(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
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(*                           Group Theory in Coq                            *)
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(*                                Coq V5.10                                 *)
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(*			         Gilles Kahn 				    *)
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(*                                  INRIA                                   *)
(*                             Sophia-Antipolis                             *)
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(*				 January 1996				    *)
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Theorem auxsub :
forall (H : Group U) (x : U), subgroup U H Gr -> In U (G_ U H) x -> In U G x.