let T be non empty TopSpace; :: thesis: for F being Subset-Family of T holds union (Cl (Int (Cl F))) c= Cl (Int (Cl (union F)))
let F be Subset-Family of T; :: thesis: union (Cl (Int (Cl F))) c= Cl (Int (Cl (union F)))
A1: Cl (union (Int (Cl F))) c= Cl (Int (Cl (union F))) by Th50, PRE_TOPC:19;
union (Cl (Int (Cl F))) c= Cl (union (Int (Cl F))) by Th15;
hence union (Cl (Int (Cl F))) c= Cl (Int (Cl (union F))) by A1; :: thesis: verum