Page "Euclidean domain" Paragraph 17

The property ( EF1 ) can be restated as follows: for any principal ideal I of R with nonzero generator b, all nonzero classes of the quotient ring R / I have a representative r with.

Since the possible values of f are well-ordered, this property can be established by proving for any r ( not in I ) with minimal value of f ( r ) in its class.

Note that for a Euclidean function that is so established there need not exist an effective method to determine q and r in ( EF1 ).