let E be set ; :: thesis: for A being Subset of (E ^omega )
for m, n being Nat holds (A ? ) |^ m,n c= A *
let A be Subset of (E ^omega ); :: thesis: for m, n being Nat holds (A ? ) |^ m,n c= A *
let m, n be Nat; :: thesis: (A ? ) |^ m,n c= A *

per cases ( m <= n or m > n ) ;

suppose m <= n ; :: thesis: (A ? ) |^ m,n c= A *

then (A ? ) |^ m,n = A |^ 0 ,n by Th98;
hence (A ? ) |^ m,n c= A * by Th32; :: thesis: verum

end;

suppose m > n ; :: thesis: (A ? ) |^ m,n c= A *

then (A ? ) |^ m,n = {} by Th21;
hence (A ? ) |^ m,n c= A * by XBOOLE_1:2; :: thesis: verum

end;

end;