proposition: Lemma take_fresh : forall (n : nat) (s : seq A) (a : A), fresh s a -> fresh (take n s) a.
proof: Proof. intro n; induction n. intros s a H; rewrite take0; simpl; auto. intros s a H; destruct s; simpl; auto. simpl; split. by inversion H. apply IHn; by inversion H. Defined.
imports: ssreflect CSetoids CSetoidFun CFields CPolynomials Program Omega Equivalence Morphisms Wf Morphisms CRings CRing_Homomorphisms Rational Setoid CPoly_NthCoeff CPoly_Degree CReals Intervals CauchySeq IntervalFunct MoreIntervals MoreFunctions Composition seq