?- consult('count.pro').
% count.pro compiled 0.00 sec, 0 bytes

Yes
?- count(4,[4,3,4,5,6],C).

C = 2

Yes
?- count(3,[4,3,4,5,6],C).

C = 1

Yes
?- count(5,[4,3,4,5,6,5,5,5,5],C).

C = 5

Yes
?- singleton_count([5,6,7,8,9,1,1],C).

C = 5

Yes
?- singleton_count([5,6,9,9,9,1,1],C).

C = 2

Yes
?- singleton_count([5,9,9,9,9,1,1],C).

C = 1

Yes
?- doubleton_count([5,9,9,3,1,1],C).

C = 2

Yes
?- doubleton_count([5,9,4,3,1,1],C).

C = 1

Yes
?- doubleton_count([5,5,4,4,1,1],C).

C = 3