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Update imo_proofs/imo_1985_p6.lean

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  1. imo_proofs/imo_1985_p6.lean +2 -3
imo_proofs/imo_1985_p6.lean CHANGED
@@ -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 : β„• β†’ NNReal β†’ ℝ)
@@ -1318,6 +1317,7 @@ lemma imo_1985_p6_nnreal
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  exact aux_unique f h₁ hmoβ‚€ h₇ x y hxβ‚€ hyβ‚€
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  theorem imo_1985_p6
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  (f : β„• β†’ ℝ β†’ ℝ)
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  (hβ‚€ : βˆ€ x, f 1 x = x)
@@ -1325,7 +1325,7 @@ theorem imo_1985_p6
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  βˆƒ! a, βˆ€ n, 0 < n β†’ 0 < f n a ∧ f n a < f (n + 1) a ∧ f (n + 1) a < 1 := by
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  let fn : β„• β†’ NNReal β†’ ℝ := fun n x => f n x
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  have hfn₁: βˆ€ n x, 0 < n β†’ 0 ≀ x β†’ fn n x = f n x := by
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- exact fun n x a a ↦ rfl
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  have hβ‚‚: βˆƒ! a, βˆ€ (n : β„•), 0 < n β†’ 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 ↦ hβ‚€ ↑x) fun n x ↦ h₁ n ↑x
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  obtain ⟨a, haβ‚€, haβ‚βŸ© := hβ‚‚
@@ -1353,4 +1353,3 @@ theorem imo_1985_p6
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  exact (hyβ‚€ 1 (by decide)).1
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  have hyβ‚…: (0:ℝ) < 0 := by exact lt_trans hyβ‚„ hy₃
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  exact (lt_self_iff_false 0).mp hyβ‚…
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-
 
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  import Mathlib
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  lemma aux_1
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  (f : β„• β†’ NNReal β†’ ℝ)
 
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  exact aux_unique f h₁ hmoβ‚€ h₇ x y hxβ‚€ hyβ‚€
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+
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  theorem imo_1985_p6
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  (f : β„• β†’ ℝ β†’ ℝ)
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  (hβ‚€ : βˆ€ x, f 1 x = x)
 
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  βˆƒ! a, βˆ€ n, 0 < n β†’ 0 < f n a ∧ f n a < f (n + 1) a ∧ f (n + 1) a < 1 := by
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  let fn : β„• β†’ NNReal β†’ ℝ := fun n x => f n x
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  have hfn₁: βˆ€ n x, 0 < n β†’ 0 ≀ x β†’ fn n x = f n x := by
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+ exact fun n x _ _ ↦ rfl
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  have hβ‚‚: βˆƒ! a, βˆ€ (n : β„•), 0 < n β†’ 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 ↦ hβ‚€ ↑x) fun n x ↦ h₁ n ↑x
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  obtain ⟨a, haβ‚€, haβ‚βŸ© := hβ‚‚
 
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  exact (hyβ‚€ 1 (by decide)).1
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  have hyβ‚…: (0:ℝ) < 0 := by exact lt_trans hyβ‚„ hy₃
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  exact (lt_self_iff_false 0).mp hyβ‚