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 a,b,c being Function of Y,BOOLEAN holds (a '&' 'not' b) 'or'
(b '&' 'not' c) 'or' (c '&' 'not' a)= (b '&' 'not' a) 'or' (c '&' 'not' b) 'or'
  (a '&' 'not' c)
proof
  let a,b,c be Function of Y,BOOLEAN;
  (a '&' 'not' b) 'or' (b '&' 'not' c) 'or' (c '&' 'not' a) '<' (b '&'
  'not' a) 'or' (c '&' 'not' b) 'or' (a '&' 'not' c) & (b '&' 'not' a) 'or' (c
'&' 'not' b) 'or' (a '&' 'not' c) '<' (a '&' 'not' b) 'or' (b '&' 'not' c) 'or'
  (c '&' 'not' a) by Lm1;
  hence thesis by BVFUNC_1:15;
end;
