consider AFV being strict AffVect;
reconsider AS = AFV as non empty AffinStruct ;
( ( for a, b, c being Element of AS st a,b // c,c holds
a = b ) & ( for a, b, c, d, p, q being Element of AS st a,b // p,q & c,d // p,q holds
a,b // c,d ) & ( for a, b, c being Element of AS ex d being Element of AS st a,b // c,d ) & ( for a, b, c, a', b', c' being Element of AS st a,b // a',b' & a,c // a',c' holds
b,c // b',c' ) & ( for a, c being Element of AS ex b being Element of AS st a,b // b,c ) & ( for a, b, c, d being Element of AS st a,b // c,d holds
a,c // b,d ) ) by TDGROUP:21;
then AS is WeakAffVect-like by Def1;
hence ex b₁ being non empty AffinStruct st
( b₁ is strict & not b₁ is trivial & b₁ is WeakAffVect-like ) ; :: thesis: verum