reserve a,b,p,k,l,m,n,s,h,i,j,t,i1,i2 for natural Number;

theorem
  for A being finite set holds A is trivial iff card A < 2
proof
  let A be finite set;
  hereby
    assume
A1:  A is trivial;
    per cases;
    suppose
      A is empty;
      hence card A < 2;
    end;
    suppose
      A is non empty;
      then ex x being object st A = {x} by A1,ZFMISC_1:131;
      then card A = 1 by CARD_1:30;
      hence card A < 2;
    end;
  end;
  assume
A2: card A < 2;
  per cases by A2,NAT_1:23;
  suppose card A = 0;
    hence thesis;
  end;
  suppose card A = 1;
    then A is 1-element by CARD_1:def 7;
   hence thesis;
  end;
end;
