Property redeclaration error when widened in multiple extensions

prop.m

// clang -c -o /dev/null prop.m

#import <Foundation/NSObject.h>

@interface Obj : NSObject /*Public*/
@end

@interface Obj ( /*Internal*/ )
@property (readonly, retain, nonatomic) NSObject *prop;
@end

@interface Obj ( /*Private*/ )
@property (readwrite, retain, nonatomic) NSObject *prop;
@end

@implementation Obj
@synthesize prop;
@end