Image and preïmage

The image map of a bijection is a bijection

Given a bijection , the image map is also a bijection. #m/thm/general Moreover:

Proof

Let be a bijection between arbitrary sets, It follows that for a given subset

thus . Likewise, for a given subset

thus . Therefore , hence is a bijection with inverse .

#state/tidy | #lang/en | #SemBr