Documentation Verification Report

Basic

📁 Source: Mathlib/RingTheory/WittVector/Basic.lean

Statistics

MetricCount
DefinitionsconstantCoeff, ghostComponent, ghostEquiv, ghostMap, instCommRing, map, mapFun, tacticMap_fun_tac, «tacticGhost_fun_tac_,_»
9
TheoremsconstantCoeff_apply, ghostComponent_apply, ghostEquiv_coe, bijective_of_invertible, ghostMap_apply, instNontrivial, add, injective, intCast, mul, natCast, neg, nsmul, one, pow, sub, surjective, zero, zsmul, map_coeff, map_eq_zero_iff, map_id, map_injective, map_surjective, matrix_vecEmpty_coeff, pow_dvd_ghostComponent_of_dvd_coeff
26
Total35

WittVector

Definitions

NameCategoryTheorems
constantCoeff 📖CompOp
4 mathmath: constantCoeff_surjective, quotientPEquiv_mk, ker_constantCoeff, constantCoeff_apply
ghostComponent 📖CompOp
13 mathmath: ghostComponent_apply, ghostComponent_verschiebungFun, pow_dvd_ghostComponent_of_dvd_coeff, ghostComponent_frobeniusFun, ker_map_le_ker_mk_comp_ghostComponent, ghostMap_apply, ghostComponent_verschiebung, ghostComponent_zero_verschiebung, ghostComponent_frobenius, quotEquivOfEq_ghostComponentModPPow, ghostComponent_zero_verschiebungFun, ghostComponent_teichmuller, ghostComponentModPPow_map_mk
ghostEquiv 📖CompOp
1 mathmath: ghostEquiv_coe
ghostMap 📖CompOp
3 mathmath: ghostMap.bijective_of_invertible, ghostMap_apply, ghostEquiv_coe
instCommRing 📖CompOp
104 mathmath: ghostMap.bijective_of_invertible, map_id, coeff_truncate, toZModPow_compat, constantCoeff_surjective, teichmuller_mul_pow_coeff_of_ne, verschiebung_zmod, truncate_comp_lift, ghostComponent_apply, ghostComponent_verschiebungFun, eq_iterate_verschiebung, IsocrystalHom.frob_equivariant, frobeniusEquiv_symm_apply, TruncatedWittVector.iInf_ker_truncate, factorPowSucc_comp_fontaineThetaModPPow, map_teichmuller, verschiebung_coeff_succ, map_coeff, TruncatedWittVector.truncate_wittVector_truncate, factorPowSucc_fontaineThetaModPPow_eq, teichmuller_zero, iterate_verschiebung_mul, verschiebung_nonzero, frobenius_isPoly, truncate_surjective, mk_pow_fontaineTheta, verschiebung_injective, map_injective, fromPadicInt_comp_toPadicInt, frobenius_bijective, frobenius_frobeniusRotation, instIsDomain, sum_coeff_eq_coeff_sum, mem_span_p_pow_iff_le_coeff_eq_zero, IsocrystalEquiv.frob_equivariant, pow_dvd_ghostComponent_of_dvd_coeff, mem_ker_truncate, fromPadicInt_comp_toPadicInt_ext, TruncatedWittVector.truncate_comp_wittVector_truncate, ghostComponent_frobeniusFun, exists_eq_pow_p_mul', isDiscreteValuationRing, iterate_verschiebung_coeff_eq_zero, dvd_sub_sum_teichmuller_iterateFrobeniusEquiv_coeff, IsPoly.map, ker_map_le_ker_mk_comp_ghostComponent, fontaineThetaModPPow_teichmuller, verschiebung_coeff_zero, iterate_frobenius_coeff, inv_pair₂, irreducible, exists_frobenius_solution_fractionRing, ghostComponentModPPow_teichmuller_coeff, iterate_verschiebung_iterate_frobenius, verschiebung_mul_frobenius, coeff_frobenius_charP, liftEquiv_apply, isAdicCompleteIdealSpanP, ghostMap_apply, inv_pair₁, ghostComponent_verschiebung, surjective_fontaineTheta, map_verschiebung, verschiebung_frobenius, fontaineTheta_teichmuller, truncate_lift, ghostComponent_zero_verschiebung, StandardOneDimIsocrystal.frobenius_apply, iterate_verschiebung_mul_coeff, liftEquiv_symm_apply_coe, quotientPEquiv_mk, toPadicInt_comp_fromPadicInt_ext, map_eq_zero_iff, toPadicInt_comp_fromPadicInt, verschiebung_shift, ghostComponent_frobenius, isUnit_of_coeff_zero_ne_zero, verschiebung_frobenius_comm, quotEquivOfEq_ghostComponentModPPow, teichmuller_coeff_zero, iterate_verschiebung_mul_left, iterate_verschiebung_coeff, frobeniusEquiv_apply, truncate_mk', map_surjective, IsPoly₂.map, verschiebung_coeff_add_one, ker_constantCoeff, teichmuller_mul_pow_coeff, aeval_verschiebungPoly, verschiebung_isPoly, constantCoeff_apply, coe_mkUnit, mem_span_p_iff_coeff_zero_eq_zero, ghostEquiv_coe, teichmuller_coeff_pos, mk_fontaineTheta, ghostComponent_zero_verschiebungFun, coeff_frobenius, frobenius_verschiebung, ghostComponent_teichmuller, truncate_liftFun, ghostComponentModPPow_map_mk, frobenius_zmodp
map 📖CompOp
13 mathmath: map_id, frobeniusEquiv_symm_apply, map_teichmuller, map_coeff, map_injective, frobenius_eq_map_frobenius, IsPoly.map, ker_map_le_ker_mk_comp_ghostComponent, map_verschiebung, map_eq_zero_iff, map_surjective, IsPoly₂.map, ghostComponentModPPow_map_mk
mapFun 📖CompOp
13 mathmath: mapFun.zero, mapFun.surjective, mapFun.nsmul, mapFun.add, mapFun.one, mapFun.sub, mapFun.pow, mapFun.mul, mapFun.zsmul, mapFun.intCast, mapFun.natCast, mapFun.injective, mapFun.neg
«tacticGhost_fun_tac_,_» 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
constantCoeff_apply 📖mathematicalDFunLike.coe
RingHom
WittVector
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
instCommRing
RingHom.instFunLike
constantCoeff
coeff
ghostComponent_apply 📖mathematicalDFunLike.coe
RingHom
WittVector
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
instCommRing
RingHom.instFunLike
ghostComponent
AlgHom
MvPolynomial
Int.instCommRing
MvPolynomial.commSemiring
MvPolynomial.algebra
Algebra.id
Ring.toIntAlgebra
CommRing.toRing
AlgHom.funLike
MvPolynomial.aeval
coeff
wittPolynomial
ghostEquiv_coe 📖mathematicalRingHomClass.toRingHom
RingEquiv
WittVector
instMul
Pi.instMul
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
instAdd
Pi.instAdd
Distrib.toAdd
EquivLike.toFunLike
RingEquiv.instEquivLike
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
instCommRing
Pi.nonAssocSemiring
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
ghostEquiv
ghostMap
RingEquivClass.toRingHomClass
RingEquiv.instRingEquivClass
ghostMap_apply 📖mathematicalDFunLike.coe
RingHom
WittVector
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
instCommRing
Pi.nonAssocSemiring
RingHom.instFunLike
ghostMap
ghostComponent
instNontrivial 📖mathematicalNontrivial
WittVector
RingHom.domain_nontrivial
map_coeff 📖mathematicalcoeff
DFunLike.coe
RingHom
WittVector
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
instCommRing
RingHom.instFunLike
map
map_eq_zero_iff 📖mathematicalDFunLike.coe
RingHom
WittVector
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
instCommRing
RingHom.instFunLike
map
instZero
coeff
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
zero_coeff
ext
map_id 📖mathematicalmap
RingHom.id
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
WittVector
instCommRing
RingHom.ext
ext
map_injective 📖mathematicalDFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
WittVector
instCommRing
map
mapFun.injective
map_surjective 📖mathematicalDFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
WittVector
instCommRing
map
mapFun.surjective
matrix_vecEmpty_coeff 📖mathematicalcoeff
Matrix.vecEmpty
WittVector
pow_dvd_ghostComponent_of_dvd_coeff 📖mathematicalsemigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
NonUnitalCommSemiring.toNonUnitalSemiring
NonUnitalCommRing.toNonUnitalCommSemiring
CommRing.toNonUnitalCommRing
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
coeff
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
DFunLike.coe
RingHom
WittVector
Semiring.toNonAssocSemiring
instCommRing
RingHom.instFunLike
ghostComponent
ghostComponent_apply
wittPolynomial.eq_1
MvPolynomial.aeval_sum
Finset.dvd_sum
MvPolynomial.aeval_monomial
map_pow
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
map_natCast
Finsupp.prod_single_index
pow_zero
pow_add
mul_comm
mul_dvd_mul_left
pow_dvd_pow_of_dvd_of_le
LE.le.trans
LT.lt.succ_le
pow_left_mono
Nat.instMulLeftMono
covariant_swap_mul_of_covariant_mul
Nat.Prime.two_le
Fact.out

WittVector.ghostMap

Theorems

NameKindAssumesProvesValidatesDepends On
bijective_of_invertible 📖mathematicalFunction.Bijective
WittVector
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
WittVector.instCommRing
Pi.nonAssocSemiring
RingHom.instFunLike
WittVector.ghostMap
RingEquiv.bijective

WittVector.mapFun

Definitions

NameCategoryTheorems
tacticMap_fun_tac 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
add 📖mathematicalWittVector.mapFun
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
WittVector
WittVector.instAdd
WittVector.ext
WittVector.add_coeff
MvPolynomial.map_aeval
MvPolynomial.eval₂Hom_congr
RingHom.ext_int
Fintype.complete
injective 📖mathematicalWittVector
WittVector.mapFun
WittVector.ext
intCast 📖mathematicalWittVector.mapFun
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
WittVector
WittVector.instIntCast
natCast
neg
mul 📖mathematicalWittVector.mapFun
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
WittVector
WittVector.instMul
WittVector.ext
WittVector.mul_coeff
MvPolynomial.map_aeval
MvPolynomial.eval₂Hom_congr
RingHom.ext_int
Fintype.complete
natCast 📖mathematicalWittVector.mapFun
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
WittVector
WittVector.instNatCast
zero
add
one
neg 📖mathematicalWittVector.mapFun
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
WittVector
WittVector.instNeg
WittVector.ext
WittVector.neg_coeff
MvPolynomial.map_aeval
MvPolynomial.eval₂Hom_congr
RingHom.ext_int
Fintype.complete
nsmul 📖mathematicalWittVector.mapFun
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
WittVector
WittVector.hasNatScalar
WittVector.ext
WittVector.nsmul_coeff
MvPolynomial.map_aeval
MvPolynomial.eval₂Hom_congr
RingHom.ext_int
Fintype.complete
one 📖mathematicalWittVector.mapFun
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
WittVector
WittVector.instOne
WittVector.ext
WittVector.one_coeff_zero
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
WittVector.one_coeff_eq_of_pos
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
contravariant_swap_add_of_contravariant_add
contravariant_lt_of_covariant_le
Nat.instNoMaxOrder
Nat.instCanonicallyOrderedAdd
map_zero
MonoidWithZeroHomClass.toZeroHomClass
pow 📖mathematicalWittVector.mapFun
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
WittVector
WittVector.hasNatPow
WittVector.ext
WittVector.pow_coeff
MvPolynomial.map_aeval
MvPolynomial.eval₂Hom_congr
RingHom.ext_int
Fintype.complete
sub 📖mathematicalWittVector.mapFun
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
WittVector
WittVector.instSub
WittVector.ext
WittVector.sub_coeff
MvPolynomial.map_aeval
MvPolynomial.eval₂Hom_congr
RingHom.ext_int
Fintype.complete
surjective 📖mathematicalWittVector
WittVector.mapFun
WittVector.ext
zero 📖mathematicalWittVector.mapFun
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
WittVector
WittVector.instZero
WittVector.ext
WittVector.zero_coeff
map_zero
MonoidWithZeroHomClass.toZeroHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
zsmul 📖mathematicalWittVector.mapFun
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
WittVector
WittVector.hasIntScalar
WittVector.ext
WittVector.zsmul_coeff
MvPolynomial.map_aeval
MvPolynomial.eval₂Hom_congr
RingHom.ext_int
Fintype.complete

---

← Back to Index