id stringlengths 15 24 | file_name stringlengths 26 35 | text stringlengths 157 5.23k | text_vector listlengths 4.1k 4.1k | last_modified stringdate 2025-09-23 00:00:00 2025-09-23 00:00:00 |
|---|---|---|---|---|
lean_workbook_10009 | lean_workbook_10009_clean.lean | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_10009 (a b c: ℝ) (ha : a ≥ 0 ∧ b ≥ 0 ∧ c ≥ 0 ∧ a + b + c = 1): a^3 + b^3 + c^3 + (15 * a * b * c)/4 ≥ 1/4 := by
cases' le_total a b with hab hab <;> cases' le_total b c with hbc hbc <;> case... | [
0.020516838878393173,
0.005668092519044876,
-0.011019853875041008,
-0.003195354947820306,
0.004956427961587906,
0.03005227819085121,
0.005850818008184433,
0.012166512198746204,
-0.01106228306889534,
-0.0046097333543002605,
0.004319233354181051,
0.012321792542934418,
0.019374383613467216,
-... | 2025-09-23 |
lean_workbook_10012 | lean_workbook_10012_clean.lean | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
theorem lean_workbook_10012 (a b : ℝ) (h₁ : 0 < a ∧ 0 < b) (h₂ : a ≥ 2 * b) : (a ^ 2 / b + b ^ 2 / a) ≥ 9 * a / 4 := by
field_simp [h₁.1.ne', h₁.2.ne']
rw [div_le_div_iff] <;>
nlinarith [sq_nonneg (a - 2... | [
0.020432207733392715,
0.0018770541064441204,
-0.026782473549246788,
-0.0008693362469784915,
0.00385491200722754,
0.028241699561476707,
0.0015057292766869068,
-0.0011981024872511625,
-0.017648065462708473,
0.00963650643825531,
0.00642431853339076,
0.011978644877672195,
0.01145599689334631,
... | 2025-09-23 |
lean_workbook_10013 | lean_workbook_10013_clean.lean | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | [0.020687617361545563,0.002806325675919652,-0.0063289133831858635,0.01673058234155178,-0.00703912973(...TRUNCATED) | 2025-09-23 |
lean_workbook_10014 | lean_workbook_10014_clean.lean | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | [0.0356341153383255,-0.006803108379244804,-0.012516285292804241,-0.01446020882576704,0.0137998573482(...TRUNCATED) | 2025-09-23 |
lean_workbook_10016 | lean_workbook_10016_clean.lean | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | [0.028417404741048813,0.003310107160359621,-0.011195319704711437,0.0026199694257229567,-0.0014967959(...TRUNCATED) | 2025-09-23 |
lean_workbook_1001 | lean_workbook_1001_clean.lean | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | [0.008369983173906803,0.019845087081193924,-0.015941685065627098,-0.005520350765436888,0.00640585506(...TRUNCATED) | 2025-09-23 |
lean_workbook_10026 | lean_workbook_10026_clean.lean | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | [0.017368696630001068,0.0009606044623069465,-0.012585824355483055,-0.00922426674515009,0.00569616025(...TRUNCATED) | 2025-09-23 |
lean_workbook_1002 | lean_workbook_1002_clean.lean | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | [0.04579528048634529,0.00659654475748539,-0.002586094895377755,-0.013182173483073711,0.0114769320935(...TRUNCATED) | 2025-09-23 |
lean_workbook_10036 | lean_workbook_10036_clean.lean | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | [0.032450661063194275,-0.003832892281934619,-0.000712506880518049,0.002984982682392001,0.00313631258(...TRUNCATED) | 2025-09-23 |
lean_workbook_10039 | lean_workbook_10039_clean.lean | "import Mathlib\nimport Aesop\n\nset_option maxHeartbeats 0\n\nopen BigOperators Real Nat Topology R(...TRUNCATED) | [0.027352293953299522,0.006634712219238281,-0.014668699353933334,-0.007181523833423853,0.00480316858(...TRUNCATED) | 2025-09-23 |
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