The Decisions on the Rules of Golf have several senerios that cover this situation. The rule is that the provisional ball becomes the ball in play when it is played from a spot closer to the hole that the original ball is believed to be. You do not have to look for your original ball. You could have walked up to your provisional ball and played a stroke with it and then your original ball would be deemed lost even if your opponent found it after that. Now if you had holed your provisional ball you would need to actually retrieve it from the hole before your opponent finds your original ball. Now by playing your provisional ball quickly you may be playing out of turn and your opponent could recall your stroke and ask you to replay the shot. But hey you did it once you can do it again.

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