let E be set ; :: thesis: for A being Subset of (E ^omega)
for m, n being Nat st m <= n & n > 0 & <%> E in A holds
(A |^ (m,n)) * = A *
let A be Subset of (E ^omega); :: thesis: for m, n being Nat st m <= n & n > 0 & <%> E in A holds
(A |^ (m,n)) * = A *
let m, n be Nat; :: thesis: ( m <= n & n > 0 & <%> E in A implies (A |^ (m,n)) * = A * )
assume that
A1: m <= n and
A2: n > 0 and
A3: <%> E in A ; :: thesis: (A |^ (m,n)) * = A *
thus (A |^ (m,n)) * = (A |^ n) * by A1, A3, Th34
.= A * by A2, A3, Th16 ; :: thesis: verum