theorem
  Int A is non empty implies A is finite
  proof
    assume Int A is non empty;
    then consider x being object such that
    A1: x in Int A;
    consider L be Linear_Combination of A such that
   A2: L is convex & x=Sum L by A1,Th10;
   Carrier L=A by A1,A2,Th11;
   hence A is finite;
 end;
