:: deftheorem Def1 defines WeakAffVect-like AFVECT0:def 1 :
for IT being non empty AffinStruct holds
( IT is WeakAffVect-like iff ( ( for a, b, c being Element of IT st a,b // c,c holds
a = b ) & ( for a, b, c, d, p, q being Element of IT st a,b // p,q & c,d // p,q holds
a,b // c,d ) & ( for a, b, c being Element of IT ex d being Element of IT st a,b // c,d ) & ( for a, b, c, a9, b9, c9 being Element of IT st a,b // a9,b9 & a,c // a9,c9 holds
b,c // b9,c9 ) & ( for a, c being Element of IT ex b being Element of IT st a,b // b,c ) & ( for a, b, c, d being Element of IT st a,b // c,d holds
a,c // b,d ) ) );