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

theorem Th1:
  'not' I_el(Y)=O_el(Y) & 'not' O_el(Y)=I_el(Y)
proof
A1: for x being Element of Y holds ('not' O_el Y).x= TRUE
  proof
    let x be Element of Y;
    ('not' O_el Y).x= 'not' (O_el Y).x & (O_el Y).x= FALSE by Def10,
MARGREL1:def 19;
    hence thesis;
  end;
  for x being Element of Y holds ('not' I_el Y).x= FALSE
  proof
    let x be Element of Y;
    ('not' I_el Y).x= 'not' ((I_el Y).x) & (I_el Y).x= TRUE by Def11,
MARGREL1:def 19;
    hence thesis;
  end;
  hence thesis by A1,Def10,Def11;
end;
