Numbers : also axiomatize constants 1 and 2.

 Initially, I was using notation 1 := (S 0) and so on. But then, when
 implementing by NArith or ZArith, some lemmas statements were filled
 with Nsucc's and Zsucc's instead of 1 and 2's.

 Concerning BigN, things are rather complicated: zero, one, two
 aren't inlined during the functor application creating BigN.
 This is deliberate, at least for the other operations like BigN.add.
 And anyway, since zero, one, two are defined too early in NMake,
 we don't have 0%bigN in the body of BigN.zero but something complex that
 reduce to 0%bigN, same for one and two. Fortunately, apply or
 rewrite of generic lemmas seem to work, even if there's BigZ.zero
 on one side and 0 on the other...

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13555 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 5 insertions, 0 deletions

diff --git a/theories/Numbers/Integer/Abstract/ZAddOrder.v b/theories/Numbers/Integer/Abstract/ZAddOrder.v
index eb27e63782..b5ca908b40 100644
--- a/theories/Numbers/Integer/Abstract/ZAddOrder.v
+++ b/theories/Numbers/Integer/Abstract/ZAddOrder.v
@@ -102,6 +102,11 @@ Proof.
 intro n. rewrite (opp_le_mono 0 n). now rewrite opp_0.
 Qed.
 
+Theorem lt_m1_0 : -(1) < 0.
+Proof.
+apply opp_neg_pos, lt_0_1.
+Qed.
+
 Theorem sub_lt_mono_l : forall n m p, n < m <-> p - m < p - n.
 Proof.
 intros n m p. do 2 rewrite <- add_opp_r. rewrite <- add_lt_mono_l.