proposition: Lemma dd_type_ind : forall P, P [::] -> (forall (a : A), P [:: a]) -> (forall (a b : A) (s : seq A), P s -> P (a :: s) -> P (b :: s) -> P (a :: b :: s)) -> (forall (s : seq A), P s).
proof: Proof. intros. Admitted. Lemma permutation_refl : forall s : seq A, permutation s s. Proof. intros. induction s using dd_type_ind. apply permutation_nil. apply permutation_singleton. apply permutation_skip. exact IHs. exact IHs0. exact IHs1. Qed.
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 bigopsClass