# A Coq library on Floating-point arithmetic

Global Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (1655 entries)
Lemma Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (1389 entries)
Constructor Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (35 entries)
Inductive Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (18 entries)
Definition Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (145 entries)
Library Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (68 entries)

# Global Index

## A

abeLeab [lemma, in FmaErr]
absFBounded [lemma, in Fbound]
absolu_comp_mult [lemma, in Faux]
absolu_INR [lemma, in Faux]
absolu_lt_nz [lemma, in Faux]
absolu_Zopp [lemma, in Faux]
absolu_Zs [lemma, in Faux]
absolu_Zs_neg [lemma, in Faux]
abs_lt_MSB [lemma, in MSB]
addExp [definition, in FexpPlus]
AddExpGeUnderf [lemma, in discriminant3]
AddExpGeUnderf2 [lemma, in discriminant3]
AddExpGe1Underf [lemma, in discriminant3]
AddExpGe1Underf2 [lemma, in discriminant3]
addExpIsExp [lemma, in FexpPlus]
addExpIsVal [lemma, in FexpPlus]
AddOddEven [lemma, in FmaEmul]
AddOddEven2 [lemma, in FmaEmul]
AddOddEven_aux [lemma, in FmaEmul]
AddOddEven_aux_aux [lemma, in FmaEmul]
AddOddEven_can [lemma, in FmaEmul]
AddOddOdd [lemma, in FmaEmul]
AddOddOdd2 [lemma, in FmaEmul]
AddOddOdd2_can [lemma, in FmaEmul]
AddOddOdd_aux [lemma, in FmaEmul]
AddOddOdd_aux_aux [lemma, in FmaEmul]
AddOddOdd_can [lemma, in FmaEmul]
AddStep [lemma, in FexpAdd]
AllFloat [library]
app_length [lemma, in Fexp2]
arg_reduct_exists_k_zH [lemma, in FArgReduct2]
AScal2 [lemma, in Closest2Prop]
Axpy [library]
AxpyFLessu_Fmac [lemma, in Axpy]
AxpyPos [lemma, in Axpy]
AxpyPos_Fmac [lemma, in Axpy]
Axpy_aux1 [lemma, in Axpy]
Axpy_aux1_aux1 [lemma, in Axpy]
Axpy_aux1_aux2 [lemma, in Axpy]
Axpy_aux1_aux3 [lemma, in Axpy]
Axpy_aux2 [lemma, in Axpy]
Axpy_aux3 [lemma, in Axpy]
Axpy_opt [lemma, in Axpy]
Axpy_opt_Fmac [lemma, in Axpy]
Axpy_Simpl1 [lemma, in Axpy]
Axpy_Simpl1bis [lemma, in Axpy]
Axpy_Simpl2 [lemma, in Axpy]
Axpy_tFlessu [lemma, in Axpy]

## B

be2MuchSmaller [lemma, in FmaErr]
bimplybplusNorm [lemma, in Veltkamp]
binary_value_Zle [lemma, in IEEE]
BLoop1 [lemma, in PradixE]
BLoop2 [lemma, in PradixE]
BLoop3 [lemma, in PradixE]
BLoop4 [lemma, in PradixE]
BminusSameExp [lemma, in Fprop]
BminusSameExpAux [lemma, in Fprop]
BminusSameExpNeg [lemma, in Fprop]
boundBoundNat [lemma, in Fmin]
BoundedBounded [lemma, in DoubleRound]
BoundedL [lemma, in Dekker]
BoundedL [lemma, in FmaErr]
boundedNorMinGivesExp [lemma, in Fnorm]
boundedNorMinGivesExp2 [lemma, in FIA64elem]
Boundedt1 [lemma, in Dekker]
Boundedt2 [lemma, in Dekker]
Boundedt3 [lemma, in Dekker]
Boundedt4 [lemma, in Dekker]
Boundedt4_aux [lemma, in Dekker]
Boundedx1y1 [lemma, in Dekker]
Boundedx1y1_aux [lemma, in Dekker]
Boundedx1y2 [lemma, in Dekker]
Boundedx1y2_aux [lemma, in Dekker]
Boundedx2y1 [lemma, in Dekker]
Boundedx2y1_aux [lemma, in Dekker]
Boundedx2y2 [lemma, in Dekker]
boundNat [definition, in Fmin]
boundNatCorrect [lemma, in Fmin]
boundNormalMult [lemma, in MSBProp]
boundOnePrecision [lemma, in MSBProp]
boundR [definition, in Fmin]
boundRCorrect1 [lemma, in Fmin]
boundRCorrect2 [lemma, in Fmin]
boundRrOpp [lemma, in Fmin]
bound3Sum [lemma, in ThreeSum2]

## C

CanonicFulp [lemma, in FroundProp]
CanonicFulp [lemma, in FminOp]
cases [lemma, in discriminant3]
Closest [definition, in Closest]
Closest [library]
Closestbbext [lemma, in Dekker]
Closestbbplus [lemma, in Veltkamp]
Closestbplusb [lemma, in Veltkamp]
ClosestClosest [lemma, in Veltkamp]
ClosestCompatible [lemma, in Closest]
ClosestErrorBound [lemma, in ClosestProp]
ClosestErrorBoundNormal [lemma, in ClosestProp]
ClosestErrorBoundNormal2_aux [lemma, in ClosestProp]
ClosestErrorBoundNormal_aux [lemma, in ClosestProp]
ClosestErrorBound2 [lemma, in ClosestProp]
ClosestErrorExp [lemma, in ClosestProp]
ClosestErrorExpStrict [lemma, in ClosestProp]
ClosestExp [lemma, in ClosestProp]
ClosestFabs [lemma, in ClosestProp]
ClosestIdem [lemma, in ClosestProp]
ClosestImplyEven [lemma, in Veltkamp]
ClosestImplyEven_int [lemma, in Veltkamp]
ClosestInfPredExp [lemma, in DblRndOdd]
closestLessMultAbs [lemma, in ClosestMult]
closestLessMultNeg [lemma, in ClosestMult]
closestLessMultPos [lemma, in ClosestMult]
ClosestMax [lemma, in Closest]
ClosestMaxEq [lemma, in Closest]
ClosestMax1 [lemma, in FminOp]
ClosestMax2 [lemma, in FminOp]
ClosestMin [lemma, in Closest]
ClosestMinEq [lemma, in Closest]
ClosestMinOrMax [lemma, in Closest]
ClosestMin1 [lemma, in FminOp]
ClosestMin2 [lemma, in FminOp]
ClosestMonotone [lemma, in Closest]
ClosestMult [library]
ClosestM1 [lemma, in ClosestProp]
ClosestOpp [lemma, in ClosestProp]
ClosestPlus [library]
ClosestProp [library]
ClosestPropHigham25 [lemma, in ClosestProp]
ClosestRoundedModeP [lemma, in Closest]
ClosestRoundeGeNormal [lemma, in FmaErr]
ClosestRoundeLeNormal [lemma, in FmaErr]
ClosestStrict [lemma, in DblRndOdd]
ClosestStrictPos [lemma, in DblRndOdd]
ClosestStrictPred [lemma, in DblRndOdd]
ClosestSuccPred [lemma, in Veltkamp]
ClosestSymmetric [lemma, in Closest]
ClosestTotal [lemma, in Closest]
ClosestUlp [lemma, in ClosestProp]
ClosestZero [lemma, in Dekker]
ClosestZero1 [lemma, in FmaErr]
ClosestZero2 [lemma, in FmaErr]
Closest2Plus [library]
Closest2Prop [library]
compare_SUP_dec [lemma, in Paux]
CompatibleP [definition, in Fround]
CompatiblePI [definition, in FnormI]
cons_neq [lemma, in Fexp2]
Contradict1 [lemma, in sTactic]
Contradict2 [lemma, in sTactic]
Contradict3 [lemma, in sTactic]
convert_not_O [lemma, in Faux]

## D

DblRndOdd [library]
DblRndStable [lemma, in DoubleRound]
Dekker [lemma, in Fast2Sum]
Dekker [lemma, in Dekker]
Dekker [library]
DekkerDiff [lemma, in Fast2Diff]
DekkerN [lemma, in Dekker]
DekkerS1 [lemma, in Dekker]
DekkerS2 [lemma, in Dekker]
Dekker1 [lemma, in Fast2Sum]
Dekker1 [lemma, in Dekker]
Dekker2 [lemma, in Fast2Sum]
Dekker2 [lemma, in Dekker]
Dekker2_aux [lemma, in Dekker]
Dekker3 [lemma, in Fast2Sum]
Dekker_aux [lemma, in Dekker]
delta_inf [lemma, in FArgReduct2]
delta_inf [lemma, in discriminant2]
delta_inf [lemma, in discriminant]
dexact [lemma, in discriminant3]
dExpPrim [lemma, in Dekker]
dExpPrimEq [lemma, in Dekker]
digit [definition, in Digit]
Digit [library]
digitAdd [lemma, in Digit]
digitAux [definition, in Digit]
digitAuxLess [lemma, in Digit]
digitAuxMore [lemma, in Digit]
digitAux1 [lemma, in Digit]
digitGivesBoundedNum [lemma, in Fnorm]
digitInv [lemma, in Digit]
digitLess [lemma, in Digit]
digitMore [lemma, in Digit]
digitnNormMin [lemma, in Fnorm]
digitNotZero [lemma, in Digit]
digitO [lemma, in Digit]
digitPredVNumiSPrecision [lemma, in Fnorm]
digitVNumiSPrecision [lemma, in Fnorm]
digit1 [lemma, in Digit]
digit_abs [lemma, in Digit]
digit_anti_monotone_lt [lemma, in Digit]
digit_bound [lemma, in Digit]
digit_minus1 [lemma, in Digit]
digit_monotone [lemma, in Digit]
discri [lemma, in discriminant]
discriminant [library]
discriminant2 [library]
discriminant3 [library]
discri1 [lemma, in discriminant2]
discri1 [lemma, in discriminant]
discri10 [lemma, in discriminant3]
discri11 [lemma, in discriminant3]
discri12 [lemma, in discriminant3]
discri13 [lemma, in discriminant3]
discri14 [lemma, in discriminant3]
discri15 [lemma, in discriminant3]
discri16 [lemma, in discriminant3]
discri2 [lemma, in discriminant2]
discri2 [lemma, in discriminant]
discri3 [lemma, in discriminant]
discri3 [lemma, in discriminant2]
discri4 [lemma, in discriminant]
discri4 [lemma, in discriminant2]
discri5 [lemma, in discriminant2]
discri5 [lemma, in discriminant]
discri6 [lemma, in discriminant]
discri6 [lemma, in discriminant2]
discri7 [lemma, in discriminant]
discri7 [lemma, in discriminant2]
discri8 [lemma, in discriminant2]
discri8 [lemma, in discriminant]
discri9 [lemma, in discriminant2]
discri9 [lemma, in discriminant]
DivFirstCase [lemma, in FexpDiv]
Divnk [lemma, in Divnk]
Divnk [library]
Divnk_error [lemma, in Divnk]
Divnk_FexpyGe [lemma, in Divnk]
Divnk_FexpyLe [lemma, in Divnk]
Divnk_FexpyLe2 [lemma, in Divnk]
DivSecondCase [lemma, in FexpDiv]
div2IsBetween [lemma, in FroundProp]
div2IsBetweenPos [lemma, in FroundProp]
DoubleRound [library]
DoubleRound2 [lemma, in DoubleRound]
dp_dq_le [lemma, in discriminant2]
dp_dq_le [lemma, in discriminant]
dsd [definition, in FexpDiv]
dsdAbs [lemma, in FexpDiv]
dsdinv [lemma, in FexpDiv]
dsdmult [lemma, in FexpDiv]
dsdsym [lemma, in FexpDiv]
dsdtrans [lemma, in FexpDiv]
dsdwi1qiD [lemma, in FexpDiv]

## E

EFast2Sum [library]
eLe [lemma, in Dekker]
endof [definition, in Fexp2]
endof_length [lemma, in Fexp2]
endof_Rle_length [lemma, in FexpAdd]
epLe [lemma, in Veltkamp]
eqEqual [lemma, in Veltkamp]
eqExpLess [lemma, in Fbound]
eqExpMax [lemma, in Fbound]
eqGe [lemma, in Veltkamp]
eqLe [lemma, in Veltkamp]
eqLeep [lemma, in Veltkamp]
eqLe2 [lemma, in Veltkamp]
EqListFloat [inductive, in Fexp2]
EqListFloatnil [constructor, in Fexp2]
EqListFloatTop [constructor, in Fexp2]
EqListFloat_length [lemma, in Fexp2]
EqListFloat_sum [lemma, in Fexp2]
EqSpeTwice [lemma, in FminOp]
ErrFmaApprox [lemma, in FmaErrApprox]
ErrFmaApprox_1 [lemma, in FmaErrApprox]
ErrFmaApprox_1_aux [lemma, in FmaErrApprox]
ErrFmaApprox_2 [lemma, in FmaErrApprox]
ErrFmaApprox_2_aux [lemma, in FmaErrApprox]
errorBoundedDiv [lemma, in FroundDivSqrt]
errorBoundedDivClosest [lemma, in FroundDivSqrt]
errorBoundedDivSimplHyp [lemma, in FroundDivSqrt]
errorBoundedDivToZero [lemma, in FroundDivSqrt]
ErrorBoundedIplus [lemma, in Fast2Sum]
errorBoundedModuloCan [lemma, in FroundDivSqrt]
errorBoundedModulo_aux [lemma, in FroundDivSqrt]
errorBoundedModulo_aux_y [lemma, in FroundDivSqrt]
errorBoundedMult [lemma, in FroundMult]
errorBoundedMultClosest [lemma, in ClosestMult]
errorBoundedMultClosest_aux [lemma, in ClosestMult]
errorBoundedMultClosest_Can [lemma, in discriminant]
errorBoundedMultClosest_Can [lemma, in discriminant2]
errorBoundedMultExp [lemma, in FroundMult]
errorBoundedMultExpPos [lemma, in FroundMult]
errorBoundedMultExp_aux [lemma, in FroundMult]
errorBoundedMultMax [lemma, in FroundMult]
errorBoundedMultMin [lemma, in FroundMult]
errorBoundedMultNeg [lemma, in FroundMult]
errorBoundedMultPos [lemma, in FroundMult]
errorBoundedPlus [lemma, in ClosestPlus]
errorBoundedPlusAbs [lemma, in ClosestPlus]
errorBoundedPlusLe [lemma, in ClosestPlus]
errorBoundedRem [lemma, in FroundDivSqrt]
errorBoundedSqrt [lemma, in FroundDivSqrt]
Even [definition, in Fodd]
EvenBound [lemma, in EFast2Sum]
EvenClosest [definition, in Closest]
EvenClosestbbplus [lemma, in Veltkamp]
EvenClosestbplusb [lemma, in Veltkamp]
EvenClosestCompatible [lemma, in Closest]
EvenClosestFabs [lemma, in discriminant2]
EvenClosestFabs [lemma, in discriminant]
EvenClosestMax1 [lemma, in FminOp]
EvenClosestMax2 [lemma, in FminOp]
EvenClosestMinOrMax [lemma, in Closest]
EvenClosestMin1 [lemma, in FminOp]
EvenClosestMin2 [lemma, in FminOp]
EvenClosestMonotone [lemma, in Closest]
EvenClosestMonotone2 [lemma, in discriminant]
EvenClosestMonotone2 [lemma, in discriminant2]
EvenClosestRoundedModeP [lemma, in Closest]
EvenClosestSymmetric [lemma, in Closest]
EvenClosestTotal [lemma, in Closest]
EvenClosestUniqueP [lemma, in Closest]
EvenExp [lemma, in Fodd]
EvenFNSuccFNSuccMid [lemma, in Closest2Prop]
EvenMultInv [lemma, in Fodd]
EvenMult1 [lemma, in Fodd]
EvenMult2 [lemma, in Fodd]
EvenNOdd [lemma, in Fodd]
EvenNormalize [lemma, in DblRndOdd]
EvenO [lemma, in Fodd]
EvenOpp [lemma, in Fodd]
EvenPlusInv1 [lemma, in Fodd]
EvenPlusInv2 [lemma, in Fodd]
EvenPlus1 [lemma, in Fodd]
EvenPlus2 [lemma, in Fodd]
EvenSOdd [lemma, in Fodd]
EvenSOddInv [lemma, in Fodd]
ExactMinusInterval [lemma, in FroundPlus]
ExactMinusIntervalAux [lemma, in FroundPlus]
ExactMinusIntervalAux1 [lemma, in FroundPlus]
ExactSum_Near [lemma, in Axpy]
existExp [lemma, in Fexp]
exists_k [lemma, in FArgReduct2]
exp [definition, in Paux]
Expbe1 [lemma, in FmaErr]
expBoundedInv [lemma, in Fexp]
expInv [lemma, in Fexp]
expNormalize [definition, in Fexp]
expNormalizeCorrect [lemma, in Fexp]
expNormalizeExp [lemma, in Fexp]
Expo_zero_or_pos [lemma, in IEEE]
expPlus [lemma, in Paux]
ExpRev_aux [lemma, in Fexp2]
Expr1 [lemma, in FmaErr]
expValue [definition, in Fexp]
expValueApp [lemma, in Fexp]
expValueRev [lemma, in Fexp]
exp3Sum [lemma, in ThreeSum2]
exp_alpha_le [lemma, in FArgReduct3]
Exp_aux [lemma, in Fexp2]
exp_gamma_enough [lemma, in FArgReduct4]
exp_gamma_enough2 [lemma, in FArgReduct3]
exp_gamma_enough3 [lemma, in FArgReduct3]
exp_le_inv [lemma, in RND]
exp_ln_powerRZ [lemma, in RND]
exp_monotone [lemma, in RND]
ExtDekker [lemma, in EFast2Sum]
ExtDekkerDiff [lemma, in Fast2Diff]
ExtMDekker [lemma, in EFast2Sum]
ExtMDekkerDiff [lemma, in Fast2Diff]
ExtMDekker1 [lemma, in EFast2Sum]

## F

Fabs [definition, in Fop]
Fabs_correct [lemma, in Fop]
Fabs_correct1 [lemma, in Fop]
Fabs_correct2 [lemma, in Fop]
Fabs_Fexp [lemma, in FIA64elem]
Fabs_Fzero [lemma, in Fop]
FArgReduct [library]
FArgReduct2 [library]
FArgReduct3 [library]
FArgReduct4 [library]
Farg_reduct_bounded_diff [lemma, in FArgReduct4]
Fast2Diff [library]
Fast2Sum [library]
Faux [library]
Fbound [inductive, in Fbound]
Fbound [library]
Fbounded [definition, in Fbound]
FboundedEqExp [lemma, in Fbound]
FboundedEqExpPos [lemma, in Fbound]
FboundedExp [lemma, in Fbound]
FboundedFzero [lemma, in Fbound]
FboundedI [definition, in FboundI]
FboundedIFzero [lemma, in FboundI]
FboundedMbound [lemma, in Fnorm]
FboundedMboundPos [lemma, in Fnorm]
FboundedMbound2 [lemma, in Veltkamp]
FboundedMbound2Pos [lemma, in Veltkamp]
FboundedNum [lemma, in Fbound]
FboundedOne [lemma, in Fnorm]
FBoundedPred [lemma, in FPred]
FBoundedScale [lemma, in Fbound]
FboundedShiftLess [lemma, in Fbound]
FBoundedSuc [lemma, in FSucc]
FboundedZeroSameExp [lemma, in Fbound]
FboundI [inductive, in FboundI]
FboundI [library]
FboundNext [lemma, in Fnorm]
Fcanonic [definition, in Fnorm]
FcanonicBound [lemma, in Fnorm]
FcanonicFabs [lemma, in Fnorm]
FcanonicFnormalizeEq [lemma, in Fnorm]
FcanonicFopp [lemma, in Fnorm]
FcanonicI [definition, in FboundI]
FcanonicIBoundedI [lemma, in FboundI]
FcanonicIUnique [lemma, in FboundI]
FcanonicLeastExp [lemma, in Fnorm]
FcanonicLePos [lemma, in Fnorm]
FcanonicLtNeg [lemma, in Fnorm]
FcanonicLtPos [lemma, in Fnorm]
FcanonicNegFexpRlt [lemma, in Fnorm]
FcanonicNnormMin [lemma, in Fnorm]
FcanonicPosFexpRlt [lemma, in Fnorm]
FcanonicPpred [lemma, in Fnorm]
FcanonicUnique [lemma, in Fnorm]
Fcanonic_Rle_Zle [lemma, in Fnorm]
Fcomp [library]
Fcompare [definition, in Fcomp]
Fcompare_correct [lemma, in FminOp]
Fdiff [definition, in Fcomp]
Fdiff_correct [lemma, in Fcomp]
Fdigit [definition, in Float]
FdigitEq [lemma, in Float]
Fdigit_abs [lemma, in Fop]
Fdigit_opp [lemma, in Fop]
Feq [definition, in Fcomp]
Feq_bool [definition, in Fcomp]
Feq_bool_correct_f [lemma, in Fcomp]
Feq_bool_correct_r [lemma, in Fcomp]
Feq_bool_correct_t [lemma, in Fcomp]
Feven [definition, in Fodd]
FEvenD [lemma, in Fodd]
FevenFop [lemma, in Fodd]
FevenMakesFNeven [lemma, in FmaEmul]
FevenNormMin [lemma, in Closest2Prop]
FevenO [lemma, in Fodd]
FevenOrFodd [lemma, in Fodd]
FevenPred [lemma, in Fodd]
FevenSuc [lemma, in Fodd]
FevenSucProp [lemma, in Fodd]
Fexp [library]
FexpAdd [library]
FexpAdd_aux [lemma, in FexpAdd]
FexpAdd_aux2 [lemma, in FexpAdd]
FexpAdd_main [lemma, in FexpAdd]
FexpDiv [library]
FexpDivConv [lemma, in FexpDiv]
FexpEpsilon_aux [lemma, in FexpDiv]
FexpGeUnderf [lemma, in discriminant3]
FexpPlus [library]
Fexp2 [library]
Fexp_le_LSB [lemma, in MSB]
Fexp_le_MSB [lemma, in MSB]
Fexp_u [lemma, in FArgReduct2]
Fexp_x_aprox_zh_gamma [lemma, in FArgReduct4]
Fge [definition, in Fcomp]
Fge_Zge [lemma, in Fcomp]
Fgt [definition, in Fcomp]
Fgt_Zgt [lemma, in Fcomp]
FIA64elem [library]
FindMin [definition, in FminOp]
Finduct [library]
FinductNeg [lemma, in Finduct]
FinductNegAux [lemma, in Finduct]
FinductPos [lemma, in Finduct]
FinductPosAux [lemma, in Finduct]
firstNormalPos [definition, in Fnorm]
firstNormalPosNormal [lemma, in Fnorm]
firstNormalPos_eq [lemma, in RND]
First_Comput_ok [lemma, in FArgReduct4]
Fle [definition, in Fcomp]
FLess [definition, in Axpy]
Fle_bool [definition, in Fcomp]
Fle_bool_correct_f [lemma, in Fcomp]
Fle_bool_correct_r [lemma, in Fcomp]
Fle_bool_correct_t [lemma, in Fcomp]
Fle_Fge [lemma, in Fcomp]
Fle_refl [lemma, in Fcomp]
Fle_trans [lemma, in Fcomp]
Fle_Zle [lemma, in Fcomp]
float [inductive, in Float]
Float [library]
floatDec [lemma, in Float]
floatEq [lemma, in Float]
float_equals_IEEE [lemma, in IEEE]
Float_To_IEEE [definition, in IEEE]
Float_To_IEEE_fn [lemma, in IEEE]
Float_To_IEEE_To_Float [lemma, in IEEE]
Flt [definition, in Fcomp]
Flt_bool [definition, in Fcomp]
Flt_bool_correct_f [lemma, in Fcomp]
Flt_bool_correct_r [lemma, in Fcomp]
Flt_bool_correct_t [lemma, in Fcomp]
Flt_Fgt [lemma, in Fcomp]
Flt_Zlt [lemma, in Fcomp]
Fmac_arg_reduct_correct1 [lemma, in FArgReduct2]
Fmac_arg_reduct_correct1_aux [lemma, in FArgReduct2]
Fmac_arg_reduct_correct1_aux2 [lemma, in FArgReduct2]
Fmac_arg_reduct_correct2 [lemma, in FArgReduct2]
Fmac_arg_reduct_correct3 [lemma, in FArgReduct3]
FmaEmul [lemma, in FmaEmul]
FmaEmul [library]
FmaEmulAux [lemma, in FmaEmul]
FmaErr [lemma, in FmaErr]
FmaErr [library]
FmaErrApprox [library]
FmaErr_aux [lemma, in FmaErr]
FmaErr_aux1 [lemma, in FmaErr]
FmaErr_aux2 [lemma, in FmaErr]
FmaErr_Even [lemma, in FmaErr]
FmaxRep [lemma, in Fmin]
Fma_FTS [lemma, in FmaErr]
Fma_FTS_Even [lemma, in FmaErr]
Fmin [library]
FminOp [library]
FminOp_correct1 [lemma, in FminOp]
FminOp_correct2 [lemma, in FminOp]
FminOp_correct3 [lemma, in FminOp]
FminOp_correct4 [lemma, in FminOp]
FminOp_correct5 [lemma, in FminOp]
FminOp_correct6 [lemma, in FminOp]
FminOp_correct7 [lemma, in FminOp]
FminRep [lemma, in Fmin]
Fminus [definition, in Fop]
Fminus_correct [lemma, in Fop]
Fmult [definition, in Fop]
FmultRadixInv [lemma, in ClosestProp]
Fmult_correct [definition, in Fop]
FNeven [definition, in Fodd]
FNEvenD [lemma, in Fodd]
FNevenEq [lemma, in Fodd]
FNevenFop [lemma, in Fodd]
FNevenOrFNodd [lemma, in Fodd]
FNevenPred [lemma, in Fodd]
FNevenSuc [lemma, in Fodd]
FNI [definition, in FboundI]
FNIAux [definition, in FboundI]
FNIAuxLess [lemma, in FboundI]
FNIAuxMore [lemma, in FboundI]
FNILess [lemma, in FboundI]
FNIMore [lemma, in FboundI]
FNodd [definition, in Fodd]
FNoddEq [lemma, in Fodd]
FNoddFop [lemma, in Fodd]
FnOddNEven [lemma, in Fodd]
FNoddPred [lemma, in Fodd]
FNoddSuc [lemma, in Fodd]
Fnorm [library]
Fnormal [definition, in Fnorm]
FnormalBound [lemma, in Fnorm]
FnormalBoundAbs [lemma, in Fnorm]
FnormalBoundAbs2 [lemma, in Fnorm]
FnormalBounded [lemma, in Fnorm]
FnormalFabs [lemma, in Fnorm]
FnormalFop [lemma, in Fnorm]
FnormalI [definition, in FboundI]
FnormalINotZero [lemma, in FboundI]
FnormalIUnique [lemma, in FboundI]
FnormalIUnique_aux [lemma, in FboundI]
Fnormalize [definition, in Fnorm]
FnormalizeBounded [lemma, in Fnorm]
FnormalizeCanonic [lemma, in Fnorm]
FnormalizeCorrect [lemma, in Fnorm]
FnormalizeI [definition, in FboundI]
FnormalizeIBounded [lemma, in FboundI]
FnormalizeICorrect [lemma, in FboundI]
FnormalizeIFcanonicI [lemma, in FboundI]
Fnormalize_Fopp [lemma, in Fnorm]
FnormalLtFirstNormalNeg [lemma, in Fnorm]
FnormalLtFirstNormalPos [lemma, in Fnorm]
FnormalLtNeg [lemma, in Fnorm]
FnormalLtPos [lemma, in Fnorm]
FnormalNnormMin [lemma, in Fnorm]
FnormalNotZero [lemma, in Fnorm]
FnormalPpred [lemma, in Fnorm]
FnormalPrecision [lemma, in Fnorm]
FnormalUnique [lemma, in Fnorm]
FnormI [library]
FNormTo_IEEE [definition, in IEEE]
FNorm_or_Subnorm [lemma, in IEEE]
FNPred [definition, in FPred]
FNPredCanonic [lemma, in FPred]
FNPredFopFNSucc [lemma, in FPred]
FNPredLt [lemma, in FPred]
FNPredProp [lemma, in FPred]
FNPredSuc [lemma, in FPred]
FNPredSucEq [lemma, in FPred]
FNSucc [definition, in FSucc]
FNSuccCanonic [lemma, in FSucc]
FNSuccEq [lemma, in FSucc]
FNSuccFNSuccMid [lemma, in FSucc]
FNSuccLt [lemma, in FSucc]
FNSuccProp [lemma, in FSucc]
FNSuccUlpPos [lemma, in FroundProp]
FNSuccUlpPos [lemma, in FminOp]
FNSucPred [lemma, in FPred]
FNSucPredEq [lemma, in FPred]
Fodd [definition, in Fodd]
Fodd [library]
FoddFop [lemma, in Fodd]
FoddPred [lemma, in Fodd]
FoddSuc [lemma, in Fodd]
Fop [library]
Fopp [definition, in Fop]
FoppBoundedI [lemma, in FnormI]
FoppBoundedIExp [lemma, in FnormI]
FoppBoundedIInv [lemma, in FnormI]
FoppBoundedIInv_aux [lemma, in FnormI]
FoppBoundedI2 [lemma, in FnormI]
Fopp_correct [lemma, in Fop]
Fopp_Fminus [lemma, in Fop]
Fopp_Fminus_dist [lemma, in Fop]
Fopp_Fopp [lemma, in Fop]
FopRepAux [lemma, in Fbound]
Fplus [definition, in Fop]
Fplus_correct [lemma, in Fop]
FPred [definition, in FPred]
FPred [library]
FPredCanonic [lemma, in FPred]
FPredDiff1 [lemma, in FPred]
FPredDiff2 [lemma, in FPred]
FPredDiff3 [lemma, in FPred]
FPredFopFSucc [lemma, in FPred]
FPredLt [lemma, in FPred]
FPredProp [lemma, in FPred]
FPredSimpl1 [lemma, in FPred]
FPredSimpl2 [lemma, in FPred]
FPredSimpl3 [lemma, in FPred]
FPredSimpl4 [lemma, in FPred]
FPredSuc [lemma, in FPred]
FpredUlpPos [lemma, in ClosestProp]
FPredZleEq [lemma, in FPred]
Fprop [library]
Fround [library]
FroundDivSqrt [library]
FroundMult [library]
FroundPlus [library]
FroundProp [library]
Fshift [definition, in Float]
FshiftAdd [lemma, in Float]
FshiftCorrect [lemma, in Float]
FshiftCorrectInv [lemma, in Float]
FshiftCorrectSym [lemma, in Float]
FshiftFdigit [lemma, in Float]
FshiftO [lemma, in Float]
Fsubnormal [definition, in Fnorm]
FsubnormalBound [lemma, in Fnorm]
FsubnormalDigit [lemma, in Fnorm]
FsubnormalFbounded [lemma, in Fnorm]
FsubnormalFexp [lemma, in Fnorm]
FsubnormalI [definition, in FboundI]
FsubnormalIUnique [lemma, in FboundI]
FsubnormalLt [lemma, in Fnorm]
FsubnormalLtFirstNormalPos [lemma, in Fnorm]
FsubnormalnormalLtNeg [lemma, in Fnorm]
FsubnormalnormalLtPos [lemma, in Fnorm]
FsubnormalUnique [lemma, in Fnorm]
FsubnormFabs [lemma, in Fnorm]
FsubnormFopp [lemma, in Fnorm]
FSubnormTo_IEEE [definition, in IEEE]
FSucc [definition, in FSucc]
FSucc [library]
FSuccCanonic [lemma, in FSucc]
FSuccDiffPos [lemma, in FroundProp]
FSuccDiffPos [lemma, in FminOp]
FSuccDiff1 [lemma, in FSucc]
FSuccDiff2 [lemma, in FSucc]
FSuccDiff3 [lemma, in FSucc]
FSuccLt [lemma, in FSucc]
FSuccNegCanonic [lemma, in FSucc]
FSuccNormNegNormMin [lemma, in FSucc]
FSuccNormNegNotNormMin [lemma, in FSucc]
FSuccNormPos [lemma, in FSucc]
FSuccPosNotMax [lemma, in FSucc]
FSuccProp [lemma, in FSucc]
FSuccPropNeg [lemma, in FSucc]
FSuccPropPos [lemma, in FSucc]
FSuccSimpl1 [lemma, in FSucc]
FSuccSimpl2 [lemma, in FSucc]
FSuccSimpl3 [lemma, in FSucc]
FSuccSimpl4 [lemma, in FSucc]
FSuccSubnormal [lemma, in FSucc]
FSuccSubnormNearNormMin [lemma, in FSucc]
FSuccSubnormNotNearNormMin [lemma, in FSucc]
FSuccUlpPos [lemma, in FminOp]
FSuccUlpPos [lemma, in FroundProp]
FSuccZleEq [lemma, in FSucc]
FSucFSucMid [lemma, in FSucc]
FSucPred [lemma, in FPred]
FtoR [definition, in Float]
FtoREqInv1 [lemma, in Float]
FtoREqInv2 [lemma, in Float]
FtoR_Zpred_exp [lemma, in IEEE]
FTS [lemma, in ThreeSumProps]
FTSinSum3_allcases [lemma, in ThreeSumProps]
FTS_correct [lemma, in FArgReduct4]
FTS_correct_aux [lemma, in FArgReduct4]
Fulp [definition, in FroundProp]
FulpComp [lemma, in FroundProp]
FulpDiv [lemma, in FexpDiv]
FulpFabs [lemma, in FroundProp]
FulpFPredGePos [lemma, in FroundProp]
FulpFPredLe [lemma, in ClosestProp]
FulpFPred_not_pow [lemma, in FArgReduct]
FulpGe [lemma, in FroundProp]
FulpLe [lemma, in FroundProp]
FulpLeGeneral [lemma, in Axpy]
FulpLe2 [lemma, in FroundProp]
FulpPred [lemma, in FroundProp]
FulpPredCan [lemma, in FroundProp]
FulpRinv_div [lemma, in FIA64elem]
FulpRinv_div_not [lemma, in FIA64elem]
FulpSuc [lemma, in FroundProp]
FulpSucCan [lemma, in FroundProp]
FUlp_Le_LSigB [lemma, in FroundProp]
Fulp_le_twice_l [lemma, in discriminant]
Fulp_le_twice_l [lemma, in discriminant2]
Fulp_le_twice_r [lemma, in discriminant]
Fulp_le_twice_r [lemma, in discriminant2]
Fulp_le_twice_r_round [lemma, in discriminant2]
Fulp_le_twice_r_round [lemma, in discriminant]
Fulp_pow [lemma, in FIA64elem]
Fulp_R1 [lemma, in FIA64elem]
Fulp_zero [lemma, in FroundProp]
FvalScale [lemma, in Fbound]
Fweight [definition, in Finduct]
FweightEq [lemma, in Finduct]
FweightLt [lemma, in Finduct]
FweightZle [lemma, in Finduct]
Fzero [definition, in Float]
FzeroisReallyZero [lemma, in Float]
FzeroisZero [lemma, in Fbound]
Fzero_opp [lemma, in Fop]

## G

gaCorrect [lemma, in FmaErr]
gamma2_le [lemma, in FArgReduct4]
gamma_exp [lemma, in FArgReduct2]
gamma_ge2 [lemma, in FArgReduct4]
gamma_ge2 [lemma, in FArgReduct3]
gamma_p [lemma, in FArgReduct3]
gatCorrect [lemma, in FmaErr]
Goal1 [lemma, in PradixE]
Goal2 [lemma, in PradixE]
Goal3 [lemma, in PradixE]
Goal4 [lemma, in PradixE]
Goal5b [lemma, in PradixE]
Goal5_6b [lemma, in PradixE]
Goal6 [lemma, in PradixE]
Goal7b [lemma, in PradixE]
Goal8b [lemma, in PradixE]
Goal9b [lemma, in PradixE]
growExp [definition, in FexpPlus]
growExpIsExp [lemma, in FexpPlus]
growExpIsVal [lemma, in FexpPlus]

## H

Half_Closest_Round [lemma, in discriminant2]
Half_Closest_Round [lemma, in discriminant]
hd [definition, in Fexp2]
hdexp [definition, in Fexp2]
hxExact [lemma, in Veltkamp]

## I

IEEE [library]
IEEE_canonic [definition, in IEEE]
IEEE_Float [inductive, in IEEE]
IEEE_normal [definition, in IEEE]
IEEE_normalToR [definition, in IEEE]
IEEE_Pos_To_Float [definition, in IEEE]
IEEE_precision [inductive, in IEEE]
IEEE_shift_mantissa [definition, in IEEE]
IEEE_subnormal [definition, in IEEE]
IEEE_subnormalToR [definition, in IEEE]
IEEE_To_Float [definition, in IEEE]
IEEE_To_Float_Bounded [lemma, in IEEE]
IEEE_To_Float_To_IEEE [lemma, in IEEE]
IEEE_To_R [definition, in IEEE]
IminusBounded [lemma, in Fast2Sum]
IminusComp [lemma, in EFast2Sum]
IminusCorrect [lemma, in Fast2Sum]
IminusCorrectEq [lemma, in TwoSum]
IminusFminus [lemma, in Fast2Sum]
IminusId [lemma, in Fast2Sum]
IminusInv [lemma, in Fast2Sum]
IminusOl [lemma, in Fast2Sum]
IminusOp [lemma, in TwoSum]
Iminus2Exact [lemma, in TwoSum]
ImplyClosest [lemma, in Veltkamp]
ImplyClosestStrict [lemma, in Veltkamp]
ImplyClosestStrict2 [lemma, in Veltkamp]
InBinade [lemma, in FroundProp]
InDomain [definition, in IEEE]
InegAbsInf [lemma, in FexpDiv]
InegAbsSup [lemma, in FexpDiv]
Inegdsd [lemma, in FexpDiv]
IneqEq [lemma, in discriminant3]
inject_nat_convert [lemma, in Faux]
inject_nat_eq [lemma, in Faux]
inj_abs [lemma, in Faux]
inj_oZ1 [lemma, in Zdivides]
inj_pred [lemma, in Faux]
INR_inv [lemma, in Faux]
INR_lt_nm [lemma, in Faux]
Int_part_INR [lemma, in Faux]
Int_part_IZR [lemma, in Faux]
in_map_inv [lemma, in Zenum]
IplusBounded [lemma, in Fast2Sum]
IplusCorrectEq [lemma, in TwoSum]
IplusOl [lemma, in TwoSum]
IplusOr [lemma, in Fast2Sum]
IRNDD [definition, in RND]
IRNDD_correct1 [lemma, in RND]
IRNDD_correct2 [lemma, in RND]
IRNDD_correct3 [lemma, in RND]
IRNDD_eq [lemma, in RND]
IRNDD_monotone [lemma, in RND]
IRNDD_pos [lemma, in RND]
IRNDD_projector [lemma, in RND]
isBounded [lemma, in Fbound]
isBoundedI [lemma, in FboundI]
IsCanExp [inductive, in Fexp2]
IsCanExpBounded [lemma, in Fexp2]
IsCanExpNil [constructor, in Fexp2]
IsCanExpTop [constructor, in Fexp2]
IsEqual [constructor, in Fexp2]
IsEqual [constructor, in FexpAdd]
IsExp [inductive, in Fexp2]
IsExpansion [inductive, in Fexp]
IsExpansionAddInv [lemma, in FexpPlus]
IsExpansionCons [lemma, in FexpPlus]
IsExpansionConsInv [lemma, in FexpPlus]
IsExpansionConsInvAux [lemma, in FexpPlus]
IsExpansionGrowConsInvAux [lemma, in FexpPlus]
IsExpansionNil [constructor, in Fexp]
IsExpansionSingle [constructor, in Fexp]
IsExpansionSkip [lemma, in FexpPlus]
IsExpansionTop [constructor, in Fexp]
IsExpansionTop1 [constructor, in Fexp]
IsExpansionTop2 [constructor, in Fexp]
IsExpansion_comp1 [lemma, in Fexp]
IsExpansion_comp2 [lemma, in Fexp]
isExpInv [lemma, in Fexp2]
IsExpNil [constructor, in Fexp2]
IsExpSingle [constructor, in Fexp2]
isExpSkip [lemma, in Fexp2]
IsExpTop [constructor, in Fexp2]
IsExpZle [lemma, in Fexp2]
isMax [definition, in Fmin]
isMaxComp [lemma, in FroundProp]
isMaxI [definition, in FnormI]
isMax_inv1 [lemma, in Fmin]
isMin [definition, in Fmin]
isMinComp [lemma, in FroundProp]
isMinI [definition, in FnormI]
isMin_inv1 [lemma, in Fmin]
IsNzExpansion [inductive, in Fexp]
IsNzExpansionInv [lemma, in Fexp]
isNzExpansionIsExpansion [lemma, in Fexp]
IsNzExpansionNil [constructor, in Fexp]
IsNzExpansionNilR [constructor, in Fexp]
IsNzExpansionR [inductive, in Fexp]
IsNzExpansionRInv [lemma, in Fexp]
isNzExpansionRIsNzExpansion [lemma, in Fexp]
IsNzExpansionSingle [constructor, in Fexp]
IsNzExpansionSingleR [constructor, in Fexp]
IsNzExpansionTop [constructor, in Fexp]
IsNzExpansionTopR [constructor, in Fexp]
IsRleEpsExp [inductive, in FexpAdd]
IsRleEpsExpNil [constructor, in FexpAdd]
IsRleEpsExpSingle [constructor, in FexpAdd]
IsRleEpsExpTop [constructor, in FexpAdd]
IsRleExp [inductive, in Fexp2]
IsRleExpNil [constructor, in Fexp2]
IsRleExpRev [inductive, in Fexp2]
IsRleExpRevComp [lemma, in Fexp2]
IsRleExpRevIsExp [lemma, in Fexp2]
IsRleExpRevNil [constructor, in Fexp2]
IsRleExpRevSingle [constructor, in Fexp2]
IsRleExpRev_IsRleExp [lemma, in Fexp2]
IsRleExpSingle [constructor, in Fexp2]
IsRleExpTop [constructor, in Fexp2]
IsRleExp_IsRleExpRev [lemma, in Fexp2]
IsRleRevExpTop [constructor, in Fexp2]
is_Fzero [definition, in Float]
is_FzeroP [lemma, in Float]
is_Fzero_rep1 [lemma, in Float]
is_Fzero_rep2 [lemma, in Float]
IZR_inv [lemma, in Faux]
IZR_zero [lemma, in Faux]
IZR_zero_r [lemma, in Faux]

## K

Knuth [lemma, in TwoSum]

## L

last [definition, in Fexp2]
lastexp [definition, in Fexp2]
last_hd [lemma, in Fexp2]
LeExp [lemma, in FmaErrApprox]
LeExpRound [lemma, in FmaErr]
LeExpRound2 [lemma, in FmaErr]
LeExp1 [lemma, in FmaErrApprox]
LeExp2 [lemma, in FmaErrApprox]
LeExp3 [lemma, in FmaErrApprox]
LeFnumZERO [lemma, in Fcomp]
LeFulpPos [lemma, in FroundProp]
LeR0Fnum [lemma, in Fcomp]
LessExpBound [lemma, in Fbound]
LexicoCanI [lemma, in FnormI]
LexicoNegCanI [lemma, in FnormI]
LexicoPosCanI [lemma, in FnormI]
LeZEROFnum [lemma, in Fcomp]
le_mult_anti_compatibility [lemma, in Faux]
le_next [lemma, in Faux]
le_refl_eq [lemma, in Faux]
le_Rle [lemma, in Faux]
ln_radix_pos [lemma, in RND]
Loop0 [lemma, in PradixE]
Loop1 [lemma, in PradixE]
Loop2 [lemma, in PradixE]
Loop3 [lemma, in PradixE]
Loop4 [lemma, in PradixE]
Loop6c [lemma, in PradixE]
LSB [definition, in MSB]
LSBMinus [lemma, in FroundPlus]
LSBPlus [lemma, in FroundPlus]
LSB_abs [lemma, in MSB]
LSB_comp [lemma, in MSB]
LSB_le_abs [lemma, in MSB]
LSB_le_MSB [lemma, in MSB]
LSB_opp [lemma, in MSB]
LSB_Pred [lemma, in FmaErr]
LSB_rep [lemma, in MSB]
LSB_rep_min [lemma, in MSB]
LSB_shift [lemma, in MSB]
lte_comp_mult [lemma, in Faux]
LtFnumZERO [lemma, in Float]
LtFsubnormal [lemma, in Fnorm]
LtR0Fnum [lemma, in Fcomp]
lt_comp_mult [lemma, in Faux]
lt_comp_mult_l [lemma, in Faux]
lt_comp_mult_r [lemma, in Faux]
lt_le_pred [lemma, in Faux]
lt_minus_inv [lemma, in Faux]
lt_mult_anti_compatibility [lemma, in Faux]
lt_next [lemma, in Faux]
lt_Rlt [lemma, in Faux]
lt_S_le [lemma, in Faux]
lt_Zlt_inv [lemma, in Faux]

## M

MaxBinade [lemma, in Fmin]
MaxCompatible [lemma, in Fround]
maxDiv [definition, in MSB]
maxDivCorrect [lemma, in MSB]
maxDivLess [lemma, in MSB]
maxDivLt [lemma, in MSB]
maxDivPlus [lemma, in MSB]
maxDivSimpl [lemma, in MSB]
maxDivSimplAux [lemma, in MSB]
maxDivSimplInv [lemma, in MSB]
maxDivSimplInvAux [lemma, in MSB]
maxDivUnique [lemma, in MSB]
maxDivUniqueDigit [lemma, in MSB]
maxDivUniqueInverse [lemma, in MSB]
maxDivUniqueInverseDigit [lemma, in MSB]
maxDiv_abs [lemma, in MSB]
maxDiv_opp [lemma, in MSB]
MaxEq [lemma, in Fmin]
MaxEx [lemma, in Fmin]
maxFbounded [lemma, in Fbound]
MaxFloat [lemma, in Fnorm]
maxMax [lemma, in Fbound]
maxMaxBis [lemma, in Fnorm]
maxMax1 [lemma, in Fnorm]
MaxMin [lemma, in Fmin]
MaxOppMin [lemma, in Fmin]
MaxRoundedModeP [lemma, in Fround]
MaxUniqueP [lemma, in Fround]
Maxwiwi1 [lemma, in FexpDiv]
mBFadic_correct1 [lemma, in Fmin]
mBFadic_correct2 [lemma, in Fmin]
mBFadic_correct3 [lemma, in Fmin]
mBFadic_correct4 [lemma, in Fmin]
mBFloat [definition, in Fmin]
mBPadic_Fbounded [lemma, in Fmin]
MDekker [lemma, in Fast2Sum]
MDekkerAux1 [lemma, in Fast2Sum]
MDekkerAux2 [lemma, in Fast2Sum]
MDekkerAux3 [lemma, in Fast2Sum]
MDekkerAux4 [lemma, in Fast2Sum]
MDekkerAux5 [lemma, in Fast2Sum]
MDekkerDiff [lemma, in Fast2Diff]
MDekkerDiffAux1 [lemma, in Fast2Diff]
Midpoint_aux [lemma, in FmaErr]
Midpoint_aux_aux [lemma, in FmaErr]
MinBinade [lemma, in Fmin]
MinCompatible [lemma, in Fround]
MinEq [lemma, in Fmin]
MinEx [lemma, in Fmin]
MinExList [lemma, in Fmin]
MinMax [lemma, in Fmin]
MinOppMax [lemma, in Fmin]
MinOrMax [definition, in MinOrMax]
MinOrMax [library]
MinOrMaxP [definition, in Fround]
MinOrMaxPI [definition, in FnormI]
MinOrMaxRep [lemma, in Fround]
MinOrMax1 [lemma, in MinOrMax]
MinOrMax2 [lemma, in MinOrMax]
MinOrMax3 [lemma, in MinOrMax]
MinOrMax3_aux [lemma, in MinOrMax]
MinOrMax_Fopp [lemma, in MinOrMax]
MinOrMax_Rlt [lemma, in MinOrMax]
MinRoundedModeP [lemma, in Fround]
MinUniqueP [lemma, in Fround]
minusRoundRep [lemma, in FroundPlus]
minusSameExp [lemma, in Fop]
minus_inv_lt [lemma, in Faux]
minus_inv_lt_aux [lemma, in Faux]
minus_le [lemma, in Faux]
minus_minus [lemma, in Faux]
minus_Zminus_precq [lemma, in FArgReduct2]
min_n_0 [lemma, in Faux]
min_or [lemma, in Faux]
mkIsNzAux [lemma, in Fexp]
MKnuth [lemma, in TwoSum]
MKnuthOpp [lemma, in TwoSum]
MKnuth1 [lemma, in TwoSum]
MKnuth2 [lemma, in TwoSum]
MKnuth3 [lemma, in TwoSum]
MKnuth4 [lemma, in TwoSum]
MKnuth5 [lemma, in TwoSum]
MKnuth6 [lemma, in TwoSum]
MKnuth7 [lemma, in TwoSum]
MonotoneMax [lemma, in Fmin]
MonotoneMin [lemma, in Fmin]
MonotoneP [definition, in Fmin]
MonotonePI [definition, in FnormI]
mProd [definition, in Zenum]
mProd_correct [lemma, in Zenum]
mProd_correct_rev1 [lemma, in Zenum]
mProd_correct_rev2 [lemma, in Zenum]
MSB [definition, in MSB]
MSB [library]
MSBBoundNotZero [lemma, in FroundProp]
MSBisMin [lemma, in FroundProp]
MSBProp [library]
MSBroundLSB [lemma, in FroundPlus]
MSBtoZero [lemma, in FroundProp]
MSB_abs [lemma, in MSB]
MSB_comp [lemma, in MSB]
MSB_le_abs [lemma, in MSB]
MSB_le_mult [lemma, in MSB]
MSB_le_multAux [lemma, in MSB]
MSB_mix [lemma, in MSB]
MSB_monotone [lemma, in MSB]
MSB_monotoneAux [lemma, in MSB]
MSB_opp [lemma, in MSB]
MSB_shift [lemma, in MSB]
multExpMin [lemma, in FroundMult]
multExpUpperBound [lemma, in FroundMult]
mult_eq_inv [lemma, in Faux]
mult_le_MSB [lemma, in MSB]
mult_le_MSBAux [lemma, in MSB]
mZlist [definition, in Zenum]
mZlist_aux [definition, in Zenum]
mZlist_aux_correct [lemma, in Zenum]
mZlist_aux_correct_rev1 [lemma, in Zenum]
mZlist_aux_correct_rev2 [lemma, in Zenum]
mZlist_correct [lemma, in Zenum]
mZlist_correct_rev1 [lemma, in Zenum]
mZlist_correct_rev2 [lemma, in Zenum]

## N

natEq [definition, in Faux]
nat_div_one [lemma, in FnormI]
NconvertO [lemma, in Faux]
NDivides_minus [lemma, in Zdivides]
NearEqual [inductive, in FexpAdd]
NearEqual [inductive, in Fexp2]
NearestInteger [lemma, in FroundDivSqrt]
NEq_INR [lemma, in Faux]
NEq_INRO [lemma, in Faux]
NEq_INR1 [lemma, in Faux]
NEq_IZRO [lemma, in Faux]
NisFzeroComp [lemma, in Float]
nNormMimLtvNum [lemma, in FSucc]
nNormMin [definition, in Fnorm]
nNormPos [lemma, in Fnorm]
nNrMMimLevNum [lemma, in Fnorm]
None [constructor, in Option]
NormalAndSubNormalNotEq [lemma, in Fnorm]
NormalbPrim [lemma, in Dekker]
NormalIandSubnormalINotEq [lemma, in FboundI]
NormalNotSubNormal [lemma, in Fnorm]
Normal_and_exp [lemma, in FArgReduct2]
Normal_and_exp2 [lemma, in FArgReduct2]
Normal_ge [lemma, in Divnk]
Normal_le [lemma, in Divnk]
NotDividesDigit [lemma, in Zdivides]
notEqLt [lemma, in Faux]
NotR0NotZero [lemma, in FminOp]
NotZmultZero [lemma, in Faux]
not_O_lt [lemma, in Faux]
NroundN [lemma, in FroundProp]

## O

Odd [definition, in Fodd]
OddEvenDec [lemma, in Fodd]
OddExp [lemma, in Fodd]
OddMult [lemma, in Fodd]
OddMultInv [lemma, in Fodd]
OddNEven [lemma, in Fodd]
OddOpp [lemma, in Fodd]
OddPlusInv1 [lemma, in Fodd]
OddPlusInv2 [lemma, in Fodd]
OddPlus1 [lemma, in Fodd]
OddPlus2 [lemma, in Fodd]
OddSEven [lemma, in Fodd]
OddSEvenInv [lemma, in Fodd]
Odd1 [lemma, in Fodd]
odd_even_lem [lemma, in Paux]
OneErrorOnly [lemma, in FArgReduct4]
oneExp_le [lemma, in Float]
oneExp_lt [lemma, in Float]
oneExp_Zle [lemma, in Float]
oneExp_Zlt [lemma, in Float]
OneMoreR [constructor, in FexpAdd]
OneMoreR [constructor, in Fexp2]
oneZplus [lemma, in Fop]
oppBounded [lemma, in Fbound]
oppBoundedInv [lemma, in Fbound]
OppositeIUnique [lemma, in FnormI]
OppositeIUnique_1 [lemma, in FnormI]
OppositeIUnique_2 [lemma, in FnormI]
Option [inductive, in Option]
Option [library]
OutSum3 [lemma, in ThreeSum2]
oZ [definition, in Paux]
oZ1 [definition, in Zdivides]
oZ1_oZ [lemma, in FminOp]

## P

Paux [library]
Pdiv [definition, in Paux]
PdivBound [definition, in Paux]
PdivBound_correct [lemma, in Paux]
PdivBound_correct1 [lemma, in Paux]
PdivBound_correct2 [lemma, in Paux]
PdivBound_correct3 [lemma, in Paux]
PdivBound_correct4 [lemma, in Paux]
Pdivless [definition, in Paux]
PdivlessAux [definition, in Paux]
Pdivless1 [lemma, in Paux]
Pdivless2 [lemma, in Paux]
Pdivless_correct [lemma, in Paux]
Pdiv_correct [lemma, in Paux]
pGeUnderf [lemma, in discriminant3]
pGivesDigit [lemma, in Fnorm]
plusClosestLowerBound [lemma, in Closest2Plus]
plusClosestLowerBoundAux1 [lemma, in Closest2Plus]
plusClosestLowerBoundAux2 [lemma, in Closest2Plus]
plusErrorBound1 [lemma, in ClosestPlus]
plusErrorBound1bis [lemma, in ClosestPlus]
plusErrorBound1withZero [lemma, in ClosestPlus]
plusErrorBound2 [lemma, in Closest2Plus]
plusExactExp [lemma, in ClosestPlus]
plusExactExpCanonic [lemma, in ClosestPlus]
plusExactR0 [lemma, in ClosestPlus]
plusExactSub [lemma, in FmaEmul]
plusExact1 [lemma, in ClosestPlus]
plusExact1bis [lemma, in ClosestPlus]
plusExact2 [lemma, in ClosestPlus]
plusExact2Aux [lemma, in ClosestPlus]
plusExp [definition, in Veltkamp]
plusExpBound [lemma, in FroundPlus]
plusExpMin [lemma, in FroundPlus]
plusExpUpperBound [lemma, in FroundPlus]
plusUpperBound [lemma, in Closest2Plus]
PminPos [lemma, in FroundProp]
pNormal_absolu_min [lemma, in Fnorm]
positive_exp [definition, in Paux]
positive_exp_correct [lemma, in Paux]
PosNormMin [lemma, in Fnorm]
pos_eq_bool [definition, in Faux]
pos_eq_bool_correct [lemma, in Faux]
pos_length [definition, in Digit]
pos_length_pow [lemma, in Digit]
powerRZSumRle [lemma, in Dekker]
powerRZSumRle [lemma, in FmaErr]
powerRZ_add [lemma, in Rpow]
powerRZ_le [lemma, in Rpow]
powerRZ_lt [lemma, in Rpow]
powerRZ_NOR [lemma, in Rpow]
powerRZ_O [lemma, in Rpow]
powerRZ_R1 [lemma, in Rpow]
powerRZ_Zopp [lemma, in Rpow]
powerRZ_Zs [lemma, in Rpow]
powerRZ_1 [lemma, in Rpow]
pow_add [lemma, in Rpow]
pow_lt [lemma, in Rpow]
pow_NR0 [lemma, in Rpow]
pow_O [lemma, in Rpow]
pow_RN_plus [lemma, in Rpow]
pow_R1 [lemma, in Rpow]
pow_1 [lemma, in Rpow]
pPos [lemma, in Veltkamp]
pPred [definition, in Fnorm]
pPredMoreThanOne [lemma, in ClosestPlus]
pPredMoreThanRadix [lemma, in ClosestPlus]
PradixE [library]
precisionNotZero [lemma, in DblRndOdd]
prec1_Greater_Than_One [lemma, in FArgReduct2]
ProjectMax [lemma, in Fmin]
ProjectMaxI [lemma, in FnormI]
ProjectMin [lemma, in Fmin]
ProjectMinI [lemma, in FnormI]
ProjectorP [definition, in Fmin]
ProjectorPI [definition, in FnormI]
pSubnormal_absolu_min [lemma, in Fnorm]
ptonat_def1 [lemma, in Faux]
pUCanonic_absolu [lemma, in Fnorm]
PuissLessThanHalf [lemma, in ThreeSumProps]
p'GivesBound [lemma, in Veltkamp]
p'GivesBound2 [lemma, in Veltkamp]
p''GivesBound [lemma, in Dekker]
P_le_two_Q [lemma, in discriminant2]
P_le_two_Q [lemma, in discriminant]
P_positive [lemma, in discriminant]
P_positive [lemma, in discriminant2]

## Q

qGeUnderf [lemma, in discriminant3]
qNeg [lemma, in Veltkamp]
Q_le_two_P [lemma, in discriminant2]
Q_le_two_P [lemma, in discriminant]
Q_positive [lemma, in discriminant2]
Q_positive [lemma, in discriminant]

## R

Rabsolu_left1 [lemma, in Faux]
Rabsolu_Zabs [lemma, in Faux]
radixNotZero [lemma, in DblRndOdd]
radixRangeBoundExp [lemma, in Finduct]
radixRangeBoundExp [lemma, in FroundPlus]
rCeil [definition, in FminOp]
rCeil_correct [lemma, in FminOp]
rClosestEven [definition, in FminOp]
rClosestEvenPos [definition, in FminOp]
rClosestEvenPos_correct [lemma, in FminOp]
rClosestEven_correct [lemma, in FminOp]
Rdiv_Rle [lemma, in FArgReduct]
ReductRangeI [lemma, in FnormI]
ReductRangeIInv [lemma, in FnormI]
ReqGivesEqwithSameExp [lemma, in Float]
rev_length [lemma, in Fexp2]
rev_sum [lemma, in Fexp2]
rExact [constructor, in FminOp]
rExp [lemma, in Dekker]
rFloat [definition, in FminOp]
rFloor [definition, in FminOp]
rFloor_correct [lemma, in FminOp]
RinvClosestRinvMaxRle [lemma, in FArgReduct]
RinvClosestRinvMaxRle_Neg [lemma, in FArgReduct]
RinvClosestRinvMaxRle_Pos [lemma, in FArgReduct]
RinvClosestRinvMaxRle_pow [lemma, in FArgReduct]
RinvClosestRinvMaxRle_pow2 [lemma, in FArgReduct]
Rinv_powerRZ [lemma, in Rpow]
RleBoundRoundl [lemma, in FroundProp]
RleBoundRoundr [lemma, in FroundProp]
Rledouble [lemma, in Faux]
RleFexpFabs [lemma, in Fop]
RleMaxR0 [lemma, in FroundProp]
RleMinR0 [lemma, in FroundProp]
RleRoundedAbs [lemma, in FmaErrApprox]
RleRoundedLessR0 [lemma, in FroundProp]
RleRoundedR0 [lemma, in FroundProp]
RleRRounded [lemma, in Veltkamp]
RleR0Rminus [lemma, in FminOp]
Rle_err_pow2 [lemma, in Divnk]
Rle_Fexp_eq_Zle [lemma, in Fcomp]
Rle_floats_isMax_Neg [lemma, in FArgReduct]
Rle_floats_isMax_Pos [lemma, in FArgReduct]
Rle_Float_Zle [lemma, in Float]
Rle_INR [lemma, in Faux]
Rle_IZR [lemma, in Faux]
Rle_IZRO [lemma, in Faux]
Rle_IZR1 [lemma, in Faux]
Rle_monotone_exp [lemma, in Float]
Rle_monotony_contra_exp [lemma, in Float]
Rle_mult_pos [lemma, in FexpAdd]
Rle_powerRZ [lemma, in Rpow]
Rle_Rinv [lemma, in Faux]
Rle_Rminus_ZERO [lemma, in ThreeSumProps]
Rle_R0_Ropp [lemma, in Faux]
RlIt2 [lemma, in Faux]
Rltdouble [lemma, in Faux]
RltSpeTwice1 [lemma, in FminOp]
RltSpeTwice2 [lemma, in FminOp]
Rlt2 [lemma, in Faux]
Rlt_Fexp_eq_Zlt [lemma, in Fcomp]
Rlt_Float_Zlt [lemma, in Float]
Rlt_INR1 [lemma, in Faux]
Rlt_IZR [lemma, in Faux]
Rlt_IZRO [lemma, in Faux]
Rlt_IZR1 [lemma, in Faux]
Rlt_monotony_contra_exp [lemma, in Float]
Rlt_monotony_exp [lemma, in Float]
Rlt_pow [lemma, in Rpow]
Rlt_powerRZ [lemma, in Rpow]
Rlt_pow_R1 [lemma, in Rpow]
Rlt_RinvDouble [lemma, in Faux]
Rlt_Rminus_ZERO [lemma, in Faux]
Rlt_R0_Ropp [lemma, in Faux]
RmaxAbs [lemma, in Faux]
RmaxLess1 [lemma, in Faux]
RmaxLess2 [lemma, in Faux]
RmaxProp [lemma, in FexpDiv]
RmaxRmult [lemma, in Faux]
RmaxSym [lemma, in Faux]
Rmax_simpl1 [lemma, in FexpDiv]
Rmin_eq [lemma, in FArgReduct]
Rmin_1 [lemma, in FArgReduct]
Rmin_2 [lemma, in FArgReduct]
Rmult_IZR [lemma, in Faux]
RND [library]
RND_ClosestUp [definition, in RND]
RND_ClosestUp_canonic [lemma, in RND]
RND_ClosestUp_correct [lemma, in RND]
RND_EvenClosest [definition, in RND]
RND_EvenClosest_canonic [lemma, in RND]
RND_EvenClosest_correct [lemma, in RND]
RND_Max [definition, in RND]
RND_Max_canonic [lemma, in RND]
RND_Max_correct [lemma, in RND]
RND_Max_Pos [definition, in RND]
RND_Max_Pos_canonic [lemma, in RND]
RND_Max_Pos_correct [lemma, in RND]
RND_Max_Pos_Rle [lemma, in RND]
RND_Min [definition, in RND]
RND_Min_canonic [lemma, in RND]
RND_Min_correct [lemma, in RND]
RND_Min_Pos [definition, in RND]
RND_Min_Pos_bounded_aux [lemma, in RND]
RND_Min_Pos_canonic [lemma, in RND]
RND_Min_Pos_correct [lemma, in RND]
RND_Min_Pos_monotone [lemma, in RND]
RND_Min_Pos_projector [lemma, in RND]
RND_Min_Pos_Rle [lemma, in RND]
RND_Zero [definition, in RND]
RND_Zero_canonic [lemma, in RND]
RND_Zero_correct [lemma, in RND]
rOp [definition, in FminOp]
RoundAbsMonotonel [lemma, in FroundProp]
RoundAbsMonotoner [lemma, in FroundProp]
RoundBound [lemma, in ClosestPlus]
roundedModeAbsMult [lemma, in FroundProp]
RoundedModeBounded [lemma, in FroundProp]
RoundedModeErrorExpStrict [lemma, in FroundProp]
roundedModeLessMult [lemma, in FroundProp]
roundedModeMoreMult [lemma, in FroundProp]
RoundedModeMult [lemma, in FroundProp]
RoundedModeMultAbs [lemma, in FroundProp]
RoundedModeMultLess [lemma, in FroundProp]
RoundedModeP [definition, in Fround]
RoundedModePI [definition, in FnormI]
RoundedModeProjectorIdem [lemma, in FroundProp]
RoundedModeProjectorIdemEq [lemma, in FroundProp]
RoundedModeProjectorIdemI [lemma, in FnormI]
RoundedModeP_inv1 [lemma, in Fround]
RoundedModeP_inv2 [lemma, in Fround]
RoundedModeP_inv3 [lemma, in Fround]
RoundedModeP_inv4 [lemma, in Fround]
RoundedModeRep [lemma, in Fround]
RoundedModeUlp [lemma, in FroundProp]
RoundedProjector [lemma, in Fround]
RoundedProjectorI [lemma, in FnormI]
RoundGeGeneral [lemma, in Axpy]
RoundGeNormal [lemma, in discriminant3]
RoundLeGeneral [lemma, in Axpy]
RoundLeNormal [lemma, in discriminant3]
RoundLessThanIsMax [lemma, in Fround]
RoundLSBMax [lemma, in FroundProp]
RoundMSBmax [lemma, in FroundProp]
RoundMSBmin [lemma, in FroundProp]
Rpow [library]
Rpow_eq_inv [lemma, in Rpow]
Rpow_R1 [lemma, in Rpow]
rResult [inductive, in FminOp]
rRound [constructor, in FminOp]
rToZero [definition, in FminOp]
rToZero_correct [lemma, in FminOp]
R0LeFnum [lemma, in Fcomp]
R0LtFnum [lemma, in Fcomp]
R0RltRlePred [lemma, in FPred]
R0RltRleSucc [lemma, in FSucc]

## S

sameExpEq [lemma, in Float]
ScalableRoundedModeP [lemma, in Fround]
Second_Comput_ok [lemma, in FArgReduct4]
SGe [lemma, in Dekker]
SLe [lemma, in Dekker]
Some [constructor, in Option]
sTactic [library]
Step [definition, in FexpAdd]
Sterbenz [lemma, in Fprop]
SterbenzApprox [lemma, in FArgReduct]
SterbenzApproxI [lemma, in FnormI]
SterbenzApproxI_aux1 [lemma, in FnormI]
SterbenzApproxI_aux2 [lemma, in FnormI]
SterbenzApproxI_pos [lemma, in FnormI]
SterbenzApproxI_1 [lemma, in FnormI]
SterbenzApproxI_2 [lemma, in FnormI]
SterbenzApproxI_3 [lemma, in FnormI]
SterbenzApproxI_4 [lemma, in FnormI]
SterbenzApprox2 [lemma, in FArgReduct]
SterbenzApprox3 [lemma, in FArgReduct2]
SterbenzApprox_weak_1 [lemma, in FArgReduct]
SterbenzAux [lemma, in Fprop]
Sterbenzbis [lemma, in FArgReduct2]
SterbenzI [lemma, in FnormI]
SterbenzIAux1 [lemma, in FnormI]
SterbenzIAux2 [lemma, in FnormI]
SterbenzIAux2A [lemma, in FnormI]
SterbenzIAux2B [lemma, in FnormI]
SterbenzOppI [lemma, in FnormI]
Subexact [lemma, in FmaErr]
sum [definition, in Fexp2]
sum_app [lemma, in Fexp2]
sum_IsExp [lemma, in Fexp2]
SymmetricP [definition, in Fround]
s2Ge [lemma, in Dekker]
s2Le [lemma, in Dekker]

## T

tBounded [lemma, in FmaErrApprox]
tBounded_aux [lemma, in FmaErrApprox]
ThreeSumLoop [lemma, in ThreeSumProps]
ThreeSumProps [library]
ThreeSum2 [library]
tLe [lemma, in FmaErrApprox]
ToInfinityCompatible [lemma, in Fround]
ToInfinityMinOrMax [lemma, in Fround]
ToInfinityMonotone [lemma, in Fround]
ToInfinityP [definition, in Fround]
ToInfinityRoundedModeP [lemma, in Fround]
ToInfinitySymmetric [lemma, in Fround]
ToInfinityTotal [lemma, in Fround]
ToInfinityUniqueP [lemma, in Fround]
TotalP [definition, in Fround]
TotalPI [definition, in FnormI]
ToZeroCompatible [lemma, in Fround]
ToZeroMinOrMax [lemma, in Fround]
ToZeroMonotone [lemma, in Fround]
ToZeroP [definition, in Fround]
ToZeroRoundedModeP [lemma, in Fround]
ToZeroSymmetric [lemma, in Fround]
ToZeroTotal [lemma, in Fround]
ToZeroUniqueP [lemma, in Fround]
To_Odd [definition, in DblRndOdd]
To_OddCompatible [lemma, in DblRndOdd]
To_OddMinOrMax [lemma, in DblRndOdd]
To_OddMonotone [lemma, in DblRndOdd]
To_OddRoundedModeP [lemma, in DblRndOdd]
To_OddSymmetricP [lemma, in DblRndOdd]
To_OddTotal [lemma, in DblRndOdd]
To_OddUniqueP [lemma, in DblRndOdd]
To_Odd_Even_is_Even [lemma, in DblRndOdd]
To_Odd_Even_is_Even_nNormMin [lemma, in DblRndOdd]
To_Odd_Odd_is_Odd [lemma, in FmaEmul]
Twice_EvenClosest_Round [lemma, in discriminant]
Twice_EvenClosest_Round [lemma, in discriminant2]
TwoMoreThanOne [lemma, in Closest2Prop]
TwoMoreThanOne [lemma, in discriminant2]
TwoMoreThanOne [lemma, in discriminant3]
TwoMoreThanOne [lemma, in Closest2Plus]
TwoMoreThanOne [lemma, in discriminant]
TwoMoreThanOne [lemma, in Axpy]
TwoMoreThanOneR [lemma, in Axpy]
TwoSum [library]
TwoSumExp [lemma, in FexpPlus]
TwoSumLt1 [lemma, in FexpPlus]
TwoSumLt2 [lemma, in FexpPlus]
TwoSumNonNul [lemma, in ThreeSum2]
TwoSumNul [lemma, in ThreeSum2]
TwoSumOl1 [lemma, in FexpPlus]
TwoSumOl2 [lemma, in FexpPlus]
TwoSumOneNul [lemma, in ThreeSum2]
TwoSumOneNul2 [lemma, in ThreeSum2]
TwoSumOr1 [lemma, in FexpPlus]
TwoSumOr2 [lemma, in FexpPlus]
TwoSumProp [lemma, in FmaErr]
t_exact [lemma, in discriminant2]
t_exact [lemma, in discriminant]

## U

uhPos [lemma, in FmaErrApprox]
UlpFlessuGe [lemma, in Axpy]
UlpFlessuGe2 [lemma, in Axpy]
UlpFlessuGe_aux [lemma, in Axpy]
Ulp_Le_LSigB [lemma, in MSB]
Underf_Err [definition, in Dekker]
Underf_Err1 [lemma, in Dekker]
Underf_Err2 [lemma, in Dekker]
Underf_Err2_aux [lemma, in Dekker]
Underf_Err3 [lemma, in Dekker]
Underf_Err3_bis [lemma, in Dekker]
UniqueP [definition, in Fround]
UnMoinsPos [lemma, in FmaErr]
u_bounds [lemma, in FArgReduct2]

## V

Veltkamp [lemma, in Veltkamp]
Veltkamp [library]
Veltkampb' [lemma, in Dekker]
VeltkampEven [lemma, in Veltkamp]
VeltkampEvenN [lemma, in Veltkamp]
VeltkampEvenN_aux [lemma, in Veltkamp]
VeltkampEvenS [lemma, in Veltkamp]
VeltkampEven1 [lemma, in Veltkamp]
VeltkampEven2 [lemma, in Veltkamp]
VeltkampEven_pos [lemma, in Veltkamp]
VeltkampN [lemma, in Veltkamp]
VeltkampN_aux [lemma, in Veltkamp]
VeltkampS [lemma, in Veltkamp]
VeltkampU [lemma, in Veltkamp]
Veltkamp_aux [lemma, in Veltkamp]
Veltkamp_aux_aux [lemma, in Veltkamp]
Veltkamp_pos [lemma, in Veltkamp]
Veltkamp_tail [lemma, in Veltkamp]
Veltkamp_tail2 [lemma, in Veltkamp]
Veltkamp_tail_aux [lemma, in Veltkamp]
vLe [lemma, in FmaErrApprox]
vLe_aux [lemma, in FmaErrApprox]
vNumbMoreThanOne [lemma, in Fnorm]
vNumPrecision [lemma, in Fnorm]
vNum_eq_Zpower [lemma, in FArgReduct2]
vNum_eq_Zpower [lemma, in IEEE]
vNum_eq_Zpower_bmoinsq [lemma, in FArgReduct2]
vNum_eq_Zpower_bzH [lemma, in FArgReduct2]
vNum_eq_Zpower_bzH2 [lemma, in FArgReduct2]
vNum_eq_Zpower_bzH2_fn [lemma, in FArgReduct2]
vNum_eq_Zpower_bzH_fn [lemma, in FArgReduct2]
vNum_eq_Zpower_b1 [lemma, in FArgReduct2]
vNum_eq_Zpower_b1bis [lemma, in FArgReduct2]
v_neq_zero [lemma, in FArgReduct4]

## W

wLe [lemma, in FmaErrApprox]

## X

xLe2y [lemma, in FmaErr]
xLe2y_aux1 [lemma, in FmaErr]
xLe2y_aux2 [lemma, in FmaErr]
x1y2Le [lemma, in Dekker]
x2y1Le [lemma, in Dekker]
x2y2Le [lemma, in Dekker]
x_over_zHgamma_eq [lemma, in FArgReduct2]

## Y

yLe2x [lemma, in FmaErr]
yLe2x_aux [lemma, in FmaErr]

## Z

Zabs_absolu [lemma, in Faux]
Zabs_eq_case [lemma, in Zdivides]
Zabs_eq_opp [lemma, in Faux]
Zabs_intro [lemma, in Faux]
Zabs_tri [lemma, in Zdivides]
Zabs_Zmult [lemma, in Faux]
Zabs_Zopp [lemma, in Faux]
Zabs_Zs [lemma, in Faux]
Zcompare_correct [lemma, in Digit]
Zcompare_EGAL [lemma, in Faux]
Zdivides [definition, in Zdivides]
Zdivides [library]
ZdividesDiv [lemma, in Zdivides]
ZDividesLe [lemma, in Zdivides]
ZdividesLessPow [lemma, in Zdivides]
ZdividesMult [lemma, in Zdivides]
ZdividesP [definition, in Zdivides]
ZdividesTrans [lemma, in Zdivides]
ZdividesZquotient [lemma, in Zdivides]
ZdividesZquotientInv [lemma, in Zdivides]
Zdivides1 [lemma, in Zdivides]
ZDivides_add [lemma, in Zdivides]
ZDivides_mult [lemma, in Zdivides]
Zenum [library]
Zeq_mult_simpl [lemma, in Zdivides]
Zeq_Zs [lemma, in Faux]
Zero_le_oZ [lemma, in Zdivides]
ZevenP [definition, in FminOp]
ZevenP_correct [lemma, in FminOp]
zH1Pos [lemma, in FArgReduct2]
zH1_eq [lemma, in FArgReduct2]
zH_exp_N [lemma, in FArgReduct4]
ZleAbs [lemma, in Faux]
ZleLe [lemma, in Faux]
Zle_abs [lemma, in Faux]
Zle_monotony_contra_abs_pow [lemma, in Fbound]
Zle_mult_gen [lemma, in Faux]
Zle_next [lemma, in Faux]
Zle_n_Zpred [lemma, in Faux]
Zle_powerRZ [lemma, in Rpow]
Zle_Rle [lemma, in Faux]
Zle_Zabs [lemma, in Faux]
Zle_Zabs_inv1 [lemma, in Faux]
Zle_Zabs_inv2 [lemma, in Faux]
Zle_ZERO_Zabs [lemma, in Faux]
Zle_Zminus_ZERO [lemma, in Faux]
Zle_Zmult_comp_l [lemma, in Faux]
Zle_Zmult_comp_r [lemma, in Faux]
Zle_Zopp [lemma, in Faux]
Zle_Zopp_Inv [lemma, in Faux]
Zle_Zpred [lemma, in Faux]
Zle_Zpred_inv [lemma, in Faux]
Zle_Zpred_Zlt [lemma, in Faux]
Zle_Zpred_Zpred [lemma, in Faux]
ZltNormMinVnum [lemma, in FSucc]
Zlt_absolu [lemma, in Faux]
Zlt_MSB_LSB [lemma, in Fexp]
Zlt_mult_simpl_l [lemma, in Faux]
Zlt_mult_ZERO [lemma, in Faux]
Zlt_next [lemma, in Faux]
Zlt_not_eq [lemma, in Faux]
Zlt_not_eq_rev [lemma, in Faux]
Zlt_powerRZ [lemma, in Rpow]
Zlt_Rlt [lemma, in Faux]
Zlt_Zabs_intro [lemma, in Faux]
Zlt_Zabs_inv1 [lemma, in Faux]
Zlt_Zabs_inv2 [lemma, in Faux]
Zlt_Zabs_Zpred [lemma, in Faux]
Zlt_ZERO_Zle_ONE [lemma, in Faux]
Zlt_Zminus_ZERO [lemma, in Faux]
Zlt_Zopp [lemma, in Faux]
Zlt_Zopp_Inv [lemma, in Faux]
Zlt_Zpower_nat [lemma, in FboundI]
Zlt_1_O [lemma, in Faux]
zL_over_zH [lemma, in FArgReduct2]
Zmax [definition, in Faux]
ZmaxLe1 [lemma, in Faux]
ZmaxLe2 [lemma, in Faux]
ZmaxSym [lemma, in Faux]
Zmax_case [lemma, in FArgReduct4]
Zmax_le1 [lemma, in Faux]
Zmax_le2 [lemma, in Faux]
Zminus_n_predm [lemma, in Faux]
Zmin_le1 [lemma, in Faux]
Zmin_le2 [lemma, in Faux]
Zmin_sym [lemma, in Faux]
Zmin_Zle [lemma, in Faux]
Zmin_Zlt [lemma, in FmaErr]
Zmin_Zmax [lemma, in Faux]
Zopp_Zpred_Zs [lemma, in Faux]
zPos [lemma, in FmaErrApprox]
Zpos_eq_eq [lemma, in FmaEmul]
Zpower_nat_anti_eq [lemma, in Digit]
Zpower_nat_anti_monotone_le [lemma, in Digit]
Zpower_nat_anti_monotone_lt [lemma, in Digit]
Zpower_nat_exp [lemma, in FminOp]
Zpower_nat_is_pos [lemma, in IEEE]
Zpower_nat_less [lemma, in Digit]
Zpower_nat_monotone_le [lemma, in Digit]
Zpower_nat_monotone_lt [lemma, in Digit]
Zpower_nat_monotone_S [lemma, in Digit]
Zpower_nat_O [lemma, in Faux]
Zpower_nat_powerRZ_absolu [lemma, in Rpow]
Zpower_nat_S [lemma, in FboundI]
Zpower_nat_Z_powerRZ [lemma, in Rpow]
Zpower_nat_1 [lemma, in Faux]
Zpower_NR0 [lemma, in Rpow]
Zpower_NR1 [lemma, in Rpow]
Zpred_Zle_Zabs_intro [lemma, in Faux]
Zpred_Zopp_Zs [lemma, in Faux]
Zquotient [definition, in Zdivides]
ZquotientMonotone [lemma, in Zdivides]
ZquotientPos [lemma, in Zdivides]
ZquotientProp [lemma, in Zdivides]
ZquotientUnique [lemma, in Zdivides]
ZquotientZopp [lemma, in Zdivides]
Zquotient1 [lemma, in Zdivides]
Zquotient_mult_comp [lemma, in Zdivides]
ZroundZ [lemma, in FroundProp]
Z2pos [definition, in FminOp]
Z2pos_correct [lemma, in FminOp]
Z_div_one [lemma, in FnormI]
Z_eq_bool [definition, in Faux]
Z_eq_bool_correct [lemma, in Faux]
Z_O_1 [lemma, in Faux]

# Lemma Index

## A

abeLeab [in FmaErr]
absFBounded [in Fbound]
absolu_comp_mult [in Faux]
absolu_INR [in Faux]
absolu_lt_nz [in Faux]
absolu_Zopp [in Faux]
absolu_Zs [in Faux]
absolu_Zs_neg [in Faux]
abs_lt_MSB [in MSB]
AddExpGeUnderf [in discriminant3]
AddExpGeUnderf2 [in discriminant3]
AddExpGe1Underf [in discriminant3]
AddExpGe1Underf2 [in discriminant3]
addExpIsExp [in FexpPlus]
addExpIsVal [in FexpPlus]
AddOddEven [in FmaEmul]
AddOddEven2 [in FmaEmul]
AddOddEven_aux [in FmaEmul]
AddOddEven_aux_aux [in FmaEmul]
AddOddEven_can [in FmaEmul]
AddOddOdd [in FmaEmul]
AddOddOdd2 [in FmaEmul]
AddOddOdd2_can [in FmaEmul]
AddOddOdd_aux [in FmaEmul]
AddOddOdd_aux_aux [in FmaEmul]
AddOddOdd_can [in FmaEmul]
AddStep [in FexpAdd]
app_length [in Fexp2]
arg_reduct_exists_k_zH [in FArgReduct2]
AScal2 [in Closest2Prop]
AxpyFLessu_Fmac [in Axpy]
AxpyPos [in Axpy]
AxpyPos_Fmac [in Axpy]
Axpy_aux1 [in Axpy]
Axpy_aux1_aux1 [in Axpy]
Axpy_aux1_aux2 [in Axpy]
Axpy_aux1_aux3 [in Axpy]
Axpy_aux2 [in Axpy]
Axpy_aux3 [in Axpy]
Axpy_opt [in Axpy]
Axpy_opt_Fmac [in Axpy]
Axpy_Simpl1 [in Axpy]
Axpy_Simpl1bis [in Axpy]
Axpy_Simpl2 [in Axpy]
Axpy_tFlessu [in Axpy]

## B

be2MuchSmaller [in FmaErr]
bimplybplusNorm [in Veltkamp]
binary_value_Zle [in IEEE]
BLoop1 [in PradixE]
BLoop2 [in PradixE]
BLoop3 [in PradixE]
BLoop4 [in PradixE]
BminusSameExp [in Fprop]
BminusSameExpAux [in Fprop]
BminusSameExpNeg [in Fprop]
boundBoundNat [in Fmin]
BoundedBounded [in DoubleRound]
BoundedL [in Dekker]
BoundedL [in FmaErr]
boundedNorMinGivesExp [in Fnorm]
boundedNorMinGivesExp2 [in FIA64elem]
Boundedt1 [in Dekker]
Boundedt2 [in Dekker]
Boundedt3 [in Dekker]
Boundedt4 [in Dekker]
Boundedt4_aux [in Dekker]
Boundedx1y1 [in Dekker]
Boundedx1y1_aux [in Dekker]
Boundedx1y2 [in Dekker]
Boundedx1y2_aux [in Dekker]
Boundedx2y1 [in Dekker]
Boundedx2y1_aux [in Dekker]
Boundedx2y2 [in Dekker]
boundNatCorrect [in Fmin]
boundNormalMult [in MSBProp]
boundOnePrecision [in MSBProp]
boundRCorrect1 [in Fmin]
boundRCorrect2 [in Fmin]
boundRrOpp [in Fmin]
bound3Sum [in ThreeSum2]

## C

CanonicFulp [in FroundProp]
CanonicFulp [in FminOp]
cases [in discriminant3]
Closestbbext [in Dekker]
Closestbbplus [in Veltkamp]
Closestbplusb [in Veltkamp]
ClosestClosest [in Veltkamp]
ClosestCompatible [in Closest]
ClosestErrorBound [in ClosestProp]
ClosestErrorBoundNormal [in ClosestProp]
ClosestErrorBoundNormal2_aux [in ClosestProp]
ClosestErrorBoundNormal_aux [in ClosestProp]
ClosestErrorBound2 [in ClosestProp]
ClosestErrorExp [in ClosestProp]
ClosestErrorExpStrict [in ClosestProp]
ClosestExp [in ClosestProp]
ClosestFabs [in ClosestProp]
ClosestIdem [in ClosestProp]
ClosestImplyEven [in Veltkamp]
ClosestImplyEven_int [in Veltkamp]
ClosestInfPredExp [in DblRndOdd]
closestLessMultAbs [in ClosestMult]
closestLessMultNeg [in ClosestMult]
closestLessMultPos [in ClosestMult]
ClosestMax [in Closest]
ClosestMaxEq [in Closest]
ClosestMax1 [in FminOp]
ClosestMax2 [in FminOp]
ClosestMin [in Closest]
ClosestMinEq [in Closest]
ClosestMinOrMax [in Closest]
ClosestMin1 [in FminOp]
ClosestMin2 [in FminOp]
ClosestMonotone [in Closest]
ClosestM1 [in ClosestProp]
ClosestOpp [in ClosestProp]
ClosestPropHigham25 [in ClosestProp]
ClosestRoundedModeP [in Closest]
ClosestRoundeGeNormal [in FmaErr]
ClosestRoundeLeNormal [in FmaErr]
ClosestStrict [in DblRndOdd]
ClosestStrictPos [in DblRndOdd]
ClosestStrictPred [in DblRndOdd]
ClosestSuccPred [in Veltkamp]
ClosestSymmetric [in Closest]
ClosestTotal [in Closest]
ClosestUlp [in ClosestProp]
ClosestZero [in Dekker]
ClosestZero1 [in FmaErr]
ClosestZero2 [in FmaErr]
compare_SUP_dec [in Paux]
cons_neq [in Fexp2]
Contradict1 [in sTactic]
Contradict2 [in sTactic]
Contradict3 [in sTactic]
convert_not_O [in Faux]

## D

DblRndStable [in DoubleRound]
Dekker [in Fast2Sum]
Dekker [in Dekker]
DekkerDiff [in Fast2Diff]
DekkerN [in Dekker]
DekkerS1 [in Dekker]
DekkerS2 [in Dekker]
Dekker1 [in Fast2Sum]
Dekker1 [in Dekker]
Dekker2 [in Fast2Sum]
Dekker2 [in Dekker]
Dekker2_aux [in Dekker]
Dekker3 [in Fast2Sum]
Dekker_aux [in Dekker]
delta_inf [in FArgReduct2]
delta_inf [in discriminant2]
delta_inf [in discriminant]
dexact [in discriminant3]
dExpPrim [in Dekker]
dExpPrimEq [in Dekker]
digitAdd [in Digit]
digitAuxLess [in Digit]
digitAuxMore [in Digit]
digitAux1 [in Digit]
digitGivesBoundedNum [in Fnorm]
digitInv [in Digit]
digitLess [in Digit]
digitMore [in Digit]
digitnNormMin [in Fnorm]
digitNotZero [in Digit]
digitO [in Digit]
digitPredVNumiSPrecision [in Fnorm]
digitVNumiSPrecision [in Fnorm]
digit1 [in Digit]
digit_abs [in Digit]
digit_anti_monotone_lt [in Digit]
digit_bound [in Digit]
digit_minus1 [in Digit]
digit_monotone [in Digit]
discri [in discriminant]
discri1 [in discriminant2]
discri1 [in discriminant]
discri10 [in discriminant3]
discri11 [in discriminant3]
discri12 [in discriminant3]
discri13 [in discriminant3]
discri14 [in discriminant3]
discri15 [in discriminant3]
discri16 [in discriminant3]
discri2 [in discriminant2]
discri2 [in discriminant]
discri3 [in discriminant]
discri3 [in discriminant2]
discri4 [in discriminant]
discri4 [in discriminant2]
discri5 [in discriminant2]
discri5 [in discriminant]
discri6 [in discriminant]
discri6 [in discriminant2]
discri7 [in discriminant]
discri7 [in discriminant2]
discri8 [in discriminant2]
discri8 [in discriminant]
discri9 [in discriminant2]
discri9 [in discriminant]
DivFirstCase [in FexpDiv]
Divnk [in Divnk]
Divnk_error [in Divnk]
Divnk_FexpyGe [in Divnk]
Divnk_FexpyLe [in Divnk]
Divnk_FexpyLe2 [in Divnk]
DivSecondCase [in FexpDiv]
div2IsBetween [in FroundProp]
div2IsBetweenPos [in FroundProp]
DoubleRound2 [in DoubleRound]
dp_dq_le [in discriminant2]
dp_dq_le [in discriminant]
dsdAbs [in FexpDiv]
dsdinv [in FexpDiv]
dsdmult [in FexpDiv]
dsdsym [in FexpDiv]
dsdtrans [in FexpDiv]
dsdwi1qiD [in FexpDiv]

## E

eLe [in Dekker]
endof_length [in Fexp2]
endof_Rle_length [in FexpAdd]
epLe [in Veltkamp]
eqEqual [in Veltkamp]
eqExpLess [in Fbound]
eqExpMax [in Fbound]
eqGe [in Veltkamp]
eqLe [in Veltkamp]
eqLeep [in Veltkamp]
eqLe2 [in Veltkamp]
EqListFloat_length [in Fexp2]
EqListFloat_sum [in Fexp2]
EqSpeTwice [in FminOp]
ErrFmaApprox [in FmaErrApprox]
ErrFmaApprox_1 [in FmaErrApprox]
ErrFmaApprox_1_aux [in FmaErrApprox]
ErrFmaApprox_2 [in FmaErrApprox]
ErrFmaApprox_2_aux [in FmaErrApprox]
errorBoundedDiv [in FroundDivSqrt]
errorBoundedDivClosest [in FroundDivSqrt]
errorBoundedDivSimplHyp [in FroundDivSqrt]
errorBoundedDivToZero [in FroundDivSqrt]
ErrorBoundedIplus [in Fast2Sum]
errorBoundedModuloCan [in FroundDivSqrt]
errorBoundedModulo_aux [in FroundDivSqrt]
errorBoundedModulo_aux_y [in FroundDivSqrt]
errorBoundedMult [in FroundMult]
errorBoundedMultClosest [in ClosestMult]
errorBoundedMultClosest_aux [in ClosestMult]
errorBoundedMultClosest_Can [in discriminant]
errorBoundedMultClosest_Can [in discriminant2]
errorBoundedMultExp [in FroundMult]
errorBoundedMultExpPos [in FroundMult]
errorBoundedMultExp_aux [in FroundMult]
errorBoundedMultMax [in FroundMult]
errorBoundedMultMin [in FroundMult]
errorBoundedMultNeg [in FroundMult]
errorBoundedMultPos [in FroundMult]
errorBoundedPlus [in ClosestPlus]
errorBoundedPlusAbs [in ClosestPlus]
errorBoundedPlusLe [in ClosestPlus]
errorBoundedRem [in FroundDivSqrt]
errorBoundedSqrt [in FroundDivSqrt]
EvenBound [in EFast2Sum]
EvenClosestbbplus [in Veltkamp]
EvenClosestbplusb [in Veltkamp]
EvenClosestCompatible [in Closest]
EvenClosestFabs [in discriminant2]
EvenClosestFabs [in discriminant]
EvenClosestMax1 [in FminOp]
EvenClosestMax2 [in FminOp]
EvenClosestMinOrMax [in Closest]
EvenClosestMin1 [in FminOp]
EvenClosestMin2 [in FminOp]
EvenClosestMonotone [in Closest]
EvenClosestMonotone2 [in discriminant]
EvenClosestMonotone2 [in discriminant2]
EvenClosestRoundedModeP [in Closest]
EvenClosestSymmetric [in Closest]
EvenClosestTotal [in Closest]
EvenClosestUniqueP [in Closest]
EvenExp [in Fodd]
EvenFNSuccFNSuccMid [in Closest2Prop]
EvenMultInv [in Fodd]
EvenMult1 [in Fodd]
EvenMult2 [in Fodd]
EvenNOdd [in Fodd]
EvenNormalize [in DblRndOdd]
EvenO [in Fodd]
EvenOpp [in Fodd]
EvenPlusInv1 [in Fodd]
EvenPlusInv2 [in Fodd]
EvenPlus1 [in Fodd]
EvenPlus2 [in Fodd]
EvenSOdd [in Fodd]
EvenSOddInv [in Fodd]
ExactMinusInterval [in FroundPlus]
ExactMinusIntervalAux [in FroundPlus]
ExactMinusIntervalAux1 [in FroundPlus]
ExactSum_Near [in Axpy]
existExp [in Fexp]
exists_k [in FArgReduct2]
Expbe1 [in FmaErr]
expBoundedInv [in Fexp]
expInv [in Fexp]
expNormalizeCorrect [in Fexp]
expNormalizeExp [in Fexp]
Expo_zero_or_pos [in IEEE]
expPlus [in Paux]
ExpRev_aux [in Fexp2]
Expr1 [in FmaErr]
expValueApp [in Fexp]
expValueRev [in Fexp]
exp3Sum [in ThreeSum2]
exp_alpha_le [in FArgReduct3]
Exp_aux [in Fexp2]
exp_gamma_enough [in FArgReduct4]
exp_gamma_enough2 [in FArgReduct3]
exp_gamma_enough3 [in FArgReduct3]
exp_le_inv [in RND]
exp_ln_powerRZ [in RND]
exp_monotone [in RND]
ExtDekker [in EFast2Sum]
ExtDekkerDiff [in Fast2Diff]
ExtMDekker [in EFast2Sum]
ExtMDekkerDiff [in Fast2Diff]
ExtMDekker1 [in EFast2Sum]

## F

Fabs_correct [in Fop]
Fabs_correct1 [in Fop]
Fabs_correct2 [in Fop]
Fabs_Fexp [in FIA64elem]
Fabs_Fzero [in Fop]
Farg_reduct_bounded_diff [in FArgReduct4]
FboundedEqExp [in Fbound]
FboundedEqExpPos [in Fbound]
FboundedExp [in Fbound]
FboundedFzero [in Fbound]
FboundedIFzero [in FboundI]
FboundedMbound [in Fnorm]
FboundedMboundPos [in Fnorm]
FboundedMbound2 [in Veltkamp]
FboundedMbound2Pos [in Veltkamp]
FboundedNum [in Fbound]
FboundedOne [in Fnorm]
FBoundedPred [in FPred]
FBoundedScale [in Fbound]
FboundedShiftLess [in Fbound]
FBoundedSuc [in FSucc]
FboundedZeroSameExp [in Fbound]
FboundNext [in Fnorm]
FcanonicBound [in Fnorm]
FcanonicFabs [in Fnorm]
FcanonicFnormalizeEq [in Fnorm]
FcanonicFopp [in Fnorm]
FcanonicIBoundedI [in FboundI]
FcanonicIUnique [in FboundI]
FcanonicLeastExp [in Fnorm]
FcanonicLePos [in Fnorm]
FcanonicLtNeg [in Fnorm]
FcanonicLtPos [in Fnorm]
FcanonicNegFexpRlt [in Fnorm]
FcanonicNnormMin [in Fnorm]
FcanonicPosFexpRlt [in Fnorm]
FcanonicPpred [in Fnorm]
FcanonicUnique [in Fnorm]
Fcanonic_Rle_Zle [in Fnorm]
Fcompare_correct [in FminOp]
Fdiff_correct [in Fcomp]
FdigitEq [in Float]
Fdigit_abs [in Fop]
Fdigit_opp [in Fop]
Feq_bool_correct_f [in Fcomp]
Feq_bool_correct_r [in Fcomp]
Feq_bool_correct_t [in Fcomp]
FEvenD [in Fodd]
FevenFop [in Fodd]
FevenMakesFNeven [in FmaEmul]
FevenNormMin [in Closest2Prop]
FevenO [in Fodd]
FevenOrFodd [in Fodd]
FevenPred [in Fodd]
FevenSuc [in Fodd]
FevenSucProp [in Fodd]
FexpAdd_aux [in FexpAdd]
FexpAdd_aux2 [in FexpAdd]
FexpAdd_main [in FexpAdd]
FexpDivConv [in FexpDiv]
FexpEpsilon_aux [in FexpDiv]
FexpGeUnderf [in discriminant3]
Fexp_le_LSB [in MSB]
Fexp_le_MSB [in MSB]
Fexp_u [in FArgReduct2]
Fexp_x_aprox_zh_gamma [in FArgReduct4]
Fge_Zge [in Fcomp]
Fgt_Zgt [in Fcomp]
FinductNeg [in Finduct]
FinductNegAux [in Finduct]
FinductPos [in Finduct]
FinductPosAux [in Finduct]
firstNormalPosNormal [in Fnorm]
firstNormalPos_eq [in RND]
First_Comput_ok [in FArgReduct4]
Fle_bool_correct_f [in Fcomp]
Fle_bool_correct_r [in Fcomp]
Fle_bool_correct_t [in Fcomp]
Fle_Fge [in Fcomp]
Fle_refl [in Fcomp]
Fle_trans [in Fcomp]
Fle_Zle [in Fcomp]
floatDec [in Float]
floatEq [in Float]
float_equals_IEEE [in IEEE]
Float_To_IEEE_fn [in IEEE]
Float_To_IEEE_To_Float [in IEEE]
Flt_bool_correct_f [in Fcomp]
Flt_bool_correct_r [in Fcomp]
Flt_bool_correct_t [in Fcomp]
Flt_Fgt [in Fcomp]
Flt_Zlt [in Fcomp]
Fmac_arg_reduct_correct1 [in FArgReduct2]
Fmac_arg_reduct_correct1_aux [in FArgReduct2]
Fmac_arg_reduct_correct1_aux2 [in FArgReduct2]
Fmac_arg_reduct_correct2 [in FArgReduct2]
Fmac_arg_reduct_correct3 [in FArgReduct3]
FmaEmul [in FmaEmul]
FmaEmulAux [in FmaEmul]
FmaErr [in FmaErr]
FmaErr_aux [in FmaErr]
FmaErr_aux1 [in FmaErr]
FmaErr_aux2 [in FmaErr]
FmaErr_Even [in FmaErr]
FmaxRep [in Fmin]
Fma_FTS [in FmaErr]
Fma_FTS_Even [in FmaErr]
FminOp_correct1 [in FminOp]
FminOp_correct2 [in FminOp]
FminOp_correct3 [in FminOp]
FminOp_correct4 [in FminOp]
FminOp_correct5 [in FminOp]
FminOp_correct6 [in FminOp]
FminOp_correct7 [in FminOp]
FminRep [in Fmin]
Fminus_correct [in Fop]
FmultRadixInv [in ClosestProp]
FNEvenD [in Fodd]
FNevenEq [in Fodd]
FNevenFop [in Fodd]
FNevenOrFNodd [in Fodd]
FNevenPred [in Fodd]
FNevenSuc [in Fodd]
FNIAuxLess [in FboundI]
FNIAuxMore [in FboundI]
FNILess [in FboundI]
FNIMore [in FboundI]
FNoddEq [in Fodd]
FNoddFop [in Fodd]
FnOddNEven [in Fodd]
FNoddPred [in Fodd]
FNoddSuc [in Fodd]
FnormalBound [in Fnorm]
FnormalBoundAbs [in Fnorm]
FnormalBoundAbs2 [in Fnorm]
FnormalBounded [in Fnorm]
FnormalFabs [in Fnorm]
FnormalFop [in Fnorm]
FnormalINotZero [in FboundI]
FnormalIUnique [in FboundI]
FnormalIUnique_aux [in FboundI]
FnormalizeBounded [in Fnorm]
FnormalizeCanonic [in Fnorm]
FnormalizeCorrect [in Fnorm]
FnormalizeIBounded [in FboundI]
FnormalizeICorrect [in FboundI]
FnormalizeIFcanonicI [in FboundI]
Fnormalize_Fopp [in Fnorm]
FnormalLtFirstNormalNeg [in Fnorm]
FnormalLtFirstNormalPos [in Fnorm]
FnormalLtNeg [in Fnorm]
FnormalLtPos [in Fnorm]
FnormalNnormMin [in Fnorm]
FnormalNotZero [in Fnorm]
FnormalPpred [in Fnorm]
FnormalPrecision [in Fnorm]
FnormalUnique [in Fnorm]
FNorm_or_Subnorm [in IEEE]
FNPredCanonic [in FPred]
FNPredFopFNSucc [in FPred]
FNPredLt [in FPred]
FNPredProp [in FPred]
FNPredSuc [in FPred]
FNPredSucEq [in FPred]
FNSuccCanonic [in FSucc]
FNSuccEq [in FSucc]
FNSuccFNSuccMid [in FSucc]
FNSuccLt [in FSucc]
FNSuccProp [in FSucc]
FNSuccUlpPos [in FroundProp]
FNSuccUlpPos [in FminOp]
FNSucPred [in FPred]
FNSucPredEq [in FPred]
FoddFop [in Fodd]
FoddPred [in Fodd]
FoddSuc [in Fodd]
FoppBoundedI [in FnormI]
FoppBoundedIExp [in FnormI]
FoppBoundedIInv [in FnormI]
FoppBoundedIInv_aux [in FnormI]
FoppBoundedI2 [in FnormI]
Fopp_correct [in Fop]
Fopp_Fminus [in Fop]
Fopp_Fminus_dist [in Fop]
Fopp_Fopp [in Fop]
FopRepAux [in Fbound]
Fplus_correct [in Fop]
FPredCanonic [in FPred]
FPredDiff1 [in FPred]
FPredDiff2 [in FPred]
FPredDiff3 [in FPred]
FPredFopFSucc [in FPred]
FPredLt [in FPred]
FPredProp [in FPred]
FPredSimpl1 [in FPred]
FPredSimpl2 [in FPred]
FPredSimpl3 [in FPred]
FPredSimpl4 [in FPred]
FPredSuc [in FPred]
FpredUlpPos [in ClosestProp]
FPredZleEq [in FPred]
FshiftAdd [in Float]
FshiftCorrect [in Float]
FshiftCorrectInv [in Float]
FshiftCorrectSym [in Float]
FshiftFdigit [in Float]
FshiftO [in Float]
FsubnormalBound [in Fnorm]
FsubnormalDigit [in Fnorm]
FsubnormalFbounded [in Fnorm]
FsubnormalFexp [in Fnorm]
FsubnormalIUnique [in FboundI]
FsubnormalLt [in Fnorm]
FsubnormalLtFirstNormalPos [in Fnorm]
FsubnormalnormalLtNeg [in Fnorm]
FsubnormalnormalLtPos [in Fnorm]
FsubnormalUnique [in Fnorm]
FsubnormFabs [in Fnorm]
FsubnormFopp [in Fnorm]
FSuccCanonic [in FSucc]
FSuccDiffPos [in FroundProp]
FSuccDiffPos [in FminOp]
FSuccDiff1 [in FSucc]
FSuccDiff2 [in FSucc]
FSuccDiff3 [in FSucc]
FSuccLt [in FSucc]
FSuccNegCanonic [in FSucc]
FSuccNormNegNormMin [in FSucc]
FSuccNormNegNotNormMin [in FSucc]
FSuccNormPos [in FSucc]
FSuccPosNotMax [in FSucc]
FSuccProp [in FSucc]
FSuccPropNeg [in FSucc]
FSuccPropPos [in FSucc]
FSuccSimpl1 [in FSucc]
FSuccSimpl2 [in FSucc]
FSuccSimpl3 [in FSucc]
FSuccSimpl4 [in FSucc]
FSuccSubnormal [in FSucc]
FSuccSubnormNearNormMin [in FSucc]
FSuccSubnormNotNearNormMin [in FSucc]
FSuccUlpPos [in FminOp]
FSuccUlpPos [in FroundProp]
FSuccZleEq [in FSucc]
FSucFSucMid [in FSucc]
FSucPred [in FPred]
FtoREqInv1 [in Float]
FtoREqInv2 [in Float]
FtoR_Zpred_exp [in IEEE]
FTS [in ThreeSumProps]
FTSinSum3_allcases [in ThreeSumProps]
FTS_correct [in FArgReduct4]
FTS_correct_aux [in FArgReduct4]
FulpComp [in FroundProp]
FulpDiv [in FexpDiv]
FulpFabs [in FroundProp]
FulpFPredGePos [in FroundProp]
FulpFPredLe [in ClosestProp]
FulpFPred_not_pow [in FArgReduct]
FulpGe [in FroundProp]
FulpLe [in FroundProp]
FulpLeGeneral [in Axpy]
FulpLe2 [in FroundProp]
FulpPred [in FroundProp]
FulpPredCan [in FroundProp]
FulpRinv_div [in FIA64elem]
FulpRinv_div_not [in FIA64elem]
FulpSuc [in FroundProp]
FulpSucCan [in FroundProp]
FUlp_Le_LSigB [in FroundProp]
Fulp_le_twice_l [in discriminant]
Fulp_le_twice_l [in discriminant2]
Fulp_le_twice_r [in discriminant]
Fulp_le_twice_r [in discriminant2]
Fulp_le_twice_r_round [in discriminant2]
Fulp_le_twice_r_round [in discriminant]
Fulp_pow [in FIA64elem]
Fulp_R1 [in FIA64elem]
Fulp_zero [in FroundProp]
FvalScale [in Fbound]
FweightEq [in Finduct]
FweightLt [in Finduct]
FweightZle [in Finduct]
FzeroisReallyZero [in Float]
FzeroisZero [in Fbound]
Fzero_opp [in Fop]

## G

gaCorrect [in FmaErr]
gamma2_le [in FArgReduct4]
gamma_exp [in FArgReduct2]
gamma_ge2 [in FArgReduct4]
gamma_ge2 [in FArgReduct3]
gamma_p [in FArgReduct3]
gatCorrect [in FmaErr]
Goal1 [in PradixE]
Goal2 [in PradixE]
Goal3 [in PradixE]
Goal4 [in PradixE]
Goal5b [in PradixE]
Goal5_6b [in PradixE]
Goal6 [in PradixE]
Goal7b [in PradixE]
Goal8b [in PradixE]
Goal9b [in PradixE]
growExpIsExp [in FexpPlus]
growExpIsVal [in FexpPlus]

## H

Half_Closest_Round [in discriminant2]
Half_Closest_Round [in discriminant]
hxExact [in Veltkamp]

## I

IEEE_To_Float_Bounded [in IEEE]
IEEE_To_Float_To_IEEE [in IEEE]
IminusBounded [in Fast2Sum]
IminusComp [in EFast2Sum]
IminusCorrect [in Fast2Sum]
IminusCorrectEq [in TwoSum]
IminusFminus [in Fast2Sum]
IminusId [in Fast2Sum]
IminusInv [in Fast2Sum]
IminusOl [in Fast2Sum]
IminusOp [in TwoSum]
Iminus2Exact [in TwoSum]
ImplyClosest [in Veltkamp]
ImplyClosestStrict [in Veltkamp]
ImplyClosestStrict2 [in Veltkamp]
InBinade [in FroundProp]
InegAbsInf [in FexpDiv]
InegAbsSup [in FexpDiv]
Inegdsd [in FexpDiv]
IneqEq [in discriminant3]
inject_nat_convert [in Faux]
inject_nat_eq [in Faux]
inj_abs [in Faux]
inj_oZ1 [in Zdivides]
inj_pred [in Faux]
INR_inv [in Faux]
INR_lt_nm [in Faux]
Int_part_INR [in Faux]
Int_part_IZR [in Faux]
in_map_inv [in Zenum]
IplusBounded [in Fast2Sum]
IplusCorrectEq [in TwoSum]
IplusOl [in TwoSum]
IplusOr [in Fast2Sum]
IRNDD_correct1 [in RND]
IRNDD_correct2 [in RND]
IRNDD_correct3 [in RND]
IRNDD_eq [in RND]
IRNDD_monotone [in RND]
IRNDD_pos [in RND]
IRNDD_projector [in RND]
isBounded [in Fbound]
isBoundedI [in FboundI]
IsCanExpBounded [in Fexp2]
IsExpansionAddInv [in FexpPlus]
IsExpansionCons [in FexpPlus]
IsExpansionConsInv [in FexpPlus]
IsExpansionConsInvAux [in FexpPlus]
IsExpansionGrowConsInvAux [in FexpPlus]
IsExpansionSkip [in FexpPlus]
IsExpansion_comp1 [in Fexp]
IsExpansion_comp2 [in Fexp]
isExpInv [in Fexp2]
isExpSkip [in Fexp2]
IsExpZle [in Fexp2]
isMaxComp [in FroundProp]
isMax_inv1 [in Fmin]
isMinComp [in FroundProp]
isMin_inv1 [in Fmin]
IsNzExpansionInv [in Fexp]
isNzExpansionIsExpansion [in Fexp]
IsNzExpansionRInv [in Fexp]
isNzExpansionRIsNzExpansion [in Fexp]
IsRleExpRevComp [in Fexp2]
IsRleExpRevIsExp [in Fexp2]
IsRleExpRev_IsRleExp [in Fexp2]
IsRleExp_IsRleExpRev [in Fexp2]
is_FzeroP [in Float]
is_Fzero_rep1 [in Float]
is_Fzero_rep2 [in Float]
IZR_inv [in Faux]
IZR_zero [in Faux]
IZR_zero_r [in Faux]

## K

Knuth [in TwoSum]

## L

last_hd [in Fexp2]
LeExp [in FmaErrApprox]
LeExpRound [in FmaErr]
LeExpRound2 [in FmaErr]
LeExp1 [in FmaErrApprox]
LeExp2 [in FmaErrApprox]
LeExp3 [in FmaErrApprox]
LeFnumZERO [in Fcomp]
LeFulpPos [in FroundProp]
LeR0Fnum [in Fcomp]
LessExpBound [in Fbound]
LexicoCanI [in FnormI]
LexicoNegCanI [in FnormI]
LexicoPosCanI [in FnormI]
LeZEROFnum [in Fcomp]
le_mult_anti_compatibility [in Faux]
le_next [in Faux]
le_refl_eq [in Faux]
le_Rle [in Faux]
ln_radix_pos [in RND]
Loop0 [in PradixE]
Loop1 [in PradixE]
Loop2 [in PradixE]
Loop3 [in PradixE]
Loop4 [in PradixE]
Loop6c [in PradixE]
LSBMinus [in FroundPlus]
LSBPlus [in FroundPlus]
LSB_abs [in MSB]
LSB_comp [in MSB]
LSB_le_abs [in MSB]
LSB_le_MSB [in MSB]
LSB_opp [in MSB]
LSB_Pred [in FmaErr]
LSB_rep [in MSB]
LSB_rep_min [in MSB]
LSB_shift [in MSB]
lte_comp_mult [in Faux]
LtFnumZERO [in Float]
LtFsubnormal [in Fnorm]
LtR0Fnum [in Fcomp]
lt_comp_mult [in Faux]
lt_comp_mult_l [in Faux]
lt_comp_mult_r [in Faux]
lt_le_pred [in Faux]
lt_minus_inv [in Faux]
lt_mult_anti_compatibility [in Faux]
lt_next [in Faux]
lt_Rlt [in Faux]
lt_S_le [in Faux]
lt_Zlt_inv [in Faux]

## M

MaxBinade [in Fmin]
MaxCompatible [in Fround]
maxDivCorrect [in MSB]
maxDivLess [in MSB]
maxDivLt [in MSB]
maxDivPlus [in MSB]
maxDivSimpl [in MSB]
maxDivSimplAux [in MSB]
maxDivSimplInv [in MSB]
maxDivSimplInvAux [in MSB]
maxDivUnique [in MSB]
maxDivUniqueDigit [in MSB]
maxDivUniqueInverse [in MSB]
maxDivUniqueInverseDigit [in MSB]
maxDiv_abs [in MSB]
maxDiv_opp [in MSB]
MaxEq [in Fmin]
MaxEx [in Fmin]
maxFbounded [in Fbound]
MaxFloat [in Fnorm]
maxMax [in Fbound]
maxMaxBis [in Fnorm]
maxMax1 [in Fnorm]
MaxMin [in Fmin]
MaxOppMin [in Fmin]
MaxRoundedModeP [in Fround]
MaxUniqueP [in Fround]
Maxwiwi1 [in FexpDiv]
mBFadic_correct1 [in Fmin]
mBFadic_correct2 [in Fmin]
mBFadic_correct3 [in Fmin]
mBFadic_correct4 [in Fmin]
mBPadic_Fbounded [in Fmin]
MDekker [in Fast2Sum]
MDekkerAux1 [in Fast2Sum]
MDekkerAux2 [in Fast2Sum]
MDekkerAux3 [in Fast2Sum]
MDekkerAux4 [in Fast2Sum]
MDekkerAux5 [in Fast2Sum]
MDekkerDiff [in Fast2Diff]
MDekkerDiffAux1 [in Fast2Diff]
Midpoint_aux [in FmaErr]
Midpoint_aux_aux [in FmaErr]
MinBinade [in Fmin]
MinCompatible [in Fround]
MinEq [in Fmin]
MinEx [in Fmin]
MinExList [in Fmin]
MinMax [in Fmin]
MinOppMax [in Fmin]
MinOrMaxRep [in Fround]
MinOrMax1 [in MinOrMax]
MinOrMax2 [in MinOrMax]
MinOrMax3 [in MinOrMax]
MinOrMax3_aux [in MinOrMax]
MinOrMax_Fopp [in MinOrMax]
MinOrMax_Rlt [in MinOrMax]
MinRoundedModeP [in Fround]
MinUniqueP [in Fround]
minusRoundRep [in FroundPlus]
minusSameExp [in Fop]
minus_inv_lt [in Faux]
minus_inv_lt_aux [in Faux]
minus_le [in Faux]
minus_minus [in Faux]
minus_Zminus_precq [in FArgReduct2]
min_n_0 [in Faux]
min_or [in Faux]
mkIsNzAux [in Fexp]
MKnuth [in TwoSum]
MKnuthOpp [in TwoSum]
MKnuth1 [in TwoSum]
MKnuth2 [in TwoSum]
MKnuth3 [in TwoSum]
MKnuth4 [in TwoSum]
MKnuth5 [in TwoSum]
MKnuth6 [in TwoSum]
MKnuth7 [in TwoSum]
MonotoneMax [in Fmin]
MonotoneMin [in Fmin]
mProd_correct [in Zenum]
mProd_correct_rev1 [in Zenum]
mProd_correct_rev2 [in Zenum]
MSBBoundNotZero [in FroundProp]
MSBisMin [in FroundProp]
MSBroundLSB [in FroundPlus]
MSBtoZero [in FroundProp]
MSB_abs [in MSB]
MSB_comp [in MSB]
MSB_le_abs [in MSB]
MSB_le_mult [in MSB]
MSB_le_multAux [in MSB]
MSB_mix [in MSB]
MSB_monotone [in MSB]
MSB_monotoneAux [in MSB]
MSB_opp [in MSB]
MSB_shift [in MSB]
multExpMin [in FroundMult]
multExpUpperBound [in FroundMult]
mult_eq_inv [in Faux]
mult_le_MSB [in MSB]
mult_le_MSBAux [in MSB]
mZlist_aux_correct [in Zenum]
mZlist_aux_correct_rev1 [in Zenum]
mZlist_aux_correct_rev2 [in Zenum]
mZlist_correct [in Zenum]
mZlist_correct_rev1 [in Zenum]
mZlist_correct_rev2 [in Zenum]

## N

nat_div_one [in FnormI]
NconvertO [in Faux]
NDivides_minus [in Zdivides]
NearestInteger [in FroundDivSqrt]
NEq_INR [in Faux]
NEq_INRO [in Faux]
NEq_INR1 [in Faux]
NEq_IZRO [in Faux]
NisFzeroComp [in Float]
nNormMimLtvNum [in FSucc]
nNormPos [in Fnorm]
nNrMMimLevNum [in Fnorm]
NormalAndSubNormalNotEq [in Fnorm]
NormalbPrim [in Dekker]
NormalIandSubnormalINotEq [in FboundI]
NormalNotSubNormal [in Fnorm]
Normal_and_exp [in FArgReduct2]
Normal_and_exp2 [in FArgReduct2]
Normal_ge [in Divnk]
Normal_le [in Divnk]
NotDividesDigit [in Zdivides]
notEqLt [in Faux]
NotR0NotZero [in FminOp]
NotZmultZero [in Faux]
not_O_lt [in Faux]
NroundN [in FroundProp]

## O

OddEvenDec [in Fodd]
OddExp [in Fodd]
OddMult [in Fodd]
OddMultInv [in Fodd]
OddNEven [in Fodd]
OddOpp [in Fodd]
OddPlusInv1 [in Fodd]
OddPlusInv2 [in Fodd]
OddPlus1 [in Fodd]
OddPlus2 [in Fodd]
OddSEven [in Fodd]
OddSEvenInv [in Fodd]
Odd1 [in Fodd]
odd_even_lem [in Paux]
OneErrorOnly [in FArgReduct4]
oneExp_le [in Float]
oneExp_lt [in Float]
oneExp_Zle [in Float]
oneExp_Zlt [in Float]
oneZplus [in Fop]
oppBounded [in Fbound]
oppBoundedInv [in Fbound]
OppositeIUnique [in FnormI]
OppositeIUnique_1 [in FnormI]
OppositeIUnique_2 [in FnormI]
OutSum3 [in ThreeSum2]
oZ1_oZ [in FminOp]

## P

PdivBound_correct [in Paux]
PdivBound_correct1 [in Paux]
PdivBound_correct2 [in Paux]
PdivBound_correct3 [in Paux]
PdivBound_correct4 [in Paux]
Pdivless1 [in Paux]
Pdivless2 [in Paux]
Pdivless_correct [in Paux]
Pdiv_correct [in Paux]
pGeUnderf [in discriminant3]
pGivesDigit [in Fnorm]
plusClosestLowerBound [in Closest2Plus]
plusClosestLowerBoundAux1 [in Closest2Plus]
plusClosestLowerBoundAux2 [in Closest2Plus]
plusErrorBound1 [in ClosestPlus]
plusErrorBound1bis [in ClosestPlus]
plusErrorBound1withZero [in ClosestPlus]
plusErrorBound2 [in Closest2Plus]
plusExactExp [in ClosestPlus]
plusExactExpCanonic [in ClosestPlus]
plusExactR0 [in ClosestPlus]
plusExactSub [in FmaEmul]
plusExact1 [in ClosestPlus]
plusExact1bis [in ClosestPlus]
plusExact2 [in ClosestPlus]
plusExact2Aux [in ClosestPlus]
plusExpBound [in FroundPlus]
plusExpMin [in FroundPlus]
plusExpUpperBound [in FroundPlus]
plusUpperBound [in Closest2Plus]
PminPos [in FroundProp]
pNormal_absolu_min [in Fnorm]
positive_exp_correct [in Paux]
PosNormMin [in Fnorm]
pos_eq_bool_correct [in Faux]
pos_length_pow [in Digit]
powerRZSumRle [in Dekker]
powerRZSumRle [in FmaErr]
powerRZ_add [in Rpow]
powerRZ_le [in Rpow]
powerRZ_lt [in Rpow]
powerRZ_NOR [in Rpow]
powerRZ_O [in Rpow]
powerRZ_R1 [in Rpow]
powerRZ_Zopp [in Rpow]
powerRZ_Zs [in Rpow]
powerRZ_1 [in Rpow]
pow_add [in Rpow]
pow_lt [in Rpow]
pow_NR0 [in Rpow]
pow_O [in Rpow]
pow_RN_plus [in Rpow]
pow_R1 [in Rpow]
pow_1 [in Rpow]
pPos [in Veltkamp]
pPredMoreThanOne [in ClosestPlus]
pPredMoreThanRadix [in ClosestPlus]
precisionNotZero [in DblRndOdd]
prec1_Greater_Than_One [in FArgReduct2]
ProjectMax [in Fmin]
ProjectMaxI [in FnormI]
ProjectMin [in Fmin]
ProjectMinI [in FnormI]
pSubnormal_absolu_min [in Fnorm]
ptonat_def1 [in Faux]
pUCanonic_absolu [in Fnorm]
PuissLessThanHalf [in ThreeSumProps]
p'GivesBound [in Veltkamp]
p'GivesBound2 [in Veltkamp]
p''GivesBound [in Dekker]
P_le_two_Q [in discriminant2]
P_le_two_Q [in discriminant]
P_positive [in discriminant]
P_positive [in discriminant2]

## Q

qGeUnderf [in discriminant3]
qNeg [in Veltkamp]
Q_le_two_P [in discriminant2]
Q_le_two_P [in discriminant]
Q_positive [in discriminant2]
Q_positive [in discriminant]

## R

Rabsolu_left1 [in Faux]
Rabsolu_Zabs [in Faux]
radixNotZero [in DblRndOdd]
radixRangeBoundExp [in Finduct]
radixRangeBoundExp [in FroundPlus]
rCeil_correct [in FminOp]
rClosestEvenPos_correct [in FminOp]
rClosestEven_correct [in FminOp]
Rdiv_Rle [in FArgReduct]
ReductRangeI [in FnormI]
ReductRangeIInv [in FnormI]
ReqGivesEqwithSameExp [in Float]
rev_length [in Fexp2]
rev_sum [in Fexp2]
rExp [in Dekker]
rFloor_correct [in FminOp]
RinvClosestRinvMaxRle [in FArgReduct]
RinvClosestRinvMaxRle_Neg [in FArgReduct]
RinvClosestRinvMaxRle_Pos [in FArgReduct]
RinvClosestRinvMaxRle_pow [in FArgReduct]
RinvClosestRinvMaxRle_pow2 [in FArgReduct]
Rinv_powerRZ [in Rpow]
RleBoundRoundl [in FroundProp]
RleBoundRoundr [in FroundProp]
Rledouble [in Faux]
RleFexpFabs [in Fop]
RleMaxR0 [in FroundProp]
RleMinR0 [in FroundProp]
RleRoundedAbs [in FmaErrApprox]
RleRoundedLessR0 [in FroundProp]
RleRoundedR0 [in FroundProp]
RleRRounded [in Veltkamp]
RleR0Rminus [in FminOp]
Rle_err_pow2 [in Divnk]
Rle_Fexp_eq_Zle [in Fcomp]
Rle_floats_isMax_Neg [in FArgReduct]
Rle_floats_isMax_Pos [in FArgReduct]
Rle_Float_Zle [in Float]
Rle_INR [in Faux]
Rle_IZR [in Faux]
Rle_IZRO [in Faux]
Rle_IZR1 [in Faux]
Rle_monotone_exp [in Float]
Rle_monotony_contra_exp [in Float]
Rle_mult_pos [in FexpAdd]
Rle_powerRZ [in Rpow]
Rle_Rinv [in Faux]
Rle_Rminus_ZERO [in ThreeSumProps]
Rle_R0_Ropp [in Faux]
RlIt2 [in Faux]
Rltdouble [in Faux]
RltSpeTwice1 [in FminOp]
RltSpeTwice2 [in FminOp]
Rlt2 [in Faux]
Rlt_Fexp_eq_Zlt [in Fcomp]
Rlt_Float_Zlt [in Float]
Rlt_INR1 [in Faux]
Rlt_IZR [in Faux]
Rlt_IZRO [in Faux]
Rlt_IZR1 [in Faux]
Rlt_monotony_contra_exp [in Float]
Rlt_monotony_exp [in Float]
Rlt_pow [in Rpow]
Rlt_powerRZ [in Rpow]
Rlt_pow_R1 [in Rpow]
Rlt_RinvDouble [in Faux]
Rlt_Rminus_ZERO [in Faux]
Rlt_R0_Ropp [in Faux]
RmaxAbs [in Faux]
RmaxLess1 [in Faux]
RmaxLess2 [in Faux]
RmaxProp [in FexpDiv]
RmaxRmult [in Faux]
RmaxSym [in Faux]
Rmax_simpl1 [in FexpDiv]
Rmin_eq [in FArgReduct]
Rmin_1 [in FArgReduct]
Rmin_2 [in FArgReduct]
Rmult_IZR [in Faux]
RND_ClosestUp_canonic [in RND]
RND_ClosestUp_correct [in RND]
RND_EvenClosest_canonic [in RND]
RND_EvenClosest_correct [in RND]
RND_Max_canonic [in RND]
RND_Max_correct [in RND]
RND_Max_Pos_canonic [in RND]
RND_Max_Pos_correct [in RND]
RND_Max_Pos_Rle [in RND]
RND_Min_canonic [in RND]
RND_Min_correct [in RND]
RND_Min_Pos_bounded_aux [in RND]
RND_Min_Pos_canonic [in RND]
RND_Min_Pos_correct [in RND]
RND_Min_Pos_monotone [in RND]
RND_Min_Pos_projector [in RND]
RND_Min_Pos_Rle [in RND]
RND_Zero_canonic [in RND]
RND_Zero_correct [in RND]
RoundAbsMonotonel [in FroundProp]
RoundAbsMonotoner [in FroundProp]
RoundBound [in ClosestPlus]
roundedModeAbsMult [in FroundProp]
RoundedModeBounded [in FroundProp]
RoundedModeErrorExpStrict [in FroundProp]
roundedModeLessMult [in FroundProp]
roundedModeMoreMult [in FroundProp]
RoundedModeMult [in FroundProp]
RoundedModeMultAbs [in FroundProp]
RoundedModeMultLess [in FroundProp]
RoundedModeProjectorIdem [in FroundProp]
RoundedModeProjectorIdemEq [in FroundProp]
RoundedModeProjectorIdemI [in FnormI]
RoundedModeP_inv1 [in Fround]
RoundedModeP_inv2 [in Fround]
RoundedModeP_inv3 [in Fround]
RoundedModeP_inv4 [in Fround]
RoundedModeRep [in Fround]
RoundedModeUlp [in FroundProp]
RoundedProjector [in Fround]
RoundedProjectorI [in FnormI]
RoundGeGeneral [in Axpy]
RoundGeNormal [in discriminant3]
RoundLeGeneral [in Axpy]
RoundLeNormal [in discriminant3]
RoundLessThanIsMax [in Fround]
RoundLSBMax [in FroundProp]
RoundMSBmax [in FroundProp]
RoundMSBmin [in FroundProp]
Rpow_eq_inv [in Rpow]
Rpow_R1 [in Rpow]
rToZero_correct [in FminOp]
R0LeFnum [in Fcomp]
R0LtFnum [in Fcomp]
R0RltRlePred [in FPred]
R0RltRleSucc [in FSucc]

## S

sameExpEq [in Float]
ScalableRoundedModeP [in Fround]
Second_Comput_ok [in FArgReduct4]
SGe [in Dekker]
SLe [in Dekker]
Sterbenz [in Fprop]
SterbenzApprox [in FArgReduct]
SterbenzApproxI [in FnormI]
SterbenzApproxI_aux1 [in FnormI]
SterbenzApproxI_aux2 [in FnormI]
SterbenzApproxI_pos [in FnormI]
SterbenzApproxI_1 [in FnormI]
SterbenzApproxI_2 [in FnormI]
SterbenzApproxI_3 [in FnormI]
SterbenzApproxI_4 [in FnormI]
SterbenzApprox2 [in FArgReduct]
SterbenzApprox3 [in FArgReduct2]
SterbenzApprox_weak_1 [in FArgReduct]
SterbenzAux [in Fprop]
Sterbenzbis [in FArgReduct2]
SterbenzI [in FnormI]
SterbenzIAux1 [in FnormI]
SterbenzIAux2 [in FnormI]
SterbenzIAux2A [in FnormI]
SterbenzIAux2B [in FnormI]
SterbenzOppI [in FnormI]
Subexact [in FmaErr]
sum_app [in Fexp2]
sum_IsExp [in Fexp2]
s2Ge [in Dekker]
s2Le [in Dekker]

## T

tBounded [in FmaErrApprox]
tBounded_aux [in FmaErrApprox]
ThreeSumLoop [in ThreeSumProps]
tLe [in FmaErrApprox]
ToInfinityCompatible [in Fround]
ToInfinityMinOrMax [in Fround]
ToInfinityMonotone [in Fround]
ToInfinityRoundedModeP [in Fround]
ToInfinitySymmetric [in Fround]
ToInfinityTotal [in Fround]
ToInfinityUniqueP [in Fround]
ToZeroCompatible [in Fround]
ToZeroMinOrMax [in Fround]
ToZeroMonotone [in Fround]
ToZeroRoundedModeP [in Fround]
ToZeroSymmetric [in Fround]
ToZeroTotal [in Fround]
ToZeroUniqueP [in Fround]
To_OddCompatible [in DblRndOdd]
To_OddMinOrMax [in DblRndOdd]
To_OddMonotone [in DblRndOdd]
To_OddRoundedModeP [in DblRndOdd]
To_OddSymmetricP [in DblRndOdd]
To_OddTotal [in DblRndOdd]
To_OddUniqueP [in DblRndOdd]
To_Odd_Even_is_Even [in DblRndOdd]
To_Odd_Even_is_Even_nNormMin [in DblRndOdd]
To_Odd_Odd_is_Odd [in FmaEmul]
Twice_EvenClosest_Round [in discriminant]
Twice_EvenClosest_Round [in discriminant2]
TwoMoreThanOne [in Closest2Prop]
TwoMoreThanOne [in discriminant2]
TwoMoreThanOne [in discriminant3]
TwoMoreThanOne [in Closest2Plus]
TwoMoreThanOne [in discriminant]
TwoMoreThanOne [in Axpy]
TwoMoreThanOneR [in Axpy]
TwoSumExp [in FexpPlus]
TwoSumLt1 [in FexpPlus]
TwoSumLt2 [in FexpPlus]
TwoSumNonNul [in ThreeSum2]
TwoSumNul [in ThreeSum2]
TwoSumOl1 [in FexpPlus]
TwoSumOl2 [in FexpPlus]
TwoSumOneNul [in ThreeSum2]
TwoSumOneNul2 [in ThreeSum2]
TwoSumOr1 [in FexpPlus]
TwoSumOr2 [in FexpPlus]
TwoSumProp [in FmaErr]
t_exact [in discriminant2]
t_exact [in discriminant]

## U

uhPos [in FmaErrApprox]
UlpFlessuGe [in Axpy]
UlpFlessuGe2 [in Axpy]
UlpFlessuGe_aux [in Axpy]
Ulp_Le_LSigB [in MSB]
Underf_Err1 [in Dekker]
Underf_Err2 [in Dekker]
Underf_Err2_aux [in Dekker]
Underf_Err3 [in Dekker]
Underf_Err3_bis [in Dekker]
UnMoinsPos [in FmaErr]
u_bounds [in FArgReduct2]

## V

Veltkamp [in Veltkamp]
Veltkampb' [in Dekker]
VeltkampEven [in Veltkamp]
VeltkampEvenN [in Veltkamp]
VeltkampEvenN_aux [in Veltkamp]
VeltkampEvenS [in Veltkamp]
VeltkampEven1 [in Veltkamp]
VeltkampEven2 [in Veltkamp]
VeltkampEven_pos [in Veltkamp]
VeltkampN [in Veltkamp]
VeltkampN_aux [in Veltkamp]
VeltkampS [in Veltkamp]
VeltkampU [in Veltkamp]
Veltkamp_aux [in Veltkamp]
Veltkamp_aux_aux [in Veltkamp]
Veltkamp_pos [in Veltkamp]
Veltkamp_tail [in Veltkamp]
Veltkamp_tail2 [in Veltkamp]
Veltkamp_tail_aux [in Veltkamp]
vLe [in FmaErrApprox]
vLe_aux [in FmaErrApprox]
vNumbMoreThanOne [in Fnorm]
vNumPrecision [in Fnorm]
vNum_eq_Zpower [in FArgReduct2]
vNum_eq_Zpower [in IEEE]
vNum_eq_Zpower_bmoinsq [in FArgReduct2]
vNum_eq_Zpower_bzH [in FArgReduct2]
vNum_eq_Zpower_bzH2 [in FArgReduct2]
vNum_eq_Zpower_bzH2_fn [in FArgReduct2]
vNum_eq_Zpower_bzH_fn [in FArgReduct2]
vNum_eq_Zpower_b1 [in FArgReduct2]
vNum_eq_Zpower_b1bis [in FArgReduct2]
v_neq_zero [in FArgReduct4]

## W

wLe [in FmaErrApprox]

## X

xLe2y [in FmaErr]
xLe2y_aux1 [in FmaErr]
xLe2y_aux2 [in FmaErr]
x1y2Le [in Dekker]
x2y1Le [in Dekker]
x2y2Le [in Dekker]
x_over_zHgamma_eq [in FArgReduct2]

## Y

yLe2x [in FmaErr]
yLe2x_aux [in FmaErr]

## Z

Zabs_absolu [in Faux]
Zabs_eq_case [in Zdivides]
Zabs_eq_opp [in Faux]
Zabs_intro [in Faux]
Zabs_tri [in Zdivides]
Zabs_Zmult [in Faux]
Zabs_Zopp [in Faux]
Zabs_Zs [in Faux]
Zcompare_correct [in Digit]
Zcompare_EGAL [in Faux]
ZdividesDiv [in Zdivides]
ZDividesLe [in Zdivides]
ZdividesLessPow [in Zdivides]
ZdividesMult [in Zdivides]
ZdividesTrans [in Zdivides]
ZdividesZquotient [in Zdivides]
ZdividesZquotientInv [in Zdivides]
Zdivides1 [in Zdivides]
ZDivides_add [in Zdivides]
ZDivides_mult [in Zdivides]
Zeq_mult_simpl [in Zdivides]
Zeq_Zs [in Faux]
Zero_le_oZ [in Zdivides]
ZevenP_correct [in FminOp]
zH1Pos [in FArgReduct2]
zH1_eq [in FArgReduct2]
zH_exp_N [in FArgReduct4]
ZleAbs [in Faux]
ZleLe [in Faux]
Zle_abs [in Faux]
Zle_monotony_contra_abs_pow [in Fbound]
Zle_mult_gen [in Faux]
Zle_next [in Faux]
Zle_n_Zpred [in Faux]
Zle_powerRZ [in Rpow]
Zle_Rle [in Faux]
Zle_Zabs [in Faux]
Zle_Zabs_inv1 [in Faux]
Zle_Zabs_inv2 [in Faux]
Zle_ZERO_Zabs [in Faux]
Zle_Zminus_ZERO [in Faux]
Zle_Zmult_comp_l [in Faux]
Zle_Zmult_comp_r [in Faux]
Zle_Zopp [in Faux]
Zle_Zopp_Inv [in Faux]
Zle_Zpred [in Faux]
Zle_Zpred_inv [in Faux]
Zle_Zpred_Zlt [in Faux]
Zle_Zpred_Zpred [in Faux]
ZltNormMinVnum [in FSucc]
Zlt_absolu [in Faux]
Zlt_MSB_LSB [in Fexp]
Zlt_mult_simpl_l [in Faux]
Zlt_mult_ZERO [in Faux]
Zlt_next [in Faux]
Zlt_not_eq [in Faux]
Zlt_not_eq_rev [in Faux]
Zlt_powerRZ [in Rpow]
Zlt_Rlt [in Faux]
Zlt_Zabs_intro [in Faux]
Zlt_Zabs_inv1 [in Faux]
Zlt_Zabs_inv2 [in Faux]
Zlt_Zabs_Zpred [in Faux]
Zlt_ZERO_Zle_ONE [in Faux]
Zlt_Zminus_ZERO [in Faux]
Zlt_Zopp [in Faux]
Zlt_Zopp_Inv [in Faux]
Zlt_Zpower_nat [in FboundI]
Zlt_1_O [in Faux]
zL_over_zH [in FArgReduct2]
ZmaxLe1 [in Faux]
ZmaxLe2 [in Faux]
ZmaxSym [in Faux]
Zmax_case [in FArgReduct4]
Zmax_le1 [in Faux]
Zmax_le2 [in Faux]
Zminus_n_predm [in Faux]
Zmin_le1 [in Faux]
Zmin_le2 [in Faux]
Zmin_sym [in Faux]
Zmin_Zle [in Faux]
Zmin_Zlt [in FmaErr]
Zmin_Zmax [in Faux]
Zopp_Zpred_Zs [in Faux]
zPos [in FmaErrApprox]
Zpos_eq_eq [in FmaEmul]
Zpower_nat_anti_eq [in Digit]
Zpower_nat_anti_monotone_le [in Digit]
Zpower_nat_anti_monotone_lt [in Digit]
Zpower_nat_exp [in FminOp]
Zpower_nat_is_pos [in IEEE]
Zpower_nat_less [in Digit]
Zpower_nat_monotone_le [in Digit]
Zpower_nat_monotone_lt [in Digit]
Zpower_nat_monotone_S [in Digit]
Zpower_nat_O [in Faux]
Zpower_nat_powerRZ_absolu [in Rpow]
Zpower_nat_S [in FboundI]
Zpower_nat_Z_powerRZ [in Rpow]
Zpower_nat_1 [in Faux]
Zpower_NR0 [in Rpow]
Zpower_NR1 [in Rpow]
Zpred_Zle_Zabs_intro [in Faux]
Zpred_Zopp_Zs [in Faux]
ZquotientMonotone [in Zdivides]
ZquotientPos [in Zdivides]
ZquotientProp [in Zdivides]
ZquotientUnique [in Zdivides]
ZquotientZopp [in Zdivides]
Zquotient1 [in Zdivides]
Zquotient_mult_comp [in Zdivides]
ZroundZ [in FroundProp]
Z2pos_correct [in FminOp]
Z_div_one [in FnormI]
Z_eq_bool_correct [in Faux]
Z_O_1 [in Faux]

# Constructor Index

## E

EqListFloatnil [in Fexp2]
EqListFloatTop [in Fexp2]

## I

IsCanExpNil [in Fexp2]
IsCanExpTop [in Fexp2]
IsEqual [in Fexp2]
IsEqual [in FexpAdd]
IsExpansionNil [in Fexp]
IsExpansionSingle [in Fexp]
IsExpansionTop [in Fexp]
IsExpansionTop1 [in Fexp]
IsExpansionTop2 [in Fexp]
IsExpNil [in Fexp2]
IsExpSingle [in Fexp2]
IsExpTop [in Fexp2]
IsNzExpansionNil [in Fexp]
IsNzExpansionNilR [in Fexp]
IsNzExpansionSingle [in Fexp]
IsNzExpansionSingleR [in Fexp]
IsNzExpansionTop [in Fexp]
IsNzExpansionTopR [in Fexp]
IsRleEpsExpNil [in FexpAdd]
IsRleEpsExpSingle [in FexpAdd]
IsRleEpsExpTop [in FexpAdd]
IsRleExpNil [in Fexp2]
IsRleExpRevNil [in Fexp2]
IsRleExpRevSingle [in Fexp2]
IsRleExpSingle [in Fexp2]
IsRleExpTop [in Fexp2]
IsRleRevExpTop [in Fexp2]

## N

None [in Option]

## O

OneMoreR [in FexpAdd]
OneMoreR [in Fexp2]

## R

rExact [in FminOp]
rRound [in FminOp]

## S

Some [in Option]

# Inductive Index

## E

EqListFloat [in Fexp2]

## F

Fbound [in Fbound]
FboundI [in FboundI]
float [in Float]

## I

IEEE_Float [in IEEE]
IEEE_precision [in IEEE]
IsCanExp [in Fexp2]
IsExp [in Fexp2]
IsExpansion [in Fexp]
IsNzExpansion [in Fexp]
IsNzExpansionR [in Fexp]
IsRleEpsExp [in FexpAdd]
IsRleExp [in Fexp2]
IsRleExpRev [in Fexp2]

## N

NearEqual [in FexpAdd]
NearEqual [in Fexp2]

## O

Option [in Option]

## R

rResult [in FminOp]

# Definition Index

## A

addExp [in FexpPlus]

## B

boundNat [in Fmin]
boundR [in Fmin]

## C

Closest [in Closest]
CompatibleP [in Fround]
CompatiblePI [in FnormI]

## D

digit [in Digit]
digitAux [in Digit]
dsd [in FexpDiv]

## E

endof [in Fexp2]
Even [in Fodd]
EvenClosest [in Closest]
exp [in Paux]
expNormalize [in Fexp]
expValue [in Fexp]

## F

Fabs [in Fop]
Fbounded [in Fbound]
FboundedI [in FboundI]
Fcanonic [in Fnorm]
FcanonicI [in FboundI]
Fcompare [in Fcomp]
Fdiff [in Fcomp]
Fdigit [in Float]
Feq [in Fcomp]
Feq_bool [in Fcomp]
Feven [in Fodd]
Fge [in Fcomp]
Fgt [in Fcomp]
FindMin [in FminOp]
firstNormalPos [in Fnorm]
Fle [in Fcomp]
FLess [in Axpy]
Fle_bool [in Fcomp]
Float_To_IEEE [in IEEE]
Flt [in Fcomp]
Flt_bool [in Fcomp]
Fminus [in Fop]
Fmult [in Fop]
Fmult_correct [in Fop]
FNeven [in Fodd]
FNI [in FboundI]
FNIAux [in FboundI]
FNodd [in Fodd]
Fnormal [in Fnorm]
FnormalI [in FboundI]
Fnormalize [in Fnorm]
FnormalizeI [in FboundI]
FNormTo_IEEE [in IEEE]
FNPred [in FPred]
FNSucc [in FSucc]
Fodd [in Fodd]
Fopp [in Fop]
Fplus [in Fop]
FPred [in FPred]
Fshift [in Float]
Fsubnormal [in Fnorm]
FsubnormalI [in FboundI]
FSubnormTo_IEEE [in IEEE]
FSucc [in FSucc]
FtoR [in Float]
Fulp [in FroundProp]
Fweight [in Finduct]
Fzero [in Float]

## G

growExp [in FexpPlus]

## H

hd [in Fexp2]
hdexp [in Fexp2]

## I

IEEE_canonic [in IEEE]
IEEE_normal [in IEEE]
IEEE_normalToR [in IEEE]
IEEE_Pos_To_Float [in IEEE]
IEEE_shift_mantissa [in IEEE]
IEEE_subnormal [in IEEE]
IEEE_subnormalToR [in IEEE]
IEEE_To_Float [in IEEE]
IEEE_To_R [in IEEE]
InDomain [in IEEE]
IRNDD [in RND]
isMax [in Fmin]
isMaxI [in FnormI]
isMin [in Fmin]
isMinI [in FnormI]
is_Fzero [in Float]

## L

last [in Fexp2]
lastexp [in Fexp2]
LSB [in MSB]

## M

maxDiv [in MSB]
mBFloat [in Fmin]
MinOrMax [in MinOrMax]
MinOrMaxP [in Fround]
MinOrMaxPI [in FnormI]
MonotoneP [in Fmin]
MonotonePI [in FnormI]
mProd [in Zenum]
MSB [in MSB]
mZlist [in Zenum]
mZlist_aux [in Zenum]

## N

natEq [in Faux]
nNormMin [in Fnorm]

## O

Odd [in Fodd]
oZ [in Paux]
oZ1 [in Zdivides]

## P

Pdiv [in Paux]
PdivBound [in Paux]
Pdivless [in Paux]
PdivlessAux [in Paux]
plusExp [in Veltkamp]
positive_exp [in Paux]
pos_eq_bool [in Faux]
pos_length [in Digit]
pPred [in Fnorm]
ProjectorP [in Fmin]
ProjectorPI [in FnormI]

## R

rCeil [in FminOp]
rClosestEven [in FminOp]
rClosestEvenPos [in FminOp]
rFloat [in FminOp]
rFloor [in FminOp]
RND_ClosestUp [in RND]
RND_EvenClosest [in RND]
RND_Max [in RND]
RND_Max_Pos [in RND]
RND_Min [in RND]
RND_Min_Pos [in RND]
RND_Zero [in RND]
rOp [in FminOp]
RoundedModeP [in Fround]
RoundedModePI [in FnormI]
rToZero [in FminOp]

## S

Step [in FexpAdd]
sum [in Fexp2]
SymmetricP [in Fround]

## T

ToInfinityP [in Fround]
TotalP [in Fround]
TotalPI [in FnormI]
ToZeroP [in Fround]
To_Odd [in DblRndOdd]

## U

Underf_Err [in Dekker]
UniqueP [in Fround]

## Z

Zdivides [in Zdivides]
ZdividesP [in Zdivides]
ZevenP [in FminOp]
Zmax [in Faux]
Zquotient [in Zdivides]
Z2pos [in FminOp]
Z_eq_bool [in Faux]

# Library Index

## A

AllFloat
Axpy

## C

Closest
ClosestMult
ClosestPlus
ClosestProp
Closest2Plus
Closest2Prop

## D

DblRndOdd
Dekker
Digit
discriminant
discriminant2
discriminant3
Divnk
DoubleRound

## E

EFast2Sum

## F

FArgReduct
FArgReduct2
FArgReduct3
FArgReduct4
Fast2Diff
Fast2Sum
Faux
Fbound
FboundI
Fcomp
Fexp
FexpAdd
FexpDiv
FexpPlus
Fexp2
FIA64elem
Finduct
Float
FmaEmul
FmaErr
FmaErrApprox
Fmin
FminOp
Fnorm
FnormI
Fodd
Fop
FPred
Fprop
Fround
FroundDivSqrt
FroundMult
FroundPlus
FroundProp
FSucc

## I

IEEE

## M

MinOrMax
MSB
MSBProp

## O

Option

## P

Paux
PradixE

## R

RND
Rpow

## S

sTactic

## T

ThreeSumProps
ThreeSum2
TwoSum

## V

Veltkamp

## Z

Zdivides
Zenum

Global Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (1655 entries)
Lemma Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (1389 entries)
Constructor Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (35 entries)
Inductive Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (18 entries)
Definition Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (145 entries)
Library Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (68 entries)

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