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
card { p where p is quadratic Polynomial of (Z/ 2) : verum } = 4
by pz2, A1, A2, A3, A4, A5, CARD_2:59; verum