End MoreGroupAction.
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(* Helper lemmas for quotient actions.                                        *)
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Section MoreQuotientAction.
Variables (aT rT : finGroupType).
Variables (A : {group aT})(D : {group rT}).
Variable to : groupAction A D.

Lemma acts_qact_doms (H : {group rT}) :
H \subset D -> [acts A, on H | to] -> qact_dom to H :=: A.