mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -49,7 +49,7 @@ theorem bound (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :
       (mul_pos (mul_pos (bit0_pos zero_lt_four) (pow_pos hb 3)) (pow_pos hc 3))
   have hdenom := denom_pos ha hb hc
   rw [div_le_div_iff hdenom (sqrt_pos.mpr hsqrt)]
-  conv_lhs => rw [pow_succ', mul_assoc]
+  conv_lhs => rw [pow_succ, mul_assoc]
   apply mul_le_mul_of_nonneg_left _ (pow_pos ha 3).le
   apply le_of_pow_le_pow_left _ hdenom.le zero_lt_two
   rw [mul_pow, sq_sqrt hsqrt.le, ← sub_nonneg]

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -82,7 +82,7 @@ theorem imo2001_q2 (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :
     1 ≤
       a / sqrt (a ^ 2 + 8 * b * c) + b / sqrt (b ^ 2 + 8 * c * a) + c / sqrt (c ^ 2 + 8 * a * b) :=
   have h3 : ∀ {x : ℝ}, 0 < x → (x ^ (3 : ℝ)⁻¹) ^ 3 = x := fun x hx =>
-    show ↑3 = (3 : ℝ) by norm_num ▸ rpow_nat_inv_pow_nat hx.le three_ne_zero
+    show ↑3 = (3 : ℝ) by norm_num ▸ rpow_inv_natCast_pow hx.le three_ne_zero
   calc
     1 ≤ _ := imo2001_q2' (rpow_pos_of_pos ha _) (rpow_pos_of_pos hb _) (rpow_pos_of_pos hc _)
     _ = _ := by rw [h3 ha, h3 hb, h3 hc]

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -51,7 +51,7 @@ theorem bound (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :
   rw [div_le_div_iff hdenom (sqrt_pos.mpr hsqrt)]
   conv_lhs => rw [pow_succ', mul_assoc]
   apply mul_le_mul_of_nonneg_left _ (pow_pos ha 3).le
-  apply le_of_pow_le_pow _ hdenom.le zero_lt_two
+  apply le_of_pow_le_pow_left _ hdenom.le zero_lt_two
   rw [mul_pow, sq_sqrt hsqrt.le, ← sub_nonneg]
   calc
     (a ^ 4 + b ^ 4 + c ^ 4) ^ 2 - a ^ 2 * ((a ^ 3) ^ 2 + 8 * b ^ 3 * c ^ 3) =

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Tian Chen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tian Chen
 -/
-import Mathbin.Analysis.SpecialFunctions.Pow.Real
+import Analysis.SpecialFunctions.Pow.Real
 
 #align_import imo.imo2001_q2 from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
 

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Tian Chen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tian Chen
-
-! This file was ported from Lean 3 source module imo.imo2001_q2
-! 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.Analysis.SpecialFunctions.Pow.Real
 
+#align_import imo.imo2001_q2 from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
 /-!
 # IMO 2001 Q2
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tian Chen
 
 ! This file was ported from Lean 3 source module imo.imo2001_q2
-! 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.Analysis.SpecialFunctions.Pow.Real
 /-!
 # IMO 2001 Q2
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Let $a$, $b$, $c$ be positive reals. Prove that
 $$
 \frac{a}{\sqrt{a^2 + 8bc}} +

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

@@ -60,7 +60,6 @@ theorem bound (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :
       by ring
     _ ≥ 0 :=
       add_nonneg (add_nonneg (mul_nonneg zero_le_two (sq_nonneg _)) (sq_nonneg _)) (sq_nonneg _)
-    
 #align imo2001_q2.bound Imo2001Q2.bound
 
 theorem imo2001_q2' (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :
@@ -73,7 +72,6 @@ theorem imo2001_q2' (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :
   calc
     _ ≥ _ := add_le_add (add_le_add (bound ha hb hc) (bound hb hc ha)) (bound hc ha hb)
     _ = 1 := by rw [h₁, h₂, ← add_div, ← add_div, div_self <| ne_of_gt <| denom_pos ha hb hc]
-    
 #align imo2001_q2.imo2001_q2' Imo2001Q2.imo2001_q2'
 
 end imo2001_q2
@@ -88,6 +86,5 @@ theorem imo2001_q2 (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :
   calc
     1 ≤ _ := imo2001_q2' (rpow_pos_of_pos ha _) (rpow_pos_of_pos hb _) (rpow_pos_of_pos hc _)
     _ = _ := by rw [h3 ha, h3 hb, h3 hc]
-    
 #align imo2001_q2 imo2001_q2
 

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

A bunch of easy lemmas about Real.pow and the golf of existing lemmas with them.

Also rename log_le_log to log_le_log_iff and log_le_log' to log_le_log. Those misnames caused several proofs to bother with side conditions they didn't need.

From LeanAPAP

@@ -67,7 +67,7 @@ open Imo2001Q2
 theorem imo2001_q2 (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : ↑1 ≤
     a / sqrt (a ^ 2 + ↑8 * b * c) + b / sqrt (b ^ 2 + ↑8 * c * a) + c / sqrt (c ^ 2 + ↑8 * a * b) :=
   have h3 : ∀ {x : ℝ}, 0 < x → (x ^ (3 : ℝ)⁻¹) ^ 3 = x := fun hx =>
-    show ↑3 = (3 : ℝ) by norm_num ▸ rpow_nat_inv_pow_nat hx.le three_ne_zero
+    show ↑3 = (3 : ℝ) by norm_num ▸ rpow_inv_natCast_pow hx.le three_ne_zero
   calc
     1 ≤ _ := imo2001_q2' (rpow_pos_of_pos ha _) (rpow_pos_of_pos hb _) (rpow_pos_of_pos hc _)
     _ = _ := by rw [h3 ha, h3 hb, h3 hc]

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

Algebra.GroupPower.Order

• pow_mono → pow_right_mono
• pow_le_pow → pow_le_pow_right
• pow_le_pow_of_le_left → pow_le_pow_left
• pow_lt_pow_of_lt_left → pow_lt_pow_left
• strictMonoOn_pow → pow_left_strictMonoOn
• pow_strictMono_right → pow_right_strictMono
• pow_lt_pow → pow_lt_pow_right
• pow_lt_pow_iff → pow_lt_pow_iff_right
• pow_le_pow_iff → pow_le_pow_iff_right
• self_lt_pow → lt_self_pow
• strictAnti_pow → pow_right_strictAnti
• pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
• pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
• lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
• le_of_pow_le_pow → le_of_pow_le_pow_left
• pow_lt_pow₀ → pow_lt_pow_right₀

Algebra.GroupPower.CovariantClass

• pow_le_pow_of_le_left' → pow_le_pow_left'
• nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
• pow_lt_pow' → pow_lt_pow_right'
• nsmul_lt_nsmul → nsmul_lt_nsmul_left
• pow_strictMono_left → pow_right_strictMono'
• nsmul_strictMono_right → nsmul_left_strictMono
• StrictMono.pow_right' → StrictMono.pow_const
• StrictMono.nsmul_left → StrictMono.const_nsmul
• pow_strictMono_right' → pow_left_strictMono
• nsmul_strictMono_left → nsmul_right_strictMono
• Monotone.pow_right → Monotone.pow_const
• Monotone.nsmul_left → Monotone.const_nsmul
• lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
• lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
• pow_le_pow' → pow_le_pow_right'
• nsmul_le_nsmul → nsmul_le_nsmul_left
• pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
• nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
• le_of_pow_le_pow' → le_of_pow_le_pow_left'
• le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
• pow_le_pow_iff' → pow_le_pow_iff_right'
• nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
• pow_lt_pow_iff' → pow_lt_pow_iff_right'
• nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

Data.Nat.Pow

• Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
• Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
• Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

• pow_le_pow_iff_left
• pow_lt_pow_iff_left
• pow_right_injective
• pow_right_inj
• Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
• Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

• self_le_pow was a duplicate of le_self_pow.
• Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
• Nat.pow_right_strictMono is defeq to pow_right_strictMono.
• Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
• Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

• A bunch of proofs have been golfed.
• Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
• A few Nat lemmas have been protected.
• One docstring has been fixed.

@@ -41,7 +41,7 @@ theorem bound (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :
       = a ^ 3 * (a * sqrt ((a ^ 3) ^ 2 + (8:ℝ) * b ^ 3 * c ^ 3)) := by ring
     _ ≤ a ^ 3 * (a ^ 4 + b ^ 4 + c ^ 4) := ?_
   gcongr
-  apply le_of_pow_le_pow _ (by positivity) zero_lt_two
+  apply le_of_pow_le_pow_left two_ne_zero (by positivity)
   rw [mul_pow, sq_sqrt (by positivity), ← sub_nonneg]
   calc
     (a ^ 4 + b ^ 4 + c ^ 4) ^ 2 - a ^ 2 * ((a ^ 3) ^ 2 + 8 * b ^ 3 * c ^ 3)

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -32,8 +32,6 @@ open Real
 
 variable {a b c : ℝ}
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 namespace Imo2001Q2
 
 theorem bound (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :

@@ -32,7 +32,7 @@ open Real
 
 variable {a b c : ℝ}
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 namespace Imo2001Q2
 

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Tian Chen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tian Chen
-
-! This file was ported from Lean 3 source module imo.imo2001_q2
-! 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.Analysis.SpecialFunctions.Pow.Real
 
+#align_import imo.imo2001_q2 from "leanprover-community/mathlib"@"308826471968962c6b59c7ff82a22757386603e3"
+
 /-!
 # IMO 2001 Q2
 

Fix also some names in RingTheory.Polynomial.Eisenstein.Basic that are in the wrong namespace.

@@ -39,37 +39,30 @@ local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue
 
 namespace Imo2001Q2
 
-theorem denom_pos (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : ↑0 < a ^ 4 + b ^ 4 + c ^ 4 :=
-  add_pos (add_pos (pow_pos ha 4) (pow_pos hb 4)) (pow_pos hc 4)
-#align imo2001_q2.denom_pos Imo2001Q2.denom_pos
-
 theorem bound (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :
     a ^ 4 / (a ^ 4 + b ^ 4 + c ^ 4) ≤ a ^ 3 / sqrt ((a ^ 3) ^ 2 + ↑8 * b ^ 3 * c ^ 3) := by
-  have hsqrt := add_pos_of_nonneg_of_pos (sq_nonneg (a ^ 3))
-    (mul_pos (mul_pos (show 0 < 8 by linarith) (pow_pos hb 3)) (pow_pos hc 3))
-  have hdenom := denom_pos ha hb hc
-  rw [div_le_div_iff hdenom (sqrt_pos.mpr hsqrt)]
-  conv_lhs => rw [pow_succ', mul_assoc]
-  apply mul_le_mul_of_nonneg_left _ (pow_pos ha 3).le
-  apply le_of_pow_le_pow _ hdenom.le zero_lt_two
-  rw [mul_pow, sq_sqrt hsqrt.le, ← sub_nonneg]
+  rw [div_le_div_iff (by positivity) (by positivity)]
+  calc a ^ 4 * sqrt ((a ^ 3) ^ 2 + (8:ℝ) * b ^ 3 * c ^ 3)
+      = a ^ 3 * (a * sqrt ((a ^ 3) ^ 2 + (8:ℝ) * b ^ 3 * c ^ 3)) := by ring
+    _ ≤ a ^ 3 * (a ^ 4 + b ^ 4 + c ^ 4) := ?_
+  gcongr
+  apply le_of_pow_le_pow _ (by positivity) zero_lt_two
+  rw [mul_pow, sq_sqrt (by positivity), ← sub_nonneg]
   calc
-    (a ^ 4 + b ^ 4 + c ^ 4) ^ 2 - a ^ 2 * ((a ^ 3) ^ 2 + 8 * b ^ 3 * c ^ 3) =
-      2 * (a ^ 2 * (b ^ 2 - c ^ 2)) ^ 2 + (b ^ 4 - c ^ 4) ^ 2 +
+    (a ^ 4 + b ^ 4 + c ^ 4) ^ 2 - a ^ 2 * ((a ^ 3) ^ 2 + 8 * b ^ 3 * c ^ 3)
+      = 2 * (a ^ 2 * (b ^ 2 - c ^ 2)) ^ 2 + (b ^ 4 - c ^ 4) ^ 2 +
         (2 * (a ^ 2 * b * c - b ^ 2 * c ^ 2)) ^ 2 := by ring
-    _ ≥ 0 :=
-      add_nonneg (add_nonneg (mul_nonneg zero_le_two (sq_nonneg _)) (sq_nonneg _)) (sq_nonneg _)
+    _ ≥ 0 := by positivity
 #align imo2001_q2.bound Imo2001Q2.bound
 
 theorem imo2001_q2' (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :
     ↑1 ≤ a ^ 3 / sqrt ((a ^ 3) ^ 2 + ↑8 * b ^ 3 * c ^ 3) +
       b ^ 3 / sqrt ((b ^ 3) ^ 2 + ↑8 * c ^ 3 * a ^ 3) +
         c ^ 3 / sqrt ((c ^ 3) ^ 2 + ↑8 * a ^ 3 * b ^ 3) :=
-  have h₁ : b ^ 4 + c ^ 4 + a ^ 4 = a ^ 4 + b ^ 4 + c ^ 4 := by rw [add_comm, ← add_assoc]
-  have h₂ : c ^ 4 + a ^ 4 + b ^ 4 = a ^ 4 + b ^ 4 + c ^ 4 := by rw [add_assoc, add_comm]
+  have H : a ^ 4 + b ^ 4 + c ^ 4 ≠ 0 := by positivity
   calc
     _ ≥ _ := add_le_add (add_le_add (bound ha hb hc) (bound hb hc ha)) (bound hc ha hb)
-    _ = 1 := by rw [h₁, h₂, ← add_div, ← add_div, div_self <| ne_of_gt <| denom_pos ha hb hc]
+    _ = 1 := by ring_nf at H ⊢; field_simp
 #align imo2001_q2.imo2001_q2' Imo2001Q2.imo2001_q2'
 
 end Imo2001Q2