consider ADG being Uniquely_Two_Divisible_Group such that
A1: ex a, b being Element of ADG st a <> b by Th6;
A2: ( ( for a, b, c, a9, b9, c9 being Element of (AV ADG) st a,b // a9,b9 & a,c // a9,c9 holds
b,c // b9,c9 ) & ( for a, c being Element of (AV ADG) ex b being Element of (AV ADG) st a,b // b,c ) ) by A1, Th15;
A3: ( ( for a, b, c being Element of (AV ADG) st a,b // c,c holds
a = b ) & ( for a, b, c, b9 being Element of (AV ADG) st a,b // b,c & a,b9 // b9,c holds
b = b9 ) ) by Th15;
A4: for a, b, c, d being Element of (AV ADG) st a,b // c,d holds
a,c // b,d by A1, Th15;
( ( for a, b, c, d, p, q being Element of (AV ADG) st a,b // p,q & c,d // p,q holds
a,b // c,d ) & ( for a, b, c being Element of (AV ADG) ex d being Element of (AV ADG) st a,b // c,d ) ) by A1, Th15;
then ( not AV ADG is trivial & AV ADG is AffVect-like ) by A1, A2, A3, A4;
hence ex b₁ being non trivial AffinStruct st
( b₁ is strict & b₁ is AffVect-like ) ; :: thesis: verum