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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(****************************************************************************)
(*                 The Calculus of Inductive Constructions                  *)
(*                                                                          *)
(*                                Projet Coq                                *)
(*                                                                          *)
(*                     INRIA                        ENS-CNRS                *)
(*              Rocquencourt                        Lyon                    *)
(*                                                                          *)
(*                                Coq V5.10                                 *)
(*                              Nov 25th 1994                               *)
(*                                                                          *)
(****************************************************************************)
(*                               Simulation.v                               *)
(*                                                                          *)
(*                                Gerard Huet                               *)
(*                                                                          *)
(* Developed in V5.8  January 1993                                          *)
(* Ported    to V5.10 January 1995                                          *)
(****************************************************************************)
(* Reduction of a term by a set of redexes *)
(* Commuting mark and subst *)

(* Specifications: *)
Lemma mark_lift_rec :
forall (M : lambda) (n k : nat),
lift_rec_r (mark M) k n = mark (lift_rec M k n).
Lemma mark_lift :
forall (M : lambda) (n : nat), lift_r n (mark M) = mark (lift n M).
Lemma mark_subst_rec :
forall (N M : lambda) (n : nat),
subst_rec_r (mark M) (mark N) n = mark (subst_rec M N n).
Lemma mark_subst :
forall M N : lambda, subst_r (mark M) (mark N) = mark (subst M N).