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Showing content from http://www.lispworks.com/documentation/HyperSpec/Body/17_bb.htm below:

CLHS: Section 17.2.2

CLHS: Section 17.2.2 17.2.2 Satisfying a One-Argument Test

When using one of the functions in the next figure, the elements E of a sequence S are filtered not on the basis of the presence or absence of an object O under a two argument predicate, as with the functions described in Section 17.2.1 (Satisfying a Two-Argument Test), but rather on the basis of a one argument predicate.

assoc-if       member-if           rassoc-if          
assoc-if-not   member-if-not       rassoc-if-not      
count-if       nsubst-if           remove-if          
count-if-not   nsubst-if-not       remove-if-not      
delete-if      nsubstitute-if      subst-if           
delete-if-not  nsubstitute-if-not  subst-if-not       
find-if        position-if         substitute-if      
find-if-not    position-if-not     substitute-if-not  

Figure 17-3. Operators that have One-Argument Tests to be Satisfied

The element Ei might not be considered directly. If a :key argument is provided, it is a designator for a function of one argument to be called with each Ei as an argument, and yielding an object Zi to be used for comparison. (If there is no :key argument, Zi is Ei.)

Functions defined in this specification and having a name that ends in ``-if'' accept a first argument that is a designator for a function of one argument, Zi. An Ei is said to satisfy the test if this :test function returns a generalized boolean representing true.

Functions defined in this specification and having a name that ends in ``-if-not'' accept a first argument that is a designator for a function of one argument, Zi. An Ei is said to satisfy the test if this :test function returns a generalized boolean representing false.

17.2.2.1 Examples of Satisfying a One-Argument Test
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