1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
19 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
25 (* \VV/ **************************************************************)
27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
31 (*#***********************************************************************)
35 include "NArith/BinPos.ma".
37 include "ZArith/BinInt.ma".
39 include "Arith/Lt.ma".
41 include "Arith/Gt.ma".
43 include "Arith/Plus.ma".
45 include "Arith/Mult.ma".
48 Open Local Scope Z_scope.
51 (*#*********************************************************************)
53 (*#* Binary Integers (Pierre Cr\233\gut, CNET, Lannion, France) *)
55 (*#*********************************************************************)
57 (*#*********************************************************************)
59 (*#* Comparison on integers *)
61 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_refl.con" as lemma.
63 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_Eq_eq.con" as lemma.
65 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_Eq_iff_eq.con" as lemma.
67 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_antisym.con" as lemma.
69 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_Gt_Lt_antisym.con" as lemma.
71 (*#* Transitivity of comparison *)
73 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_Gt_trans.con" as lemma.
75 (*#* Comparison and opposite *)
77 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_opp.con" as lemma.
80 Hint Local Resolve Pcompare_refl.
83 (*#* Comparison first-order specification *)
85 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_Gt_spec.con" as lemma.
87 (*#* Comparison and addition *)
89 inline procedural "cic:/Coq/ZArith/Zcompare/weaken_Zcompare_Zplus_compatible.con" as lemma.
92 Hint Local Resolve ZC4.
95 inline procedural "cic:/Coq/ZArith/Zcompare/weak_Zcompare_Zplus_compatible.con" as lemma.
97 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_plus_compat.con" as lemma.
99 inline procedural "cic:/Coq/ZArith/Zcompare/Zplus_compare_compat.con" as lemma.
101 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_succ_Gt.con" as lemma.
103 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_Gt_not_Lt.con" as lemma.
105 (*#* Successor and comparison *)
107 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_succ_compat.con" as lemma.
109 (*#* Multiplication and comparison *)
111 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_mult_compat.con" as lemma.
113 (*#* Reverting [x ?= y] to trichotomy *)
115 inline procedural "cic:/Coq/ZArith/Zcompare/rename.con" as lemma.
117 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_elim.con" as lemma.
119 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_eq_case.con" as lemma.
121 (*#* Decompose an egality between two [?=] relations into 3 implications *)
123 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_egal_dec.con" as lemma.
125 (*#* Relating [x ?= y] to [Zle], [Zlt], [Zge] or [Zgt] *)
127 inline procedural "cic:/Coq/ZArith/Zcompare/Zle_compare.con" as lemma.
129 inline procedural "cic:/Coq/ZArith/Zcompare/Zlt_compare.con" as lemma.
131 inline procedural "cic:/Coq/ZArith/Zcompare/Zge_compare.con" as lemma.
133 inline procedural "cic:/Coq/ZArith/Zcompare/Zgt_compare.con" as lemma.
135 (*#*********************************************************************)
137 (* Other properties *)
139 inline procedural "cic:/Coq/ZArith/Zcompare/Zmult_compare_compat_l.con" as lemma.
141 inline procedural "cic:/Coq/ZArith/Zcompare/Zmult_compare_compat_r.con" as lemma.