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Run Example
(%i1)xprimep(x) := integerp(x) and (x <
 32);
(%o1)               xprimep(x) := integerp(x) and (x < 32)
(%i2) cardinality (subset (integer_partitions(30,3), lambda ([x], every (xprimep, x))));
(%o2)                                 91
(%i3) 
Run Example
xprimep(x) := integerp(x) and (x <
 41);
(%o1)               xprimep(x) := integerp(x) and (x < 41)
(%i2) cardinality (subset (integer_partitions(55,5), lambda ([x], every (xprimep, x))));
(%o2)                                5019
(%i3) 
Run Example
xprimep(x) := integerp(x) and (x <
 32);
(%o1)               xprimep(x) := integerp(x) and (x < 32)
(%i2) k: subset (integer_partitions (19, 3), lambda ([x], every (xprimep, x)));
(%o2) {[7, 6, 6], [7, 7, 5], [8, 6, 5], [8, 7, 4], [8, 8, 3], [9, 5, 5], 
[9, 6, 4], [9, 7, 3], [9, 8, 2], [9, 9, 1], [10, 5, 4], [10, 6, 3], 
[10, 7, 2], [10, 8, 1], [10, 9, 0], [11, 4, 4], [11, 5, 3], [11, 6, 2], 
[11, 7, 1], [11, 8, 0], [12, 4, 3], [12, 5, 2], [12, 6, 1], [12, 7, 0], 
[13, 3, 3], [13, 4, 2], [13, 5, 1], [13, 6, 0], [14, 3, 2], [14, 4, 1], 
[14, 5, 0], [15, 2, 2], [15, 3, 1], [15, 4, 0], [16, 2, 1], [16, 3, 0], 
[17, 1, 1], [17, 2, 0], [18, 1, 0], [19, 0, 0]}
(%i3) cardinality (k);
(%o3)                                 40
(%i4) 
[and,apply,cardinality,every,integer_partitions,integerp,lambda,map,subset] [and,cardinality,every,integer_partitions,integerp,lambda,primep,subset] [and,cardinality,every,integer_partitions,integerp,lambda,subset] [and,every,integer_partitions,integerp,lambda,subset] [append,disjoin,first,if,lambda,listify,makelist,map,mod,setify,subset] [atom,evenp,subset] [atom,lambda,subset] [atom,subset] [cardinality,every,integer_partitions,lambda,primep,subset] [cardinality,every,integer_partitions,lambda,subset] [cartesian_product,intersect,is,lambda,mod,product,setdifference,subset,union] [cartesian_product,is,lambda,product,subset] [cartesian_product,lambda,makelist,print,product,setify,subset] [cartesian_product,lambda,makelist,product,setify,subset] [cartesian_product,lambda,mod,print,product,subset,union] [cartesian_product,lambda,mod,product,subset] [concat,first,if,lambda,makelist,map,mod,setify,subset] [disjoin,first,if,lambda,listify,makelist,map,mod,setify,subset] [disjoin,first,if,lambda,makelist,map,mod,setify,subset] [do,evenp,first,if,lambda,makelist,map,return,setify,subset] [do,evenp,first,if,lambda,makelist,map,setify,subset] [do,evenp,first,lambda,makelist,map,print,setify,subset] [do,evenp,first,lambda,makelist,map,return,setify,subset] [evenp,first,if,lambda,makelist,map,rest,setify,subset] [evenp,first,if,lambda,makelist,map,setify,subset] [evenp,first,lambda,makelist,map,setify,subset] [evenp,if,lambda,makelist,map,setify,subset] [evenp,lambda,makelist,map,setify,subset] [evenp,subset] [first,gcd,if,lambda,makelist,map,setify,subset] [first,if,lambda,makelist,map,mod,return,setify,subset] [first,if,lambda,makelist,map,mod,setify,subset] [first,if,lambda,makelist,map,setify,subset] [intersect,lambda,setdifference,sublist,subset,union] [is,lambda,subset] [lambda,sublist,subset] [subset]

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