reserve x,y for set,
        r,s for Real,
        n for Nat,
        V for RealLinearSpace,
        v,u,w,p for VECTOR of V,
        A,B for Subset of V,
        Af for finite Subset of V,
        I for affinely-independent Subset of V,
        If for finite affinely-independent Subset of V,
        F for Subset-Family of V,
        L1,L2 for Linear_Combination of V;

theorem Th27:
  A\/{v} is affinely-independent iff
     A is affinely-independent & (v in A or not v in Affin A) by RLAFFIN1:82;
