Use Alloy to model a simple library

Question

In "fact F4_All_wanted_books_are_had_by_someone", I am trying to make all wanted books are on loan to some patron. Which is if a patron wants a book, it must be on load (otherwise it could be loaned to the patron that wants it). In "fact F7_Cannot_want_what_you_have", is a patron cannot want a book he or she already has. But when I tried to execute the code. it shows that there is no instance found, however, it supposed have instance found.

Before I add "fact F4" the instance still can found, but after I added F4, the instance cannot be found any more. Is there are anything wrong in "fact F4"? and how can I fix it. thanks for your help.

/**
 * The books in a library.
 */
some sig Book{}

/**
 * Patrons of the library, in general, have some books (on loan)
 * and want some other books.
 */
some sig Patron {
    has     : set Book,
    wants   : set Book
}

/**
 * The library has some books on reserve, some on the shelves,
 * and some on hold because patrons want them (are waiting for
 * them).
 *
 * Note: The books on loan are exactly those all the Patrons as
 *              a group "have".
 */
one sig Library {
    onReserve : set Book,
    onShelves   : set Book
}

/**
 *  All wanted books are on loan to some patron (that is,
 *  some patron has the wanted book). Note that a patron
 *  *MAY* have a book out that nobody else wants.
 */
fact F4_All_wanted_books_are_had_by_someone {
    all b : Patron | b.wants in b.has
}

/**
 *  Two different patrons cannot have the same book.
 */
fact F5_No_loan_conflicts {
    all disj b1, b2 : Patron | no (b1.has & b2.has)
}

/**
 *  A patron cannot want a book he or she already has.
 */
fact F7_Cannot_want_what_you_have {
    all b : Patron | no (b.wants & b.has)
}

run{
    some onReserve
    some onShelves - onReserve
    some wants
    some has
    some Patron.has - Patron.wants
    some Patron.has & Patron.wants
    some has.Book & wants.Book
} for exactly 3 Patron, exactly 8 Book

Answer 1

The meaning of your F4 is "for all patrons every book he wants is among those he has". I suggest

fact F4 {
    all p:Patron | p.wants in (Patron - p).has
}