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
105 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, exists_frobenius_solution_fractionRing_aux, 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
AddMonoidAlgebra.semiring
Finsupp
MulZeroClass.toZero
Nat.instMulZeroClass
Finsupp.instAddMonoid
Nat.instAddMonoid
AddMonoidAlgebra.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
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
instCommRing
RingHom.instFunLike
map
mapFun.injective
map_surjective 📖mathematicalDFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
WittVector
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
instCommRing
RingHom.instFunLike
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
semigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
NonUnitalCommSemiring.toNonUnitalSemiring
NonUnitalCommRing.toNonUnitalCommSemiring
CommRing.toNonUnitalCommRing
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
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
instIsRightCancelAddOfAddRightReflectLE
contravariant_swap_add_of_contravariant_add
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
instIsLeftCancelAddOfAddLeftReflectLE
IsOrderedCancelAddMonoid.toAddLeftReflectLE
Nat.instIsOrderedCancelAddMonoid
contravariant_lt_of_covariant_le
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
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

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