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Update lean4/src/putnam_1994_b3.lean
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Co-authored-by: Eric Wieser <[email protected]>
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ocfnash and eric-wieser authored Oct 23, 2024
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6 changes: 3 additions & 3 deletions lean4/src/putnam_1994_b3.lean
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Expand Up @@ -9,7 +9,7 @@ abbrev putnam_1994_b3_solution : Set ℝ := sorry
Find the set of all real numbers $k$ with the following property: For any positive, differentiable function $f$ that satisfies $f'(x)>f(x)$ for all $x$, there is some number $N$ such that $f(x)>e^{kx}$ for all $x>N$.
-/
theorem putnam_1994_b3
(S : Set (ℝ → ℝ))
(S_def : ∀ f, f ∈ S ↔ (∀ x, 0 < f x ∧ f x < deriv f x) ∧ Differentiable ℝ f) :
{k | ∀ f ∈ S, ∃ N, ∀ x > N, Real.exp (k * x) < f x} = putnam_1994_b3_solution := by
:
{k | ∀ f (hf : (∀ x, 0 < f x ∧ f x < deriv f x) ∧ Differentiable ℝ f),
∃ N, ∀ x > N, Real.exp (k * x) < f x} = putnam_1994_b3_solution := by
sorry

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