reserve V for RealLinearSpace;
reserve u,u1,u2,v,v1,v2,w,w1,y for VECTOR of V;
reserve a,a1,a2,b,b1,b2,c1,c2 for Real;
reserve x,z for set;

theorem Th1:
  Gen w,y implies OASpace(V) is OAffinSpace
proof
  assume Gen w,y;
  then for a1,a2 st a1*w + a2*y = 0.V holds a1=0 & a2=0 by ANALMETR:def 1;
  hence thesis by ANALOAF:26;
end;
