reserve Y for non empty set;
reserve B for Subset of Y;

theorem ::De'Morgan
  for a,b being Function of Y,BOOLEAN
   holds 'not' (a 'or' b)=('not' a) '&' ('not' b)
proof
  let a,b be Function of Y,BOOLEAN;
  let x be Element of Y;
  thus ('not' (a 'or' b)).x = 'not' ((a 'or' b).x) by MARGREL1:def 19
     .= 'not' (a.x 'or' b.x) by Def4
     .= ('not' a).x '&' 'not' b.x by MARGREL1:def 19
     .= ('not' a).x '&' ('not' b).x by MARGREL1:def 19
     .= (('not' a) '&' ('not' b)).x by MARGREL1:def 20;
end;
