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