
theorem Th16:
  for V being non empty RLSStruct, M being Subset of V st M is
  Affine holds M is convex
proof
  let V be non empty RLSStruct;
  let M be Subset of V;
  assume
A1: M is Affine;
  let u,v be VECTOR of V;
  let r be Real;
  assume that
  0 < r and
  r < 1 and
A2: u in M & v in M;
  set p = 1-r;
  1-p = r;
  hence thesis by A1,A2,RUSUB_4:def 4;
end;
