1 files changed, 0 insertions, 58 deletions
diff --git a/theories/Init/Tactics.v b/theories/Init/Tactics.v
index f45b541bc..78e35b11d 100644
--- a/theories/Init/Tactics.v
+++ b/theories/Init/Tactics.v
@@ -68,61 +68,3 @@ Ltac remembertac x a :=
   (set (x:=a) in *; assert (H: x=a) by reflexivity; clearbody x).
 
 Tactic Notation "remember" constr(c) "as" ident(x) := remembertac x c.
-
-(** Tactics for applying equivalences.
-
-The following code provides tactics "apply -> t", "apply <- t",
-"apply -> t in H" and "apply <- t in H". Here t is a term whose type
-consists of nested dependent and nondependent products with an
-equivalence A <-> B as the conclusion. The tactics with "->" in their
-names apply A -> B while those with "<-" in the name apply B -> A. *)
-
-(* The idea of the tactics is to first provide a term in the context
-whose type is the implication (in one of the directions), and then
-apply it. The first idea is to produce a statement "forall ..., A ->
-B" (call this type T) and then do "assert (H : T)" for a fresh H.
-Thus, T can be proved from the original equivalence and then used to
-perform the application. However, currently in Ltac it is difficult
-to produce such T from the original formula.
-
-Therefore, we first pose the original equivalence as H. If the type of
-H is a dependent product, we create an existential variable and apply
-H to this variable. If the type of H has the form C -> D, then we do a
-cut on C. Once we eliminate all products, we split (i.e., destruct)
-the conjunction into two parts and apply the relevant one. *)
-
-Ltac find_equiv H :=
-let T := type of H in
-lazymatch T with
-| ?A -> ?B =>
-  let H1 := fresh in
-  let H2 := fresh in
-  cut A;
-  [intro H1; pose proof (H H1) as H2; clear H H1;
-   rename H2 into H; find_equiv H |
-   clear H]
-| forall x : ?t, _ =>
-  let a := fresh "a" with
-      H1 := fresh "H" in
-    evar (a : t); pose proof (H a) as H1; unfold a in H1;
-    clear a; clear H; rename H1 into H; find_equiv H
-| ?A <-> ?B => idtac
-| _ => fail "The given statement does not seem to end with an equivalence"
-end.
-
-Ltac bapply lemma todo :=
-let H := fresh in
-  pose proof lemma as H;
-  find_equiv H; [todo H; clear H | .. ].
-
-Tactic Notation "apply" "->" constr(lemma) :=
-bapply lemma ltac:(fun H => destruct H as [H _]; apply H).
-
-Tactic Notation "apply" "<-" constr(lemma) :=
-bapply lemma ltac:(fun H => destruct H as [_ H]; apply H).
-
-Tactic Notation "apply" "->" constr(lemma) "in" ident(J) :=
-bapply lemma ltac:(fun H => destruct H as [H _]; apply H in J).
-
-Tactic Notation "apply" "<-" constr(lemma) "in" ident(J) :=
-bapply lemma ltac:(fun H => destruct H as [_ H]; apply H in J).