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 * ; :: thesis: verum
end;
end;