reserve a,b,c,h for Integer;
reserve k,m,n for Nat;
reserve i,j,z for Integer;
reserve p for Prime;

theorem Th96:
  rng exampleSierpinski149 c=
  { [x,y,z] where x,y,z is negative Integer: 4*x*y-x-y = z^2 }
  proof
    let y be object;
    assume y in rng f;
    then consider k being object such that
A1: k in dom f and
A2: f.k = y by FUNCT_1:def 3;
    reconsider k as Element of NATPLUS by A1;
    4*X(k)*Y(k)-X(k)-Y(k) = Z(k)^2;
    then F(k) in { [x,y,z] where x,y,z is negative Integer: 4*x*y-x-y = z^2 };
    hence thesis by A2,Def18;
  end;
