Automatic redefining

[Hassediagram]

Dear members of python-forum,

I have another problem. I think it is linked to the one i had last year (above).

I want to define a def(S,T), where:
(i) S and T are two sets (lists in Python) and such that S is a subset of T.
(ii) def(S,T) gives the list of lists K such that S \subset K \subset T. (K is "between" S and T).

For example if S=[2] and T=[2,3,4], i want to get all the lists between [2] and [2,3,4], that is, L=[[2],[2,3],[2,4],[2,3,4]].

In the program below, i define subset(T,S) as being the elements in T which are not in S. In my example, setminus(T,S)=[3,4].


Notice that:
union(A,B) is the union of the lists A and B. (the union of sets).
interzz(A,B) is the intersection of lists A and B (the intersection of sets).
doublonsL removes the lists appearing several times in the list of lists.

The program works as follows: from the infimum S=[2] (for example) and the supremum T=[2,3,4], we compute the elements setminus(T,S) which are in T but not in S. We start from L=[[2]]. The elements 3 and 4 are in T but not in S. We take elements in L and we add lists with these elements setminus(T,S). For example:

[2]
[2],[2,3]
[2],[2,4],[2,3],[2,3,4].

My program, instead of giving what i want, gives Boolean([2],[2,3,4])=
[[2, 3, 4]]. That is, [2], [2,3] and [2,4] are missing.

I guess that my program is ugly but, actually, i just need something that works. Your suggestions would probably be helpful; thank you in advance.

def doublons(LM):# This def is OK.
    LP=[]
    for k in LM:
        if k not in LP:
            LP.append(k)
    return(LP)


def doublonsL(LM): # This def is OK.
    LP=[]
    for listtt in LM:
        if listtt not in LP:
            LP.append(listtt)
    return(LP)

def union(A,B):# This def is OK. 
    uni=A
    for k in B:
        uni.append(k)
    return doublons(sorted(uni))  


def interzz(lst1, lst2): # This def is OK.
    lst3 = [value for value in lst1 if value in lst2] 
    return doublons(sorted(lst3)) 


def setminus(S,T):# This def is OK. 
    for k in T:
        S.remove(k)
    return doublons(S)


def issubset(S,T):# This def is OK. 
    if interzz(S,T)==S:
        return "true"
    else:
        return "false"


def Boolean(SQ,TQ): # The problem comes from this def.
    if issubset(SQ,TQ)=="false": # We check that S is a subset of T.
        print("error subset")
    ZED=setminus(TQ,SQ) # All the elements of TQ which are not in SQ.
    LILI=[SQ]
    MOLI=LILI[:] 
    for k in ZED:
        for PPP in MOLI:
            LILI.append(union(PPP,[k]))
        LILI=MOLI[:]
        MOLI=LILI[:]
    for kj in range(0,len(LILI)):
        LILI[kj]=sorted(doublons(LILI[kj]))
    return doublonsL(LILI) 

Wishing you a nice week,
Hassediagram.