From 6eb9b908400fd51a4d8996a47b14146eaa69371f Mon Sep 17 00:00:00 2001 From: Pierre Roux <pierre.roux@onera.fr> Date: Fri, 18 Feb 2022 12:58:34 +0100 Subject: [PATCH] Remove unused section --- util/nat.v | 32 +++++++++++--------------------- 1 file changed, 11 insertions(+), 21 deletions(-) diff --git a/util/nat.v b/util/nat.v index ad39e8a29..36d335e52 100644 --- a/util/nat.v +++ b/util/nat.v @@ -115,26 +115,16 @@ Section Interval. End Interval. -(** In the section, we introduce an additional lemma about relation - [<] over natural numbers. *) -Section NatOrderLemmas. +(* [ltn_leq_trans]: Establish that [m < p] if [m < n] and [n <= p], to mirror the + lemma [leq_ltn_trans] in [ssrnat]. - (* Mimic the way implicit arguments are used in [ssreflect]. *) - Set Implicit Arguments. - Unset Strict Implicit. + NB: There is a good reason for this lemma to be "missing" in [ssrnat] -- + since [m < n] is defined as [m.+1 <= n], [ltn_leq_trans] is just + [m.+1 <= n -> n <= p -> m.+1 <= p], that is [@leq_trans n m.+1 p]. - (* [ltn_leq_trans]: Establish that [m < p] if [m < n] and [n <= p], to mirror the - lemma [leq_ltn_trans] in [ssrnat]. - - NB: There is a good reason for this lemma to be "missing" in [ssrnat] -- - since [m < n] is defined as [m.+1 <= n], [ltn_leq_trans] is just - [m.+1 <= n -> n <= p -> m.+1 <= p], that is [@leq_trans n m.+1 p]. - - Nonetheless we introduce it here because an additional (even though - arguably redundant) lemma doesn't hurt, and for newcomers the apparent - absence of the mirror case of [leq_ltn_trans] can be somewhat confusing. *) - #[deprecated(since="0.4",note="Use leq_trans instead since n < m is just a notation for n.+1 <= m (c.f., comment in util/nat.v).")] - Lemma ltn_leq_trans n m p : m < n -> n <= p -> m < p. - Proof. exact (@leq_trans n m.+1 p). Qed. - -End NatOrderLemmas. + Nonetheless we introduce it here because an additional (even though + arguably redundant) lemma doesn't hurt, and for newcomers the apparent + absence of the mirror case of [leq_ltn_trans] can be somewhat confusing. *) +#[deprecated(since="0.4",note="Use leq_trans instead since n < m is just a notation for n.+1 <= m (c.f., comment in util/nat.v).")] +Lemma ltn_leq_trans [n m p] : m < n -> n <= p -> m < p. +Proof. exact: leq_trans. Qed. -- GitLab