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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 *)
(* residuals simulates par_red1 *)
(* Commuting unmark and subst *)
(**************************************************)
(* Reduction of a lambda term by a set of redexes *)
(**************************************************)
Definition reduction (M : lambda) (U : redexes) (N : lambda) :=
residuals (mark M) U (mark N).

Lemma reduction_function :
forall (M N P : lambda) (U : redexes),
reduction M U N -> reduction M U P -> N = P.