let E be set ; :: thesis: for A being Subset of (E ^omega )
for m, n being Nat st m <= n & n > 0 holds
(A * ) |^ m,n = A *
let A be Subset of (E ^omega ); :: thesis: for m, n being Nat st m <= n & n > 0 holds
(A * ) |^ m,n = A *
let m, n be Nat; :: thesis: ( m <= n & n > 0 implies (A * ) |^ m,n = A * )
assume that
A1: m <= n and
A2: n > 0 ; :: thesis: (A * ) |^ m,n = A *
<%> E in A * by FLANG_1:49;
hence (A * ) |^ m,n = (A * ) |^ n by A1, Th34
.= A * by A2, FLANG_1:67 ;
:: thesis: verum