+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+
+
+(* PROOF RELOCATION
+*)
+
+include "datatypes_defs/Proof.ma".
+
+inductive Lift: Nat \to Nat \to Proof \to Proof \to Prop \def
+ | lift_lref_lt: \forall jd,jh,i. i < jd \to Lift jd jh (lref i) (lref i)
+ | lift_lref_ge: \forall jd,jh,i1,i2. jd <= i1 \to (i1 + jh == i2) \to
+ Lift jd jh (lref i1) (lref i2)
+ | lift_prin : \forall jd,jh,h. Lift jd jh (prin h) (prin h)
+ | lift_impw : \forall jd,jh,p1,p2.
+ Lift jd jh p1 p2 \to Lift jd jh (impw p1) (impw p2)
+ | lift_impr : \forall jd,jh,p1,p2.
+ Lift jd jh p1 p2 \to Lift jd jh (impr p1) (impr p2)
+ | lift_impi : \forall jd,jh,p1,p2. Lift jd jh p1 p2 \to
+ \forall q1,q2. Lift jd jh q1 q2 \to
+ \forall r1,r2. Lift (succ jd) jh r1 r2 \to
+ Lift jd jh (impi p1 q1 r1) (impi p2 q2 r2)
+ | lift_scut : \forall jd,jh,p1,p2. Lift jd jh p1 p2 \to
+ \forall q1,q2. Lift jd jh q1 q2 \to
+ Lift jd jh (scut p1 q1) (scut p2 q2)
+.