{ "name": "The Dominator Table", "description": "Sites of classical dependence in Mathlib ranked by how many theorems each is uniquely responsible for — the number that would stop depending on the axiom of choice if that site alone were rebuilt. Computed as a dominator tree over the reversed dependency graph rooted at the axiom, with chains of constants that free the same theorems collapsed to a single site.", "version": "2026-08-12", "sha256": "415eb3f9bd2923d2a336dfa059fffb66bc5bc1b73f2e3cff23598f31bc44baa4", "url": "https://f-keys.com/gonzalgo/dominator-table/", "seriesDoi": "https://doi.org/10.5281/zenodo.21900625", "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", "unit": "sites, chains collapsed at a 0.97 weight ratio" }, "fields": [ "rank", "site", "kind", "theorems_dominated", "area", "eligible", "chain_length", "chain", "constant_alone" ], "displayed": [ { "key": "rank", "label": "#" }, { "key": "site", "label": "site" }, { "key": "kind", "label": "kind" }, { "key": "area", "label": "area" }, { "key": "theorems_dominated", "label": "theorems dominated" }, { "key": "eligible", "label": "eligible" } ], "rows": [ { "rank": 1, "site": "Classical.propDecidable", "kind": "definition", "theorems_dominated": 91858, "area": "classical logic", "eligible": true, "chain_length": 1, "chain": "Classical.propDecidable" }, { "rank": 2, "site": "Classical.byContradiction", "kind": "theorem", "theorems_dominated": 23550, "area": "classical logic", "eligible": true, "chain_length": 1, "chain": "Classical.byContradiction" }, { "rank": 3, "site": "CategoryTheory.Functor.category", "kind": "definition", "theorems_dominated": 5271, "area": "category theory", "eligible": true, "chain_length": 1, "chain": "CategoryTheory.Functor.category" }, { "rank": 4, "site": "Std.DHashMap.Internal.Raw.WF.out", "kind": "theorem", "theorems_dominated": 4899, "area": "Std: hash maps", "eligible": true, "chain_length": 3, "chain": "Std.DHashMap.Internal.Raw₀.isHashSelf_updateBucket_alter > Std.DHashMap.Internal.Raw₀.wfImp_alterₘ > Std.DHashMap.Internal.Raw.WF.out", "constant_alone": 4892 }, { "rank": 5, "site": "Classical.indefiniteDescription", "kind": "definition", "theorems_dominated": 4711, "area": "classical logic", "eligible": true, "chain_length": 1, "chain": "Classical.indefiniteDescription" }, { "rank": 6, "site": "Set.instCompleteAtomicBooleanAlgebra", "kind": "definition", "theorems_dominated": 3430, "area": "sets", "eligible": true, "chain_length": 1, "chain": "Set.instCompleteAtomicBooleanAlgebra" }, { "rank": 7, "site": "lt_or_eq_of_le", "kind": "theorem", "theorems_dominated": 2018, "area": "order / root namespace", "eligible": true, "chain_length": 1, "chain": "lt_or_eq_of_le" }, { "rank": 8, "site": "Set.image_univ", "kind": "theorem", "theorems_dominated": 1484, "area": "sets", "eligible": true, "chain_length": 2, "chain": "_private.Mathlib.Data.Set.Image.0.Set.image_univ._proof_1_1 > Set.image_univ", "constant_alone": 1483 }, { "rank": 9, "site": "GroupWithZero.toDivisionMonoid", "kind": "definition", "theorems_dominated": 1290, "area": "GroupWithZero", "eligible": true, "chain_length": 1, "chain": "GroupWithZero.toDivisionMonoid" }, { "rank": 10, "site": "eq_or_lt_of_le", "kind": "theorem", "theorems_dominated": 1221, "area": "order / root namespace", "eligible": true, "chain_length": 1, "chain": "eq_or_lt_of_le" }, { "rank": 11, "site": "LE.le.eq_or_lt", "kind": "theorem", "theorems_dominated": 1179, "area": "LE", "eligible": true, "chain_length": 1, "chain": "LE.le.eq_or_lt" }, { "rank": 12, "site": "CategoryTheory.Functor.comp", "kind": "definition", "theorems_dominated": 1112, "area": "category theory", "eligible": true, "chain_length": 1, "chain": "CategoryTheory.Functor.comp" }, { "rank": 13, "site": "String.toList", "kind": "definition", "theorems_dominated": 1111, "area": "strings", "eligible": true, "chain_length": 2, "chain": "String.Internal.toArray > String.toList", "constant_alone": 1109 }, { "rank": 14, "site": "AddAction.orbitRel", "kind": "definition", "theorems_dominated": 1044, "area": "AddAction", "eligible": true, "chain_length": 2, "chain": "AddAction.orbitRel._proof_3 > AddAction.orbitRel", "constant_alone": 1041 }, { "rank": 15, "site": "QuotientAddGroup.leftRel", "kind": "definition", "theorems_dominated": 1009, "area": "QuotientAddGroup", "eligible": true, "chain_length": 1, "chain": "QuotientAddGroup.leftRel" }, { "rank": 16, "site": "map_sub", "kind": "theorem", "theorems_dominated": 856, "area": "order / root namespace", "eligible": true, "chain_length": 3, "chain": "_private.Mathlib.Algebra.Group.Hom.Defs.0.map_sub'._proof_1_2 > map_sub' > map_sub", "constant_alone": 853 }, { "rank": 17, "site": "Classical.not_not", "kind": "theorem", "theorems_dominated": 792, "area": "classical logic", "eligible": true, "chain_length": 1, "chain": "Classical.not_not" }, { "rank": 18, "site": "GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra", "kind": "definition", "theorems_dominated": 722, "area": "GeneralizedBooleanAlgebra", "eligible": true, "chain_length": 2, "chain": "GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra._proof_8 > GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra", "constant_alone": 721 }, { "rank": 19, "site": "String.compare", "kind": "definition", "theorems_dominated": 702, "area": "strings", "eligible": true, "chain_length": 2, "chain": "String.compare > String.instOrd" }, { "rank": 20, "site": "Filter.comap", "kind": "definition", "theorems_dominated": 662, "area": "filters", "eligible": true, "chain_length": 2, "chain": "Filter.comap._proof_2 > Filter.comap", "constant_alone": 660 }, { "rank": 21, "site": "CategoryTheory.Functor.fromPUnit", "kind": "definition", "theorems_dominated": 616, "area": "category theory", "eligible": true, "chain_length": 1, "chain": "CategoryTheory.Functor.fromPUnit" }, { "rank": 22, "site": "LE.le.lt_or_eq", "kind": "theorem", "theorems_dominated": 583, "area": "LE", "eligible": true, "chain_length": 2, "chain": "LE.le.lt_or_eq > contravariant_le_iff_contravariant_lt_and_eq" }, { "rank": 23, "site": "List.nodup_range", "kind": "theorem", "theorems_dominated": 534, "area": "lists", "eligible": true, "chain_length": 6, "chain": "_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", "constant_alone": 514 }, { "rank": 24, "site": "Nat.testBit_two_pow_sub_succ", "kind": "theorem", "theorems_dominated": 520, "area": "Nat", "eligible": true, "chain_length": 2, "chain": "_private.Init.Data.Nat.Bitwise.Lemmas.0.Nat.testBit_two_pow_sub_succ._proof_1_3 > Nat.testBit_two_pow_sub_succ", "constant_alone": 519 }, { "rank": 25, "site": "subset_interior_iff_isOpen", "kind": "theorem", "theorems_dominated": 511, "area": "order / root namespace", "eligible": true, "chain_length": 1, "chain": "subset_interior_iff_isOpen" }, { "rank": 26, "site": "Classical.not_forall", "kind": "theorem", "theorems_dominated": 497, "area": "classical logic", "eligible": true, "chain_length": 1, "chain": "Classical.not_forall" }, { "rank": 27, "site": "Classical.em", "kind": "theorem", "theorems_dominated": 476, "area": "classical logic", "eligible": true, "chain_length": 1, "chain": "Classical.em" }, { "rank": 28, "site": "CategoryTheory.instCompleteLatticePresieve", "kind": "definition", "theorems_dominated": 450, "area": "category theory", "eligible": true, "chain_length": 1, "chain": "CategoryTheory.instCompleteLatticePresieve" }, { "rank": 29, "site": "Nat.mul_lt_mul_left", "kind": "theorem", "theorems_dominated": 440, "area": "Nat", "eligible": true, "chain_length": 2, "chain": "_private.Init.Data.Nat.Mod.0.Nat.mul_lt_mul_left._proof_1_1 > Nat.mul_lt_mul_left", "constant_alone": 439 }, { "rank": 30, "site": "MulAction.orbitRel", "kind": "definition", "theorems_dominated": 423, "area": "MulAction", "eligible": true, "chain_length": 2, "chain": "MulAction.orbitRel._proof_3 > MulAction.orbitRel", "constant_alone": 420 }, { "rank": 31, "site": "Array.foldrM_congr", "kind": "theorem", "theorems_dominated": 410, "area": "arrays", "eligible": true, "chain_length": 1, "chain": "Array.foldrM_congr" }, { "rank": 32, "site": "monotone_nat_of_le_succ", "kind": "theorem", "theorems_dominated": 405, "area": "order / root namespace", "eligible": true, "chain_length": 3, "chain": "Nat.rel_of_forall_rel_succ_of_le_of_le > Nat.rel_of_forall_rel_succ_of_le > monotone_nat_of_le_succ", "constant_alone": 399 }, { "rank": 33, "site": "WellFounded.extrinsicFix", "kind": "definition", "theorems_dominated": 398, "area": "WellFounded", "eligible": true, "chain_length": 1, "chain": "WellFounded.extrinsicFix" }, { "rank": 34, "site": "IsUnit.unit", "kind": "definition", "theorems_dominated": 397, "area": "IsUnit", "eligible": true, "chain_length": 1, "chain": "IsUnit.unit" }, { "rank": 35, "site": "BooleanAlgebra.toBiheytingAlgebra", "kind": "definition", "theorems_dominated": 381, "area": "BooleanAlgebra", "eligible": true, "chain_length": 1, "chain": "BooleanAlgebra.toBiheytingAlgebra" }, { "rank": 36, "site": "Std.DHashMap.Internal.Raw.foldRev_eq", "kind": "theorem", "theorems_dominated": 374, "area": "Std: hash maps", "eligible": true, "chain_length": 2, "chain": "Std.DHashMap.Internal.Raw.foldRev_eq > Std.DHashMap.Internal.Raw.foldRev_cons_apply" }, { "rank": 37, "site": "WellFounded.extrinsicFix₂", "kind": "definition", "theorems_dominated": 366, "area": "WellFounded", "eligible": true, "chain_length": 1, "chain": "WellFounded.extrinsicFix₂" }, { "rank": 38, "site": "Multiset.add_right_inj", "kind": "theorem", "theorems_dominated": 363, "area": "multisets", "eligible": true, "chain_length": 3, "chain": "Multiset.add_right_inj > Multiset.instAddCancelCommMonoid._proof_3 > Multiset.instAddCancelCommMonoid" }, { "rank": 39, "site": "List.eq_nil_iff_forall_not_mem", "kind": "theorem", "theorems_dominated": 363, "area": "lists", "eligible": true, "chain_length": 1, "chain": "List.eq_nil_iff_forall_not_mem" }, { "rank": 40, "site": "LinearMap.range", "kind": "definition", "theorems_dominated": 358, "area": "LinearMap", "eligible": true, "chain_length": 2, "chain": "LinearMap.range._proof_1 > LinearMap.range", "constant_alone": 357 }, { "rank": 41, "site": "Set.mul_mem_center", "kind": "theorem", "theorems_dominated": 351, "area": "sets", "eligible": true, "chain_length": 2, "chain": "_private.Mathlib.Algebra.Group.Center.0.Set.mul_mem_center._proof_1_4 > Set.mul_mem_center", "constant_alone": 350 }, { "rank": 42, "site": "Std.IterM.toArray", "kind": "definition", "theorems_dominated": 348, "area": "Std: other", "eligible": true, "chain_length": 2, "chain": "Std.IterM.toArray.go > Std.IterM.toArray", "constant_alone": 347 }, { "rank": 43, "site": "AddSubmonoid.instCompleteLattice._proof_1", "kind": "theorem", "theorems_dominated": 337, "area": "AddSubmonoid", "eligible": true, "chain_length": 1, "chain": "AddSubmonoid.instCompleteLattice._proof_1" }, { "rank": 44, "site": "CategoryTheory.shiftFunctor", "kind": "definition", "theorems_dominated": 335, "area": "category theory", "eligible": true, "chain_length": 1, "chain": "CategoryTheory.shiftFunctor" }, { "rank": 45, "site": "Lean.Name.quickCmp", "kind": "definition", "theorems_dominated": 333, "area": "Lean", "eligible": true, "chain_length": 3, "chain": "Lean.Name.quickCmpAux._f > Lean.Name.quickCmpAux > Lean.Name.quickCmp" }, { "rank": 46, "site": "Submodule.completeLattice", "kind": "definition", "theorems_dominated": 333, "area": "Submodule", "eligible": true, "chain_length": 1, "chain": "Submodule.completeLattice" }, { "rank": 47, "site": "Nat.mono_cast", "kind": "theorem", "theorems_dominated": 328, "area": "Nat", "eligible": true, "chain_length": 1, "chain": "Nat.mono_cast" }, { "rank": 48, "site": "AddSubmonoid.instCompleteLattice", "kind": "definition", "theorems_dominated": 326, "area": "AddSubmonoid", "eligible": true, "chain_length": 1, "chain": "AddSubmonoid.instCompleteLattice" }, { "rank": 49, "site": "CategoryTheory.Sieve.instCompleteLattice", "kind": "definition", "theorems_dominated": 322, "area": "category theory", "eligible": true, "chain_length": 1, "chain": "CategoryTheory.Sieve.instCompleteLattice" }, { "rank": 50, "site": "Classical.ofNonempty", "kind": "definition", "theorems_dominated": 321, "area": "classical logic", "eligible": true, "chain_length": 1, "chain": "Classical.ofNonempty" }, { "rank": 51, "site": "em", "kind": "theorem", "theorems_dominated": 316, "area": "order / root namespace", "eligible": true, "chain_length": 1, "chain": "em" }, { "rank": 52, "site": "QuotientGroup.leftRel", "kind": "definition", "theorems_dominated": 308, "area": "QuotientGroup", "eligible": true, "chain_length": 1, "chain": "QuotientGroup.leftRel" }, { "rank": 53, "site": "GroupWithZero.noZeroDivisors", "kind": "theorem", "theorems_dominated": 288, "area": "GroupWithZero", "eligible": true, "chain_length": 1, "chain": "GroupWithZero.noZeroDivisors" }, { "rank": 54, "site": "CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra", "kind": "definition", "theorems_dominated": 284, "area": "category theory", "eligible": true, "chain_length": 1, "chain": "CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra" }, { "rank": 55, "site": "Real.instLT", "kind": "definition", "theorems_dominated": 283, "area": "Real", "eligible": true, "chain_length": 4, "chain": "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", "constant_alone": 282 }, { "rank": 56, "site": "LinearEquiv.ofBijective", "kind": "definition", "theorems_dominated": 281, "area": "LinearEquiv", "eligible": true, "chain_length": 1, "chain": "LinearEquiv.ofBijective" }, { "rank": 57, "site": "IsLocallyConstant.tfae", "kind": "theorem", "theorems_dominated": 279, "area": "IsLocallyConstant", "eligible": true, "chain_length": 3, "chain": "isOpen_iff_forall_mem_open > IsLocallyConstant.tfae > IsLocallyConstant.iff_eventually_eq", "constant_alone": 278 }, { "rank": 58, "site": "zpow_ne_zero", "kind": "theorem", "theorems_dominated": 279, "area": "order / root namespace", "eligible": true, "chain_length": 1, "chain": "zpow_ne_zero" }, { "rank": 59, "site": "Set.biInter_range", "kind": "theorem", "theorems_dominated": 270, "area": "sets", "eligible": true, "chain_length": 1, "chain": "Set.biInter_range" }, { "rank": 60, "site": "Std.DTreeMap.Internal.Impl.WF.ordered", "kind": "theorem", "theorems_dominated": 266, "area": "Std: other", "eligible": true, "chain_length": 1, "chain": "Std.DTreeMap.Internal.Impl.WF.ordered" }, { "rank": 61, "site": "FreeAlgebra.lift._proof_4", "kind": "theorem", "theorems_dominated": 263, "area": "FreeAlgebra", "eligible": true, "chain_length": 1, "chain": "FreeAlgebra.lift._proof_4" }, { "rank": 62, "site": "DFinsupp.zipWith", "kind": "definition", "theorems_dominated": 262, "area": "DFinsupp", "eligible": true, "chain_length": 2, "chain": "DFinsupp.zipWith._proof_4 > DFinsupp.zipWith", "constant_alone": 261 }, { "rank": 63, "site": "eq_or_ne", "kind": "theorem", "theorems_dominated": 260, "area": "order / root namespace", "eligible": true, "chain_length": 1, "chain": "eq_or_ne" }, { "rank": 64, "site": "Equiv.ofBijective", "kind": "definition", "theorems_dominated": 258, "area": "Equiv", "eligible": true, "chain_length": 1, "chain": "Equiv.ofBijective" }, { "rank": 65, "site": "Equiv.Perm.permGroup", "kind": "definition", "theorems_dominated": 250, "area": "Equiv", "eligible": true, "chain_length": 1, "chain": "Equiv.Perm.permGroup" }, { "rank": 66, "site": "List.nodup_finRange", "kind": "theorem", "theorems_dominated": 244, "area": "lists", "eligible": true, "chain_length": 1, "chain": "List.nodup_finRange" }, { "rank": 67, "site": "NNReal", "kind": "definition", "theorems_dominated": 243, "area": "NNReal", "eligible": true, "chain_length": 1, "chain": "NNReal" }, { "rank": 68, "site": "Set.forall_mem_image2", "kind": "theorem", "theorems_dominated": 239, "area": "sets", "eligible": true, "chain_length": 2, "chain": "_private.Mathlib.Data.Set.NAry.0.Set.forall_mem_image2._proof_1_1 > Set.forall_mem_image2", "constant_alone": 238 }, { "rank": 69, "site": "Subsemigroup.center", "kind": "definition", "theorems_dominated": 238, "area": "Subsemigroup", "eligible": true, "chain_length": 1, "chain": "Subsemigroup.center" }, { "rank": 70, "site": "List.Perm.union", "kind": "theorem", "theorems_dominated": 237, "area": "lists", "eligible": true, "chain_length": 5, "chain": "List.perm_insert_swap > List.Perm.union_right > List.Perm.union > Multiset.ndunion._proof_1 > Multiset.ndunion", "constant_alone": 235 }, { "rank": 71, "site": "List.min?_eq_some_iff", "kind": "theorem", "theorems_dominated": 237, "area": "lists", "eligible": true, "chain_length": 2, "chain": "Std.instMinEqOrOfLawfulOrderLeftLeaningMin > List.min?_eq_some_iff", "constant_alone": 236 }, { "rank": 72, "site": "Int.natCast_eq_zero", "kind": "theorem", "theorems_dominated": 236, "area": "Int", "eligible": true, "chain_length": 2, "chain": "_private.Init.Data.Int.DivMod.Lemmas.0.Int.natCast_eq_zero._proof_1_1 > Int.natCast_eq_zero", "constant_alone": 235 }, { "rank": 73, "site": "Classical.choose", "kind": "definition", "theorems_dominated": 232, "area": "classical logic", "eligible": true, "chain_length": 1, "chain": "Classical.choose" }, { "rank": 74, "site": "SeminormedAddCommGroup.toIsTopologicalAddGroup", "kind": "theorem", "theorems_dominated": 231, "area": "SeminormedAddCommGroup", "eligible": true, "chain_length": 1, "chain": "SeminormedAddCommGroup.toIsTopologicalAddGroup" }, { "rank": 75, "site": "isOpen_iff_nhds", "kind": "theorem", "theorems_dominated": 230, "area": "order / root namespace", "eligible": true, "chain_length": 1, "chain": "isOpen_iff_nhds" }, { "rank": 76, "site": "Classical.or_iff_not_imp_left", "kind": "theorem", "theorems_dominated": 230, "area": "classical logic", "eligible": true, "chain_length": 1, "chain": "Classical.or_iff_not_imp_left" }, { "rank": 77, "site": "List.min?_eq_some_iff_subtype", "kind": "theorem", "theorems_dominated": 228, "area": "lists", "eligible": true, "chain_length": 2, "chain": "List.min?_eq_some_iff_subtype > Std.Internal.List.minEntry?_eq_some_iff" }, { "rank": 78, "site": "Nat.testBit_two_pow_sub_one", "kind": "theorem", "theorems_dominated": 224, "area": "Nat", "eligible": true, "chain_length": 1, "chain": "Nat.testBit_two_pow_sub_one" }, { "rank": 79, "site": "isOpen_iff_mem_nhds", "kind": "theorem", "theorems_dominated": 223, "area": "order / root namespace", "eligible": true, "chain_length": 1, "chain": "isOpen_iff_mem_nhds" }, { "rank": 80, "site": "and_forall_ne", "kind": "theorem", "theorems_dominated": 215, "area": "order / root namespace", "eligible": true, "chain_length": 2, "chain": "and_forall_ne > Function.forall_update_iff" }, { "rank": 81, "site": "TensorAlgebra.lift", "kind": "definition", "theorems_dominated": 211, "area": "TensorAlgebra", "eligible": true, "chain_length": 1, "chain": "TensorAlgebra.lift" }, { "rank": 82, "site": "Array.getElem_extract", "kind": "theorem", "theorems_dominated": 202, "area": "arrays", "eligible": true, "chain_length": 2, "chain": "Array.getElem_extract_loop_ge > Array.getElem_extract", "constant_alone": 201 }, { "rank": 83, "site": "IsStrictOrderedRing.toIsOrderedRing", "kind": "theorem", "theorems_dominated": 202, "area": "IsStrictOrderedRing", "eligible": true, "chain_length": 1, "chain": "IsStrictOrderedRing.toIsOrderedRing" }, { "rank": 84, "site": "CategoryTheory.Iso.refl", "kind": "definition", "theorems_dominated": 200, "area": "category theory", "eligible": true, "chain_length": 3, "chain": "_private.Mathlib.CategoryTheory.Iso.0.CategoryTheory.Iso.refl._proof_1 > CategoryTheory.Iso.refl._proof_2 > CategoryTheory.Iso.refl", "constant_alone": 198 }, { "rank": 85, "site": "InfHomClass.toOrderHomClass", "kind": "theorem", "theorems_dominated": 198, "area": "InfHomClass", "eligible": true, "chain_length": 4, "chain": "_private.Mathlib.Order.Hom.Basic.0.OrderHomClass._proof_2 > OrderHomClass._proof_3 > OrderHomClass._to_dual_cast_4 > InfHomClass.toOrderHomClass", "constant_alone": 195 }, { "rank": 86, "site": "CommGroupWithZero.toDivisionCommMonoid", "kind": "definition", "theorems_dominated": 198, "area": "CommGroupWithZero", "eligible": true, "chain_length": 1, "chain": "CommGroupWithZero.toDivisionCommMonoid" }, { "rank": 87, "site": "MonoidHom.mrange._proof_1", "kind": "theorem", "theorems_dominated": 197, "area": "MonoidHom", "eligible": true, "chain_length": 1, "chain": "MonoidHom.mrange._proof_1" }, { "rank": 88, "site": "HomologicalComplex.Hom.comm", "kind": "theorem", "theorems_dominated": 196, "area": "HomologicalComplex", "eligible": true, "chain_length": 1, "chain": "HomologicalComplex.Hom.comm" }, { "rank": 89, "site": "Multiset.eq_zero_of_forall_notMem", "kind": "theorem", "theorems_dominated": 196, "area": "multisets", "eligible": true, "chain_length": 1, "chain": "Multiset.eq_zero_of_forall_notMem" }, { "rank": 90, "site": "Equiv.symm_apply_eq", "kind": "theorem", "theorems_dominated": 196, "area": "Equiv", "eligible": true, "chain_length": 2, "chain": "_private.Mathlib.Logic.Equiv.Defs.0.Equiv.symm_apply_eq._proof_1_2 > Equiv.symm_apply_eq", "constant_alone": 195 }, { "rank": 91, "site": "Equiv.apply_eq_iff_eq_symm_apply", "kind": "theorem", "theorems_dominated": 194, "area": "Equiv", "eligible": true, "chain_length": 2, "chain": "_private.Mathlib.Logic.Equiv.Defs.0.Equiv.apply_eq_iff_eq_symm_apply._proof_1_2 > Equiv.apply_eq_iff_eq_symm_apply", "constant_alone": 193 }, { "rank": 92, "site": "IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT", "kind": "theorem", "theorems_dominated": 194, "area": "IsLeftCancelAdd", "eligible": true, "chain_length": 1, "chain": "IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT" }, { "rank": 93, "site": "Int.natCast_eq_zero._simp_1", "kind": "theorem", "theorems_dominated": 193, "area": "Int", "eligible": true, "chain_length": 1, "chain": "Int.natCast_eq_zero._simp_1" }, { "rank": 94, "site": "Int.natAbs_ediv", "kind": "theorem", "theorems_dominated": 191, "area": "Int", "eligible": true, "chain_length": 2, "chain": "Int.natAbs_ediv > Int.natAbs_ediv_of_dvd" }, { "rank": 95, "site": "SimpleGraph.edgeSet", "kind": "definition", "theorems_dominated": 190, "area": "SimpleGraph", "eligible": true, "chain_length": 2, "chain": "SimpleGraph.edgeSetEmbedding > SimpleGraph.edgeSet", "constant_alone": 186 }, { "rank": 96, "site": "Nat.cast_nonneg'", "kind": "theorem", "theorems_dominated": 188, "area": "Nat", "eligible": true, "chain_length": 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