theorem Th23:
for
G being
IncProjStr holds
(
G is
IncProjectivePlane iff (
G is
configuration & ( for
p,
q being
POINT of
G ex
M being
LINE of
G st
{p,q} on M ) & ( for
P,
Q being
LINE of
G ex
a being
POINT of
G st
a on P,
Q ) & ex
a,
b,
c,
d being
POINT of
G st
a,
b,
c,
d is_a_quadrangle ) )