) holds A |^ 0 = {(<%> E)}
let A be Subset of (E ^omega); :: thesis: A |^ 0 = {(<%> E)}
ex concat being sequence of (bool (E ^omega)) st
( A |^ 0 = concat . 0 & concat . 0 = {(<%> E)} & ( for i being Nat holds concat . (i + 1) = (concat . i) ^^ A ) ) by Def2;
hence A |^ 0 = {(<%> E)} ; :: thesis: verum