g:IGroup, a, b, c:|g|. (a = b)  ((a * c) = (b * c)  |g|) 

latex

Up	groups 1
Definitions of Statement	IMonoid, IGroup
Definitions	, t  T, P  Q, P  Q, P & Q, x f y, P  Q, x:A. B(x), IMonoid, IGroup
Lemmas	igrp wf, grp op wf, grp car wf, grp op r, grp op cancel r