Documentation Verification Report

MonomialOrder

πŸ“ Source: Mathlib/Data/Finsupp/MonomialOrder.lean

Statistics

MetricCount
Definitionsacm, lex, lo, orderBot, syn, toSyn, Β«term_β‰Ί[_]_Β», Β«term_β‰Ό[_]_Β»
8
Theoremsbot_eq_zero, eq_zero_iff, iocam, le_add_right, lex_le_iff, lex_le_iff_of_unique, lex_lt_iff, lex_lt_iff_of_unique, toSyn_eq_zero_iff, toSyn_lt_iff_ne_zero, toSyn_monotone, toSyn_strictMono, wf, zero_le, instIsOrderedCancelAddMonoidLexFinsupp
15
Total23

MonomialOrder

Definitions

NameCategoryTheorems
acm πŸ“–CompOp
43 mathmath: degree_add_of_ne, degree_sub_le, degree_reduce_lt, zero_le, toSyn_strictMono, div_single, degree_add_le, le_degree, lex_lt_iff_of_unique, degLex_le_iff, bot_eq_zero, toSyn_lt_iff_ne_zero, degree_le_iff, degree_sum_le, degree_mul_lt_iff_left_lt_of_ne_zero, degree_smul_le, degree_mul_le, le_add_right, degree_pow_le, toSyn_monotone, degLex_single_le_iff, toSyn_eq_zero_iff, degree_prod_le, div_set, degLex_lt_iff, lex_lt_iff, eq_zero_iff, div, lex_le_iff, degree_sPolynomial_le, degree_sub_leadingTerm_lt_degree, degree_monomial_le, degLex_single_lt_iff, degree_sub_LTerm_lt, sPolynomial_lt_of_degree_ne_zero_of_degree_eq, degree_sPolynomial_lt_sup_degree, degree_sub_leadingTerm_lt_iff, degree_sub_leadingTerm_le, iocam, degree_sub_LTerm_le, lex_le_iff_of_unique, degree_sPolynomial, degree_X_le_single
lex πŸ“–CompOp
4 mathmath: lex_lt_iff_of_unique, lex_lt_iff, lex_le_iff, lex_le_iff_of_unique
lo πŸ“–CompOp
43 mathmath: degree_add_of_ne, degree_sub_le, degree_reduce_lt, zero_le, toSyn_strictMono, div_single, degree_add_le, le_degree, lex_lt_iff_of_unique, degLex_le_iff, bot_eq_zero, toSyn_lt_iff_ne_zero, degree_le_iff, degree_sum_le, degree_mul_lt_iff_left_lt_of_ne_zero, degree_smul_le, degree_mul_le, le_add_right, degree_pow_le, toSyn_monotone, degLex_single_le_iff, wf, degree_prod_le, div_set, degLex_lt_iff, lex_lt_iff, eq_zero_iff, div, lex_le_iff, degree_sPolynomial_le, degree_sub_leadingTerm_lt_degree, degree_monomial_le, degLex_single_lt_iff, degree_sub_LTerm_lt, sPolynomial_lt_of_degree_ne_zero_of_degree_eq, degree_sPolynomial_lt_sup_degree, degree_sub_leadingTerm_lt_iff, degree_sub_leadingTerm_le, iocam, degree_sub_LTerm_le, lex_le_iff_of_unique, degree_sPolynomial, degree_X_le_single
orderBot πŸ“–CompOp
2 mathmath: bot_eq_zero, degree_sum_le
syn πŸ“–CompOp
44 mathmath: degree_add_of_ne, degree_sub_le, degree_reduce_lt, zero_le, toSyn_strictMono, div_single, degree_add_le, le_degree, lex_lt_iff_of_unique, degLex_le_iff, bot_eq_zero, toSyn_lt_iff_ne_zero, degree_le_iff, degree_sum_le, degree_mul_lt_iff_left_lt_of_ne_zero, degree_smul_le, degree_mul_le, le_add_right, degree_pow_le, toSyn_monotone, degLex_single_le_iff, wf, toSyn_eq_zero_iff, degree_prod_le, div_set, degLex_lt_iff, lex_lt_iff, eq_zero_iff, div, lex_le_iff, degree_sPolynomial_le, degree_sub_leadingTerm_lt_degree, degree_monomial_le, degLex_single_lt_iff, degree_sub_LTerm_lt, sPolynomial_lt_of_degree_ne_zero_of_degree_eq, degree_sPolynomial_lt_sup_degree, degree_sub_leadingTerm_lt_iff, degree_sub_leadingTerm_le, iocam, degree_sub_LTerm_le, lex_le_iff_of_unique, degree_sPolynomial, degree_X_le_single
toSyn πŸ“–CompOp
38 mathmath: degree_add_of_ne, degree_sub_le, degree_reduce_lt, toSyn_strictMono, div_single, degree_add_le, le_degree, lex_lt_iff_of_unique, degLex_le_iff, degree_le_iff, degree_sum_le, degree_mul_lt_iff_left_lt_of_ne_zero, degree_smul_le, degree_mul_le, le_add_right, degree_pow_le, toSyn_monotone, degLex_single_le_iff, toSyn_eq_zero_iff, degree_prod_le, div_set, degLex_lt_iff, lex_lt_iff, div, lex_le_iff, degree_sPolynomial_le, degree_sub_leadingTerm_lt_degree, degree_monomial_le, degLex_single_lt_iff, degree_sub_LTerm_lt, sPolynomial_lt_of_degree_ne_zero_of_degree_eq, degree_sPolynomial_lt_sup_degree, degree_sub_leadingTerm_lt_iff, degree_sub_leadingTerm_le, degree_sub_LTerm_le, lex_le_iff_of_unique, degree_sPolynomial, degree_X_le_single
Β«term_β‰Ί[_]_Β» πŸ“–CompOpβ€”
Β«term_β‰Ό[_]_Β» πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
bot_eq_zero πŸ“–mathematicalβ€”Bot.bot
syn
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
lo
orderBot
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
acm
β€”β€”
eq_zero_iff πŸ“–mathematicalβ€”syn
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
acm
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
lo
β€”eq_bot_iff
iocam πŸ“–mathematicalβ€”IsOrderedCancelAddMonoid
syn
acm
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
lo
β€”β€”
le_add_right πŸ“–mathematicalβ€”syn
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
lo
DFunLike.coe
AddEquiv
Finsupp
MulZeroClass.toZero
Nat.instMulZeroClass
Finsupp.instAdd
AddMonoid.toAddZeroClass
Nat.instAddMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
acm
EquivLike.toFunLike
AddEquiv.instEquivLike
toSyn
β€”map_add
AddMonoidHomClass.toAddHomClass
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
toSyn_monotone
le_self_add
Finsupp.instCanonicallyOrderedAddOfAddLeftMono
Nat.instCanonicallyOrderedAdd
Nat.instOrderedSub
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
lex_le_iff πŸ“–mathematicalβ€”syn
lex
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
lo
DFunLike.coe
AddEquiv
Finsupp
MulZeroClass.toZero
Nat.instMulZeroClass
Finsupp.instAdd
AddMonoid.toAddZeroClass
Nat.instAddMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
acm
EquivLike.toFunLike
AddEquiv.instEquivLike
toSyn
Lex
Finsupp.Lex.partialOrder
Nat.instPartialOrder
Equiv
Equiv.instEquivLike
toLex
β€”β€”
lex_le_iff_of_unique πŸ“–mathematicalβ€”syn
lex
IsWellOrder.toIsWellFounded
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
isWellOrder_gt
LinearOrder.toPartialOrder
Finite.to_wellFoundedGT
Finite.of_fintype
Unique.fintype
Preorder.toLE
lo
DFunLike.coe
AddEquiv
Finsupp
MulZeroClass.toZero
Nat.instMulZeroClass
Finsupp.instAdd
AddMonoid.toAddZeroClass
Nat.instAddMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
acm
EquivLike.toFunLike
AddEquiv.instEquivLike
toSyn
Finsupp.instFunLike
Unique.instInhabited
β€”IsWellOrder.toIsWellFounded
isWellOrder_gt
Finite.to_wellFoundedGT
Finite.of_fintype
lex_lt_iff πŸ“–mathematicalβ€”syn
lex
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
lo
DFunLike.coe
AddEquiv
Finsupp
MulZeroClass.toZero
Nat.instMulZeroClass
Finsupp.instAdd
AddMonoid.toAddZeroClass
Nat.instAddMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
acm
EquivLike.toFunLike
AddEquiv.instEquivLike
toSyn
Lex
Finsupp.instLTLex
Equiv
Equiv.instEquivLike
toLex
β€”β€”
lex_lt_iff_of_unique πŸ“–mathematicalβ€”syn
lex
IsWellOrder.toIsWellFounded
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
isWellOrder_gt
LinearOrder.toPartialOrder
Finite.to_wellFoundedGT
Finite.of_fintype
Unique.fintype
lo
DFunLike.coe
AddEquiv
Finsupp
MulZeroClass.toZero
Nat.instMulZeroClass
Finsupp.instAdd
AddMonoid.toAddZeroClass
Nat.instAddMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
acm
EquivLike.toFunLike
AddEquiv.instEquivLike
toSyn
Finsupp.instFunLike
Unique.instInhabited
β€”IsWellOrder.toIsWellFounded
isWellOrder_gt
Finite.to_wellFoundedGT
Finite.of_fintype
toSyn_eq_zero_iff πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
Finsupp
MulZeroClass.toZero
Nat.instMulZeroClass
syn
Finsupp.instAdd
AddMonoid.toAddZeroClass
Nat.instAddMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
acm
EquivLike.toFunLike
AddEquiv.instEquivLike
toSyn
AddZero.toZero
AddZeroClass.toAddZero
AddCommMonoid.toAddMonoid
Finsupp.instZero
β€”AddEquiv.map_eq_zero_iff
toSyn_lt_iff_ne_zero πŸ“–mathematicalβ€”syn
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
lo
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
acm
β€”bot_lt_iff_ne_bot
toSyn_monotone πŸ“–mathematicalβ€”Monotone
Finsupp
MulZeroClass.toZero
Nat.instMulZeroClass
syn
Finsupp.preorder
Nat.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
lo
DFunLike.coe
AddEquiv
Finsupp.instAdd
AddMonoid.toAddZeroClass
Nat.instAddMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
acm
EquivLike.toFunLike
AddEquiv.instEquivLike
toSyn
β€”β€”
toSyn_strictMono πŸ“–mathematicalβ€”StrictMono
Finsupp
MulZeroClass.toZero
Nat.instMulZeroClass
syn
Finsupp.preorder
Nat.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
lo
DFunLike.coe
AddEquiv
Finsupp.instAdd
AddMonoid.toAddZeroClass
Nat.instAddMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
acm
EquivLike.toFunLike
AddEquiv.instEquivLike
toSyn
β€”Monotone.strictMono_of_injective
toSyn_monotone
AddEquiv.injective
wf πŸ“–mathematicalβ€”WellFoundedLT
syn
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
lo
β€”β€”
zero_le πŸ“–mathematicalβ€”syn
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
lo
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
acm
β€”bot_le

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
instIsOrderedCancelAddMonoidLexFinsupp πŸ“–mathematicalβ€”IsOrderedCancelAddMonoid
Lex
Finsupp
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instAddCommMonoidLex
Finsupp.instAddCommMonoid
Finsupp.Lex.partialOrder
β€”covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
IsOrderedCancelAddMonoid.toIsOrderedAddMonoid
Finsupp.Lex.isOrderedCancelAddMonoid
IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT
instIsRightCancelAddLex
Finsupp.instIsRightCancelAdd
IsCancelAdd.toIsRightCancelAdd
IsOrderedCancelAddMonoid.toIsCancelAdd
contravariant_swap_add_of_contravariant_add
IsOrderedCancelAddMonoid.toAddLeftReflectLT
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
instIsLeftCancelAddLex
Finsupp.instIsLeftCancelAdd
IsCancelAdd.toIsLeftCancelAdd

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