reserve Y for non empty set;
reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds a '&' (a 'imp' b) = a '&' b
proof
  let a,b be Function of Y,BOOLEAN;
    let x be Element of Y;
    (a '&' (a 'imp' b)).x =a.x '&' (a 'imp' b).x by MARGREL1:def 20
      .=a.x '&' ('not' a.x 'or' b.x) by BVFUNC_1:def 8
      .=(a.x '&' 'not' a.x) 'or' (a.x '&' b.x) by XBOOLEAN:8
      .=FALSE 'or' (a.x '&' b.x) by XBOOLEAN:138
      .=a.x '&' b.x
      .=(a '&' b).x by MARGREL1:def 20;
    hence thesis;
end;
