{
  "name": "The Spend-Point Table",
  "description": "The 20 largest sites of classical dependence in Mathlib, each with the number of declarations in its dominator subtree that cite a choice primitive directly. Separates sites where the axiom is spent from sites that dominate theorems while inheriting the axiom from further up.",
  "version": "2026-08-12",
  "sha256": "8c7668803b226410c020aa64f0e95762a9b89b4f81b9b92574f6a1dd4028c880",
  "url": "https://f-keys.com/gonzalgo/spend-points/",
  "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",
    "axiom": "Classical.choice, via its primitives"
  },
  "fields": [
    "rank",
    "site",
    "theorems_dominated",
    "subtree_constants",
    "spenders",
    "spends_directly",
    "primitives",
    "example_dependents"
  ],
  "displayed": [
    {
      "key": "rank",
      "label": "#"
    },
    {
      "key": "site",
      "label": "site"
    },
    {
      "key": "theorems_dominated",
      "label": "theorems dominated"
    },
    {
      "key": "subtree_constants",
      "label": "subtree"
    },
    {
      "key": "spenders",
      "label": "spenders"
    },
    {
      "key": "primitives",
      "label": "primitives cited"
    }
  ],
  "rows": [
    {
      "rank": 1,
      "site": "Classical.propDecidable",
      "theorems_dominated": 91858,
      "subtree_constants": 112158,
      "spenders": 6775,
      "spends_directly": true,
      "primitives": "Classical.byContradiction x5338, Classical.propDecidable x1540",
      "example_dependents": "Std.DHashMap.Internal.Raw₀.isHashSelf_updateBucket_alter ; lt_or_eq_of_le ; _private.Mathlib.Data.Set.Image.0.Set.image_univ._proof_1_1"
    },
    {
      "rank": 2,
      "site": "Classical.byContradiction",
      "theorems_dominated": 23550,
      "subtree_constants": 30169,
      "spenders": 1854,
      "spends_directly": true,
      "primitives": "Classical.byContradiction x1854",
      "example_dependents": "_private.Mathlib.Algebra.Group.Hom.Defs.0.map_sub'._proof_1_2 ; Array.getElem_extract_loop_ge ; _private.Mathlib.CategoryTheory.Iso.0.CategoryTheory.Iso.refl._proof_1"
    },
    {
      "rank": 3,
      "site": "CategoryTheory.Functor.category",
      "theorems_dominated": 5271,
      "subtree_constants": 7558,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    },
    {
      "rank": 4,
      "site": "Std.DHashMap.Internal.Raw.WF.out",
      "theorems_dominated": 4899,
      "subtree_constants": 5000,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    },
    {
      "rank": 5,
      "site": "Classical.indefiniteDescription",
      "theorems_dominated": 4711,
      "subtree_constants": 5452,
      "spenders": 44,
      "spends_directly": true,
      "primitives": "Classical.em x30, Classical.indefiniteDescription x14",
      "example_dependents": "em ; Classical.choose ; Std.Trichotomous.rel_or_eq_or_rel_swap"
    },
    {
      "rank": 6,
      "site": "Set.instCompleteAtomicBooleanAlgebra",
      "theorems_dominated": 3430,
      "subtree_constants": 4047,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    },
    {
      "rank": 7,
      "site": "lt_or_eq_of_le",
      "theorems_dominated": 2018,
      "subtree_constants": 2151,
      "spenders": 1,
      "spends_directly": true,
      "primitives": "Classical.propDecidable x1",
      "example_dependents": "lt_or_eq_of_le"
    },
    {
      "rank": 8,
      "site": "Set.image_univ",
      "theorems_dominated": 1484,
      "subtree_constants": 1838,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    },
    {
      "rank": 9,
      "site": "GroupWithZero.toDivisionMonoid",
      "theorems_dominated": 1290,
      "subtree_constants": 1558,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    },
    {
      "rank": 10,
      "site": "eq_or_lt_of_le",
      "theorems_dominated": 1221,
      "subtree_constants": 1314,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    },
    {
      "rank": 11,
      "site": "LE.le.eq_or_lt",
      "theorems_dominated": 1179,
      "subtree_constants": 1271,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    },
    {
      "rank": 12,
      "site": "CategoryTheory.Functor.comp",
      "theorems_dominated": 1112,
      "subtree_constants": 1515,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    },
    {
      "rank": 13,
      "site": "String.toList",
      "theorems_dominated": 1111,
      "subtree_constants": 4557,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    },
    {
      "rank": 14,
      "site": "AddAction.orbitRel",
      "theorems_dominated": 1044,
      "subtree_constants": 1311,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    },
    {
      "rank": 15,
      "site": "QuotientAddGroup.leftRel",
      "theorems_dominated": 1009,
      "subtree_constants": 1271,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    },
    {
      "rank": 16,
      "site": "map_sub",
      "theorems_dominated": 856,
      "subtree_constants": 999,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    },
    {
      "rank": 17,
      "site": "Classical.not_not",
      "theorems_dominated": 792,
      "subtree_constants": 799,
      "spenders": 1,
      "spends_directly": true,
      "primitives": "Classical.propDecidable x1",
      "example_dependents": "Classical.not_not"
    },
    {
      "rank": 18,
      "site": "GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra",
      "theorems_dominated": 722,
      "subtree_constants": 828,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    },
    {
      "rank": 19,
      "site": "String.compare",
      "theorems_dominated": 702,
      "subtree_constants": 3427,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    },
    {
      "rank": 20,
      "site": "Filter.comap",
      "theorems_dominated": 662,
      "subtree_constants": 784,
      "spenders": 0,
      "spends_directly": false,
      "primitives": "(none — inherits)",
      "example_dependents": ""
    }
  ]
}