let E be set ; :: thesis: for B, A being Subset of (E ^omega )
for l being Nat st <%> E in B holds
( A c= A ^^ (B |^ l) & A c= (B |^ l) ^^ A )
let B, A be Subset of (E ^omega ); :: thesis: for l being Nat st <%> E in B holds
( A c= A ^^ (B |^ l) & A c= (B |^ l) ^^ A )
let l be Nat; :: thesis: ( <%> E in B implies ( A c= A ^^ (B |^ l) & A c= (B |^ l) ^^ A ) )
assume <%> E in B ; :: thesis: ( A c= A ^^ (B |^ l) & A c= (B |^ l) ^^ A )
then <%> E in B |^ l by FLANG_1:31;
hence ( A c= A ^^ (B |^ l) & A c= (B |^ l) ^^ A ) by FLANG_1:17; :: thesis: verum