theorem Th43:
  A is affinely-independent & B c= A implies B is affinely-independent
 proof
  assume that
   A1: A is affinely-independent and
   A2: B c=A;
  now let L be Linear_Combination of B such that
    A3: Sum L=0.V & sum L=0;
   L is Linear_Combination of A by A2,RLVECT_2:21;
   hence Carrier L={} by A1,A3,Th42;
  end;
  hence thesis by Th42;
 end;
