During the time allowed for taking an appeal from judgment of a court of record or during the pendency of such appeal, that court may, on motion, allow testimony to be perpetuated for use in the event of further proceedings before it. The motion shall state the name and address of each proposed deponent, the substance of the deponent’s expected testimony, and the reason for perpetuating it. If the court finds such perpetuation is proper to avoid a failure or delay of justice, and the depositions are not sought for discovery, it may order them taken as in rules 1.725 and 1.726. When taken and filed as thus provided, they shall be used and treated as though they had been taken pending the trial of the action.

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