let E be set ; :: thesis: for A, B being Subset of (E ^omega)

for n being Nat st <%> E in B holds

( A c= A ^^ (B |^.. n) & A c= (B |^.. n) ^^ A )

let A, B be Subset of (E ^omega); :: thesis: for n being Nat st <%> E in B holds

( A c= A ^^ (B |^.. n) & A c= (B |^.. n) ^^ A )

let n be Nat; :: thesis: ( <%> E in B implies ( A c= A ^^ (B |^.. n) & A c= (B |^.. n) ^^ A ) )

assume <%> E in B ; :: thesis: ( A c= A ^^ (B |^.. n) & A c= (B |^.. n) ^^ A )

then <%> E in B |^.. n by Th10;

hence ( A c= A ^^ (B |^.. n) & A c= (B |^.. n) ^^ A ) by FLANG_1:16; :: thesis: verum

for n being Nat st <%> E in B holds

( A c= A ^^ (B |^.. n) & A c= (B |^.. n) ^^ A )

let A, B be Subset of (E ^omega); :: thesis: for n being Nat st <%> E in B holds

( A c= A ^^ (B |^.. n) & A c= (B |^.. n) ^^ A )

let n be Nat; :: thesis: ( <%> E in B implies ( A c= A ^^ (B |^.. n) & A c= (B |^.. n) ^^ A ) )

assume <%> E in B ; :: thesis: ( A c= A ^^ (B |^.. n) & A c= (B |^.. n) ^^ A )

then <%> E in B |^.. n by Th10;

hence ( A c= A ^^ (B |^.. n) & A c= (B |^.. n) ^^ A ) by FLANG_1:16; :: thesis: verum