reserve Y for non empty set;
reserve Y for non empty set;
reserve Y for non empty set;
reserve Y for non empty set,
  a,b,c,d,e,f,g for Function of Y,BOOLEAN;
reserve Y for non empty set;

theorem
  for a1,a2,b1,b2 being Function of Y,BOOLEAN holds (a1 'imp' b1)
'&' (a2 'imp' b2) '&' (a1 'or' a2) '&' 'not'( b1 '&' b2)= (b1 'imp' a1) '&' (b2
  'imp' a2) '&' (b1 'or' b2) '&' 'not'( a1 '&' a2)
proof
  let a1,a2,b1,b2 be Function of Y,BOOLEAN;
  (a1 'imp' b1) '&' (a2 'imp' b2) '&' (a1 'or' a2) '&' 'not'( b1 '&' b2)
'<' ( b1 'imp' a1) '&' (b2 'imp' a2) '&' (b1 'or' b2) '&' 'not'( a1 '&' a2) & (
  b1 'imp' a1) '&' (b2 'imp' a2) '&' (b1 'or' b2) '&' 'not'( a1 '&' a2) '<' (a1
  'imp' b1) '&' (a2 'imp' b2) '&' (a1 'or' a2) '&' 'not'( b1 '&' b2) by Lm3;
  hence thesis by BVFUNC_1:15;
end;
