let X be Subset of ; :: thesis: for Y being closed Subset of st X c= Y holds
Cl X c= Y
let Y be closed Subset of ; :: thesis: ( X c= Y implies Cl X c= Y )
set ClX = { A where A is Subset of : ( X c= A & A is closed ) } ;
assume X c= Y ; :: thesis: Cl X c= Y
then Y in { A where A is Subset of : ( X c= A & A is closed ) } ;
hence Cl X c= Y by SETFAM_1:4; :: thesis: verum