Define predicate in prolog - list

Question

I'm struggling with this one:
Define predicate len_NM(L,N,M) which checks if a certain list of lists L contains at least N elements with length no less than M.

Answer 1

The OP stated:
Define predicate len_NM(L,N,M) which checks if a certain list of lists L contains at least N elements with length no less than M.
In this answer we do not solve the original problem, but the following variation:
Define predicate len_NM(L,N,M) which checks if a certain list of lists L contains exactly N elements with length no less than M.
Similarly to this answer, we define dcg seqq1//1 to establish the relationship between a list of non-empty lists and its flattened opposite:
seq([]) --> [].
seq([E|Es]) --> [E], seq(Es).
seqq1([]) --> [].
seqq1([Es|Ess]) --> {Es=[_|_]}, seq(Es), seqq1(Ess).
Sample use:
?- phrase(seqq1([[1,2],[3],[4]]),Xs).
Xs = [1,2,3,4].
Note that seqq1//1 works in "both directions":
?- phrase(seqq1(Xss),[1,2,3,4]).
Xss = [[1],[2],[3],[4]]
; Xss = [[1],[2],[3,4]]
; Xss = [[1],[2,3],[4]]
; Xss = [[1],[2,3,4]]
; Xss = [[1,2],[3],[4]]
; Xss = [[1,2],[3,4]]
; Xss = [[1,2,3],[4]]
; Xss = [[1,2,3,4]]
; false.
In this answer we use clpfd:
:- use_module(library(clpfd)).
Then, we define len_NM/4—using maplist/3,
length/2, tcount/3, and (#=<)/3:
len_NM(Xss,Ys,N,M) :-
M #>= 1,
N #>= 0,
phrase(seqq1(Xss),Ys),
maplist(length,Xss,Ls),
tcount(#=<(M),Ls,N).
Let's run some sample queries!
?- len_NM([[1,2,3],[4],[5,6],[7,8,9,10],[11,12]],_,N,L).
N = 5, L = 1 % five lists have length of at least one
; N = 4, L = 2 % four lists have length of at least two
; N = 2, L = 3 % two of at least three (e.g., [1,2,3] and [7,8,9,10])
; N = 1, L = 4 % one list has length of four (or more)
; N = 0, L in 5..sup. % no list has length of five (or more)
OK! How about this one?
?- append(Xs,_,[x,x,x,x,x,x]), % With `Xs` having at most 6 elements ...
N #>= 1, % ... `Xss` shall contain at least 1 list ...
len_NM(Xss,Xs,N,4). % ... having a length of 4 (or more).
Xs = [x,x,x,x], N = 1, Xss = [[x,x,x,x]]
; Xs = [x,x,x,x,x], N = 1, Xss = [[x],[x,x,x,x]]
; Xs = [x,x,x,x,x], N = 1, Xss = [[x,x,x,x],[x]]
; Xs = [x,x,x,x,x], N = 1, Xss = [[x,x,x,x,x]]
; Xs = [x,x,x,x,x,x], N = 1, Xss = [[x],[x],[x,x,x,x]]
; Xs = [x,x,x,x,x,x], N = 1, Xss = [[x],[x,x,x,x],[x]]
; Xs = [x,x,x,x,x,x], N = 1, Xss = [[x],[x,x,x,x,x]]
; Xs = [x,x,x,x,x,x], N = 1, Xss = [[x,x],[x,x,x,x]]
; Xs = [x,x,x,x,x,x], N = 1, Xss = [[x,x,x,x],[x],[x]]
; Xs = [x,x,x,x,x,x], N = 1, Xss = [[x,x,x,x],[x,x]]
; Xs = [x,x,x,x,x,x], N = 1, Xss = [[x,x,x,x,x],[x]]
; Xs = [x,x,x,x,x,x], N = 1, Xss = [[x,x,x,x,x,x]]
; false.