{ "name": "The Dominator Table", "description": "Mathlib constants ranked by how many theorems each is uniquely responsible for making classical — the number that would stop depending on the axiom of choice if that constant alone were rebuilt. Computed as a dominator tree over the reversed dependency graph rooted at the axiom.", "version": "2026-08-11", "sha256": "d5f56ac36030feacfeb3f2103c21465a0eb9083abe77ee510f2474096e48dd4f", "url": "https://f-keys.com/gonzalgo/dominator-table/", "license": "https://creativecommons.org/licenses/by/4.0/", "producedBy": { "software": "gonzalgo", "url": "https://pypi.org/project/gonzalgo/", "paper": "https://doi.org/10.5281/zenodo.21883963" }, "measured": { "Lean 4": "4.32.1 with Mathlib v4.32.1", "graph": "790,171 declarations, 30,015,601 edges", "axiom": "Classical.choice" }, "fields": [ "rank", "constant", "kind", "theorems_dominated", "area", "eligible", "route", "count_in_eligibility_file" ], "displayed": [ { "key": "rank", "label": "#" }, { "key": "constant", "label": "constant" }, { "key": "kind", "label": "kind" }, { "key": "area", "label": "area" }, { "key": "theorems_dominated", "label": "theorems dominated" }, { "key": "eligible", "label": "eligible" } ], "rows": [ { "rank": 1, "constant": "Classical.propDecidable", "kind": "definition", "theorems_dominated": 91858, "area": "classical logic", "eligible": true, "route": "Classical.propDecidable" }, { "rank": 2, "constant": "Classical.byContradiction", "kind": "theorem", "theorems_dominated": 23550, "area": "classical logic", "eligible": true, "route": "Classical.byContradiction" }, { "rank": 3, "constant": "CategoryTheory.Functor.category", "kind": "definition", "theorems_dominated": 5271, "area": "category theory", "eligible": true, "route": "CategoryTheory.Functor.category" }, { "rank": 4, "constant": "Std.DHashMap.Internal.Raw₀.isHashSelf_updateBucket_alter", "kind": "theorem", "theorems_dominated": 4899, "area": null, "eligible": null, "route": null }, { "rank": 5, "constant": "Std.DHashMap.Internal.Raw₀.wfImp_alterₘ", "kind": "theorem", "theorems_dominated": 4896, "area": null, "eligible": null, "route": null }, { "rank": 6, "constant": "Std.DHashMap.Internal.Raw.WF.out", "kind": "theorem", "theorems_dominated": 4892, "area": "Std: hash maps", "eligible": true, "route": "Std.DHashMap.Internal.Raw₀.isHashSelf_updateBucket_alter > Std.DHashMap.Internal.Raw₀.wfImp_alterₘ > Std.DHashMap.Internal.Raw.WF.out", "count_in_eligibility_file": 4899 }, { "rank": 7, "constant": "Classical.indefiniteDescription", "kind": "definition", "theorems_dominated": 4711, "area": "classical logic", "eligible": true, "route": "Classical.indefiniteDescription" }, { "rank": 8, "constant": "Set.instCompleteAtomicBooleanAlgebra", "kind": "definition", "theorems_dominated": 3430, "area": "sets", "eligible": true, "route": "Set.instCompleteAtomicBooleanAlgebra" }, { "rank": 9, "constant": "lt_or_eq_of_le", "kind": "theorem", "theorems_dominated": 2018, "area": "order / root namespace", "eligible": true, "route": "lt_or_eq_of_le" }, { "rank": 10, "constant": "_private.Mathlib.Data.Set.Image.0.Set.image_univ._proof_1_1", "kind": "theorem", "theorems_dominated": 1484, "area": null, "eligible": null, "route": null }, { "rank": 11, "constant": "Set.image_univ", "kind": "theorem", "theorems_dominated": 1483, "area": "sets", "eligible": true, "route": "_private.Mathlib.Data.Set.Image.0.Set.image_univ._proof_1_1 > Set.image_univ", "count_in_eligibility_file": 1484 }, { "rank": 12, "constant": "GroupWithZero.toDivisionMonoid", "kind": "definition", "theorems_dominated": 1290, "area": "GroupWithZero", "eligible": true, "route": "GroupWithZero.toDivisionMonoid" }, { "rank": 13, "constant": "eq_or_lt_of_le", "kind": "theorem", "theorems_dominated": 1221, "area": "order / root namespace", "eligible": true, "route": "eq_or_lt_of_le" }, { "rank": 14, "constant": "LE.le.eq_or_lt", "kind": "theorem", "theorems_dominated": 1179, "area": "LE", "eligible": true, "route": "LE.le.eq_or_lt" }, { "rank": 15, "constant": "CategoryTheory.Functor.comp", "kind": "definition", "theorems_dominated": 1112, "area": "category theory", "eligible": true, "route": "CategoryTheory.Functor.comp" }, { "rank": 16, "constant": "String.Internal.toArray", "kind": "definition", "theorems_dominated": 1111, "area": null, "eligible": null, "route": null }, { "rank": 17, "constant": "String.toList", "kind": "definition", "theorems_dominated": 1109, "area": "strings", "eligible": true, "route": "String.Internal.toArray > String.toList", "count_in_eligibility_file": 1111 }, { "rank": 18, "constant": "AddAction.orbitRel._proof_3", "kind": "theorem", "theorems_dominated": 1044, "area": null, "eligible": null, "route": null }, { "rank": 19, "constant": "AddAction.orbitRel", "kind": "definition", "theorems_dominated": 1041, "area": "AddAction", "eligible": true, "route": "AddAction.orbitRel._proof_3 > AddAction.orbitRel", "count_in_eligibility_file": 1044 }, { "rank": 20, "constant": "QuotientAddGroup.leftRel", "kind": "definition", "theorems_dominated": 1009, "area": "QuotientAddGroup", "eligible": true, "route": "QuotientAddGroup.leftRel" }, { "rank": 21, "constant": "_private.Mathlib.Algebra.Group.Hom.Defs.0.map_sub'._proof_1_2", "kind": "theorem", "theorems_dominated": 856, "area": null, "eligible": null, "route": null }, { "rank": 22, "constant": "map_sub'", "kind": "theorem", "theorems_dominated": 855, "area": null, "eligible": null, "route": null }, { "rank": 23, "constant": "map_sub", "kind": "theorem", "theorems_dominated": 853, "area": "order / root namespace", "eligible": true, "route": "_private.Mathlib.Algebra.Group.Hom.Defs.0.map_sub'._proof_1_2 > map_sub' > map_sub", "count_in_eligibility_file": 856 }, { "rank": 24, "constant": "Classical.not_not", "kind": "theorem", "theorems_dominated": 792, "area": "classical logic", "eligible": true, "route": "Classical.not_not" }, { "rank": 25, "constant": "GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra._proof_8", "kind": "theorem", "theorems_dominated": 722, "area": null, "eligible": null, "route": null }, { "rank": 26, "constant": "GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra", "kind": "definition", "theorems_dominated": 721, "area": "GeneralizedBooleanAlgebra", "eligible": true, "route": "GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra._proof_8 > GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra", "count_in_eligibility_file": 722 }, { "rank": 27, "constant": "String.compare", "kind": "definition", "theorems_dominated": 702, "area": "strings", "eligible": true, "route": "String.compare > String.instOrd" }, { "rank": 28, "constant": "String.instOrd", "kind": "definition", "theorems_dominated": 702, "area": null, "eligible": null, "route": null }, { "rank": 29, "constant": "Filter.comap._proof_2", "kind": "theorem", "theorems_dominated": 662, "area": null, "eligible": null, "route": null }, { "rank": 30, "constant": "Filter.comap", "kind": "definition", "theorems_dominated": 660, "area": "filters", "eligible": true, "route": "Filter.comap._proof_2 > Filter.comap", "count_in_eligibility_file": 662 }, { "rank": 31, "constant": "CategoryTheory.Functor.fromPUnit", "kind": "definition", "theorems_dominated": 616, "area": "category theory", "eligible": true, "route": "CategoryTheory.Functor.fromPUnit" }, { "rank": 32, "constant": "LE.le.lt_or_eq", "kind": "theorem", "theorems_dominated": 583, "area": "LE", "eligible": true, "route": "LE.le.lt_or_eq > contravariant_le_iff_contravariant_lt_and_eq" }, { "rank": 33, "constant": "contravariant_le_iff_contravariant_lt_and_eq", "kind": "theorem", "theorems_dominated": 578, "area": null, "eligible": null, "route": null }, { "rank": 34, "constant": "_private.Init.Data.List.Nat.Range.0.List.pairwise_lt_range'._proof_1_4", "kind": "theorem", "theorems_dominated": 534, "area": null, "eligible": null, "route": null }, { "rank": 35, "constant": "List.pairwise_lt_range'", "kind": "theorem", "theorems_dominated": 533, "area": null, "eligible": null, "route": null }, { "rank": 36, "constant": "List.pairwise_lt_range'._f", "kind": "definition", "theorems_dominated": 533, "area": null, "eligible": null, "route": null }, { "rank": 37, "constant": "List.nodup_range'", "kind": "theorem", "theorems_dominated": 525, "area": null, "eligible": null, "route": null }, { "rank": 38, "constant": "_private.Init.Data.Nat.Bitwise.Lemmas.0.Nat.testBit_two_pow_sub_succ._proof_1_3", "kind": "theorem", "theorems_dominated": 520, "area": null, "eligible": null, "route": null }, { "rank": 39, "constant": "Nat.testBit_two_pow_sub_succ", "kind": "theorem", "theorems_dominated": 519, "area": "Nat", "eligible": true, "route": "_private.Init.Data.Nat.Bitwise.Lemmas.0.Nat.testBit_two_pow_sub_succ._proof_1_3 > Nat.testBit_two_pow_sub_succ", "count_in_eligibility_file": 520 }, { "rank": 40, "constant": "_private.Init.Data.List.Nat.Range.0.List.nodup_range._simp_1_1", "kind": "theorem", "theorems_dominated": 515, "area": null, "eligible": null, "route": null }, { "rank": 41, "constant": "List.nodup_range", "kind": "theorem", "theorems_dominated": 514, "area": "lists", "eligible": true, "route": "_private.Init.Data.List.Nat.Range.0.List.pairwise_lt_range'._proof_1_4 > List.pairwise_lt_range'._f > List.pairwise_lt_range' > List.nodup_range' > _private.Init.Data.List.Nat.Range.0.List.nodup_range._simp_1_1 > List.nodup_range", "count_in_eligibility_file": 534 }, { "rank": 42, "constant": "subset_interior_iff_isOpen", "kind": "theorem", "theorems_dominated": 511, "area": "order / root namespace", "eligible": true, "route": "subset_interior_iff_isOpen" }, { "rank": 43, "constant": "Classical.not_forall", "kind": "theorem", "theorems_dominated": 497, "area": "classical logic", "eligible": true, "route": "Classical.not_forall" }, { "rank": 44, "constant": "Classical.em", "kind": "theorem", "theorems_dominated": 476, "area": "classical logic", "eligible": true, "route": "Classical.em" }, { "rank": 45, "constant": "CategoryTheory.instCompleteLatticePresieve", "kind": "definition", "theorems_dominated": 450, "area": "category theory", "eligible": true, "route": "CategoryTheory.instCompleteLatticePresieve" }, { "rank": 46, "constant": "_private.Init.Data.Nat.Mod.0.Nat.mul_lt_mul_left._proof_1_1", "kind": "theorem", "theorems_dominated": 440, "area": null, "eligible": null, "route": null }, { "rank": 47, "constant": "Nat.mul_lt_mul_left", "kind": "theorem", "theorems_dominated": 439, "area": "Nat", "eligible": true, "route": "_private.Init.Data.Nat.Mod.0.Nat.mul_lt_mul_left._proof_1_1 > Nat.mul_lt_mul_left", "count_in_eligibility_file": 440 }, { "rank": 48, "constant": "MulAction.orbitRel._proof_3", "kind": "theorem", "theorems_dominated": 423, "area": null, "eligible": null, "route": null }, { "rank": 49, "constant": "MulAction.orbitRel", "kind": "definition", "theorems_dominated": 420, "area": "MulAction", "eligible": true, "route": "MulAction.orbitRel._proof_3 > MulAction.orbitRel", "count_in_eligibility_file": 423 }, { "rank": 50, "constant": "Array.foldrM_congr", "kind": "theorem", "theorems_dominated": 410, "area": "arrays", "eligible": true, "route": "Array.foldrM_congr" }, { "rank": 51, "constant": "Nat.rel_of_forall_rel_succ_of_le_of_le", "kind": "theorem", "theorems_dominated": 405, "area": null, "eligible": null, "route": null }, { "rank": 52, "constant": "Nat.rel_of_forall_rel_succ_of_le", "kind": "theorem", "theorems_dominated": 400, "area": null, "eligible": null, "route": null }, { "rank": 53, "constant": "monotone_nat_of_le_succ", "kind": "theorem", "theorems_dominated": 399, "area": "order / root namespace", "eligible": true, "route": "Nat.rel_of_forall_rel_succ_of_le_of_le > Nat.rel_of_forall_rel_succ_of_le > monotone_nat_of_le_succ", "count_in_eligibility_file": 405 }, { "rank": 54, "constant": "WellFounded.extrinsicFix", "kind": "definition", "theorems_dominated": 398, "area": "WellFounded", "eligible": true, "route": "WellFounded.extrinsicFix" }, { "rank": 55, "constant": "IsUnit.unit", "kind": "definition", "theorems_dominated": 397, "area": "IsUnit", "eligible": true, "route": "IsUnit.unit" }, { "rank": 56, "constant": "BooleanAlgebra.toBiheytingAlgebra", "kind": "definition", "theorems_dominated": 381, "area": "BooleanAlgebra", "eligible": true, "route": "BooleanAlgebra.toBiheytingAlgebra" }, { "rank": 57, "constant": "Std.DHashMap.Internal.Raw.foldRev_eq", "kind": "theorem", "theorems_dominated": 374, "area": "Std: hash maps", "eligible": true, "route": "Std.DHashMap.Internal.Raw.foldRev_eq > Std.DHashMap.Internal.Raw.foldRev_cons_apply" }, { "rank": 58, "constant": "Std.DHashMap.Internal.Raw.foldRev_cons_apply", "kind": "theorem", "theorems_dominated": 373, "area": null, "eligible": null, "route": null }, { "rank": 59, "constant": "WellFounded.extrinsicFix₂", "kind": "definition", "theorems_dominated": 366, "area": "WellFounded", "eligible": true, "route": "WellFounded.extrinsicFix₂" }, { "rank": 60, "constant": "Multiset.add_right_inj", "kind": "theorem", "theorems_dominated": 363, "area": "multisets", "eligible": true, "route": "Multiset.add_right_inj > Multiset.instAddCancelCommMonoid._proof_3 > Multiset.instAddCancelCommMonoid" }, { "rank": 61, "constant": "List.eq_nil_iff_forall_not_mem", "kind": "theorem", "theorems_dominated": 363, "area": "lists", "eligible": true, "route": "List.eq_nil_iff_forall_not_mem" }, { "rank": 62, "constant": "Multiset.instAddCancelCommMonoid._proof_3", "kind": "theorem", "theorems_dominated": 361, "area": null, "eligible": null, "route": null }, { "rank": 63, "constant": "Multiset.instAddCancelCommMonoid", "kind": "definition", "theorems_dominated": 360, "area": null, "eligible": null, "route": null }, { "rank": 64, "constant": "LinearMap.range._proof_1", "kind": "theorem", "theorems_dominated": 358, "area": null, "eligible": null, "route": null }, { "rank": 65, "constant": "LinearMap.range", "kind": "definition", "theorems_dominated": 357, "area": "LinearMap", "eligible": true, "route": "LinearMap.range._proof_1 > LinearMap.range", "count_in_eligibility_file": 358 }, { "rank": 66, "constant": "_private.Mathlib.Algebra.Group.Center.0.Set.mul_mem_center._proof_1_4", "kind": "theorem", "theorems_dominated": 351, "area": null, "eligible": null, "route": null }, { "rank": 67, "constant": "Set.mul_mem_center", "kind": "theorem", "theorems_dominated": 350, "area": "sets", "eligible": true, "route": "_private.Mathlib.Algebra.Group.Center.0.Set.mul_mem_center._proof_1_4 > Set.mul_mem_center", "count_in_eligibility_file": 351 }, { "rank": 68, "constant": "Std.IterM.toArray.go", "kind": "definition", "theorems_dominated": 348, "area": null, "eligible": null, "route": null }, { "rank": 69, "constant": "Std.IterM.toArray", "kind": "definition", "theorems_dominated": 347, "area": "Std: other", "eligible": true, "route": "Std.IterM.toArray.go > Std.IterM.toArray", "count_in_eligibility_file": 348 }, { "rank": 70, "constant": "AddSubmonoid.instCompleteLattice._proof_1", "kind": "theorem", "theorems_dominated": 337, "area": "AddSubmonoid", "eligible": true, "route": "AddSubmonoid.instCompleteLattice._proof_1" }, { "rank": 71, "constant": "CategoryTheory.shiftFunctor", "kind": "definition", "theorems_dominated": 335, "area": "category theory", "eligible": true, "route": "CategoryTheory.shiftFunctor" }, { "rank": 72, "constant": "Lean.Name.quickCmpAux._f", "kind": "definition", "theorems_dominated": 333, "area": null, "eligible": null, "route": null }, { "rank": 73, "constant": "Lean.Name.quickCmpAux", "kind": "definition", "theorems_dominated": 333, "area": null, "eligible": null, "route": null }, { "rank": 74, "constant": "Lean.Name.quickCmp", "kind": "definition", "theorems_dominated": 333, "area": "Lean", "eligible": true, "route": "Lean.Name.quickCmpAux._f > Lean.Name.quickCmpAux > Lean.Name.quickCmp" }, { "rank": 75, "constant": "Submodule.completeLattice", "kind": "definition", "theorems_dominated": 333, "area": "Submodule", "eligible": true, "route": "Submodule.completeLattice" }, { "rank": 76, "constant": "Nat.mono_cast", "kind": "theorem", "theorems_dominated": 328, "area": "Nat", "eligible": true, "route": "Nat.mono_cast" }, { "rank": 77, "constant": "AddSubmonoid.instCompleteLattice", "kind": "definition", "theorems_dominated": 326, "area": "AddSubmonoid", "eligible": true, "route": "AddSubmonoid.instCompleteLattice" }, { "rank": 78, "constant": "CategoryTheory.Sieve.instCompleteLattice", "kind": "definition", "theorems_dominated": 322, "area": "category theory", "eligible": true, "route": "CategoryTheory.Sieve.instCompleteLattice" }, { "rank": 79, "constant": "Classical.ofNonempty", "kind": "definition", "theorems_dominated": 321, "area": "classical logic", "eligible": true, "route": "Classical.ofNonempty" }, { "rank": 80, "constant": "em", "kind": "theorem", "theorems_dominated": 316, "area": "order / root namespace", "eligible": true, "route": "em" }, { "rank": 81, "constant": "QuotientGroup.leftRel", "kind": "definition", "theorems_dominated": 308, "area": "QuotientGroup", "eligible": true, "route": "QuotientGroup.leftRel" }, { "rank": 82, "constant": "GroupWithZero.noZeroDivisors", "kind": "theorem", "theorems_dominated": 288, "area": "GroupWithZero", "eligible": true, "route": "GroupWithZero.noZeroDivisors" }, { "rank": 83, "constant": "CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra", "kind": "definition", "theorems_dominated": 284, "area": "category theory", "eligible": true, "route": "CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra" }, { "rank": 84, "constant": "Real.definition._@.Mathlib.Data.Real.Basic.1175651576._hygCtx._hyg.8", "kind": "definition", "theorems_dominated": 283, "area": null, "eligible": null, "route": null }, { "rank": 85, "constant": "Real.wrapped._@.Mathlib.Data.Real.Basic.1175651576._hygCtx._hyg.8", "kind": "other", "theorems_dominated": 282, "area": null, "eligible": null, "route": null }, { "rank": 86, "constant": "_private.Mathlib.Data.Real.Basic.0.Real.lt", "kind": "definition", "theorems_dominated": 282, "area": null, "eligible": null, "route": null }, { "rank": 87, "constant": "Real.instLT", "kind": "definition", "theorems_dominated": 282, "area": "Real", "eligible": true, "route": "Real.definition._@.Mathlib.Data.Real.Basic.1175651576._hygCtx._hyg.8 > Real.wrapped._@.Mathlib.Data.Real.Basic.1175651576._hygCtx._hyg.8 > _private.Mathlib.Data.Real.Basic.0.Real.lt > Real.instLT", "count_in_eligibility_file": 283 }, { "rank": 88, "constant": "LinearEquiv.ofBijective", "kind": "definition", "theorems_dominated": 281, "area": "LinearEquiv", "eligible": true, "route": "LinearEquiv.ofBijective" }, { "rank": 89, "constant": "isOpen_iff_forall_mem_open", "kind": "theorem", "theorems_dominated": 279, "area": null, "eligible": null, "route": null }, { "rank": 90, "constant": "zpow_ne_zero", "kind": "theorem", "theorems_dominated": 279, "area": "order / root namespace", "eligible": true, "route": "zpow_ne_zero" }, { "rank": 91, "constant": "IsLocallyConstant.tfae", "kind": "theorem", "theorems_dominated": 278, "area": "IsLocallyConstant", "eligible": true, "route": "isOpen_iff_forall_mem_open > IsLocallyConstant.tfae > IsLocallyConstant.iff_eventually_eq", "count_in_eligibility_file": 279 }, { "rank": 92, "constant": "IsLocallyConstant.iff_eventually_eq", "kind": "theorem", "theorems_dominated": 272, "area": null, "eligible": null, "route": null }, { "rank": 93, "constant": "Set.biInter_range", "kind": "theorem", "theorems_dominated": 270, "area": "sets", "eligible": true, "route": "Set.biInter_range" }, { "rank": 94, "constant": "Std.DTreeMap.Internal.Impl.WF.ordered", "kind": "theorem", "theorems_dominated": 266, "area": "Std: other", "eligible": true, "route": "Std.DTreeMap.Internal.Impl.WF.ordered" }, { "rank": 95, "constant": "FreeAlgebra.lift._proof_4", "kind": "theorem", "theorems_dominated": 263, "area": "FreeAlgebra", "eligible": true, "route": "FreeAlgebra.lift._proof_4" }, { "rank": 96, "constant": "DFinsupp.zipWith._proof_4", "kind": "theorem", "theorems_dominated": 262, "area": null, "eligible": null, "route": null }, { "rank": 97, "constant": "DFinsupp.zipWith", "kind": "definition", "theorems_dominated": 261, "area": "DFinsupp", "eligible": true, "route": "DFinsupp.zipWith._proof_4 > DFinsupp.zipWith", "count_in_eligibility_file": 262 }, { "rank": 98, "constant": "eq_or_ne", "kind": "theorem", "theorems_dominated": 260, "area": "order / root namespace", "eligible": true, "route": "eq_or_ne" }, { "rank": 99, "constant": "Equiv.ofBijective", "kind": "definition", "theorems_dominated": 258, "area": "Equiv", "eligible": true, "route": "Equiv.ofBijective" }, { "rank": 100, "constant": "Equiv.Perm.permGroup", "kind": "definition", "theorems_dominated": 250, "area": "Equiv", "eligible": true, "route": "Equiv.Perm.permGroup" }, { "rank": 101, "constant": "List.nodup_finRange", "kind": "theorem", "theorems_dominated": 244, "area": "lists", "eligible": true, "route": "List.nodup_finRange" }, { "rank": 102, "constant": "NNReal", "kind": "definition", "theorems_dominated": 243, "area": "NNReal", "eligible": true, "route": "NNReal" }, { "rank": 103, "constant": "_private.Mathlib.Data.Set.NAry.0.Set.forall_mem_image2._proof_1_1", "kind": "theorem", "theorems_dominated": 239, "area": null, "eligible": null, "route": null }, { "rank": 104, "constant": "Set.forall_mem_image2", "kind": "theorem", "theorems_dominated": 238, "area": "sets", "eligible": true, "route": "_private.Mathlib.Data.Set.NAry.0.Set.forall_mem_image2._proof_1_1 > Set.forall_mem_image2", "count_in_eligibility_file": 239 }, { "rank": 105, "constant": "Subsemigroup.center", "kind": "definition", "theorems_dominated": 238, "area": "Subsemigroup", "eligible": true, "route": "Subsemigroup.center" }, { "rank": 106, "constant": "List.perm_insert_swap", "kind": "theorem", "theorems_dominated": 237, "area": null, "eligible": null, "route": null }, { "rank": 107, "constant": "Std.instMinEqOrOfLawfulOrderLeftLeaningMin", "kind": "theorem", "theorems_dominated": 237, "area": null, "eligible": null, "route": null }, { "rank": 108, "constant": "List.Perm.union_right", "kind": "theorem", "theorems_dominated": 236, "area": null, "eligible": null, "route": null }, { "rank": 109, "constant": "_private.Init.Data.Int.DivMod.Lemmas.0.Int.natCast_eq_zero._proof_1_1", "kind": "theorem", "theorems_dominated": 236, "area": null, "eligible": null, "route": null }, { "rank": 110, "constant": "List.min?_eq_some_iff", "kind": "theorem", "theorems_dominated": 236, "area": "lists", "eligible": true, "route": "Std.instMinEqOrOfLawfulOrderLeftLeaningMin > List.min?_eq_some_iff", "count_in_eligibility_file": 237 }, { "rank": 111, "constant": "List.Perm.union", "kind": "theorem", "theorems_dominated": 235, "area": "lists", "eligible": true, "route": "List.perm_insert_swap > List.Perm.union_right > List.Perm.union > Multiset.ndunion._proof_1 > Multiset.ndunion", "count_in_eligibility_file": 237 }, { "rank": 112, "constant": "Int.natCast_eq_zero", "kind": "theorem", "theorems_dominated": 235, "area": "Int", "eligible": true, "route": "_private.Init.Data.Int.DivMod.Lemmas.0.Int.natCast_eq_zero._proof_1_1 > Int.natCast_eq_zero", "count_in_eligibility_file": 236 }, { "rank": 113, "constant": "Multiset.ndunion._proof_1", "kind": "theorem", "theorems_dominated": 234, "area": null, "eligible": null, "route": null }, { "rank": 114, "constant": "Multiset.ndunion", "kind": "definition", "theorems_dominated": 233, "area": null, "eligible": null, "route": null }, { "rank": 115, "constant": "Classical.choose", "kind": "definition", "theorems_dominated": 232, "area": "classical logic", "eligible": true, "route": "Classical.choose" }, { "rank": 116, "constant": "SeminormedAddCommGroup.toIsTopologicalAddGroup", "kind": "theorem", "theorems_dominated": 231, "area": "SeminormedAddCommGroup", "eligible": true, "route": 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