proposition: Lemma image_distinct_pole : forall (I A B : PO) (k : R), k <> 0 -> I <> A -> B = inversion I k A -> I <> B.
proof: Proof. intros. elim (inversion_def (I:=I) (A:=A) (B:=B) (k:=k)); intros; auto. red in |- *; intros; apply H. rewrite <- H3; rewrite <- H4; Simplscal. VReplace (vec I I) (mult_PP 0 (vec I A)). Simplscal. Qed.