\begin{theindex}

  \item {\ptt ABSORPTION}, 29
  \item axiom of extension, 3
  \item axioms for {\ptt (*)set}, 2--3

  \indexspace

  \item {\ptt BIJ\_COMPOSE}, 37
  \item {\ptt BIJ\_DEF}, 14, 37
  \item {\ptt BIJ\_EMPTY}, 37
  \item {\ptt BIJ\_ID}, 37

  \indexspace

  \item {\ptt CARD\_DEF}, 16, 38
  \item {\ptt CARD\_DELETE}, 39
  \item {\ptt CARD\_DIFF}, 39
  \item {\ptt CARD\_EMPTY}, 39
  \item {\ptt CARD\_EQ\_0}, 39
  \item {\ptt CARD\_INSERT}, 39
  \item {\ptt CARD\_INTER\_LESS\_EQ}, 39
  \item {\ptt CARD\_PSUBSET}, 39
  \item {\ptt CARD\_SING}, 16, 39
  \item {\ptt CARD\_SUBSET}, 39
  \item {\ptt CARD\_UNION}, 39
  \item {\ptt CHOICE\_DEF}, 12, 35
  \item {\ptt CHOICE\_INSERT\_REST}, 35
  \item {\ptt CHOICE\_NOT\_IN\_REST}, 35
  \item {\ptt CHOICE\_SING}, 35
  \item {\ptt COMPONENT}, 30
  \item conversions
    \subitem {\ptt DELETE\_CONV}, 11
    \subitem {\ptt FINITE\_CONV}, 15
    \subitem {\ptt IMAGE\_CONV}, 13
    \subitem {\ptt IN\_CONV}, 7--8
    \subitem {\ptt INSERT\_CONV}, 10
    \subitem {\ptt UNION\_CONV}, 9--10

  \indexspace

  \item {\ptt DECOMPOSITION}, 30
  \item {\ptt define\_finite\_set\_syntax}, 4
  \item definition
    \subitem of {\ptt (*)set}, 1--2
    \subitem of {\ptt BIJ}, 14
    \subitem of {\ptt CARD}, 16
    \subitem of {\ptt CHOICE}, 12
    \subitem of {\ptt DELETE}, 7
    \subitem of {\ptt DIFF}, 6
    \subitem of {\ptt DISJOINT}, 6
    \subitem of {\ptt EMPTY}, 2
    \subitem of {\ptt FINITE}, 15
    \subitem of {\ptt IMAGE}, 12
    \subitem of {\ptt IN}, 2
    \subitem of {\ptt INFINITE}, 15
    \subitem of {\ptt INJ}, 14
    \subitem of {\ptt INSERT}, 2, 7
    \subitem of {\ptt INTER}, 6
    \subitem of {\ptt IS\_SET\_REP}, 2
    \subitem of {\ptt LINV}, 14
    \subitem of {\ptt PSUBSET}, 5
    \subitem of {\ptt REST}, 12
    \subitem of {\ptt RINV}, 14
    \subitem of {\ptt SING}, 11
    \subitem of {\ptt SUBSET}, 5
    \subitem of {\ptt SURJ}, 14
    \subitem of {\ptt UNION}, 6
  \item {\ptt DELETE\_COMM}, 33
  \item {\ptt DELETE\_CONV}, 11, 19
  \item {\ptt DELETE\_DEF}, 7, 34
  \item {\ptt DELETE\_DELETE}, 34
  \item {\ptt DELETE\_EQ\_SING}, 38
  \item {\ptt DELETE\_INSERT}, 34
  \item {\ptt DELETE\_INTER}, 32
  \item {\ptt DELETE\_NON\_ELEMENT}, 34
  \item {\ptt DELETE\_SUBSET}, 34
  \item {\ptt DIFF\_DEF}, 6
  \item {\ptt DIFF\_DIFF}, 33
  \item {\ptt DIFF\_EMPTY}, 33
  \item {\ptt DIFF\_EQ\_EMPTY}, 33
  \item {\ptt DIFF\_INSERT}, 34
  \item {\ptt DISJOINT\_DEF}, 6, 34
  \item {\ptt DISJOINT\_DELETE\_SYM}, 35
  \item {\ptt DISJOINT\_EMPTY}, 35
  \item {\ptt DISJOINT\_EMPTY\_REFL}, 35
  \item {\ptt DISJOINT\_INSERT}, 35
  \item {\ptt DISJOINT\_SING\_EMPTY}, 38
  \item {\ptt DISJOINT\_SYM}, 35
  \item {\ptt DISJOINT\_UNION}, 35

  \indexspace

  \item {\ptt EMPTY\_DELETE}, 34
  \item {\ptt EMPTY\_DIFF}, 33
  \item {\ptt EMPTY\_SUBSET}, 5, 31
  \item {\ptt EMPTY\_UNION}, 32
  \item {\ptt EQUAL\_SING}, 38
  \item {\ptt EXTENSION}, 3, 30

  \indexspace

  \item {\ptt FINITE\_CONV}, 15
  \item {\ptt FINITE\_DEF}, 15
  \item {\ptt FINITE\_EMPTY}, 15
  \item {\ptt FINITE\_INSERT}, 15
  \item {\ptt FINITE\_ISO\_NUM}, 16
  \item {\ptt FINITE\_SET\_DEF}, 2, 29

  \indexspace

  \item {\ptt IMAGE\_11\_INFINITE}, 15
  \item {\ptt IMAGE\_COMPOSE}, 36
  \item {\ptt IMAGE\_CONV}, 13, 20
  \item {\ptt IMAGE\_DEF}, 12
  \item {\ptt IMAGE\_DELETE}, 36
  \item {\ptt IMAGE\_EMPTY}, 36
  \item {\ptt IMAGE\_EQ\_EMPTY}, 36
  \item {\ptt IMAGE\_ID}, 36
  \item {\ptt IMAGE\_IN}, 36
  \item {\ptt IMAGE\_INSERT}, 36
  \item {\ptt IMAGE\_INTER}, 36
  \item {\ptt IMAGE\_SUBSET}, 36
  \item {\ptt IMAGE\_SURJ}, 37
  \item {\ptt IMAGE\_UNION}, 36
  \item {\ptt IN\_CONV}, 7--8, 24
  \item {\ptt IN\_DELETE}, 7, 34
  \item {\ptt IN\_DELETE\_EQ}, 34
  \item {\ptt IN\_DIFF}, 6, 33
  \item {\ptt IN\_DISJOINT}, 35
  \item {\ptt IN\_IMAGE}, 12, 36
  \item {\ptt IN\_INSERT}, 3, 7, 30
  \item {\ptt IN\_INTER}, 6, 32
  \item {\ptt IN\_SING}, 38
  \item {\ptt IN\_UNION}, 6, 32
  \item induction, 3--4
  \item {\ptt INFINITE\_DEF}, 15
  \item {\ptt INJ\_COMPOSE}, 37
  \item {\ptt INJ\_DEF}, 14, 37
  \item {\ptt INJ\_EMPTY}, 37
  \item {\ptt INJ\_ID}, 37
  \item {\ptt INSERT\_COMM}, 3, 30
  \item {\ptt INSERT\_CONV}, 10, 22
  \item {\ptt INSERT\_DEF}, 7
  \item {\ptt INSERT\_DELETE}, 34
  \item {\ptt INSERT\_INSERT}, 3, 30
  \item {\ptt INSERT\_INTER}, 32
  \item {\ptt INSERT\_SING\_UNION}, 38
  \item {\ptt INSERT\_SUBSET}, 31
  \item {\ptt INSERT\_UNION}, 32
  \item {\ptt INSERT\_UNION\_EQ}, 32
  \item {\ptt INTER\_ASSOC}, 32
  \item {\ptt INTER\_COMM}, 32
  \item {\ptt INTER\_DEF}, 6
  \item {\ptt INTER\_EMPTY}, 32
  \item {\ptt INTER\_IDEMPOT}, 32
  \item {\ptt INTER\_OVER\_UNION}, 32
  \item {\ptt INTER\_SUBSET}, 32
  \item {\ptt IS\_SET\_REP}, 2, 29

  \indexspace

  \item {\ptt LESS\_CARD\_DIFF}, 39
  \item {\ptt LINV\_DEF}, 14, 37
  \item {\ptt load\_finite\_sets}, 18

  \indexspace

  \item {\ptt MEMBER\_NOT\_EMPTY}, 30

  \indexspace

  \item naming conventions
    \subitem for definitions, 2
    \subitem for membership conditions, 6
    \subitem for theorems about singletons, 11
    \subitem for theorems generally, 6
  \item {\ptt NOT\_EMPTY\_INSERT}, 30
  \item {\ptt NOT\_EMPTY\_SING}, 38
  \item {\ptt NOT\_EQUAL\_SETS}, 30
  \item {\ptt NOT\_IN\_EMPTY}, 3, 30
  \item {\ptt NOT\_INSERT\_EMPTY}, 30
  \item {\ptt NOT\_PSUBSET\_EMPTY}, 5, 31
  \item {\ptt NOT\_SING\_EMPTY}, 38
  \item {\ptt NOT\_UNIV\_PSUBSET}, 5
  \item {\ptt NUM\_SET\_WOP}, 30

  \indexspace

  \item {\ptt print\_set} (flag), 5
  \item {\ptt PSUBSET\_DEF}, 5, 31
  \item {\ptt PSUBSET\_INSERT\_SUBSET}, 31
  \item {\ptt PSUBSET\_IRREFL}, 31
  \item {\ptt PSUBSET\_MEMBER}, 31
  \item {\ptt PSUBSET\_TRANS}, 31

  \indexspace

  \item {\ptt REST\_DEF}, 12, 35
  \item {\ptt REST\_PSUBSET}, 35
  \item {\ptt REST\_SING}, 35
  \item {\ptt REST\_SUBSET}, 36
  \item {\ptt RINV\_DEF}, 14, 37

  \indexspace

  \item {\ptt SET\_CASES}, 30
  \item {\ptt SET\_INDUCT}, 3, 30
  \item {\ptt SET\_INDUCT\_TAC}, 3--4, 25
  \item {\ptt SET\_MINIMUM}, 30
  \item {\ptt set\_TY\_DEF}, 2, 29
  \item {\ptt SING}, 11, 38
  \item {\ptt SING\_DEF}, 11, 38
  \item {\ptt SING\_DELETE}, 38
  \item {\ptt SING\_IFF\_CARD1}, 39
  \item {\ptt SING\_IFF\_EMPTY\_REST}, 36
  \item {\ptt SUBSET\_ANTISYM}, 5, 31
  \item {\ptt SUBSET\_DEF}, 5, 31
  \item {\ptt SUBSET\_DELETE}, 34
  \item {\ptt SUBSET\_EMPTY}, 31
  \item {\ptt SUBSET\_INSERT}, 31
  \item {\ptt SUBSET\_INSERT\_DELETE}, 34
  \item {\ptt SUBSET\_INTER\_ABSORPTION}, 32
  \item {\ptt SUBSET\_REFL}, 5, 31
  \item {\ptt SUBSET\_TRANS}, 5, 31
  \item {\ptt SUBSET\_UNION}, 33
  \item {\ptt SUBSET\_UNION\_ABSORPTION}, 33
  \item {\ptt SUBSET\_UNIV}, 5
  \item {\ptt SURJ\_COMPOSE}, 37
  \item {\ptt SURJ\_DEF}, 14, 37
  \item {\ptt SURJ\_EMPTY}, 38
  \item {\ptt SURJ\_ID}, 38

  \indexspace

  \item tactics
    \subitem {\ptt SET\_INDUCT\_TAC}, 3--4

  \indexspace

  \item {\ptt UNION\_ASSOC}, 33
  \item {\ptt UNION\_COMM}, 33
  \item {\ptt UNION\_CONV}, 9--10, 26
  \item {\ptt UNION\_DEF}, 6
  \item {\ptt UNION\_EMPTY}, 33
  \item {\ptt UNION\_IDEMPOT}, 33
  \item {\ptt UNION\_OVER\_INTER}, 33

\end{theindex}
