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 k being Nat such that
A1: x in (A |^ (m,n)) |^ k by FLANG_1:41;
( (A |^ (m,n)) |^ k = A |^ ((m * k),(n * k)) & A |^ ((m * k),(n * k)) c= A * ) by Th32, Th40;
hence x in A * by A1; :: thesis: verum