\begin{theindex}

  \item {\ptt ABSORPTION}, 38
  \item axiom of extension, 2
  \item axiom of specification, 2
    \subitem for generalized set specifications, 3
    \subitem for set abstractions, 5

  \indexspace

  \item {\ptt BIJ\_COMPOSE}, 42
  \item {\ptt BIJ\_DEF}, 17, 42
  \item {\ptt BIJ\_EMPTY}, 42
  \item {\ptt BIJ\_ID}, 42

  \indexspace

  \item {\ptt CARD\_DEF}, 19, 46
  \item {\ptt CARD\_DELETE}, 46
  \item {\ptt CARD\_DIFF}, 46
  \item {\ptt CARD\_EMPTY}, 46
  \item {\ptt CARD\_EQ\_0}, 46
  \item {\ptt CARD\_INSERT}, 46
  \item {\ptt CARD\_INTER\_LESS\_EQ}, 46
  \item {\ptt CARD\_PSUBSET}, 46
  \item {\ptt CARD\_SING}, 19, 46
  \item {\ptt CARD\_SUBSET}, 46
  \item {\ptt CARD\_UNION}, 47
  \item {\ptt CHF}, 1
  \item {\ptt CHOICE\_DEF}, 14, 40
  \item {\ptt CHOICE\_INSERT\_REST}, 40
  \item {\ptt CHOICE\_NOT\_IN\_REST}, 40
  \item {\ptt CHOICE\_SING}, 40
  \item {\ptt COMPONENT}, 38
  \item conversions
    \subitem {\ptt DELETE\_CONV}, 13
    \subitem {\ptt FINITE\_CONV}, 18
    \subitem {\ptt IMAGE\_CONV}, 15--16
    \subitem {\ptt IN\_CONV}, 10--11
    \subitem {\ptt INSERT\_CONV}, 12--13
    \subitem {\ptt SET\_SPEC\_CONV}, 5--6
    \subitem {\ptt UNION\_CONV}, 11--12

  \indexspace

  \item {\ptt DECOMPOSITION}, 38
  \item {\ptt define\_finite\_set\_syntax}, 9
  \item {\ptt define\_new\_type\_bijections}, 1
  \item {\ptt define\_set\_abstraction\_syntax}, 3
  \item definition
    \subitem of {\ptt (*)set}, 1--2
    \subitem of {\ptt BIJ}, 17
    \subitem of {\ptt CARD}, 19
    \subitem of {\ptt CHF}, 1
    \subitem of {\ptt CHOICE}, 14
    \subitem of {\ptt DELETE}, 8
    \subitem of {\ptt DIFF}, 7
    \subitem of {\ptt DISJOINT}, 8
    \subitem of {\ptt EMPTY}, 6
    \subitem of {\ptt FINITE}, 17
    \subitem of {\ptt GSPEC}, 3
    \subitem of {\ptt IMAGE}, 15
    \subitem of {\ptt IN}, 2
    \subitem of {\ptt INFINITE}, 17
    \subitem of {\ptt INJ}, 16
    \subitem of {\ptt INSERT}, 8
    \subitem of {\ptt INTER}, 7
    \subitem of {\ptt LINV}, 17
    \subitem of {\ptt PSUBSET}, 7
    \subitem of {\ptt REST}, 14
    \subitem of {\ptt RINV}, 17
    \subitem of {\ptt SING}, 14
    \subitem of {\ptt SPEC}, 1
    \subitem of {\ptt SUBSET}, 7
    \subitem of {\ptt SURJ}, 16
    \subitem of {\ptt UNION}, 7
    \subitem of {\ptt UNIV}, 6
  \item {\ptt DELETE\_COMM}, 38
  \item {\ptt DELETE\_CONV}, 13, 23
  \item {\ptt DELETE\_DEF}, 8, 38
  \item {\ptt DELETE\_DELETE}, 38
  \item {\ptt DELETE\_EQ\_SING}, 43
  \item {\ptt DELETE\_INSERT}, 38
  \item {\ptt DELETE\_INTER}, 38
  \item {\ptt DELETE\_NON\_ELEMENT}, 38
  \item {\ptt DELETE\_SUBSET}, 39
  \item {\ptt DIFF\_DEF}, 7, 37
  \item {\ptt DIFF\_DIFF}, 37
  \item {\ptt DIFF\_EMPTY}, 37
  \item {\ptt DIFF\_EQ\_EMPTY}, 37
  \item {\ptt DIFF\_INSERT}, 39
  \item {\ptt DIFF\_UNIV}, 37
  \item {\ptt DISJOINT\_DEF}, 8, 37
  \item {\ptt DISJOINT\_DELETE\_SYM}, 37
  \item {\ptt DISJOINT\_EMPTY}, 38
  \item {\ptt DISJOINT\_EMPTY\_REFL}, 38
  \item {\ptt DISJOINT\_INSERT}, 39
  \item {\ptt DISJOINT\_SING\_EMPTY}, 43
  \item {\ptt DISJOINT\_SYM}, 38
  \item {\ptt DISJOINT\_UNION}, 38

  \indexspace

  \item {\ptt EMPTY\_DEF}, 6, 34
  \item {\ptt EMPTY\_DELETE}, 39
  \item {\ptt EMPTY\_DIFF}, 37
  \item {\ptt EMPTY\_NOT\_UNIV}, 34
  \item {\ptt EMPTY\_SUBSET}, 7, 34
  \item {\ptt EMPTY\_UNION}, 35
  \item {\ptt EQ\_UNIV}, 34
  \item {\ptt EQUAL\_SING}, 43
  \item {\ptt EXTENSION}, 2, 33

  \indexspace

  \item {\ptt FINITE\_CONV}, 18, 24
  \item {\ptt FINITE\_DEF}, 17, 44
  \item {\ptt FINITE\_DELETE}, 44
  \item {\ptt FINITE\_DIFF}, 44
  \item {\ptt FINITE\_EMPTY}, 17, 44
  \item {\ptt FINITE\_INDUCT}, 44
  \item {\ptt FINITE\_INSERT}, 17, 44
  \item {\ptt FINITE\_ISO\_NUM}, 19, 44
  \item {\ptt FINITE\_PSUBSET\_INFINITE}, 44
  \item {\ptt FINITE\_PSUBSET\_UNIV}, 44
  \item {\ptt FINITE\_SING}, 43
  \item {\ptt FINITE\_UNION}, 45

  \indexspace

  \item {\ptt GSPEC}, 3
  \item {\ptt GSPEC\_DEF}, 3, 33
  \item {\ptt GSPECIFICATION}, 3, 33

  \indexspace

  \item {\ptt IMAGE\_11\_INFINITE}, 18, 45
  \item {\ptt IMAGE\_COMPOSE}, 41
  \item {\ptt IMAGE\_CONV}, 15--16, 25
  \item {\ptt IMAGE\_DEF}, 15, 41
  \item {\ptt IMAGE\_DELETE}, 41
  \item {\ptt IMAGE\_EMPTY}, 41
  \item {\ptt IMAGE\_EQ\_EMPTY}, 41
  \item {\ptt IMAGE\_FINITE}, 45
  \item {\ptt IMAGE\_ID}, 41
  \item {\ptt IMAGE\_IN}, 41
  \item {\ptt IMAGE\_INSERT}, 41
  \item {\ptt IMAGE\_INTER}, 41
  \item {\ptt IMAGE\_SUBSET}, 41
  \item {\ptt IMAGE\_SURJ}, 42
  \item {\ptt IMAGE\_UNION}, 42
  \item {\ptt IN\_CONV}, 10--11, 28
  \item {\ptt IN\_DEF}, 2, 33
  \item {\ptt IN\_DELETE}, 9, 39
  \item {\ptt IN\_DELETE\_EQ}, 40
  \item {\ptt IN\_DIFF}, 8, 37
  \item {\ptt IN\_DISJOINT}, 38
  \item {\ptt IN\_IMAGE}, 15, 42
  \item {\ptt IN\_INFINITE\_NOT\_FINITE}, 45
  \item {\ptt IN\_INSERT}, 9, 40
  \item {\ptt IN\_INTER}, 8, 36
  \item {\ptt IN\_SING}, 43
  \item {\ptt IN\_UNION}, 8, 36
  \item {\ptt IN\_UNIV}, 6, 34
  \item {\ptt INFINITE\_DEF}, 17, 45
  \item {\ptt INFINITE\_DIFF\_FINITE}, 45
  \item {\ptt INFINITE\_SUBSET}, 45
  \item {\ptt INFINITE\_UNIV}, 45
  \item {\ptt INJ\_COMPOSE}, 42
  \item {\ptt INJ\_DEF}, 16, 42
  \item {\ptt INJ\_EMPTY}, 42
  \item {\ptt INJ\_ID}, 42
  \item {\ptt INSERT\_COMM}, 39
  \item {\ptt INSERT\_CONV}, 12--13, 27
  \item {\ptt INSERT\_DEF}, 8, 39
  \item {\ptt INSERT\_DELETE}, 39
  \item {\ptt INSERT\_DIFF}, 39
  \item {\ptt INSERT\_INSERT}, 39
  \item {\ptt INSERT\_INTER}, 39
  \item {\ptt INSERT\_SING\_UNION}, 43
  \item {\ptt INSERT\_SUBSET}, 39
  \item {\ptt INSERT\_UNION}, 39
  \item {\ptt INSERT\_UNION\_EQ}, 39
  \item {\ptt INSERT\_UNIV}, 39
  \item {\ptt INTER\_ASSOC}, 36
  \item {\ptt INTER\_COMM}, 36
  \item {\ptt INTER\_DEF}, 7, 36
  \item {\ptt INTER\_EMPTY}, 36
  \item {\ptt INTER\_FINITE}, 45
  \item {\ptt INTER\_IDEMPOT}, 36
  \item {\ptt INTER\_OVER\_UNION}, 36
  \item {\ptt INTER\_SUBSET}, 36
  \item {\ptt INTER\_UNIV}, 36

  \indexspace

  \item {\ptt LESS\_CARD\_DIFF}, 47
  \item {\ptt LINV\_DEF}, 17, 42
  \item {\ptt load\_sets}, 21

  \indexspace

  \item {\ptt MEMBER\_NOT\_EMPTY}, 34

  \indexspace

  \item naming conventions
    \subitem for definitions, 2
    \subitem for membership conditions, 8
    \subitem for theorems about singletons, 14
    \subitem for theorems generally, 7
  \item {\ptt NOT\_EMPTY\_INSERT}, 40
  \item {\ptt NOT\_EMPTY\_SING}, 43
  \item {\ptt NOT\_EQUAL\_SETS}, 33
  \item {\ptt NOT\_IN\_EMPTY}, 6, 34
  \item {\ptt NOT\_IN\_FINITE}, 45
  \item {\ptt NOT\_INSERT\_EMPTY}, 40
  \item {\ptt NOT\_PSUBSET\_EMPTY}, 7, 34
  \item {\ptt NOT\_SING\_EMPTY}, 43
  \item {\ptt NOT\_UNIV\_PSUBSET}, 7, 35
  \item {\ptt NUM\_SET\_WOP}, 34

  \indexspace

  \item {\ptt print\_set} (flag), 4, 9
  \item {\ptt PSUBSET\_DEF}, 7, 35
  \item {\ptt PSUBSET\_FINITE}, 45
  \item {\ptt PSUBSET\_INSERT\_SUBSET}, 40
  \item {\ptt PSUBSET\_IRREFL}, 35
  \item {\ptt PSUBSET\_MEMBER}, 35
  \item {\ptt PSUBSET\_TRANS}, 35
  \item {\ptt PSUBSET\_UNIV}, 35

  \indexspace

  \item {\ptt REST\_DEF}, 14, 40
  \item {\ptt REST\_PSUBSET}, 41
  \item {\ptt REST\_SING}, 41
  \item {\ptt REST\_SUBSET}, 41
  \item {\ptt RINV\_DEF}, 17, 42

  \indexspace

  \item {\ptt SET\_CASES}, 40
  \item {\ptt SET\_INDUCT\_TAC}, 18--19, 30
  \item {\ptt set\_ISO\_DEF}, 1, 33
  \item {\ptt SET\_MINIMUM}, 34
  \item {\ptt SET\_SPEC\_CONV}, 5--6, 30
  \item {\ptt set\_TY\_DEF}, 1, 33
  \item {\ptt SING}, 14, 43
  \item {\ptt SING\_DEF}, 14, 44
  \item {\ptt SING\_DELETE}, 44
  \item {\ptt SING\_FINITE}, 44
  \item {\ptt SING\_IFF\_CARD1}, 47
  \item {\ptt SING\_IFF\_EMPTY\_REST}, 41
  \item {\ptt SPEC}, 1
  \item {\ptt SPECIFICATION}, 2, 34
  \item {\ptt SUBSET\_ANTISYM}, 7, 35
  \item {\ptt SUBSET\_DEF}, 7, 35
  \item {\ptt SUBSET\_DELETE}, 40
  \item {\ptt SUBSET\_EMPTY}, 35
  \item {\ptt SUBSET\_FINITE}, 45
  \item {\ptt SUBSET\_INSERT}, 40
  \item {\ptt SUBSET\_INSERT\_DELETE}, 40
  \item {\ptt SUBSET\_INTER\_ABSORPTION}, 36
  \item {\ptt SUBSET\_REFL}, 7, 35
  \item {\ptt SUBSET\_TRANS}, 7, 35
  \item {\ptt SUBSET\_UNION}, 36
  \item {\ptt SUBSET\_UNION\_ABSORPTION}, 36
  \item {\ptt SUBSET\_UNIV}, 7, 35
  \item {\ptt SURJ\_COMPOSE}, 43
  \item {\ptt SURJ\_DEF}, 16, 43
  \item {\ptt SURJ\_EMPTY}, 43
  \item {\ptt SURJ\_ID}, 43

  \indexspace

  \item tactics
    \subitem {\ptt SET\_INDUCT\_TAC}, 18--19

  \indexspace

  \item {\ptt UNION\_ASSOC}, 36
  \item {\ptt UNION\_COMM}, 36
  \item {\ptt UNION\_CONV}, 11--12, 31
  \item {\ptt UNION\_DEF}, 7, 36
  \item {\ptt UNION\_EMPTY}, 37
  \item {\ptt UNION\_IDEMPOT}, 37
  \item {\ptt UNION\_OVER\_INTER}, 37
  \item {\ptt UNION\_UNIV}, 37
  \item {\ptt UNIV\_DEF}, 6, 34
  \item {\ptt UNIV\_NOT\_EMPTY}, 34
  \item {\ptt UNIV\_SUBSET}, 35

\end{theindex}
