id stringlengths 15 31 | source_file stringclasses 2 values | construct_type stringclasses 3 values | construct_name stringlengths 10 26 | original_code stringlengths 31 145 | corrupted_code stringlengths 32 146 | error_info dict | repair_target stringlengths 16 127 | domain stringclasses 2 values | language stringclasses 1 value | imports stringclasses 1 value |
|---|---|---|---|---|---|---|---|---|---|---|
addition_identity_2571 | manual_examples | theorem | addition_identity | theorem addition_identity (n : ℕ) : n + 0 = n := by simp | theorem addition_identity (n : ℕ) : n ++ 0 = n := by simp | {
"corrupted_token": " ++ ",
"corruption_successful": true,
"error_type": "operator_error",
"original_token": " + "
} | theorem addition_identity (n : ℕ) : n + 0 = n := by simp | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
complex_re_add_8723 | manual_examples | theorem | complex_re_add | theorem complex_re_add (z w : ℂ) : (z + w).re = z.re + w.re := by simp | theorem complex_re_add (z w : ℝ) : (z + w).re = z.re + w.re := by simp | {
"corrupted_token": "ℝ",
"corruption_successful": true,
"error_type": "type_error",
"original_token": "ℂ"
} | theorem complex_re_add (z w : ℂ) : (z + w).re = z.re + w.re := by simp | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
double_def_1590 | manual_examples | def | double_def | def double (n : ℕ) : ℕ := n + n | def double (n : Natt) : ℕ := n + n | {
"corrupted_token": "Natt",
"corruption_successful": true,
"error_type": "type_error",
"original_token": "ℕ"
} | def double (n : ℕ) : ℕ := n + n | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
matrix_scalar_distributive_3902 | manual_examples | theorem | matrix_scalar_distributive | theorem matrix_scalar_distributive (c : ℂ) (A B : Matrix (Fin 2) (Fin 2) ℂ) : c • (A + B) = c • A + c • B := by simp [smul_add] | theorem matrix_scalar_distributive (c : ℂ) (A B : Matrix (Finn 2) (Fin 2) ℂ) : c • (A + B) = c • A + c • B := by simp [smul_add] | {
"corrupted_token": "Finn",
"corruption_successful": true,
"error_type": "type_error",
"original_token": "Fin"
} | theorem matrix_scalar_distributive (c : ℂ) (A B : Matrix (Fin 2) (Fin 2) ℂ) : c • (A + B) = c • A + c • B := by simp [smul_add] | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
subtraction_self_8199 | manual_examples | theorem | subtraction_self | theorem subtraction_self (n : ℕ) : n - n = 0 := by simp | theorem subtraction_self (n : ℕ) : n - n = 0 := byy simp | {
"corrupted_token": "byy",
"corruption_successful": true,
"error_type": "syntax_error",
"original_token": "by"
} | theorem subtraction_self (n : ℕ) : n - n = 0 := by simp | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
complex_zero_mul_8661 | manual_examples | theorem | complex_zero_mul | theorem complex_zero_mul (z : ℂ) : 0 * z = 0 := by simp | theorem complex_zero_mul (z : ℂ) : 0 * z = 0 := by simpp | {
"corrupted_token": "simpp",
"corruption_successful": true,
"error_type": "syntax_error",
"original_token": "simp"
} | theorem complex_zero_mul (z : ℂ) : 0 * z = 0 := by simp | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
matrix_mul_one_2955 | manual_examples | theorem | matrix_mul_one | theorem matrix_mul_one (A : Matrix (Fin 2) (Fin 2) ℂ) : A * 1 = A := by simp | theorem matrix_mul_one (A : Matrix (Fin 2) (Fin 2) ℂ) : A ** 1 = A := by simp | {
"corrupted_token": " ** ",
"corruption_successful": true,
"error_type": "operator_error",
"original_token": " * "
} | theorem matrix_mul_one (A : Matrix (Fin 2) (Fin 2) ℂ) : A * 1 = A := by simp | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
complex_im_add_7170 | manual_examples | theorem | complex_im_add | theorem complex_im_add (z w : ℂ) : (z + w).im = z.im + w.im := by simp | theorem complex_im_add (z w : ℂ) : (z + w).im = z.im + w.im := byy simp | {
"corrupted_token": "byy",
"corruption_successful": true,
"error_type": "syntax_error",
"original_token": "by"
} | theorem complex_im_add (z w : ℂ) : (z + w).im = z.im + w.im := by simp | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
complex_add_conjugate_7145 | manual_examples | theorem | complex_add_conjugate | theorem complex_add_conjugate (z w : ℂ) : star (z + w) = star z + star w := by rw [star_add] | theorem complex_add_conjugate (z w : ℂ) : star (z + w) == star z + star w := by rw [star_add] | {
"corrupted_token": " == ",
"corruption_successful": true,
"error_type": "operator_error",
"original_token": " = "
} | theorem complex_add_conjugate (z w : ℂ) : star (z + w) = star z + star w := by rw [star_add] | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
matrix_one_mul_2874 | manual_examples | theorem | matrix_one_mul | theorem matrix_one_mul (A : Matrix (Fin 2) (Fin 2) ℂ) : 1 * A = A := by simp | theorem matrix_one_mul (A : Matrix (Fin 2) (Fin 2) ℂ) : 1 * A = A := byy simp | {
"corrupted_token": "byy",
"corruption_successful": true,
"error_type": "syntax_error",
"original_token": "by"
} | theorem matrix_one_mul (A : Matrix (Fin 2) (Fin 2) ℂ) : 1 * A = A := by simp | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
complex_one_mul_8672 | manual_examples | theorem | complex_one_mul | theorem complex_one_mul (z : ℂ) : 1 * z = z := by simp | theorem complex_one_mul (z : ℂ) : 1 * z = z := byy simp | {
"corrupted_token": "byy",
"corruption_successful": true,
"error_type": "syntax_error",
"original_token": "by"
} | theorem complex_one_mul (z : ℂ) : 1 * z = z := by simp | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
addition_commutative_6128 | manual_examples | theorem | addition_commutative | theorem addition_commutative (a b : ℕ) : a + b = b + a := by rw [Nat.add_comm] | theorem addition_commutative (a b : Natt) : a + b = b + a := by rw [Nat.add_comm] | {
"corrupted_token": "Natt",
"corruption_successful": true,
"error_type": "type_error",
"original_token": "ℕ"
} | theorem addition_commutative (a b : ℕ) : a + b = b + a := by rw [Nat.add_comm] | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
multiplication_commutative_6319 | manual_examples | theorem | multiplication_commutative | theorem multiplication_commutative (a b : ℕ) : a * b = b * a := by rw [Nat.mul_comm] | theorem multiplication_commutative (a b : ℕ) : a * b == b * a := by rw [Nat.mul_comm] | {
"corrupted_token": " == ",
"corruption_successful": true,
"error_type": "operator_error",
"original_token": " = "
} | theorem multiplication_commutative (a b : ℕ) : a * b = b * a := by rw [Nat.mul_comm] | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
distributive_law_4132 | manual_examples | theorem | distributive_law | theorem distributive_law (a b c : ℕ) : a * (b + c) = a * b + a * c := by rw [Nat.mul_add] | theorem distributive_law (a b c : ℕ) : a * (b ++ c) = a * b + a * c := by rw [Nat.mul_add] | {
"corrupted_token": " ++ ",
"corruption_successful": true,
"error_type": "operator_error",
"original_token": " + "
} | theorem distributive_law (a b c : ℕ) : a * (b + c) = a * b + a * c := by rw [Nat.mul_add] | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
matrix_neg_neg_9564 | manual_examples | theorem | matrix_neg_neg | theorem matrix_neg_neg (A : Matrix (Fin 2) (Fin 2) ℂ) : -(-A) = A := by simp | theorem matrix_neg_neg (A : Matrix (Finn 2) (Fin 2) ℂ) : -(-A) = A := by simp | {
"corrupted_token": "Finn",
"corruption_successful": true,
"error_type": "type_error",
"original_token": "Fin"
} | theorem matrix_neg_neg (A : Matrix (Fin 2) (Fin 2) ℂ) : -(-A) = A := by simp | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
square_def_7948 | manual_examples | def | square_def | def square (n : ℕ) : ℕ := n * n | deff square (n : ℕ) : ℕ := n * n | {
"corrupted_token": "deff",
"corruption_successful": true,
"error_type": "syntax_error",
"original_token": "def"
} | def square (n : ℕ) : ℕ := n * n | quantum_information_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
matrix_trace_linear_9001 | enhanced_povm_theory | lemma | matrix_trace_linear | lemma matrix_trace_linear (A B : Matrix (Fin 2) (Fin 2) ℂ) : Matrix.trace (A + B) = Matrix.trace A + Matrix.trace B := by simp [Matrix.trace_add] | lemma matrix_trace_linear (A B : Matrix (Fin 2) (Fin 2) ℂ) : Matrix.trace (A + B) = Matrix.trace A + Matrix.trace B := by simp [Matrix.trace_addd] | {
"corrupted_token": "Matrix.trace_addd",
"corruption_successful": true,
"error_type": "name_error",
"original_token": "Matrix.trace_add"
} | Matrix.trace_add | matrix_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
matrix_trace_zero_9002 | enhanced_povm_theory | lemma | matrix_trace_zero | lemma matrix_trace_zero : Matrix.trace (0 : Matrix (Fin 2) (Fin 2) ℂ) = 0 := by simp [Matrix.trace_zero] | lemma matrix_trace_zero : Matrix.trace (0 : Matrix (Fin 2) (Fin 2) ℂ) = 0 := by simp [Matrix.trace_zeero] | {
"corrupted_token": "Matrix.trace_zeero",
"corruption_successful": true,
"error_type": "name_error",
"original_token": "Matrix.trace_zero"
} | Matrix.trace_zero | matrix_theory | lean4 | import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic |
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