proposition: Lemma fact_inc_recurse : forall p n:nat, (n <= p)%nat -> (fact n <= fact p)%nat.
proof: Proof. induction p. - intros. inversion H. apply Nat.le_refl. - intros. apply Nat.le_succ_r in H. destruct H. apply (Nat.le_trans (fact n) (fact p)). apply IHp, H. apply fact_inc. subst n. apply Nat.le_refl. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.model.totalorder.QMinMax CoRN.reals.fast.CRAlternatingSum CoRN.reals.fast.CRAlternatingSum_alg CoRN.reals.fast.CRstreams CoRN.reals.fast.CRexp CoRN.reals.fast.CRpi CoRN.reals.fast.CRArith CoRN.reals.fast.CRIR Coq.QArith.Qpower Coq.QArith.Qabs CoRN.model.ordfields.Qordfield Coq.QArith.Qround CoRN.transc.Pi CoRN.reals.fast.ModulusDerivative CoRN.reals.fast.ContinuousCorrect CoRN.model.metric2.Qmetric CoRN.transc.PowerSeries CoRN.transc.SinCos Coq.NArith.Ndigits CoRN.reals.fast.Compress CoRN.reals.fast.PowerBound CoRN.tactics.CornTac MathClasses.interfaces.abstract_algebra CoRN.util.Qdlog Coq(Lia)