Updates available but manual intervention required #277
Description
Try lake update and then investigate why this update causes the lean build to fail.
Files changed in update:
- lean-toolchain
Build Output
✖ [171/173] Building HumanEvalLean.HumanEval47 (1.4s)
trace: .> LEAN_PATH=/home/runner/work/human-eval-lean/human-eval-lean/.lake/build/lib/lean /home/runner/.elan/toolchains/leanprover--lean4-nightly---nightly-2026-03-07/bin/lean /home/runner/work/human-eval-lean/human-eval-lean/HumanEvalLean/HumanEval47.lean -o /home/runner/work/human-eval-lean/human-eval-lean/.lake/build/lib/lean/HumanEvalLean/HumanEval47.olean -i /home/runner/work/human-eval-lean/human-eval-lean/.lake/build/lib/lean/HumanEvalLean/HumanEval47.ilean -c /home/runner/work/human-eval-lean/human-eval-lean/.lake/build/ir/HumanEvalLean/HumanEval47.c --setup /home/runner/work/human-eval-lean/human-eval-lean/.lake/build/ir/HumanEvalLean/HumanEval47.setup.json --json
error: HumanEvalLean/HumanEval47.lean:8:4: `Array.mergeSort` has already been declared
error: HumanEvalLean/HumanEval47.lean:13:31: `grind` failed
case grind.2
xs : Array Int
h : xs ≠ #[]
sorted : Array Int := xs.mergeSort fun x1 x2 => decide (x1 ≤ x2)
h_1 : (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size = 0
h_2 : ¬xs.size = { toList := [] }.size
⊢ False
[grind] Goal diagnostics
[facts] Asserted facts
[prop] ¬xs = { toList := [] }
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size = 0
[prop] ∀ {h₁ : xs.size = { toList := [] }.size},
∃ i, ¬∀ (hi₁ : i + 1 ≤ xs.size) (hi₂ : i + 1 ≤ { toList := [] }.size), xs[i] = { toList := [] }[i]
[prop] { toList := [] }.size = 0
[prop] { toList := [] }.size = [].length
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size = 0 →
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)) = { toList := [] }
[prop] [].length = 0
[prop] ¬xs.size = { toList := [] }.size
[eqc] True propositions
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size = 0
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)) = { toList := [] }
[prop] ∀ {h₁ : xs.size = { toList := [] }.size},
∃ i, ¬∀ (hi₁ : i + 1 ≤ xs.size) (hi₂ : i + 1 ≤ { toList := [] }.size), xs[i] = { toList := [] }[i]
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size = 0 →
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)) = { toList := [] }
[prop] { toList := [] }.size = 0
[prop] [].length = 0
[eqc] False propositions
[prop] xs = { toList := [] }
[prop] xs.size = { toList := [] }.size
[prop] xs.size = 0
[eqc] Equivalence classes
[eqc] {{ toList := [] }, xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)}
[eqc] {(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size, 0, { toList := [] }.size, [].length}
[cases] Case analyses
[cases] [2/2]: xs.size = { toList := [] }.size
[cases] source: Extensionality `Array.ext`
[ematch] E-matching patterns
[thm] Vector.toArray_empty: [@Array.mk #0 (@List.nil _)]
[thm] List.length_mergeSort: [@List.mergeSort #2 #0 #1]
[thm] Array.eq_empty_of_size_eq_zero: [@Array.size #2 #1]
[thm] Array.size_empty: [@Array.size #0 (@Array.mk _ (@List.nil _))]
[thm] List.size_toArray: [@Array.size #1 (@Array.mk _ #0)]
[thm] List.eq_nil_of_length_eq_zero: [@List.length #2 #1]
[thm] List.length_nil: [@List.length #0 (@List.nil _)]
[cutsat] Assignment satisfying linear constraints
[assign] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size := 0
[assign] xs.size := 1
[assign] { toList := [] }.size := 0
[assign] [].length := 0
[grind] Diagnostics
[thm] E-Matching instances
[thm] Array.eq_empty_of_size_eq_zero ↦ 3
[thm] Array.size_empty ↦ 1
[thm] List.eq_nil_of_length_eq_zero ↦ 1
[thm] List.length_nil ↦ 1
[thm] List.size_toArray ↦ 1
[thm] Vector.toArray_empty ↦ 1
error: HumanEvalLean/HumanEval47.lean:30:48: `grind` failed
case grind.2
xs : Array Int
h : xs ≠ #[]
h' : xs.size % 2 = 1
h_1 : (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤ xs.size / 2
h_2 : ¬xs.size = { toList := [] }.size
⊢ False
[grind] Goal diagnostics
[facts] Asserted facts
[prop] ¬xs = { toList := [] }
[prop] xs.size % 2 = 1
[prop] ↑xs.size % 2 + -1 ≤ 0
[prop] -1 * (↑xs.size % 2) ≤ 0
[prop] -1 * ↑xs.size + 2 * (↑xs.size / 2) + ↑xs.size % 2 = 0
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤ xs.size / 2
[prop] ∀ {h₁ : xs.size = { toList := [] }.size},
∃ i, ¬∀ (hi₁ : i + 1 ≤ xs.size) (hi₂ : i + 1 ≤ { toList := [] }.size), xs[i] = { toList := [] }[i]
[prop] { toList := [] }.size = 0
[prop] { toList := [] }.size = [].length
[prop] [].length = 0
[prop] ¬xs.size = { toList := [] }.size
[eqc] True propositions
[prop] ↑xs.size % 2 + -1 ≤ 0
[prop] -1 * (↑xs.size % 2) ≤ 0
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤ xs.size / 2
[prop] ∀ {h₁ : xs.size = { toList := [] }.size},
∃ i, ¬∀ (hi₁ : i + 1 ≤ xs.size) (hi₂ : i + 1 ≤ { toList := [] }.size), xs[i] = { toList := [] }[i]
[prop] { toList := [] }.size = 0
[prop] [].length = 0
[eqc] False propositions
[prop] xs = { toList := [] }
[prop] xs.size = { toList := [] }.size
[prop] xs.size = 0
[eqc] Equivalence classes
[eqc] {0, { toList := [] }.size, [].length}
[eqc] {1, xs.size % 2}
[eqc] others
[eqc] {↑1, ↑(xs.size % 2)}
[eqc] {0, -1 * ↑xs.size + 2 * (↑xs.size / 2) + ↑xs.size % 2}
[cases] Case analyses
[cases] [2/2]: xs.size = { toList := [] }.size
[cases] source: Extensionality `Array.ext`
[ematch] E-matching patterns
[thm] Vector.toArray_empty: [@Array.mk #0 (@List.nil _)]
[thm] Array.eq_empty_of_size_eq_zero: [@Array.size #2 #1]
[thm] Array.size_empty: [@Array.size #0 (@Array.mk _ (@List.nil _))]
[thm] List.size_toArray: [@Array.size #1 (@Array.mk _ #0)]
[thm] List.le_toArray: [@LE.le (Array #3) _ (@Array.mk _ #1) (@Array.mk _ #0)]
[thm] List.length_mergeSort: [@List.mergeSort #2 #0 #1]
[thm] List.eq_nil_of_length_eq_zero: [@List.length #2 #1]
[thm] List.length_nil: [@List.length #0 (@List.nil _)]
[cutsat] Assignment satisfying linear constraints
[assign] xs.size := 1
[assign] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size := 0
[assign] { toList := [] }.size := 0
[assign] [].length := 0
[ring] Ring `Int`
[basis] Basis
[_] ↑xs.size % 2 + -1 * ↑xs.size + 2 * (↑xs.size / 2) = 0
[grind] Diagnostics
[thm] E-Matching instances
[thm] Array.eq_empty_of_size_eq_zero ↦ 1
[thm] Array.size_empty ↦ 1
[thm] List.eq_nil_of_length_eq_zero ↦ 1
[thm] List.length_nil ↦ 1
[thm] List.size_toArray ↦ 1
[thm] Vector.toArray_empty ↦ 1
error: HumanEvalLean/HumanEval47.lean:31:2: `grind` failed
case grind.2.2
xs : Array Int
h : xs ≠ #[]
h' : xs.size % 2 = 1
h_1 : ¬median xs ⋯ = IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2]
h_2 : ¬xs.size = { toList := [] }.size
h_3 : ¬xs.size / 2 = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2
⊢ False
[grind] Goal diagnostics
[facts] Asserted facts
[prop] ¬xs = { toList := [] }
[prop] xs.size % 2 = 1
[prop] ↑xs.size % 2 + -1 ≤ 0
[prop] -1 * (↑xs.size % 2) ≤ 0
[prop] -1 * ↑xs.size + 2 * (↑xs.size / 2) + ↑xs.size % 2 = 0
[prop] ¬median xs ⋯ = IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2]
[prop] ∀ {h₁ : xs.size = { toList := [] }.size},
∃ i, ¬∀ (hi₁ : i + 1 ≤ xs.size) (hi₂ : i + 1 ≤ { toList := [] }.size), xs[i] = { toList := [] }[i]
[prop] { toList := [] }.size = 0
[prop] { toList := [] }.size = [].length
[prop] median xs ⋯ =
if xs.size % 2 = 1 then
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]
else
(IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1] +
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]) *
2⁻¹
[prop] ↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size % 2 + -1 ≤ 0
[prop] -1 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size % 2) ≤ 0
[prop] -1 * ↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size +
2 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2) +
↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size % 2 =
0
[prop] [].length = 0
[prop] ¬xs.size = { toList := [] }.size
[prop] ¬xs.size / 2 = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2
[eqc] True propositions
[prop] ¬xs = { toList := [] }
[prop] ↑xs.size % 2 + -1 ≤ 0
[prop] ↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size % 2 + -1 ≤ 0
[prop] -1 * (↑xs.size % 2) ≤ 0
[prop] -1 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size % 2) ≤ 0
[prop] xs.size / 2 < (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] xs.size % 2 = 1
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 <
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] ∀ {h₁ : xs.size = { toList := [] }.size},
∃ i, ¬∀ (hi₁ : i + 1 ≤ xs.size) (hi₂ : i + 1 ≤ { toList := [] }.size), xs[i] = { toList := [] }[i]
[prop] { toList := [] }.size = 0
[prop] [].length = 0
[eqc] False propositions
[prop] median xs ⋯ = IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2]
[prop] xs = { toList := [] }
[prop] xs.size = { toList := [] }.size
[prop] xs.size = 0
[prop] xs.size / 2 = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2
[eqc] Equivalence classes
[eqc] {0, { toList := [] }.size, [].length}
[eqc] {1, xs.size % 2}
[eqc] {1,
(IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2] -
IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2]) *
(IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2] -
IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2])⁻¹}
[eqc] others
[eqc] {median xs ⋯,
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2],
if xs.size % 2 = 1 then
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]
else
(IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1] +
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]) *
2⁻¹}
[eqc] {↑0,
0,
-1 * ↑xs.size + 2 * (↑xs.size / 2) + ↑xs.size % 2,
-1 * ↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size +
2 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2) +
↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size % 2}
[eqc] {↑1, ↑(xs.size % 2)}
[cases] Case analyses
[cases] [2/2]: xs.size = { toList := [] }.size
[cases] source: Extensionality `Array.ext`
[cases] [2/2]: xs.size / 2 = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2
[cases] source: Model-based theory combination at argument #6 of
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]
and
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2]
[ematch] E-matching patterns
[thm] Vector.toArray_empty: [@Array.mk #0 (@List.nil _)]
[thm] Array.eq_empty_of_size_eq_zero: [@Array.size #2 #1]
[thm] Array.size_empty: [@Array.size #0 (@Array.mk _ (@List.nil _))]
[thm] List.size_toArray: [@Array.size #1 (@Array.mk _ #0)]
[thm] List.le_toArray: [@LE.le (Array #3) _ (@Array.mk _ #1) (@Array.mk _ #0)]
[thm] median.eq_1: [median #1 #0]
[thm] List.length_mergeSort: [@List.mergeSort #2 #0 #1]
[thm] List.getElem_toArray: [@getElem (Array #3) `[Nat] _ _ _ (@Array.mk _ #2) #1 #0]
[thm] getElem?_pos: [@getElem #8 #7 #6 #5 _ #2 #1 _]
[thm] List.lt_toArray: [@LT.lt (Array #3) _ (@Array.mk _ #1) (@Array.mk _ #0)]
[thm] List.eq_nil_of_length_eq_zero: [@List.length #2 #1]
[thm] List.length_nil: [@List.length #0 (@List.nil _)]
[cutsat] Assignment satisfying linear constraints
[assign] xs.size := 3
[assign] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size := 0
[assign] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2] := 9
[assign] { toList := [] }.size := 0
[assign] (xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2] := 11
[assign] [].length := 0
[linarith] Linarith assignment for `Rat`
[assign] median xs ⋯ := 3
[assign] 「IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2]」 := 0
[assign] 「IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]」 := 3
[ring] Rings
[ring] Ring `Int`
[basis] Basis
[_] ↑xs.size % 2 + -1 * ↑xs.size + 2 * (↑xs.size / 2) = 0
[_] ↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size +
-2 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2) +
-1 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size % 2) =
0
[ring] Ring `Rat`
[basis] Basis
[_] IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2] *
(IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide
(x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2] -
IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2])⁻¹ +
-1 *
(IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2] *
(IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide
(x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2] -
IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2])⁻¹) +
-1 =
0
[grind] Diagnostics
[thm] E-Matching instances
[thm] Array.eq_empty_of_size_eq_zero ↦ 1
[thm] Array.size_empty ↦ 1
[thm] List.eq_nil_of_length_eq_zero ↦ 1
[thm] List.length_nil ↦ 1
[thm] List.size_toArray ↦ 1
[thm] Vector.toArray_empty ↦ 1
[thm] median.eq_1 ↦ 1
error: HumanEvalLean/HumanEval47.lean:35:40: `grind` failed
case grind.1.2
xs : Array Int
h : xs ≠ #[]
h' : xs.size % 2 = 0
h_1 : (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤ xs.size / 2 - 1
h_2 : -1 * (↑xs.size / 2) + 1 ≤ 0
h_3 : ¬xs.size = { toList := [] }.size
⊢ False
[grind] Goal diagnostics
[facts] Asserted facts
[prop] ¬xs = { toList := [] }
[prop] xs.size % 2 = 0
[prop] ↑xs.size % 2 + -1 ≤ 0
[prop] -1 * (↑xs.size % 2) ≤ 0
[prop] -1 * ↑xs.size + 2 * (↑xs.size / 2) + ↑xs.size % 2 = 0
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤ xs.size / 2 - 1
[prop] ↑(xs.size / 2 - 1) = if -1 * (↑xs.size / 2) + 1 ≤ 0 then ↑xs.size / 2 + -1 else 0
[prop] ∀ {h₁ : xs.size = { toList := [] }.size},
∃ i, ¬∀ (hi₁ : i + 1 ≤ xs.size) (hi₂ : i + 1 ≤ { toList := [] }.size), xs[i] = { toList := [] }[i]
[prop] { toList := [] }.size = 0
[prop] { toList := [] }.size = [].length
[prop] [].length = 0
[prop] -1 * (↑xs.size / 2) + 1 ≤ 0
[prop] ¬xs.size = { toList := [] }.size
[eqc] True propositions
[prop] ↑xs.size % 2 + -1 ≤ 0
[prop] -1 * (↑xs.size / 2) + 1 ≤ 0
[prop] -1 * (↑xs.size % 2) ≤ 0
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤ xs.size / 2 - 1
[prop] ∀ {h₁ : xs.size = { toList := [] }.size},
∃ i, ¬∀ (hi₁ : i + 1 ≤ xs.size) (hi₂ : i + 1 ≤ { toList := [] }.size), xs[i] = { toList := [] }[i]
[prop] { toList := [] }.size = 0
[prop] [].length = 0
[eqc] False propositions
[prop] xs = { toList := [] }
[prop] xs.size = { toList := [] }.size
[prop] xs.size = 0
[eqc] Equivalence classes
[eqc] {0, xs.size % 2, { toList := [] }.size, [].length}
[eqc] others
[eqc] {↑0, ↑(xs.size % 2), 0, -1 * ↑xs.size + 2 * (↑xs.size / 2) + ↑xs.size % 2}
[eqc] {↑(xs.size / 2 - 1), if -1 * (↑xs.size / 2) + 1 ≤ 0 then ↑xs.size / 2 + -1 else 0, ↑xs.size / 2 + -1}
[cases] Case analyses
[cases] [1/2]: if -1 * (↑xs.size / 2) + 1 ≤ 0 then ↑xs.size / 2 + -1 else 0
[cases] source: Initial goal
[cases] [2/2]: xs.size = { toList := [] }.size
[cases] source: Extensionality `Array.ext`
[ematch] E-matching patterns
[thm] Vector.toArray_empty: [@Array.mk #0 (@List.nil _)]
[thm] Array.eq_empty_of_size_eq_zero: [@Array.size #2 #1]
[thm] Array.size_empty: [@Array.size #0 (@Array.mk _ (@List.nil _))]
[thm] List.size_toArray: [@Array.size #1 (@Array.mk _ #0)]
[thm] List.le_toArray: [@LE.le (Array #3) _ (@Array.mk _ #1) (@Array.mk _ #0)]
[thm] List.length_mergeSort: [@List.mergeSort #2 #0 #1]
[thm] List.eq_nil_of_length_eq_zero: [@List.length #2 #1]
[thm] List.length_nil: [@List.length #0 (@List.nil _)]
[cutsat] Assignment satisfying linear constraints
[assign] xs.size := 2
[assign] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size := 0
[assign] { toList := [] }.size := 0
[assign] [].length := 0
[ring] Ring `Int`
[basis] Basis
[_] ↑xs.size % 2 + -1 * ↑xs.size + 2 * (↑xs.size / 2) = 0
[_] ↑xs.size / 2 + -1 * ↑(xs.size / 2 - 1) + -1 = 0
[grind] Diagnostics
[thm] E-Matching instances
[thm] Array.eq_empty_of_size_eq_zero ↦ 1
[thm] Array.size_empty ↦ 1
[thm] List.eq_nil_of_length_eq_zero ↦ 1
[thm] List.length_nil ↦ 1
[thm] List.size_toArray ↦ 1
[thm] Vector.toArray_empty ↦ 1
error: HumanEvalLean/HumanEval47.lean:36:36: `grind` failed
case grind.2
xs : Array Int
h : xs ≠ #[]
h' : xs.size % 2 = 0
h_1 : (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤ xs.size / 2
h_2 : ¬xs.size = { toList := [] }.size
⊢ False
[grind] Goal diagnostics
[facts] Asserted facts
[prop] ¬xs = { toList := [] }
[prop] xs.size % 2 = 0
[prop] ↑xs.size % 2 + -1 ≤ 0
[prop] -1 * (↑xs.size % 2) ≤ 0
[prop] -1 * ↑xs.size + 2 * (↑xs.size / 2) + ↑xs.size % 2 = 0
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤ xs.size / 2
[prop] ∀ {h₁ : xs.size = { toList := [] }.size},
∃ i, ¬∀ (hi₁ : i + 1 ≤ xs.size) (hi₂ : i + 1 ≤ { toList := [] }.size), xs[i] = { toList := [] }[i]
[prop] { toList := [] }.size = 0
[prop] { toList := [] }.size = [].length
[prop] [].length = 0
[prop] ¬xs.size = { toList := [] }.size
[eqc] True propositions
[prop] ↑xs.size % 2 + -1 ≤ 0
[prop] -1 * (↑xs.size % 2) ≤ 0
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤ xs.size / 2
[prop] ∀ {h₁ : xs.size = { toList := [] }.size},
∃ i, ¬∀ (hi₁ : i + 1 ≤ xs.size) (hi₂ : i + 1 ≤ { toList := [] }.size), xs[i] = { toList := [] }[i]
[prop] { toList := [] }.size = 0
[prop] [].length = 0
[eqc] False propositions
[prop] xs = { toList := [] }
[prop] xs.size = { toList := [] }.size
[prop] xs.size = 0
[eqc] Equivalence classes
[eqc] {0, xs.size % 2, { toList := [] }.size, [].length}
[eqc] others
[eqc] {↑0, ↑(xs.size % 2), 0, -1 * ↑xs.size + 2 * (↑xs.size / 2) + ↑xs.size % 2}
[cases] Case analyses
[cases] [2/2]: xs.size = { toList := [] }.size
[cases] source: Extensionality `Array.ext`
[ematch] E-matching patterns
[thm] Vector.toArray_empty: [@Array.mk #0 (@List.nil _)]
[thm] Array.eq_empty_of_size_eq_zero: [@Array.size #2 #1]
[thm] Array.size_empty: [@Array.size #0 (@Array.mk _ (@List.nil _))]
[thm] List.size_toArray: [@Array.size #1 (@Array.mk _ #0)]
[thm] List.le_toArray: [@LE.le (Array #3) _ (@Array.mk _ #1) (@Array.mk _ #0)]
[thm] List.length_mergeSort: [@List.mergeSort #2 #0 #1]
[thm] List.eq_nil_of_length_eq_zero: [@List.length #2 #1]
[thm] List.length_nil: [@List.length #0 (@List.nil _)]
[cutsat] Assignment satisfying linear constraints
[assign] xs.size := 2
[assign] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size := 0
[assign] { toList := [] }.size := 0
[assign] [].length := 0
[ring] Ring `Int`
[basis] Basis
[_] ↑xs.size % 2 + -1 * ↑xs.size + 2 * (↑xs.size / 2) = 0
[grind] Diagnostics
[thm] E-Matching instances
[thm] Array.eq_empty_of_size_eq_zero ↦ 2
[thm] Array.size_empty ↦ 1
[thm] List.eq_nil_of_length_eq_zero ↦ 1
[thm] List.length_nil ↦ 1
[thm] List.size_toArray ↦ 1
[thm] Vector.toArray_empty ↦ 1
error: HumanEvalLean/HumanEval47.lean:37:2: `grind` failed
case grind.1.2.2.1.2.2.2.1
xs : Array Int
h : xs ≠ #[]
h' : xs.size % 2 = 0
h_1 :
¬2 * median xs ⋯ =
IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1] +
IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2]
h_2 : -1 * (↑xs.size / 2) + 1 ≤ 0
h_3 : ¬xs.size = { toList := [] }.size
h_4 : ¬xs.size % 2 = 1
h_5 : -1 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2) + 1 ≤ 0
h_6 : ¬xs.size / 2 - 1 = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1
h_7 : ¬xs.size / 2 = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2
h_8 : ¬xs.size = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
h_9 : (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 = xs.size / 2 - 1
⊢ False
[grind] Goal diagnostics
[facts] Asserted facts
[prop] ¬xs = { toList := [] }
[prop] xs.size % 2 = 0
[prop] ↑xs.size % 2 + -1 ≤ 0
[prop] -1 * (↑xs.size % 2) ≤ 0
[prop] -1 * ↑xs.size + 2 * (↑xs.size / 2) + ↑xs.size % 2 = 0
[prop] ¬2 * median xs ⋯ =
IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1] +
IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2]
[prop] ↑(xs.size / 2 - 1) = if -1 * (↑xs.size / 2) + 1 ≤ 0 then ↑xs.size / 2 + -1 else 0
[prop] ∀ {h₁ : xs.size = { toList := [] }.size},
∃ i, ¬∀ (hi₁ : i + 1 ≤ xs.size) (hi₂ : i + 1 ≤ { toList := [] }.size), xs[i] = { toList := [] }[i]
[prop] { toList := [] }.size = 0
[prop] { toList := [] }.size = [].length
[prop] median xs ⋯ =
if xs.size % 2 = 1 then
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]
else
(IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1] +
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]) *
2⁻¹
[prop] [].length = 0
[prop] -1 * (↑xs.size / 2) + 1 ≤ 0
[prop] ∀ (h : xs.size / 2 - 1 + 1 ≤ (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size),
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]? =
some (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤ xs.size / 2 - 1 →
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]? = none
[prop] ∀ (h : xs.size / 2 - 1 + 1 ≤ (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size),
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]? =
some (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]
[prop] ¬xs.size = { toList := [] }.size
[prop] ¬xs.size % 2 = 1
[prop] 2 * 2⁻¹ = 1
[prop] ↑((xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1) =
if -1 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2) + 1 ≤ 0 then
↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 + -1
else 0
[prop] ↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size % 2 + -1 ≤ 0
[prop] -1 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size % 2) ≤ 0
[prop] -1 * ↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size +
2 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2) +
↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size % 2 =
0
[prop] -1 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2) + 1 ≤ 0
[prop] ∀
(h :
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1 + 1 ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size),
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]? =
some
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1 →
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]? =
none
[prop] ∀
(h :
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1 + 1 ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size),
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]? =
some
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]
[prop] ¬xs.size / 2 - 1 = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1
[prop] ¬xs.size / 2 = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2
[prop] ¬xs.size = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 = xs.size / 2 - 1
[prop] ∀
(h :
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 + 1 ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size),
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]? =
some
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]
[eqc] True propositions
[prop] ¬xs = { toList := [] }
[prop] ↑xs.size % 2 + -1 ≤ 0
[prop] ↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size % 2 + -1 ≤ 0
[prop] -1 * (↑xs.size / 2) + 1 ≤ 0
[prop] -1 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2) + 1 ≤ 0
[prop] -1 * (↑xs.size % 2) ≤ 0
[prop] -1 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size % 2) ≤ 0
[prop] xs.size / 2 < (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] xs.size / 2 - 1 < (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 = xs.size / 2 - 1
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]? =
some (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]
[prop] xs.size / 2 - 1 + 1 ≤ (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 <
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1 <
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] ∀ {h₁ : xs.size = { toList := [] }.size},
∃ i, ¬∀ (hi₁ : i + 1 ≤ xs.size) (hi₂ : i + 1 ≤ { toList := [] }.size), xs[i] = { toList := [] }[i]
[prop] ∀ (h : xs.size / 2 - 1 + 1 ≤ (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size),
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]? =
some (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]
[prop] { toList := [] }.size = 0
[prop] (xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]? =
some
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]
[prop] (xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]? =
some
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 + 1 ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1 + 1 ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤ xs.size / 2 - 1 →
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]? = none
[prop] ∀
(h :
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 + 1 ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size),
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]? =
some
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]
[prop] ∀
(h :
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1 + 1 ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size),
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]? =
some
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]
[prop] [].length = 0
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1 →
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]? =
none
[eqc] False propositions
[prop] 2 * median xs ⋯ =
IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1] +
IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2]
[prop] xs = { toList := [] }
[prop] xs.size = { toList := [] }.size
[prop] xs.size = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] xs.size = 0
[prop] xs.size / 2 = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2
[prop] xs.size % 2 = 1
[prop] xs.size / 2 - 1 = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]? = none
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤ xs.size / 2 - 1
[prop] (xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]? =
none
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1
[eqc] Equivalence classes
[eqc] {median xs ⋯,
(IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1] +
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]) *
2⁻¹}
[eqc] {if xs.size % 2 = 1 then
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]
else
(IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1] +
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]) *
2⁻¹}
[eqc] {0, xs.size % 2, { toList := [] }.size, [].length}
[eqc] {1,
2 * 2⁻¹,
(2 * median xs ⋯ -
(IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1] +
IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2])) *
(2 * median xs ⋯ -
(IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1] +
IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2]))⁻¹}
[eqc] {-1 • IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1],
-1 •
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]}
[eqc] {xs.size / 2 - 1, (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2}
[eqc] {(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1],
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]}
[eqc] {some (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1],
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]?,
some
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2],
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]?}
[eqc] {xs.size / 2 - 1 + 1, (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 + 1}
[eqc] {1 •
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2],
1 • IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]}
[eqc] {some
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1],
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]?}
[eqc] others
[eqc] {IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1],
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]}
[eqc] {↑0,
↑(xs.size % 2),
0,
-1 * ↑xs.size + 2 * (↑xs.size / 2) + ↑xs.size % 2,
-1 * ↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size +
2 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2) +
↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size % 2}
[eqc] {↑(xs.size / 2 - 1),
if -1 * (↑xs.size / 2) + 1 ≤ 0 then ↑xs.size / 2 + -1 else 0,
↑xs.size / 2 + -1,
↑((xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2)}
[eqc] {if -1 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2) + 1 ≤ 0 then
↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 + -1
else 0,
↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 + -1,
↑((xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1)}
[cases] Case analyses
[cases] [1/2]: if -1 * (↑xs.size / 2) + 1 ≤ 0 then ↑xs.size / 2 + -1 else 0
[cases] source: Initial goal
[cases] [2/2]: xs.size = { toList := [] }.size
[cases] source: Extensionality `Array.ext`
[cases] [2/2]: if xs.size % 2 = 1 then
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]
else
(IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1] +
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]) *
2⁻¹
[cases] source: E-matching `median.eq_1`
[cases] [1/2]: if -1 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2) + 1 ≤ 0 then
↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 + -1
else 0
[cases] source: E-matching `getElem?_pos`
[cases] [2/2]: xs.size / 2 - 1 = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1
[cases] source: Model-based theory combination at argument #6 of
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]
and
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]
[cases] [2/2]: xs.size / 2 = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2
[cases] source: Model-based theory combination at argument #6 of
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]
and
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2]
[cases] [2/2]: xs.size = (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[cases] source: Model-based theory combination at argument #4 of
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2
and
xs.size / 2
[cases] [1/2]: (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 = xs.size / 2 - 1
[cases] source: Model-based theory combination at argument #6 of
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]
and
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]
[ematch] E-matching patterns
[thm] Vector.toArray_empty: [@Array.mk #0 (@List.nil _)]
[thm] Array.eq_empty_of_size_eq_zero: [@Array.size #2 #1]
[thm] Array.size_empty: [@Array.size #0 (@Array.mk _ (@List.nil _))]
[thm] List.size_toArray: [@Array.size #1 (@Array.mk _ #0)]
[thm] List.le_toArray: [@LE.le (Array #3) _ (@Array.mk _ #1) (@Array.mk _ #0)]
[thm] median.eq_1: [median #1 #0]
[thm] List.length_mergeSort: [@List.mergeSort #2 #0 #1]
[thm] List.getElem_toArray: [@getElem (Array #3) `[Nat] _ _ _ (@Array.mk _ #2) #1 #0]
[thm] getElem?_pos: [@getElem #8 #7 #6 #5 _ #2 #1 _]
[thm] List.lt_toArray: [@LT.lt (Array #3) _ (@Array.mk _ #1) (@Array.mk _ #0)]
[thm] List.eq_nil_of_length_eq_zero: [@List.length #2 #1]
[thm] List.length_nil: [@List.length #0 (@List.nil _)]
[thm] Array.getElem?_eq_none: [@Array.size #3 #1, @getElem? (Array _) `[Nat] _ _ _ #1 #2]
[thm] List.getElem?_toArray: [@getElem? (Array #2) `[Nat] _ _ _ (@Array.mk _ #1) #0]
[thm] getElem?_neg: [@getElem? #8 #7 #6 #5 #4 #2 #1]
[thm] getElem?_pos: [@getElem? #8 #7 #6 #5 #4 #2 #1]
[thm] Option.some_le_some: [@LE.le (Option #3) _ (@some _ #1) (@some _ #0)]
[thm] Option.some_lt_some: [@LT.lt (Option #3) _ (@some _ #1) (@some _ #0)]
[thm] Option.not_some_le_none: [@LE.le (Option #2) _ (@some _ #0) (@none _)]
[thm] Option.none_le: [@LE.le (Option #2) _ (@none _) #0]
[thm] Option.none_lt_some: [@LT.lt (Option #2) _ (@none _) (@some _ #0)]
[thm] Option.not_lt_none: [@LT.lt (Option #2) _ #0 (@none _)]
[cutsat] Assignment satisfying linear constraints
[assign] xs.size := 4
[assign] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size := 2
[assign] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2] := 10
[assign] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1] := 9
[assign] { toList := [] }.size := 0
[assign] (xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2] := 9
[assign] (xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1] := 15
[assign] [].length := 0
[linarith] Linarith assignment for `Rat`
[assign] median xs ⋯ := 12
[assign] 「IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2]」 := 0
[assign] 「IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1]」 := 0
[assign] 「IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2]」 := 0
[assign] 「IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]」 := 2
[ring] Rings
[ring] Ring `Int`
[basis] Basis
[_] ↑xs.size % 2 + -1 * ↑xs.size + 2 * (↑xs.size / 2) = 0
[_] ↑xs.size / 2 + -1 * ↑(xs.size / 2 - 1) + -1 = 0
[_] ↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size +
-2 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2) +
-1 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size % 2) =
0
[_] ↑((xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1) +
-1 * (↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2) +
1 =
0
[ring] Ring `Lean.Grind.Ring.OfSemiring.Q Nat`
[diseqs] Disequalities
[_] ¬↑(xs.size / 2 - 1) + -1 * ↑((xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1) = 0
[ring] Ring `Rat`
[basis] Basis
[_] IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2] *
(2 * median xs ⋯ -
(IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1] +
IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2]))⁻¹ +
-1 *
((2 * median xs ⋯ -
(IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1] +
IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2]))⁻¹ *
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide
(x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1]) +
1 =
0
[_] 2 * median xs ⋯ +
-1 *
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide
(x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2 - 1] +
-1 *
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2] =
0
[_] IntCast.intCast (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))[xs.size / 2 - 1] +
-1 *
IntCast.intCast
(xs.mergeSort fun x1 x2 =>
decide (x1 + -1 * x2 ≤ 0))[(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size / 2] =
0
[_] 2 * 2⁻¹ + -1 = 0
[grind] Diagnostics
[thm] E-Matching instances
[thm] getElem?_pos ↦ 5
[thm] getElem?_neg ↦ 2
[thm] Array.eq_empty_of_size_eq_zero ↦ 1
[thm] Array.size_empty ↦ 1
[thm] List.eq_nil_of_length_eq_zero ↦ 1
[thm] List.length_nil ↦ 1
[thm] List.size_toArray ↦ 1
[thm] Vector.toArray_empty ↦ 1
[thm] median.eq_1 ↦ 1
error: HumanEvalLean/HumanEval47.lean:46:2: `grind` failed
case grind
xs : Array Int
h : ¬List.Pairwise (fun x1 x2 => x1 + -1 * x2 ≤ 0) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList
⊢ False
[grind] Goal diagnostics
[facts] Asserted facts
[prop] ¬List.Pairwise (fun x1 x2 => x1 + -1 * x2 ≤ 0) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList
[eqc] False propositions
[prop] List.Pairwise (fun x1 x2 => x1 + -1 * x2 ≤ 0) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList
[ematch] E-matching patterns
[thm] List.pairwise_mergeSort: [@List.mergeSort #4 #0 #3]
error: HumanEvalLean/HumanEval47.lean:49:2: `grind` failed
case grind.1
xs : Array Int
h : ¬(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).Perm xs
w : Int
h_2 : ¬List.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList = List.count w xs.toList
left :
(List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).Perm
(List.filter (fun x => decide (x = w)) xs.toList)
right :
∀ (a : Int),
List.count a (List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList) =
List.count a (List.filter (fun x => decide (x = w)) xs.toList)
⊢ False
[grind] Goal diagnostics
[facts] Asserted facts
[prop] ¬(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).Perm xs
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.Perm xs.toList →
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).Perm xs
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.Perm xs.toList =
∀ (a : Int),
List.count a (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList = List.count a xs.toList
[prop] ¬List.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList = List.count w xs.toList
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.Perm xs.toList →
List.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList = List.count w xs.toList
[prop] List.count w xs.toList = Array.count w xs
[prop] List.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList =
Array.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))
[prop] List.count w xs.toList ≤ xs.toList.length
[prop] List.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.length
[prop] List.count w xs.toList = (List.filter (fun x => decide (x = w)) xs.toList).length
[prop] List.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList =
(List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).length
[prop] Array.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)) =
(Array.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))).size
[prop] Array.count w xs = (Array.filter (fun x => decide (x = w)) xs).size
[prop] Array.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)) ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] Array.count w xs ≤ xs.size
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.length =
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] xs.toList.length = xs.size
[prop] (List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).length ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.length
[prop] (List.filter (fun x => decide (x = w)) xs.toList).length ≤ xs.toList.length
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.Perm xs.toList →
(List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).Perm
(List.filter (fun x => decide (x = w)) xs.toList)
[prop] (List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).Perm
(List.filter (fun x => decide (x = w)) xs.toList) =
∀ (a : Int),
List.count a
(List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList) =
List.count a (List.filter (fun x => decide (x = w)) xs.toList)
[prop] (Array.filter (fun x => decide (x = w)) xs).size ≤ xs.size
[prop] (Array.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))).size ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] (List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).Perm
(List.filter (fun x => decide (x = w)) xs.toList)
[prop] ∀ (a : Int),
List.count a
(List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList) =
List.count a (List.filter (fun x => decide (x = w)) xs.toList)
[eqc] True propositions
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.Perm xs.toList →
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).Perm xs
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.Perm xs.toList =
∀ (a : Int),
List.count a (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList = List.count a xs.toList
[prop] List.count w xs.toList ≤ xs.toList.length
[prop] List.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.length
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.Perm xs.toList →
List.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList = List.count w xs.toList
[prop] (List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).Perm
(List.filter (fun x => decide (x = w)) xs.toList)
[prop] (List.filter (fun x => decide (x = w)) xs.toList).length ≤ xs.toList.length
[prop] (List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).length ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.length
[prop] Array.count w xs ≤ xs.size
[prop] Array.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)) ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.Perm xs.toList →
(List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).Perm
(List.filter (fun x => decide (x = w)) xs.toList)
[prop] (List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).Perm
(List.filter (fun x => decide (x = w)) xs.toList) =
∀ (a : Int),
List.count a
(List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList) =
List.count a (List.filter (fun x => decide (x = w)) xs.toList)
[prop] (Array.filter (fun x => decide (x = w)) xs).size ≤ xs.size
[prop] (Array.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))).size ≤
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size
[prop] ∀ (a : Int),
List.count a
(List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList) =
List.count a (List.filter (fun x => decide (x = w)) xs.toList)
[eqc] False propositions
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).Perm xs
[prop] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.Perm xs.toList
[prop] List.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList = List.count w xs.toList
[prop] ∀ (a : Int),
List.count a (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList = List.count a xs.toList
[eqc] Equivalence classes
[eqc] {List.count w xs.toList,
(List.filter (fun x => decide (x = w)) xs.toList).length,
Array.count w xs,
(Array.filter (fun x => decide (x = w)) xs).size}
[eqc] {List.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList,
(List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).length,
Array.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)),
(Array.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))).size}
[eqc] {xs.toList.length, xs.size}
[eqc] {(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.length,
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size}
[eqc] {xs.toList.length = 0, xs.size = 0}
[eqc] {(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.length = 0,
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size = 0}
[eqc] {(List.filter (fun x => decide (x = w)) xs.toList).length = 0,
(Array.filter (fun x => decide (x = w)) xs).size = 0}
[eqc] {(List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).length =
0,
(Array.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))).size = 0}
[eqc] others
[eqc] {↑xs.size, ↑xs.toList.length}
[eqc] {↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size,
↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.length}
[eqc] {↑(List.count w xs.toList),
↑(List.filter (fun x => decide (x = w)) xs.toList).length,
↑(Array.count w xs),
↑(Array.filter (fun x => decide (x = w)) xs).size}
[eqc] {↑(List.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList),
↑(List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).length,
↑(Array.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))),
↑(Array.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))).size}
[cases] Case analyses
[cases] [1/2]: (List.filter (fun x => decide (x = w))
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).Perm
(List.filter (fun x => decide (x = w)) xs.toList) =
∀ (a : Int),
List.count a
(List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList) =
List.count a (List.filter (fun x => decide (x = w)) xs.toList)
[cases] source: E-matching `List.perm_iff_count`
[ematch] E-matching patterns
[thm] List.mergeSort_perm: [@List.mergeSort #2 #1 #0]
[thm] Array.Perm.of_toList_perm: [@Array.Perm #3 #2 #1]
[thm] List.perm_iff_count: [@List.Perm #4 #1 #0]
[thm] List.Perm.count: [@List.Perm #6 #3 #2, @List.count _ #5 #0 #3]
[thm] List.Perm.count: [@List.Perm #6 #3 #2, @List.count _ #5 #0 #2]
[thm] Array.count_toList: [@List.count #3 #2 #0 (@Array.toList _ #1)]
[thm] List.count_le_length: [@List.count #3 #2 #1 #0]
[thm] List.count_eq_length_filter: [@List.count #3 #2 #1 #0]
[thm] Array.count_eq_size_filter: [@Array.count #3 #2 #1 #0]
[thm] Array.count_le_size: [@Array.count #3 #2 #1 #0]
[thm] Array.length_toList: [@List.length #1 (@Array.toList _ #0)]
[thm] List.eq_nil_of_length_eq_zero: [@List.length #2 #1]
[thm] List.length_filter_le: [@List.length #2 (@List.filter _ #1 #0)]
[thm] List.Perm.filter: [@List.Perm #4 #2 #1, @List.filter _ #3 #2]
[thm] List.Perm.filter: [@List.Perm #4 #2 #1, @List.filter _ #3 #1]
[thm] Array.eq_empty_of_size_eq_zero: [@Array.size #2 #1]
[thm] Array.size_filter_le: [@Array.size #2 (@Array.filter _ #1 #0 `[0] (@Array.size _ #0))]
[thm] Array.toList_filter: [@Array.toList #2 (@Array.filter _ #1 #0 `[0] (@Array.size _ #0))]
[thm] local_0: [@List.count `[Int] `[instBEqOfDecidableEq] #0 `[List.filter (fun x => decide (x = w))
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList]]
[thm] local_0: [@List.count `[Int] `[instBEqOfDecidableEq] #0 `[List.filter (fun x => decide (x = w)) xs.toList]]
[cutsat] Assignment satisfying linear constraints
[assign] w := 2
[assign] List.count w xs.toList := 0
[assign] List.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList := 1
[assign] xs.toList.length := 0
[assign] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.length := 1
[assign] (List.filter (fun x => decide (x = w)) xs.toList).length := 0
[assign] (List.filter (fun x => decide (x = w))
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).length := 1
[assign] Array.count w xs := 0
[assign] Array.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)) := 1
[assign] xs.size := 0
[assign] (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size := 1
[assign] (Array.filter (fun x => decide (x = w)) xs).size := 0
[assign] (Array.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))).size := 1
[ring] Ring `Int`
[basis] Basis
[_] ↑(List.count w xs.toList) + -1 * ↑(Array.count w xs) = 0
[_] ↑xs.toList.length + -1 * ↑xs.size = 0
[_] ↑(List.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList) +
-1 * ↑(Array.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))) =
0
[_] ↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList.length +
-1 * ↑(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).size =
0
[_] ↑(Array.count w (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))) +
-1 *
↑(List.filter (fun x => decide (x = w))
(xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).length =
0
[_] ↑(Array.count w xs) + -1 * ↑(List.filter (fun x => decide (x = w)) xs.toList).length = 0
[_] ↑(List.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0)).toList).length +
-1 *
↑(Array.filter (fun x => decide (x = w)) (xs.mergeSort fun x1 x2 => decide (x1 + -1 * x2 ≤ 0))).size =
0
[_] ↑(List.filter (fun x => decide (x = w)) xs.toList).length +
-1 * ↑(Array.filter (fun x => decide (x = w)) xs).size =
0
[grind] Diagnostics
[thm] E-Matching instances
[thm] Array.count_eq_size_filter ↦ 2
[thm] Array.count_le_size ↦ 2
[thm] Array.count_toList ↦ 2
[thm] Array.length_toList ↦ 2
[thm] Array.size_filter_le ↦ 2
[thm] List.count_eq_length_filter ↦ 2
[thm] List.count_le_length ↦ 2
[thm] List.length_filter_le ↦ 2
[thm] List.perm_iff_count ↦ 2
[thm] Array.Perm.of_toList_perm ↦ 1
[thm] List.Perm.count ↦ 1
[thm] List.Perm.filter ↦ 1
error: Lean exited with code 1
✖ [172/173] Building HumanEvalLean.HumanEval0 (4.2s)
trace: .> LEAN_PATH=/home/runner/work/human-eval-lean/human-eval-lean/.lake/build/lib/lean /home/runner/.elan/toolchains/leanprover--lean4-nightly---nightly-2026-03-07/bin/lean /home/runner/work/human-eval-lean/human-eval-lean/HumanEvalLean/HumanEval0.lean -o /home/runner/work/human-eval-lean/human-eval-lean/.lake/build/lib/lean/HumanEvalLean/HumanEval0.olean -i /home/runner/work/human-eval-lean/human-eval-lean/.lake/build/lib/lean/HumanEvalLean/HumanEval0.ilean -c /home/runner/work/human-eval-lean/human-eval-lean/.lake/build/ir/HumanEvalLean/HumanEval0.c --setup /home/runner/work/human-eval-lean/human-eval-lean/.lake/build/ir/HumanEvalLean/HumanEval0.setup.json --json
error: HumanEvalLean/HumanEval0.lean:41:4: a non-private declaration `Subarray.mergeSort` has already been declared
error: HumanEvalLean/HumanEval0.lean:54:4: a non-private declaration `Array.mergeSort` has already been declared
error: HumanEvalLean/HumanEval0.lean:152:8: a non-private declaration `Subarray.toList_mergeSort` has already been declared
error: HumanEvalLean/HumanEval0.lean:159:8: a non-private declaration `Array.toList_mergeSort` has already been declared
error: HumanEvalLean/HumanEval0.lean:170:8: a non-private declaration `Array.size_mergeSort` has already been declared
error: HumanEvalLean/HumanEval0.lean:174:8: a non-private declaration `Array.mergeSort_perm` has already been declared
error: HumanEvalLean/HumanEval0.lean:178:8: a non-private declaration `Array.pairwise_mergeSort` has already been declared
error: Lean exited with code 1
Some required targets logged failures:
- HumanEvalLean.HumanEval47
- HumanEvalLean.HumanEval0
error: build failed