theorem Th67:
  Affin conv A = Affin A
 proof
  thus Affin conv A c=Affin A by Th51,Th65;
  let x be object;
  assume x in Affin A;
  then x in {Sum L where L is Linear_Combination of A:sum L=1} by Th59;
  then consider L be Linear_Combination of A such that
   A1: x=Sum L and
   A2: sum L=1;
  reconsider K=L as Linear_Combination of conv A by Lm1,RLVECT_2:21;
  Sum K in {Sum M where M is Linear_Combination of conv A:sum M=1} by A2;
  hence thesis by A1,Th59;
 end;
