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diff --git a/tests/test-local-repository--car-member.el b/tests/test-local-repository--car-member.el
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+;;; test-local-repository--car-member.el --- Tests for car-member -*- lexical-binding: t -*-
+
+;;; Commentary:
+;; Tests for `car-member' in local-repository.el — the predicate
+;; localrepo-initialize uses to check whether an archive id is already
+;; registered in package-archives / package-archive-priorities.
+
+;;; Code:
+
+(require 'ert)
+(require 'local-repository)
+
+;;; Normal Cases
+
+(ert-deftest test-local-repository-car-member-found ()
+  "Normal: VALUE present as a car returns the matching tail (non-nil)."
+  (should (equal (car-member 'b '((a . 1) (b . 2) (c . 3)))
+                 '(b c))))
+
+(ert-deftest test-local-repository-car-member-not-found ()
+  "Normal: VALUE absent from every car returns nil."
+  (should-not (car-member 'z '((a . 1) (b . 2)))))
+
+(ert-deftest test-local-repository-car-member-string-car ()
+  "Normal: car comparison uses `equal', so string keys match by value."
+  (should (car-member "localrepo"
+                      '(("gnu" . "url1") ("localrepo" . "url2")))))
+
+;;; Boundary Cases
+
+(ert-deftest test-local-repository-car-member-empty-list ()
+  "Boundary: an empty list never matches."
+  (should-not (car-member 'a nil)))
+
+(ert-deftest test-local-repository-car-member-single-match ()
+  "Boundary: a single-element list whose car matches returns non-nil."
+  (should (car-member 'only '((only . 1)))))
+
+(ert-deftest test-local-repository-car-member-single-no-match ()
+  "Boundary: a single-element list whose car differs returns nil."
+  (should-not (car-member 'x '((only . 1)))))
+
+(ert-deftest test-local-repository-car-member-nil-value-with-nil-car ()
+  "Boundary: a nil VALUE matches a cons whose car is nil."
+  (should (car-member nil '((nil . 1) (a . 2)))))
+
+(ert-deftest test-local-repository-car-member-nil-value-no-nil-car ()
+  "Boundary: a nil VALUE with no nil car returns nil."
+  (should-not (car-member nil '((a . 1) (b . 2)))))
+
+;;; Error Cases
+
+(ert-deftest test-local-repository-car-member-non-cons-element ()
+  "Error: a non-cons element makes `car' signal wrong-type-argument."
+  (should-error (car-member 'x '(1 2)) :type 'wrong-type-argument))
+
+(provide 'test-local-repository--car-member)
+;;; test-local-repository--car-member.el ends here