Documentation Verification Report

Complex

πŸ“ Source: Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean

Statistics

MetricCount
Definitionscpow, instPow
2
Theoremsconj_cpow, conj_cpow_eq_ite, cpow_add, cpow_conj, cpow_def, cpow_def_of_ne_zero, cpow_eq_pow, cpow_eq_zero_iff, cpow_intCast, cpow_int_mul, cpow_int_mul', cpow_mul, cpow_mul_int, cpow_mul_nat, cpow_mul_ofNat, cpow_natCast, cpow_nat_inv_pow, cpow_nat_mul, cpow_nat_mul', cpow_ne_zero_iff, cpow_ne_zero_iff_of_exponent_ne_zero, cpow_neg, cpow_neg_one, cpow_ofNat, cpow_ofNat_inv_pow, cpow_ofNat_mul, cpow_ofNat_mul', cpow_one, cpow_sub, cpow_two, cpow_zero, eq_zero_cpow_iff, inv_cpow, inv_cpow_eq_ite, inv_cpow_eq_ite', isSquare, mul_cpow_ofReal_nonneg, natCast_add_one_cpow_ne_zero, natCast_cpow_natCast_mul, natCast_mul_natCast_cpow, one_cpow, pow_cpow_nat_inv, pow_cpow_ofNat_inv, sq_cpow_two_inv, zero_cpow, zero_cpow_eq_iff
46
Total48

Complex

Definitions

NameCategoryTheorems
cpow πŸ“–CompOp
1 mathmath: cpow_eq_pow
instPow πŸ“–CompOp
288 mathmath: HadamardThreeLines.norm_le_interpStrip_of_mem_verticalClosedStrip_eps, HurwitzZeta.hasSum_int_hurwitzZetaOdd, cpow_intCast, hasSum_mellin_pi_mul_sq', continuousAt_const_cpow, differentiable_const_cpow_of_neZero, completedZeta_eq_tsum_of_one_lt_re, Gammaℝ_def, HurwitzZeta.hasSum_int_hurwitzZetaEven, DirichletCharacter.LSeries_eulerProduct_tprod, isTheta_cpow_rpow, AnalyticOn.cpow, ZMod.LFunction_one_sub, one_add_cpow_hasFPowerSeriesAt_zero, tsum_exp_neg_mul_int_sq, not_integrableOn_Ioi_cpow, deriv_cpow_const, GaussianFourier.integral_cexp_neg_mul_sq_norm, ContinuousWithinAt.cpow, DifferentiableOn.cpow_const, betaIntegral_scaled, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, cpow_mul_ofReal_nonneg, fourierIntegral_gaussian_innerProductSpace', fourier_gaussian_pi', jacobiThetaβ‚‚_functional_equation, HasStrictDerivAt.cpow, GaussianFourier.integral_cexp_neg_mul_sq_norm_add, cpow_neg_one, AnalyticWithinAt.cpow, HurwitzZeta.jacobiThetaβ‚‚'_functional_equation', continuous_const_cpow, integrableOn_Ioi_norm_cpow_of_lt, ZMod.completedLFunction_def_even, HasDerivAt.cpow, DirichletCharacter.LFunction_changeLevel, fourier_gaussian_innerProductSpace, DirichletCharacter.IsPrimitive.completedLFunction_one_sub, hasDerivAt_GammaIntegral, deriv_ofReal_cpow_const, HurwitzZeta.hasSum_nat_sinZeta, DifferentiableOn.const_cpow, ZMod.LFunction_def_odd, DifferentiableOn.cpow, hasStrictFDerivAt_cpow', cpow_ofNat_mul', LSeries.term_def, riemannZeta_one_sub, DifferentiableAt.const_cpow, integrableOn_Ioi_cpow_iff, setIntegral_Ioi_zero_cpow, deriv_norm_ofReal_cpow, natCast_mul_natCast_cpow, ofReal_cpow, tendsto_one_add_cpow_exp_of_tendsto, HurwitzZeta.hasSum_hurwitzZeta_of_one_lt_re, AnalyticOnNhd.cpow, ofReal_cpow_of_nonpos, integrableOn_Ioi_norm_cpow_iff, HurwitzZeta.expZeta_one_sub, fourierIntegral_gaussian_pi, hasSum_mellin, mellinInv_eq_fourierIntegralInv, norm_cpow_of_ne_zero, norm_ofReal_cpow_eventually_eq_atTop, DifferentiableWithinAt.const_cpow, cpow_sub, continuousAt_cpow_const_of_re_pos, HasDerivWithinAt.const_cpow, HurwitzZeta.hasSum_nat_completedCosZeta, tendsto_sub_mul_tsum_nat_cpow, partialGamma_add_one, norm_cpow_of_imp, DirichletCharacter.LSeries_changeLevel, mellinInv_eq_fourierInv, fourier_gaussian_innerProductSpace', HurwitzZeta.hasSum_nat_hurwitzZetaEven, LSeries.term_of_ne_zero, ZMod.completedLFunction_def_odd, cpow_eq_zero_iff, IsExpCmpFilter.isLittleO_exp_cpow, integral_cpow, Real.tendsto_integral_gaussian_smul', hasStrictFDerivAt_cpow, cpow_ofReal_re, LSeries_eq_mul_integral_of_nonneg, HasFDerivWithinAt.cpow, HasStrictFDerivAt.const_cpow, riemannZeta_eulerProduct_exp_log, HurwitzZeta.cosZeta_one_sub, jacobiTheta_S_smul, inv_cpow_eq_ite', zeta_eq_tsum_one_div_nat_cpow, norm_cpow_real, continuousAt_cpow, isBigO_cpow_rpow, cpow_neg, cpow_nat_mul, intervalIntegral.intervalIntegrable_cpow, HurwitzZeta.hasSum_int_cosZeta, hasStrictDerivAt_const_cpow, HasDerivWithinAt.cpow, intervalIntegral.integrableOn_Ioo_cpow_iff, integrableOn_Ioi_deriv_ofReal_cpow, one_add_cpow_hasFPowerSeriesAt_zero, HurwitzZeta.hasSum_nat_cosZeta, DirichletCharacter.LFunctionTrivChar_eq_mul_riemannZeta, pow_cpow_ofNat_inv, hasFDerivAt_cpow, conj_cpow, ContinuousOn.cpow_const, HadamardThreeLines.interpStrip_eq_of_pos, HurwitzZeta.hasSum_expZeta_of_one_lt_re, inv_cpow_eq_ite, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow, inv_cpow, mul_cpow_ofReal_nonneg, ZMod.completedLFunction_eq, zero_cpow_eq_iff, tsum_exp_neg_quadratic, Differentiable.cpow, HurwitzZeta.hurwitzZetaEven_one_sub, hasSum_mellin_pi_mul, conj_cpow_eq_ite, inv_natCast_cpow_ofReal_pos, DifferentiableWithinAt.cpow_const, zero_cpow_eq_nhds, cpow_mul_nat, continuousAt_ofReal_cpow, integral_cexp_quadratic, Gammaβ„‚_def, cpow_natCast, HasStrictDerivAt.cpow_const, cpow_inv_two_im_eq_sqrt, cpow_inv_two_re, zero_cpow, continuousAt_cpow_zero_of_re_pos, ZMod.LFunction_def_even, Filter.Tendsto.cpow, HurwitzZeta.hasSum_nat_completedSinZeta, LSeries_eq_mul_integral, norm_natCast_cpow_of_pos, fourierIntegral_gaussian_innerProductSpace, cpow_mul, zeta_eq_tsum_one_div_nat_add_one_cpow, cpow_one, norm_prime_cpow_le_one_half, tendsto_one_add_div_cpow_exp, jacobiThetaβ‚‚'_functional_equation, continuousAt_const_cpow', pow_cpow_nat_inv, natCast_cpow_natCast_mul, DifferentiableAt.ofReal_cpow_const, Continuous.cpow, GammaSeq_eq_betaIntegral_of_re_pos, deriv_const_cpow, cpow_ofNat_mul, norm_natCast_cpow_pos_of_pos, LSeries.term_of_ne_zero', Filter.Tendsto.const_cpow, riemannZeta_eulerProduct, hasSum_mellin_pi_mulβ‚€, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, betaIntegral_convergent, AnalyticAt.cpow, DirichletCharacter.LSeries_eulerProduct_hasProd, HasStrictDerivAt.const_cpow, isTheta_cpow_const_rpow, DifferentiableWithinAt.cpow, continuousAt_cpow_const, differentiableAt_const_cpow_of_neZero, eq_zero_cpow_iff, Continuous.const_cpow, DirichletCharacter.LSeries_eulerProduct_exp_log, HasFDerivWithinAt.const_cpow, ZMod.completedLFunction_one_sub_odd, HadamardThreeLines.interpStrip_eq_of_mem_verticalStrip, integrableOn_Ioi_cpow_of_lt, GaussianFourier.integral_cexp_neg_mul_sq_add_real_mul_I, mellin_convergent_iff_norm, GaussianFourier.integral_cexp_neg_mul_sum_add, continuous_ofReal_cpow_const, one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, fourierIntegral_gaussian, LSeries.tendsto_cpow_mul_atTop, ContinuousAt.cpow, HurwitzZeta.hasSum_nat_hurwitzZetaEven_of_mem_Icc, HurwitzZeta.hurwitzZeta_one_sub, DifferentiableAt.cpow_const, one_cpow, isBigO_deriv_ofReal_cpow_const_atTop, derivWithin_const_cpow, hasDerivAt_ofReal_cpow_const, cpow_eq_pow, cpow_nat_mul', one_add_cpow_hasFPowerSeriesOnBall_zero, hasStrictDerivAt_cpow_const, GammaSeq_eq_approx_Gamma_integral, cpow_ofReal_im, cpow_add, cpow_nat_inv_pow, HasStrictFDerivAt.cpow, deriv_cpow_const, summable_one_div_nat_cpow, cpow_int_mul', HadamardThreeLines.eventuallyle, cpow_conj, GaussianFourier.integral_cexp_neg_sum_mul_add, ContinuousOn.const_cpow, norm_cpow_inv_nat, LSeries.term_defβ‚€, HurwitzZeta.hasSum_int_sinZeta, ArithmeticFunction.LSeries_zeta_eulerProduct_exp_log, cpow_eq_nhds', cpow_def, cpow_mul_int, hasDerivAt_ofReal_cpow_const', Real.tendsto_integral_gaussian_smul, Gamma_mul_Gamma_add_half, cpow_inv_two_im_eq_neg_sqrt, integral_Ioi_cpow_of_lt, LSeries.pow_mul_term_eq, intervalIntegral.intervalIntegrable_cpow', norm_natCast_cpow_le_norm_natCast_cpow_iff, norm_natCast_cpow_le_norm_natCast_cpow_of_pos, norm_cpow_eq_rpow_re_of_nonneg, IsExpCmpFilter.isLittleO_cpow_exp, integral_gaussian_complex, ContinuousOn.cpow, HasDerivWithinAt.cpow_const, betaIntegral_convergent_left, continuousAt_cpow_of_re_pos, cpow_int_mul, one_add_cpow_hasFPowerSeriesOnBall_zero, riemannZeta_eulerProduct_tprod, cpow_eq_nhds, ZMod.completedLFunction_one_sub_even, hasMellin_cpow_Ioc, integral_mul_cpow_one_add_sq, isTheta_deriv_ofReal_cpow_const_atTop, cpow_mul_ofNat, ContinuousAt.const_cpow, norm_cpow_le, hasMeasurablePow, cpow_def_of_ne_zero, HurwitzZeta.hasSum_int_completedCosZeta, HasFDerivAt.cpow, GammaIntegral_convergent, abs_cpow_inv_two_im, HasDerivAt.const_cpow, HurwitzZeta.hurwitzZetaOdd_one_sub, HurwitzZeta.hasSum_int_completedSinZeta, MellinConvergent.cpow_smul, HurwitzZeta.hasSum_nat_hurwitzZetaOdd_of_mem_Icc, riemannZeta_eulerProduct_hasProd, DirichletCharacter.LSeries_eulerProduct, Differentiable.const_cpow, cpow_zero, norm_cpow_eq_rpow_re_of_pos, cpow_ofNat_inv_pow, HurwitzZeta.hasSum_int_completedHurwitzZetaEven, mellin_cpow_smul, DifferentiableAt.cpow, integral_cpow_mul_exp_neg_mul_Ioi, IsExpCmpFilter.isLittleO_cpow_mul_exp, HurwitzZeta.sinZeta_one_sub, cpow_ofNat, approx_Gamma_integral_tendsto_Gamma_integral, cpow_two, IsExpCmpFilter.isTheta_cpow_exp_re_mul_log, Gamma_one_half_eq, sq_cpow_two_inv, Real.rpow_def, continuousAt_ofReal_cpow_const, LSeries_eq_mul_integral', integrableOn_Ioi_deriv_norm_ofReal_cpow, fourier_gaussian_pi, norm_natCast_cpow_of_re_ne_zero, fourierIntegral_gaussian_pi', integral_gaussian_complex_Ioi, hasSum_mellin_pi_mul_sq, mellin_comp_mul_left, cpow_ofReal, HasFDerivAt.const_cpow, mellin_comp_mul_right, HasDerivAt.cpow_const, ContinuousWithinAt.const_cpow

Theorems

NameKindAssumesProvesValidatesDepends On
conj_cpow πŸ“–mathematicalβ€”Complex
instPow
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
RingHom.instFunLike
starRingEnd
instStarRing
β€”conj_cpow_eq_ite
conj_cpow_eq_ite πŸ“–mathematicalβ€”Complex
instPow
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
RingHom.instFunLike
starRingEnd
instStarRing
Real
arg
Real.pi
Real.decidableEq
β€”instNontrivial
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
map_zero
MonoidWithZeroHomClass.toZeroHomClass
map_mul
NonUnitalRingHomClass.toMulHomClass
RingHomClass.toNonUnitalRingHomClass
conj_conj
log_conj_eq_ite
cpow_add πŸ“–mathematicalβ€”Complex
instPow
instAdd
instMul
β€”mul_ite
ite_mul
mul_add
Distrib.leftDistribClass
exp_add
cpow_conj πŸ“–mathematicalβ€”Complex
instPow
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
RingHom.instFunLike
starRingEnd
instStarRing
β€”conj_cpow
conj_conj
cpow_def πŸ“–mathematicalβ€”Complex
instPow
instZero
instDecidableEq
instOne
exp
instMul
log
β€”β€”
cpow_def_of_ne_zero πŸ“–mathematicalβ€”Complex
instPow
exp
instMul
log
β€”β€”
cpow_eq_pow πŸ“–mathematicalβ€”cpow
Complex
instPow
β€”β€”
cpow_eq_zero_iff πŸ“–mathematicalβ€”Complex
instPow
instZero
β€”NeZero.charZero_one
instCharZero
cpow_intCast πŸ“–mathematicalβ€”Complex
instPow
instIntCast
DivInvMonoid.toZPow
instDivInvMonoid
β€”mul_one
cpow_one
cpow_int_mul
cpow_int_mul πŸ“–mathematicalβ€”Complex
instPow
instMul
instIntCast
DivInvMonoid.toZPow
instDivInvMonoid
β€”eq_or_ne
Int.cast_zero
MulZeroClass.zero_mul
cpow_zero
zpow_zero
MulZeroClass.mul_zero
one_zpow
zero_cpow
NormMulClass.toNoZeroDivisors
NormedDivisionRing.toNormMulClass
instCharZero
zero_zpow
cpow_def_of_ne_zero
mul_left_comm
exp_int_mul
cpow_int_mul' πŸ“–mathematicalReal
Real.instLT
Real.instNeg
Real.pi
Real.instMul
Real.instIntCast
arg
Real.instLE
Complex
instPow
instMul
instIntCast
DivInvMonoid.toZPow
instDivInvMonoid
β€”cpow_mul
MulZeroClass.mul_zero
log_im
zero_add
mul_comm
cpow_intCast
cpow_mul πŸ“–mathematicalReal
Real.instLT
Real.instNeg
Real.pi
im
Complex
instMul
log
Real.instLE
instPowβ€”NeZero.charZero_one
instCharZero
log_one
MulZeroClass.zero_mul
exp_zero
NormMulClass.toNoZeroDivisors
NormedDivisionRing.toNormMulClass
MulZeroClass.mul_zero
log_exp
mul_assoc
cpow_mul_int πŸ“–mathematicalβ€”Complex
instPow
instMul
instIntCast
DivInvMonoid.toZPow
instDivInvMonoid
β€”mul_comm
cpow_int_mul
cpow_mul_nat πŸ“–mathematicalβ€”Complex
instPow
instMul
instNatCast
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
β€”mul_comm
cpow_nat_mul
cpow_mul_ofNat πŸ“–mathematicalβ€”Complex
instPow
instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
β€”cpow_mul_nat
cpow_natCast πŸ“–mathematicalβ€”Complex
instPow
instNatCast
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
β€”mul_one
cpow_one
cpow_nat_mul
cpow_nat_inv_pow πŸ“–mathematicalβ€”Complex
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
instPow
instInv
instNatCast
β€”cpow_nat_mul
mul_inv_cancelβ‚€
Nat.cast_zero
instCharZero
cpow_one
cpow_nat_mul πŸ“–mathematicalβ€”Complex
instPow
instMul
instNatCast
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
β€”zpow_natCast
Int.cast_natCast
cpow_int_mul
cpow_nat_mul' πŸ“–mathematicalReal
Real.instLT
Real.instNeg
Real.pi
Real.instMul
Real.instNatCast
arg
Real.instLE
Complex
instPow
instMul
instNatCast
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
β€”cpow_int_mul'
cpow_ne_zero_iff πŸ“–mathematicalβ€”Complex
instZero
β€”cpow_eq_zero_iff
not_and_or
cpow_ne_zero_iff_of_exponent_ne_zero πŸ“–β€”β€”β€”β€”β€”
cpow_neg πŸ“–mathematicalβ€”Complex
instPow
instNeg
instInv
β€”mul_neg
inv_one
inv_zero
exp_neg
cpow_neg_one πŸ“–mathematicalβ€”Complex
instPow
instNeg
instOne
instInv
β€”cpow_one
cpow_neg
cpow_ofNat πŸ“–mathematicalβ€”Complex
instPow
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
β€”cpow_natCast
cpow_ofNat_inv_pow πŸ“–mathematicalβ€”Complex
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
instPow
instInv
β€”cpow_nat_inv_pow
Nat.AtLeastTwo.toNeZero
cpow_ofNat_mul πŸ“–mathematicalβ€”Complex
instPow
instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
β€”cpow_nat_mul
cpow_ofNat_mul' πŸ“–mathematicalReal
Real.instLT
Real.instNeg
Real.pi
Real.instMul
instOfNatAtLeastTwo
Real.instNatCast
arg
Real.instLE
Complex
instPow
instMul
instNatCast
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
β€”cpow_nat_mul'
cpow_one πŸ“–mathematicalβ€”Complex
instPow
instOne
β€”NeZero.charZero_one
instCharZero
cpow_def
one_ne_zero
mul_one
exp_log
cpow_sub πŸ“–mathematicalβ€”Complex
instPow
instSub
DivInvMonoid.toDiv
instDivInvMonoid
β€”sub_eq_add_neg
cpow_add
cpow_neg
div_eq_mul_inv
cpow_two πŸ“–mathematicalβ€”Complex
instPow
instOfNatAtLeastTwo
instNatCast
Nat.instAtLeastTwoHAddOfNat
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
β€”cpow_ofNat
Nat.instAtLeastTwoHAddOfNat
cpow_zero πŸ“–mathematicalβ€”Complex
instPow
instZero
instOne
β€”MulZeroClass.mul_zero
exp_zero
eq_zero_cpow_iff πŸ“–mathematicalβ€”Complex
instPow
instZero
instOne
β€”zero_cpow_eq_iff
inv_cpow πŸ“–mathematicalβ€”Complex
instPow
instInv
β€”inv_cpow_eq_ite
inv_cpow_eq_ite πŸ“–mathematicalβ€”Complex
instPow
instInv
Real
arg
Real.pi
Real.decidableEq
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
RingHom.instFunLike
starRingEnd
instStarRing
β€”log_inv_eq_ite
instNontrivial
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
ite_mul
neg_mul
RCLike.conj_inv
map_zero
MonoidWithZeroHomClass.toZeroHomClass
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
exp_neg
inv_one
inv_zero
map_mul
NonUnitalRingHomClass.toMulHomClass
RingHomClass.toNonUnitalRingHomClass
conj_conj
inv_cpow_eq_ite' πŸ“–mathematicalβ€”Complex
instInv
instPow
Real
arg
Real.pi
Real.decidableEq
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
RingHom.instFunLike
starRingEnd
instStarRing
β€”inv_cpow_eq_ite
conj_conj
inv_cpow
isSquare πŸ“–mathematicalβ€”IsSquare
Complex
instMul
β€”Nat.instAtLeastTwoHAddOfNat
cpow_ofNat_inv_pow
mul_cpow_ofReal_nonneg πŸ“–mathematicalReal
Real.instLE
Real.instZero
Complex
instPow
instMul
ofReal
β€”eq_or_ne
cpow_zero
mul_one
eq_or_lt_of_le
ofReal_zero
MulZeroClass.zero_mul
zero_cpow
MulZeroClass.mul_zero
ofReal_ne_zero
LT.lt.ne'
cpow_def_of_ne_zero
mul_ne_zero
NormMulClass.toNoZeroDivisors
NormedDivisionRing.toNormMulClass
log_ofReal_mul
ofReal_log
add_mul
Distrib.rightDistribClass
exp_add
natCast_add_one_cpow_ne_zero πŸ“–β€”β€”β€”β€”cpow_eq_zero_iff
Nat.cast_one
Nat.cast_zero
instCharZero
natCast_cpow_natCast_mul πŸ“–mathematicalβ€”Complex
instPow
instNatCast
instMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
β€”cpow_nat_mul'
natCast_arg
MulZeroClass.mul_zero
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
LT.lt.le
Real.pi_pos
natCast_mul_natCast_cpow πŸ“–mathematicalβ€”Complex
instPow
instMul
instNatCast
β€”mul_cpow_ofReal_nonneg
Nat.cast_nonneg
Real.instIsOrderedRing
ofReal_natCast
one_cpow πŸ“–mathematicalβ€”Complex
instPow
instOne
β€”cpow_def
NeZero.charZero_one
instCharZero
log_one
MulZeroClass.zero_mul
exp_zero
pow_cpow_nat_inv πŸ“–mathematicalReal
Real.instLT
Real.instNeg
DivInvMonoid.toDiv
Real.instDivInvMonoid
Real.pi
Real.instNatCast
arg
Real.instLE
Complex
instPow
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
instInv
instNatCast
β€”cpow_nat_mul'
div_lt_iffβ‚€'
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
Real.instIsStrictOrderedRing
Nat.cast_pos
Real.instIsOrderedRing
Real.instNontrivial
Ne.bot_lt
neg_div
le_div_iffβ‚€'
mul_inv_cancelβ‚€
Nat.cast_ne_zero
instCharZero
cpow_one
pow_cpow_ofNat_inv πŸ“–mathematicalReal
Real.instLT
Real.instNeg
DivInvMonoid.toDiv
Real.instDivInvMonoid
Real.pi
instOfNatAtLeastTwo
Real.instNatCast
arg
Real.instLE
Complex
instPow
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
instInv
instNatCast
β€”pow_cpow_nat_inv
Nat.AtLeastTwo.toNeZero
sq_cpow_two_inv πŸ“–mathematicalReal
Real.instLT
Real.instZero
re
Complex
instPow
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
instInv
instOfNatAtLeastTwo
instNatCast
Nat.instAtLeastTwoHAddOfNat
β€”pow_cpow_ofNat_inv
Nat.instAtLeastTwoHAddOfNat
neg_pi_div_two_lt_arg_iff
arg_le_pi_div_two_iff
LT.lt.le
zero_cpow πŸ“–mathematicalβ€”Complex
instPow
instZero
β€”β€”
zero_cpow_eq_iff πŸ“–mathematicalβ€”Complex
instPow
instZero
instOne
β€”zero_cpow
cpow_zero

---

← Back to Index