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

theorem Red1:
  (a 'imp' b) 'imp' (b 'imp' a) = b 'imp' a
proof
  (a 'imp' b) 'imp' (b 'imp' a) =('not' a 'or' b) 'imp' (b 'imp' a) by
BVFUNC_4:8
    .=('not' a 'or' b) 'imp' ('not' b 'or' a) by BVFUNC_4:8
    .='not' ('not' a 'or' b) 'or' ('not' b 'or' a) by BVFUNC_4:8
    .=('not' 'not' a '&' 'not' b) 'or' ('not' b 'or' a) by BVFUNC_1:13
    .=((a '&' 'not' b) 'or' 'not' b) 'or' a by BVFUNC_1:8
    .=((a 'or' 'not' b) '&' ('not' b 'or' 'not' b)) 'or' a by BVFUNC_1:11
    .=((a 'or' 'not' b) 'or' a) '&' ('not' b 'or' a) by BVFUNC_1:11
    .=('not' b 'or' (a 'or' a)) '&' ('not' b 'or' a) by BVFUNC_1:8
    .=('not' b 'or' a);
  hence thesis by BVFUNC_4:8;
end;
