Section FieldMulCyclic.
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(* A classic application to finite multiplicative subgroups of fields. *)
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Variables (gT : finGroupType) (G : {group gT}).

Lemma field_mul_group_cyclic (F : fieldType) (f : gT -> F) :
{in G &, {morph f : u v / u * v >-> (u * v)%R}} ->
{in G, forall x, f x = 1%R <-> x = 1} ->
cyclic G.