Documentation Verification Report

Basic

πŸ“ Source: Mathlib/Order/CompleteLattice/Basic.lean

Statistics

MetricCount
DefinitionscompleteLattice, infSet, instCompleteLattice, supSet, infSet, instCompleteLattice, supSet, instCompleteLattice, instCompleteLinearOrder
9
TheoremsiInf, iSup, le_map_iInf, le_map_iInfβ‚‚, le_map_sInf, map_iSup_le, map_iSupβ‚‚_le, map_sSup_le, sInf, sSup, biInf_comp, biSup_comp, iInf_comp, iInf_congr, iSup_comp, iSup_congr, iInf_comp, iInf_congr, iSup_comp, iSup_congr, iInf_eq, iSup_eq, iInf, iInf_comp_eq, iSup, iSup_comp_eq, le_map_iSup, le_map_iSupβ‚‚, le_map_sSup, map_iInf_le, map_iInfβ‚‚_le, map_sInf_le, sInf, sSup, map_iInf, map_iInfβ‚‚, map_iSup, map_iSupβ‚‚, map_sInf, map_sInf_eq_sInf_symm_preimage, map_sSup, map_sSup_eq_sSup_symm_preimage, fst_iInf, fst_iSup, fst_sInf, fst_sSup, iInf_mk, iSup_mk, snd_iInf, snd_iSup, snd_sInf, snd_sSup, swap_iInf, swap_iSup, swap_sInf, swap_sSup, iInf_comp, iInf_congr, iSup_comp, iSup_congr, biInf_congr, biInf_congr', biInf_const, biInf_ge_eq_iInf, biInf_ge_eq_inf, biInf_ge_eq_of_monotone, biInf_gt_eq_iInf, biInf_inf, biInf_le, biInf_le_biSup, biInf_le_eq_iInf, biInf_le_eq_inf, biInf_le_eq_of_antitone, biInf_lt_eq_iInf, biInf_mono, biInf_prod, biInf_prod', biSup_congr, biSup_congr', biSup_const, biSup_ge_eq_iSup, biSup_ge_eq_of_antitone, biSup_ge_eq_sup, biSup_gt_eq_iSup, biSup_le_eq_iSup, biSup_le_eq_of_monotone, biSup_le_eq_sup, biSup_lt_eq_iSup, biSup_mono, biSup_prod, biSup_prod', biSup_sup, binary_relation_sInf_iff, binary_relation_sSup_iff, bot_lt_iSup, eq_singleton_bot_of_sSup_eq_bot_of_nonempty, eq_singleton_top_of_sInf_eq_top_of_nonempty, iInf_Prop_eq, iInf_and, iInf_and', iInf_apply, iInf_comm, iInf_congr, iInf_congr_Prop, iInf_const, iInf_const_mono, iInf_dite, iInf_emptyset, iInf_eq_bot, iInf_eq_dif, iInf_eq_if, iInf_eq_of_forall_ge_of_forall_gt_exists_lt, iInf_eq_top, iInf_exists, iInf_extend_top, iInf_false, iInf_iInf_eq_left, iInf_iInf_eq_right, iInf_image, iInf_image2, iInf_inf, iInf_inf_eq, iInf_insert, iInf_ite, iInf_le, iInf_le_iInf_of_subset, iInf_le_iInfβ‚‚, iInf_le_iSup, iInf_le_of_le, iInf_lt_top, iInf_mono, iInf_mono', iInf_ne_top_subtype, iInf_neg, iInf_of_empty, iInf_of_isEmpty, iInf_option, iInf_option_elim, iInf_or, iInf_pair, iInf_plift_down, iInf_plift_up, iInf_pos, iInf_prod, iInf_prod', iInf_psigma, iInf_psigma', iInf_range, iInf_range', iInf_sigma, iInf_sigma', iInf_singleton, iInf_split, iInf_split_single, iInf_subtype, iInf_subtype', iInf_subtype'', iInf_sum, iInf_top, iInf_true, iInf_ulift, iInf_union, iInf_unique, iInf_univ, iInfβ‚‚_comm, iInfβ‚‚_eq_bot, iInfβ‚‚_eq_top, iInfβ‚‚_le, iInfβ‚‚_le_of_le, iInfβ‚‚_mono, iInfβ‚‚_mono', iSup_Prop_eq, iSup_and, iSup_and', iSup_apply, iSup_bot, iSup_comm, iSup_comp_le, iSup_congr, iSup_congr_Prop, iSup_const, iSup_const_le, iSup_const_mono, iSup_dite, iSup_emptyset, iSup_eq_bot, iSup_eq_dif, iSup_eq_if, iSup_eq_of_forall_le_of_forall_lt_exists_gt, iSup_eq_top, iSup_exists, iSup_extend_bot, iSup_false, iSup_iInf_le_iInf_iSup, iSup_iSup_eq_left, iSup_iSup_eq_right, iSup_image, iSup_image2, iSup_insert, iSup_ite, iSup_le, iSup_le_iSup_of_subset, iSup_le_iff, iSup_lt_iff, iSup_mono, iSup_mono', iSup_ne_bot_subtype, iSup_neg, iSup_of_empty, iSup_of_empty', iSup_option, iSup_option_elim, iSup_or, iSup_pair, iSup_plift_down, iSup_plift_up, iSup_pos, iSup_prod, iSup_prod', iSup_psigma, iSup_psigma', iSup_range, iSup_range', iSup_sigma, iSup_sigma', iSup_singleton, iSup_split, iSup_split_single, iSup_subtype, iSup_subtype', iSup_subtype'', iSup_sum, iSup_sup, iSup_sup_eq, iSup_true, iSup_ulift, iSup_union, iSup_unique, iSup_univ, iSupβ‚‚_comm, iSupβ‚‚_eq_bot, iSupβ‚‚_eq_top, iSupβ‚‚_le, iSupβ‚‚_le_iSup, iSupβ‚‚_le_iff, iSupβ‚‚_mono, iSupβ‚‚_mono', inf_biInf, inf_iInf, isGLB_biInf, isGLB_iInf, isLUB_biSup, isLUB_iSup, le_biSup, le_iInf, le_iInf_comp, le_iInf_const, le_iInf_iff, le_iInfβ‚‚, le_iInfβ‚‚_iff, le_iSup, le_iSup_of_le, le_iSupβ‚‚, le_iSupβ‚‚_of_le, le_sInf_inter, lt_iInf_iff, sInf_Prop_eq, sInf_apply, sInf_diff_singleton_top, sInf_empty, sInf_eq_iInf, sInf_eq_iInf', sInf_eq_of_forall_ge_of_forall_gt_exists_lt, sInf_eq_top, sInf_image, sInf_image', sInf_image2, sInf_insert, sInf_le_sInf_of_isCoinitialFor, sInf_le_sInf_of_subset_insert_top, sInf_le_sSup, sInf_pair, sInf_prod, sInf_range, sInf_singleton, sInf_union, sInf_univ, sInf_upperBounds_eq_csSup, sInf_upperBounds_eq_sSup, sSup_Prop_eq, sSup_apply, sSup_diff_singleton_bot, sSup_empty, sSup_eq_bot, sSup_eq_bot', sSup_eq_iSup, sSup_eq_iSup', sSup_eq_of_forall_le_of_forall_lt_exists_gt, sSup_image, sSup_image', sSup_image2, sSup_insert, sSup_inter_le, sSup_le_sSup_of_isCofinalFor, sSup_le_sSup_of_subset_insert_bot, sSup_lowerBounds_eq_sInf, sSup_pair, sSup_prod, sSup_range, sSup_singleton, sSup_union, sSup_univ, sup_biSup, sup_iSup, unary_relation_sInf_iff, unary_relation_sSup_iff
316
Total325

Antitone

Theorems

NameKindAssumesProvesValidatesDepends On
iInf πŸ“–mathematicalAntitone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
Pi.infSet
CompleteSemilatticeInf.toInfSet
β€”sInf
iSup πŸ“–mathematicalAntitone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
Pi.supSet
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”sSup
le_map_iInf πŸ“–mathematicalAntitone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iInf
CompleteSemilatticeInf.toInfSet
β€”Monotone.le_map_iSup
dual_left
le_map_iInfβ‚‚ πŸ“–mathematicalAntitone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iInf
CompleteSemilatticeInf.toInfSet
β€”Monotone.le_map_iSupβ‚‚
dual_left
le_map_sInf πŸ“–mathematicalAntitone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
InfSet.sInf
CompleteSemilatticeInf.toInfSet
β€”Monotone.le_map_sSup
dual_left
map_iSup_le πŸ“–mathematicalAntitone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iInf
CompleteSemilatticeInf.toInfSet
β€”le_iInf
le_iSup
map_iSupβ‚‚_le πŸ“–mathematicalAntitone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iInf
CompleteSemilatticeInf.toInfSet
β€”le_map_iInfβ‚‚
dual
map_sSup_le πŸ“–mathematicalAntitone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iInf
CompleteSemilatticeInf.toInfSet
Set
Set.instMembership
β€”sSup_eq_iSup
map_iSupβ‚‚_le
sInf πŸ“–mathematicalAntitone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
InfSet.sInf
Pi.infSet
CompleteSemilatticeInf.toInfSet
β€”iInf_mono
sSup πŸ“–mathematicalAntitone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
SupSet.sSup
Pi.supSet
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_mono

Equiv

Theorems

NameKindAssumesProvesValidatesDepends On
biInf_comp πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
Set.image
DFunLike.coe
Equiv
EquivLike.toFunLike
instEquivLike
symm
β€”biSup_comp
biSup_comp πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
Set.image
DFunLike.coe
Equiv
EquivLike.toFunLike
instEquivLike
symm
β€”iSup_subtype'
iSup_comp
iInf_comp πŸ“–mathematicalβ€”iInf
DFunLike.coe
Equiv
EquivLike.toFunLike
instEquivLike
β€”iSup_comp
iInf_congr πŸ“–mathematicalDFunLike.coe
Equiv
EquivLike.toFunLike
instEquivLike
iInfβ€”iSup_congr
iSup_comp πŸ“–mathematicalβ€”iSup
DFunLike.coe
Equiv
EquivLike.toFunLike
instEquivLike
β€”Function.Surjective.iSup_comp
surjective
iSup_congr πŸ“–mathematicalDFunLike.coe
Equiv
EquivLike.toFunLike
instEquivLike
iSupβ€”Function.Surjective.iSup_congr
surjective

Function.Injective

Definitions

NameCategoryTheorems
completeLattice πŸ“–CompOpβ€”

Function.Surjective

Theorems

NameKindAssumesProvesValidatesDepends On
iInf_comp πŸ“–mathematicalβ€”iInfβ€”iSup_comp
iInf_congr πŸ“–mathematicalβ€”iInfβ€”iSup_congr
iSup_comp πŸ“–mathematicalβ€”iSupβ€”range_comp
iSup_congr πŸ“–mathematicalβ€”iSupβ€”iSup_comp

IsGLB

Theorems

NameKindAssumesProvesValidatesDepends On
iInf_eq πŸ“–mathematicalIsGLB
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Set.range
iInf
CompleteSemilatticeInf.toInfSet
β€”sInf_eq

IsLUB

Theorems

NameKindAssumesProvesValidatesDepends On
iSup_eq πŸ“–mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Set.range
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”sSup_eq

Monotone

Theorems

NameKindAssumesProvesValidatesDepends On
iInf πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
Pi.infSet
CompleteSemilatticeInf.toInfSet
β€”sInf
iInf_comp_eq πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
iInf
CompleteSemilatticeInf.toInfSet
β€”le_antisymm
iInf_mono'
le_iInf_comp
iSup πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
Pi.supSet
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”sSup
iSup_comp_eq πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”le_antisymm
iSup_comp_le
iSup_mono'
le_map_iSup πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_le
le_iSup
le_map_iSupβ‚‚ πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSupβ‚‚_le
le_iSupβ‚‚
le_map_sSup πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
SupSet.sSup
β€”sSup_eq_iSup
le_map_iSupβ‚‚
map_iInf_le πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
iInf
CompleteSemilatticeInf.toInfSet
β€”Antitone.map_iSup_le
dual_left
map_iInfβ‚‚_le πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
iInf
CompleteSemilatticeInf.toInfSet
β€”le_map_iSupβ‚‚
dual
map_sInf_le πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
InfSet.sInf
CompleteSemilatticeInf.toInfSet
iInf
Set
Set.instMembership
β€”Antitone.map_sSup_le
dual_left
sInf πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
InfSet.sInf
Pi.infSet
CompleteSemilatticeInf.toInfSet
β€”iInf_mono
sSup πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
SupSet.sSup
Pi.supSet
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_mono

OrderIso

Theorems

NameKindAssumesProvesValidatesDepends On
map_iInf πŸ“–mathematicalβ€”DFunLike.coe
OrderIso
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
instFunLikeOrderIso
iInf
CompleteSemilatticeInf.toInfSet
β€”map_iSup
map_iInfβ‚‚ πŸ“–mathematicalβ€”DFunLike.coe
OrderIso
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
instFunLikeOrderIso
iInf
CompleteSemilatticeInf.toInfSet
β€”map_iSupβ‚‚
map_iSup πŸ“–mathematicalβ€”DFunLike.coe
OrderIso
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
instFunLikeOrderIso
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”eq_of_forall_ge_iff
Function.Surjective.forall
surjective
le_iff_le
map_iSupβ‚‚ πŸ“–mathematicalβ€”DFunLike.coe
OrderIso
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
instFunLikeOrderIso
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”eq_of_forall_ge_iff
Function.Surjective.forall
surjective
le_iff_le
map_sInf πŸ“–mathematicalβ€”DFunLike.coe
OrderIso
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
instFunLikeOrderIso
InfSet.sInf
CompleteSemilatticeInf.toInfSet
iInf
Set
Set.instMembership
β€”map_sSup
map_sInf_eq_sInf_symm_preimage πŸ“–mathematicalβ€”DFunLike.coe
OrderIso
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
instFunLikeOrderIso
InfSet.sInf
CompleteSemilatticeInf.toInfSet
Set.preimage
symm
β€”map_sInf
sInf_image
image_eq_preimage_symm
map_sSup πŸ“–mathematicalβ€”DFunLike.coe
OrderIso
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
instFunLikeOrderIso
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iSup
Set
Set.instMembership
β€”sSup_eq_iSup
map_iSup
map_sSup_eq_sSup_symm_preimage πŸ“–mathematicalβ€”DFunLike.coe
OrderIso
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
instFunLikeOrderIso
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set.preimage
symm
β€”map_sSup
sSup_image
image_eq_preimage_symm

Pi

Definitions

NameCategoryTheorems
infSet πŸ“–CompOp
27 mathmath: Antitone.iInf, Antitone.sInf, CategoryTheory.ObjectProperty.preservesLimitsOfShape_eq_iSup, iInf_apply, AddCon.coe_iInf, Monotone.sInf, LinearGrowth.linearGrowthInf_biInf, Ideal.Filtration.sInf_N, Ideal.Filtration.iInf_N, unary_relation_sInf_iff, sInf_apply, Con.coe_iInf, AddCon.coe_sInf, OrderHom.coe_iInf, RingCon.coe_iInf, ExpGrowth.expGrowthInf_iInf, RingCon.coe_sInf, AlgebraicGeometry.Scheme.IdealSheafData.ideal_iInf, LinearGrowth.linearGrowthInf_iInf, ExpGrowth.expGrowthInf_biInf, aeSeq.iInf, CategoryTheory.ObjectProperty.preservesColimitsOfShape_eq_iSup, Con.coe_sInf, AlgebraicGeometry.Scheme.IdealSheafData.ideal_biInf, binary_relation_sInf_iff, Monotone.iInf, Setoid.sInf_def
instCompleteLattice πŸ“–CompOpβ€”
supSet πŸ“–CompOp
54 mathmath: unary_relation_sSup_iff, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sSup, Set.iSup_mulIndicator, RingCon.sSup_def, MeasureTheory.OuterMeasure.coe_iSup, ConvexOn.univ_sSup_of_countable_affine_eq, Antitone.sSup, MeasureTheory.SimpleFunc.iSup_coe_eapprox, Ideal.Filtration.sSup_N, ExpGrowth.expGrowthSup_biSup, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsISup, ConvexOn.sSup_of_countable_affine_eq, Setoid.sSup_def, ConvexOn.real_univ_sSup_of_countable_affine_eq, LinearGrowth.linearGrowthSup_biSup, binary_relation_sSup_iff, CategoryTheory.ObjectProperty.isoClosure_iSup, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, ConvexOn.sSup_of_nat_affine_eq, CompleteLattice.Ο‰ScottContinuous.iSup, CategoryTheory.ObjectProperty.instEssentiallySmallISupOfSmall, CategoryTheory.ObjectProperty.HasCardinalLT.iSup, Seminorm.coe_sSup_eq', CompleteLattice.Ο‰ScottContinuous.sSup, aeSeq.iSup, ConvexOn.real_univ_sSup_affine_eq, AddCon.sSup_def, hasCardinalLT_subtype_iSup, MeasureTheory.Measure.LebesgueDecomposition.iSup_mem_measurableLE', Seminorm.continuous_iSup, Seminorm.coe_sSup_eq, ConvexOn.univ_sSup_affine_eq, ConvexOn.real_univ_sSup_of_nat_affine_eq, ConvexOn.real_sSup_of_countable_affine_eq, LinearGrowth.linearGrowthSup_iSup, Set.iSup_indicator, Antitone.iSup, AlgebraicGeometry.Scheme.IdealSheafData.ideal_iSup, Con.sSup_def, Seminorm.coe_iSup_eq, ConvexOn.real_sSup_of_nat_affine_eq, iSup_apply, ExpGrowth.expGrowthSup_iSup, Monotone.iSup, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.iSup_P, Ideal.Filtration.iSup_N, OrderHom.coe_iSup, ConvexOn.sSup_affine_eq, CategoryTheory.ObjectProperty.instSmallISupOfSmall, Monotone.sSup, sSup_apply, ConvexOn.real_sSup_affine_eq, ConvexOn.univ_sSup_of_nat_affine_eq, CategoryTheory.ObjectProperty.prop_iSup_iff

Prod

Definitions

NameCategoryTheorems
infSet πŸ“–CompOp
9 mathmath: sInf_prod, iInf_mk, infsInfHom_apply, fst_iInf, swap_iInf, swap_sInf, fst_sInf, snd_iInf, snd_sInf
instCompleteLattice πŸ“–CompOpβ€”
supSet πŸ“–CompOp
9 mathmath: sSup_prod, swap_sSup, fst_iSup, iSup_mk, swap_iSup, supsSupHom_apply, fst_sSup, snd_iSup, snd_sSup

Theorems

NameKindAssumesProvesValidatesDepends On
fst_iInf πŸ“–mathematicalβ€”iInf
infSet
β€”Set.range_comp
fst_iSup πŸ“–mathematicalβ€”iSup
supSet
β€”Set.range_comp
fst_sInf πŸ“–mathematicalβ€”InfSet.sInf
infSet
Set.image
β€”β€”
fst_sSup πŸ“–mathematicalβ€”SupSet.sSup
supSet
Set.image
β€”β€”
iInf_mk πŸ“–mathematicalβ€”iInf
infSet
β€”fst_iInf
snd_iInf
iSup_mk πŸ“–mathematicalβ€”iSup
supSet
β€”fst_iSup
snd_iSup
snd_iInf πŸ“–mathematicalβ€”iInf
infSet
β€”Set.range_comp
snd_iSup πŸ“–mathematicalβ€”iSup
supSet
β€”Set.range_comp
snd_sInf πŸ“–mathematicalβ€”InfSet.sInf
infSet
Set.image
β€”β€”
snd_sSup πŸ“–mathematicalβ€”SupSet.sSup
supSet
Set.image
β€”β€”
swap_iInf πŸ“–mathematicalβ€”iInf
infSet
β€”swap_sInf
swap_iSup πŸ“–mathematicalβ€”iSup
supSet
β€”swap_sSup
swap_sInf πŸ“–mathematicalβ€”InfSet.sInf
infSet
Set.image
β€”Set.image_comp
swap_sSup πŸ“–mathematicalβ€”SupSet.sSup
supSet
Set.image
β€”Set.image_comp

Prop

Definitions

NameCategoryTheorems
instCompleteLattice πŸ“–CompOp
52 mathmath: CategoryTheory.ObjectProperty.InheritedFromTarget.instMin, unary_relation_sSup_iff, CategoryTheory.ObjectProperty.preservesLimitsOfShape_eq_iSup, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsMin, AddCon.sup_def, sSup_Prop_eq, RingCon.sSup_def, Locale.localePointOfSpacePoint_toFun, AddCon.coe_iInf, RingCon.sup_def, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsISup, Con.coe_inf, RingCon.coe_inf, Setoid.sSup_def, iInf_Prop_eq, binary_relation_sSup_iff, CategoryTheory.ObjectProperty.isoClosure_iSup, CategoryTheory.ObjectProperty.instEssentiallySmallMax, CategoryTheory.ObjectProperty.instSmallMin, unary_relation_sInf_iff, CategoryTheory.ObjectProperty.instIsStableUnderShiftByMin, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsMax, CategoryTheory.ObjectProperty.prop_sup_iff, Con.coe_iInf, CategoryTheory.ObjectProperty.instEssentiallySmallISupOfSmall, AddCon.coe_sInf, Con.sup_def, Locale.PT.isOpen_iff, RingCon.coe_iInf, AddCon.sSup_def, CategoryTheory.ObjectProperty.InheritedFromSource.instMin, Setoid.inf_def, Locale.openOfElementHom_toFun, RingCon.coe_sInf, Setoid.sup_def, Topology.IsScott.Ο‰ScottContinuous_iff_continuous, iSup_Prop_eq, CategoryTheory.ObjectProperty.isoClosure_sup, CategoryTheory.ObjectProperty.instIsStableUnderShiftMin, CategoryTheory.ObjectProperty.preservesColimitsOfShape_eq_iSup, Con.coe_sInf, CategoryTheory.ObjectProperty.instContainsZeroMinOfIsClosedUnderIsomorphisms, Con.sSup_def, sInf_Prop_eq, CategoryTheory.ObjectProperty.instSmallMax, CategoryTheory.ObjectProperty.prop_inf_iff, CategoryTheory.ObjectProperty.instSmallMin_1, binary_relation_sInf_iff, CategoryTheory.ObjectProperty.instSmallISupOfSmall, AddCon.coe_inf, Setoid.sInf_def, CategoryTheory.ObjectProperty.prop_iSup_iff
instCompleteLinearOrder πŸ“–CompOp
12 mathmath: CategoryTheory.ObjectProperty.HasCardinalLT.sup, hasCardinalLT_subtype_max, CategoryTheory.ObjectProperty.IsLocal.inf, Relation.cutExpand_le_invImage_lex, CategoryTheory.ObjectProperty.instIsTriangulatedClosedβ‚‚MinOfIsClosedUnderIsomorphisms, CategoryTheory.ObjectProperty.HasCardinalLT.iSup, hasCardinalLT_subtype_iSup, AlgebraicGeometry.geometrically_inf, MeasureTheory.ae_eq_set_symmDiff, CategoryTheory.ObjectProperty.instIsTriangulatedMinOfIsClosedUnderIsomorphisms, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.iSup_P, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.sup_P

Set.BijOn

Theorems

NameKindAssumesProvesValidatesDepends On
iInf_comp πŸ“–mathematicalSet.BijOniInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
β€”image_eq
iInf_image
iInf_congr πŸ“–mathematicalSet.BijOniInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
β€”iInf_congr_Prop
iInf_comp
iSup_comp πŸ“–mathematicalSet.BijOniSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
β€”image_eq
iSup_image
iSup_congr πŸ“–mathematicalSet.BijOniSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
β€”iSup_congr_Prop
iSup_comp

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
biInf_congr πŸ“–mathematicalβ€”iInfβ€”biSup_congr
biInf_congr' πŸ“–mathematicalβ€”iInfβ€”β€”
biInf_const πŸ“–mathematicalSet.NonemptyiInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
β€”biSup_const
biInf_ge_eq_iInf πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
β€”biInf_le_eq_iInf
biInf_ge_eq_inf πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
Preorder.toLT
β€”biSup_ge_eq_sup
biInf_ge_eq_of_monotone πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
Preorder.toLE
β€”biInf_le_eq_of_antitone
Monotone.dual_left
biInf_gt_eq_iInf πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”biInf_lt_eq_iInf
OrderDual.noMaxOrder
biInf_inf πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”biSup_sup
biInf_le πŸ“–mathematicalSet
Set.instMembership
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”iInfβ‚‚_le
biInf_le_biSup πŸ“–mathematicalSet.NonemptyPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
Set
Set.instMembership
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”LE.le.trans
biInf_le
le_biSup
biInf_le_eq_iInf πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
β€”biSup_le_eq_iSup
biInf_le_eq_inf πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
Preorder.toLT
β€”biSup_le_eq_sup
biInf_le_eq_of_antitone πŸ“–mathematicalAntitone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
Preorder.toLE
β€”biSup_le_eq_of_monotone
Antitone.dual_right
biInf_lt_eq_iInf πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”biSup_lt_eq_iSup
biInf_mono πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”iInf_mono
iInf_const_mono
biInf_prod πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
SProd.sprod
Set.instSProd
β€”biSup_prod
biInf_prod' πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
SProd.sprod
Set.instSProd
β€”biInf_prod
biSup_congr πŸ“–mathematicalβ€”iSupβ€”iSup_congr
biSup_congr' πŸ“–mathematicalβ€”iSupβ€”β€”
biSup_const πŸ“–mathematicalSet.NonemptyiSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
β€”iSup_subtype''
iSup_const
Set.nonempty_coe_sort
biSup_ge_eq_iSup πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Preorder.toLE
β€”biSup_le_eq_iSup
biSup_ge_eq_of_antitone πŸ“–mathematicalAntitone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Preorder.toLE
β€”biSup_le_eq_of_monotone
Antitone.dual_left
biSup_ge_eq_sup πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Preorder.toLT
β€”iSup_split_single
iSup_congr_Prop
iSup_pos
iSup_and'
biSup_gt_eq_iSup πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”biSup_lt_eq_iSup
OrderDual.noMaxOrder
biSup_le_eq_iSup πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Preorder.toLE
β€”le_antisymm
iSup_le
iSupβ‚‚_le
le_iSup
le_iSup_of_le
le_iSupβ‚‚_of_le
le_rfl
biSup_le_eq_of_monotone πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Preorder.toLE
β€”le_antisymm
iSupβ‚‚_le_iff
le_iSup_of_le
ge_of_eq
iSup_pos
le_rfl
biSup_le_eq_sup πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Preorder.toLT
β€”iSup_split_single
iSup_congr_Prop
iSup_pos
iSup_and'
sup_comm
biSup_lt_eq_iSup πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”le_antisymm
iSup_le
iSupβ‚‚_le
le_iSup
NoMaxOrder.exists_gt
le_iSup_of_le
le_iSupβ‚‚_of_le
le_rfl
biSup_mono πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_mono
iSup_const_mono
biSup_prod πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
SProd.sprod
Set.instSProd
β€”iSup_prod
iSup_congr_Prop
iSup_and
iSup_congr
iSup_comm
biSup_prod' πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
SProd.sprod
Set.instSProd
β€”biSup_prod
biSup_sup πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_subtype'
iSup_sup
binary_relation_sInf_iff πŸ“–mathematicalβ€”InfSet.sInf
Pi.infSet
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Prop.instCompleteLattice
β€”iInf_apply
iInf_Prop_eq
binary_relation_sSup_iff πŸ“–mathematicalβ€”SupSet.sSup
Pi.supSet
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Prop.instCompleteLattice
Set
Set.instMembership
β€”iSup_apply
iSup_Prop_eq
bot_lt_iSup πŸ“–mathematicalβ€”Preorder.toLT
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Bot.bot
OrderBot.toBot
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”β€”
eq_singleton_bot_of_sSup_eq_bot_of_nonempty πŸ“–mathematicalSupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
Set.Nonempty
Set
Set.instSingletonSet
β€”Set.eq_singleton_iff_nonempty_unique_mem
sSup_eq_bot
eq_singleton_top_of_sInf_eq_top_of_nonempty πŸ“–mathematicalInfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
Set.Nonempty
Set
Set.instSingletonSet
β€”eq_singleton_bot_of_sSup_eq_bot_of_nonempty
iInf_Prop_eq πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Prop.instCompleteLattice
β€”le_antisymm
iInf_and πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iSup_and
iInf_and' πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iInf_and
iInf_apply πŸ“–mathematicalβ€”iInf
Pi.infSet
β€”iSup_apply
iInf_comm πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iSup_comm
iInf_congr πŸ“–mathematicalβ€”iInfβ€”β€”
iInf_congr_Prop πŸ“–mathematicalβ€”iInfβ€”β€”
iInf_const πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iSup_const
iInf_const_mono πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”le_iInf
iInf_le
iInf_dite πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”iSup_dite
iInf_emptyset πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
Set.instEmptyCollection
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”iInf_congr_Prop
iInf_neg
iInf_top
iInf_eq_bot πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
CompleteLinearOrder.toCompleteLattice
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedHeytingAlgebra.toLattice
HeytingAlgebra.toGeneralizedHeytingAlgebra
BiheytingAlgebra.toHeytingAlgebra
CompleteLinearOrder.toBiheytingAlgebra
HeytingAlgebra.toOrderBot
Preorder.toLT
CompleteSemilatticeInf.toPartialOrder
β€”β€”
iInf_eq_dif πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”iSup_eq_dif
iInf_eq_if πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”iInf_eq_dif
iInf_eq_of_forall_ge_of_forall_gt_exists_lt πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLT
iInf
CompleteSemilatticeInf.toInfSet
β€”iSup_eq_of_forall_le_of_forall_lt_exists_gt
iInf_eq_top πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”sInf_eq_top
Set.forall_mem_range
iInf_exists πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iSup_exists
iInf_extend_top πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Function.extend
Top.top
Pi.instTopForall
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”iSup_extend_bot
iInf_false πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”iInf_neg
iInf_iInf_eq_left πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iSup_iSup_eq_left
iInf_iInf_eq_right πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iSup_iSup_eq_right
iInf_image πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
Set.image
β€”iSup_image
iInf_image2 πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
Set.image2
β€”iSup_image2
iInf_inf πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iInf_inf_eq
iInf_const
iInf_inf_eq πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”iSup_sup_eq
iInf_insert πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
Set.instInsert
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”iInf_union
iInf_iInf_eq_left
iInf_ite πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”iInf_dite
iInf_le πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”sInf_le
iInf_le_iInf_of_subset πŸ“–mathematicalSet
Set.instHasSubset
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
Set.instMembership
β€”biInf_mono
iInf_le_iInfβ‚‚ πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”le_iInfβ‚‚
iInf_le
iInf_le_iSup πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”LE.le.trans
iInf_le
le_iSup
iInf_le_of_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”LE.le.trans
iInf_le
iInf_lt_top πŸ“–mathematicalβ€”Preorder.toLT
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”β€”
iInf_mono πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”le_iInf
iInf_le_of_le
iInf_mono' πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”le_iInf
iInf_le_of_le
iInf_ne_top_subtype πŸ“–mathematicalβ€”iInf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iSup_ne_bot_subtype
iInf_neg πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”le_antisymm
le_top
le_iInf
iInf_of_empty πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”iSup_of_empty
iInf_of_isEmpty πŸ“–mathematicalβ€”iInf
InfSet.sInf
Set
Set.instEmptyCollection
β€”Set.range_eq_empty
iInf_option πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”iSup_option
iInf_option_elim πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”iSup_option_elim
iInf_or πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”iSup_or
iInf_pair πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
Set.instInsert
Set.instSingletonSet
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”iInf_insert
iInf_singleton
iInf_plift_down πŸ“–mathematicalβ€”iInfβ€”Function.Surjective.iInf_congr
PLift.down_surjective
iInf_plift_up πŸ“–mathematicalβ€”iInfβ€”Function.Surjective.iInf_congr
PLift.up_surjective
iInf_pos πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”le_antisymm
iInf_le
le_iInf
le_rfl
iInf_prod πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iSup_prod
iInf_prod' πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iInf_prod
iInf_psigma πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”eq_of_forall_le_iff
iInf_psigma' πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iInf_psigma
iInf_range πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
Set.range
β€”iSup_range
iInf_range' πŸ“–mathematicalβ€”iInf
Set.Elem
Set.range
Set
Set.instMembership
β€”iSup_range'
iInf_sigma πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iSup_sigma
iInf_sigma' πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iInf_sigma
iInf_singleton πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
Set.instSingletonSet
β€”iInf_congr_Prop
iInf_iInf_eq_left
iInf_split πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”iSup_split
iInf_split_single πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”iSup_split_single
iInf_subtype πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iSup_subtype
iInf_subtype' πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iInf_subtype
iInf_subtype'' πŸ“–mathematicalβ€”iInf
Set.Elem
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
β€”iInf_subtype
iInf_sum πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”iSup_sum
iInf_top πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”top_unique
le_iInf_const
iInf_true πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iInf_pos
iInf_ulift πŸ“–mathematicalβ€”iInfβ€”Set.ext
iInf_union πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
Set.instUnion
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”iSup_union
iInf_unique πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Unique.instInhabited
β€”Unique.eq_default
iInf_const
iInf_univ πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
Set.univ
β€”iInf_congr_Prop
iInf_pos
iInfβ‚‚_comm πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iInf_comm
iInfβ‚‚_eq_bot πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
CompleteLinearOrder.toCompleteLattice
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedHeytingAlgebra.toLattice
HeytingAlgebra.toGeneralizedHeytingAlgebra
BiheytingAlgebra.toHeytingAlgebra
CompleteLinearOrder.toBiheytingAlgebra
HeytingAlgebra.toOrderBot
Preorder.toLT
CompleteSemilatticeInf.toPartialOrder
β€”iInf_psigma'
iInfβ‚‚_eq_top πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”β€”
iInfβ‚‚_le πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”iInf_le_of_le
iInf_le
iInfβ‚‚_le_of_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”LE.le.trans
iInfβ‚‚_le
iInfβ‚‚_mono πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”iInf_mono
iInfβ‚‚_mono' πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”le_iInfβ‚‚
iInfβ‚‚_le_of_le
iSup_Prop_eq πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Prop.instCompleteLattice
β€”le_antisymm
iSup_and πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”le_antisymm
iSup_le
le_iSupβ‚‚
iSupβ‚‚_le
le_iSup
iSup_and' πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_and
iSup_apply πŸ“–mathematicalβ€”iSup
Pi.supSet
β€”iSup.eq_1
sSup_apply
Set.image_eq_range
Set.range_comp
iSup_bot πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”bot_unique
iSup_const_le
iSup_comm πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”le_antisymm
iSup_le
iSup_mono
le_iSup
iSup_comp_le πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_mono'
le_rfl
iSup_congr πŸ“–mathematicalβ€”iSupβ€”β€”
iSup_congr_Prop πŸ“–mathematicalβ€”iSupβ€”β€”
iSup_const πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup.eq_1
Set.range_const
sSup_singleton
iSup_const_le πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_le
le_rfl
iSup_const_mono πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_le
le_iSup
iSup_dite πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”iSup_sup_eq
iSup_congr_Prop
iSup_pos
iSup_neg
sup_of_le_left
sup_of_le_right
iSup_emptyset πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
Set.instEmptyCollection
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”iSup_congr_Prop
iSup_neg
iSup_bot
iSup_eq_bot πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”sSup_eq_bot
Set.forall_mem_range
iSup_eq_dif πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”iSup_congr_Prop
iSup_pos
iSup_neg
iSup_eq_if πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”iSup_eq_dif
iSup_eq_of_forall_le_of_forall_lt_exists_gt πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Preorder.toLT
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”sSup_eq_of_forall_le_of_forall_lt_exists_gt
Set.forall_mem_range
Set.exists_range_iff
iSup_eq_top πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
CompleteLinearOrder.toCompleteLattice
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
CompleteLinearOrder.toBiheytingAlgebra
CoheytingAlgebra.toOrderTop
Preorder.toLT
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
β€”β€”
iSup_exists πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”le_antisymm
iSup_le
le_iSupβ‚‚
iSupβ‚‚_le
le_iSup
iSup_extend_bot πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Function.extend
Bot.bot
Pi.instBotForall
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”iSup_split
iSup_exists
iSup_comm
iSup_iSup_eq_right
Function.Injective.extend_apply
iSup_congr_Prop
Function.extend_apply'
iSup_bot
sup_of_le_left
iSup_false πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”iSup_neg
iSup_iInf_le_iInf_iSup πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iInf
CompleteSemilatticeInf.toInfSet
β€”iSup_le
iInf_mono
le_iSup
iSup_iSup_eq_left πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”LE.le.antisymm'
le_iSupβ‚‚
iSup_le
le_refl
iSup_iSup_eq_right πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”LE.le.antisymm'
le_iSupβ‚‚
iSupβ‚‚_le
le_refl
iSup_image πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
Set.image
β€”sSup_image
Set.image_comp
iSup_image2 πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
Set.image2
β€”Set.image_prod
iSup_image
biSup_prod
iSup_insert πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
Set.instInsert
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”iSup_union
iSup_iSup_eq_left
iSup_ite πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”iSup_dite
iSup_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”sSup_le
iSup_le_iSup_of_subset πŸ“–mathematicalSet
Set.instHasSubset
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set.instMembership
β€”biSup_mono
iSup_le_iff πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”isLUB_le_iff
isLUB_iSup
Set.forall_mem_range
iSup_lt_iff πŸ“–mathematicalβ€”Preorder.toLT
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Preorder.toLE
β€”le_iSup
LE.le.trans_lt
iSup_le
iSup_mono πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_le
le_iSup_of_le
iSup_mono' πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_le
le_iSup_of_le
iSup_ne_bot_subtype πŸ“–mathematicalβ€”iSup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_bot
LE.le.antisymm
iSup_comp_le
iSup_mono'
Mathlib.Tactic.Push.not_forall_eq
bot_le
Eq.le
iSup_neg πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”le_antisymm
iSup_le
bot_le
iSup_of_empty πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”iSup_of_empty'
sSup_empty
iSup_of_empty' πŸ“–mathematicalβ€”iSup
SupSet.sSup
Set
Set.instEmptyCollection
β€”Set.range_eq_empty
iSup_option πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”eq_of_forall_ge_iff
iSup_option_elim πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”iSup_option
iSup_or πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”le_antisymm
iSup_le
le_sup_of_le_left
le_iSup
le_sup_of_le_right
sup_le
iSup_comp_le
iSup_pair πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
Set.instInsert
Set.instSingletonSet
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”iSup_insert
iSup_singleton
iSup_plift_down πŸ“–mathematicalβ€”iSupβ€”Function.Surjective.iSup_congr
PLift.down_surjective
iSup_plift_up πŸ“–mathematicalβ€”iSupβ€”Function.Surjective.iSup_congr
PLift.up_surjective
iSup_pos πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”le_antisymm
iSup_le
le_rfl
le_iSup
iSup_prod πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”eq_of_forall_ge_iff
iSup_prod' πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_prod
iSup_psigma πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”eq_of_forall_ge_iff
iSup_psigma' πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_psigma
iSup_range πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
Set.range
β€”iSup_subtype''
iSup_range'
iSup_range' πŸ“–mathematicalβ€”iSup
Set.Elem
Set.range
Set
Set.instMembership
β€”iSup.eq_1
Set.image_eq_range
Set.range_comp'
iSup_sigma πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”eq_of_forall_ge_iff
iSup_sigma' πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_sigma
iSup_singleton πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
Set.instSingletonSet
β€”iSup_congr_Prop
iSup_iSup_eq_left
iSup_split πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”iSup_congr_Prop
iSup_pos
iSup_union
iSup_split_single πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”iSup_iSup_eq_left
iSup_split
iSup_subtype πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”le_antisymm
iSup_le
le_iSupβ‚‚
iSupβ‚‚_le
le_iSup
iSup_subtype' πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_subtype
iSup_subtype'' πŸ“–mathematicalβ€”iSup
Set.Elem
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
β€”iSup_subtype
iSup_sum πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”eq_of_forall_ge_iff
iSup_sup πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_sup_eq
iSup_const
iSup_sup_eq πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”le_antisymm
iSup_le
sup_le_sup
le_iSup
sup_le
iSup_mono
le_sup_left
le_sup_right
iSup_true πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_pos
iSup_ulift πŸ“–mathematicalβ€”iSupβ€”Set.ext
iSup_union πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
Set.instUnion
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”iSup_congr_Prop
iSup_or
iSup_sup_eq
iSup_unique πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Unique.instInhabited
β€”Unique.eq_default
iSup_const
iSup_univ πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
Set.univ
β€”iSup_congr_Prop
iSup_pos
iSupβ‚‚_comm πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_comm
iSupβ‚‚_eq_bot πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”β€”
iSupβ‚‚_eq_top πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
CompleteLinearOrder.toCompleteLattice
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
CompleteLinearOrder.toBiheytingAlgebra
CoheytingAlgebra.toOrderTop
Preorder.toLT
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
β€”iSup_psigma'
iSupβ‚‚_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_le
iSupβ‚‚_le_iSup πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSupβ‚‚_le
le_iSup
iSupβ‚‚_le_iff πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”β€”
iSupβ‚‚_mono πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_mono
iSupβ‚‚_mono' πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSupβ‚‚_le
le_iSupβ‚‚_of_le
inf_biInf πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”sup_biSup
inf_iInf πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iInf_inf_eq
iInf_const
isGLB_biInf πŸ“–mathematicalβ€”IsGLB
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Set.image
iInf
CompleteSemilatticeInf.toInfSet
Set
Set.instMembership
β€”iInf_subtype'
Set.range_comp
Subtype.range_coe
isGLB_iInf
isGLB_iInf πŸ“–mathematicalβ€”IsGLB
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Set.range
iInf
CompleteSemilatticeInf.toInfSet
β€”isGLB_sInf
isLUB_biSup πŸ“–mathematicalβ€”IsLUB
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Set.image
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
β€”iSup_subtype'
Set.range_comp
Subtype.range_coe
isLUB_iSup
isLUB_iSup πŸ“–mathematicalβ€”IsLUB
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Set.range
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”isLUB_sSup
le_biSup πŸ“–mathematicalSet
Set.instMembership
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”biInf_le
le_iInf πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”le_sInf
le_iInf_comp πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”iInf_mono'
le_rfl
le_iInf_const πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”le_iInf
le_rfl
le_iInf_iff πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”le_isGLB_iff
isGLB_iInf
Set.forall_mem_range
le_iInfβ‚‚ πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”le_iInf
le_iInfβ‚‚_iff πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
β€”β€”
le_iSup πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”le_sSup
le_iSup_of_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”LE.le.trans
le_iSup
le_iSupβ‚‚ πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”le_iSup_of_le
le_iSup
le_iSupβ‚‚_of_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”LE.le.trans
le_iSupβ‚‚
le_sInf_inter πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
InfSet.sInf
CompleteSemilatticeInf.toInfSet
Set
Set.instInter
β€”sSup_inter_le
lt_iInf_iff πŸ“–mathematicalβ€”Preorder.toLT
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iInf
CompleteSemilatticeInf.toInfSet
Preorder.toLE
β€”iInf_le
LT.lt.trans_le
le_iInf
sInf_Prop_eq πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Prop.instCompleteLattice
β€”β€”
sInf_apply πŸ“–mathematicalβ€”InfSet.sInf
Pi.infSet
iInf
Set.Elem
Set
Set.instMembership
β€”β€”
sInf_diff_singleton_top πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instSDiff
Set.instSingletonSet
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”sSup_diff_singleton_bot
sInf_empty πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instEmptyCollection
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”IsGLB.sInf_eq
isGLB_empty
sInf_eq_iInf πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
iInf
Set
Set.instMembership
β€”sSup_eq_iSup
sInf_eq_iInf' πŸ“–mathematicalβ€”InfSet.sInf
iInf
Set.Elem
Set
Set.instMembership
β€”sSup_eq_iSup'
sInf_eq_of_forall_ge_of_forall_gt_exists_lt πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
Preorder.toLT
InfSet.sInf
CompleteSemilatticeInf.toInfSet
β€”sSup_eq_of_forall_le_of_forall_lt_exists_gt
sInf_eq_top πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”sSup_eq_bot
sInf_image πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set.image
iInf
Set
Set.instMembership
β€”sSup_image
sInf_image' πŸ“–mathematicalβ€”InfSet.sInf
Set.image
iInf
Set.Elem
Set
Set.instMembership
β€”iInf.eq_1
Set.image_eq_range
sInf_image2 πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set.image2
iInf
Set
Set.instMembership
β€”Set.image_prod
sInf_image
biInf_prod
sInf_insert πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instInsert
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”IsGLB.sInf_eq
IsGLB.insert
isGLB_sInf
sInf_le_sInf_of_isCoinitialFor πŸ“–mathematicalIsCoinitialFor
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
InfSet.sInf
CompleteSemilatticeInf.toInfSet
β€”IsGreatest.mono
isGLB_sInf
lowerBounds_mono_of_isCoinitialFor
sInf_le_sInf_of_subset_insert_top πŸ“–mathematicalSet
Set.instHasSubset
Set.instInsert
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
InfSet.sInf
CompleteSemilatticeInf.toInfSet
β€”LE.le.trans_eq'
sInf_le_sInf
sInf_insert
top_inf_eq
sInf_le_sSup πŸ“–mathematicalSet.NonemptyPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
InfSet.sInf
CompleteSemilatticeInf.toInfSet
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”isGLB_le_isLUB
isGLB_sInf
isLUB_sSup
sInf_pair πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instInsert
Set.instSingletonSet
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”IsGLB.sInf_eq
isGLB_pair
sInf_prod πŸ“–mathematicalSet.NonemptyInfSet.sInf
Prod.infSet
SProd.sprod
Set
Set.instSProd
β€”Set.fst_image_prod
Set.snd_image_prod
sInf_range πŸ“–mathematicalβ€”InfSet.sInf
Set.range
iInf
β€”β€”
sInf_singleton πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
Set
Set.instSingletonSet
β€”IsGLB.sInf_eq
isGLB_singleton
sInf_union πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instUnion
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”IsGLB.sInf_eq
IsGLB.union
isGLB_sInf
sInf_univ πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set.univ
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”IsGLB.sInf_eq
isGLB_univ
sInf_upperBounds_eq_csSup πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
upperBounds
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”sInf_upperBounds_eq_sSup
sInf_upperBounds_eq_sSup πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
upperBounds
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”IsGLB.unique
isGLB_sInf
IsLeast.isGLB
isLUB_sSup
sSup_Prop_eq πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Prop.instCompleteLattice
Set
Set.instMembership
β€”β€”
sSup_apply πŸ“–mathematicalβ€”SupSet.sSup
Pi.supSet
iSup
Set.Elem
Set
Set.instMembership
β€”β€”
sSup_diff_singleton_bot πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instSDiff
Set.instSingletonSet
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”LE.le.antisymm
sSup_le_sSup
Set.diff_subset
sSup_le_sSup_of_subset_insert_bot
Set.subset_insert_diff_singleton
sSup_empty πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instEmptyCollection
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”IsLUB.sSup_eq
isLUB_empty
sSup_eq_bot πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”bot_unique
le_sSup
sSup_le
le_bot_iff
sSup_eq_bot' πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
Set
Set.instEmptyCollection
Set.instSingletonSet
β€”sSup_eq_bot
Set.subset_singleton_iff_eq
Set.subset_singleton_iff
sSup_eq_iSup πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iSup
Set
Set.instMembership
β€”le_antisymm
sSup_le
le_iSupβ‚‚
iSupβ‚‚_le
le_sSup
sSup_eq_iSup' πŸ“–mathematicalβ€”SupSet.sSup
iSup
Set.Elem
Set
Set.instMembership
β€”iSup.eq_1
Subtype.range_coe
sSup_eq_of_forall_le_of_forall_lt_exists_gt πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
Preorder.toLT
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”LE.le.eq_of_not_lt
sSup_le
LT.lt.false
LE.le.trans_lt
le_sSup
sSup_image πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set.image
iSup
Set
Set.instMembership
β€”iSup_subtype''
sSup_image'
sSup_image' πŸ“–mathematicalβ€”SupSet.sSup
Set.image
iSup
Set.Elem
Set
Set.instMembership
β€”iSup.eq_1
Set.image_eq_range
sSup_image2 πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set.image2
iSup
Set
Set.instMembership
β€”Set.image_prod
sSup_image
biSup_prod
sSup_insert πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instInsert
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”IsLUB.sSup_eq
IsLUB.insert
isLUB_sSup
sSup_inter_le πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instInter
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”sSup_le
le_inf
le_sSup
sSup_le_sSup_of_isCofinalFor πŸ“–mathematicalIsCofinalFor
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeSup.toPartialOrder
SupSet.sSup
CompleteSemilatticeSup.toSupSet
β€”IsLeast.mono
isLUB_sSup
upperBounds_mono_of_isCofinalFor
sSup_le_sSup_of_subset_insert_bot πŸ“–mathematicalSet
Set.instHasSubset
Set.instInsert
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”LE.le.trans_eq
sSup_le_sSup
sSup_insert
bot_sup_eq
sSup_lowerBounds_eq_sInf πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
lowerBounds
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
InfSet.sInf
CompleteSemilatticeInf.toInfSet
β€”IsLUB.unique
isLUB_sSup
IsGreatest.isLUB
isGLB_sInf
sSup_pair πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instInsert
Set.instSingletonSet
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”IsLUB.sSup_eq
isLUB_pair
sSup_prod πŸ“–mathematicalSet.NonemptySupSet.sSup
Prod.supSet
SProd.sprod
Set
Set.instSProd
β€”Set.fst_image_prod
Set.snd_image_prod
sSup_range πŸ“–mathematicalβ€”SupSet.sSup
Set.range
iSup
β€”β€”
sSup_singleton πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
Set
Set.instSingletonSet
β€”IsLUB.sSup_eq
isLUB_singleton
sSup_union πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instUnion
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”IsLUB.sSup_eq
IsLUB.union
isLUB_sSup
sSup_univ πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set.univ
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
β€”IsLUB.sSup_eq
isLUB_univ
sup_biSup πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”sup_comm
iSup_congr_Prop
biSup_sup
sup_iSup πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_sup_eq
iSup_const
unary_relation_sInf_iff πŸ“–mathematicalβ€”InfSet.sInf
Pi.infSet
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Prop.instCompleteLattice
β€”iInf_Prop_eq
unary_relation_sSup_iff πŸ“–mathematicalβ€”SupSet.sSup
Pi.supSet
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Prop.instCompleteLattice
Set
Set.instMembership
β€”iSup_Prop_eq

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