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Update lean4/src/putnam_1986_a5.lean
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Co-authored-by: Eric Wieser <[email protected]>
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GeorgeTsoukalas and eric-wieser authored Dec 6, 2024
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3 changes: 2 additions & 1 deletion lean4/src/putnam_1986_a5.lean
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Expand Up @@ -7,6 +7,7 @@ theorem putnam_1986_a5
(n : ℕ) (hn : 1 ≤ n)
(f : Fin n → ((Fin n → ℝ) → ℝ))
(hf : ∀ i, ContDiff ℝ 2 (f i))
(hf' : ∀ i j : Fin n, ∃ C : ℝ, ∀ x : Fin n → ℝ, fderiv ℝ (f i) x (Pi.single j 1) - fderiv ℝ (f j) x (Pi.single i 1) = C)
(C : Fin n → Fin n → ℝ)
(hf' : ∀ i j : Fin n, ∀ x : Fin n → ℝ, fderiv ℝ (f i) x (Pi.single j 1) - fderiv ℝ (f j) x (Pi.single i 1) = C i j)
: ∃ g : (Fin n → ℝ) → ℝ, ∀ i : Fin n, IsLinearMap ℝ (λ x ↦ f i x + fderiv ℝ g x (Pi.single i 1)) :=
sorry

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