Definition div O E E' A B C :=
  exists IB : Tpoint, inv O E E' B IB /\ Prod O E E' A IB C.

(* Specifications: *)
Lemma div_exists : forall A B, Col O E A -> Col O E B -> exists C, div O E E' A B C.
Lemma div_uniqueness : forall A B C1 C2, div O E E' A B C1 -> div O E E' A B C2 -> C1 = C2.
Lemma div_col : forall A B C : Tpoint, div O E E' A B C -> Col O E C.
Lemma div_f : forall A B, Col O E A -> Col O E B -> {C | div O E E' A B C}.