Skip to content

Commit

Permalink
deprecated aliases
Browse files Browse the repository at this point in the history
  • Loading branch information
YaelDillies committed Nov 24, 2024
1 parent 291655f commit 26d2dba
Show file tree
Hide file tree
Showing 14 changed files with 205 additions and 1 deletion.
20 changes: 20 additions & 0 deletions Mathlib/Algebra/DirectSum/Module.lean
Original file line number Diff line number Diff line change
Expand Up @@ -322,6 +322,9 @@ theorem IsInternal.submodule_iSup_eq_top (h : IsInternal A) : iSup A = ⊤ := by
theorem IsInternal.submodule_iSupIndep (h : IsInternal A) : iSupIndep A :=
iSupIndep_of_dfinsupp_lsum_injective _ h.injective

@[deprecated (since := "2024-11-24")]
alias IsInternal.submodule_independent := IsInternal.submodule_iSupIndep

/-- Given an internal direct sum decomposition of a module `M`, and a basis for each of the
components of the direct sum, the disjoint union of these bases is a basis for `M`. -/
noncomputable def IsInternal.collectedBasis (h : IsInternal A) {α : ι → Type*}
Expand Down Expand Up @@ -395,13 +398,21 @@ theorem isInternal_submodule_of_iSupIndep_of_iSup_eq_top {A : ι → Submodule R
(LinearMap.range_eq_top (f := DFinsupp.lsum _ _)).1 <|
(Submodule.iSup_eq_range_dfinsupp_lsum _).symm.trans hs⟩

@[deprecated (since := "2024-11-24")]
alias isInternal_submodule_of_independent_of_iSup_eq_top :=
isInternal_submodule_of_iSupIndep_of_iSup_eq_top

/-- `iff` version of `DirectSum.isInternal_submodule_of_iSupIndep_of_iSup_eq_top`,
`DirectSum.IsInternal.iSupIndep`, and `DirectSum.IsInternal.submodule_iSup_eq_top`. -/
theorem isInternal_submodule_iff_iSupIndep_and_iSup_eq_top (A : ι → Submodule R M) :
IsInternal A ↔ iSupIndep A ∧ iSup A = ⊤ :=
fun i ↦ ⟨i.submodule_iSupIndep, i.submodule_iSup_eq_top⟩,
And.rec isInternal_submodule_of_iSupIndep_of_iSup_eq_top⟩

@[deprecated (since := "2024-11-24")]
alias isInternal_submodule_iff_independent_and_iSup_eq_top :=
isInternal_submodule_iff_iSupIndep_and_iSup_eq_top

/-- If a collection of submodules has just two indices, `i` and `j`, then
`DirectSum.IsInternal` is equivalent to `isCompl`. -/
theorem isInternal_submodule_iff_isCompl (A : ι → Submodule R M) {i j : ι} (hij : i ≠ j)
Expand Down Expand Up @@ -430,17 +441,26 @@ lemma isInternal_biSup_submodule_of_iSupIndep {A : ι → Submodule R M} (s : Se
change m ∈ ((A i).comap p.subtype).map p.subtype ↔ _
rw [Submodule.map_comap_subtype, inf_of_le_right (hp i i.property)]

@[deprecated (since := "2024-11-24")]
alias isInternal_biSup_submodule_of_independent := isInternal_biSup_submodule_of_iSupIndep

/-! Now copy the lemmas for subgroup and submonoids. -/


theorem IsInternal.addSubmonoid_iSupIndep {M : Type*} [AddCommMonoid M] {A : ι → AddSubmonoid M}
(h : IsInternal A) : iSupIndep A :=
iSupIndep_of_dfinsupp_sumAddHom_injective _ h.injective

@[deprecated (since := "2024-11-24")]
alias IsInternal.addSubmonoid_independent := IsInternal.addSubmonoid_iSupIndep

theorem IsInternal.addSubgroup_iSupIndep {G : Type*} [AddCommGroup G] {A : ι → AddSubgroup G}
(h : IsInternal A) : iSupIndep A :=
iSupIndep_of_dfinsupp_sumAddHom_injective' _ h.injective

@[deprecated (since := "2024-11-24")]
alias IsInternal.addSubgroup_independent := IsInternal.addSubgroup_iSupIndep

end Ring

end Submodule
Expand Down
3 changes: 3 additions & 0 deletions Mathlib/Algebra/Lie/Submodule.lean
Original file line number Diff line number Diff line change
Expand Up @@ -518,6 +518,9 @@ theorem iSupIndep_iff_coe_toSubmodule {ι : Type*} {N : ι → LieSubmodule R L
iSupIndep N ↔ iSupIndep fun i ↦ (N i : Submodule R M) := by
simp [iSupIndep_def, disjoint_iff_coe_toSubmodule]

@[deprecated (since := "2024-11-24")]
alias independent_iff_coe_toSubmodule := iSupIndep_iff_coe_toSubmodule

theorem iSup_eq_top_iff_coe_toSubmodule {ι : Sort*} {N : ι → LieSubmodule R L M} :
⨆ i, N i = ⊤ ↔ ⨆ i, (N i : Submodule R M) = ⊤ := by
rw [← iSup_coe_toSubmodule, ← top_coeSubmodule (L := L), coe_toSubmodule_eq_iff]
Expand Down
7 changes: 7 additions & 0 deletions Mathlib/Algebra/Lie/Weights/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -674,17 +674,24 @@ lemma iSupIndep_genWeightSpace [NoZeroSMulDivisors R M] :
exact Module.End.independent_iInf_maxGenEigenspace_of_forall_mapsTo (toEnd R L M)
(fun x y φ z ↦ (genWeightSpaceOf M φ y).lie_mem)

@[deprecated (since := "2024-11-24")] alias independent_genWeightSpace := iSupIndep_genWeightSpace

lemma iSupIndep_genWeightSpace' [NoZeroSMulDivisors R M] :
iSupIndep fun χ : Weight R L M ↦ genWeightSpace M χ :=
(iSupIndep_genWeightSpace R L M).comp <|
Subtype.val_injective.comp (Weight.equivSetOf R L M).injective

@[deprecated (since := "2024-11-24")] alias independent_genWeightSpace' := iSupIndep_genWeightSpace'

lemma iSupIndep_genWeightSpaceOf [NoZeroSMulDivisors R M] (x : L) :
iSupIndep fun (χ : R) ↦ genWeightSpaceOf M χ x := by
rw [LieSubmodule.iSupIndep_iff_coe_toSubmodule]
dsimp [genWeightSpaceOf]
exact (toEnd R L M x).independent_genEigenspace _

@[deprecated (since := "2024-11-24")]
alias independent_genWeightSpaceOf := iSupIndep_genWeightSpaceOf

lemma finite_genWeightSpaceOf_ne_bot [NoZeroSMulDivisors R M] [IsNoetherian R M] (x : L) :
{χ : R | genWeightSpaceOf M χ x ≠ ⊥}.Finite :=
WellFoundedGT.finite_ne_bot_of_iSupIndep (iSupIndep_genWeightSpaceOf R L M x)
Expand Down
3 changes: 3 additions & 0 deletions Mathlib/Algebra/Module/Torsion.lean
Original file line number Diff line number Diff line change
Expand Up @@ -113,6 +113,9 @@ theorem iSupIndep.linearIndependent' {ι R M : Type*} {v : ι → M} [Ring R]
rw [← Submodule.mem_bot R, ← h_ne_zero i]
simpa using this

@[deprecated (since := "2024-11-24")]
alias CompleteLattice.Independent.linear_independent' := iSupIndep.linearIndependent'

end TorsionOf

section
Expand Down
6 changes: 6 additions & 0 deletions Mathlib/GroupTheory/NoncommPiCoprod.lean
Original file line number Diff line number Diff line change
Expand Up @@ -73,6 +73,9 @@ theorem eq_one_of_noncommProd_eq_one_of_iSupIndep {ι : Type*} (s : Finset ι) (
· exact heq1i
· refine ih hcomm hmem.2 heq1S _ h

@[deprecated (since := "2024-11-24")]
alias eq_one_of_noncommProd_eq_one_of_independent := eq_one_of_noncommProd_eq_one_of_iSupIndep

end Subgroup

section FamilyOfMonoids
Expand Down Expand Up @@ -215,6 +218,9 @@ theorem injective_noncommPiCoprod_of_iSupIndep [Fintype ι]
apply hinj
simp [this i (Finset.mem_univ i)]

@[deprecated (since := "2024-11-24")]
alias injective_noncommPiCoprod_of_independent := injective_noncommPiCoprod_of_iSupIndep

@[to_additive]
theorem independent_range_of_coprime_order
(hcomm : Pairwise fun i j : ι => ∀ (x : H i) (y : H j), Commute (ϕ i x) (ϕ j y))
Expand Down
30 changes: 30 additions & 0 deletions Mathlib/LinearAlgebra/DFinsupp.lean
Original file line number Diff line number Diff line change
Expand Up @@ -410,6 +410,9 @@ theorem iSupIndep_iff_forall_dfinsupp (p : ι → Submodule R N) :
refine forall_congr' fun i => Subtype.forall'.trans ?_
simp_rw [Submodule.coe_eq_zero]

@[deprecated (since := "2024-11-24")]
alias independent_iff_forall_dfinsupp := iSupIndep_iff_forall_dfinsupp

/- If `DFinsupp.lsum` applied with `Submodule.subtype` is injective then the submodules are
iSupIndep. -/
theorem iSupIndep_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
Expand All @@ -423,13 +426,19 @@ theorem iSupIndep_of_dfinsupp_lsum_injective (p : ι → Submodule R N)
have := DFunLike.ext_iff.mp (h hv) i
simpa [eq_comm] using this

@[deprecated (since := "2024-11-24")]
alias independent_of_dfinsupp_lsum_injective := iSupIndep_of_dfinsupp_lsum_injective

/- If `DFinsupp.sumAddHom` applied with `AddSubmonoid.subtype` is injective then the additive
submonoids are independent. -/
theorem iSupIndep_of_dfinsupp_sumAddHom_injective (p : ι → AddSubmonoid N)
(h : Function.Injective (sumAddHom fun i => (p i).subtype)) : iSupIndep p := by
rw [← iSupIndep_map_orderIso_iff (AddSubmonoid.toNatSubmodule : AddSubmonoid N ≃o _)]
exact iSupIndep_of_dfinsupp_lsum_injective _ h

@[deprecated (since := "2024-11-24")]
alias independent_of_dfinsupp_sumAddHom_injective := iSupIndep_of_dfinsupp_sumAddHom_injective

/-- Combining `DFinsupp.lsum` with `LinearMap.toSpanSingleton` is the same as
`Finsupp.linearCombination` -/
theorem lsum_comp_mapRange_toSpanSingleton [∀ m : R, Decidable (m ≠ 0)] (p : ι → Submodule R N)
Expand All @@ -455,6 +464,9 @@ theorem iSupIndep_of_dfinsupp_sumAddHom_injective' (p : ι → AddSubgroup N)
rw [← iSupIndep_map_orderIso_iff (AddSubgroup.toIntSubmodule : AddSubgroup N ≃o _)]
exact iSupIndep_of_dfinsupp_lsum_injective _ h

@[deprecated (since := "2024-11-24")]
alias independent_of_dfinsupp_sumAddHom_injective' := iSupIndep_of_dfinsupp_sumAddHom_injective'

/-- The canonical map out of a direct sum of a family of submodules is injective when the submodules
are `iSupIndep`.
Expand All @@ -480,13 +492,19 @@ theorem iSupIndep.dfinsupp_lsum_injective {p : ι → Submodule R N} (h : iSupIn
rwa [← erase_add_single i m, LinearMap.map_add, lsum_single, Submodule.subtype_apply,
add_eq_zero_iff_eq_neg, ← Submodule.coe_neg] at hm

@[deprecated (since := "2024-11-24")]
alias Independent.dfinsupp_lsum_injective := iSupIndep.dfinsupp_lsum_injective

/-- The canonical map out of a direct sum of a family of additive subgroups is injective when the
additive subgroups are `iSupIndep`. -/
theorem iSupIndep.dfinsupp_sumAddHom_injective {p : ι → AddSubgroup N} (h : iSupIndep p) :
Function.Injective (sumAddHom fun i => (p i).subtype) := by
rw [← iSupIndep_map_orderIso_iff (AddSubgroup.toIntSubmodule : AddSubgroup N ≃o _)] at h
exact h.dfinsupp_lsum_injective

@[deprecated (since := "2024-11-24")]
alias Independent.dfinsupp_sumAddHom_injective := iSupIndep.dfinsupp_sumAddHom_injective

/-- A family of submodules over an additive group are independent if and only iff `DFinsupp.lsum`
applied with `Submodule.subtype` is injective.
Expand All @@ -496,12 +514,18 @@ theorem iSupIndep_iff_dfinsupp_lsum_injective (p : ι → Submodule R N) :
iSupIndep p ↔ Function.Injective (lsum ℕ (M := fun i ↦ ↥(p i)) fun i => (p i).subtype) :=
⟨iSupIndep.dfinsupp_lsum_injective, iSupIndep_of_dfinsupp_lsum_injective p⟩

@[deprecated (since := "2024-11-24")]
alias independent_iff_dfinsupp_lsum_injective := iSupIndep_iff_dfinsupp_lsum_injective

/-- A family of additive subgroups over an additive group are independent if and only if
`DFinsupp.sumAddHom` applied with `AddSubgroup.subtype` is injective. -/
theorem iSupIndep_iff_dfinsupp_sumAddHom_injective (p : ι → AddSubgroup N) :
iSupIndep p ↔ Function.Injective (sumAddHom fun i => (p i).subtype) :=
⟨iSupIndep.dfinsupp_sumAddHom_injective, iSupIndep_of_dfinsupp_sumAddHom_injective' p⟩

@[deprecated (since := "2024-11-24")]
alias independent_iff_dfinsupp_sumAddHom_injective := iSupIndep_iff_dfinsupp_sumAddHom_injective

/-- If a family of submodules is independent, then a choice of nonzero vector from each submodule
forms a linearly independent family.
Expand All @@ -525,12 +549,18 @@ theorem iSupIndep.linearIndependent [NoZeroSMulDivisors R N] {ι} (p : ι → Su
simp only [coe_zero, Pi.zero_apply, ZeroMemClass.coe_zero, smul_eq_zero, ha] at this
simpa

@[deprecated (since := "2024-11-24")]
alias Independent.linearIndependent := iSupIndep.linearIndependent

theorem iSupIndep_iff_linearIndependent_of_ne_zero [NoZeroSMulDivisors R N] {ι} {v : ι → N}
(h_ne_zero : ∀ i, v i ≠ 0) : (iSupIndep fun i => R ∙ v i) ↔ LinearIndependent R v :=
let _ := Classical.decEq ι
fun hv => hv.linearIndependent _ (fun i => Submodule.mem_span_singleton_self <| v i) h_ne_zero,
fun hv => hv.iSupIndep_span_singleton⟩

@[deprecated (since := "2024-11-24")]
alias independent_iff_linearIndependent_of_ne_zero := iSupIndep_iff_linearIndependent_of_ne_zero

end Ring

namespace LinearMap
Expand Down
3 changes: 3 additions & 0 deletions Mathlib/LinearAlgebra/Dimension/Finite.lean
Original file line number Diff line number Diff line change
Expand Up @@ -261,6 +261,9 @@ theorem iSupIndep.subtype_ne_bot_le_rank [Nontrivial R]
have : LinearIndependent R v := (hV.comp Subtype.coe_injective).linearIndependent _ hvV hv
exact this.cardinal_lift_le_rank

@[deprecated (since := "2024-11-24")]
alias CompleteLattice.Independent.subtype_ne_bot_le_rank := iSupIndep.subtype_ne_bot_le_rank

variable [Module.Finite R M] [StrongRankCondition R]

theorem iSupIndep.subtype_ne_bot_le_finrank_aux
Expand Down
2 changes: 2 additions & 0 deletions Mathlib/LinearAlgebra/Eigenspace/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -718,6 +718,8 @@ theorem eigenspaces_iSupIndep [NoZeroSMulDivisors R M] (f : End R M) :
iSupIndep f.eigenspace :=
(f.independent_genEigenspace 1).mono fun _ ↦ le_rfl

@[deprecated (since := "2024-11-24")] alias eigenspaces_independent := eigenspaces_iSupIndep

/-- Eigenvectors corresponding to distinct eigenvalues of a linear operator are linearly
independent. -/
theorem eigenvectors_linearIndependent' {ι : Type*} [NoZeroSMulDivisors R M]
Expand Down
3 changes: 3 additions & 0 deletions Mathlib/LinearAlgebra/LinearIndependent.lean
Original file line number Diff line number Diff line change
Expand Up @@ -928,6 +928,9 @@ theorem LinearIndependent.iSupIndep_span_singleton (hv : LinearIndependent R v)
ext
simp

@[deprecated (since := "2024-11-24")]
alias LinearIndependent.independent_span_singleton := LinearIndependent.iSupIndep_span_singleton

variable (R)

theorem exists_maximal_independent' (s : ι → M) :
Expand Down
3 changes: 3 additions & 0 deletions Mathlib/LinearAlgebra/Projectivization/Independence.lean
Original file line number Diff line number Diff line change
Expand Up @@ -66,6 +66,9 @@ theorem independent_iff_iSupIndep : Independent f ↔ iSupIndep fun i => (f i).s
· simpa only [Function.comp_apply, submodule_eq] using Submodule.mem_span_singleton_self _
· exact rep_nonzero (f i)

@[deprecated (since := "2024-11-24")]
alias independent_iff_completeLattice_independent := independent_iff_iSupIndep

/-- A linearly dependent family of nonzero vectors gives a dependent family of points
in projective space. -/
inductive Dependent : (ι → ℙ K V) → Prop
Expand Down
40 changes: 39 additions & 1 deletion Mathlib/Order/CompactlyGenerated/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -293,16 +293,26 @@ theorem WellFoundedGT.finite_of_sSupIndep [WellFoundedGT α] {s : Set α}
rw [← hs, eq_comm, inf_eq_left]
exact le_sSup hx₀

@[deprecated (since := "2024-11-24")]
alias CompleteLattice.WellFoundedGT.finite_of_setIndependent := WellFoundedGT.finite_of_sSupIndep

theorem WellFoundedGT.finite_ne_bot_of_iSupIndep [WellFoundedGT α]
{ι : Type*} {t : ι → α} (ht : iSupIndep t) : Set.Finite {i | t i ≠ ⊥} := by
refine Finite.of_finite_image (Finite.subset ?_ (image_subset_range t _)) ht.injOn
exact WellFoundedGT.finite_of_sSupIndep ht.sSupIndep_range

@[deprecated (since := "2024-11-24")]
alias CompleteLattice.WellFoundedGT.finite_ne_bot_of_independent :=
WellFoundedGT.finite_ne_bot_of_iSupIndep

theorem WellFoundedGT.finite_of_iSupIndep [WellFoundedGT α] {ι : Type*}
{t : ι → α} (ht : iSupIndep t) (h_ne_bot : ∀ i, t i ≠ ⊥) : Finite ι :=
haveI := (WellFoundedGT.finite_of_sSupIndep ht.sSupIndep_range).to_subtype
Finite.of_injective_finite_range (ht.injective h_ne_bot)

@[deprecated (since := "2024-11-24")]
alias CompleteLattice.WellFoundedGT.finite_of_independent := WellFoundedGT.finite_of_iSupIndep

theorem WellFoundedLT.finite_of_sSupIndep [WellFoundedLT α] {s : Set α}
(hs : sSupIndep s) : s.Finite := by
by_contra inf
Expand All @@ -315,16 +325,26 @@ theorem WellFoundedLT.finite_of_sSupIndep [WellFoundedLT α] {s : Set α}
· exact (RelEmbedding.natGT a lt).not_wellFounded_of_decreasing_seq wellFounded_lt
exact ⟨(e i).2.1, fun h ↦ n.lt_succ_self.not_le <| hi.trans_eq <| e.2 <| Subtype.val_injective h⟩

@[deprecated (since := "2024-11-24")]
alias CompleteLattice.WellFoundedLT.finite_of_setIndependent := WellFoundedLT.finite_of_sSupIndep

theorem WellFoundedLT.finite_ne_bot_of_iSupIndep [WellFoundedLT α]
{ι : Type*} {t : ι → α} (ht : iSupIndep t) : Set.Finite {i | t i ≠ ⊥} := by
refine Finite.of_finite_image (Finite.subset ?_ (image_subset_range t _)) ht.injOn
exact WellFoundedLT.finite_of_sSupIndep ht.sSupIndep_range

@[deprecated (since := "2024-11-24")]
alias CompleteLattice.WellFoundedLT.finite_ne_bot_of_independent :=
WellFoundedLT.finite_ne_bot_of_iSupIndep

theorem WellFoundedLT.finite_of_iSupIndep [WellFoundedLT α] {ι : Type*}
{t : ι → α} (ht : iSupIndep t) (h_ne_bot : ∀ i, t i ≠ ⊥) : Finite ι :=
haveI := (WellFoundedLT.finite_of_sSupIndep ht.sSupIndep_range).to_subtype
Finite.of_injective_finite_range (ht.injective h_ne_bot)

@[deprecated (since := "2024-11-24")]
alias CompleteLattice.WellFoundedLT.finite_of_independent := WellFoundedLT.finite_of_iSupIndep

/-- A complete lattice is said to be compactly generated if any
element is the `sSup` of compact elements. -/
class IsCompactlyGenerated (α : Type*) [CompleteLattice α] : Prop where
Expand Down Expand Up @@ -427,6 +447,9 @@ theorem sSupIndep_iff_finite {s : Set α} :
· rw [Finset.coe_insert, Set.insert_subset_iff]
exact ⟨ha, Set.Subset.trans ht diff_subset⟩⟩

@[deprecated (since := "2024-11-24")]
alias CompleteLattice.setIndependent_iff_finite := sSupIndep_iff_finite

lemma iSupIndep_iff_supIndep_of_injOn {ι : Type*} {f : ι → α}
(hf : InjOn f {i | f i ≠ ⊥}) :
iSupIndep f ↔ ∀ (s : Finset ι), s.SupIndep f := by
Expand All @@ -450,6 +473,9 @@ lemma iSupIndep_iff_supIndep_of_injOn {ι : Type*} {f : ι → α}
rw [Finset.supIndep_iff_disjoint_erase] at h
exact h i (Finset.mem_insert_self i _)

@[deprecated (since := "2024-11-24")]
alias CompleteLattice.independent_iff_supIndep_of_injOn := iSupIndep_iff_supIndep_of_injOn

theorem sSupIndep_iUnion_of_directed {η : Type*} {s : η → Set α}
(hs : Directed (· ⊆ ·) s) (h : ∀ i, sSupIndep (s i)) :
sSupIndep (⋃ i, s i) := by
Expand All @@ -464,11 +490,17 @@ theorem sSupIndep_iUnion_of_directed {η : Type*} {s : η → Set α}
exfalso
exact hη ⟨i⟩

@[deprecated (since := "2024-11-24")]
alias CompleteLattice.setIndependent_iUnion_of_directed := sSupIndep_iUnion_of_directed

theorem iSupIndep_sUnion_of_directed {s : Set (Set α)} (hs : DirectedOn (· ⊆ ·) s)
(h : ∀ a ∈ s, sSupIndep a) : sSupIndep (⋃₀ s) := by
rw [Set.sUnion_eq_iUnion]
exact sSupIndep_iUnion_of_directed hs.directed_val (by simpa using h)

@[deprecated (since := "2024-11-24")]
alias CompleteLattice.independent_sUnion_of_directed := iSupIndep_sUnion_of_directed

end

namespace CompleteLattice
Expand Down Expand Up @@ -496,7 +528,7 @@ alias _root_.WellFounded.isSupClosedCompact := WellFoundedGT.isSupClosedCompact
@[deprecated (since := "2024-10-07")]
alias WellFounded.finite_of_setIndependent := WellFoundedGT.finite_of_sSupIndep
@[deprecated (since := "2024-10-07")]
alias WellFounded.finite_ne_bot_of_iSupIndep := WellFoundedGT.finite_ne_bot_of_iSupIndep
alias WellFounded.finite_ne_bot_of_independent := WellFoundedGT.finite_ne_bot_of_iSupIndep
@[deprecated (since := "2024-10-07")]
alias WellFounded.finite_of_independent := WellFoundedGT.finite_of_iSupIndep
@[deprecated (since := "2024-10-07")]
Expand Down Expand Up @@ -632,11 +664,17 @@ theorem exists_sSupIndep_isCompl_sSup_atoms (h : sSup { a : α | IsAtom a } =
· exact s_atoms x hx
· exact ha

@[deprecated (since := "2024-11-24")]
alias exists_setIndependent_isCompl_sSup_atoms := exists_sSupIndep_isCompl_sSup_atoms

theorem exists_sSupIndep_of_sSup_atoms_eq_top (h : sSup { a : α | IsAtom a } = ⊤) :
∃ s : Set α, sSupIndep s ∧ sSup s = ⊤ ∧ ∀ ⦃a⦄, a ∈ s → IsAtom a :=
let ⟨s, s_ind, s_top, s_atoms⟩ := exists_sSupIndep_isCompl_sSup_atoms h ⊥
⟨s, s_ind, eq_top_of_isCompl_bot s_top.symm, s_atoms⟩

@[deprecated (since := "2024-11-24")]
alias exists_setIndependent_of_sSup_atoms_eq_top := exists_sSupIndep_of_sSup_atoms_eq_top

/-- See [Theorem 6.6][calugareanu]. -/
theorem complementedLattice_of_sSup_atoms_eq_top (h : sSup { a : α | IsAtom a } = ⊤) :
ComplementedLattice α :=
Expand Down
Loading

0 comments on commit 26d2dba

Please sign in to comment.