proposition: Lemma alignes_ordre_cycle : forall A B C : PO, alignes A B C -> alignes B C A.
proof: Proof. intros. halignes H x. discrimine B C; auto with geo. cut (1 + - x <> 0); intros. apply colineaire_alignes with (/ (1 + - x)). VReplace (vec B C) (add_PP (vec B A) (vec A C)). rewrite H0. Fieldvec (1 + - x). apply distinct_col_nonun with (2 := H0); auto. Qed.