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(* 02110-1301 USA                                                     *)
(** %\subsection*{ support :  algebra\_omissions.v }%*)
(** - In this file I prove some results that do not pertain to linear algebra at all. Instead, they could have been proven solely for the algebra distribution. This is also why I do not use the syntactic sugar as defined in equal_syntax.v and more_syntax.v *)
From Algebra Require Export Group_facts.
Set Implicit Arguments.
Unset Strict Implicit.

Lemma group_inverse_inj :
forall (G : GROUP) (g g' : G),
Equal (group_inverse _ g) (group_inverse _ g') -> Equal g g'.