Variable O E E' : Tpoint.
Variable grid_ok : ~ Col O E E'.

(* Specifications: *)
Lemma prod_exists : forall A B,
Col O E A -> Col O E B ->
exists C, Prod O E E' A B C.
Lemma prod_uniqueness : forall A B C1 C2,
Prod O E E' A B C1 ->
Prod O E E' A B C2 ->
C1 = C2.