let E be set ; :: thesis: for A being Subset of (E ^omega )
for m, n being Nat st m > 0 holds
A |^ m,n c= A +
let A be Subset of (E ^omega ); :: thesis: for m, n being Nat st m > 0 holds
A |^ m,n c= A +
let m, n be Nat; :: thesis: ( m > 0 implies A |^ m,n c= A + )
assume A1: m > 0 ; :: thesis: A |^ m,n c= A +
let x be set ; :: 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 FLANG_2:19;
hence x in A + by A1, Th48; :: thesis: verum