Description: Define indexed union. Definition indexed union in Stoll p. 45. In
most applications, A is independent of x (although this is not
required by the definition), and B depends on x i.e. can be read
informally as B ( x ) . We call x the index, A the index
set, and B the indexed set. In most books, x e. A is written as
a subscript or underneath a union symbol U. . We use a special
union symbol U_ to make it easier to distinguish from plain class
union. In many theorems, you will see that x and A are in the
same distinct variable group (meaning A cannot depend on x ) and
that B and x do not share a distinct variable group (meaning
that can be thought of as B ( x ) i.e. can be substituted with a
class expression containing x ). An alternate definition tying
indexed union to ordinary union is dfiun2 . Theorem uniiun provides
a definition of ordinary union in terms of indexed union. Theorems
fniunfv and funiunfv are useful when B is a function.
(Contributed by NM, 27-Jun-1998)