Learn English – How to describe two different objects

"Proximity" usually is not quantified in the way your example requires. Saying "This reduces the proximity of A and B to zero" means that A and B become less close to an origin, zero; for example, one might become quite negative, the other quite positive; or both could become quite large while steadily growing closer together. (This is true, for example, of x and x+1/x as x goes to infinity.) In short, reduction of proximity of A and B to the origin need not dictate whether A and B get closer together.

The construction "reduces the distance to zero" also has the problem of being unclear about whether it refers to distance between two points rather than distances between two points and an origin. For clarity, say "The distance between A and B reduces to zero" or "A and B approach and then coincide", or become equal, etc.

We would not use coincide unless we were talking of significant events/situations/days that happen, unusually, to occur on the same day, as in " In 20XX, Chinese New Year coincides with western New Year. If there is nothing significant about the dates, we'd just say something like "The 24th of Shawwal is the 12th of October in the Gregorian/Western calendar"..