(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
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(*                 The Calculus of Inductive Constructions                  *)
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(*                                Projet Coq                                *)
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(*                     INRIA                        ENS-CNRS                *)
(*              Rocquencourt                        Lyon                    *)
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(*                                Coq V5.10                                 *)
(*                              Nov 25th 1994                               *)
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(*                                 Newman.v                                 *)
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(*          Projet Coq  - Calculus of Inductive Constructions V5.8           *)
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(*      Meta-theory of the explicit substitution calculus lambda-env         *)
(*      Amokrane Saibi                                                       *)
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(*      September 1993                                                       *)
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(* Theoreme de Newman *)
Section NewmanS.
Variable A : Set.
Variable R : A -> A -> Prop.
Hypothesis N : explicit_noetherian _ R.
Hypothesis C : explicit_local_confluence _ R.

Theorem Newman : explicit_confluence _ R.
unfold explicit_confluence in |- *; intro x; pattern x in |- *;
apply (noetherian_induction1 A R N).