Section Cyclic.
Variable gT : finGroupType.
Implicit Types (a x y : gT) (A B : {set gT}) (G K H : {group gT}).
Definition cyclic A := [exists x, A == <[x]>].
Canonical Zpm_morphism := Morphism ZpmM.
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(*        Generator                                                    *)
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Definition generator (A : {set gT}) a := A == <[a]>.

Lemma generator_cycle a : generator <[a]> a.