Rework of GenericMinMax: new axiomatic, split logical/decidable parts, Leibniz part

 Moreover, instantiation like MinMax are now made without redefining
 generic properties (easier maintenance). We start using inner modules
 for qualifying (e.g. Z.max_comm).

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12638 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 13 insertions, 78 deletions

diff --git a/theories/QArith/Qminmax.v b/theories/QArith/Qminmax.v
index e9d2f79ab..ae9cc4605 100644
--- a/theories/QArith/Qminmax.v
+++ b/theories/QArith/Qminmax.v
@@ -25,106 +25,41 @@ Module QHasMinMax <: HasMinMax Q_as_OT.
  Definition min_spec := QMM.min_spec.
 End QHasMinMax.
 
-(** We obtain hence all the generic properties of max and min. *)
+Module Q.
 
-Module Import QMinMaxProps := MinMaxProperties Q_as_OT QHasMinMax.
-
-Definition Qmax_case_strong := max_case_strong.
-Definition Qmax_case := max_case.
-Definition Qmax_monotone := max_monotone.
-Definition Qmax_spec := max_spec.
-Definition Qmax_spec_le := max_spec_le.
-Definition Qmax_dec := max_dec.
-Definition Qmax_unicity := max_unicity.
-Definition Qmax_unicity_ext := max_unicity_ext.
-Definition Qmax_id := max_id.
-Notation Qmax_idempotent := Qmax_id (only parsing).
-Definition Qmax_assoc := max_assoc.
-Definition Qmax_comm := max_comm.
-Definition Qmax_l := max_l.
-Definition Qmax_r := max_r.
-Definition Nle_max_l := le_max_l.
-Definition Nle_max_r := le_max_r.
-Definition Qmax_le := max_le.
-Definition Qmax_le_iff := max_le_iff.
-Definition Qmax_lt_iff := max_lt_iff.
-Definition Qmax_lub_l := max_lub_l.
-Definition Qmax_lub_r := max_lub_r.
-Definition Qmax_lub := max_lub.
-Definition Qmax_lub_iff := max_lub_iff.
-Definition Qmax_lub_lt := max_lub_lt.
-Definition Qmax_lub_lt_iff := max_lub_lt_iff.
-Definition Qmax_le_compat_l := max_le_compat_l.
-Definition Qmax_le_compat_r := max_le_compat_r.
-Definition Qmax_le_compat := max_le_compat.
-
-Definition Qmin_case_strong := min_case_strong.
-Definition Qmin_case := min_case.
-Definition Qmin_monotone := min_monotone.
-Definition Qmin_spec := min_spec.
-Definition Qmin_spec_le := min_spec_le.
-Definition Qmin_dec := min_dec.
-Definition Qmin_unicity := min_unicity.
-Definition Qmin_unicity_ext := min_unicity_ext.
-Definition Qmin_id := min_id.
-Notation Qmin_idempotent := Qmin_id (only parsing).
-Definition Qmin_assoc := min_assoc.
-Definition Qmin_comm := min_comm.
-Definition Qmin_l := min_l.
-Definition Qmin_r := min_r.
-Definition Nle_min_l := le_min_l.
-Definition Nle_min_r := le_min_r.
-Definition Qmin_le := min_le.
-Definition Qmin_le_iff := min_le_iff.
-Definition Qmin_lt_iff := min_lt_iff.
-Definition Qmin_glb_l := min_glb_l.
-Definition Qmin_glb_r := min_glb_r.
-Definition Qmin_glb := min_glb.
-Definition Qmin_glb_iff := min_glb_iff.
-Definition Qmin_glb_lt := min_glb_lt.
-Definition Qmin_glb_lt_iff := min_glb_lt_iff.
-Definition Qmin_le_compat_l := min_le_compat_l.
-Definition Qmin_le_compat_r := min_le_compat_r.
-Definition Qmin_le_compat := min_le_compat.
-
-Definition Qmin_max_absorption := min_max_absorption.
-Definition Qmax_min_absorption := max_min_absorption.
-Definition Qmax_min_distr := max_min_distr.
-Definition Qmin_max_distr := min_max_distr.
-Definition Qmax_min_modular := max_min_modular.
-Definition Qmin_max_modular := min_max_modular.
-Definition Qmax_min_disassoc := max_min_disassoc.
-Definition Qmax_min_antimonotone := max_min_antimonotone.
-Definition Qmin_max_antimonotone := min_max_antimonotone.
+(** We obtain hence all the generic properties of max and min. *)
 
+Include MinMaxProperties Q_as_OT QHasMinMax.
 
 
 (** * Properties specific to the [Q] domain *)
 
 (** Compatibilities (consequences of monotonicity) *)
 
-Lemma Qplus_max_distr_l : forall n m p, Qmax (p + n) (p + m) == p + Qmax n m.
+Lemma plus_max_distr_l : forall n m p, Qmax (p + n) (p + m) == p + Qmax n m.
 Proof.
- intros. apply Qmax_monotone.
+ intros. apply max_monotone.
  intros x x' Hx; rewrite Hx; auto with qarith.
  intros x x' Hx. apply Qplus_le_compat; q_order.
 Qed.
 
-Lemma Qplus_max_distr_r : forall n m p, Qmax (n + p) (m + p) == Qmax n m + p.
+Lemma plus_max_distr_r : forall n m p, Qmax (n + p) (m + p) == Qmax n m + p.
 Proof.
  intros. rewrite (Qplus_comm n p), (Qplus_comm m p), (Qplus_comm _ p).
- apply Qplus_max_distr_l.
+ apply plus_max_distr_l.
 Qed.
 
-Lemma Qplus_min_distr_l : forall n m p, Qmin (p + n) (p + m) == p + Qmin n m.
+Lemma plus_min_distr_l : forall n m p, Qmin (p + n) (p + m) == p + Qmin n m.
 Proof.
- intros. apply Qmin_monotone.
+ intros. apply min_monotone.
  intros x x' Hx; rewrite Hx; auto with qarith.
  intros x x' Hx. apply Qplus_le_compat; q_order.
 Qed.
 
-Lemma Qplus_min_distr_r : forall n m p, Qmin (n + p) (m + p) == Qmin n m + p.
+Lemma plus_min_distr_r : forall n m p, Qmin (n + p) (m + p) == Qmin n m + p.
 Proof.
  intros. rewrite (Qplus_comm n p), (Qplus_comm m p), (Qplus_comm _ p).
- apply Qplus_min_distr_l.
+ apply plus_min_distr_l.
 Qed.
+
+End Q.
\ No newline at end of file