imo.imo2005_q3 | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

30882647

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

08b081ea

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Manuel Candales. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Manuel Candales
 -/
-import Mathbin.Data.Real.Basic
-import Mathbin.Tactic.Positivity
+import Data.Real.Basic
+import Tactic.Positivity
 
 #align_import imo.imo2005_q3 from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"

08b081ea

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Manuel Candales. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Manuel Candales
-
-! This file was ported from Lean 3 source module imo.imo2005_q3
-! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Real.Basic
 import Mathbin.Tactic.Positivity
 
+#align_import imo.imo2005_q3 from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
 /-!
 # IMO 2005 Q3

08b081ea

bump to nightly-2023-07-17-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa

a159b65f

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Manuel Candales
 
 ! This file was ported from Lean 3 source module imo.imo2005_q3
-! leanprover-community/mathlib commit 308826471968962c6b59c7ff82a22757386603e3
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Tactic.Positivity
 
 /-!
 # IMO 2005 Q3
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 Let `x`, `y` and `z` be positive real numbers such that `xyz ≥ 1`. Prove that:
 `(x^5 - x^2)/(x^5 + y^2 + z^2) + (y^5 - y^2)/(y^5 + z^2 + x^2) + (z^5 - z^2)/(z^5 + x^2 + y^2) ≥ 0`

30882647

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -55,7 +55,6 @@ theorem key_insight (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) (h : x
       refine' (div_le_div_right h₄).mpr _; simp
       exact (le_mul_iff_one_le_right (pow_pos hx 2)).mpr h
     _ = (x ^ 2 - y * z) / (x ^ 2 + y ^ 2 + z ^ 2) := by field_simp [h₂.ne', h₃.ne']; ring
-    
 #align imo2005_q3.key_insight Imo2005Q3.key_insight
 
 end imo2005_q3
@@ -83,6 +82,5 @@ theorem imo2005_q3 (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) (h : x *
     _ ≥ 0 :=
       div_nonneg (by linarith [sq_nonneg (x - y), sq_nonneg (y - z), sq_nonneg (z - x)])
         (by linarith [sq_nonneg x, sq_nonneg y, sq_nonneg z])
-    
 #align imo2005_q3 imo2005_q3

30882647

bump to nightly-2023-06-07-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

176da745

Changes in mathlib4

mathlib3

mathlib4

30882647

style: cleanup by putting by on the same line as := (#8407)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

5e9b46ed

Diff

@@ -36,9 +36,7 @@ theorem key_insight (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) (h : x
     ring
   have h₅ :
     (x ^ 3 - 1) ^ 2 * x ^ 2 * (y ^ 2 + z ^ 2) /
-        ((x ^ 5 + y ^ 2 + z ^ 2) * (x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2))) ≥
-      0 :=
-    by positivity
+        ((x ^ 5 + y ^ 2 + z ^ 2) * (x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2))) ≥ 0 := by positivity
   calc
     (x ^ 5 - x ^ 2) / (x ^ 5 + y ^ 2 + z ^ 2)
       ≥ (x ^ 5 - x ^ 2 * 1) / (x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2)) := by linarith only [key, h₅]

30882647

chore: split Data.Real.Basic (#8356)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

43e32656

Diff

@@ -5,6 +5,8 @@ Authors: Manuel Candales
 -/
 import Mathlib.Data.Real.Basic
 import Mathlib.Tactic.Positivity
+import Mathlib.Tactic.FieldSimp
+import Mathlib.Tactic.Linarith
 
 #align_import imo.imo2005_q3 from "leanprover-community/mathlib"@"308826471968962c6b59c7ff82a22757386603e3"

30882647

field_simp: Use positivity as a discharger (#6312)

The main reasons is that having h : 0 < denom in the context should suffice for field_simp to do its job, without the need to manually pass h.ne or similar.

Quite a few have := … ≠ 0 could be dropped, and some field_simp calls no longer need explicit arguments; this is promising.

This does break some proofs where field_simp was not used as a closing tactic, and it now shuffles terms around a bit different. These were fixed. Using field_simp in the middle of a proof seems rather fragile anyways.

As a drive-by contribution, positivity now knows about π > 0.

fixes: #4835

Co-authored-by: Matthew Ballard <matt@mrb.email>

6b391efa

Diff

@@ -25,9 +25,6 @@ namespace Imo2005Q3
 
 theorem key_insight (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) (h : x * y * z ≥ 1) :
     (x ^ 5 - x ^ 2) / (x ^ 5 + y ^ 2 + z ^ 2) ≥ (x ^ 2 - y * z) / (x ^ 2 + y ^ 2 + z ^ 2) := by
-  have h₁ : x ^ 5 + y ^ 2 + z ^ 2 ≠ 0 := by positivity
-  have h₃ : x ^ 2 + y ^ 2 + z ^ 2 ≠ 0 := by positivity
-  have h₄ : x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2) ≠ 0 := by positivity
   have key :
     (x ^ 5 - x ^ 2) / (x ^ 5 + y ^ 2 + z ^ 2) -
         (x ^ 5 - x ^ 2 * 1) / (x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2)) =

30882647

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Manuel Candales. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Manuel Candales
-
-! This file was ported from Lean 3 source module imo.imo2005_q3
-! leanprover-community/mathlib commit 308826471968962c6b59c7ff82a22757386603e3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Real.Basic
 import Mathlib.Tactic.Positivity
 
+#align_import imo.imo2005_q3 from "leanprover-community/mathlib"@"308826471968962c6b59c7ff82a22757386603e3"
+
 /-!
 # IMO 2005 Q3
 Let `x`, `y` and `z` be positive real numbers such that `xyz ≥ 1`. Prove that:

30882647

feat: rewrites at location (#4157)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

cef370e3

Diff

@@ -28,16 +28,15 @@ namespace Imo2005Q3
 
 theorem key_insight (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) (h : x * y * z ≥ 1) :
     (x ^ 5 - x ^ 2) / (x ^ 5 + y ^ 2 + z ^ 2) ≥ (x ^ 2 - y * z) / (x ^ 2 + y ^ 2 + z ^ 2) := by
-  have h₁ : 0 < x ^ 5 + y ^ 2 + z ^ 2 := by positivity
-  have h₂ : 0 < x ^ 3 := by positivity
-  have h₃ : 0 < x ^ 2 + y ^ 2 + z ^ 2 := by positivity
-  have h₄ : 0 < x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2) := by positivity
+  have h₁ : x ^ 5 + y ^ 2 + z ^ 2 ≠ 0 := by positivity
+  have h₃ : x ^ 2 + y ^ 2 + z ^ 2 ≠ 0 := by positivity
+  have h₄ : x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2) ≠ 0 := by positivity
   have key :
     (x ^ 5 - x ^ 2) / (x ^ 5 + y ^ 2 + z ^ 2) -
-        (x ^ 5 - x ^ 2) / (x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2)) =
+        (x ^ 5 - x ^ 2 * 1) / (x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2)) =
       (x ^ 3 - 1) ^ 2 * x ^ 2 * (y ^ 2 + z ^ 2) /
         ((x ^ 5 + y ^ 2 + z ^ 2) * (x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2))) := by
-    field_simp [h₁.ne', h₄.ne']
+    field_simp
     ring
   have h₅ :
     (x ^ 3 - 1) ^ 2 * x ^ 2 * (y ^ 2 + z ^ 2) /
@@ -45,13 +44,10 @@ theorem key_insight (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) (h : x
       0 :=
     by positivity
   calc
-    (x ^ 5 - x ^ 2) / (x ^ 5 + y ^ 2 + z ^ 2) ≥
-        (x ^ 5 - x ^ 2) / (x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2)) :=
-      by linarith [key, h₅]
-    _ ≥ (x ^ 5 - x ^ 2 * (x * y * z)) / (x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2)) := by
-      refine' (div_le_div_right h₄).mpr _; simp only [sub_le_sub_iff_left]
-      exact (le_mul_iff_one_le_right (pow_pos hx 2)).mpr h
-    _ = (x ^ 2 - y * z) / (x ^ 2 + y ^ 2 + z ^ 2) := by field_simp [h₂.ne', h₃.ne']; ring
+    (x ^ 5 - x ^ 2) / (x ^ 5 + y ^ 2 + z ^ 2)
+      ≥ (x ^ 5 - x ^ 2 * 1) / (x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2)) := by linarith only [key, h₅]
+    _ ≥ (x ^ 5 - x ^ 2 * (x * y * z)) / (x ^ 3 * (x ^ 2 + y ^ 2 + z ^ 2)) := by gcongr
+    _ = (x ^ 2 - y * z) / (x ^ 2 + y ^ 2 + z ^ 2) := by field_simp; ring
 #align imo2005_q3.key_insight Imo2005Q3.key_insight
 
 end Imo2005Q3
@@ -67,13 +63,7 @@ theorem imo2005_q3 (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) (h : x *
           (z ^ 5 - z ^ 2) / (z ^ 5 + x ^ 2 + y ^ 2) ≥
         (x ^ 2 - y * z) / (x ^ 2 + y ^ 2 + z ^ 2) + (y ^ 2 - z * x) / (y ^ 2 + z ^ 2 + x ^ 2) +
           (z ^ 2 - x * y) / (z ^ 2 + x ^ 2 + y ^ 2) := by
-      linarith [key_insight x y z hx hy hz h, key_insight y z x hy hz hx (by linarith [h]),
-        key_insight z x y hz hx hy (by linarith [h])]
-    _ = 1 / 2 * ((x - y) ^ 2 + (y - z) ^ 2 + (z - x) ^ 2) / (x ^ 2 + y ^ 2 + z ^ 2) := by
-      have h₁ : y ^ 2 + z ^ 2 + x ^ 2 = x ^ 2 + y ^ 2 + z ^ 2; ring
-      have h₂ : z ^ 2 + x ^ 2 + y ^ 2 = x ^ 2 + y ^ 2 + z ^ 2; ring
-      rw [h₁, h₂]; ring
-    _ ≥ 0 :=
-      div_nonneg (by linarith [sq_nonneg (x - y), sq_nonneg (y - z), sq_nonneg (z - x)])
-        (by linarith [sq_nonneg x, sq_nonneg y, sq_nonneg z])
+      gcongr ?_ + ?_ + ?_ <;> apply key_insight <;> linarith
+    _ = 1 / 2 * ((x - y) ^ 2 + (y - z) ^ 2 + (z - x) ^ 2) / (x ^ 2 + y ^ 2 + z ^ 2) := by ring
+    _ ≥ 0 := by positivity
 #align imo2005_q3 imo2005_q3

30882647

feat: port NumberTheory.DiophantineApproximation (#5126)

851314e3

`imo.imo2005_q3` ⟷ `Archive.Imo.Imo2005Q3`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 3 + 202

imo.imo2005_q3 ⟷ Archive.Imo.Imo2005Q3

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 3 + 202

`imo.imo2005_q3` ⟷ `Archive.Imo.Imo2005Q3`