Add a Coq realization for int.Div2.

Makefile.in

@@ -865,7 +865,7 @@ endif
 
 ifeq (@enable_coq_libs@,yes)
 
-COQLIBS_INT_FILES = Abs ComputerDivision EuclideanDivision Int MinMax Power
+COQLIBS_INT_FILES = Abs ComputerDivision Div2 EuclideanDivision Int MinMax Power
 COQLIBS_INT_ALL_FILES = Exponentiation $(COQLIBS_INT_FILES)
 COQLIBS_INT = $(addprefix lib/coq/int/, $(COQLIBS_INT_ALL_FILES))
 

lib/coq/int/Div2.v

+(* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import BuiltIn.
+Require BuiltIn.
+Require int.Int.
+
+Require Import int.EuclideanDivision.
+
+(* Why3 goal *)
+Lemma div2 : forall (x:Z), exists y:Z, (x = (2%Z * y)%Z) \/
+  (x = ((2%Z * y)%Z + 1%Z)%Z).
+Proof.
+intros x.
+exists (div x 2).
+refine (_ (Mod_bound x 2 _) (Div_mod x 2 _)) ; try easy.
+intros H1 H2.
+simpl in H1.
+omega.
+Qed.
+
+