let E be set ; :: thesis: for B, A 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 B, A 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_1:17; :: thesis: verum