Commit 2026-08-24 10:14 2c99b7bf

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refactor(Data/Set): split long file Lattice.lean (#43030) Split this > 1500 line file into 4 smaller files:

  • Mathlib.Data.Set.Lattice.Indexed (655 lines): indexed unions and intersections, monotonicity, complements, proposition indexing, and reindexing.
  • Mathlib.Data.Set.Lattice.Bounded (645 lines): bounded unions and intersections, sUnion/sInter, products, directed unions, and surjective reindexing.
  • Mathlib.Data.Set.Lattice.Disjoint (139 lines): disjoint indexed families and equivalences with dependent sums.
  • Mathlib.Data.Set.Lattice.Order (125 lines): intervals, natural-number tails, and interaction with complete-lattice suprema and infima. I tried to do the usual "deprecation stub in a follow-up PR" trick to get git to associate the pre-split history of the file with one of the post-split files, but it doesn't seem to have worked, probably because none of the post-split files match enough of the pre-split file. So I'm merging the deprecation-stub PR back into this one.

Estimated changes

deleted theorem Antitone.iInter_nat_add
deleted theorem Monotone.iUnion_nat_add
deleted theorem Set.BijOn.iInter_comp
deleted theorem Set.BijOn.iInter_congr
deleted theorem Set.BijOn.iUnion_comp
deleted theorem Set.BijOn.iUnion_congr
deleted theorem Set.Ici_iSup
deleted theorem Set.Ici_iSup₂
deleted theorem Set.Ici_sSup
deleted theorem Set.Iic_iInf
deleted theorem Set.Iic_iInf₂
deleted theorem Set.Iic_sInf
deleted theorem Set.Nonempty.of_sUnion
deleted theorem Set.Sigma.univ
deleted theorem Set.biInter_and'
deleted theorem Set.biInter_and
deleted theorem Set.biInter_const
deleted theorem Set.biInter_empty
deleted theorem Set.biInter_eq_iInter
deleted theorem Set.biInter_ge
deleted theorem Set.biInter_ge_eq_iInf
deleted theorem Set.biInter_gt_eq_iInf
deleted theorem Set.biInter_iUnion
deleted theorem Set.biInter_insert
deleted theorem Set.biInter_inter
deleted theorem Set.biInter_le
deleted theorem Set.biInter_le_eq_iInter
deleted theorem Set.biInter_lt_eq_iInter
deleted theorem Set.biInter_mono
deleted theorem Set.biInter_pair
deleted theorem Set.biInter_singleton
deleted theorem Set.biInter_subset_of_mem
deleted theorem Set.biInter_union
deleted theorem Set.biInter_univ
deleted theorem Set.biUnion_and'
deleted theorem Set.biUnion_and
deleted theorem Set.biUnion_const
deleted theorem Set.biUnion_empty
deleted theorem Set.biUnion_eq_iUnion
deleted theorem Set.biUnion_ge
deleted theorem Set.biUnion_ge_eq_iUnion
deleted theorem Set.biUnion_gt_eq_iUnion
deleted theorem Set.biUnion_iUnion
deleted theorem Set.biUnion_insert
deleted theorem Set.biUnion_le
deleted theorem Set.biUnion_le_eq_iUnion
deleted theorem Set.biUnion_lt_eq_iUnion
deleted theorem Set.biUnion_mono
deleted theorem Set.biUnion_of_singleton
deleted theorem Set.biUnion_pair
deleted theorem Set.biUnion_self
deleted theorem Set.biUnion_singleton
deleted theorem Set.biUnion_union
deleted theorem Set.biUnion_univ
deleted theorem Set.biUnion_univ_pi
deleted theorem Set.compl_iInter
deleted theorem Set.compl_iInter₂
deleted theorem Set.compl_iUnion
deleted theorem Set.compl_iUnion₂
deleted theorem Set.compl_sInter
deleted theorem Set.compl_sUnion
deleted theorem Set.directedOn_iUnion
deleted theorem Set.directedOn_sUnion
deleted theorem Set.disjoint_iUnion_left
deleted theorem Set.disjoint_iUnion_right
deleted theorem Set.disjoint_sUnion_left
deleted theorem Set.disjoint_sUnion_right
deleted theorem Set.exists_mem_biUnion
deleted theorem Set.exists_mem_iUnion
deleted theorem Set.exists_mem_iUnion₂
deleted theorem Set.forall_mem_biUnion
deleted theorem Set.forall_mem_iUnion
deleted theorem Set.forall_mem_iUnion₂
deleted theorem Set.iInf_eq_dif
deleted theorem Set.iInter_and
deleted theorem Set.iInter_coe_set
deleted theorem Set.iInter_comm
deleted theorem Set.iInter_congr
deleted theorem Set.iInter_congr_Prop
deleted theorem Set.iInter_const
deleted theorem Set.iInter_dite
deleted theorem Set.iInter_eq_const
deleted theorem Set.iInter_eq_empty_iff
deleted theorem Set.iInter_eq_if
deleted theorem Set.iInter_eq_univ
deleted theorem Set.iInter_exists
deleted theorem Set.iInter_false
deleted theorem Set.iInter_iInter_eq_left
deleted theorem Set.iInter_inter
deleted theorem Set.iInter_inter_distrib
deleted theorem Set.iInter_ite
deleted theorem Set.iInter_mono''
deleted theorem Set.iInter_mono'
deleted theorem Set.iInter_mono
deleted theorem Set.iInter_ofPred
deleted theorem Set.iInter_of_empty
deleted theorem Set.iInter_option
deleted theorem Set.iInter_or
deleted theorem Set.iInter_plift_down
deleted theorem Set.iInter_plift_up
deleted theorem Set.iInter_psigma'
deleted theorem Set.iInter_psigma
deleted theorem Set.iInter_sigma'
deleted theorem Set.iInter_sigma
deleted theorem Set.iInter_subset
deleted theorem Set.iInter_subset_iUnion
deleted theorem Set.iInter_subtype
deleted theorem Set.iInter_sum
deleted theorem Set.iInter_true
deleted theorem Set.iInter_union
deleted theorem Set.iInter_univ
deleted theorem Set.iInter₂_comm
deleted theorem Set.iInter₂_congr
deleted theorem Set.iInter₂_mono'
deleted theorem Set.iInter₂_mono
deleted theorem Set.iInter₂_subset
deleted theorem Set.iInter₂_union
deleted theorem Set.iUnion_and
deleted theorem Set.iUnion_coe_set
deleted theorem Set.iUnion_comm
deleted theorem Set.iUnion_congr
deleted theorem Set.iUnion_congr_Prop
deleted theorem Set.iUnion_const
deleted theorem Set.iUnion_dite
deleted theorem Set.iUnion_empty
deleted theorem Set.iUnion_eq_const
deleted theorem Set.iUnion_eq_dif
deleted theorem Set.iUnion_eq_empty
deleted theorem Set.iUnion_eq_if
deleted theorem Set.iUnion_eq_range_sigma
deleted theorem Set.iUnion_eq_univ_iff
deleted theorem Set.iUnion_exists
deleted theorem Set.iUnion_false
deleted theorem Set.iUnion_iInter_subset
deleted theorem Set.iUnion_iUnion_eq_left
deleted theorem Set.iUnion_inter
deleted theorem Set.iUnion_inter_subset
deleted theorem Set.iUnion_ite
deleted theorem Set.iUnion_le_nat
deleted theorem Set.iUnion_mono''
deleted theorem Set.iUnion_mono'
deleted theorem Set.iUnion_mono
deleted theorem Set.iUnion_nonempty_index
deleted theorem Set.iUnion_nonempty_self
deleted theorem Set.iUnion_ofPred
deleted theorem Set.iUnion_of_empty
deleted theorem Set.iUnion_of_singleton
deleted theorem Set.iUnion_option
deleted theorem Set.iUnion_or
deleted theorem Set.iUnion_plift_down
deleted theorem Set.iUnion_plift_up
deleted theorem Set.iUnion_psigma'
deleted theorem Set.iUnion_psigma
deleted theorem Set.iUnion_sdiff
deleted theorem Set.iUnion_sigma'
deleted theorem Set.iUnion_sigma
deleted theorem Set.iUnion_subset
deleted theorem Set.iUnion_subset_iff
deleted theorem Set.iUnion_subtype
deleted theorem Set.iUnion_sum
deleted theorem Set.iUnion_sumElim
deleted theorem Set.iUnion_true
deleted theorem Set.iUnion_union
deleted theorem Set.iUnion_union_distrib
deleted theorem Set.iUnion_univ_pi
deleted theorem Set.iUnion₂_comm
deleted theorem Set.iUnion₂_congr
deleted theorem Set.iUnion₂_eq_univ_iff
deleted theorem Set.iUnion₂_inter
deleted theorem Set.iUnion₂_mono'
deleted theorem Set.iUnion₂_mono
deleted theorem Set.iUnion₂_subset
deleted theorem Set.iUnion₂_subset_iff
deleted theorem Set.insert_iInter
deleted theorem Set.insert_iUnion
deleted theorem Set.inter_biInter
deleted theorem Set.inter_eq_iInter
deleted theorem Set.inter_iInter
deleted theorem Set.inter_iInter_nat_succ
deleted theorem Set.inter_iUnion
deleted theorem Set.inter_iUnion₂
deleted theorem Set.mem_biInter
deleted theorem Set.mem_biUnion
deleted theorem Set.mem_iInter_of_mem
deleted theorem Set.mem_iInter₂
deleted theorem Set.mem_iInter₂_of_mem
deleted theorem Set.mem_iUnion_of_mem
deleted theorem Set.mem_iUnion₂
deleted theorem Set.mem_iUnion₂_of_mem
deleted theorem Set.mem_sUnion_of_mem
deleted theorem Set.nonempty_biUnion
deleted theorem Set.nonempty_iInter
deleted theorem Set.nonempty_iInter₂
deleted theorem Set.nonempty_iUnion
deleted theorem Set.nonempty_sInter
deleted theorem Set.nonempty_sUnion
deleted theorem Set.ofPred_exists
deleted theorem Set.ofPred_forall
deleted theorem Set.pi_def
deleted theorem Set.pi_sdiff_pi_subset
deleted theorem Set.sInter_empty
deleted theorem Set.sInter_eq_biInter
deleted theorem Set.sInter_eq_empty_iff
deleted theorem Set.sInter_eq_iInter
deleted theorem Set.sInter_eq_univ
deleted theorem Set.sInter_iUnion
deleted theorem Set.sInter_image2
deleted theorem Set.sInter_image
deleted theorem Set.sInter_insert
deleted theorem Set.sInter_pair
deleted theorem Set.sInter_range
deleted theorem Set.sInter_singleton
deleted theorem Set.sInter_subset_of_mem
deleted theorem Set.sInter_subset_sInter
deleted theorem Set.sInter_union
deleted theorem Set.sInter_union_sInter
deleted theorem Set.sUnion_empty
deleted theorem Set.sUnion_eq_biUnion
deleted theorem Set.sUnion_eq_empty
deleted theorem Set.sUnion_eq_iUnion
deleted theorem Set.sUnion_eq_univ_iff
deleted theorem Set.sUnion_iUnion
deleted theorem Set.sUnion_image2
deleted theorem Set.sUnion_image
deleted theorem Set.sUnion_insert
deleted theorem Set.sUnion_inter_sUnion
deleted theorem Set.sUnion_mem_empty_univ
deleted theorem Set.sUnion_mono_subsets
deleted theorem Set.sUnion_mono_supsets
deleted theorem Set.sUnion_pair
deleted theorem Set.sUnion_powerset_gc
deleted theorem Set.sUnion_range
deleted theorem Set.sUnion_singleton
deleted theorem Set.sUnion_subset
deleted theorem Set.sUnion_subset_iff
deleted theorem Set.sUnion_subset_sUnion
deleted theorem Set.sUnion_union
deleted theorem Set.sdiff_iInter
deleted theorem Set.sdiff_iUnion
deleted def Set.sigmaToiUnion
deleted theorem Set.subset_biUnion_of_mem
deleted theorem Set.subset_iInter
deleted theorem Set.subset_iInter_iff
deleted theorem Set.subset_iInter₂
deleted theorem Set.subset_iInter₂_iff
deleted theorem Set.subset_iUnion
deleted theorem Set.subset_iUnion₂
deleted theorem Set.subset_powerset_iff
deleted theorem Set.subset_sInter
deleted theorem Set.subset_sInter_iff
deleted theorem Set.subset_sUnion_of_mem
deleted theorem Set.union_eq_iUnion
deleted theorem Set.union_iInter
deleted theorem Set.union_iInter₂
deleted theorem Set.union_iUnion
deleted theorem Set.union_iUnion_nat_succ
deleted theorem Set.univ_pi_eq_iInter
deleted theorem exists_sUnion
deleted theorem forall_sUnion
deleted theorem iInf_iUnion
deleted theorem iInf_sUnion
deleted theorem iSup_iUnion
deleted theorem iSup_sUnion
deleted theorem sInf_sUnion
deleted theorem sSup_iUnion
deleted theorem sSup_sUnion
added theorem Set.Nonempty.of_sUnion
added theorem Set.Sigma.univ
added theorem Set.biInter_const
added theorem Set.biInter_empty
added theorem Set.biInter_eq_iInter
added theorem Set.biInter_ge
added theorem Set.biInter_ge_eq_iInf
added theorem Set.biInter_gt_eq_iInf
added theorem Set.biInter_iUnion
added theorem Set.biInter_insert
added theorem Set.biInter_inter
added theorem Set.biInter_le
added theorem Set.biInter_mono
added theorem Set.biInter_pair
added theorem Set.biInter_singleton
added theorem Set.biInter_union
added theorem Set.biInter_univ
added theorem Set.biUnion_const
added theorem Set.biUnion_empty
added theorem Set.biUnion_eq_iUnion
added theorem Set.biUnion_ge
added theorem Set.biUnion_iUnion
added theorem Set.biUnion_insert
added theorem Set.biUnion_le
added theorem Set.biUnion_mono
added theorem Set.biUnion_pair
added theorem Set.biUnion_self
added theorem Set.biUnion_singleton
added theorem Set.biUnion_union
added theorem Set.biUnion_univ
added theorem Set.biUnion_univ_pi
added theorem Set.compl_sInter
added theorem Set.compl_sUnion
added theorem Set.directedOn_iUnion
added theorem Set.directedOn_sUnion
added theorem Set.iInter_coe_set
added theorem Set.iInter_of_empty
added theorem Set.iInter_subtype
added theorem Set.iInter₂_union
added theorem Set.iUnion_coe_set
added theorem Set.iUnion_eq_univ_iff
added theorem Set.iUnion_of_empty
added theorem Set.iUnion_subtype
added theorem Set.iUnion_sumElim
added theorem Set.iUnion_univ_pi
added theorem Set.iUnion₂_inter
added theorem Set.inter_biInter
added theorem Set.inter_eq_iInter
added theorem Set.inter_iUnion₂
added theorem Set.mem_biInter
added theorem Set.mem_biUnion
added theorem Set.mem_sUnion_of_mem
added theorem Set.nonempty_iInter
added theorem Set.nonempty_iInter₂
added theorem Set.nonempty_sInter
added theorem Set.nonempty_sUnion
added theorem Set.pi_def
added theorem Set.pi_sdiff_pi_subset
added theorem Set.sInter_empty
added theorem Set.sInter_eq_biInter
added theorem Set.sInter_eq_iInter
added theorem Set.sInter_eq_univ
added theorem Set.sInter_iUnion
added theorem Set.sInter_image2
added theorem Set.sInter_image
added theorem Set.sInter_insert
added theorem Set.sInter_pair
added theorem Set.sInter_range
added theorem Set.sInter_singleton
added theorem Set.sInter_union
added theorem Set.sUnion_empty
added theorem Set.sUnion_eq_biUnion
added theorem Set.sUnion_eq_empty
added theorem Set.sUnion_eq_iUnion
added theorem Set.sUnion_eq_univ_iff
added theorem Set.sUnion_iUnion
added theorem Set.sUnion_image2
added theorem Set.sUnion_image
added theorem Set.sUnion_insert
added theorem Set.sUnion_pair
added theorem Set.sUnion_powerset_gc
added theorem Set.sUnion_range
added theorem Set.sUnion_singleton
added theorem Set.sUnion_subset
added theorem Set.sUnion_subset_iff
added theorem Set.sUnion_union
added theorem Set.subset_sInter
added theorem Set.subset_sInter_iff
added theorem Set.union_eq_iUnion
added theorem Set.union_iInter₂
added theorem Set.univ_pi_eq_iInter
added theorem Set.BijOn.iInter_comp
added theorem Set.BijOn.iInter_congr
added theorem Set.BijOn.iUnion_comp
added theorem Set.BijOn.iUnion_congr
added theorem Set.biInter_and'
added theorem Set.biInter_and
added theorem Set.biUnion_and'
added theorem Set.biUnion_and
added theorem Set.compl_iInter
added theorem Set.compl_iInter₂
added theorem Set.compl_iUnion
added theorem Set.compl_iUnion₂
added theorem Set.exists_mem_biUnion
added theorem Set.exists_mem_iUnion
added theorem Set.forall_mem_biUnion
added theorem Set.forall_mem_iUnion
added theorem Set.iInf_eq_dif
added theorem Set.iInter_and
added theorem Set.iInter_comm
added theorem Set.iInter_congr
added theorem Set.iInter_congr_Prop
added theorem Set.iInter_const
added theorem Set.iInter_dite
added theorem Set.iInter_eq_const
added theorem Set.iInter_eq_if
added theorem Set.iInter_eq_univ
added theorem Set.iInter_exists
added theorem Set.iInter_false
added theorem Set.iInter_inter
added theorem Set.iInter_ite
added theorem Set.iInter_mono''
added theorem Set.iInter_mono'
added theorem Set.iInter_mono
added theorem Set.iInter_ofPred
added theorem Set.iInter_option
added theorem Set.iInter_or
added theorem Set.iInter_plift_down
added theorem Set.iInter_plift_up
added theorem Set.iInter_psigma'
added theorem Set.iInter_psigma
added theorem Set.iInter_sigma'
added theorem Set.iInter_sigma
added theorem Set.iInter_subset
added theorem Set.iInter_sum
added theorem Set.iInter_true
added theorem Set.iInter_union
added theorem Set.iInter_univ
added theorem Set.iInter₂_comm
added theorem Set.iInter₂_congr
added theorem Set.iInter₂_mono'
added theorem Set.iInter₂_mono
added theorem Set.iInter₂_subset
added theorem Set.iUnion_and
added theorem Set.iUnion_comm
added theorem Set.iUnion_congr
added theorem Set.iUnion_congr_Prop
added theorem Set.iUnion_const
added theorem Set.iUnion_dite
added theorem Set.iUnion_empty
added theorem Set.iUnion_eq_const
added theorem Set.iUnion_eq_dif
added theorem Set.iUnion_eq_empty
added theorem Set.iUnion_eq_if
added theorem Set.iUnion_exists
added theorem Set.iUnion_false
added theorem Set.iUnion_inter
added theorem Set.iUnion_ite
added theorem Set.iUnion_mono''
added theorem Set.iUnion_mono'
added theorem Set.iUnion_mono
added theorem Set.iUnion_ofPred
added theorem Set.iUnion_option
added theorem Set.iUnion_or
added theorem Set.iUnion_plift_down
added theorem Set.iUnion_plift_up
added theorem Set.iUnion_psigma'
added theorem Set.iUnion_psigma
added theorem Set.iUnion_sdiff
added theorem Set.iUnion_sigma'
added theorem Set.iUnion_sigma
added theorem Set.iUnion_subset
added theorem Set.iUnion_subset_iff
added theorem Set.iUnion_sum
added theorem Set.iUnion_true
added theorem Set.iUnion_union
added theorem Set.iUnion₂_comm
added theorem Set.iUnion₂_congr
added theorem Set.iUnion₂_mono'
added theorem Set.iUnion₂_mono
added theorem Set.iUnion₂_subset
added theorem Set.insert_iInter
added theorem Set.insert_iUnion
added theorem Set.inter_iInter
added theorem Set.inter_iUnion
added theorem Set.mem_iInter_of_mem
added theorem Set.mem_iInter₂
added theorem Set.mem_iUnion_of_mem
added theorem Set.mem_iUnion₂
added theorem Set.nonempty_biUnion
added theorem Set.nonempty_iUnion
added theorem Set.ofPred_exists
added theorem Set.ofPred_forall
added theorem Set.sdiff_iInter
added theorem Set.sdiff_iUnion
added theorem Set.subset_iInter
added theorem Set.subset_iInter_iff
added theorem Set.subset_iInter₂
added theorem Set.subset_iUnion
added theorem Set.subset_iUnion₂
added theorem Set.union_iInter
added theorem Set.union_iUnion
added theorem Set.Ici_iSup
added theorem Set.Ici_iSup₂
added theorem Set.Ici_sSup
added theorem Set.Iic_iInf
added theorem Set.Iic_iInf₂
added theorem Set.Iic_sInf
added theorem Set.iUnion_le_nat
added theorem exists_sUnion
added theorem forall_sUnion
added theorem iInf_iUnion
added theorem iInf_sUnion
added theorem iSup_iUnion
added theorem iSup_sUnion
added theorem sInf_sUnion
added theorem sSup_iUnion
added theorem sSup_sUnion