Fix a naming bug reported by Arnaud Spiwack, allow instance search to create evars and try to solve them too.

Finally, rework tactics on setoids and design a saturating tactic to help solve goals on any setoid.



git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10428 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 28 insertions, 0 deletions

diff --git a/theories/Classes/SetoidTactics.v b/theories/Classes/SetoidTactics.v
index 4832f1d72..7be514169 100644
--- a/theories/Classes/SetoidTactics.v
+++ b/theories/Classes/SetoidTactics.v
@@ -35,3 +35,31 @@ Ltac setoideq :=
     [ |- @eq ?A ?X ?Y ] => apply (setoideq_eq (a:=A) X Y)
   end.
 
+Ltac setoid_tactic :=
+  match goal with
+    | [ H : ?eq ?x ?y |- ?eq ?y ?x ] => sym ; apply H
+    | [ |- ?eq ?x ?x ] => refl
+    | [ H : ?eq ?x ?y, H' : ?eq ?y ?z |- ?eq' ?x ?z ] => trans y ; [ apply H | apply H' ]
+    | [ H : ?eq ?x ?y, H' : ?eq ?z ?y |- ?eq' ?x ?z ] => trans y ; [ apply H | sym ; apply H' ]
+    | [ H : ?eq ?y ?x, H' : ?eq ?z ?y |- ?eq' ?x ?z ] => trans y ; [ sym ; apply H | sym ; apply H' ]
+    | [ H : ?eq ?y ?x, H' : ?eq ?y ?z |- ?eq' ?x ?z ] => trans y ; [ sym ; apply H | apply H' ]
+      
+    | [ H : ?eq ?x ?y |- @equiv _ _ _ ?y ?x ] => sym ; apply H
+    | [ |- @equiv _ _ _ ?x ?x ] => refl
+    | [ H : ?eq ?x ?y, H' : ?eq ?y ?z |- @equiv _ _ _ ?x ?z ] => trans y ; [ apply H | apply H' ]
+    | [ H : ?eq ?x ?y, H' : ?eq ?z ?y |- @equiv _ _ _ ?x ?z ] => trans y ; [ apply H | sym ; apply H' ]
+    | [ H : ?eq ?y ?x, H' : ?eq ?z ?y |- @equiv _ _ _ ?x ?z ] => trans y ; [ sym ; apply H | sym ; apply H' ]
+    | [ H : ?eq ?y ?x, H' : ?eq ?y ?z |- @equiv _ _ _ ?x ?z ] => trans y ; [ sym ; apply H | apply H' ]
+
+    | [ H : @equiv ?A ?R ?s ?x ?y |- @equiv _ _ _ ?y ?x ] => sym ; apply H
+    | [ |- @equiv _ _ _ ?x ?x ] => refl
+    | [ H : @equiv ?A ?R ?s ?x ?y, H' : @equiv ?A ?R ?s ?y ?z |- @equiv _ _ _ ?x ?z ] => trans y ; [ apply H | apply H' ]
+    | [ H : @equiv ?A ?R ?s ?x ?y, H' : @equiv ?A ?R ?s ?z ?y |- @equiv _ _ _ ?x ?z ] => trans y ; [ apply H | sym ; apply H' ]
+    | [ H : @equiv ?A ?R ?s ?y ?x, H' : @equiv ?A ?R ?s ?z ?y |- @equiv _ _ _ ?x ?z ] => trans y ; [ sym ; apply H | sym ; apply H' ]
+    | [ H : @equiv ?A ?R ?s ?y ?x, H' : @equiv ?A ?R ?s ?y ?z |- @equiv _ _ _ ?x ?z ] => trans y ; [ sym ; apply H | apply H' ]
+
+    | [ H : not (@equiv ?A ?R ?s ?X ?X) |- _ ] => elim H ; refl
+    | [ H : not (@equiv ?A ?R ?s ?X ?Y), H' : @equiv ?A ?R ?s ?Y ?X |- _ ] => elim H ; sym ; apply H
+    | [ H : not (@equiv ?A ?R ?s ?X ?Y), H' : ?R ?Y ?X |- _ ] => elim H ; sym ; apply H
+    | [ H : not (@equiv ?A ?R ?s ?X ?Y) |- False ] => elim H ; clear H ; setoid_tac
+  end.