1 files changed, 0 insertions, 54 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZPred.v b/theories/Numbers/Integer/Abstract/ZPred.v
deleted file mode 100644
index 4814ab086..000000000
--- a/theories/Numbers/Integer/Abstract/ZPred.v
+++ /dev/null
@@ -1,54 +0,0 @@
-Axiom succ_pred : forall x : Z, S (P x) == x.
-Add Morphism P with signature E ==> E as pred_wd.
-
-Theorem pred_inj : forall x y, P x == P y -> x == y.
-Proof.
-intros x y H.
-setoid_replace x with (S (P x)); [| symmetry; apply succ_pred].
-setoid_replace y with (S (P y)); [| symmetry; apply succ_pred].
-now rewrite H.
-Qed.
-
-Theorem pred_succ : forall x, P (S x) == x.
-Proof.
-intro x.
-apply succ_inj.
-now rewrite succ_pred.
-Qed.
-
-(* The following tactics are intended for replacing a certain
-occurrence of a term t in the goal by (S (P t)) or by (P (S t)).
-Unfortunately, this cannot be done by setoid_replace tactic for two
-reasons. First, it seems impossible to do rewriting when one side of
-the equation in question (succ_pred or pred_succ) is a variable, due to bug 1604.
-This does not work even when the predicate is an identifier (e.g.,
-when one tries to rewrite (A x) into (A (S (P x)))). Second, the
-setoid_rewrite tactic, like the ordinary rewrite tactic, does not
-allow specifying the exact occurrence of the term to be rewritten. Now
-while not in the setoid context, this occurrence can be specified
-using the pattern tactic, it does not work with setoids, since pattern
-creates a lambda abstractuion, and setoid_rewrite does not work with
-them. *)
-
-Ltac rewrite_succP t set_tac repl thm :=
-let x := fresh "x" in
-set_tac x t;
-setoid_replace x with (repl x); [| symmetry; apply thm];
-unfold x; clear x.
-
-Tactic Notation "rewrite_succ_pred" constr(t) :=
-rewrite_succP t ltac:(fun x t => (set (x := t))) (fun x => (S (P x))) succ_pred.
-
-Tactic Notation "rewrite_succ_pred" constr(t) "at" integer(k) :=
-rewrite_succP t ltac:(fun x t => (set (x := t) in |-* at k)) (fun x => (S (P x))) succ_pred.
-
-Tactic Notation "rewrite_pred_succ" constr(t) :=
-rewrite_succP t ltac:(fun x t => (set (x := t))) (fun x => (P (S x))) pred_succ.
-
-Tactic Notation "rewrite_pred_succ" constr(t) "at" integer(k) :=
-rewrite_succP t ltac:(fun x t => (set (x := t) in |-* at k)) (fun x => (P (S x))) pred_succ.
-
-(* One can add tactic notations for replacements in assumptions rather
-than in the goal. For the reason of many possible variants, the core
-of the tactic is factored out. *)
-