Datasets:

maxRyeery
/

VeriSoftBench

id int64 1 500	thm_name stringlengths 5 86	thm_stmt stringlengths 30 2.63k	lean_root stringclasses 23 values	rel_path stringlengths 13 61	imports listlengths 0 35	used_lib_defs listlengths 1 144	used_repo_defs listlengths 1 251	lib_lemmas listlengths 1 172	repo_lemmas listlengths 1 148	used_local_defs listlengths 0 85	used_local_lemmas listlengths 0 57	local_ctx stringlengths 35 30.7k	target_theorem stringlengths 33 1.57k	ground_truth_proof stringlengths 6 26.5k	nesting_depth int64 1 27	transitive_dep_count int64 1 480	subset_aristotle bool 2 classes	category stringclasses 5 values
1	Binius.BinaryBasefold.fiberwise_dist_lt_imp_dist_lt_unique_decoding_radius	theorem fiberwise_dist_lt_imp_dist_lt_unique_decoding_radius (i : Fin ℓ) (steps : ℕ) [NeZero steps] (h_i_add_steps : i.val + steps ≤ ℓ) (f : OracleFunction 𝔽q β (h_ℓ_add_R_rate := h_ℓ_add_R_rate) ⟨i, by omega⟩) (h_fw_dist_lt : fiberwiseClose 𝔽q β (h_ℓ_add_R_rate := h_ℓ_add_R_rate) (i := i) (steps := ste...	ArkLib	ArkLib/ProofSystem/Binius/BinaryBasefold/Prelude.lean	[ "import ArkLib.Data.MvPolynomial.Multilinear", "import ArkLib.Data.CodingTheory.Basic", "import ArkLib.Data.FieldTheory.AdditiveNTT.AdditiveNTT", "import ArkLib.Data.Nat.Bitwise", "import ArkLib.Data.CodingTheory.ReedSolomon", "import ArkLib.Data.Vector.Basic", "import ArkLib.ProofSystem.Sumcheck.Spec.S...	[ { "name": "Fin", "module": "Init.Prelude" }, { "name": "Subspace", "module": "Mathlib.Algebra.Module.Submodule.Basic" }, { "name": "Set", "module": "Mathlib.Data.Set.Defs" }, { "name": "Set.Ico", "module": "Mathlib.Order.Interval.Set.Defs" }, { "name": "Submodule"...	[ { "name": "hammingDist", "content": "notation \"Δ₀(\" u \", \" v \")\" => hammingDist u v" }, { "name": "distFromCode", "content": "notation \"Δ₀(\" u \", \" C \")\" => distFromCode u C" }, { "name": "scoped macro_rules", "content": "scoped macro_rules\n \| `(ρ $t:term) => `(LinearCo...	[ { "name": "Fin.is_le", "module": "Init.Data.Fin.Lemmas" }, { "name": "Nat.lt_of_add_right_lt", "module": "Init.Data.Nat.Basic" }, { "name": "Nat.lt_of_le_of_lt", "module": "Init.Prelude" }, { "name": "Fin.eta", "module": "Init.Data.Fin.Lemmas" }, { "name": "add_ze...	[ { "name": "Xⱼ_zero_eq_one", "content": "lemma Xⱼ_zero_eq_one (ℓ : ℕ) (h_ℓ : ℓ ≤ r) :\n Xⱼ 𝔽q β ℓ h_ℓ ⟨0, by exact Nat.two_pow_pos ℓ⟩ = 1" }, { "name": "lt_add_of_pos_right_of_le", "content": "@[simp]\nlemma lt_add_of_pos_right_of_le (a b c : ℕ) [NeZero c] (h : a ≤ b) : a < b + c" }, { ...	[ { "name": "Binius.BinaryBasefold.OracleFunction", "content": "abbrev OracleFunction (i : Fin (ℓ + 1)) : Type _ := sDomain 𝔽q β h_ℓ_add_R_rate ⟨i, by admit /- proof elided -/\n ⟩ → L" }, { "name": "Binius.BinaryBasefold.fiber_coeff", "content": "noncomputable def fiber_coeff\n (i : Fin r) ...	[ { "name": "Binius.BinaryBasefold.fin_ℓ_steps_lt_ℓ_add_R", "content": "omit [NeZero ℓ] in\nlemma fin_ℓ_steps_lt_ℓ_add_R (i : Fin ℓ) (steps : ℕ) (h : i.val + steps ≤ ℓ)\n : i.val + steps < ℓ + 𝓡" }, { "name": "Binius.BinaryBasefold.qMap_total_fiber_repr_coeff", "content": "lemma qMap_total_fib...	import ArkLib.Data.CodingTheory.BerlekampWelch.BerlekampWelch import ArkLib.Data.CodingTheory.ReedSolomon import ArkLib.Data.FieldTheory.AdditiveNTT.AdditiveNTT import ArkLib.Data.MvPolynomial.Multilinear import ArkLib.Data.Vector.Basic import ArkLib.ProofSystem.Sumcheck.Spec.SingleRound namespace Binius.BinaryBa...	theorem fiberwise_dist_lt_imp_dist_lt_unique_decoding_radius (i : Fin ℓ) (steps : ℕ) [NeZero steps] (h_i_add_steps : i.val + steps ≤ ℓ) (f : OracleFunction 𝔽q β (h_ℓ_add_R_rate := h_ℓ_add_R_rate) ⟨i, by omega⟩) (h_fw_dist_lt : fiberwiseClose 𝔽q β (h_ℓ_add_R_rate := h_ℓ_add_R_rate) (i := i) (steps := ste...	:= by unfold fiberwiseClose at h_fw_dist_lt unfold hammingClose -- 2 * Δ₀(f, ↑(BBF_Code 𝔽q β ⟨↑i, ⋯⟩)) < ↑(BBF_CodeDistance ℓ 𝓡 ⟨↑i, ⋯⟩) let d_fw := fiberwiseDistance 𝔽q β (i := i) steps h_i_add_steps f let C_i := (BBF_Code 𝔽q β (h_ℓ_add_R_rate := h_ℓ_add_R_rate) ⟨i, by omega⟩) let d_H := Code.distFromC...	7	232	false	Applied verif.
2	ConcreteBinaryTower.minPoly_of_powerBasisSucc_generator	@[simp] theorem minPoly_of_powerBasisSucc_generator (k : ℕ) : (minpoly (ConcreteBTField k) (powerBasisSucc k).gen) = X^2 + (Z k) • X + 1	ArkLib	ArkLib/Data/FieldTheory/BinaryField/Tower/Impl.lean	[ "import ArkLib.Data.FieldTheory.BinaryField.Tower.Prelude", "import ArkLib.Data.FieldTheory.BinaryField.Tower.Basic", "import ArkLib.Data.Classes.DCast" ]	[ { "name": "Eq", "module": "Init.Prelude" }, { "name": "id", "module": "Init.Prelude" }, { "name": "BitVec", "module": "Init.Prelude" }, { "name": "Nat", "module": "Init.Prelude" }, { "name": "BitVec.cast", "module": "Init.Data.BitVec.Basic" }, { "name"...	[ { "name": "GaloisField", "content": "notation : 10 \"GF(\" term : 10 \")\" => GaloisField term 1" }, { "name": "DCast", "content": "class DCast (α : Sort) (β : α → Sort) where\n dcast : ∀ {a a' : α}, a = a' → β a → β a'\n dcast_id : ∀ {a : α}, dcast (Eq.refl a) = id" }, { "name": "su...	[ { "name": "Nat.sub_add_cancel", "module": "Init.Data.Nat.Basic" }, { "name": "Nat.sub_zero", "module": "Init.Data.Nat.Basic" }, { "name": "BitVec.ofNat_toNat", "module": "Init.Data.BitVec.Bootstrap" }, { "name": "BitVec.setWidth_eq", "module": "Init.Data.BitVec.Lemmas" ...	[ { "name": "one_le_two_pow_n", "content": "theorem one_le_two_pow_n (n : ℕ) : 1 ≤ 2 ^ n" }, { "name": "dcast_eq", "content": "@[simp]\ntheorem dcast_eq : dcast (Eq.refl a) b = b" }, { "name": "one_le_sub_consecutive_two_pow", "content": "theorem one_le_sub_consecutive_two_pow (n : ℕ):...	[ { "name": "ConcreteBinaryTower.ConcreteBTField", "content": "def ConcreteBTField : ℕ → Type := fun k => BitVec (2 ^ k)" }, { "name": "ConcreteBinaryTower.BitVec", "content": "instance BitVec.instDCast : DCast Nat BitVec where\n dcast h := BitVec.cast h\n dcast_id := by admit /- proof elided -/...	[ { "name": "ConcreteBinaryTower.cast_ConcreteBTField_eq", "content": "lemma cast_ConcreteBTField_eq (k m : ℕ) (h_eq : k = m) :\n ConcreteBTField k = ConcreteBTField m" }, { "name": "ConcreteBinaryTower.BitVec.dcast_id", "content": "theorem BitVec.dcast_id {n : Nat} (bv : BitVec n) :\n DCast.dca...	import ArkLib.Data.Classes.DCast import ArkLib.Data.FieldTheory.BinaryField.Tower.Basic namespace ConcreteBinaryTower open Polynomial def ConcreteBTField : ℕ → Type := fun k => BitVec (2 ^ k) section BitVecDCast instance BitVec.instDCast : DCast Nat BitVec where dcast h := BitVec.cast h dcast_id := by admit /...	@[simp] theorem minPoly_of_powerBasisSucc_generator (k : ℕ) : (minpoly (ConcreteBTField k) (powerBasisSucc k).gen) = X^2 + (Z k) • X + 1 :=	:= by unfold powerBasisSucc simp only rw [←C_mul'] letI: Fintype (ConcreteBTField k) := (getBTFResult k).instFintype refine Eq.symm (minpoly.unique' (ConcreteBTField k) (Z (k + 1)) ?_ ?_ ?_) · exact (definingPoly_is_monic (s:=Z (k))) · exact aeval_definingPoly_at_Z_succ k · intro q h_degQ_lt_deg_minPoly...	16	324	false	Applied verif.
3	AdditiveNTT.evaluation_poly_split_identity	theorem evaluation_poly_split_identity (i : Fin (ℓ)) (coeffs : Fin (2 ^ (ℓ - i)) → L) : let P_i: L[X] := intermediateEvaluationPoly 𝔽q β h_ℓ_add_R_rate ⟨i, by omega⟩ coeffs let P_even_i_plus_1: L[X] := evenRefinement 𝔽q β h_ℓ_add_R_rate i coeffs let P_odd_i_plus_1: L[X] := oddRefinement 𝔽q β h_ℓ_add_R_rate...	ArkLib	ArkLib/Data/FieldTheory/AdditiveNTT/AdditiveNTT.lean	[ "import ArkLib.Data.FieldTheory.AdditiveNTT.NovelPolynomialBasis", "import Mathlib.Data.Finsupp.Defs", "import ArkLib.Data.Fin.BigOperators", "import Mathlib.Tactic", "import ArkLib.Data.Nat.Bitwise", "import Mathlib.LinearAlgebra.LinearIndependent.Defs" ]	[ { "name": "Fin", "module": "Init.Prelude" }, { "name": "Subspace", "module": "Mathlib.Algebra.Module.Submodule.Basic" }, { "name": "Set", "module": "Mathlib.Data.Set.Defs" }, { "name": "Set.Ico", "module": "Mathlib.Order.Interval.Set.Defs" }, { "name": "Submodule"...	[ { "name": "W", "content": "noncomputable def W (i : Fin r) : L[X] :=\n ∏ u : U 𝔽q β i, (X - C u.val)" }, { "name": "U", "content": "def U (i : Fin r) : Subspace 𝔽q L := Submodule.span 𝔽q (β '' (Set.Ico 0 i))" }, { "name": "normalizedW", "content": "noncomputable def normalizedW (...	[ { "name": "Polynomial.comp_assoc", "module": "Mathlib.Algebra.Polynomial.Eval.Defs" }, { "name": "implies_true", "module": "Init.SimpLemmas" }, { "name": "Fin.coe_ofNat_eq_mod", "module": "Mathlib.Data.Fin.Basic" }, { "name": "Fin.foldl_succ", "module": "Init.Data.Fin.Fol...	[ { "name": "Xⱼ_zero_eq_one", "content": "lemma Xⱼ_zero_eq_one (ℓ : ℕ) (h_ℓ : ℓ ≤ r) :\n Xⱼ 𝔽q β ℓ h_ℓ ⟨0, by exact Nat.two_pow_pos ℓ⟩ = 1" }, { "name": "getBit_eq_succ_getBit_of_mul_two_add_one", "content": "lemma getBit_eq_succ_getBit_of_mul_two_add_one {n k : ℕ} : getBit (k+1) (2*n + 1) = get...	[ { "name": "AdditiveNTT.qMap", "content": "noncomputable def qMap (i : Fin r) : L[X] :=\n let constMultiplier := ((W 𝔽q β i).eval (β i))^(Fintype.card 𝔽q)\n / ((W 𝔽q β (i + 1)).eval (β (i + 1)))\n C constMultiplier * ∏ c: 𝔽q, (X - C (algebraMap 𝔽q L c))" }, { "name": "AdditiveNTT.intermedia...	[ { "name": "AdditiveNTT.Polynomial.foldl_comp", "content": "omit [Fintype L] [DecidableEq L] in\ntheorem Polynomial.foldl_comp (n : ℕ) (f : Fin n → L[X]) : ∀ initInner initOuter: L[X],\n Fin.foldl (n:=n) (fun acc j => (f j).comp acc) (initOuter.comp initInner)\n = (Fin.foldl (n:=n) (fun acc j => (f j)....	import ArkLib.Data.FieldTheory.AdditiveNTT.NovelPolynomialBasis import Mathlib.Tactic import Mathlib.Data.Finsupp.Defs import Mathlib.LinearAlgebra.LinearIndependent.Defs open Polynomial AdditiveNTT Module namespace AdditiveNTT variable {r : ℕ} [NeZero r] variable {L : Type u} [Field L] [Fintype L] [DecidableEq ...	theorem evaluation_poly_split_identity (i : Fin (ℓ)) (coeffs : Fin (2 ^ (ℓ - i)) → L) : let P_i: L[X] :=	:= intermediateEvaluationPoly 𝔽q β h_ℓ_add_R_rate ⟨i, by omega⟩ coeffs let P_even_i_plus_1: L[X] := evenRefinement 𝔽q β h_ℓ_add_R_rate i coeffs let P_odd_i_plus_1: L[X] := oddRefinement 𝔽q β h_ℓ_add_R_rate i coeffs let q_i: L[X] := qMap 𝔽q β ⟨i, by omega⟩ P_i = (P_even_i_plus_1.comp q_i) + X * (P_odd_i_plus...	7	78	false	Applied verif.
4	Nat.getBit_repr	theorem getBit_repr {ℓ : Nat} : ∀ j, j < 2^ℓ → j = ∑ k ∈ Finset.Icc 0 (ℓ-1), (getBit k j) * 2^k	ArkLib	ArkLib/Data/Nat/Bitwise.lean	[ "import Mathlib.Algebra.Order.BigOperators.Group.Finset", "import ArkLib.Data.Fin.BigOperators", "import Mathlib.Algebra.BigOperators.Ring.Finset", "import Mathlib.Data.Nat.Bitwise", "import Mathlib.Data.Finsupp.Basic", "import Mathlib.Algebra.Order.Ring.Star", "import Mathlib.Data.Nat.Digits.Defs", "...	[ { "name": "Nat", "module": "Init.Prelude" }, { "name": "Finset", "module": "Mathlib.Data.Finset.Defs" }, { "name": "Finset.Icc", "module": "Mathlib.Order.Interval.Finset.Defs" }, { "name": "And", "module": "Init.Prelude" }, { "name": "AddCommMonoid", "module":...	[ { "name": "...", "content": "..." } ]	[ { "name": "Nat.shiftRight_add", "module": "Init.Data.Nat.Bitwise.Basic" }, { "name": "add_comm", "module": "Mathlib.Algebra.Group.Defs" }, { "name": "Finset.Icc_self", "module": "Mathlib.Order.Interval.Finset.Basic" }, { "name": "Finset.mem_Icc", "module": "Mathlib.Order....	[ { "name": "sum_Icc_split", "content": "theorem sum_Icc_split {α : Type*} [AddCommMonoid α] (f : ℕ → α) (a b c : ℕ)\n (h₁ : a ≤ b) (h₂ : b ≤ c):\n ∑ i ∈ Finset.Icc a c, f i = ∑ i ∈ Finset.Icc a b, f i + ∑ i ∈ Finset.Icc (b+1) c, f i" } ]	[ { "name": "Nat.getBit", "content": "def getBit (k n : Nat) : Nat := (n >>> k) &&& 1" } ]	[ { "name": "Nat.getBit_of_shiftRight", "content": "lemma getBit_of_shiftRight {n p : ℕ}:\n ∀ k, getBit k (n >>> p) = getBit (k+p) n" } ]	import ArkLib.Data.Fin.BigOperators import Mathlib.Algebra.BigOperators.Ring.Finset import Mathlib.Algebra.Order.Ring.Star import Mathlib.Data.Nat.Bitwise import Mathlib.Data.Nat.Digits.Defs import Mathlib.Data.Finsupp.Basic import Mathlib.Algebra.Order.BigOperators.Group.Finset import Mathlib.Algebra.BigOperato...	theorem getBit_repr {ℓ : Nat} : ∀ j, j < 2^ℓ → j = ∑ k ∈ Finset.Icc 0 (ℓ-1), (getBit k j) * 2^k :=	:= by induction ℓ with \| zero => -- Base case : ℓ = 0 intro j h_j have h_j_zero : j = 0 := by exact Nat.lt_one_iff.mp h_j subst h_j_zero simp only [zero_tsub, Finset.Icc_self, Finset.sum_singleton, pow_zero, mul_one] unfold getBit rw [Nat.shiftRight_zero, Nat.and_one_is_mod] \| succ ℓ₁ ...	2	24	true	Applied verif.
5	Nat.getBit_of_binaryFinMapToNat	lemma getBit_of_binaryFinMapToNat {n : ℕ} (m : Fin n → ℕ) (h_binary: ∀ j: Fin n, m j ≤ 1) : ∀ k: ℕ, Nat.getBit k (binaryFinMapToNat m h_binary).val = if h_k: k < n then m ⟨k, by omega⟩ else 0	ArkLib	ArkLib/Data/Nat/Bitwise.lean	[ "import Mathlib.Algebra.Order.BigOperators.Group.Finset", "import ArkLib.Data.Fin.BigOperators", "import Mathlib.Algebra.BigOperators.Ring.Finset", "import Mathlib.Data.Nat.Bitwise", "import Mathlib.Data.Finsupp.Basic", "import Mathlib.Algebra.Order.Ring.Star", "import Mathlib.Data.Nat.Digits.Defs", "...	[ { "name": "Nat", "module": "Init.Prelude" }, { "name": "Fin", "module": "Init.Prelude" }, { "name": "Finset", "module": "Mathlib.Data.Finset.Defs" }, { "name": "Finset.univ", "module": "Mathlib.Data.Fintype.Defs" }, { "name": "Ne", "module": "Init.Core" }, ...	[ { "name": "...", "content": "..." } ]	[ { "name": "Nat.and_one_is_mod", "module": "Init.Data.Nat.Bitwise.Lemmas" }, { "name": "Nat.mod_lt", "module": "Init.Prelude" }, { "name": "Nat.ofNat_pos", "module": "Mathlib.Data.Nat.Cast.Order.Ring" }, { "name": "gt_iff_lt", "module": "Init.Core" }, { "name": "Na...	[ { "name": "List.getElem_append_left{α", "content": "theorem List.getElem_append_left{α : Type u_1} {l₁ l₂ : List α} {i : Nat} (hn : i < l₁.length) :\\n(l₁ ++ l₂)[i] = l₁[i]" } ]	[ { "name": "Nat.getBit", "content": "def getBit (k n : Nat) : Nat := (n >>> k) &&& 1" }, { "name": "Nat.binaryFinMapToNat", "content": "def binaryFinMapToNat {n : ℕ} (m : Fin n → ℕ) (h_binary : ∀ j: Fin n, m j ≤ 1) : Fin (2^n) :=" } ]	[ { "name": "Nat.getBit_lt_2", "content": "lemma getBit_lt_2 {k n : Nat} : getBit k n < 2" }, { "name": "Nat.getBit_eq_testBit", "content": "lemma getBit_eq_testBit (k n : Nat) : getBit k n = if n.testBit k then 1 else 0" }, { "name": "Nat.getBit_zero_eq_zero", "content": "lemma getBit...	import ArkLib.Data.Fin.BigOperators import Mathlib.Algebra.BigOperators.Ring.Finset import Mathlib.Algebra.Order.Ring.Star import Mathlib.Data.Nat.Bitwise import Mathlib.Data.Nat.Digits.Defs import Mathlib.Data.Finsupp.Basic import Mathlib.Algebra.Order.BigOperators.Group.Finset import Mathlib.Algebra.BigOperato...	lemma getBit_of_binaryFinMapToNat {n : ℕ} (m : Fin n → ℕ) (h_binary: ∀ j: Fin n, m j ≤ 1) : ∀ k: ℕ, Nat.getBit k (binaryFinMapToNat m h_binary).val = if h_k: k < n then m ⟨k, by omega⟩ else 0 :=	:= by -- We prove this by induction on `n`. induction n with \| zero => intro k; simp only [Nat.pow_zero, Fin.val_eq_zero, not_lt_zero', ↓reduceDIte] exact getBit_zero_eq_zero \| succ n ih => -- Inductive step: Assume the property holds for `n`, prove it for `n+1`. have h_lt: 2^n - 1 < 2^n := ...	4	104	true	Applied verif.
6	ConcreteBinaryTower.towerEquiv_commutes_left_diff	"lemma towerEquiv_commutes_left_diff (i d : ℕ) : ∀ r : ConcreteBTField i,\n (AlgebraTower.algeb(...TRUNCATED)	ArkLib	ArkLib/Data/FieldTheory/BinaryField/Tower/Impl.lean	["import ArkLib.Data.FieldTheory.BinaryField.Tower.Prelude","import ArkLib.Data.FieldTheory.BinaryFi(...TRUNCATED)	[{"name":"Eq","module":"Init.Prelude"},{"name":"id","module":"Init.Prelude"},{"name":"BitVec","modul(...TRUNCATED)	[{"name":"GaloisField","content":"notation : 10 \"GF(\" term : 10 \")\" => GaloisField term 1"},{"na(...TRUNCATED)	[{"name":"Ne.dite_eq_left_iff","module":"Mathlib.Logic.Basic"},{"name":"Nat.add_one_sub_one","module(...TRUNCATED)	[{"name":"one_le_two_pow_n","content":"theorem one_le_two_pow_n (n : ℕ) : 1 ≤ 2 ^ n"},{"name":"d(...TRUNCATED)	[{"name":"ConcreteBinaryTower.ConcreteBTField","content":"def ConcreteBTField : ℕ → Type := fun (...TRUNCATED)	[{"name":"ConcreteBinaryTower.cast_ConcreteBTField_eq","content":"lemma cast_ConcreteBTField_eq (k m(...TRUNCATED)	"import ArkLib.Data.Classes.DCast\n\nimport ArkLib.Data.FieldTheory.BinaryField.Tower.Basic\n\nnames(...TRUNCATED)	"lemma towerEquiv_commutes_left_diff (i d : ℕ) : ∀ r : ConcreteBTField i,\n (AlgebraTower.algeb(...TRUNCATED)	":= by\n -- If d = 0, then this is trivial\n -- For d > 0 : let j = i+d\n -- lhs of goal : righ(...TRUNCATED)	10	306	false	Applied verif.
7	AdditiveNTT.intermediateNormVpoly_comp	"omit [DecidableEq L] [DecidableEq 𝔽q] h_Fq_char_prime hF₂ hβ_lin_indep h_β₀_eq_1 in\ntheor(...TRUNCATED)	ArkLib	ArkLib/Data/FieldTheory/AdditiveNTT/AdditiveNTT.lean	["import ArkLib.Data.FieldTheory.AdditiveNTT.NovelPolynomialBasis","import Mathlib.Data.Finsupp.Defs(...TRUNCATED)	[{"name":"Fin","module":"Init.Prelude"},{"name":"Subspace","module":"Mathlib.Algebra.Module.Submodul(...TRUNCATED)	[{"name":"W","content":"noncomputable def W (i : Fin r) : L[X] :=\n ∏ u : U 𝔽q β i, (X - C u.(...TRUNCATED)	[{"name":"Fin.cast_eq_self","module":"Mathlib.Data.Fin.Basic"},{"name":"Fin.coe_cast","module":"Init(...TRUNCATED)	[{"name":"Xⱼ_zero_eq_one","content":"lemma Xⱼ_zero_eq_one (ℓ : ℕ) (h_ℓ : ℓ ≤ r) :\n X(...TRUNCATED)	[{"name":"AdditiveNTT.qMap","content":"noncomputable def qMap (i : Fin r) : L[X] :=\n let constMult(...TRUNCATED)	[]	"import ArkLib.Data.FieldTheory.AdditiveNTT.NovelPolynomialBasis\n\nimport Mathlib.Tactic\n\nimport (...TRUNCATED)	"omit [DecidableEq L] [DecidableEq 𝔽q] h_Fq_char_prime hF₂ hβ_lin_indep h_β₀_eq_1 in\ntheor(...TRUNCATED)	":= by\n induction l using Fin.succRecOnSameFinType with\n \| zero =>\n simp only [Fin.coe_ofNat(...TRUNCATED)	5	38	false	Applied verif.
8	AdditiveNTT.inductive_rec_form_W_comp	"omit h_Fq_char_prime hF₂ in\nlemma inductive_rec_form_W_comp (i : Fin r) (h_i_add_1 : i + 1 < r)\(...TRUNCATED)	ArkLib	ArkLib/Data/FieldTheory/AdditiveNTT/NovelPolynomialBasis.lean	["import Mathlib.Algebra.Polynomial.Degree.Definitions","import ArkLib.Data.Fin.BigOperators","impor(...TRUNCATED)	[{"name":"Fin","module":"Init.Prelude"},{"name":"Subspace","module":"Mathlib.Algebra.Module.Submodul(...TRUNCATED)	[ { "name": "getBit", "content": "def getBit (k n : Nat) : Nat := (n >>> k) &&& 1" } ]	[{"name":"Fact.out","module":"Mathlib.Logic.Basic"},{"name":"Fin.le_zero_iff'","module":"Mathlib.Dat(...TRUNCATED)	[{"name":"Fin.lt_succ'","content":"lemma Fin.lt_succ' (a : Fin r) (h_a_add_1 : a + 1 < r) : a < a + (...TRUNCATED)	[{"name":"AdditiveNTT.U","content":"def U (i : Fin r) : Subspace 𝔽q L := Submodule.span 𝔽q (β(...TRUNCATED)	[{"name":"AdditiveNTT.βᵢ_not_in_Uᵢ","content":"lemma βᵢ_not_in_Uᵢ (i : Fin r) :\n β i (...TRUNCATED)	"import ArkLib.Data.Nat.Bitwise\n\nimport ArkLib.Data.Polynomial.Frobenius\n\nimport ArkLib.Data.Pol(...TRUNCATED)	"omit h_Fq_char_prime hF₂ in\nlemma inductive_rec_form_W_comp (i : Fin r) (h_i_add_1 : i + 1 < r)\(...TRUNCATED)	":= by\n intro p\n set W_i := W 𝔽q β i\n set q := Fintype.card 𝔽q\n set v := W_i.eval (β(...TRUNCATED)	6	229	false	Applied verif.
9	AdditiveNTT.odd_index_intermediate_novel_basis_decomposition	"lemma odd_index_intermediate_novel_basis_decomposition\n (i : Fin ℓ) (j : Fin (2 ^ (ℓ - i - (...TRUNCATED)	ArkLib	ArkLib/Data/FieldTheory/AdditiveNTT/AdditiveNTT.lean	["import ArkLib.Data.FieldTheory.AdditiveNTT.NovelPolynomialBasis","import Mathlib.Data.Finsupp.Defs(...TRUNCATED)	[{"name":"Fin","module":"Init.Prelude"},{"name":"Subspace","module":"Mathlib.Algebra.Module.Submodul(...TRUNCATED)	[{"name":"W","content":"noncomputable def W (i : Fin r) : L[X] :=\n ∏ u : U 𝔽q β i, (X - C u.(...TRUNCATED)	[{"name":"Polynomial.comp_assoc","module":"Mathlib.Algebra.Polynomial.Eval.Defs"},{"name":"implies_t(...TRUNCATED)	[{"name":"Xⱼ_zero_eq_one","content":"lemma Xⱼ_zero_eq_one (ℓ : ℕ) (h_ℓ : ℓ ≤ r) :\n X(...TRUNCATED)	[{"name":"AdditiveNTT.qMap","content":"noncomputable def qMap (i : Fin r) : L[X] :=\n let constMult(...TRUNCATED)	[{"name":"AdditiveNTT.Polynomial.foldl_comp","content":"omit [Fintype L] [DecidableEq L] in\ntheorem(...TRUNCATED)	"import ArkLib.Data.FieldTheory.AdditiveNTT.NovelPolynomialBasis\n\nimport Mathlib.Tactic\n\nimport (...TRUNCATED)	"lemma odd_index_intermediate_novel_basis_decomposition\n (i : Fin ℓ) (j : Fin (2 ^ (ℓ - i - (...TRUNCATED)	":= by\n unfold intermediateNovelBasisX\n rw [prod_comp]\n -- ∏ k ∈ Fin (ℓ - i), (Wₖ⁽(...TRUNCATED)	5	50	false	Applied verif.
10	AdditiveNTT.finToBinaryCoeffs_sDomainToFin	"omit h_β₀_eq_1 in\nlemma finToBinaryCoeffs_sDomainToFin (i : Fin r) (h_i : i < ℓ + R_rate)\n (...TRUNCATED)	ArkLib	ArkLib/Data/FieldTheory/AdditiveNTT/AdditiveNTT.lean	["import ArkLib.Data.FieldTheory.AdditiveNTT.NovelPolynomialBasis","import Mathlib.Data.Finsupp.Defs(...TRUNCATED)	[{"name":"Nat","module":"Init.Prelude"},{"name":"Fin","module":"Init.Prelude"},{"name":"Subspace","m(...TRUNCATED)	[{"name":"getBit","content":"def getBit (k n : Nat) : Nat := (n >>> k) &&& 1"},{"name":"normalizedW"(...TRUNCATED)	[{"name":"Fintype.card_le_one_iff_subsingleton","module":"Mathlib.Data.Fintype.EquivFin"},{"name":"F(...TRUNCATED)	[{"name":"Xⱼ_zero_eq_one","content":"lemma Xⱼ_zero_eq_one (ℓ : ℕ) (h_ℓ : ℓ ≤ r) :\n X(...TRUNCATED)	[{"name":"AdditiveNTT.sDomain","content":"noncomputable def sDomain (i : Fin r) : Subspace 𝔽q L :(...TRUNCATED)	[{"name":"AdditiveNTT.𝔽q_element_eq_zero_or_eq_one","content":"omit h_Fq_char_prime in\nlemma (...TRUNCATED)	"import ArkLib.Data.FieldTheory.AdditiveNTT.NovelPolynomialBasis\n\nimport Mathlib.Tactic\n\nimport (...TRUNCATED)	"omit h_β₀_eq_1 in\nlemma finToBinaryCoeffs_sDomainToFin (i : Fin r) (h_i : i < ℓ + R_rate)\n (...TRUNCATED)	":= (sDomainToFin 𝔽q β h_ℓ_add_R_rate i h_i) x\n finToBinaryCoeffs 𝔽q (i := i) (idx :=po(...TRUNCATED)	5	84	false	Applied verif.

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VeriSoftBench

VeriSoftBench is a benchmark for evaluating neural theorem provers on software verification tasks in Lean 4.

The dataset contains 500 theorem-proving tasks drawn from 23 real-world Lean 4 repositories spanning compiler verification, type system formalization, applied verification (zero-knowledge proofs, smart contracts), semantic frameworks, and more.

📄 Paper (arXiv): https://arxiv.org/html/2602.18307v1
💻 Full benchmark + pipeline + setup: https://github.com/utopia-group/VeriSoftBench

Dataset Contents

This Hugging Face release contains the dataset of the benchmark tasks only. For the full end-to-end evaluation pipeline, please refer to the Github repository:

👉 https://github.com/utopia-group/VeriSoftBench

Each task in verisoftbench.jsonl contains:

Theorem name, statement, and source location
Filtered dependencies (library defs, repo defs, local context, lemmas)
Ground truth proof
Metadata (category, difficulty metrics, Aristotle subset membership)

Citation

@misc{xin2026verisoftbenchrepositoryscaleformalverification,
      title={VeriSoftBench: Repository-Scale Formal Verification Benchmarks for Lean}, 
      author={Yutong Xin and Qiaochu Chen and Greg Durrett and Işil Dillig},
      year={2026},
      eprint={2602.18307},
      archivePrefix={arXiv},
      primaryClass={cs.SE},
      url={https://arxiv.org/abs/2602.18307}, 
}

Downloads last month: 16

Size of downloaded dataset files:

9.22 MB

Size of the auto-converted Parquet files:

6.84 MB

Number of rows:

500

Paper for maxRyeery/VeriSoftBench

VeriSoftBench: Repository-Scale Formal Verification Benchmarks for Lean

Paper • 2602.18307 • Published Feb 20