
theorem
card(the set of all p where p is quadratic Polynomial of Z/2) = 4
proof
H1: X^2.0 = 0.(Z/2) & X^2.1 = 0.(Z/2)by qua1;
H2: X^2+1.0 = 1.(Z/2) & X^2+1.1 = 0.(Z/2) by qua1;
H3: X^2+X.0 = 0.(Z/2) & X^2+X.1 = 1.(Z/2) by qua1;
A1: X^2 <> X^2+1     by H1,qua1;
A2: X^2 <> X^2+X     by H1,qua1;
A3: X^2 <> X^2+X+1   by H1,qua1;
A4: X^2+1 <> X^2+X   by H2,qua1;
A5: X^2+1 <> X^2+X+1 by H2,qua1;
    X^2+X <> X^2+X+1 by H3,qua1;
hence thesis by pz2,A1,A2,A3,A4,A5,CARD_2:59;
end;
