Section fconnect.

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(* Lemma orbitPcycle is of type "The Following Are Equivalent", which means  *)
(* all four statements are equivalent to each other. In order to use it, one *)
(* has to apply it to the natural numbers corresponding to the line, e.g.    *)
(* `orbitPcycle 0 2 : fcycle f (orbit x) <-> exists k, iter k.+1 f x = x`.   *)
(* examples of this are in order_id_cycle and fconnnect_f.                   *)
(* One may also use lemma all_iffLR to get a one sided implication, as in    *)
(* orderPcycle.                                                              *)
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Lemma orbitPcycle {x} : [<->