diff options
author | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2011-01-03 18:51:13 +0000 |
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committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2011-01-03 18:51:13 +0000 |
commit | 8e2d90a6a9f4480026afd433fc997d9958f76a38 (patch) | |
tree | 6a92d154766a3a8934b91705acf79cc994a42061 /theories/Classes/Morphisms_Prop.v | |
parent | 05662999c9ab0183c0f97fc18579379142ac7b38 (diff) |
Numbers: some improvements in proofs
- a ltac solve_proper which generalizes solve_predicate_wd and co
- using le_elim is nicer that (apply le_lteq; destruct ...)
- "apply ->" can now be "apply" most of the time.
Benefit: NumPrelude is now almost empty
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13762 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Classes/Morphisms_Prop.v')
-rw-r--r-- | theories/Classes/Morphisms_Prop.v | 30 |
1 files changed, 30 insertions, 0 deletions
diff --git a/theories/Classes/Morphisms_Prop.v b/theories/Classes/Morphisms_Prop.v index d4ce9aaa9..256bcc377 100644 --- a/theories/Classes/Morphisms_Prop.v +++ b/theories/Classes/Morphisms_Prop.v @@ -107,3 +107,33 @@ Program Instance all_inverse_impl_morphism {A : Type} : unfold pointwise_relation, all in *. intuition ; specialize (H x0) ; intuition. Qed. + +(** Equivalent points are simultaneously accessible or not *) + +Instance Acc_pt_morphism {A:Type}(E R : A->A->Prop) + `(Equivalence _ E) `(Proper _ (E==>E==>iff) R) : + Proper (E==>iff) (Acc R). +Proof. + apply proper_sym_impl_iff; auto with *. + intros x y EQ WF. apply Acc_intro; intros z Hz. + rewrite <- EQ in Hz. now apply Acc_inv with x. +Qed. + +(** Equivalent relations have the same accessible points *) + +Instance Acc_rel_morphism {A:Type} : + Proper (@relation_equivalence A ==> Logic.eq ==> iff) (@Acc A). +Proof. + apply proper_sym_impl_iff_2. red; now symmetry. red; now symmetry. + intros R R' EQ a a' Ha WF. subst a'. + induction WF as [x _ WF']. constructor. + intros y Ryx. now apply WF', EQ. +Qed. + +(** Equivalent relations are simultaneously well-founded or not *) + +Instance well_founded_morphism {A : Type} : + Proper (@relation_equivalence A ==> iff) (@well_founded A). +Proof. + unfold well_founded. solve_proper. +Qed. |