Update imo_proofs/imo_1985_p6.lean
Browse files
imo_proofs/imo_1985_p6.lean
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@@ -1,6 +1,5 @@
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import Mathlib
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-
set_option linter.unusedVariables.analyzeTactics true
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lemma aux_1
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(f : ℕ → NNReal → ℝ)
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@@ -1318,6 +1317,7 @@ lemma imo_1985_p6_nnreal
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exact aux_unique f h₁ hmo₀ h₇ x y hx₀ hy₀
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theorem imo_1985_p6
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(f : ℕ → ℝ → ℝ)
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(h₀ : ∀ x, f 1 x = x)
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@@ -1325,7 +1325,7 @@ theorem imo_1985_p6
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∃! a, ∀ n, 0 < n → 0 < f n a ∧ f n a < f (n + 1) a ∧ f (n + 1) a < 1 := by
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let fn : ℕ → NNReal → ℝ := fun n x => f n x
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have hfn₁: ∀ n x, 0 < n → 0 ≤ x → fn n x = f n x := by
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exact fun n x
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have h₂: ∃! a, ∀ (n : ℕ), 0 < n → 0 < fn n a ∧ fn n a < fn (n + 1) a ∧ fn (n + 1) a < 1 := by
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exact imo_1985_p6_nnreal fn (fun x ↦ h₀ ↑x) fun n x ↦ h₁ n ↑x
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obtain ⟨a, ha₀, ha₁⟩ := h₂
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@@ -1353,4 +1353,3 @@ theorem imo_1985_p6
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exact (hy₀ 1 (by decide)).1
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have hy₅: (0:ℝ) < 0 := by exact lt_trans hy₄ hy₃
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exact (lt_self_iff_false 0).mp hy₅
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-
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import Mathlib
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lemma aux_1
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(f : ℕ → NNReal → ℝ)
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exact aux_unique f h₁ hmo₀ h₇ x y hx₀ hy₀
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+
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theorem imo_1985_p6
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(f : ℕ → ℝ → ℝ)
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(h₀ : ∀ x, f 1 x = x)
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∃! a, ∀ n, 0 < n → 0 < f n a ∧ f n a < f (n + 1) a ∧ f (n + 1) a < 1 := by
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let fn : ℕ → NNReal → ℝ := fun n x => f n x
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have hfn₁: ∀ n x, 0 < n → 0 ≤ x → fn n x = f n x := by
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+
exact fun n x _ _ ↦ rfl
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have h₂: ∃! a, ∀ (n : ℕ), 0 < n → 0 < fn n a ∧ fn n a < fn (n + 1) a ∧ fn (n + 1) a < 1 := by
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exact imo_1985_p6_nnreal fn (fun x ↦ h₀ ↑x) fun n x ↦ h₁ n ↑x
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obtain ⟨a, ha₀, ha₁⟩ := h₂
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exact (hy₀ 1 (by decide)).1
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have hy₅: (0:ℝ) < 0 := by exact lt_trans hy₄ hy₃
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exact (lt_self_iff_false 0).mp hy₅
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