REMOVE1.html -- ACL2 Version 6.3

### REMOVE1

remove first occurrences, testing using `eql`

    Major Section:  ACL2-BUILT-INS

    General Forms:
    (remove1 x lst)
    (remove1 x lst :test 'eql)   ; same as above (eql as equality test)
    (remove1 x lst :test 'eq)    ; same, but eq is equality test
    (remove1 x lst :test 'equal) ; same, but equal is equality test

`(Remove1 x lst)` is equal to `lst` if `x` is not a member of `lst`, else is the result of removing the first occurrences of `x` from `lst`. The optional keyword, `:TEST`, has no effect logically, but provides the test (default `eql`) used for comparing `x` with successive elements of `lst`.

Also see remove.

The guard for a call of `remove1` depends on the test. In all cases, the second argument must satisfy `true-listp`. If the test is `eql`, then either the first argument must be suitable for `eql` (see eqlablep) or the second argument must satisfy `eqlable-listp`. If the test is `eq`, then either the first argument must be a symbol or the second argument must satisfy `symbol-listp`.

See equality-variants for a discussion of the relation between `remove1` and its variants:

> `(remove1-eq x lst)` is equivalent to `(remove1 x lst :test 'eq)`;

> `(remove1-equal x lst)` is equivalent to `(remove1 x lst :test 'equal)`.

In particular, reasoning about any of these primitives reduces to reasoning about the function `remove1-equal`.