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-rw-r--r--theories/Numbers/Natural/Abstract/NAxioms.v3
-rw-r--r--theories/Numbers/Natural/Abstract/NDefOps.v2
-rw-r--r--theories/Numbers/Natural/Abstract/NIso.v6
-rw-r--r--theories/Numbers/Natural/Abstract/NStrongRec.v2
4 files changed, 8 insertions, 5 deletions
diff --git a/theories/Numbers/Natural/Abstract/NAxioms.v b/theories/Numbers/Natural/Abstract/NAxioms.v
index b360c016f3..78e38b3cf3 100644
--- a/theories/Numbers/Natural/Abstract/NAxioms.v
+++ b/theories/Numbers/Natural/Abstract/NAxioms.v
@@ -72,5 +72,8 @@ Axiom recursion_succ :
End NAxiomsRec.
+Module Type NAxiomsRecSig := NAxiomsMiniSig <+ NAxiomsRec.
+Module Type NAxiomsRecSig' := NAxiomsMiniSig' <+ NAxiomsRec.
+
Module Type NAxiomsFullSig := NAxiomsSig <+ NAxiomsRec.
Module Type NAxiomsFullSig' := NAxiomsSig' <+ NAxiomsRec.
diff --git a/theories/Numbers/Natural/Abstract/NDefOps.v b/theories/Numbers/Natural/Abstract/NDefOps.v
index 8d11b5ce33..9af668487f 100644
--- a/theories/Numbers/Natural/Abstract/NDefOps.v
+++ b/theories/Numbers/Natural/Abstract/NDefOps.v
@@ -15,7 +15,7 @@ Require Export NStrongRec.
(** In this module, we derive generic implementations of usual operators
just via the use of a [recursion] function. *)
-Module NdefOpsProp (Import N : NAxiomsFullSig').
+Module NdefOpsProp (Import N : NAxiomsRecSig').
Include NStrongRecProp N.
(** Nullity Test *)
diff --git a/theories/Numbers/Natural/Abstract/NIso.v b/theories/Numbers/Natural/Abstract/NIso.v
index 3a48b79972..1fe6ed9bf5 100644
--- a/theories/Numbers/Natural/Abstract/NIso.v
+++ b/theories/Numbers/Natural/Abstract/NIso.v
@@ -10,7 +10,7 @@
Require Import NBase.
-Module Homomorphism (N1 N2 : NAxiomsFullSig).
+Module Homomorphism (N1 N2 : NAxiomsRecSig).
Local Notation "n == m" := (N2.eq n m) (at level 70, no associativity).
@@ -51,7 +51,7 @@ Qed.
End Homomorphism.
-Module Inverse (N1 N2 : NAxiomsFullSig).
+Module Inverse (N1 N2 : NAxiomsRecSig).
Module Import NBasePropMod1 := NBaseProp N1.
(* This makes the tactic induct available. Since it is taken from
@@ -74,7 +74,7 @@ Qed.
End Inverse.
-Module Isomorphism (N1 N2 : NAxiomsFullSig).
+Module Isomorphism (N1 N2 : NAxiomsRecSig).
Module Hom12 := Homomorphism N1 N2.
Module Hom21 := Homomorphism N2 N1.
diff --git a/theories/Numbers/Natural/Abstract/NStrongRec.v b/theories/Numbers/Natural/Abstract/NStrongRec.v
index 26cf2d64a6..a52a52e766 100644
--- a/theories/Numbers/Natural/Abstract/NStrongRec.v
+++ b/theories/Numbers/Natural/Abstract/NStrongRec.v
@@ -13,7 +13,7 @@ and proves its properties *)
Require Export NSub.
-Module NStrongRecProp (Import N : NAxiomsFullSig').
+Module NStrongRecProp (Import N : NAxiomsRecSig').
Include NSubProp N.
Section StrongRecursion.