let E be set ; :: thesis: for A being Subset of (E ^omega )
for m, n being Nat st m <= n & <%> E in A holds
(A |^ m,n) * = (A * ) |^ m,n
let A be Subset of (E ^omega ); :: thesis: for m, n being Nat st m <= n & <%> E in A holds
(A |^ m,n) * = (A * ) |^ m,n
let m, n be Nat; :: thesis: ( m <= n & <%> E in A implies (A |^ m,n) * = (A * ) |^ m,n )
assume that
A1: m <= n and
A2: <%> E in A ; :: thesis: (A |^ m,n) * = (A * ) |^ m,n
( (A |^ m,n) * = (A |^ n) * & (A * ) |^ m,n = (A * ) |^ n ) by A1, A2, Th34, FLANG_1:49;
hence (A |^ m,n) * = (A * ) |^ m,n by A2, Th17; :: thesis: verum