let T be TopStruct ; :: thesis: for F, G being Subset-Family of T st F is closed & G is closed holds
F \/ G is closed
let F, G be Subset-Family of T; :: thesis: ( F is closed & G is closed implies F \/ G is closed )
assume A1: ( F is closed & G is closed ) ; :: thesis: F \/ G is closed
let P be Subset of T; :: according to TOPS_2:def 2 :: thesis: ( P in F \/ G implies P is closed )
assume P in F \/ G ; :: thesis: P is closed
then ( P in F or P in G ) by XBOOLE_0:def 3;
hence P is closed by A1; :: thesis: verum