let E be set ; :: thesis: for A, B being Subset of (E ^omega)
for m, n being Nat st m <= n & <%> E in B holds
( A c= A ^^ (B |^ (m,n)) & A c= (B |^ (m,n)) ^^ A )
let A, B be Subset of (E ^omega); :: thesis: for m, n being Nat st m <= n & <%> E in B holds
( A c= A ^^ (B |^ (m,n)) & A c= (B |^ (m,n)) ^^ A )
let m, n be Nat; :: thesis: ( m <= n & <%> E in B implies ( A c= A ^^ (B |^ (m,n)) & A c= (B |^ (m,n)) ^^ A ) )
assume ( m <= n & <%> E in B ) ; :: thesis: ( A c= A ^^ (B |^ (m,n)) & A c= (B |^ (m,n)) ^^ A )
then <%> E in B |^ (m,n) by Th33;
hence ( A c= A ^^ (B |^ (m,n)) & A c= (B |^ (m,n)) ^^ A ) by FLANG_1:16; :: thesis: verum