6 R" i" w$ E3 @5 v7 _! K3 i" \Formal Sets . I/ I! I9 _/ m; qA formal set consists of the subset of elements of some carrier set (structure) on which a certain predicate assumes the value `true'. ! L+ Q# g8 b/ t/ u- Q, O( l7 D- s2 ]$ v* f2 J- p4 i
The only set-theoretic operations that can be performed on formal sets are union, intersection, difference and symmetric difference, and element membership testing. : n6 {: t+ {# A2 a( g
0 F9 ?$ g+ ^0 S
5 l2 ^2 o! E6 w0 H " R5 {' m0 a$ t* t1 hS := { 1 .. 5};6 ^$ ~, x+ v/ m, n3 Z0 ^; a, c2 Z1 l
> P := PowerSet(S);: ]$ K/ ?7 g% u0 c8 p
P; / v- z. F6 |6 K, n3 e4 W, VPFS:=PowerFormalSet(S);4 m" h1 g. I, a, P3 U3 Z# k
PFS; 9 t% |$ b) p( u5 eF := { 2, 4 }; ; V% H9 |* _; FFF := { 2/3, 4 };7 T7 k2 ?& d" I, q1 D5 N9 d
# \; Y6 m# f5 w: N6 q8 I F in P; " R1 x! e+ s; O/ ^( k$ }7 P$ X4 {FF in P;1 s9 s0 h7 {3 C
F in PFS; 6 x; I% ]- I4 ^8 o9 GFF in PFS;* a+ V! B( I+ x Q5 C2 e9 k4 i' S
Set of subsets of { 1 .. 5 } 6 q* v" L# z$ c: t7 r- m& sSet of formal subsets of { 1 .. 5 } 2 q9 }8 W3 M c, N4 rtrue - U7 k" s1 D; B" [& Efalse' U: M- F0 f2 b& E8 o
/ G; t9 K5 n( l2 D2 c: m! Z0 K>> F in PFS; 5 K G$ X, Z- D. j! {1 Z) W ^- u: ?* D$ a! A- y4 g0 |: z4 q( G
Runtime error in 'in': Bad argument types ) Y. D6 q W) ?% ?. C5 |* `* Q9 _/ ? }7 t) h
4 G9 `8 I( z% U, g>> FF in PFS;; I1 w9 Y0 b9 b: P: n
^ . `, B! M `7 P& n5 b' D2 WRuntime error in 'in': Bad argument types