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 consider mn being Nat such that
m <= mn and
mn <= n and
A1: x in (A *) |^ mn by Th19;
(A *) |^ mn c= A * by FLANG_1:65;
hence x in A * by A1; :: thesis: verum