:: deftheorem defines Pappian ANPROJ_2:def 13 :
for IT being non empty CollStr holds
( IT is Pappian iff for o, p1, p2, p3, q1, q2, q3, r1, r2, r3 being Element of IT st o <> p2 & o <> p3 & p2 <> p3 & p1 <> p2 & p1 <> p3 & o <> q2 & o <> q3 & q2 <> q3 & q1 <> q2 & q1 <> q3 & not o,p1,q1 are_collinear & o,p1,p2 are_collinear & o,p1,p3 are_collinear & o,q1,q2 are_collinear & o,q1,q3 are_collinear & p1,q2,r3 are_collinear & q1,p2,r3 are_collinear & p1,q3,r2 are_collinear & p3,q1,r2 are_collinear & p2,q3,r1 are_collinear & p3,q2,r1 are_collinear holds
r1,r2,r3 are_collinear );