\begin{theindex}

  \item {\ptt abs}, 21
  \item {\ptt ABS\_NEG\_LEMMA}, 55
  \item {\ptt ABS\_SUM}, 23
  \item {\ptt ACS}, 63
  \item {\ptt acs}, 63
  \item {\ptt ACS\_BOUNDS}, 63
  \item {\ptt ACS\_COS}, 63
  \item {\ptt ASN}, 63
  \item {\ptt asn}, 63
  \item {\ptt ASN\_BOUNDS}, 63
  \item {\ptt ASN\_SIN}, 63
  \item {\ptt ATN}, 63
  \item {\ptt atn}, 64
  \item {\ptt ATN\_BOUNDS}, 64
  \item {\ptt ATN\_TAN}, 64

  \indexspace

  \item {\ptt ball}, 40
  \item {\ptt BALL\_NEIGH}, 40
  \item {\ptt BALL\_OPEN}, 40
  \item {\ptt bounded}, 44

  \indexspace

  \item {\ptt cauchy}, 55
  \item {\ptt CHAIN\_LEMMA1}, 48
  \item {\ptt CHAIN\_LEMMA2}, 48
  \item {\ptt closed}, 40
  \item {\ptt CLOSED\_LIMPT}, 40
  \item {\ptt compl}, 40
  \item {\ptt COMPL\_MEM}, 40
  \item {\ptt CONT\_ADD}, 48
  \item {\ptt CONT\_ATTAINS}, 48
  \item {\ptt CONT\_ATTAINS2}, 48
  \item {\ptt CONT\_BOUNDED}, 49
  \item {\ptt CONT\_CONST}, 49
  \item {\ptt CONT\_DIV}, 49
  \item {\ptt CONT\_HASSUP}, 49
  \item {\ptt CONT\_INV}, 49
  \item {\ptt CONT\_MUL}, 49
  \item {\ptt CONT\_NEG}, 49
  \item {\ptt CONT\_SUB}, 49
  \item {\ptt contl}, 48
  \item {\ptt CONTL\_LIM}, 48
  \item {\ptt convergent}, 55
  \item {\ptt cos}, 64
  \item {\ptt COS\_0}, 64
  \item {\ptt COS\_2}, 64
  \item {\ptt COS\_ACS}, 64
  \item {\ptt COS\_ADD}, 64
  \item {\ptt COS\_BOUND}, 64
  \item {\ptt COS\_BOUNDS}, 64
  \item {\ptt COS\_CONVERGES}, 64
  \item {\ptt COS\_DOUBLE}, 65
  \item {\ptt COS\_FDIFF}, 65
  \item {\ptt COS\_ISZERO}, 65
  \item {\ptt COS\_NEG}, 65
  \item {\ptt COS\_NPI}, 65
  \item {\ptt COS\_PAIRED}, 65
  \item {\ptt COS\_PERIODIC}, 65
  \item {\ptt COS\_PERIODIC\_PI}, 65
  \item {\ptt COS\_PI}, 65
  \item {\ptt COS\_PI2}, 65
  \item {\ptt COS\_POS\_PI}, 65
  \item {\ptt COS\_POS\_PI2}, 65
  \item {\ptt COS\_SIN}, 66
  \item {\ptt COS\_TOTAL}, 66
  \item {\ptt COS\_ZERO}, 66
  \item {\ptt COS\_ZERO\_LEMMA}, 66
  \item {\ptt CUT\_BOUNDED}, 9
  \item {\ptt CUT\_DOWN}, 9
  \item {\ptt CUT\_ISACUT}, 9
  \item {\ptt CUT\_NEARTOP\_ADD}, 9
  \item {\ptt CUT\_NEARTOP\_MUL}, 9
  \item {\ptt CUT\_NONEMPTY}, 9
  \item {\ptt cut\_of\_hrat}, 9
  \item {\ptt CUT\_STRADDLE}, 9
  \item {\ptt CUT\_UBOUND}, 9
  \item {\ptt CUT\_UP}, 9

  \indexspace

  \item {\ptt DIFF\_ADD}, 49
  \item {\ptt DIFF\_CHAIN}, 49
  \item {\ptt DIFF\_CMUL}, 50
  \item {\ptt DIFF\_CONST}, 50
  \item {\ptt DIFF\_CONT}, 50
  \item {\ptt DIFF\_COS}, 66
  \item {\ptt DIFF\_DIV}, 50
  \item {\ptt DIFF\_EXP}, 66
  \item {\ptt DIFF\_INV}, 50
  \item {\ptt DIFF\_ISCONST}, 50
  \item {\ptt DIFF\_ISCONST\_ALL}, 50
  \item {\ptt DIFF\_ISCONST\_END}, 50
  \item {\ptt DIFF\_LCONST}, 50
  \item {\ptt DIFF\_LDEC}, 51
  \item {\ptt DIFF\_LINC}, 51
  \item {\ptt DIFF\_LMAX}, 51
  \item {\ptt DIFF\_LMIN}, 51
  \item {\ptt DIFF\_MUL}, 51
  \item {\ptt DIFF\_NEG}, 51
  \item {\ptt DIFF\_POW}, 51
  \item {\ptt DIFF\_SIN}, 66
  \item {\ptt DIFF\_SUB}, 51
  \item {\ptt DIFF\_SUM}, 51
  \item {\ptt DIFF\_TAN}, 66
  \item {\ptt DIFF\_UNIQ}, 51
  \item {\ptt DIFF\_X}, 52
  \item {\ptt DIFF\_XM1}, 52
  \item {\ptt differentiable}, 49
  \item {\ptt diffl}, 49
  \item {\ptt diffs}, 60
  \item {\ptt DIFFS\_EQUIV}, 60
  \item {\ptt DIFFS\_LEMMA}, 60
  \item {\ptt DIFFS\_LEMMA2}, 61
  \item {\ptt DIFFS\_NEG}, 61
  \item {\ptt dorder}, 44
  \item {\ptt DORDER\_LEMMA}, 44
  \item {\ptt DORDER\_NGE}, 44
  \item {\ptt DORDER\_TENDSTO}, 44

  \indexspace

  \item {\ptt EQUAL\_CUTS}, 10
  \item {\ptt exp}, 66
  \item {\ptt EXP\_0}, 66
  \item {\ptt EXP\_ADD}, 66
  \item {\ptt EXP\_ADD\_MUL}, 66
  \item {\ptt EXP\_CONVERGES}, 66
  \item {\ptt EXP\_FDIFF}, 67
  \item {\ptt EXP\_INJ}, 67
  \item {\ptt EXP\_LE\_X}, 67
  \item {\ptt EXP\_LN}, 67
  \item {\ptt EXP\_LT\_1}, 67
  \item {\ptt EXP\_MONO\_IMP}, 67
  \item {\ptt EXP\_MONO\_LE}, 67
  \item {\ptt EXP\_MONO\_LT}, 67
  \item {\ptt EXP\_N}, 67
  \item {\ptt EXP\_NEG}, 67
  \item {\ptt EXP\_NEG\_MUL}, 67
  \item {\ptt EXP\_NEG\_MUL2}, 67
  \item {\ptt EXP\_NZ}, 67
  \item {\ptt EXP\_POS\_LE}, 67
  \item {\ptt EXP\_POS\_LT}, 67
  \item {\ptt EXP\_SUB}, 67
  \item {\ptt EXP\_TOTAL}, 68
  \item {\ptt EXP\_TOTAL\_LEMMA}, 68

  \indexspace

  \item {\ptt GP}, 55
  \item {\ptt GP\_FINITE}, 55

  \indexspace

  \item {\ptt hrat\_1}, 5
  \item {\ptt hrat\_add}, 5
  \item {\ptt HRAT\_ADD\_ASSOC}, 5
  \item {\ptt HRAT\_ADD\_SYM}, 5
  \item {\ptt HRAT\_ADD\_TOTAL}, 5
  \item {\ptt HRAT\_ARCH}, 5
  \item {\ptt HRAT\_DOWN}, 10
  \item {\ptt HRAT\_DOWN2}, 10
  \item {\ptt HRAT\_EQ\_LADD}, 10
  \item {\ptt HRAT\_EQ\_LMUL}, 10
  \item {\ptt HRAT\_GT\_L1}, 10
  \item {\ptt HRAT\_GT\_LMUL1}, 10
  \item {\ptt hrat\_inv}, 6
  \item {\ptt HRAT\_INV\_MUL}, 10
  \item {\ptt HRAT\_LDISTRIB}, 6
  \item {\ptt hrat\_lt}, 10
  \item {\ptt HRAT\_LT\_ADD2}, 10
  \item {\ptt HRAT\_LT\_ADDL}, 10
  \item {\ptt HRAT\_LT\_ADDR}, 10
  \item {\ptt HRAT\_LT\_ANTISYM}, 10
  \item {\ptt HRAT\_LT\_GT}, 10
  \item {\ptt HRAT\_LT\_L1}, 10
  \item {\ptt HRAT\_LT\_LADD}, 11
  \item {\ptt HRAT\_LT\_LMUL}, 11
  \item {\ptt HRAT\_LT\_LMUL1}, 11
  \item {\ptt HRAT\_LT\_MUL2}, 11
  \item {\ptt HRAT\_LT\_NE}, 11
  \item {\ptt HRAT\_LT\_R1}, 11
  \item {\ptt HRAT\_LT\_RADD}, 11
  \item {\ptt HRAT\_LT\_REFL}, 11
  \item {\ptt HRAT\_LT\_RMUL}, 11
  \item {\ptt HRAT\_LT\_RMUL1}, 11
  \item {\ptt HRAT\_LT\_TOTAL}, 11
  \item {\ptt HRAT\_LT\_TRANS}, 11
  \item {\ptt HRAT\_MEAN}, 11
  \item {\ptt hrat\_mul}, 6
  \item {\ptt HRAT\_MUL\_ASSOC}, 6
  \item {\ptt HRAT\_MUL\_LID}, 6
  \item {\ptt HRAT\_MUL\_LINV}, 6
  \item {\ptt HRAT\_MUL\_RID}, 11
  \item {\ptt HRAT\_MUL\_RINV}, 11
  \item {\ptt HRAT\_MUL\_SYM}, 6
  \item {\ptt HRAT\_NOZERO}, 6
  \item {\ptt HRAT\_RDISTRIB}, 12
  \item {\ptt HRAT\_SUCINT}, 6
  \item {\ptt hrat\_sucint}, 6
  \item {\ptt hrat\_TY\_DEF}, 6
  \item {\ptt hrat\_tybij}, 6
  \item {\ptt HRAT\_UP}, 12
  \item {\ptt hreal\_1}, 12
  \item {\ptt hreal\_add}, 12
  \item {\ptt HREAL\_ADD\_ASSOC}, 12
  \item {\ptt HREAL\_ADD\_ISACUT}, 12
  \item {\ptt HREAL\_ADD\_SYM}, 12
  \item {\ptt HREAL\_ADD\_TOTAL}, 12
  \item {\ptt HREAL\_EQ\_ADDL}, 14
  \item {\ptt HREAL\_EQ\_ADDR}, 14
  \item {\ptt HREAL\_EQ\_LADD}, 14
  \item {\ptt hreal\_inv}, 12
  \item {\ptt HREAL\_INV\_ISACUT}, 12
  \item {\ptt HREAL\_LDISTRIB}, 12
  \item {\ptt HREAL\_LT}, 12
  \item {\ptt hreal\_lt}, 13
  \item {\ptt HREAL\_LT\_ADD2}, 14
  \item {\ptt HREAL\_LT\_ADDL}, 14
  \item {\ptt HREAL\_LT\_ADDR}, 15
  \item {\ptt HREAL\_LT\_GT}, 15
  \item {\ptt HREAL\_LT\_LADD}, 15
  \item {\ptt HREAL\_LT\_LEMMA}, 13
  \item {\ptt HREAL\_LT\_NE}, 15
  \item {\ptt HREAL\_LT\_REFL}, 15
  \item {\ptt HREAL\_LT\_TOTAL}, 13
  \item {\ptt hreal\_mul}, 13
  \item {\ptt HREAL\_MUL\_ASSOC}, 13
  \item {\ptt HREAL\_MUL\_ISACUT}, 13
  \item {\ptt HREAL\_MUL\_LID}, 13
  \item {\ptt HREAL\_MUL\_LINV}, 13
  \item {\ptt HREAL\_MUL\_SYM}, 13
  \item {\ptt HREAL\_NOZERO}, 13
  \item {\ptt hreal\_of\_real}, 15
  \item {\ptt hreal\_of\_treal}, 15
  \item {\ptt HREAL\_RDISTRIB}, 15
  \item {\ptt hreal\_sub}, 13
  \item {\ptt HREAL\_SUB\_ADD}, 13
  \item {\ptt HREAL\_SUB\_ISACUT}, 13
  \item {\ptt HREAL\_SUP}, 13
  \item {\ptt hreal\_sup}, 14
  \item {\ptt HREAL\_SUP\_ISACUT}, 14
  \item {\ptt hreal\_TY\_DEF}, 14
  \item {\ptt hreal\_tybij}, 14

  \indexspace

  \item {\ptt intersect\_def}, 40
  \item {\ptt INTERVAL\_LEMMA}, 52
  \item {\ptt isacut}, 14
  \item {\ptt ISACUT\_HRAT}, 14
  \item {\ptt ismet}, 40
  \item {\ptt ISMET\_R1}, 40
  \item {\ptt istopology}, 40
  \item {\ptt IVT}, 52
  \item {\ptt IVT2}, 52
  \item {\ptt IVT\_SUPLEMMA}, 52
  \item {\ptt IVT\_SUPLEMMA2}, 52

  \indexspace

  \item {\ptt LIM}, 53
  \item {\ptt lim}, 55
  \item {\ptt LIM\_ADD}, 53
  \item {\ptt LIM\_BOUNDED}, 53
  \item {\ptt LIM\_CONST}, 53
  \item {\ptt LIM\_DIV}, 53
  \item {\ptt LIM\_EQUAL}, 53
  \item {\ptt LIM\_INV}, 53
  \item {\ptt LIM\_MUL}, 53
  \item {\ptt LIM\_NEG}, 53
  \item {\ptt LIM\_NULL}, 53
  \item {\ptt LIM\_NULL\_MUL}, 54
  \item {\ptt LIM\_SUB}, 54
  \item {\ptt LIM\_TENDS}, 44
  \item {\ptt LIM\_TENDS2}, 45
  \item {\ptt LIM\_TRANSFORM}, 54
  \item {\ptt LIM\_UNIQ}, 54
  \item {\ptt LIM\_X}, 54
  \item {\ptt limpt}, 41
  \item {\ptt ln}, 68
  \item {\ptt LN\_1}, 68
  \item {\ptt LN\_DIV}, 68
  \item {\ptt LN\_EXP}, 68
  \item {\ptt LN\_INJ}, 68
  \item {\ptt LN\_INV}, 68
  \item {\ptt LN\_MONO\_LE}, 68
  \item {\ptt LN\_MONO\_LT}, 68
  \item {\ptt LN\_MUL}, 68
  \item {\ptt LN\_POW}, 68

  \indexspace

  \item {\ptt MAX\_LEMMA}, 55
  \item {\ptt METRIC\_ISMET}, 41
  \item {\ptt METRIC\_NZ}, 41
  \item {\ptt METRIC\_POS}, 41
  \item {\ptt METRIC\_SAME}, 41
  \item {\ptt METRIC\_SYM}, 41
  \item {\ptt METRIC\_TRIANGLE}, 41
  \item {\ptt metric\_TY\_DEF}, 41
  \item {\ptt metric\_tybij}, 41
  \item {\ptt METRIC\_ZERO}, 41
  \item {\ptt mono}, 55
  \item {\ptt MONO\_SUC}, 55
  \item {\ptt mr1}, 41
  \item {\ptt MR1\_ADD}, 41
  \item {\ptt MR1\_ADD\_LT}, 41
  \item {\ptt MR1\_ADD\_POS}, 41
  \item {\ptt MR1\_BETWEEN1}, 41
  \item {\ptt MR1\_BOUNDED}, 45
  \item {\ptt MR1\_DEF}, 42
  \item {\ptt MR1\_LIMPT}, 42
  \item {\ptt MR1\_SUB}, 42
  \item {\ptt MR1\_SUB\_LE}, 42
  \item {\ptt MR1\_SUB\_LT}, 42
  \item {\ptt mtop}, 42
  \item {\ptt mtop\_istopology}, 42
  \item {\ptt MTOP\_LIMPT}, 42
  \item {\ptt MTOP\_OPEN}, 42
  \item {\ptt MTOP\_TENDS}, 45
  \item {\ptt MTOP\_TENDS\_UNIQ}, 45
  \item {\ptt MVT}, 54
  \item {\ptt MVT\_LEMMA}, 54

  \indexspace

  \item {\ptt neigh}, 42
  \item {\ptt NET\_ABS}, 45
  \item {\ptt NET\_ADD}, 45
  \item {\ptt NET\_CONV\_BOUNDED}, 45
  \item {\ptt NET\_CONV\_IBOUNDED}, 46
  \item {\ptt NET\_CONV\_NZ}, 46
  \item {\ptt NET\_DIV}, 46
  \item {\ptt NET\_INV}, 46
  \item {\ptt NET\_LE}, 46
  \item {\ptt NET\_MUL}, 46
  \item {\ptt NET\_NEG}, 47
  \item {\ptt NET\_NULL}, 47
  \item {\ptt NET\_NULL\_ADD}, 47
  \item {\ptt NET\_NULL\_CMUL}, 47
  \item {\ptt NET\_NULL\_MUL}, 47
  \item {\ptt NET\_SUB}, 47
  \item {\ptt null}, 42

  \indexspace

  \item {\ptt OPEN\_NEIGH}, 42
  \item {\ptt OPEN\_OWN\_NEIGH}, 42
  \item {\ptt OPEN\_SUBOPEN}, 43
  \item {\ptt OPEN\_UNOPEN}, 43

  \indexspace

  \item {\ptt pi}, 68
  \item {\ptt PI2}, 68
  \item {\ptt PI2\_BOUNDS}, 68
  \item {\ptt PI\_POS}, 69
  \item {\ptt pow}, 23
  \item {\ptt POW\_0}, 23
  \item {\ptt POW\_1}, 23
  \item {\ptt POW\_2}, 23
  \item {\ptt POW\_2\_LE1}, 23
  \item {\ptt POW\_2\_LT}, 23
  \item {\ptt POW\_ABS}, 23
  \item {\ptt POW\_ADD}, 23
  \item {\ptt POW\_INV}, 23
  \item {\ptt POW\_LE}, 23
  \item {\ptt POW\_M1}, 23
  \item {\ptt POW\_MINUS1}, 23
  \item {\ptt POW\_MUL}, 23
  \item {\ptt POW\_NZ}, 24
  \item {\ptt POW\_PLUS1}, 24
  \item {\ptt POW\_POS}, 24
  \item {\ptt POW\_POS\_LT}, 24
  \item {\ptt POWDIFF}, 61
  \item {\ptt POWDIFF\_LEMMA}, 61
  \item {\ptt POWREV}, 61
  \item {\ptt POWSER\_INSIDE}, 61
  \item {\ptt POWSER\_INSIDEA}, 61

  \indexspace

  \item {\ptt r0}, 15
  \item {\ptt r1}, 15
  \item {\ptt REAL}, 24
  \item {\ptt REAL\_0}, 24
  \item {\ptt REAL\_1}, 24
  \item {\ptt REAL\_10}, 15, 24
  \item {\ptt REAL\_ABS\_0}, 21
  \item {\ptt REAL\_ABS\_1}, 21
  \item {\ptt REAL\_ABS\_ABS}, 21
  \item {\ptt REAL\_ABS\_BETWEEN}, 21
  \item {\ptt REAL\_ABS\_BETWEEN1}, 21
  \item {\ptt REAL\_ABS\_BETWEEN2}, 21
  \item {\ptt REAL\_ABS\_BOUND}, 21
  \item {\ptt REAL\_ABS\_BOUNDS}, 21
  \item {\ptt REAL\_ABS\_CASES}, 21
  \item {\ptt REAL\_ABS\_CIRCLE}, 21
  \item {\ptt REAL\_ABS\_DIV}, 22
  \item {\ptt REAL\_ABS\_INV}, 22
  \item {\ptt REAL\_ABS\_LE}, 22
  \item {\ptt REAL\_ABS\_LT\_MUL2}, 22
  \item {\ptt REAL\_ABS\_MUL}, 22
  \item {\ptt REAL\_ABS\_N}, 22
  \item {\ptt REAL\_ABS\_NEG}, 22
  \item {\ptt REAL\_ABS\_NZ}, 22
  \item {\ptt REAL\_ABS\_POS}, 22
  \item {\ptt REAL\_ABS\_POW2}, 22
  \item {\ptt REAL\_ABS\_REFL}, 22
  \item {\ptt REAL\_ABS\_SIGN}, 22
  \item {\ptt REAL\_ABS\_SIGN2}, 22
  \item {\ptt REAL\_ABS\_STILLNZ}, 22
  \item {\ptt REAL\_ABS\_SUB}, 22
  \item {\ptt REAL\_ABS\_SUB\_ABS}, 22
  \item {\ptt REAL\_ABS\_TRIANGLE}, 23
  \item {\ptt REAL\_ABS\_ZERO}, 23
  \item {\ptt REAL\_ADD}, 24
  \item {\ptt real\_add}, 15
  \item {\ptt REAL\_ADD2\_SUB2}, 24
  \item {\ptt REAL\_ADD\_ASSOC}, 15, 24
  \item {\ptt REAL\_ADD\_LID}, 15, 24
  \item {\ptt REAL\_ADD\_LID\_UNIQ}, 24
  \item {\ptt REAL\_ADD\_LINV}, 16, 24
  \item {\ptt REAL\_ADD\_RID}, 24
  \item {\ptt REAL\_ADD\_RID\_UNIQ}, 24
  \item {\ptt REAL\_ADD\_RINV}, 25
  \item {\ptt REAL\_ADD\_SUB}, 25
  \item {\ptt REAL\_ADD\_SUB2}, 25
  \item {\ptt REAL\_ADD\_SYM}, 16, 25
  \item {\ptt REAL\_ARCH}, 25
  \item {\ptt REAL\_ARCH\_LEAST}, 25
  \item {\ptt REAL\_DIFFSQ}, 25
  \item {\ptt real\_div}, 25
  \item {\ptt REAL\_DIV\_LMUL}, 25
  \item {\ptt REAL\_DIV\_LZERO}, 25
  \item {\ptt REAL\_DIV\_MUL2}, 25
  \item {\ptt REAL\_DIV\_REFL}, 25
  \item {\ptt REAL\_DIV\_RMUL}, 25
  \item {\ptt REAL\_DOUBLE}, 25
  \item {\ptt REAL\_DOWN}, 25
  \item {\ptt REAL\_DOWN2}, 26
  \item {\ptt REAL\_ENTIRE}, 26
  \item {\ptt REAL\_EQ\_IMP\_LE}, 26
  \item {\ptt REAL\_EQ\_LADD}, 26
  \item {\ptt REAL\_EQ\_LMUL}, 26
  \item {\ptt REAL\_EQ\_LMUL2}, 26
  \item {\ptt REAL\_EQ\_LMUL\_IMP}, 26
  \item {\ptt REAL\_EQ\_NEG}, 26
  \item {\ptt REAL\_EQ\_RADD}, 26
  \item {\ptt REAL\_EQ\_RMUL}, 26
  \item {\ptt REAL\_EQ\_RMUL\_IMP}, 26
  \item {\ptt REAL\_EQ\_SUB\_LADD}, 26
  \item {\ptt REAL\_EQ\_SUB\_RADD}, 26
  \item {\ptt REAL\_FACT\_NZ}, 26
  \item {\ptt real\_ge}, 26
  \item {\ptt real\_gt}, 26
  \item {\ptt REAL\_HALF\_DOUBLE}, 27
  \item {\ptt REAL\_INJ}, 27
  \item {\ptt real\_inv}, 16
  \item {\ptt REAL\_INV1}, 27
  \item {\ptt REAL\_INV\_1OVER}, 27
  \item {\ptt REAL\_INV\_LT1}, 27
  \item {\ptt REAL\_INV\_MUL}, 27
  \item {\ptt REAL\_INV\_NZ}, 27
  \item {\ptt REAL\_INV\_POS}, 27
  \item {\ptt REAL\_INVINV}, 27
  \item {\ptt REAL\_ISO\_EQ}, 16
  \item {\ptt REAL\_LDISTRIB}, 16, 27
  \item {\ptt REAL\_LE}, 27
  \item {\ptt real\_le}, 27
  \item {\ptt REAL\_LE1\_POW2}, 27
  \item {\ptt REAL\_LE\_01}, 28
  \item {\ptt REAL\_LE\_ADD}, 28
  \item {\ptt REAL\_LE\_ADD2}, 28
  \item {\ptt REAL\_LE\_ADDL}, 28
  \item {\ptt REAL\_LE\_ADDR}, 28
  \item {\ptt REAL\_LE\_ANTISYM}, 28
  \item {\ptt REAL\_LE\_DOUBLE}, 28
  \item {\ptt REAL\_LE\_LADD}, 28
  \item {\ptt REAL\_LE\_LDIV}, 28
  \item {\ptt REAL\_LE\_LMUL}, 28
  \item {\ptt REAL\_LE\_LMUL\_IMP}, 28
  \item {\ptt REAL\_LE\_LT}, 28
  \item {\ptt REAL\_LE\_MUL}, 28
  \item {\ptt REAL\_LE\_MUL2}, 29
  \item {\ptt REAL\_LE\_NEG}, 29
  \item {\ptt REAL\_LE\_NEGL}, 29
  \item {\ptt REAL\_LE\_NEGR}, 29
  \item {\ptt REAL\_LE\_NEGTOTAL}, 29
  \item {\ptt REAL\_LE\_POW2}, 29
  \item {\ptt REAL\_LE\_RADD}, 29
  \item {\ptt REAL\_LE\_RDIV}, 29
  \item {\ptt REAL\_LE\_REFL}, 29
  \item {\ptt REAL\_LE\_RMUL}, 29
  \item {\ptt REAL\_LE\_RMUL\_IMP}, 29
  \item {\ptt REAL\_LE\_SQUARE}, 29
  \item {\ptt REAL\_LE\_SUB\_LADD}, 29
  \item {\ptt REAL\_LE\_SUB\_RADD}, 29
  \item {\ptt REAL\_LE\_TOTAL}, 29
  \item {\ptt REAL\_LE\_TRANS}, 30
  \item {\ptt REAL\_LET\_ADD}, 27
  \item {\ptt REAL\_LET\_ADD2}, 27
  \item {\ptt REAL\_LET\_ANTISYM}, 27
  \item {\ptt REAL\_LET\_TOTAL}, 28
  \item {\ptt REAL\_LET\_TRANS}, 28
  \item {\ptt REAL\_LINV\_UNIQ}, 30
  \item {\ptt REAL\_LNEG\_UNIQ}, 30
  \item {\ptt REAL\_LT}, 30
  \item {\ptt real\_lt}, 16
  \item {\ptt REAL\_LT1\_POW2}, 30
  \item {\ptt REAL\_LT\_01}, 30
  \item {\ptt REAL\_LT\_1}, 30
  \item {\ptt REAL\_LT\_ADD}, 30
  \item {\ptt REAL\_LT\_ADD1}, 30
  \item {\ptt REAL\_LT\_ADD2}, 30
  \item {\ptt REAL\_LT\_ADD\_SUB}, 31
  \item {\ptt REAL\_LT\_ADDL}, 30
  \item {\ptt REAL\_LT\_ADDNEG}, 31
  \item {\ptt REAL\_LT\_ADDNEG2}, 31
  \item {\ptt REAL\_LT\_ADDR}, 31
  \item {\ptt REAL\_LT\_ANTISYM}, 31
  \item {\ptt REAL\_LT\_FRACTION}, 31
  \item {\ptt REAL\_LT\_FRACTION\_0}, 31
  \item {\ptt REAL\_LT\_GT}, 31
  \item {\ptt REAL\_LT\_HALF1}, 31
  \item {\ptt REAL\_LT\_HALF2}, 31
  \item {\ptt REAL\_LT\_IADD}, 16, 31
  \item {\ptt REAL\_LT\_IMP\_LE}, 31
  \item {\ptt REAL\_LT\_IMP\_NE}, 31
  \item {\ptt REAL\_LT\_INV}, 31
  \item {\ptt REAL\_LT\_LADD}, 31
  \item {\ptt REAL\_LT\_LE}, 31
  \item {\ptt REAL\_LT\_LMUL}, 32
  \item {\ptt REAL\_LT\_LMUL\_0}, 32
  \item {\ptt REAL\_LT\_LMUL\_IMP}, 32
  \item {\ptt REAL\_LT\_MUL}, 16, 32
  \item {\ptt REAL\_LT\_MUL2}, 32
  \item {\ptt REAL\_LT\_MULTIPLE}, 32
  \item {\ptt REAL\_LT\_NEG}, 32
  \item {\ptt REAL\_LT\_NEGTOTAL}, 32
  \item {\ptt REAL\_LT\_NZ}, 32
  \item {\ptt REAL\_LT\_RADD}, 32
  \item {\ptt REAL\_LT\_RDIV}, 32
  \item {\ptt REAL\_LT\_RDIV\_0}, 32
  \item {\ptt REAL\_LT\_REFL}, 16, 32
  \item {\ptt REAL\_LT\_RMUL}, 32
  \item {\ptt REAL\_LT\_RMUL\_0}, 32
  \item {\ptt REAL\_LT\_RMUL\_IMP}, 33
  \item {\ptt REAL\_LT\_SUB\_LADD}, 33
  \item {\ptt REAL\_LT\_SUB\_RADD}, 33
  \item {\ptt REAL\_LT\_TOTAL}, 16, 33
  \item {\ptt REAL\_LT\_TRANS}, 16, 33
  \item {\ptt REAL\_LTE\_ADD}, 30
  \item {\ptt REAL\_LTE\_ADD2}, 30
  \item {\ptt REAL\_LTE\_ANTSYM}, 30
  \item {\ptt REAL\_LTE\_TOTAL}, 30
  \item {\ptt REAL\_LTE\_TRANS}, 30
  \item {\ptt REAL\_MEAN}, 33
  \item {\ptt REAL\_MUL}, 33
  \item {\ptt real\_mul}, 16
  \item {\ptt REAL\_MUL\_ASSOC}, 16, 33
  \item {\ptt REAL\_MUL\_LID}, 16, 33
  \item {\ptt REAL\_MUL\_LINV}, 17, 33
  \item {\ptt REAL\_MUL\_LZERO}, 33
  \item {\ptt REAL\_MUL\_RID}, 33
  \item {\ptt REAL\_MUL\_RINV}, 33
  \item {\ptt REAL\_MUL\_RZERO}, 33
  \item {\ptt REAL\_MUL\_SYM}, 17, 33
  \item {\ptt real\_neg}, 17
  \item {\ptt REAL\_NEG\_0}, 34
  \item {\ptt REAL\_NEG\_ADD}, 34
  \item {\ptt REAL\_NEG\_EQ}, 34
  \item {\ptt REAL\_NEG\_EQ0}, 34
  \item {\ptt REAL\_NEG\_GE0}, 34
  \item {\ptt REAL\_NEG\_GT0}, 34
  \item {\ptt REAL\_NEG\_INV}, 34
  \item {\ptt REAL\_NEG\_LE0}, 34
  \item {\ptt REAL\_NEG\_LMUL}, 34
  \item {\ptt REAL\_NEG\_LT0}, 34
  \item {\ptt REAL\_NEG\_MINUS1}, 34
  \item {\ptt REAL\_NEG\_MUL2}, 34
  \item {\ptt REAL\_NEG\_RMUL}, 34
  \item {\ptt REAL\_NEG\_SUB}, 34
  \item {\ptt REAL\_NEGNEG}, 33
  \item {\ptt REAL\_NOT\_LE}, 34
  \item {\ptt REAL\_NOT\_LT}, 34
  \item {\ptt REAL\_NZ\_IMP\_LT}, 35
  \item {\ptt real\_of\_hreal}, 17
  \item {\ptt real\_of\_num}, 35
  \item {\ptt REAL\_OVER1}, 35
  \item {\ptt REAL\_POASQ}, 35
  \item {\ptt REAL\_POS}, 17, 35
  \item {\ptt REAL\_POS\_NZ}, 35
  \item {\ptt REAL\_POW2\_ABS}, 35
  \item {\ptt REAL\_RDISTRIB}, 35
  \item {\ptt REAL\_RINV\_UNIQ}, 35
  \item {\ptt REAL\_RNEG\_UNIQ}, 35
  \item {\ptt real\_sub}, 35
  \item {\ptt REAL\_SUB\_0}, 35
  \item {\ptt REAL\_SUB\_ABS}, 35
  \item {\ptt REAL\_SUB\_ADD}, 35
  \item {\ptt REAL\_SUB\_ADD2}, 35
  \item {\ptt REAL\_SUB\_INV2}, 36
  \item {\ptt REAL\_SUB\_LDISTRIB}, 36
  \item {\ptt REAL\_SUB\_LE}, 36
  \item {\ptt REAL\_SUB\_LNEG}, 36
  \item {\ptt REAL\_SUB\_LT}, 36
  \item {\ptt REAL\_SUB\_LZERO}, 36
  \item {\ptt REAL\_SUB\_NEG2}, 36
  \item {\ptt REAL\_SUB\_RDISTRIB}, 36
  \item {\ptt REAL\_SUB\_REFL}, 36
  \item {\ptt REAL\_SUB\_RNEG}, 36
  \item {\ptt REAL\_SUB\_RZERO}, 36
  \item {\ptt REAL\_SUB\_SUB}, 36
  \item {\ptt REAL\_SUB\_SUB2}, 36
  \item {\ptt REAL\_SUB\_TRIANGLE}, 36
  \item {\ptt REAL\_SUMSQ}, 36
  \item {\ptt REAL\_SUP}, 37
  \item {\ptt REAL\_SUP\_ALLPOS}, 17, 37
  \item {\ptt REAL\_SUP\_EXISTS}, 37
  \item {\ptt REAL\_SUP\_LE}, 37
  \item {\ptt REAL\_SUP\_SOMEPOS}, 37
  \item {\ptt REAL\_SUP\_UBOUND}, 37
  \item {\ptt REAL\_SUP\_UBOUND\_LE}, 37
  \item {\ptt real\_TY\_DEF}, 17
  \item {\ptt real\_tybij}, 17
  \item {\ptt ROLLE}, 54
  \item {\ptt root}, 69
  \item {\ptt ROOT\_0}, 69
  \item {\ptt ROOT\_1}, 69
  \item {\ptt ROOT\_LN}, 69
  \item {\ptt ROOT\_LT\_LEMMA}, 69
  \item {\ptt ROOT\_POW\_POS}, 69

  \indexspace

  \item {\ptt SEQ}, 55
  \item {\ptt SEQ\_ABS}, 56
  \item {\ptt SEQ\_ABS\_IMP}, 56
  \item {\ptt SEQ\_ADD}, 56
  \item {\ptt SEQ\_BCONV}, 56
  \item {\ptt SEQ\_BOUNDED}, 56
  \item {\ptt SEQ\_CAUCHY}, 56
  \item {\ptt SEQ\_CBOUNDED}, 56
  \item {\ptt SEQ\_CONST}, 56
  \item {\ptt SEQ\_DIRECT}, 56
  \item {\ptt SEQ\_DIV}, 56
  \item {\ptt SEQ\_ICONV}, 56
  \item {\ptt SEQ\_INV}, 56
  \item {\ptt SEQ\_INV0}, 56
  \item {\ptt SEQ\_LE}, 57
  \item {\ptt SEQ\_LIM}, 57
  \item {\ptt SEQ\_MONOSUB}, 57
  \item {\ptt SEQ\_MUL}, 57
  \item {\ptt SEQ\_NEG}, 57
  \item {\ptt SEQ\_NEG\_BOUNDED}, 57
  \item {\ptt SEQ\_NEG\_CONV}, 57
  \item {\ptt SEQ\_POWER}, 57
  \item {\ptt SEQ\_POWER\_ABS}, 57
  \item {\ptt SEQ\_SBOUNDED}, 57
  \item {\ptt SEQ\_SUB}, 57
  \item {\ptt SEQ\_SUBLE}, 57
  \item {\ptt SEQ\_SUC}, 57
  \item {\ptt SEQ\_TENDS}, 47
  \item {\ptt SEQ\_UNIQ}, 57
  \item {\ptt SER\_0}, 58
  \item {\ptt SER\_ABS}, 58
  \item {\ptt SER\_ACONV}, 58
  \item {\ptt SER\_ADD}, 58
  \item {\ptt SER\_CAUCHY}, 58
  \item {\ptt SER\_CDIV}, 58
  \item {\ptt SER\_CMUL}, 58
  \item {\ptt SER\_COMPAR}, 58
  \item {\ptt SER\_COMPARA}, 58
  \item {\ptt SER\_GROUP}, 58
  \item {\ptt SER\_LE}, 58
  \item {\ptt SER\_LE2}, 59
  \item {\ptt SER\_NEG}, 59
  \item {\ptt SER\_OFFSET}, 59
  \item {\ptt SER\_PAIR}, 59
  \item {\ptt SER\_POS\_LE}, 59
  \item {\ptt SER\_POS\_LT}, 59
  \item {\ptt SER\_POS\_LT\_PAIR}, 59
  \item {\ptt SER\_RATIO}, 59
  \item {\ptt SER\_SUB}, 59
  \item {\ptt SER\_ZERO}, 59
  \item {\ptt SETOK\_LE\_LT}, 37
  \item {\ptt sin}, 69
  \item {\ptt SIN\_0}, 69
  \item {\ptt SIN\_ADD}, 69
  \item {\ptt SIN\_ASN}, 69
  \item {\ptt SIN\_BOUND}, 69
  \item {\ptt SIN\_BOUNDS}, 69
  \item {\ptt SIN\_CIRCLE}, 70
  \item {\ptt SIN\_CONVERGES}, 70
  \item {\ptt SIN\_COS}, 70
  \item {\ptt SIN\_COS\_ADD}, 70
  \item {\ptt SIN\_COS\_NEG}, 70
  \item {\ptt SIN\_DOUBLE}, 70
  \item {\ptt SIN\_FDIFF}, 70
  \item {\ptt SIN\_NEG}, 70
  \item {\ptt SIN\_NEGLEMMA}, 71
  \item {\ptt SIN\_NPI}, 71
  \item {\ptt SIN\_PAIRED}, 71
  \item {\ptt SIN\_PERIODIC}, 71
  \item {\ptt SIN\_PERIODIC\_PI}, 71
  \item {\ptt SIN\_PI}, 71
  \item {\ptt SIN\_PI2}, 71
  \item {\ptt SIN\_POS}, 71
  \item {\ptt SIN\_POS\_PI}, 71
  \item {\ptt SIN\_POS\_PI2}, 71
  \item {\ptt SIN\_TOTAL}, 72
  \item {\ptt SIN\_ZERO}, 72
  \item {\ptt SIN\_ZERO\_LEMMA}, 72
  \item {\ptt sqrt}, 72
  \item {\ptt SQRT\_0}, 72
  \item {\ptt SQRT\_1}, 72
  \item {\ptt SQRT\_POW2}, 72
  \item {\ptt subseq}, 60
  \item {\ptt SUBSEQ\_SUC}, 60
  \item {\ptt subset}, 43
  \item {\ptt SUBSET\_ANTISYM}, 43
  \item {\ptt SUBSET\_REFL}, 43
  \item {\ptt SUBSET\_TRANS}, 43
  \item {\ptt Sum}, 37
  \item {\ptt sum}, 37
  \item {\ptt SUM\_0}, 37
  \item {\ptt SUM\_1}, 38
  \item {\ptt SUM\_2}, 38
  \item {\ptt SUM\_ABS}, 38
  \item {\ptt SUM\_ABS\_LE}, 38
  \item {\ptt SUM\_ADD}, 38
  \item {\ptt SUM\_BOUND}, 38
  \item {\ptt SUM\_CMUL}, 38
  \item {\ptt Sum\_DEF}, 38
  \item {\ptt SUM\_DIFF}, 38
  \item {\ptt SUM\_EQ}, 38
  \item {\ptt SUM\_EQ\_GEN}, 38
  \item {\ptt SUM\_GROUP}, 38
  \item {\ptt SUM\_LE}, 38
  \item {\ptt SUM\_NSUB}, 38
  \item {\ptt SUM\_OFFSET}, 39
  \item {\ptt SUM\_PERMUTE\_0}, 39
  \item {\ptt SUM\_POS}, 39
  \item {\ptt SUM\_POS\_GEN}, 39
  \item {\ptt SUM\_REINDEX}, 39
  \item {\ptt SUM\_SUBST}, 39
  \item {\ptt SUM\_SUMMABLE}, 60
  \item {\ptt SUM\_TWO}, 39
  \item {\ptt SUM\_UNIQ}, 60
  \item {\ptt SUM\_ZERO}, 39
  \item {\ptt suminf}, 60
  \item {\ptt summable}, 60
  \item {\ptt SUMMABLE\_SUM}, 60
  \item {\ptt sums}, 60
  \item {\ptt sup}, 39
  \item {\ptt SUP\_ALLPOS\_LEMMA1}, 17
  \item {\ptt SUP\_ALLPOS\_LEMMA2}, 17
  \item {\ptt SUP\_ALLPOS\_LEMMA3}, 17
  \item {\ptt SUP\_ALLPOS\_LEMMA4}, 17
  \item {\ptt SUP\_BOUNDED}, 54
  \item {\ptt SUP\_LEMMA1}, 39
  \item {\ptt SUP\_LEMMA2}, 39
  \item {\ptt SUP\_LEMMA3}, 39
  \item {\ptt SUP\_UBOUNDED}, 54

  \indexspace

  \item {\ptt tan}, 72
  \item {\ptt TAN\_0}, 72
  \item {\ptt TAN\_ADD}, 72
  \item {\ptt TAN\_ATN}, 72
  \item {\ptt TAN\_DOUBLE}, 72
  \item {\ptt TAN\_NEG}, 73
  \item {\ptt TAN\_NPI}, 73
  \item {\ptt TAN\_PERIODIC}, 73
  \item {\ptt TAN\_PI}, 73
  \item {\ptt TAN\_POS\_PI2}, 73
  \item {\ptt TAN\_TOTAL}, 73
  \item {\ptt TAN\_TOTAL\_LEMMA}, 73
  \item {\ptt TAN\_TOTAL\_POS}, 73
  \item {\ptt tends}, 48
  \item {\ptt tends\_num\_real}, 60
  \item {\ptt tends\_real\_real}, 55
  \item {\ptt tendsto}, 48
  \item {\ptt TERMDIFF}, 61
  \item {\ptt TERMDIFF\_LEMMA1}, 62
  \item {\ptt TERMDIFF\_LEMMA2}, 62
  \item {\ptt TERMDIFF\_LEMMA3}, 62
  \item {\ptt TERMDIFF\_LEMMA4}, 62
  \item {\ptt TERMDIFF\_LEMMA5}, 62
  \item {\ptt TOPOLOGY}, 43
  \item {\ptt topology\_TY\_DEF}, 43
  \item {\ptt topology\_tybij}, 43
  \item {\ptt TOPOLOGY\_UNION}, 43
  \item {\ptt trat\_1}, 6
  \item {\ptt trat\_add}, 7
  \item {\ptt TRAT\_ADD\_ASSOC}, 7
  \item {\ptt TRAT\_ADD\_SYM}, 7
  \item {\ptt TRAT\_ADD\_SYM\_EQ}, 7
  \item {\ptt TRAT\_ADD\_TOTAL}, 7
  \item {\ptt TRAT\_ADD\_WELLDEFINED}, 7
  \item {\ptt TRAT\_ADD\_WELLDEFINED2}, 7
  \item {\ptt TRAT\_ARCH}, 7
  \item {\ptt trat\_eq}, 7
  \item {\ptt TRAT\_EQ\_AP}, 7
  \item {\ptt TRAT\_EQ\_EQUIV}, 7
  \item {\ptt TRAT\_EQ\_REFL}, 7
  \item {\ptt TRAT\_EQ\_SYM}, 8
  \item {\ptt TRAT\_EQ\_TRANS}, 8
  \item {\ptt trat\_inv}, 8
  \item {\ptt TRAT\_INV\_WELLDEFINED}, 8
  \item {\ptt TRAT\_LDISTRIB}, 8
  \item {\ptt trat\_mul}, 8
  \item {\ptt TRAT\_MUL\_ASSOC}, 8
  \item {\ptt TRAT\_MUL\_LID}, 8
  \item {\ptt TRAT\_MUL\_LINV}, 8
  \item {\ptt TRAT\_MUL\_SYM}, 8
  \item {\ptt TRAT\_MUL\_SYM\_EQ}, 8
  \item {\ptt TRAT\_MUL\_WELLDEFINED}, 8
  \item {\ptt TRAT\_MUL\_WELLDEFINED2}, 8
  \item {\ptt TRAT\_NOZERO}, 9
  \item {\ptt TRAT\_SUCINT}, 9
  \item {\ptt trat\_sucint}, 9
  \item {\ptt TRAT\_SUCINT\_0}, 9
  \item {\ptt treal\_0}, 17
  \item {\ptt treal\_1}, 18
  \item {\ptt TREAL\_10}, 18
  \item {\ptt treal\_add}, 18
  \item {\ptt TREAL\_ADD\_ASSOC}, 18
  \item {\ptt TREAL\_ADD\_LID}, 18
  \item {\ptt TREAL\_ADD\_LINV}, 18
  \item {\ptt TREAL\_ADD\_SYM}, 18
  \item {\ptt TREAL\_ADD\_WELLDEF}, 18
  \item {\ptt TREAL\_ADD\_WELLDEFR}, 18
  \item {\ptt TREAL\_BIJ}, 18
  \item {\ptt TREAL\_BIJ\_WELLDEF}, 18
  \item {\ptt treal\_eq}, 18
  \item {\ptt TREAL\_EQ\_AP}, 18
  \item {\ptt TREAL\_EQ\_EQUIV}, 19
  \item {\ptt TREAL\_EQ\_REFL}, 19
  \item {\ptt TREAL\_EQ\_SYM}, 19
  \item {\ptt TREAL\_EQ\_TRANS}, 19
  \item {\ptt treal\_inv}, 19
  \item {\ptt TREAL\_INV\_WELLDEF}, 19
  \item {\ptt TREAL\_ISO}, 19
  \item {\ptt TREAL\_LDISTRIB}, 19
  \item {\ptt treal\_lt}, 19
  \item {\ptt TREAL\_LT\_ADD}, 19
  \item {\ptt TREAL\_LT\_MUL}, 19
  \item {\ptt TREAL\_LT\_REFL}, 19
  \item {\ptt TREAL\_LT\_TOTAL}, 20
  \item {\ptt TREAL\_LT\_TRANS}, 20
  \item {\ptt TREAL\_LT\_WELLDEF}, 20
  \item {\ptt TREAL\_LT\_WELLDEFL}, 20
  \item {\ptt TREAL\_LT\_WELLDEFR}, 20
  \item {\ptt treal\_mul}, 20
  \item {\ptt TREAL\_MUL\_ASSOC}, 20
  \item {\ptt TREAL\_MUL\_LID}, 20
  \item {\ptt TREAL\_MUL\_LINV}, 20
  \item {\ptt TREAL\_MUL\_SYM}, 20
  \item {\ptt TREAL\_MUL\_WELLDEF}, 20
  \item {\ptt TREAL\_MUL\_WELLDEFR}, 20
  \item {\ptt treal\_neg}, 20
  \item {\ptt TREAL\_NEG\_WELLDEF}, 21
  \item {\ptt treal\_of\_hreal}, 21

  \indexspace

  \item {\ptt Union}, 43
  \item {\ptt union\_def}, 43
  \item {\ptt universe}, 43

\end{theindex}
