reserve X,Y,Z,Z1,Z2,D for set,x,y for object;

theorem Th6:
  X <> {} & X c= Y implies meet Y c= meet X
proof
  assume that
A1: X <> {} and
A2: X c= Y;
  let x be object;
  assume x in meet Y;
  then for Z st Z in X holds x in Z by A2,Def1;
  hence thesis by A1,Def1;
end;
