let T be non empty TopSpace; :: thesis: for F being Subset-Family of T holds Cl (Int (Cl (meet F))) c= meet (Cl (Int (Cl F)))
let F be Subset-Family of T; :: thesis: Cl (Int (Cl (meet F))) c= meet (Cl (Int (Cl F)))
A1: Cl (Int (Cl (meet F))) c= Cl (meet (Int (Cl F))) by Th51, PRE_TOPC:19;
Cl (meet (Int (Cl F))) c= meet (Cl (Int (Cl F))) by Th14;
hence Cl (Int (Cl (meet F))) c= meet (Cl (Int (Cl F))) by A1; :: thesis: verum