Section Grid.
Variable O E E' : Tpoint.
Variable grid_ok : ~ Col O E E'.
(** We are not faithful to Tarski's def because for uniqueness we do not need the assumption that A and B are on line OE as it is implied by the definition of sum. *)

Lemma sum_par_strict : forall A B C A' C', Ar2 O E E' A B C -> A <> O -> Pj E E' A A' -> Col O E' A' -> Pj O E A' C' -> Pj O E' B C' -> Pj E' E C' C
-> A' <> O /\ (Par_strict O E A' C' \/ B = O).