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every

Run Example
(%i1)xprimep(x) :=  (x <
 32);
(%o1)                        xprimep(x) := x < 32
(%i2) d: subset (integer_partitions (12,3), lambda ([x], every (xprimep, x)));
(%o2) {[4, 4, 4], [5, 4, 3], [5, 5, 2], [6, 3, 3], [6, 4, 2], [6, 5, 1], 
[6, 6, 0], [7, 3, 2], [7, 4, 1], [7, 5, 0], [8, 2, 2], [8, 3, 1], [8, 4, 0], 
[9, 2, 1], [9, 3, 0], [10, 1, 1], [10, 2, 0], [11, 1, 0], [12, 0, 0]}
(%i3) cardinality (d);
(%o3)                                 19
(%i4) s: integer_partitions (12,3);
(%o4) {[4, 4, 4], [5, 4, 3], [5, 5, 2], [6, 3, 3], [6, 4, 2], [6, 5, 1], 
[6, 6, 0], [7, 3, 2], [7, 4, 1], [7, 5, 0], [8, 2, 2], [8, 3, 1], [8, 4, 0], 
[9, 2, 1], [9, 3, 0], [10, 1, 1], [10, 2, 0], [11, 1, 0], [12, 0, 0]}
(%i5) cardinality(s);
(%o5)                                 19
(%i6) 
Run Example
xprimep(x) :=  (x <
 32);
(%o1)                        xprimep(x) := x < 32
(%i2) d: subset (integer_partitions (10,3), lambda ([x], every (xprimep, x)));
(%o2) {[4, 3, 3], [4, 4, 2], [5, 3, 2], [5, 4, 1], [5, 5, 0], [6, 2, 2], 
[6, 3, 1], [6, 4, 0], [7, 2, 1], [7, 3, 0], [8, 1, 1], [8, 2, 0], [9, 1, 0], 
[10, 0, 0]}
(%i3) cardinality (d);
(%o3)                                 14
(%i4) s: integer_partitions (10,3);
(%o4) {[4, 3, 3], [4, 4, 2], [5, 3, 2], [5, 4, 1], [5, 5, 0], [6, 2, 2], 
[6, 3, 1], [6, 4, 0], [7, 2, 1], [7, 3, 0], [8, 1, 1], [8, 2, 0], [9, 1, 0], 
[10, 0, 0]}
(%i5) cardinality(s);
(%o5)                                 14
(%i6) m: subset (integer_partitions (10,3), lambda ([x], every ("=", [x],[y])));
(%o6)                                 {}
(%i7) cardinality (m);
(%o7)                                  0
(%i8) 
Run Example
xprimep(x) :=  (x <
 32);
(%o1)                        xprimep(x) := x < 32
(%i2) d: subset (integer_partitions (8,3), lambda ([x], every (xprimep, x)));
(%o2) {[3, 3, 2], [4, 2, 2], [4, 3, 1], [4, 4, 0], [5, 2, 1], [5, 3, 0], 
                                    [6, 1, 1], [6, 2, 0], [7, 1, 0], [8, 0, 0]}
(%i3) cardinality (d);
(%o3)                                 10
(%i4) s: integer_partitions (8,3);
(%o4) {[3, 3, 2], [4, 2, 2], [4, 3, 1], [4, 4, 0], [5, 2, 1], [5, 3, 0], 
                                    [6, 1, 1], [6, 2, 0], [7, 1, 0], [8, 0, 0]}
(%i5) cardinality(s);
(%o5)                                 10
(%i6) 

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