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Fix 2018 B5 (again)
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This was previously "fixed" in c75c0b0
but unfortunately an error remained.

Alternative spellings of the basis element `fun k ↦ if k = i then 1 else 0`
are:
 * `if i = 0 then ![1, 0] else ![0, 1]`
 * `LinearMap.stdBasis ℝ _ i 1`
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ocfnash committed Sep 4, 2024
1 parent 5de1d00 commit 46e120f
Showing 1 changed file with 3 additions and 3 deletions.
6 changes: 3 additions & 3 deletions lean4/src/putnam_2018_b5.lean
Original file line number Diff line number Diff line change
Expand Up @@ -6,8 +6,8 @@ open Function
theorem putnam_2018_b5
(f : (Fin 2 → ℝ) → (Fin 2 → ℝ))
(h₁ : ContDiff ℝ 1 f)
(h₂ : ∀ x i j, 0 < fderiv ℝ f x i j)
(h₃ : ∀ x, 0 < fderiv ℝ f x 0 0 * fderiv ℝ f x 1 1 -
(1 / 4) * (fderiv ℝ f x 0 1 + fderiv ℝ f x 1 0) ^ 2) :
(h₂ : ∀ x i j, 0 < fderiv ℝ f x (fun k ↦ if k = i then 1 else 0) j)
(h₃ : ∀ x, 0 < fderiv ℝ f x ![1, 0] 0 * fderiv ℝ f x ![0, 1] 1 -
(1 / 4) * (fderiv ℝ f x ![1, 0] 1 + fderiv ℝ f x ![0, 1] 0) ^ 2) :
Injective f :=
sorry

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