Documentation Verification Report

Disjoint

📁 Source: Mathlib/Order/Disjoint.lean

Statistics

MetricCount
DefinitionsCodisjoint, ComplementedLattice, Complementeds, hasCoeT, instBoundedOrder, instDistribLattice, instInhabited, instMax, instMin, IsCompl, IsComplemented
11
Theoremsdual, eq_iff, eq_top, eq_top_of_ge, eq_top_of_le, eq_top_of_self, inf_left, inf_right, left_le_of_le_inf_left, left_le_of_le_inf_right, mono, mono_left, mono_right, ne, ne_bot_of_ne_top, ne_bot_of_ne_top', ne_iff, of_codisjoint_sup_of_le, of_codisjoint_sup_of_le', out, sup_left, sup_left', sup_lt_right_of_left_ne_bot, sup_right, sup_right', top_le, exists_isCompl, instOrderDual, codisjoint_coe, coe_bot, coe_inf, coe_inj, coe_injective, coe_le_coe, coe_lt_coe, coe_sup, coe_top, disjoint_coe, instComplementedLattice, isCompl_coe, mk_bot, mk_inf_mk, mk_sup_mk, mk_top, dual, eq_bot, eq_bot_of_ge, eq_bot_of_le, eq_bot_of_self, eq_iff, inf_left, inf_left', inf_right, inf_right', le_bot, le_of_codisjoint, left_le_of_le_sup_left, left_le_of_le_sup_right, mono, mono_left, mono_right, ne, ne_iff, ne_top_of_ne_bot, of_disjoint_inf_of_le, of_disjoint_inf_of_le', out, right_lt_sup_of_left_ne_bot, sup_left, sup_right, Antitone, codisjoint, disjoint, disjoint_left_iff, disjoint_right_iff, dual, inf_eq_bot, inf_left_eq_bot_iff, inf_left_le_of_le_sup_right, inf_right_eq_bot_iff, inf_sup, le_left_iff, le_right_iff, le_sup_right_iff_inf_left_le, left_le_iff, left_unique, ofDual, of_eq, of_le, right_le_iff, right_unique, sup_eq_top, sup_inf, inf, sup, codisjoint_iff, disjoint_iff, isCompl_iff, instComplementedLattice, bot_codisjoint, codisjoint_assoc, codisjoint_bot, codisjoint_comm, codisjoint_iff, codisjoint_iff_le_sup, codisjoint_inf_left, codisjoint_inf_right, codisjoint_left_comm, codisjoint_ofDual_iff, codisjoint_of_subsingleton, codisjoint_right_comm, codisjoint_self, codisjoint_toDual_iff, codisjoint_top_left, codisjoint_top_right, complementedLattice_iff, disjoint_assoc, disjoint_bot_left, disjoint_bot_right, disjoint_comm, disjoint_iff, disjoint_iff_inf_le, disjoint_left_comm, disjoint_ofDual_iff, disjoint_of_le_iff_left_eq_bot, disjoint_of_subsingleton, disjoint_right_comm, disjoint_self, disjoint_sup_left, disjoint_sup_right, disjoint_toDual_iff, disjoint_top, eq_bot_of_isCompl_top, eq_bot_of_top_isCompl, eq_top_of_bot_isCompl, eq_top_of_isCompl_bot, isCompl_bot_top, isCompl_comm, isCompl_iff, isCompl_iff', isCompl_ofDual_iff, isCompl_toDual_iff, isCompl_top_bot, isComplemented_bot, isComplemented_top, symmetric_codisjoint, symmetric_disjoint, top_disjoint
148
Total159

Codisjoint

Theorems

NameKindAssumesProvesValidatesDepends On
dual 📖mathematicalCodisjointDisjoint
OrderDual
OrderDual.instPartialOrder
OrderDual.instOrderBot
Preorder.toLE
PartialOrder.toPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
eq_iff 📖mathematicalCodisjointTop.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
eq_top 📖mathematicalCodisjoint
SemilatticeSup.toPartialOrder
SemilatticeSup.toMax
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
top_unique
top_le
eq_top_of_ge 📖mathematicalCodisjoint
Preorder.toLE
PartialOrder.toPreorder
Top.top
OrderTop.toTop
eq_top_of_le
symm
eq_top_of_le 📖mathematicalCodisjoint
Preorder.toLE
PartialOrder.toPreorder
Top.top
OrderTop.toTop
eq_top_iff
le_rfl
eq_top_of_self 📖mathematicalCodisjointTop.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
codisjoint_self
inf_left 📖mathematicalCodisjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeInf.toMincodisjoint_inf_left
inf_right 📖mathematicalCodisjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeInf.toMincodisjoint_inf_right
left_le_of_le_inf_left 📖Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeInf.toMin
Codisjoint
left_le_of_le_inf_right
inf_comm
left_le_of_le_inf_right 📖Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeInf.toMin
Codisjoint
Disjoint.left_le_of_le_sup_right
symm
mono 📖Preorder.toLE
PartialOrder.toPreorder
Codisjoint
LE.le.trans'
mono_left 📖Preorder.toLE
PartialOrder.toPreorder
Codisjoint
mono
le_rfl
mono_right 📖Preorder.toLE
PartialOrder.toPreorder
Codisjoint
mono
le_rfl
ne 📖Codisjointcodisjoint_self
ne_bot_of_ne_top 📖Codisjoint
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
ne_bot_of_ne_top' 📖Codisjoint
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
ne_bot_of_ne_top
symm
ne_iff 📖Codisjoint
of_codisjoint_sup_of_le 📖Codisjoint
SemilatticeSup.toPartialOrder
SemilatticeSup.toMax
Preorder.toLE
PartialOrder.toPreorder
codisjoint_iff
eq_top_of_le
le_sup_of_le_left
of_codisjoint_sup_of_le' 📖Codisjoint
SemilatticeSup.toPartialOrder
SemilatticeSup.toMax
Preorder.toLE
PartialOrder.toPreorder
codisjoint_iff
eq_top_of_le
le_sup_of_le_right
out 📖mathematicalCodisjoint
Preorder.toLE
PartialOrder.toPreorder
Top.top
OrderTop.toTop
top_le_iff
sup_left 📖mathematicalCodisjoint
SemilatticeSup.toPartialOrder
SemilatticeSup.toMaxmono_left
le_sup_left
sup_left' 📖mathematicalCodisjoint
SemilatticeSup.toPartialOrder
SemilatticeSup.toMaxmono_left
le_sup_right
sup_lt_right_of_left_ne_bot 📖mathematicalCodisjoint
SemilatticeInf.toPartialOrder
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toMin
LE.le.lt_of_ne'
inf_le_right
top_le_iff
le_rfl
inf_eq_right
sup_right 📖mathematicalCodisjoint
SemilatticeSup.toPartialOrder
SemilatticeSup.toMaxmono_right
le_sup_left
sup_right' 📖mathematicalCodisjoint
SemilatticeSup.toPartialOrder
SemilatticeSup.toMaxmono_right
le_sup_right
top_le 📖mathematicalCodisjoint
SemilatticeSup.toPartialOrder
Preorder.toLE
PartialOrder.toPreorder
Top.top
OrderTop.toTop
SemilatticeSup.toMax
codisjoint_iff_le_sup

ComplementedLattice

Theorems

NameKindAssumesProvesValidatesDepends On
exists_isCompl 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
instOrderDual 📖mathematicalComplementedLattice
OrderDual
OrderDual.instLattice
OrderDual.instBoundedOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
exists_isCompl
IsCompl.dual

Complementeds

Definitions

NameCategoryTheorems
hasCoeT 📖CompOp
instBoundedOrder 📖CompOp
8 mathmath: mk_bot, coe_top, codisjoint_coe, instComplementedLattice, mk_top, coe_bot, isCompl_coe, disjoint_coe
instDistribLattice 📖CompOp
1 mathmath: instComplementedLattice
instInhabited 📖CompOp
instMax 📖CompOp
2 mathmath: mk_sup_mk, coe_sup
instMin 📖CompOp
2 mathmath: coe_inf, mk_inf_mk

Theorems

NameKindAssumesProvesValidatesDepends On
codisjoint_coe 📖mathematicalCodisjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
IsComplemented
Complementeds
Subtype.partialOrder
instBoundedOrder
codisjoint_iff
coe_sup
coe_top
coe_bot 📖mathematicalIsComplemented
Bot.bot
Complementeds
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
BoundedOrder.toOrderBot
instBoundedOrder
coe_inf 📖mathematicalIsComplemented
DistribLattice.toLattice
Complementeds
instMin
SemilatticeInf.toMin
Lattice.toSemilatticeInf
coe_inj 📖mathematicalIsComplemented
coe_injective 📖mathematicalIsComplementedSubtype.coe_injective
coe_le_coe 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
IsComplemented
Complementeds
coe_lt_coe 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
IsComplemented
Complementeds
coe_sup 📖mathematicalIsComplemented
DistribLattice.toLattice
Complementeds
instMax
SemilatticeSup.toMax
Lattice.toSemilatticeSup
coe_top 📖mathematicalIsComplemented
Top.top
Complementeds
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
BoundedOrder.toOrderTop
instBoundedOrder
disjoint_coe 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
IsComplemented
Complementeds
Subtype.partialOrder
instBoundedOrder
disjoint_iff
coe_inf
coe_bot
instComplementedLattice 📖mathematicalComplementedLattice
Complementeds
DistribLattice.toLattice
instDistribLattice
instBoundedOrder
IsCompl.symm
isCompl_coe
isCompl_coe 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
IsComplemented
Complementeds
Subtype.partialOrder
instBoundedOrder
mk_bot 📖mathematicalIsComplemented
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
BoundedOrder.toOrderBot
isComplemented_bot
instBoundedOrder
isComplemented_bot
Subtype.mk_bot
mk_inf_mk 📖mathematicalIsComplemented
DistribLattice.toLattice
Complementeds
instMin
SemilatticeInf.toMin
Lattice.toSemilatticeInf
IsComplemented.inf
mk_sup_mk 📖mathematicalIsComplemented
DistribLattice.toLattice
Complementeds
instMax
SemilatticeSup.toMax
Lattice.toSemilatticeSup
IsComplemented.sup
mk_top 📖mathematicalIsComplemented
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
BoundedOrder.toOrderTop
isComplemented_top
instBoundedOrder
isComplemented_top
Subtype.mk_top

Disjoint

Theorems

NameKindAssumesProvesValidatesDepends On
dual 📖mathematicalDisjointCodisjoint
OrderDual
OrderDual.instPartialOrder
OrderDual.instOrderTop
Preorder.toLE
PartialOrder.toPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
eq_bot 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
SemilatticeInf.toMin
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
bot_unique
le_bot
eq_bot_of_ge 📖mathematicalDisjoint
Preorder.toLE
PartialOrder.toPreorder
Bot.bot
OrderBot.toBot
eq_bot_of_le
symm
eq_bot_of_le 📖mathematicalDisjoint
Preorder.toLE
PartialOrder.toPreorder
Bot.bot
OrderBot.toBot
eq_bot_iff
le_rfl
eq_bot_of_self 📖mathematicalDisjointBot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
disjoint_self
eq_iff 📖mathematicalDisjointBot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
inf_left 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
SemilatticeInf.toMinmono_left
inf_le_left
inf_left' 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
SemilatticeInf.toMinmono_left
inf_le_right
inf_right 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
SemilatticeInf.toMinmono_right
inf_le_left
inf_right' 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
SemilatticeInf.toMinmono_right
inf_le_right
le_bot 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toMin
Bot.bot
OrderBot.toBot
disjoint_iff_inf_le
le_of_codisjoint 📖Disjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
Codisjoint
BoundedOrder.toOrderTop
inf_top_eq
bot_sup_eq
eq_bot
Codisjoint.eq_top
sup_inf_right
inf_le_inf_right
le_sup_left
left_le_of_le_sup_left 📖Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeSup.toMax
Lattice.toSemilatticeSup
Disjoint
left_le_of_le_sup_right
sup_comm
left_le_of_le_sup_right 📖Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeSup.toMax
Lattice.toSemilatticeSup
Disjoint
le_of_inf_le_sup_le
le_trans
le_bot
bot_le
sup_le
le_sup_right
mono 📖Preorder.toLE
PartialOrder.toPreorder
Disjoint
LE.le.trans
mono_left 📖Preorder.toLE
PartialOrder.toPreorder
Disjoint
mono
le_rfl
mono_right 📖Preorder.toLE
PartialOrder.toPreorder
Disjoint
mono
le_rfl
ne 📖Disjointdisjoint_self
ne_iff 📖Disjoint
ne_top_of_ne_bot 📖Disjoint
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
of_disjoint_inf_of_le 📖Disjoint
SemilatticeInf.toPartialOrder
SemilatticeInf.toMin
Preorder.toLE
PartialOrder.toPreorder
disjoint_iff
eq_bot_of_le
inf_le_of_left_le
of_disjoint_inf_of_le' 📖Disjoint
SemilatticeInf.toPartialOrder
SemilatticeInf.toMin
Preorder.toLE
PartialOrder.toPreorder
disjoint_iff
eq_bot_of_le
inf_le_of_right_le
out 📖mathematicalDisjoint
Preorder.toLE
PartialOrder.toPreorder
Bot.bot
OrderBot.toBot
right_lt_sup_of_left_ne_bot 📖mathematicalDisjoint
SemilatticeSup.toPartialOrder
Preorder.toLT
PartialOrder.toPreorder
SemilatticeSup.toMax
LE.le.lt_of_ne
le_sup_right
le_bot_iff
le_rfl
sup_eq_right
sup_left 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeSup.toMax
Lattice.toSemilatticeSup
disjoint_sup_left
sup_right 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeSup.toMax
Lattice.toSemilatticeSup
disjoint_sup_right

IsCompl

Theorems

NameKindAssumesProvesValidatesDepends On
Antitone 📖IsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
Preorder.toLE
PartialOrder.toPreorder
right_le_iff
Codisjoint.mono_right
codisjoint
symm
codisjoint 📖mathematicalIsComplCodisjoint
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
disjoint 📖mathematicalIsComplDisjoint
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
disjoint_left_iff 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
Disjoint
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
disjoint_iff
inf_left_eq_bot_iff
disjoint_right_iff 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
Disjoint
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
disjoint_left_iff
symm
dual 📖mathematicalIsComplOrderDual
OrderDual.instPartialOrder
OrderDual.instBoundedOrder
Preorder.toLE
PartialOrder.toPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
codisjoint
disjoint
inf_eq_bot 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
SemilatticeInf.toMin
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
BoundedOrder.toOrderBot
Disjoint.eq_bot
disjoint
inf_left_eq_bot_iff 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeInf.toMin
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
BoundedOrder.toOrderBot
le_bot_iff
le_sup_right_iff_inf_left_le
bot_sup_eq
inf_left_le_of_le_sup_right 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
SemilatticeInf.toMininf_le_inf
le_rfl
inf_sup_right
inf_eq_bot
symm
sup_bot_eq
inf_le_left
inf_right_eq_bot_iff 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeInf.toMin
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
BoundedOrder.toOrderBot
inf_left_eq_bot_iff
symm
inf_sup 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeInf.toMin
SemilatticeSup.toMax
Lattice.toSemilatticeSup
symm
sup_inf
le_left_iff 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
Preorder.toLE
PartialOrder.toPreorder
Disjoint
BoundedOrder.toOrderBot
disjoint_right_iff
le_right_iff 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
Preorder.toLE
PartialOrder.toPreorder
Disjoint
BoundedOrder.toOrderBot
le_left_iff
symm
le_sup_right_iff_inf_left_le 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
SemilatticeInf.toMin
inf_left_le_of_le_sup_right
dual
symm
left_le_iff 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
Preorder.toLE
PartialOrder.toPreorder
Codisjoint
BoundedOrder.toOrderTop
le_left_iff
dual
left_unique 📖IsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
right_unique
symm
ofDual 📖mathematicalIsCompl
OrderDual
OrderDual.instPartialOrder
OrderDual.instBoundedOrder
Preorder.toLE
PartialOrder.toPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
codisjoint
disjoint
of_eq 📖mathematicalSemilatticeInf.toMin
Lattice.toSemilatticeInf
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
BoundedOrder.toOrderBot
SemilatticeSup.toMax
Lattice.toSemilatticeSup
Top.top
OrderTop.toTop
BoundedOrder.toOrderTop
IsCompldisjoint_iff
codisjoint_iff
of_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
SemilatticeInf.toMin
Bot.bot
OrderBot.toBot
BoundedOrder.toOrderBot
Top.top
OrderTop.toTop
BoundedOrder.toOrderTop
SemilatticeSup.toMax
Lattice.toSemilatticeSup
IsCompl
right_le_iff 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
Preorder.toLE
PartialOrder.toPreorder
Codisjoint
BoundedOrder.toOrderTop
left_le_iff
symm
right_unique 📖IsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
le_antisymm
Antitone
le_refl
sup_eq_top 📖mathematicalIsCompl
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
SemilatticeSup.toMax
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
BoundedOrder.toOrderTop
Codisjoint.eq_top
codisjoint
sup_inf 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeSup.toMax
Lattice.toSemilatticeSup
SemilatticeInf.toMin
of_eq
inf_sup_right
inf_assoc
inf_eq_bot
bot_inf_eq
bot_sup_eq
inf_left_comm
inf_bot_eq
sup_inf_left
sup_comm
sup_assoc
sup_eq_top
sup_top_eq
top_inf_eq
sup_left_comm

IsComplemented

Theorems

NameKindAssumesProvesValidatesDepends On
inf 📖mathematicalIsComplemented
DistribLattice.toLattice
SemilatticeInf.toMin
Lattice.toSemilatticeInf
IsCompl.inf_sup
sup 📖mathematicalIsComplemented
DistribLattice.toLattice
SemilatticeSup.toMax
Lattice.toSemilatticeSup
IsCompl.sup_inf

Prod

Theorems

NameKindAssumesProvesValidatesDepends On
codisjoint_iff 📖mathematicalCodisjoint
instPartialOrder
instOrderTop
Preorder.toLE
PartialOrder.toPreorder
disjoint_iff
disjoint_iff 📖mathematicalDisjoint
instPartialOrder
instOrderBot
Preorder.toLE
PartialOrder.toPreorder
bot_le
isCompl_iff 📖mathematicalIsCompl
instPartialOrder
instBoundedOrder
Preorder.toLE
PartialOrder.toPreorder

Subsingleton

Theorems

NameKindAssumesProvesValidatesDepends On
instComplementedLattice 📖mathematicalComplementedLatticedisjoint_bot_right
codisjoint_top_right

(root)

Definitions

NameCategoryTheorems
Codisjoint 📖MathDef
86 mathmath: symmetric_codisjoint, codisjoint_iff_compl_le_right, codisjoint_bot, Disjoint.dual, Prop.codisjoint_iff, codisjoint_bihimp_sup, AddSubgroup.map_eq_range_iff, codisjoint_of_subsingleton, codisjoint_inf_right, hnot_le_iff_codisjoint_left, IsCompl.left_le_iff, codisjoint_iff_compl_le_left, codisjoint_hnot_right, UpperSet.codisjoint_coe, codisjoint_assoc, disjoint_toDual_iff, Set.Icc.codisjoint_iff, codisjoint_iff, bihimp_le_iff_left, Submodule.codisjoint_iff_exists_add_eq, Prod.codisjoint_iff, bihimp_le_iff_right, Finset.codisjoint_left, codisjoint_self, codisjoint_comm, Complementeds.codisjoint_coe, disjoint_ofDual_iff, isCompl_iff, himp_le, RingOfIntegers.not_dvd_exponent_iff, codisjoint_iff_le_sup, CompleteSublattice.codisjoint_iff, codisjoint_ofDual_iff, AddMonoid.Coprod.codisjoint_mrange_inl_mrange_inr, codisjoint_top_left, Set.Ici.codisjoint_iff, AddSubgroup.codisjoint_addSubgroupOf_sup, IsCompl.right_le_iff, hnot_eq_sInf_codisjoint, IsCoatom.codisjoint_of_ne, Concept.codisjoint_extent_intent, Finset.codisjoint_right, IsCoatom.not_codisjoint_iff_le, Ideal.isCoprime_tfae, LE.le.codisjoint_hnot_right, codisjoint_hnot_left, codisjoint_toDual_iff, AddMonoid.Coprod.codisjoint_range_inl_range_inr, Pi.codisjoint_iff, bot_codisjoint, bihimp_eq_inf, Subgroup.map_eq_range_iff, Finsupp.codisjoint_supported_supported_iff, isLeast_hnot, Module.End.invtSubmodule.codisjoint_iff, codisjoint_top_right, LE.le.codisjoint_hnot_left, Set.Iic.codisjoint_iff, codisjoint_hnot_hnot_left_iff, codisjoint_map_orderIso_iff, LieSubmodule.codisjoint_toSubmodule, isCompl_iff', codisjoint_inf_left, Subgroup.codisjoint_subgroupOf_sup, Set.Ici.isCompl_iff, codisjoint_himp_self_left, LinearMap.eventually_codisjoint_ker_pow_range_pow, codisjoint_left_comm, IsCompl.codisjoint, Monoid.Coprod.codisjoint_range_inl_range_inr, UpperSet.codisjoint_prod, Finset.codisjoint_inf_left, codisjoint_right_comm, Ideal.isCoprime_iff_codisjoint, codisjoint_himp_self_right, Set.Ioc.codisjoint_iff, Module.End.invtSubmodule.codisjoint_mk_iff, AlgebraicGeometry.Scheme.codisjoint_zeroLocus, hnot_le_iff_codisjoint_right, IsModularLattice.exists_inf_eq_and_codisjoint, Monoid.Coprod.codisjoint_mrange_inl_mrange_inr, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, Finset.codisjoint_inf_right, IsCoatom.not_le_iff_codisjoint, IsCoprime.codisjoint, codisjoint_hnot_hnot_right_iff
ComplementedLattice 📖CompData
20 mathmath: OrderIso.complementedLattice_iff, IsCompactlyGenerated.BooleanGenerators.complementedLattice_of_sSup_eq_top, Subsingleton.instComplementedLattice, CompleteSublattice.isComplemented_iff, IsModularLattice.complementedLattice_Ici, IsSemisimpleModule.toComplementedLattice, complementedLattice_iff, complementedLattice_of_sSup_atoms_eq_top, OrderIso.complementedLattice, Set.Iic.complementedLattice_iff, isSemisimpleModule_iff, complementedLattice_of_isAtomistic, Complementeds.instComplementedLattice, BooleanAlgebra.toComplementedLattice, Submodule.complementedLattice, IsSimpleOrder.instComplementedLattice, complementedLattice_iff_isAtomistic, ComplementedLattice.instOrderDual, IsModularLattice.complementedLattice_Iic, IsModularLattice.complementedLattice_Icc
Complementeds 📖CompOp
12 mathmath: Complementeds.coe_le_coe, Complementeds.coe_top, Complementeds.mk_sup_mk, Complementeds.codisjoint_coe, Complementeds.coe_inf, Complementeds.instComplementedLattice, Complementeds.coe_bot, Complementeds.isCompl_coe, Complementeds.coe_lt_coe, Complementeds.mk_inf_mk, Complementeds.disjoint_coe, Complementeds.coe_sup
IsCompl 📖CompData
84 mathmath: isCompl_toDual_iff, TopCat.binaryCofan_isColimit_iff, CategoryTheory.Limits.Types.binaryCofan_isColimit_iff, Disjoint.exists_isCompl, MonoidAlgebra.Submodule.exists_isCompl, ImplicitFunctionData.isCompl_ker, LieAlgebra.IsKilling.isCompl_ker_weight_span_coroot, CompleteSublattice.isComplemented_iff, isCompl_ofDual_iff, Submodule.ClosedComplemented.exists_isClosed_isCompl, LinearMap.BilinForm.restrict_nondegenerate_iff_isCompl_orthogonal, Set.isCompl_range_some_none, isCompl_comm, complementedLattice_iff, LieSubmodule.isCompl_toSubmodule, Submodule.coe_isComplEquivProj_symm_apply, Module.Dual.isCompl_ker_of_disjoint_of_ne_bot, LinearMap.isCompl_range_inl_inr, MeasureTheory.SignedMeasure.exists_isCompl_positive_negative, Concept.isCompl_extent_intent, Subgroup.IsComplement'.isCompl, LinearMap.BilinForm.isCompl_orthogonal_iff_disjoint, LinearMap.isCompl_iSup_ker_pow_iInf_range_pow, LieAlgebra.InvariantForm.orthogonal_isCompl, LinearMap.IsProj.isCompl, Codisjoint.exists_isCompl, LinearMap.IsPerfectCompl.isCompl_right, Module.End.invtSubmodule.isCompl_iff, Order.Ideal.PrimePair.isCompl_I_F, isCompl_iff, Int.isCompl_even_odd, exists_sSupIndep_isCompl_sSup_atoms, AlgebraicGeometry.isCompl_range_inl_inr, ComplementedLattice.exists_isCompl, Prop.isCompl_iff, CompleteSublattice.isCompl_iff, RootPairing.isCompl_rootSpan_ker_rootForm, Submodule.isCompl_orthogonal_of_hasOrthogonalProjection, DirectSum.IsInternal.isCompl, eq_compl_iff_isCompl, Submodule.coe_isComplEquivProj_apply, Set.Icc.isCompl_iff, LieIdeal.isCompl_killingCompl, LinearMap.eventually_isCompl_ker_pow_range_pow, LieModule.isCompl_genWeightSpace_zero_posFittingComp, Submodule.isCompl_iff_disjoint, Set.isCompl_range_inl_range_inr, Module.End.invtSubmodule.isCompl_mk_iff, LieAlgebra.InvariantForm.orthogonal_isCompl_toSubmodule, AlgebraicGeometry.isCompl_opensRange_inl_inr, IsCompl.of_eq, LinearMap.IsIdempotentElem.isCompl, Submodule.exists_isCompl, isCompl_iff', compl_eq_iff_isCompl, symmDiff_eq_top, Set.Iic.isCompl_iff, isCompl_compl, Complementeds.isCompl_coe, Module.End.isSemisimple_iff', Set.Ici.isCompl_iff, isCompl_bot_top, LinearMap.isCompl_span_singleton_orthogonal, IsCompl.of_le, Pi.isCompl_iff, Submodule.isCompl_span_singleton_of_isCoatom_of_notMem, LinearMap.isCompl_of_proj, Nat.isCompl_even_odd, isCompl_top_bot, Submodule.closedComplemented_iff_isClosed_exists_isClosed_isCompl, RootPairing.isCompl_corootSpan_ker_corootForm, CliffordAlgebra.evenOdd_isCompl, DirectSum.isInternal_submodule_iff_isCompl, Prod.isCompl_iff, OnePoint.isCompl_range_coe_infty, LinearMap.IsPerfectCompl.isCompl_left, Module.End.isSemisimple_iff, LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate, Filter.isCompl_principal, bihimp_eq_bot, OrderIso.isCompl_iff, LinearMap.BilinForm.isCompl_span_singleton_orthogonal, AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAt, LieModule.isCompl_genWeightSpaceOf_zero_posFittingCompOf
IsComplemented 📖MathDef
15 mathmath: Complementeds.coe_le_coe, Complementeds.mk_bot, Complementeds.coe_top, isComplemented_bot, Complementeds.codisjoint_coe, Complementeds.coe_inf, Complementeds.mk_top, Complementeds.coe_bot, Complementeds.isCompl_coe, Complementeds.coe_lt_coe, Complementeds.disjoint_coe, Complementeds.coe_injective, Complementeds.coe_sup, Complementeds.coe_inj, isComplemented_top

Theorems

NameKindAssumesProvesValidatesDepends On
bot_codisjoint 📖mathematicalCodisjoint
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
Bot.bot
OrderBot.toBot
BoundedOrder.toOrderBot
Top.top
OrderTop.toTop
top_unique
bot_le
le_rfl
LE.le.trans_eq'
codisjoint_assoc 📖mathematicalCodisjoint
SemilatticeSup.toPartialOrder
SemilatticeSup.toMax
codisjoint_bot 📖mathematicalCodisjoint
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
Bot.bot
OrderBot.toBot
BoundedOrder.toOrderBot
Top.top
OrderTop.toTop
top_unique
le_rfl
bot_le
LE.le.trans_eq'
codisjoint_comm 📖mathematicalCodisjointforall_swap
codisjoint_iff 📖mathematicalCodisjoint
SemilatticeSup.toPartialOrder
SemilatticeSup.toMax
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
codisjoint_iff_le_sup
top_le_iff
codisjoint_iff_le_sup 📖mathematicalCodisjoint
SemilatticeSup.toPartialOrder
Preorder.toLE
PartialOrder.toPreorder
Top.top
OrderTop.toTop
SemilatticeSup.toMax
le_sup_left
le_sup_right
LE.le.trans'
sup_le
codisjoint_inf_left 📖mathematicalCodisjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeInf.toMin
sup_inf_right
codisjoint_inf_right 📖mathematicalCodisjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeInf.toMin
sup_inf_left
codisjoint_left_comm 📖mathematicalCodisjoint
SemilatticeSup.toPartialOrder
SemilatticeSup.toMax
codisjoint_ofDual_iff 📖mathematicalCodisjoint
DFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
Disjoint
OrderDual.instPartialOrder
OrderDual.instOrderBot
Preorder.toLE
PartialOrder.toPreorder
codisjoint_of_subsingleton 📖mathematicalCodisjointge_of_eq
codisjoint_right_comm 📖mathematicalCodisjoint
SemilatticeSup.toPartialOrder
SemilatticeSup.toMax
codisjoint_self 📖mathematicalCodisjoint
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
top_unique
le_rfl
LE.le.trans_eq'
codisjoint_toDual_iff 📖mathematicalCodisjoint
OrderDual
OrderDual.instPartialOrder
OrderDual.instOrderTop
Preorder.toLE
PartialOrder.toPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
Disjoint
codisjoint_top_left 📖mathematicalCodisjoint
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
codisjoint_top_right 📖mathematicalCodisjoint
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
complementedLattice_iff 📖mathematicalComplementedLattice
IsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
disjoint_assoc 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
SemilatticeInf.toMin
disjoint_bot_left 📖mathematicalDisjoint
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
disjoint_bot_right 📖mathematicalDisjoint
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
disjoint_comm 📖mathematicalDisjointforall_swap
disjoint_iff 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
SemilatticeInf.toMin
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
disjoint_iff_inf_le
le_bot_iff
disjoint_iff_inf_le 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toMin
Bot.bot
OrderBot.toBot
inf_le_left
inf_le_right
LE.le.trans
le_inf
disjoint_left_comm 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
SemilatticeInf.toMin
disjoint_ofDual_iff 📖mathematicalDisjoint
DFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
Codisjoint
OrderDual.instPartialOrder
OrderDual.instOrderTop
Preorder.toLE
PartialOrder.toPreorder
disjoint_of_le_iff_left_eq_bot 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
Disjoint
Bot.bot
OrderBot.toBot
disjoint_of_subsingleton 📖mathematicalDisjointle_of_eq
disjoint_right_comm 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
SemilatticeInf.toMin
disjoint_self 📖mathematicalDisjoint
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
bot_unique
le_rfl
LE.le.trans_eq
disjoint_sup_left 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeSup.toMax
Lattice.toSemilatticeSup
inf_sup_right
disjoint_sup_right 📖mathematicalDisjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
SemilatticeSup.toMax
Lattice.toSemilatticeSup
inf_sup_left
disjoint_toDual_iff 📖mathematicalDisjoint
OrderDual
OrderDual.instPartialOrder
OrderDual.instOrderBot
Preorder.toLE
PartialOrder.toPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
Codisjoint
disjoint_top 📖mathematicalDisjoint
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
Top.top
OrderTop.toTop
BoundedOrder.toOrderTop
Bot.bot
OrderBot.toBot
bot_unique
le_rfl
le_top
LE.le.trans_eq
eq_bot_of_isCompl_top 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
BoundedOrder.toOrderTop
Bot.bot
OrderBot.toBot
BoundedOrder.toOrderBot
eq_top_of_isCompl_bot
IsCompl.dual
eq_bot_of_top_isCompl 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
BoundedOrder.toOrderTop
Bot.bot
OrderBot.toBot
BoundedOrder.toOrderBot
eq_top_of_bot_isCompl
IsCompl.dual
eq_top_of_bot_isCompl 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
BoundedOrder.toOrderBot
Top.top
OrderTop.toTop
BoundedOrder.toOrderTop
eq_top_of_isCompl_bot
IsCompl.symm
eq_top_of_isCompl_bot 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
BoundedOrder.toOrderBot
Top.top
OrderTop.toTop
BoundedOrder.toOrderTop
sup_bot_eq
IsCompl.sup_eq_top
isCompl_bot_top 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
BoundedOrder.toOrderBot
Top.top
OrderTop.toTop
BoundedOrder.toOrderTop
IsCompl.of_eq
bot_inf_eq
sup_top_eq
isCompl_comm 📖mathematicalIsComplIsCompl.symm
isCompl_iff 📖mathematicalIsCompl
Disjoint
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
Codisjoint
BoundedOrder.toOrderTop
IsCompl.disjoint
IsCompl.codisjoint
isCompl_iff' 📖mathematicalIsCompl
Codisjoint
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
Disjoint
BoundedOrder.toOrderBot
IsCompl.codisjoint
IsCompl.disjoint
isCompl_ofDual_iff 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
OrderDual.instPartialOrder
OrderDual.instBoundedOrder
Preorder.toLE
PartialOrder.toPreorder
IsCompl.dual
IsCompl.ofDual
isCompl_toDual_iff 📖mathematicalIsCompl
OrderDual
OrderDual.instPartialOrder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
OrderDual.instBoundedOrder
Preorder.toLE
PartialOrder.toPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
IsCompl.ofDual
IsCompl.dual
isCompl_top_bot 📖mathematicalIsCompl
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
BoundedOrder.toOrderTop
Bot.bot
OrderBot.toBot
BoundedOrder.toOrderBot
IsCompl.of_eq
inf_bot_eq
top_sup_eq
isComplemented_bot 📖mathematicalIsComplemented
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
BoundedOrder.toOrderBot
isCompl_bot_top
isComplemented_top 📖mathematicalIsComplemented
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
BoundedOrder.toOrderTop
isCompl_top_bot
symmetric_codisjoint 📖mathematicalSymmetric
Codisjoint
Codisjoint.symm
symmetric_disjoint 📖mathematicalSymmetric
Disjoint
Disjoint.symm
top_disjoint 📖mathematicalDisjoint
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
Top.top
OrderTop.toTop
BoundedOrder.toOrderTop
Bot.bot
OrderBot.toBot
bot_unique
le_top
le_rfl
LE.le.trans_eq

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