Functions · medium

Statement, exactly as the model and Lean see it

theorem lg_target {G : Type u_1} {H : Type u_2} [AddCommGroup G] [LinearOrder G] [IsOrderedAddMonoid G] [AddCommGroup H] [PartialOrder H] [IsOrderedAddMonoid H] {f : G → H} (h₁ : ∀ (x : G), f (-x) = -f x) (h₂ : StrictAntiOn f (Set.Ici 0)) : StrictAnti f := by

Mathlib declaration: strictAnti_of_odd_strictAntiOn_nonneg
Held-out module: Mathlib.Order.Monotone.Odd
Banned modules (itself + downstream): 21
Reference proof premises (reachable / held-out): 1 / 1

Traces

Each configuration's full record: what was retrieved, what the model wrote, what Lean said back.

Not verified1 model calls · 1 Lean checks · $0.00006

Attempts

sample 0 · round 0Syntax error1.8 s model time

Proof

intro x y
cases le_total x y with hxy hyx
· exact h₂ x y hxy
· rw [h₁ x, h₁ y, h₂ y x hyx]

What Lean printed (this is all the model sees on repair)

5:27: error: unknown tactic
5:21: error: Invalid syntax for case analysis tactic: The `with` keyword must be followed by a tactic or by an alternative (e.g. `| zero =>`), but here it is followed by the identifier `hxy`.

Reference proof

Mathlib's own source for this declaration, shown for comparison. It may use lemmas the prover is not allowed to use.

/-- An odd function on a linear ordered additive commutative group is strictly antitone on the whole
group provided that it is strictly antitone on `Set.Ici 0`. -/
theorem strictAnti_of_odd_strictAntiOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
    (h₂ : StrictAntiOn f (Ici 0)) : StrictAnti f :=
  strictMono_of_odd_strictMonoOn_nonneg (H := Hᵒᵈ) h₁ h₂