(a) A motion to postpone a trial on account of the absence of evidence shall, if required by the opposite party, be made only upon affidavit showing the materiality of the evidence expected to be obtained and that due diligence has been used to obtain it. If the motion is for an absent witness, the affidavit must show what facts the affiant believes the witness will prove and not merely show the effect of the facts in evidence, that the affiant believes them to be true, and that the witness is not absent by the consent, connivance, or procurement of the party asking the postponement.
(b) If thereupon the adverse party will admit that on trial the absent witness, if present, would testify to the statement contained in the application for a continuance, then the trial shall not be postponed for that cause. However, the opposite party may controvert the statement so set forth in the motion for continuance by evidence.