let T be non empty TopSpace; :: thesis: for p, q being Element of (Open_setLatt T) holds
( p [= q iff p c= q )
let p, q be Element of (Open_setLatt T); :: thesis: ( p [= q iff p c= q )
( ( p [= q implies p "\/" q = q ) & ( p "\/" q = q implies p [= q ) & p "\/" q = p \/ q ) by Def2, LATTICES:def 3;
hence ( p [= q iff p c= q ) by XBOOLE_1:7, XBOOLE_1:12; :: thesis: verum