theorem Th65:
  conv A c= Affin A
 proof
  let x be object;
  assume A1: x in conv A;
  then reconsider A1=A as non empty Subset of V;
  conv(A1)={Sum(L) where L is Convex_Combination of A1:L in ConvexComb(V)}
by CONVEX3:5;
  then consider L be Convex_Combination of A1 such that
   A2: Sum L=x and
   L in ConvexComb(V) by A1;
  sum L=1 by Th62;
  then x in {Sum K where K is Linear_Combination of A:sum K=1} by A2;
  hence thesis by Th59;
 end;
