proposition: Lemma similitude_rapport_un : forall (I A : PO) (a : R), rotation I a A = similitude I 1 a A.
proof: Proof. intros. discrimine I A. rewrite <- rotation_def_centre; rewrite <- similitude_def_centre; auto. lra. elim existence_rotation_Ia with (I := I) (M := A) (a := a); intros B; intros. cut (B = homothetie 1 I B); intros. 2: apply homothetie_identite. rewrite <- H0. apply composee_rotation_homothetie_pos with B; auto. lra. Qed.