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chore(Data): rename setOf to Set.ofPred#41507

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YaelDillies:set_of_pred
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chore(Data): rename setOf to Set.ofPred#41507
YaelDillies wants to merge 6 commits into
leanprover-community:masterfrom
YaelDillies:set_of_pred

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@YaelDillies

@YaelDillies YaelDillies commented Jul 8, 2026

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This is in prevision of making Set a one-field structure. ofPred will then be the constructor.

Generated by Claude Opus then reviewed line-by-line by myself.

Assisted-by: Claude Opus 4.8


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This is in prevision of making `Set` a one-field structure. `ofPred` will then be the constructor.
@YaelDillies YaelDillies changed the title chore(Data): rename setOf to Set.ofPred` chore(Data): rename setOf to Set.ofPred Jul 8, 2026
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PR summary 5f06fbf1f8

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff (regex)

+ AddAction.properVAdd_iff_isCompact_setOf_inter_nonempty
+ Antitone.countable_setOfPred_two_preimages
+ AntitoneOn.countable_setOfPred_two_preimages
+ ContinuousMap.dense_setOfPred_contDiff
+ Convex.setOfPred_const_imp
+ Convex.setOfPred_gauge_le
+ Countable.ofPred_finite
+ DefinableFun.ofPred_eq
+ DefinableFun.ofPred_eq_const
+ Equicontinuous.isClosed_setOfPred_tendsto
+ Filter.TotallyBounded.isCompact_setOfPred_clusterPt
+ Filter.TotallyBounded.totallyBounded_setOfPred_clusterPt
+ Ideal.setOfPred_isPrincipal_wellFoundedOn_gt
+ Indep.closure_eq_setOfPred_isBasis_insert
+ Indep.isBasis_setOfPred_insert_isBasis
+ IsAntichain.eq_setOfPred_maximal
+ IsAntichain.eq_setOfPred_minimal
+ IsClosed.setOfPred_mapsTo
+ IsGδ.setOfPred_continuousAt
+ IsGδ.setOfPred_irrational
+ IsGδ.setOfPred_liouville
+ IsHamiltonian.setOfPred_support
+ LHom.setOfPred_realize_onFormula
+ LinearOrderedAddCommGroup.wellFoundedOn_setOfPred_ge_gt_iff_nonempty_discrete
+ LinearOrderedAddCommGroup.wellFoundedOn_setOfPred_le_lt_iff_nonempty_discrete
+ LinearOrderedCommGroup.wellFoundedOn_setOfPred_ge_gt_iff_nonempty_discrete
+ LinearOrderedCommGroup.wellFoundedOn_setOfPred_le_lt_iff_nonempty_discrete
+ LinearOrderedCommGroupWithZero.wellFoundedOn_setOfPred_ge_gt_iff_nonempty_discrete_of_ne_zero
+ LinearOrderedCommGroupWithZero.wellFoundedOn_setOfPred_le_lt_iff_nonempty_discrete_of_ne_zero
+ MeasurableSet.setOfPred_finite
+ MeasurableSet.setOfPred_infinite
+ MeromorphicOn.codiscreteWithin_setOfPred_ne_zero
+ Monotone.countable_setOfPred_two_preimages
+ MonotoneOn.countable_setOfPred_two_preimages
+ MulAction.properSMul_iff_isCompact_setOfPred_inter_nonempty
+ Nat.isSemilinearSet_setOfPred_eq
+ Nat.isSemilinearSet_setOfPred_mulVec_eq
+ ProperSMul.isCompact_setOfPred_inter_nonempty
+ ProperVAdd.isCompact_setOf_inter_nonempty
+ Ring.KrullDimLE.minimalPrimes_eq_setOfPred_isMaximal
+ Ring.KrullDimLE.minimalPrimes_eq_setOfPred_isPrime
+ Set.coe_ofPred
+ Set.ofPred
+ Valuation.exists_setOfPred_restrict_le_iff
+ Walk.setOfPred_length_eq_add_one
+ Walk.setOfPred_length_eq_zero
+ Walk.setOfPred_length_eq_zero_of_ne
+ WfDvdMonoid.of_setOfPred_isPrincipal_wellFoundedOn_gt
+ _root_.Irreducible.maximalIdeal_eq_setOfPred_le_v_coe
+ _root_.Irreducible.maximalIdeal_pow_eq_setOfPred_le_v_coe_pow
+ _root_.Set.Ioc_mem_ofPred_Ioc_le
+ _root_.convex_setOfPred_holderOnWith
+ _root_.convex_setOfPred_holderWith
+ addSubmonoid_closure_setOfPred_eq_monomial
+ add_closure_setOfPred_eq_single
+ ae_finite_setOfPred_mem
+ aeconst_of_dense_setOfPred_preimage_smul_ae
+ aeconst_of_dense_setOfPred_preimage_smul_eq
+ aeconst_of_dense_setOf_preimage_vadd_ae
+ aeconst_of_dense_setOf_preimage_vadd_eq
+ antitone_ofPred
+ bddAbove_setOfPred_infinite_setOfPred_apply_eq
+ bddAbove_setOfPred_k_lt_card
+ closure_inter_setOfPred_isNonloop_eq
+ closure_setOfPred_im_lt
+ closure_setOfPred_lt_im
+ closure_setOfPred_lt_re
+ closure_setOfPred_re_lt
+ codiscreteWithin_setOfPred_analyticOrderAt_eq_zero_or_top
+ codiscreteWithin_setOfPred_meromorphicOrderAt_eq_zero_or_top
+ codiscrete_setOfPred_analyticOrderAt_eq_zero_or_top
+ codiscrete_setOfPred_meromorphicOrderAt_eq_zero_or_top
+ coe_setOfPred
+ coe_span_singleton_eq_setOfPred_le_v_algebraMap
+ coe_span_singleton_eq_setOfPred_le_v_coe
+ compl_image_ofPred
+ compl_ofPred
+ compl_setOfPred_mem
+ countable_ofPred_finite_subset
+ countable_ofPred_nonempty_of_disjoint
+ countable_setOfPred_covBy_right
+ countable_setOfPred_isolated_left
+ countable_setOfPred_isolated_left_within
+ countable_setOfPred_isolated_right
+ countable_setOfPred_isolated_right_within
+ countable_setOf_covBy_left
+ diagSet_eq_setOfPred_isDiag
+ edgeSet_eq_setOfPred_exists_isLink
+ eq_mem_ofPred
+ eq_setOfPred_le_sSup_and_isAtom
+ equivSetOfPred
+ exists_infinite_setOfPred_apply_eq
+ exists_isSemilinearSet_setOfPred_le
+ finite_setOfPred_absNorm_eq
+ finite_setOfPred_absNorm_le
+ finite_setOfPred_absNorm_le₀
+ finite_setOfPred_addOrderOf_eq
+ finite_setOfPred_apply_eq_iff_not_small
+ finite_setOfPred_apply_eq_k_add_one
+ finite_setOfPred_bounded
+ finite_setOfPred_isIntegral_nat_mul_and_mulHeight₁_le
+ finite_setOfPred_isMin
+ finite_setOfPred_isRestriction
+ finite_setOfPred_isRoot
+ finite_setOfPred_k_lt_card
+ finite_setOfPred_logHeight₁_le
+ finite_setOfPred_matroid
+ finite_setOfPred_mem
+ finite_setOfPred_mulHeight_nat_le
+ finite_setOfPred_mulHeight₁_le
+ finite_setOfPred_pattern_support_eq
+ finite_setOfPred_prod_infinitePlace_iSup_le
+ finite_setOfPred_setGcd_dvd_and_mem_span
+ frontier_setOfPred_im_le
+ frontier_setOfPred_im_lt
+ frontier_setOfPred_le_im
+ frontier_setOfPred_le_re
+ frontier_setOfPred_le_re_and_im_le
+ frontier_setOfPred_le_re_and_le_im
+ frontier_setOfPred_lt_im
+ frontier_setOfPred_lt_re
+ frontier_setOfPred_re_le
+ frontier_setOfPred_re_lt
+ generateFrom_setOfPred_isOpen
+ iInter_ofPred
+ iInter_setOfPred_subset
+ iUnion_ofPred
+ iUnion_smul_eq_ofPred_exists
+ iUnion_vadd_eq_setOf_exists
+ image_antitone_setOfPred_minimal
+ image_antitone_setOfPred_minimal_mem
+ image_antitone_setOf_maximal
+ image_antitone_setOf_maximal_mem
+ image_monotone_setOfPred_minimal
+ image_monotone_setOfPred_minimal_mem
+ image_monotone_setOf_maximal
+ image_monotone_setOf_maximal_mem
+ image_setOf_maximal
+ infinite_setOfPred_apply_eq_anti
+ infinite_setOfPred_apply_eq_iff_small
+ infinite_setOfPred_apply_eq_k
+ infinite_setOfPred_apply_eq_one
+ infinite_setOfPred_prime
+ infinite_setOfPred_prime_and_eq_mod
+ infinite_setOfPred_prime_and_modEq
+ infinite_setOfPred_prime_modEq_one
+ infinite_setOfPred_pseudoprimes
+ injOn_setOfPred_apply_add_one_eq_of_M_le
+ injOn_setOfPred_mem_Icc_setOfPred_lower_eq
+ instance {k : ℕ} : Fintype (fiber α k) := inferInstanceAs <| Fintype (Set.ofPred _)
+ integral_lt_integral_of_ae_le_of_measure_setOfPred_lt_ne_zero
+ inter_ofPred_eq_sep
+ inter_preimage_setOfPred_minimal_eq_of_subset
+ inter_preimage_setOf_maximal_eq_of_subset
+ interior_setOfPred_eq
+ interior_setOfPred_im_le
+ interior_setOfPred_le_im
+ interior_setOfPred_le_re
+ interior_setOfPred_re_le
+ inv_ofPred
+ isClopen_setOfPred_analyticOrderAt_eq_top
+ isClopen_setOfPred_mapsTo
+ isClopen_setOfPred_meromorphicOrderAt_eq_top
+ isClopen_setOfPred_rel
+ isClosed_setOfPred_blockTriangular
+ isClosed_setOfPred_clusterPt
+ isClosed_setOfPred_concaveOn
+ isClosed_setOfPred_convexOn
+ isClosed_setOfPred_iff
+ isClosed_setOfPred_inseparable
+ isClosed_setOfPred_isCompactOperator
+ isClosed_setOfPred_lipschitzOnWith
+ isClosed_setOfPred_lipschitzWith
+ isClosed_setOfPred_map_inv
+ isClosed_setOfPred_map_mul
+ isClosed_setOfPred_map_one
+ isClosed_setOfPred_map_smul
+ isClosed_setOfPred_mapsTo
+ isClosed_setOfPred_preimage_ae_eq
+ isClosed_setOfPred_specializes
+ isClosed_setOfPred_sublevelLeft_subset
+ isClosed_setOfPred_tendsto_birkhoffAverage
+ isClosed_setOf_map_add
+ isClosed_setOf_map_neg
+ isClosed_setOf_map_zero
+ isCofinal_setOfPred_imp_lt
+ isCompact_setOfPred_finiteMeasure_eq_of_compactSpace
+ isCompact_setOfPred_finiteMeasure_le_of_compactSpace
+ isCompact_setOfPred_finiteMeasure_le_of_isCompact
+ isCompact_setOfPred_finiteMeasure_mass_eq_compl_isCompact_le
+ isCompact_setOfPred_finiteMeasure_mass_le_compl_isCompact_le
+ isCompact_setOfPred_probabilityMeasure_mass_eq_compl_isCompact_le
+ isComplete_setOfPred_eqOn
+ isConnected_setOfPred_sOppSide
+ isConnected_setOfPred_sSameSide
+ isConnected_setOfPred_sameRay
+ isConnected_setOfPred_sameRay_and_ne_zero
+ isConnected_setOfPred_wOppSide
+ isConnected_setOfPred_wSameSide
+ isLowerSet_setOfPred
+ isOpen_setOfPred_affineIndependent
+ isOpen_setOfPred_disjoint_nhds_nhds
+ isOpen_setOfPred_eventually_nhds
+ isOpen_setOfPred_eventually_nhdsWithin
+ isOpen_setOfPred_harmonicAt
+ isOpen_setOfPred_linearIndependent
+ isOpen_setOfPred_mapsTo
+ isOpen_setOfPred_mem
+ isOpen_setOfPred_mem_nhds_and_isMaxOn_norm
+ isOpen_setOfPred_nat_le_rank
+ isOpen_setOfPred_range_subset
+ isOpen_setOf_rel
+ isPreconnected_setOfPred_sOppSide
+ isPreconnected_setOfPred_sSameSide
+ isPreconnected_setOfPred_wOppSide
+ isPreconnected_setOfPred_wSameSide
+ isPrincipal_iff_exists_eq_setOfPred_valuation_le
+ isSemilinearSet_setOfPred_eq
+ isStarProjection_iff_mem_extremePoints_setOfPred_nonneg_inter_unitClosedBall
+ isUpperSet_setOfPred
+ maximalIdeal_eq_setOfPred_le_v_algebraMap
+ maximalIdeal_pow_eq_setOfPred_le_v_algebraMap_pow
+ measurableSet_setOfPred
+ measurable_setOfPred
+ measure_setOfPred_frequently_eq_zero
+ mem_ofPred
+ mem_ofPred_eq
+ monotone_ofPred
+ neg_setOf
+ nonempty_setOfPred_infinite_setOfPred_apply_eq
+ notMem_ofPred_iff
+ not_bddAbove_setOfPred_isPrincipal
+ not_bddAbove_setOfPred_prime
+ ofPred_and
+ ofPred_bijective
+ ofPred_bot
+ ofPred_eq_eq_singleton
+ ofPred_eq_eq_singleton'
+ ofPred_exists
+ ofPred_false
+ ofPred_forall
+ ofPred_inj
+ ofPred_injective
+ ofPred_inter_eq_sep
+ ofPred_mem_eq
+ ofPred_mem_list_eq_replicate
+ ofPred_mem_list_eq_singleton_of_nodup
+ ofPred_or
+ ofPred_subset
+ ofPred_subset_ofPred
+ ofPred_subset_ofPred_of_imp
+ ofPred_top
+ ofPred_true
+ ordConnected_setOfPred_closedEBall_subset
+ ordConnected_setOfPred_eball_subset
+ polarSubmodule_eq_setOfPred
+ preimage_ofPred_eq
+ preimage_setOfPred_dist
+ schnirelmannDensity_setOfPred_Odd
+ schnirelmannDensity_setOfPred_even
+ schnirelmannDensity_setOfPred_mod_eq_one
+ schnirelmannDensity_setOfPred_modeq_one
+ schnirelmannDensity_setOfPred_prime
+ self_subset_setOfPred_gauge_le_one
+ sep_ofPred
+ sep_subset_ofPred
+ setOfMaximalIsoSetOfMinimal
+ setOfPred
+ setOfPredMinimalIsoSetOfPredMaximal
+ setOfPred_apply_eq_of_apply_big_of_N'_le
+ setOfPred_apply_symm_eq_image_setOfPred
+ setOfPred_dep_eq
+ setOfPred_dual_isBase_eq
+ setOfPred_gauge_le_eq
+ setOfPred_gauge_lt_eq
+ setOfPred_gauge_lt_one_eq_interior
+ setOfPred_gauge_lt_one_eq_self_of_isOpen
+ setOfPred_gauge_lt_one_subset_self
+ setOfPred_indep_eq
+ setOfPred_index_eq_univ
+ setOfPred_isClosed_eq_range_closure
+ setOfPred_isExtremePt_eq_bot
+ setOfPred_isExtremePt_isAdmissible
+ setOfPred_isMaximal_finite
+ setOfPred_isNonloop_eq
+ setOfPred_isOpen
+ setOfPred_isOpen_iSup
+ setOfPred_isOpen_injective
+ setOfPred_isOpen_sSup
+ setOfPred_isOpen_sup
+ setOfPred_isPreconnected_eq_of_ordered
+ setOfPred_isPreconnected_subset_of_ordered
+ setOfPred_isPrime_finite
+ setOfPred_isUnit_inter_mul_comm
+ setOfPred_liouvilleWith_subset_aux
+ setOfPred_liouville_eq_iInter_iUnion
+ setOfPred_liouville_eq_irrational_inter_iInter_iUnion
+ setOfPred_maximal_antichain
+ setOfPred_mem
+ setOfPred_mem_cons
+ setOfPred_mem_eq
+ setOfPred_mem_eq_empty_iff
+ setOfPred_mem_eq_univ_iff
+ setOfPred_mem_integer_eq_closedBall
+ setOfPred_minimal_antichain
+ setOfPred_minimal_subset
+ setOfPred_odd_degree_eq
+ setOfPred_polynomial_valuation_lt_one_and_ne_zero_nonempty
+ setOfPred_pow_dvd_eq_Icc_factorization
+ setOfPred_riemannianEDist_lt_subset_nhds
+ setOfPred_root_add_zsmul_eq_Icc_of_linearIndependent
+ setOfPred_root_add_zsmul_mem_eq_Icc
+ setOfPred_root_sub_zsmul_mem_eq_Icc
+ setOfPred_sOppSide_eq_image2
+ setOfPred_sSameSide_eq_image2
+ setOfPred_sublevelLeft_subset
+ setOfPred_subset_eq_empty_iff
+ setOfPred_subset_eq_univ_iff
+ setOfPred_wOppSide_eq_image2
+ setOfPred_wSameSide_eq_image2
+ setOf_maximal_subset
+ span_setOfPred_mem_eq_top
+ subset_ofPred
+ subsingleton_setOfPred_mem_iff_pairwise_disjoint
+ surjective_count_of_infinite_setOfPred
+ volume_iUnion_setOfPred_liouvilleWith
+ volume_setOfPred_liouville
++ dense_setOfPred_finite
++ image_setOfPred_minimal
++ isClosed_setOfPred_continuous
++ isClosed_setOfPred_totallyBounded
++ setOfPred_mem_sym2
++ toFinset_ofPred
++-- dense_setOf_finite
++-- image_setOf_minimal
++-- isClosed_setOf_continuous
++-- isClosed_setOf_totallyBounded
++-- setOf
++-- setOf_mem_eq
++-- setOf_mem_sym2
++-- toFinset_setOf
- Nat.isSemilinearSet_setOf_eq
- _root_.Irreducible.maximalIdeal_eq_setOf_le_v_coe
- _root_.Irreducible.maximalIdeal_pow_eq_setOf_le_v_coe_pow
- _root_.Set.Ioc_mem_setOf_Ioc_le
- _root_.convex_setOf_holderOnWith
- _root_.convex_setOf_holderWith
- exists_isSemilinearSet_setOf_le
- finite_setOf_bounded
- finite_setOf_isIntegral_nat_mul_and_mulHeight₁_le
- instance {k : ℕ} : Fintype (fiber α k) := inferInstanceAs <| Fintype (setOf _)

You can run this locally as follows
## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean -- pending)

Computed after the build finishes.


No changes to strong technical debt.

No changes to weak technical debt.

Current commit 5f06fbf1f8
Reference commit 2f35248703

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@YaelDillies YaelDillies added t-data Data (lists, quotients, numbers, etc) LLM-generated PRs with substantial input from LLMs - review accordingly labels Jul 9, 2026

@themathqueen themathqueen left a comment

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Don't think there's a need for both Generated by: and Assisted by:, either one suffices, I think

Comment thread Archive/Wiedijk100Theorems/Konigsberg.lean Outdated
@themathqueen

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Note that this conflicts with #39110, namely the naming Set.ofPred there is used as an equivalence rather than the renaming of setOf. And these PRs in general take over that PR, so I think it's safe to say we can close that?
I'd like to at least wait for CI to pass here before closing anything though.

@YaelDillies

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#39110 is doing eps of the required work. I have the whole refactor building locally.

@YaelDillies

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Don't think there's a need for both Generated by: and Assisted by:, either one suffices, I think

The former is an informal description of how I used LLM tools. The latter is in a machine-readable format that follows the Linux kernel contribution convention.

@SnirBroshi

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I think merging the small bit will help the review & merge effort (compared to a +3k PR), but I should first fix any incompatibilities with your full PR (and also solve conflicts on my side so that you don't get any).

Does it not?

@YaelDillies

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I think merging the small bit will help the review & merge effort (compared to a +3k PR)

I doubt so, because your small bits are going against what I am doing in #41506. But don't worry I am going to extract the fixes that can be made on master 😉

@themathqueen

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@SnirBroshi, I don't think you should waste time on trying to make that PR more compatible with these (it's far more work than you think, the full PR is huge). Your PR should've been merged 2 months ago (but Yury got busy, I'm assuming), but now with these new PRs, I'm not so sure anymore. I haven't checked, but I think the same stuff is basically in Yaël's PR anyway?

Anyway, I think this PR would be easier to review than the rest since it's just a renaming PR. I'll set aside an hour of review time to do this later when it's fully ready.

Comment on lines 80 to 87
/-lemma autEmbedding_range :
Set.range (autEmbedding F) =
⋂ (f : Arrow C), { a | F.map f.hom ≫ (a f.right).hom = (a f.left).hom ≫ F.map f.hom } := by
ext a
simp only [Set.mem_range, id_obj, Set.mem_iInter, Set.mem_setOf_eq]
simp only [Set.mem_range, id_obj, Set.mem_iInter, Set.mem_ofPred_eq]
refine ⟨fun ⟨σ, h⟩ i ↦ h.symm ▸ σ.hom.naturality i.hom, fun h ↦ ?_⟩
· use NatIso.ofComponents a (fun {X Y} f ↦ h ⟨X, Y, f⟩)
rfl-/

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do you know why this is commented out?

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No clue, but probably out of scope to touch it in this PR?

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Yeah, definitely out of scope

Comment thread Mathlib/Geometry/Manifold/Riemannian/Basic.lean Outdated
Comment thread Mathlib/ModelTheory/Arithmetic/Presburger/Semilinear/Basic.lean Outdated
Comment thread Mathlib/ModelTheory/Arithmetic/Presburger/Semilinear/Basic.lean Outdated
Comment thread Mathlib/ModelTheory/Semantics.lean Outdated
Comment thread Mathlib/ModelTheory/Substructures.lean Outdated
Comment thread Mathlib/Data/Set/Insert.lean
Comment thread Mathlib/Data/Sym/Sym2.lean Outdated
Comment thread Mathlib/NumberTheory/Transcendental/Liouville/Residual.lean
@@ -258,6 +258,9 @@ def abbreviationDict : Std.HashMap String String := .ofList [

("neTop", "NeBot"),
("decidableSucc", "DecidablePred"),
-- `Set.ofPred` is not dual to `Set.ofSucc`

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what is Set.ofSucc?

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It doesn't exist and that's the point. If you don't add the line below (which we can't see here, please make multiline comments!), then to_dual tries translating ofPred to ofSucc.

@themathqueen themathqueen added the awaiting-author A reviewer has asked the author a question or requested changes. label Jul 10, 2026
@SnirBroshi

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Hey, could you also rename List.set_of_mem_cons and Set.compl_image_set_of?
I wanted to fix their set_of to setOf, but if this PR will merge soon we can avoid double deprecations.

@YaelDillies YaelDillies removed the awaiting-author A reviewer has asked the author a question or requested changes. label Jul 13, 2026
Comment on lines +261 to +263
-- `Set.ofPred` is not dual to `Set.ofSucc`
("ofSucc", "OfPred"),
("setOfSucc", "SetOfPred"),

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Sorry for not making a multiline comment before.

Anyway, I see. Let's keep this comment unresolved for other reviewers (especially because I don't fully understand this).

@themathqueen

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I think there are some things to fix outside of mathlib btw, in docs/100.yaml, docs/1000.yaml and docs/undergrad.yaml

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3 participants