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 *
let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in A |^ (m,n) or x in A * )
assume x in A |^ (m,n) ; :: thesis: x in A *
then ex k being Nat st
( m <= k & k <= n & x in A |^ k ) by Th19;
hence x in A * by FLANG_1:41; :: thesis: verum