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;

theorem
  a 'imp' (b '&' c) '<' a 'imp' b
proof
  let z be Element of Y;
A1: (a 'imp' (b '&' c)).z =('not' a 'or' (b '&' c)).z by BVFUNC_4:8
    .=('not' a).z 'or' (b '&' c).z by BVFUNC_1:def 4
    .=('not' a).z 'or' (b.z '&' c.z) by MARGREL1:def 20;
  assume
A2: (a 'imp' (b '&' c)).z=TRUE;
  now
    assume (a 'imp' b).z<>TRUE;
    then (a 'imp' b).z=FALSE by XBOOLEAN:def 3;
    then ('not' a 'or' b).z=FALSE by BVFUNC_4:8;
    then
A3: ('not' a).z 'or' b.z=FALSE by BVFUNC_1:def 4;
    ('not' a).z 'or' (b.z '&' c.z) =(('not' a).z 'or' b.z) '&' (('not' a).
    z 'or' c.z) by XBOOLEAN:9
      .=FALSE by A3;
    hence contradiction by A2,A1;
  end;
  hence thesis;
end;
