Imported Upstream version 8.4dfsgupstream/8.4dfsg

1 files changed, 41 insertions, 40 deletions

diff --git a/theories/PArith/Pnat.v b/theories/PArith/Pnat.v
index f9df70bd..31e88a40 100644
--- a/theories/PArith/Pnat.v
+++ b/theories/PArith/Pnat.v
@@ -1,7 +1,7 @@
 (* -*- coding: utf-8 -*- *)
 (************************************************************************)
 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012     *)
 (*   \VV/  **************************************************************)
 (*    //   *      This file is distributed under the terms of the       *)
 (*         *       GNU Lesser General Public License Version 2.1        *)
@@ -30,7 +30,7 @@ Qed.
 
 Theorem inj_add p q : to_nat (p + q) = to_nat p + to_nat q.
 Proof.
- revert q. induction p using Pind; intros q.
+ revert q. induction p using peano_ind; intros q.
  now rewrite add_1_l, inj_succ.
  now rewrite add_succ_l, !inj_succ, IHp.
 Qed.
@@ -378,55 +378,56 @@ End SuccNat2Pos.
 
 (** For compatibility, old names and old-style lemmas *)
 
-Notation Psucc_S := Pos2Nat.inj_succ (only parsing).
-Notation Pplus_plus := Pos2Nat.inj_add (only parsing).
-Notation Pmult_mult := Pos2Nat.inj_mul (only parsing).
-Notation Pcompare_nat_compare := Pos2Nat.inj_compare (only parsing).
-Notation nat_of_P_xH := Pos2Nat.inj_1 (only parsing).
-Notation nat_of_P_xO := Pos2Nat.inj_xO (only parsing).
-Notation nat_of_P_xI := Pos2Nat.inj_xI (only parsing).
-Notation nat_of_P_is_S := Pos2Nat.is_succ (only parsing).
-Notation nat_of_P_pos := Pos2Nat.is_pos (only parsing).
-Notation nat_of_P_inj_iff := Pos2Nat.inj_iff (only parsing).
-Notation nat_of_P_inj := Pos2Nat.inj (only parsing).
-Notation Plt_lt := Pos2Nat.inj_lt (only parsing).
-Notation Pgt_gt := Pos2Nat.inj_gt (only parsing).
-Notation Ple_le := Pos2Nat.inj_le (only parsing).
-Notation Pge_ge := Pos2Nat.inj_ge (only parsing).
-Notation Pminus_minus := Pos2Nat.inj_sub (only parsing).
-Notation iter_nat_of_P := @Pos2Nat.inj_iter (only parsing).
-
-Notation nat_of_P_of_succ_nat := SuccNat2Pos.id_succ (only parsing).
-Notation P_of_succ_nat_of_P := Pos2SuccNat.id_succ (only parsing).
-
-Notation nat_of_P_succ_morphism := Pos2Nat.inj_succ (only parsing).
-Notation nat_of_P_plus_morphism := Pos2Nat.inj_add (only parsing).
-Notation nat_of_P_mult_morphism := Pos2Nat.inj_mul (only parsing).
-Notation nat_of_P_compare_morphism := Pos2Nat.inj_compare (only parsing).
-Notation lt_O_nat_of_P := Pos2Nat.is_pos (only parsing).
-Notation ZL4 := Pos2Nat.is_succ (only parsing).
-Notation nat_of_P_o_P_of_succ_nat_eq_succ := SuccNat2Pos.id_succ (only parsing).
-Notation P_of_succ_nat_o_nat_of_P_eq_succ := Pos2SuccNat.id_succ (only parsing).
-Notation pred_o_P_of_succ_nat_o_nat_of_P_eq_id := Pos2SuccNat.pred_id (only parsing).
+Notation Psucc_S := Pos2Nat.inj_succ (compat "8.3").
+Notation Pplus_plus := Pos2Nat.inj_add (compat "8.3").
+Notation Pmult_mult := Pos2Nat.inj_mul (compat "8.3").
+Notation Pcompare_nat_compare := Pos2Nat.inj_compare (compat "8.3").
+Notation nat_of_P_xH := Pos2Nat.inj_1 (compat "8.3").
+Notation nat_of_P_xO := Pos2Nat.inj_xO (compat "8.3").
+Notation nat_of_P_xI := Pos2Nat.inj_xI (compat "8.3").
+Notation nat_of_P_is_S := Pos2Nat.is_succ (compat "8.3").
+Notation nat_of_P_pos := Pos2Nat.is_pos (compat "8.3").
+Notation nat_of_P_inj_iff := Pos2Nat.inj_iff (compat "8.3").
+Notation nat_of_P_inj := Pos2Nat.inj (compat "8.3").
+Notation Plt_lt := Pos2Nat.inj_lt (compat "8.3").
+Notation Pgt_gt := Pos2Nat.inj_gt (compat "8.3").
+Notation Ple_le := Pos2Nat.inj_le (compat "8.3").
+Notation Pge_ge := Pos2Nat.inj_ge (compat "8.3").
+Notation Pminus_minus := Pos2Nat.inj_sub (compat "8.3").
+Notation iter_nat_of_P := @Pos2Nat.inj_iter (compat "8.3").
+
+Notation nat_of_P_of_succ_nat := SuccNat2Pos.id_succ (compat "8.3").
+Notation P_of_succ_nat_of_P := Pos2SuccNat.id_succ (compat "8.3").
+
+Notation nat_of_P_succ_morphism := Pos2Nat.inj_succ (compat "8.3").
+Notation nat_of_P_plus_morphism := Pos2Nat.inj_add (compat "8.3").
+Notation nat_of_P_mult_morphism := Pos2Nat.inj_mul (compat "8.3").
+Notation nat_of_P_compare_morphism := Pos2Nat.inj_compare (compat "8.3").
+Notation lt_O_nat_of_P := Pos2Nat.is_pos (compat "8.3").
+Notation ZL4 := Pos2Nat.is_succ (compat "8.3").
+Notation nat_of_P_o_P_of_succ_nat_eq_succ := SuccNat2Pos.id_succ (compat "8.3").
+Notation P_of_succ_nat_o_nat_of_P_eq_succ := Pos2SuccNat.id_succ (compat "8.3").
+Notation pred_o_P_of_succ_nat_o_nat_of_P_eq_id := Pos2SuccNat.pred_id (compat "8.3").
 
 Lemma nat_of_P_minus_morphism p q :
- Pcompare p q Eq = Gt -> Pos.to_nat (p - q) = Pos.to_nat p - Pos.to_nat q.
-Proof (fun H => Pos2Nat.inj_sub p q (ZC1 _ _ H)).
+ Pos.compare_cont p q Eq = Gt ->
+  Pos.to_nat (p - q) = Pos.to_nat p - Pos.to_nat q.
+Proof (fun H => Pos2Nat.inj_sub p q (Pos.gt_lt _ _ H)).
 
 Lemma nat_of_P_lt_Lt_compare_morphism p q :
- Pcompare p q Eq = Lt -> Pos.to_nat p < Pos.to_nat q.
+ Pos.compare_cont p q Eq = Lt -> Pos.to_nat p < Pos.to_nat q.
 Proof (proj1 (Pos2Nat.inj_lt p q)).
 
 Lemma nat_of_P_gt_Gt_compare_morphism p q :
- Pcompare p q Eq = Gt -> Pos.to_nat p > Pos.to_nat q.
+ Pos.compare_cont p q Eq = Gt -> Pos.to_nat p > Pos.to_nat q.
 Proof (proj1 (Pos2Nat.inj_gt p q)).
 
 Lemma nat_of_P_lt_Lt_compare_complement_morphism p q :
- Pos.to_nat p < Pos.to_nat q -> Pcompare p q Eq = Lt.
+ Pos.to_nat p < Pos.to_nat q -> Pos.compare_cont p q Eq = Lt.
 Proof (proj2 (Pos2Nat.inj_lt p q)).
 
 Definition nat_of_P_gt_Gt_compare_complement_morphism p q :
- Pos.to_nat p > Pos.to_nat q -> Pcompare p q Eq = Gt.
+ Pos.to_nat p > Pos.to_nat q -> Pos.compare_cont p q Eq = Gt.
 Proof (proj2 (Pos2Nat.inj_gt p q)).
 
 (** Old intermediate results about [Pmult_nat] *)
@@ -445,7 +446,7 @@ Proof.
 Qed.
 
 Lemma Pmult_nat_succ_morphism :
- forall p n, Pmult_nat (Psucc p) n = n + Pmult_nat p n.
+ forall p n, Pmult_nat (Pos.succ p) n = n + Pmult_nat p n.
 Proof.
  intros. now rewrite !Pmult_nat_mult, Pos2Nat.inj_succ.
 Qed.
@@ -457,7 +458,7 @@ Proof.
 Qed.
 
 Theorem Pmult_nat_plus_carry_morphism :
- forall p q n, Pmult_nat (Pplus_carry p q) n = n + Pmult_nat (p + q) n.
+ forall p q n, Pmult_nat (Pos.add_carry p q) n = n + Pmult_nat (p + q) n.
 Proof.
  intros. now rewrite Pos.add_carry_spec, Pmult_nat_succ_morphism.
 Qed.