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(*  Reflected boolean property and morphic image, injection, bijection *)
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Section MorphicImage.
Variables aT rT : finGroupType.
Variables (D : {group aT}) (f : {morphism D >-> rT}) (x : aT).
Hypothesis Dx : x \in D.

Lemma eq_subG_cyclic G H K :
cyclic G -> H \subset G -> K \subset G -> (H :==: K) = (#|H| == #|K|).