make the code that does the mixin checks work with define-local-member-name

closes PR 11279
closes PR 12397

collects/racket/private/class-internal.rkt

@@ -5014,9 +5014,11 @@ An example
     [(_ (from ...) (to ...) clauses ...)
      (let ([extract-renamed-names
             (λ (x)
-              (map (λ (x) (syntax-case x ()
-                            [(internal-name external-name) (syntax external-name)]
-                            [else x]))
+              (map (λ (x) 
+                     (localize
+                      (syntax-case x ()
+                        [(internal-name external-name) (syntax external-name)]
+                        [else x])))
                    (syntax->list x)))])
        (define (get-super-names stx)
          (syntax-case stx (inherit rename 
@@ -5077,7 +5079,7 @@ An example
                  (let ([to-ids to] ...)
                    (check-mixin-from-interfaces (list from-ids ...))
                    (check-mixin-to-interfaces (list to-ids ...))
-                   (check-interface-includes (list (quote super-vars) ...)
+                   (check-interface-includes (list (quasiquote super-vars) ...)
                                              (list from-ids ...))
                    mixin-expr)))))))]))
 

collects/tests/racket/object.rktl

@@ -1675,4 +1675,25 @@
 
 ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
 
+;; ----------------------------------------
+;; Mixins
+
+(let ()
+  (define-local-member-name m)
+  (define i<%> (interface () m n))
+  (define mix
+    (mixin (i<%>) ()
+      (inherit m n)
+      (super-new)
+      (define/public (x) (+ (m) (n)))))
+  (define c%
+    (class* object% (i<%>)
+      (define/public (m) 1)
+      (define/public (n) 2)
+      (super-new)))
+  (test 3 'mixin-with-local-member-names (send (new (mix c%)) x)))
+  
+
+
 (report-errs)
+