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diff --git a/theories/Numbers/Integer/Axioms/ZAxioms.v b/theories/Numbers/Integer/Axioms/ZAxioms.v
deleted file mode 100644
index 6527bd11c..000000000
--- a/theories/Numbers/Integer/Axioms/ZAxioms.v
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@@ -1,119 +0,0 @@
-Require Export ZDomain.
-
-Module Type IntSignature.
-Declare Module Export ZDomainModule : ZDomainSignature.
-Open Local Scope IntScope.
-
-Parameter Inline O : Z.
-Parameter Inline S : Z -> Z.
-Parameter Inline P : Z -> Z.
-
-Notation "0" := O : IntScope.
-
-Add Morphism S with signature E ==> E as S_wd.
-Add Morphism P with signature E ==> E as P_wd.
-
-Axiom S_inj : forall x y : Z, S x == S y -> x == y.
-Axiom S_P : forall x : Z, S (P x) == x.
-
-Axiom induction :
-  forall Q : Z -> Prop,
-    pred_wd E Q -> Q 0 ->
-    (forall x, Q x -> Q (S x)) ->
-    (forall x, Q x -> Q (P x)) -> forall x, Q x.
-
-End IntSignature.
-
-Module IntProperties (Import IntModule : IntSignature).
-Module Export ZDomainPropertiesModule := ZDomainProperties ZDomainModule.
-Open Local Scope IntScope.
-
-Ltac induct n :=
-  try intros until n;
-  pattern n; apply induction; clear n;
-  [unfold NumPrelude.pred_wd;
-  let n := fresh "n" in
-  let m := fresh "m" in
-  let H := fresh "H" in intros n m H; qmorphism n m | | |].
-
-Theorem P_inj : forall x y, P x == P y -> x == y.
-Proof.
-intros x y H.
-setoid_replace x with (S (P x)); [| symmetry; apply S_P].
-setoid_replace y with (S (P y)); [| symmetry; apply S_P].
-now rewrite H.
-Qed.
-
-Theorem P_S : forall x, P (S x) == x.
-Proof.
-intro x.
-apply S_inj.
-now rewrite S_P.
-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 (S_P or P_S) 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 (Q x) into (Q (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_SP 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_S_P" constr(t) :=
-rewrite_SP t ltac:(fun x t => (set (x := t))) (fun x => (S (P x))) S_P.
-
-Tactic Notation "rewrite_S_P" constr(t) "at" integer(k) :=
-rewrite_SP t ltac:(fun x t => (set (x := t) in |-* at k)) (fun x => (S (P x))) S_P.
-
-Tactic Notation "rewrite_P_S" constr(t) :=
-rewrite_SP t ltac:(fun x t => (set (x := t))) (fun x => (P (S x))) P_S.
-
-Tactic Notation "rewrite_P_S" constr(t) "at" integer(k) :=
-rewrite_SP t ltac:(fun x t => (set (x := t) in |-* at k)) (fun x => (P (S x))) P_S.
-
-(* 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. *)
-
-Section Induction.
-
-Variable Q : Z -> Prop.
-Hypothesis Q_wd : pred_wd E Q.
-
-Add Morphism Q with signature E ==> iff as Q_morph.
-Proof Q_wd.
-
-Theorem induction_n :
-  forall n, Q n ->
-    (forall m, Q m -> Q (S m)) ->
-    (forall m, Q m -> Q (P m)) -> forall m, Q m.
-Proof.
-induct n.
-intros; now apply induction.
-intros n IH H1 H2 H3; apply IH; try assumption. apply H3 in H1; now rewrite P_S in H1.
-intros n IH H1 H2 H3; apply IH; try assumption. apply H2 in H1; now rewrite S_P in H1.
-Qed.
-
-End Induction.
-
-Ltac induct_n k n :=
-  try intros until k;
-  pattern k; apply induction_n with (n := n); clear k;
-  [unfold NumPrelude.pred_wd;
-  let n := fresh "n" in
-  let m := fresh "m" in
-  let H := fresh "H" in intros n m H; qmorphism n m | | |].
-
-End IntProperties.