\indexentry{more_arithmetic, theory@{\ptt more\_arithmetic}, theory}{3}
\indexentry{ineq, theory@{\ptt ineq}, theory}{4}
\indexentry{EQ\_LESS\_EQ@{\ptt EQ\_LESS\_EQ}}{4}
\indexentry{NOT\_EQ\_LESS\_EQ@{\ptt NOT\_EQ\_LESS\_EQ}}{4}
\indexentry{LESS\_EQ\_LESS\_EQ\_EQ@{\ptt LESS\_EQ\_LESS\_EQ\_EQ}}{4}
\indexentry{zero\_ineq, theory@{\ptt zero\_ineq}, theory}{4}
\indexentry{M\_LESS\_0\_LESS@{\ptt M\_LESS\_0\_LESS}}{4}
\indexentry{LESS1EQ0@{\ptt LESS1EQ0}}{4}
\indexentry{NOT\_EQ\_0@{\ptt NOT\_EQ\_0}}{4}
\indexentry{LESS\_EQ\_0\_EQ@{\ptt LESS\_EQ\_0\_EQ}}{4}
\indexentry{GREATER\_NOT\_ZERO@{\ptt GREATER\_NOT\_ZERO}}{4}
\indexentry{NOT\_0\_AND\_MORE@{\ptt NOT\_0\_AND\_MORE}}{4}
\indexentry{suc, theory@{\ptt suc}, theory}{4}
\indexentry{NOT\_SUC\_LESS\_EQ\_0@{\ptt NOT\_SUC\_LESS\_EQ\_0}}{4}
\indexentry{SUC\_GREATER\_EQ\_SUC@{\ptt SUC\_GREATER\_EQ\_SUC}}{4}
\indexentry{NOT\_SUC\_LESS\_EQ\_SELF@{\ptt NOT\_SUC\_LESS\_EQ\_SELF}}{4}
\indexentry{SUC\_NOT\_0@{\ptt SUC\_NOT\_0}}{4}
\indexentry{pre, theory@{\ptt pre}, theory}{5}
\indexentry{SUC\_PRE@{\ptt SUC\_PRE}}{5}
\indexentry{PRE\_MONO@{\ptt PRE\_MONO}}{5}
\indexentry{PRE\_LESS\_EQ@{\ptt PRE\_LESS\_EQ}}{5}
\indexentry{PRE\_ADD@{\ptt PRE\_ADD}}{5}
\indexentry{PRE\_K\_K@{\ptt PRE\_K\_K}}{5}
\indexentry{add, theory@{\ptt add}, theory}{5}
\indexentry{LESS\_EQ\_ADD1@{\ptt LESS\_EQ\_ADD1}}{5}
\indexentry{ADD\_SYM\_ASSOC@{\ptt ADD\_SYM\_ASSOC}}{5}
\indexentry{LESS\_EQ\_SPLIT@{\ptt LESS\_EQ\_SPLIT}}{5}
\indexentry{ADDL\_GREATER@{\ptt ADDL\_GREATER}}{5}
\indexentry{LESS\_ADD1@{\ptt LESS\_ADD1}}{5}
\indexentry{sub, theory@{\ptt sub}, theory}{5}
\indexentry{SUB\_LE\_ADD@{\ptt SUB\_LE\_ADD}}{5}
\indexentry{NOT\_0\_SUB@{\ptt NOT\_0\_SUB}}{5}
\indexentry{ADD\_SUB\_SYM@{\ptt ADD\_SUB\_SYM}}{5}
\indexentry{SUB\_ADD\_SELF@{\ptt SUB\_ADD\_SELF}}{5}
\indexentry{SUB\_BOTH\_SIDES@{\ptt SUB\_BOTH\_SIDES}}{5}
\indexentry{mult, theory@{\ptt mult}, theory}{6}
\indexentry{LESS\_MONO\_MULT1@{\ptt LESS\_MONO\_MULT1}}{6}
\indexentry{LESS\_MULT\_PLUS\_DIFF@{\ptt LESS\_MULT\_PLUS\_DIFF}}{6}
\indexentry{LEFT\_SUB\_DISTRIB@{\ptt LEFT\_SUB\_DISTRIB}}{6}
\indexentry{ONE\_LESS\_TWO\_EXP\_SUC@{\ptt ONE\_LESS\_TWO\_EXP\_SUC}}{6}
\indexentry{div_mod, theory@{\ptt div\_mod}, theory}{6}
\indexentry{DIV@{\ptt DIV}}{6}
\indexentry{MOD@{\ptt MOD}}{6}
\indexentry{SUC\_MOD\_SELF@{\ptt SUC\_MOD\_SELF}}{6}
\indexentry{SUC\_DIV\_SELF@{\ptt SUC\_DIV\_SELF}}{6}
\indexentry{ADD\_DIV\_ADD\_DIV@{\ptt ADD\_DIV\_ADD\_DIV}}{6}
\indexentry{MOD\_MULT\_MOD@{\ptt MOD\_MULT\_MOD}}{6}
\indexentry{min\_max, theory@{\ptt min\_max}, theory}{6}
\indexentry{MAX@{\ptt MAX}}{6}
\indexentry{MIN@{\ptt MIN}}{6}
\indexentry{MAX\_DEF@{\ptt MAX\_DEF}}{6}
\indexentry{MIN\_DEF@{\ptt MIN\_DEF}}{6}
\indexentry{MAX\_0@{\ptt MAX\_0}}{7}
\indexentry{MAX\_SYM@{\ptt MAX\_SYM}}{7}
\indexentry{MAX\_REFL@{\ptt MAX\_REFL}}{7}
\indexentry{MIN\_0@{\ptt MIN\_0}}{7}
\indexentry{MIN\_SYM@{\ptt MIN\_SYM}}{7}
\indexentry{MIN\_REFL@{\ptt MIN\_REFL}}{7}
\indexentry{odd_even, theory@{\ptt odd\_even}, theory}{7}
\indexentry{ODD@{\ptt ODD}}{7}
\indexentry{EVEN@{\ptt EVEN}}{7}
\indexentry{EVEN\_ODD\_0@{\ptt EVEN\_ODD\_0}}{7}
\indexentry{EVEN\_ODD\_SUC@{\ptt EVEN\_ODD\_SUC}}{7}
\indexentry{EVEN\_IMPL\_MULT@{\ptt EVEN\_IMPL\_MULT}}{7}
\indexentry{load\_more\_arithmetic@{\ptt load\_more\_arithmetic}|(}{9}
\indexentry{load\_more\_arithmetic@{\ptt load\_more\_arithmetic}|)}{9}
\indexentry{GEN\_INDUCT\_RULE@{\ptt GEN\_INDUCT\_RULE}}{11}
\indexentry{GEN\_INDUCT\_TAC@{\ptt GEN\_INDUCT\_TAC}}{12}
\indexentry{NUM\_EQ\_PLUS\_CONV@{\ptt NUM\_EQ\_PLUS\_CONV}}{12}
\indexentry{NUM\_LESS\_EQ\_PLUS\_CONV@{\ptt NUM\_LESS\_EQ\_PLUS\_CONV}}{13}
\indexentry{NUM\_LESS\_PLUS\_CONV@{\ptt NUM\_LESS\_PLUS\_CONV}}{13}
\indexentry{GEN\_INDUCTION@{\ptt GEN\_INDUCTION}}{15}
\indexentry{GREATER\_EQ\_ANTISYM@{\ptt GREATER\_EQ\_ANTISYM}}{15}
\indexentry{LESS\_EQ\_LESS\_EQ\_EQ@{\ptt LESS\_EQ\_LESS\_EQ\_EQ}}{15}
\indexentry{LESS\_IS\_NOT\_LESS\_OR\_EQ@{\ptt LESS\_IS\_NOT\_LESS\_OR\_EQ}}{15}
\indexentry{NOT\_EQ\_LESS\_EQ@{\ptt NOT\_EQ\_LESS\_EQ}}{15}
\indexentry{NOT\_LESS\_AND\_GREATER@{\ptt NOT\_LESS\_AND\_GREATER}}{15}
\indexentry{GREATER\_NOT\_ZERO@{\ptt GREATER\_NOT\_ZERO}}{15}
\indexentry{LESS1EQ0@{\ptt LESS1EQ0}}{16}
\indexentry{LESS\_EQ\_0\_EQ@{\ptt LESS\_EQ\_0\_EQ}}{16}
\indexentry{M\_LESS\_0\_LESS@{\ptt M\_LESS\_0\_LESS}}{16}
\indexentry{NOT\_0\_AND\_MORE@{\ptt NOT\_0\_AND\_MORE}}{16}
\indexentry{NOT\_EQ\_0@{\ptt NOT\_EQ\_0}}{16}
\indexentry{LESS\_EQ\_LESS\_SUC@{\ptt LESS\_EQ\_LESS\_SUC}}{16}
\indexentry{NOT\_0\_GREATER\_EQ\_SUC@{\ptt NOT\_0\_GREATER\_EQ\_SUC}}{16}
\indexentry{NOT\_FORALL\_SUC\_LESS\_EQ@{\ptt NOT\_FORALL\_SUC\_LESS\_EQ}}{16}
\indexentry{NOT\_SUC\_LESS\_EQ\_SELF@{\ptt NOT\_SUC\_LESS\_EQ\_SELF}}{16}
\indexentry{SUC\_0@{\ptt SUC\_0}}{16}
\indexentry{SUC\_GREATER\_EQ\_SUC@{\ptt SUC\_GREATER\_EQ\_SUC}}{16}
\indexentry{SUC\_LESS\_EQ@{\ptt SUC\_LESS\_EQ}}{16}
\indexentry{SUC\_NOT\_0@{\ptt SUC\_NOT\_0}}{16}
\indexentry{LESS\_IMP\_LESS\_EQ\_PRE@{\ptt LESS\_IMP\_LESS\_EQ\_PRE}}{17}
\indexentry{PRE\_ADD@{\ptt PRE\_ADD}}{17}
\indexentry{PRE\_K\_K@{\ptt PRE\_K\_K}}{17}
\indexentry{PRE\_LESS@{\ptt PRE\_LESS}}{17}
\indexentry{PRE\_LESS\_EQ@{\ptt PRE\_LESS\_EQ}}{17}
\indexentry{PRE\_MONO@{\ptt PRE\_MONO}}{17}
\indexentry{PRE\_MONO\_LESS\_EQ@{\ptt PRE\_MONO\_LESS\_EQ}}{17}
\indexentry{SUC\_LESS\_EQ\_PRE@{\ptt SUC\_LESS\_EQ\_PRE}}{17}
\indexentry{SUC\_LESS\_PRE@{\ptt SUC\_LESS\_PRE}}{17}
\indexentry{SUC\_PRE@{\ptt SUC\_PRE}}{17}
\indexentry{ADDL\_GREATER@{\ptt ADDL\_GREATER}}{17}
\indexentry{ADDL\_GREATER\_EQ@{\ptt ADDL\_GREATER\_EQ}}{17}
\indexentry{ADDR\_GREATER@{\ptt ADDR\_GREATER}}{17}
\indexentry{ADDR\_GREATER\_EQ@{\ptt ADDR\_GREATER\_EQ}}{18}
\indexentry{ADD\_EQ\_LESS\_EQ@{\ptt ADD\_EQ\_LESS\_EQ}}{18}
\indexentry{ADD\_EQ\_LESS\_IMP\_LESS@{\ptt ADD\_EQ\_LESS\_IMP\_LESS}}{18}
\indexentry{ADD\_GREATER\_EQ@{\ptt ADD\_GREATER\_EQ}}{18}
\indexentry{ADD\_MONO\_LESS@{\ptt ADD\_MONO\_LESS}}{18}
\indexentry{ADD\_SUC\_0@{\ptt ADD\_SUC\_0}}{18}
\indexentry{ADD\_SYM\_ASSOC@{\ptt ADD\_SYM\_ASSOC}}{18}
\indexentry{GREATER\_EQ\_SPLIT@{\ptt GREATER\_EQ\_SPLIT}}{18}
\indexentry{LESS\_ADD1@{\ptt LESS\_ADD1}}{18}
\indexentry{LESS\_ADD\_ASSOC@{\ptt LESS\_ADD\_ASSOC}}{18}
\indexentry{LESS\_EQ\_ADD1@{\ptt LESS\_EQ\_ADD1}}{18}
\indexentry{LESS\_EQ\_MONO\_ADD\_EQ0@{\ptt LESS\_EQ\_MONO\_ADD\_EQ0}}{18}
\indexentry{LESS\_EQ\_MONO\_ADD\_EQ1@{\ptt LESS\_EQ\_MONO\_ADD\_EQ1}}{18}
\indexentry{LESS\_EQ\_SPLIT@{\ptt LESS\_EQ\_SPLIT}}{18}
\indexentry{LESS\_LESS\_EQ@{\ptt LESS\_LESS\_EQ}}{18}
\indexentry{LESS\_LESS\_EQ\_MONO@{\ptt LESS\_LESS\_EQ\_MONO}}{19}
\indexentry{LESS\_LESS\_MONO@{\ptt LESS\_LESS\_MONO}}{19}
\indexentry{LESS\_TRANS\_ADD@{\ptt LESS\_TRANS\_ADD}}{19}
\indexentry{NOT\_1\_TWICE@{\ptt NOT\_1\_TWICE}}{19}
\indexentry{NOT\_ADD\_LESS@{\ptt NOT\_ADD\_LESS}}{19}
\indexentry{NOT\_LESS\_IMP\_LESS\_EQ\_ADD1@{\ptt NOT\_LESS\_IMP\_LESS\_EQ\_ADD1}}{19}
\indexentry{SUC\_LESS\_N\_LESS@{\ptt SUC\_LESS\_N\_LESS}}{19}
\indexentry{SUM\_LESS@{\ptt SUM\_LESS}}{19}
\indexentry{ADD\_EQ\_IMP\_SUB\_EQ@{\ptt ADD\_EQ\_IMP\_SUB\_EQ}}{19}
\indexentry{ADD\_LESS\_EQ\_SUB@{\ptt ADD\_LESS\_EQ\_SUB}}{19}
\indexentry{ADD\_SUB\_SYM@{\ptt ADD\_SUB\_SYM}}{19}
\indexentry{GREATER\_EQ\_SUB\_LESS\_TO\_ADD@{\ptt GREATER\_EQ\_SUB\_LESS\_TO\_ADD}}{19}
\indexentry{LESS\_EQ\_ADD\_SUB1@{\ptt LESS\_EQ\_ADD\_SUB1}}{19}
\indexentry{LESS\_EQ\_SUB\_1@{\ptt LESS\_EQ\_SUB\_1}}{19}
\indexentry{LESS\_EQ\_SUB\_ADD@{\ptt LESS\_EQ\_SUB\_ADD}}{20}
\indexentry{LESS\_PRE@{\ptt LESS\_PRE}}{20}
\indexentry{LESS\_SUB\_IMP\_INV@{\ptt LESS\_SUB\_IMP\_INV}}{20}
\indexentry{LESS\_SUB\_IMP\_SUM\_LESS@{\ptt LESS\_SUB\_IMP\_SUM\_LESS}}{20}
\indexentry{LESS\_SUB\_TO\_ADDL\_LESS@{\ptt LESS\_SUB\_TO\_ADDL\_LESS}}{20}
\indexentry{LESS\_SUB\_TO\_ADDR\_LESS@{\ptt LESS\_SUB\_TO\_ADDR\_LESS}}{20}
\indexentry{LESS\_TWICE\_IMP\_LESS\_SUB@{\ptt LESS\_TWICE\_IMP\_LESS\_SUB}}{20}
\indexentry{NOT\_0\_SUB@{\ptt NOT\_0\_SUB}}{20}
\indexentry{NOT\_LESS\_SUB@{\ptt NOT\_LESS\_SUB}}{20}
\indexentry{NOT\_SUB\_0@{\ptt NOT\_SUB\_0}}{20}
\indexentry{PRE\_LESS\_LESS\_SUC@{\ptt PRE\_LESS\_LESS\_SUC}}{20}
\indexentry{PRE\_SUB\_SUC@{\ptt PRE\_SUB\_SUC}}{20}
\indexentry{SMALLER\_SUM@{\ptt SMALLER\_SUM}}{20}
\indexentry{SUB\_1\_LESS@{\ptt SUB\_1\_LESS}}{20}
\indexentry{SUB\_1\_LESS\_EQ@{\ptt SUB\_1\_LESS\_EQ}}{20}
\indexentry{SUB\_ADD\_SELF@{\ptt SUB\_ADD\_SELF}}{20}
\indexentry{SUB\_BOTH\_SIDES@{\ptt SUB\_BOTH\_SIDES}}{21}
\indexentry{SUB\_EQ\_SUB\_ADD\_SUB@{\ptt SUB\_EQ\_SUB\_ADD\_SUB}}{21}
\indexentry{SUB\_GREATER\_0@{\ptt SUB\_GREATER\_0}}{21}
\indexentry{SUB\_GREATER\_EQ\_ADD@{\ptt SUB\_GREATER\_EQ\_ADD}}{21}
\indexentry{SUB\_LESS\_BOTH\_SIDES@{\ptt SUB\_LESS\_BOTH\_SIDES}}{21}
\indexentry{SUB\_LESS\_EQ\_SUB1@{\ptt SUB\_LESS\_EQ\_SUB1}}{21}
\indexentry{SUB\_LESS\_EQ\_SUB\_SUC@{\ptt SUB\_LESS\_EQ\_SUB\_SUC}}{21}
\indexentry{SUB\_LESS\_TO\_LESS\_ADDL@{\ptt SUB\_LESS\_TO\_LESS\_ADDL}}{21}
\indexentry{SUB\_LESS\_TO\_LESS\_ADDR@{\ptt SUB\_LESS\_TO\_LESS\_ADDR}}{21}
\indexentry{SUB\_LE\_ADD@{\ptt SUB\_LE\_ADD}}{21}
\indexentry{SUB\_PRE\_SUB\_1@{\ptt SUB\_PRE\_SUB\_1}}{21}
\indexentry{SUB\_SUB\_ID@{\ptt SUB\_SUB\_ID}}{21}
\indexentry{SUB\_SUC@{\ptt SUB\_SUC}}{21}
\indexentry{SUB\_SUC\_PRE\_SUB@{\ptt SUB\_SUC\_PRE\_SUB}}{21}
\indexentry{SUC\_SUB@{\ptt SUC\_SUB}}{21}
\indexentry{EXP1@{\ptt EXP1}}{22}
\indexentry{LESS\_MONO\_MULT1@{\ptt LESS\_MONO\_MULT1}}{22}
\indexentry{LESS\_MULT\_PLUS\_DIFF@{\ptt LESS\_MULT\_PLUS\_DIFF}}{22}
\indexentry{NOT\_MULT\_LESS\_0@{\ptt NOT\_MULT\_LESS\_0}}{22}
\indexentry{ONE\_LESS\_EQ\_TWO\_EXP@{\ptt ONE\_LESS\_EQ\_TWO\_EXP}}{22}
\indexentry{ONE\_LESS\_TWO\_EXP\_SUC@{\ptt ONE\_LESS\_TWO\_EXP\_SUC}}{22}
\indexentry{ZERO\_LESS\_TWO\_EXP@{\ptt ZERO\_LESS\_TWO\_EXP}}{22}
\indexentry{ADD\_DIV\_ADD\_DIV@{\ptt ADD\_DIV\_ADD\_DIV}}{22}
\indexentry{ADD\_DIV\_SUC\_DIV@{\ptt ADD\_DIV\_SUC\_DIV}}{22}
\indexentry{DIV\_DIV\_DIV\_MULT@{\ptt DIV\_DIV\_DIV\_MULT}}{22}
\indexentry{DIV\_ONE@{\ptt DIV\_ONE}}{22}
\indexentry{LESS\_DIV\_EQ\_ZERO@{\ptt LESS\_DIV\_EQ\_ZERO}}{22}
\indexentry{LESS\_EQ\_MONO\_DIV@{\ptt LESS\_EQ\_MONO\_DIV}}{22}
\indexentry{MOD\_MULT\_MOD@{\ptt MOD\_MULT\_MOD}}{23}
\indexentry{MULT\_DIV@{\ptt MULT\_DIV}}{23}
\indexentry{SUC\_DIV\_CASES@{\ptt SUC\_DIV\_CASES}}{23}
\indexentry{SUC\_DIV\_SELF@{\ptt SUC\_DIV\_SELF}}{23}
\indexentry{SUC\_MOD@{\ptt SUC\_MOD}}{23}
\indexentry{SUC\_MOD\_SELF@{\ptt SUC\_MOD\_SELF}}{23}
\indexentry{MAX\_0@{\ptt MAX\_0}}{23}
\indexentry{MAX\_DEF@{\ptt MAX\_DEF}}{23}
\indexentry{MAX\_REFL@{\ptt MAX\_REFL}}{23}
\indexentry{MAX\_SUC@{\ptt MAX\_SUC}}{23}
\indexentry{MAX\_SYM@{\ptt MAX\_SYM}}{23}
\indexentry{MIN\_0@{\ptt MIN\_0}}{23}
\indexentry{MIN\_DEF@{\ptt MIN\_DEF}}{23}
\indexentry{MIN\_REFL@{\ptt MIN\_REFL}}{23}
\indexentry{MIN\_SUC@{\ptt MIN\_SUC}}{24}
\indexentry{MIN\_SYM@{\ptt MIN\_SYM}}{24}
\indexentry{SUC\_MAX@{\ptt SUC\_MAX}}{24}
\indexentry{SUC\_MIN@{\ptt SUC\_MIN}}{24}
\indexentry{EVEN\_MULT@{\ptt EVEN\_MULT}}{24}
\indexentry{EVEN\_ODD\_0@{\ptt EVEN\_ODD\_0}}{24}
\indexentry{EVEN\_ODD\_PLUS\_CASES@{\ptt EVEN\_ODD\_PLUS\_CASES}}{24}
\indexentry{EVEN\_ODD\_SUC@{\ptt EVEN\_ODD\_SUC}}{24}
\indexentry{MULT\_EVEN@{\ptt MULT\_EVEN}}{24}
\indexentry{MULT\_ODD@{\ptt MULT\_ODD}}{24}
\indexentry{NOT\_EVEN\_ODD\_SUC\_EVEN\_ODD@{\ptt NOT\_EVEN\_ODD\_SUC\_EVEN\_ODD}}{24}
\indexentry{ODD\_MULT@{\ptt ODD\_MULT}}{24}
