什麽是形式集合Formal Sets/PowerFormalSet？

lilianjie

哪位能给理解下：
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Formal Sets
A formal set consists of the subset of elements of some carrier set (structure) on which a certain predicate assumes the value `true'.

2 M& Y+ Q! {  s7 k, n5 Z( gThe only set-theoretic operations that can be performed on formal sets are union, intersection, difference and symmetric difference, and element membership testing.
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4 A7 P4 D) P5 Y$ q3 a" `3 {( s: OS := { 1 .. 5};
+ ]/ a: h% a: G5 i> P := PowerSet(S);
P;
3 a4 n% Q. z; K7 q' u9 a; K. C# bPFS:=PowerFormalSet(S);
5 \$ x6 ], h& _. E6 YPFS;
F := { 2, 4 };
2 w' A! b& d& l( P# WFF := { 2/3, 4 };

F in P;
FF in P;
F in PFS;
FF in PFS;
Set of subsets of { 1 .. 5 }
- n8 g9 M( Y; i4 F: j" O5 k5 j& ZSet of formal subsets of { 1 .. 5 }
" O( \0 X' }. c6 H. L+ S" R4 htrue
' }8 h! I* r8 d0 D/ xfalse

9 Z/ c# n/ i6 \8 [" H7 F>>  F in PFS;
      ^
4 c  Z( {( K# e" B5 r3 SRuntime error in 'in': Bad argument types

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; @) e3 p% |2 _" p7 o) V& y>> FF in PFS;
1 D. ]9 Z# J1 J, x      ^
7 H% s0 w) T- {Runtime error in 'in': Bad argument types