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_1:48;
hence (A |^ (m,n)) * = (A *) |^ (m,n) by A2, Th17; :: thesis: verum