let T be non empty TopSpace; :: thesis: for F being Subset-Family of T holds union (Int (Cl F)) c= Int (Cl (union F))
let F be Subset-Family of T; :: thesis: union (Int (Cl F)) c= Int (Cl (union F))
A1: Int (union (Cl F)) c= Int (Cl (union F)) by Th15, TOPS_1:19;
union (Int (Cl F)) c= Int (union (Cl F)) by Th27;
hence union (Int (Cl F)) c= Int (Cl (union F)) by A1; :: thesis: verum