\indexentry{definition!of (*)set@of {\ptt (*)set}|(}{1}
\indexentry{definition!of IS\_SET\_REP@of {\ptt IS\_SET\_REP}}{2}
\indexentry{IS\_SET\_REP@{\ptt IS\_SET\_REP}}{2}
\indexentry{set\_TY\_DEF@{\ptt set\_TY\_DEF}}{2}
\indexentry{naming conventions!for definitions|(}{2}
\indexentry{naming conventions!for definitions|)}{2}
\indexentry{definition!of (*)set@of {\ptt (*)set}|)}{2}
\indexentry{axioms for (*)set@axioms for {\ptt (*)set}|(}{2}
\indexentry{definition!of IN@of {\ptt IN}}{2}
\indexentry{definition!of EMPTY@of {\ptt EMPTY}}{2}
\indexentry{definition!of INSERT@of {\ptt INSERT}}{2}
\indexentry{FINITE\_SET\_DEF@{\ptt FINITE\_SET\_DEF}}{2}
\indexentry{induction}{3}
\indexentry{NOT\_IN\_EMPTY@{\ptt NOT\_IN\_EMPTY}}{3}
\indexentry{IN\_INSERT@{\ptt IN\_INSERT}}{3}
\indexentry{INSERT\_INSERT@{\ptt INSERT\_INSERT}}{3}
\indexentry{INSERT\_COMM@{\ptt INSERT\_COMM}}{3}
\indexentry{induction|(}{3}
\indexentry{SET\_INDUCT@{\ptt SET\_INDUCT}}{3}
\indexentry{induction|)}{3}
\indexentry{EXTENSION@{\ptt EXTENSION}}{3}
\indexentry{axiom of extension}{3}
\indexentry{axioms for (*)set@axioms for {\ptt (*)set}|)}{3}
\indexentry{induction|(}{3}
\indexentry{SET\_INDUCT\_TAC@{\ptt SET\_INDUCT\_TAC}|(}{3}
\indexentry{tactics!SET\_INDUCT\_TAC@{\ptt SET\_INDUCT\_TAC}|(}{3}
\indexentry{SET\_INDUCT\_TAC@{\ptt SET\_INDUCT\_TAC}|)}{4}
\indexentry{tactics!SET\_INDUCT\_TAC@{\ptt SET\_INDUCT\_TAC}|)}{4}
\indexentry{induction|)}{4}
\indexentry{define\_finite\_set\_syntax@{\ptt define\_finite\_set\_syntax}}{4}
\indexentry{print\_set@{\ptt print\_set} (flag)}{5}
\indexentry{definition!of SUBSET@of {\ptt SUBSET}}{5}
\indexentry{SUBSET\_DEF@{\ptt SUBSET\_DEF}}{5}
\indexentry{definition!of PSUBSET@of {\ptt PSUBSET}}{5}
\indexentry{PSUBSET\_DEF@{\ptt PSUBSET\_DEF}}{5}
\indexentry{SUBSET\_TRANS@{\ptt SUBSET\_TRANS}}{5}
\indexentry{SUBSET\_REFL@{\ptt SUBSET\_REFL}}{5}
\indexentry{SUBSET\_ANTISYM@{\ptt SUBSET\_ANTISYM}}{5}
\indexentry{EMPTY\_SUBSET@{\ptt EMPTY\_SUBSET}}{5}
\indexentry{SUBSET\_UNIV@{\ptt SUBSET\_UNIV}}{5}
\indexentry{NOT\_PSUBSET\_EMPTY@{\ptt NOT\_PSUBSET\_EMPTY}}{5}
\indexentry{NOT\_UNIV\_PSUBSET@{\ptt NOT\_UNIV\_PSUBSET}}{5}
\indexentry{naming conventions!for theorems generally|(}{6}
\indexentry{naming conventions!for theorems generally|)}{6}
\indexentry{definition!of UNION@of {\ptt UNION}}{6}
\indexentry{UNION\_DEF@{\ptt UNION\_DEF}}{6}
\indexentry{definition!of INTER@of {\ptt INTER}}{6}
\indexentry{INTER\_DEF@{\ptt INTER\_DEF}}{6}
\indexentry{definition!of DIFF@of {\ptt DIFF}}{6}
\indexentry{DIFF\_DEF@{\ptt DIFF\_DEF}}{6}
\indexentry{naming conventions!for membership conditions|(}{6}
\indexentry{naming conventions!for membership conditions|)}{6}
\indexentry{IN\_UNION@{\ptt IN\_UNION}}{6}
\indexentry{IN\_INTER@{\ptt IN\_INTER}}{6}
\indexentry{IN\_DIFF@{\ptt IN\_DIFF}}{6}
\indexentry{definition!of DISJOINT@of {\ptt DISJOINT}}{6}
\indexentry{DISJOINT\_DEF@{\ptt DISJOINT\_DEF}}{6}
\indexentry{definition!of INSERT@of {\ptt INSERT}}{7}
\indexentry{INSERT\_DEF@{\ptt INSERT\_DEF}}{7}
\indexentry{definition!of DELETE@of {\ptt DELETE}}{7}
\indexentry{DELETE\_DEF@{\ptt DELETE\_DEF}}{7}
\indexentry{IN\_INSERT@{\ptt IN\_INSERT}}{7}
\indexentry{IN\_DELETE@{\ptt IN\_DELETE}}{7}
\indexentry{IN\_CONV@{\ptt IN\_CONV}|(}{7}
\indexentry{conversions!IN\_CONV@{\ptt IN\_CONV}|(}{7}
\indexentry{IN\_CONV@{\ptt IN\_CONV}|)}{8}
\indexentry{conversions!IN\_CONV@{\ptt IN\_CONV}|)}{8}
\indexentry{UNION\_CONV@{\ptt UNION\_CONV}|(}{9}
\indexentry{conversions!UNION\_CONV@{\ptt UNION\_CONV}|(}{9}
\indexentry{UNION\_CONV@{\ptt UNION\_CONV}|)}{10}
\indexentry{conversions!UNION\_CONV@{\ptt UNION\_CONV}|)}{10}
\indexentry{INSERT\_CONV@{\ptt INSERT\_CONV}|(}{10}
\indexentry{conversions!INSERT\_CONV@{\ptt INSERT\_CONV}|(}{10}
\indexentry{INSERT\_CONV@{\ptt INSERT\_CONV}|)}{10}
\indexentry{conversions!INSERT\_CONV@{\ptt INSERT\_CONV}|)}{10}
\indexentry{DELETE\_CONV@{\ptt DELETE\_CONV}|(}{11}
\indexentry{conversions!DELETE\_CONV@{\ptt DELETE\_CONV}|(}{11}
\indexentry{DELETE\_CONV@{\ptt DELETE\_CONV}|)}{11}
\indexentry{conversions!DELETE\_CONV@{\ptt DELETE\_CONV}|)}{11}
\indexentry{definition!of SING@of {\ptt SING}}{11}
\indexentry{SING\_DEF@{\ptt SING\_DEF}}{11}
\indexentry{SING@{\ptt SING}}{11}
\indexentry{SING@{\ptt SING}}{11}
\indexentry{naming conventions!for theorems about singletons|(}{11}
\indexentry{naming conventions!for theorems about singletons|)}{11}
\indexentry{definition!of CHOICE@of {\ptt CHOICE}}{12}
\indexentry{CHOICE\_DEF@{\ptt CHOICE\_DEF}}{12}
\indexentry{definition!of REST@of {\ptt REST}}{12}
\indexentry{REST\_DEF@{\ptt REST\_DEF}}{12}
\indexentry{definition!of IMAGE@of {\ptt IMAGE}}{12}
\indexentry{IMAGE\_DEF@{\ptt IMAGE\_DEF}}{12}
\indexentry{IN\_IMAGE@{\ptt IN\_IMAGE}}{12}
\indexentry{IMAGE\_CONV@{\ptt IMAGE\_CONV}|(}{13}
\indexentry{conversions!IMAGE\_CONV@{\ptt IMAGE\_CONV}|(}{13}
\indexentry{IMAGE\_CONV@{\ptt IMAGE\_CONV}|)}{13}
\indexentry{conversions!IMAGE\_CONV@{\ptt IMAGE\_CONV}|)}{13}
\indexentry{definition!of INJ@of {\ptt INJ}}{14}
\indexentry{INJ\_DEF@{\ptt INJ\_DEF}}{14}
\indexentry{definition!of SURJ@of {\ptt SURJ}}{14}
\indexentry{SURJ\_DEF@{\ptt SURJ\_DEF}}{14}
\indexentry{definition!of BIJ@of {\ptt BIJ}}{14}
\indexentry{BIJ\_DEF@{\ptt BIJ\_DEF}}{14}
\indexentry{definition!of LINV@of {\ptt LINV}}{14}
\indexentry{LINV\_DEF@{\ptt LINV\_DEF}}{14}
\indexentry{definition!of RINV@of {\ptt RINV}}{14}
\indexentry{RINV\_DEF@{\ptt RINV\_DEF}}{14}
\indexentry{definition!of FINITE@of {\ptt FINITE}}{15}
\indexentry{FINITE\_DEF@{\ptt FINITE\_DEF}}{15}
\indexentry{FINITE\_EMPTY@{\ptt FINITE\_EMPTY}}{15}
\indexentry{FINITE\_INSERT@{\ptt FINITE\_INSERT}}{15}
\indexentry{definition!of INFINITE@of {\ptt INFINITE}}{15}
\indexentry{INFINITE\_DEF@{\ptt INFINITE\_DEF}}{15}
\indexentry{IMAGE\_11\_INFINITE@{\ptt IMAGE\_11\_INFINITE}}{15}
\indexentry{FINITE\_CONV@{\ptt FINITE\_CONV}|(}{15}
\indexentry{conversions!FINITE\_CONV@{\ptt FINITE\_CONV}|(}{15}
\indexentry{FINITE\_CONV@{\ptt FINITE\_CONV}|)}{15}
\indexentry{conversions!FINITE\_CONV@{\ptt FINITE\_CONV}|)}{15}
\indexentry{definition!of CARD@of {\ptt CARD}}{16}
\indexentry{CARD\_DEF@{\ptt CARD\_DEF}}{16}
\indexentry{CARD\_SING@{\ptt CARD\_SING}}{16}
\indexentry{FINITE\_ISO\_NUM@{\ptt FINITE\_ISO\_NUM}}{16}
\indexentry{load\_finite\_sets@{\ptt load\_finite\_sets}|(}{18}
\indexentry{load\_finite\_sets@{\ptt load\_finite\_sets}|)}{18}
\indexentry{DELETE\_CONV@{\ptt DELETE\_CONV}}{19}
\indexentry{IMAGE\_CONV@{\ptt IMAGE\_CONV}}{20}
\indexentry{INSERT\_CONV@{\ptt INSERT\_CONV}}{22}
\indexentry{IN\_CONV@{\ptt IN\_CONV}}{24}
\indexentry{SET\_INDUCT\_TAC@{\ptt SET\_INDUCT\_TAC}}{25}
\indexentry{UNION\_CONV@{\ptt UNION\_CONV}}{26}
\indexentry{FINITE\_SET\_DEF@{\ptt FINITE\_SET\_DEF}}{29}
\indexentry{IS\_SET\_REP@{\ptt IS\_SET\_REP}}{29}
\indexentry{set\_TY\_DEF@{\ptt set\_TY\_DEF}}{29}
\indexentry{ABSORPTION@{\ptt ABSORPTION}}{29}
\indexentry{COMPONENT@{\ptt COMPONENT}}{30}
\indexentry{DECOMPOSITION@{\ptt DECOMPOSITION}}{30}
\indexentry{EXTENSION@{\ptt EXTENSION}}{30}
\indexentry{INSERT\_COMM@{\ptt INSERT\_COMM}}{30}
\indexentry{INSERT\_INSERT@{\ptt INSERT\_INSERT}}{30}
\indexentry{IN\_INSERT@{\ptt IN\_INSERT}}{30}
\indexentry{MEMBER\_NOT\_EMPTY@{\ptt MEMBER\_NOT\_EMPTY}}{30}
\indexentry{NOT\_EMPTY\_INSERT@{\ptt NOT\_EMPTY\_INSERT}}{30}
\indexentry{NOT\_EQUAL\_SETS@{\ptt NOT\_EQUAL\_SETS}}{30}
\indexentry{NOT\_INSERT\_EMPTY@{\ptt NOT\_INSERT\_EMPTY}}{30}
\indexentry{NOT\_IN\_EMPTY@{\ptt NOT\_IN\_EMPTY}}{30}
\indexentry{NUM\_SET\_WOP@{\ptt NUM\_SET\_WOP}}{30}
\indexentry{SET\_CASES@{\ptt SET\_CASES}}{30}
\indexentry{SET\_INDUCT@{\ptt SET\_INDUCT}}{30}
\indexentry{SET\_MINIMUM@{\ptt SET\_MINIMUM}}{30}
\indexentry{EMPTY\_SUBSET@{\ptt EMPTY\_SUBSET}}{31}
\indexentry{INSERT\_SUBSET@{\ptt INSERT\_SUBSET}}{31}
\indexentry{NOT\_PSUBSET\_EMPTY@{\ptt NOT\_PSUBSET\_EMPTY}}{31}
\indexentry{PSUBSET\_DEF@{\ptt PSUBSET\_DEF}}{31}
\indexentry{PSUBSET\_INSERT\_SUBSET@{\ptt PSUBSET\_INSERT\_SUBSET}}{31}
\indexentry{PSUBSET\_IRREFL@{\ptt PSUBSET\_IRREFL}}{31}
\indexentry{PSUBSET\_MEMBER@{\ptt PSUBSET\_MEMBER}}{31}
\indexentry{PSUBSET\_TRANS@{\ptt PSUBSET\_TRANS}}{31}
\indexentry{SUBSET\_ANTISYM@{\ptt SUBSET\_ANTISYM}}{31}
\indexentry{SUBSET\_DEF@{\ptt SUBSET\_DEF}}{31}
\indexentry{SUBSET\_EMPTY@{\ptt SUBSET\_EMPTY}}{31}
\indexentry{SUBSET\_INSERT@{\ptt SUBSET\_INSERT}}{31}
\indexentry{SUBSET\_REFL@{\ptt SUBSET\_REFL}}{31}
\indexentry{SUBSET\_TRANS@{\ptt SUBSET\_TRANS}}{31}
\indexentry{DELETE\_INTER@{\ptt DELETE\_INTER}}{32}
\indexentry{EMPTY\_UNION@{\ptt EMPTY\_UNION}}{32}
\indexentry{INSERT\_INTER@{\ptt INSERT\_INTER}}{32}
\indexentry{INSERT\_UNION@{\ptt INSERT\_UNION}}{32}
\indexentry{INSERT\_UNION\_EQ@{\ptt INSERT\_UNION\_EQ}}{32}
\indexentry{INTER\_ASSOC@{\ptt INTER\_ASSOC}}{32}
\indexentry{INTER\_COMM@{\ptt INTER\_COMM}}{32}
\indexentry{INTER\_EMPTY@{\ptt INTER\_EMPTY}}{32}
\indexentry{INTER\_IDEMPOT@{\ptt INTER\_IDEMPOT}}{32}
\indexentry{INTER\_OVER\_UNION@{\ptt INTER\_OVER\_UNION}}{32}
\indexentry{INTER\_SUBSET@{\ptt INTER\_SUBSET}}{32}
\indexentry{IN\_INTER@{\ptt IN\_INTER}}{32}
\indexentry{IN\_UNION@{\ptt IN\_UNION}}{32}
\indexentry{SUBSET\_INTER\_ABSORPTION@{\ptt SUBSET\_INTER\_ABSORPTION}}{32}
\indexentry{SUBSET\_UNION@{\ptt SUBSET\_UNION}}{33}
\indexentry{SUBSET\_UNION\_ABSORPTION@{\ptt SUBSET\_UNION\_ABSORPTION}}{33}
\indexentry{UNION\_ASSOC@{\ptt UNION\_ASSOC}}{33}
\indexentry{UNION\_COMM@{\ptt UNION\_COMM}}{33}
\indexentry{UNION\_EMPTY@{\ptt UNION\_EMPTY}}{33}
\indexentry{UNION\_IDEMPOT@{\ptt UNION\_IDEMPOT}}{33}
\indexentry{UNION\_OVER\_INTER@{\ptt UNION\_OVER\_INTER}}{33}
\indexentry{DIFF\_DIFF@{\ptt DIFF\_DIFF}}{33}
\indexentry{DIFF\_EMPTY@{\ptt DIFF\_EMPTY}}{33}
\indexentry{DIFF\_EQ\_EMPTY@{\ptt DIFF\_EQ\_EMPTY}}{33}
\indexentry{EMPTY\_DIFF@{\ptt EMPTY\_DIFF}}{33}
\indexentry{IN\_DIFF@{\ptt IN\_DIFF}}{33}
\indexentry{DELETE\_COMM@{\ptt DELETE\_COMM}}{33}
\indexentry{DELETE\_DEF@{\ptt DELETE\_DEF}}{34}
\indexentry{DELETE\_DELETE@{\ptt DELETE\_DELETE}}{34}
\indexentry{DELETE\_INSERT@{\ptt DELETE\_INSERT}}{34}
\indexentry{DELETE\_NON\_ELEMENT@{\ptt DELETE\_NON\_ELEMENT}}{34}
\indexentry{DELETE\_SUBSET@{\ptt DELETE\_SUBSET}}{34}
\indexentry{DIFF\_INSERT@{\ptt DIFF\_INSERT}}{34}
\indexentry{EMPTY\_DELETE@{\ptt EMPTY\_DELETE}}{34}
\indexentry{INSERT\_DELETE@{\ptt INSERT\_DELETE}}{34}
\indexentry{IN\_DELETE@{\ptt IN\_DELETE}}{34}
\indexentry{IN\_DELETE\_EQ@{\ptt IN\_DELETE\_EQ}}{34}
\indexentry{SUBSET\_DELETE@{\ptt SUBSET\_DELETE}}{34}
\indexentry{SUBSET\_INSERT\_DELETE@{\ptt SUBSET\_INSERT\_DELETE}}{34}
\indexentry{DISJOINT\_DEF@{\ptt DISJOINT\_DEF}}{34}
\indexentry{DISJOINT\_DELETE\_SYM@{\ptt DISJOINT\_DELETE\_SYM}}{35}
\indexentry{DISJOINT\_EMPTY@{\ptt DISJOINT\_EMPTY}}{35}
\indexentry{DISJOINT\_EMPTY\_REFL@{\ptt DISJOINT\_EMPTY\_REFL}}{35}
\indexentry{DISJOINT\_INSERT@{\ptt DISJOINT\_INSERT}}{35}
\indexentry{DISJOINT\_SYM@{\ptt DISJOINT\_SYM}}{35}
\indexentry{DISJOINT\_UNION@{\ptt DISJOINT\_UNION}}{35}
\indexentry{IN\_DISJOINT@{\ptt IN\_DISJOINT}}{35}
\indexentry{CHOICE\_DEF@{\ptt CHOICE\_DEF}}{35}
\indexentry{CHOICE\_INSERT\_REST@{\ptt CHOICE\_INSERT\_REST}}{35}
\indexentry{CHOICE\_NOT\_IN\_REST@{\ptt CHOICE\_NOT\_IN\_REST}}{35}
\indexentry{CHOICE\_SING@{\ptt CHOICE\_SING}}{35}
\indexentry{REST\_DEF@{\ptt REST\_DEF}}{35}
\indexentry{REST\_PSUBSET@{\ptt REST\_PSUBSET}}{35}
\indexentry{REST\_SING@{\ptt REST\_SING}}{35}
\indexentry{REST\_SUBSET@{\ptt REST\_SUBSET}}{36}
\indexentry{SING\_IFF\_EMPTY\_REST@{\ptt SING\_IFF\_EMPTY\_REST}}{36}
\indexentry{IMAGE\_COMPOSE@{\ptt IMAGE\_COMPOSE}}{36}
\indexentry{IMAGE\_DELETE@{\ptt IMAGE\_DELETE}}{36}
\indexentry{IMAGE\_EMPTY@{\ptt IMAGE\_EMPTY}}{36}
\indexentry{IMAGE\_EQ\_EMPTY@{\ptt IMAGE\_EQ\_EMPTY}}{36}
\indexentry{IMAGE\_ID@{\ptt IMAGE\_ID}}{36}
\indexentry{IMAGE\_IN@{\ptt IMAGE\_IN}}{36}
\indexentry{IMAGE\_INSERT@{\ptt IMAGE\_INSERT}}{36}
\indexentry{IMAGE\_INTER@{\ptt IMAGE\_INTER}}{36}
\indexentry{IMAGE\_SUBSET@{\ptt IMAGE\_SUBSET}}{36}
\indexentry{IMAGE\_UNION@{\ptt IMAGE\_UNION}}{36}
\indexentry{IN\_IMAGE@{\ptt IN\_IMAGE}}{36}
\indexentry{BIJ\_COMPOSE@{\ptt BIJ\_COMPOSE}}{37}
\indexentry{BIJ\_DEF@{\ptt BIJ\_DEF}}{37}
\indexentry{BIJ\_EMPTY@{\ptt BIJ\_EMPTY}}{37}
\indexentry{BIJ\_ID@{\ptt BIJ\_ID}}{37}
\indexentry{IMAGE\_SURJ@{\ptt IMAGE\_SURJ}}{37}
\indexentry{INJ\_COMPOSE@{\ptt INJ\_COMPOSE}}{37}
\indexentry{INJ\_DEF@{\ptt INJ\_DEF}}{37}
\indexentry{INJ\_EMPTY@{\ptt INJ\_EMPTY}}{37}
\indexentry{INJ\_ID@{\ptt INJ\_ID}}{37}
\indexentry{LINV\_DEF@{\ptt LINV\_DEF}}{37}
\indexentry{RINV\_DEF@{\ptt RINV\_DEF}}{37}
\indexentry{SURJ\_COMPOSE@{\ptt SURJ\_COMPOSE}}{37}
\indexentry{SURJ\_DEF@{\ptt SURJ\_DEF}}{37}
\indexentry{SURJ\_EMPTY@{\ptt SURJ\_EMPTY}}{38}
\indexentry{SURJ\_ID@{\ptt SURJ\_ID}}{38}
\indexentry{DELETE\_EQ\_SING@{\ptt DELETE\_EQ\_SING}}{38}
\indexentry{DISJOINT\_SING\_EMPTY@{\ptt DISJOINT\_SING\_EMPTY}}{38}
\indexentry{EQUAL\_SING@{\ptt EQUAL\_SING}}{38}
\indexentry{INSERT\_SING\_UNION@{\ptt INSERT\_SING\_UNION}}{38}
\indexentry{IN\_SING@{\ptt IN\_SING}}{38}
\indexentry{NOT\_EMPTY\_SING@{\ptt NOT\_EMPTY\_SING}}{38}
\indexentry{NOT\_SING\_EMPTY@{\ptt NOT\_SING\_EMPTY}}{38}
\indexentry{SING@{\ptt SING}}{38}
\indexentry{SING\_DEF@{\ptt SING\_DEF}}{38}
\indexentry{SING\_DELETE@{\ptt SING\_DELETE}}{38}
\indexentry{CARD\_DEF@{\ptt CARD\_DEF}}{38}
\indexentry{CARD\_DELETE@{\ptt CARD\_DELETE}}{39}
\indexentry{CARD\_DIFF@{\ptt CARD\_DIFF}}{39}
\indexentry{CARD\_EMPTY@{\ptt CARD\_EMPTY}}{39}
\indexentry{CARD\_EQ\_0@{\ptt CARD\_EQ\_0}}{39}
\indexentry{CARD\_INSERT@{\ptt CARD\_INSERT}}{39}
\indexentry{CARD\_INTER\_LESS\_EQ@{\ptt CARD\_INTER\_LESS\_EQ}}{39}
\indexentry{CARD\_PSUBSET@{\ptt CARD\_PSUBSET}}{39}
\indexentry{CARD\_SING@{\ptt CARD\_SING}}{39}
\indexentry{CARD\_SUBSET@{\ptt CARD\_SUBSET}}{39}
\indexentry{CARD\_UNION@{\ptt CARD\_UNION}}{39}
\indexentry{LESS\_CARD\_DIFF@{\ptt LESS\_CARD\_DIFF}}{39}
\indexentry{SING\_IFF\_CARD1@{\ptt SING\_IFF\_CARD1}}{39}
