
theorem
  for V being RealLinearSpace, M being non empty Subset of V, L1,L2
being Convex_Combination of M, r being Real st 0 < r & r < 1 holds r*L1 + (1-r)
  *L2 is Convex_Combination of M
proof
  let V be RealLinearSpace;
  let M be non empty Subset of V;
  let L1,L2 be Convex_Combination of M;
  let r be Real;
A1: r*L1 is Linear_Combination of M & (1-r)*L2 is Linear_Combination of M by
RLVECT_2:44;
  assume 0 < r & r < 1;
  hence thesis by A1,Th8,RLVECT_2:38;
end;
