proposition: Lemma natcofaceleh ( i n upper : nat ) ( p : natleh n upper ) : natleh ( natcoface i n ) ( S upper ).
proof: Proof. intros. unfold natcoface. destruct ( natgtb i n ). - apply natlthtoleh. apply (natlehlthtrans _ upper ). + assumption. + apply natlthnsn. - apply p. Defined.
imports: UniMath.Tactics.EnsureStructuredProofs UniMath.Foundations.PartA UniMath.Foundations.Propositions UniMath.Foundations.NaturalNumbers UniMath.Algebra.RigsAndRings UniMath.Algebra.Domains_and_Fields UniMath.NumberSystems.Integers UniMath.Algebra.Monoids