reserve x,y for set,
        r,s for Real,
        n for Nat,
        V for RealLinearSpace,
        v,u,w,p for VECTOR of V,
        A,B for Subset of V,
        Af for finite Subset of V,
        I for affinely-independent Subset of V,
        If for finite affinely-independent Subset of V,
        F for Subset-Family of V,
        L1,L2 for Linear_Combination of V;

theorem
  A c< B implies conv A misses Int B
  proof
    assume A1: A c<B;
    assume conv A meets Int B;
    then ex x being object st x in conv A & x in Int B by XBOOLE_0:3;
    hence contradiction by A1,Def1;
  end;
