theorem Th10:
  x in Int A implies ex L be Linear_Combination of A st L is convex & x = Sum L
  proof
    assume A1: x in Int A;
    then reconsider A1=A as non empty Subset of V;
    x in conv A by A1,Def1;
    then x in {Sum L where L is Convex_Combination of A1:L in ConvexComb(V)}
      by CONVEX3:5;
    then ex L be Convex_Combination of A1 st x=Sum L & L in ConvexComb(V);
    hence thesis;
  end;
