analysis.special_functions.log.monotone ⟷ Mathlib.Analysis.SpecialFunctions.Log.Monotone

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Bolton Bailey. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bolton Bailey
 -/
-import Mathbin.Analysis.SpecialFunctions.Pow.Real
+import Analysis.SpecialFunctions.Pow.Real
 
 #align_import analysis.special_functions.log.monotone from "leanprover-community/mathlib"@"1b0a28e1c93409dbf6d69526863cd9984ef652ce"
 

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Bolton Bailey. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bolton Bailey
-
-! This file was ported from Lean 3 source module analysis.special_functions.log.monotone
-! leanprover-community/mathlib commit 1b0a28e1c93409dbf6d69526863cd9984ef652ce
-! 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 analysis.special_functions.log.monotone from "leanprover-community/mathlib"@"1b0a28e1c93409dbf6d69526863cd9984ef652ce"
+
 /-!
 # Logarithm Tonality
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -35,6 +35,7 @@ namespace Real
 
 variable {x y : ℝ}
 
+#print Real.log_mul_self_monotoneOn /-
 theorem log_mul_self_monotoneOn : MonotoneOn (fun x : ℝ => log x * x) {x | 1 ≤ x} :=
   by
   -- TODO: can be strengthened to exp (-1) ≤ x
@@ -45,7 +46,9 @@ theorem log_mul_self_monotoneOn : MonotoneOn (fun x : ℝ => log x * x) {x | 1 
   refine' mul_le_mul ((log_le_log x_pos y_pos).mpr hxy) hxy (le_of_lt x_pos) _
   rwa [le_log_iff_exp_le y_pos, Real.exp_zero]
 #align real.log_mul_self_monotone_on Real.log_mul_self_monotoneOn
+-/
 
+#print Real.log_div_self_antitoneOn /-
 theorem log_div_self_antitoneOn : AntitoneOn (fun x : ℝ => log x / x) {x | exp 1 ≤ x} :=
   by
   simp only [AntitoneOn, mem_set_of_eq]
@@ -61,7 +64,9 @@ theorem log_div_self_antitoneOn : AntitoneOn (fun x : ℝ => log x / x) {x | exp
     _ ≤ log x * (y / x - 1) := (le_mul_of_one_le_left hyx hlogx)
     _ = log x / x * y - log x := by ring
 #align real.log_div_self_antitone_on Real.log_div_self_antitoneOn
+-/
 
+#print Real.log_div_self_rpow_antitoneOn /-
 theorem log_div_self_rpow_antitoneOn {a : ℝ} (ha : 0 < a) :
     AntitoneOn (fun x : ℝ => log x / x ^ a) {x | exp (1 / a) ≤ x} :=
   by
@@ -91,13 +96,16 @@ theorem log_div_self_rpow_antitoneOn {a : ℝ} (ha : 0 < a) :
       exact le_of_lt (exp_pos (1 / a))
     exact rpow_le_rpow x_nonneg hxy (le_of_lt ha)
 #align real.log_div_self_rpow_antitone_on Real.log_div_self_rpow_antitoneOn
+-/
 
+#print Real.log_div_sqrt_antitoneOn /-
 theorem log_div_sqrt_antitoneOn : AntitoneOn (fun x : ℝ => log x / sqrt x) {x | exp 2 ≤ x} :=
   by
   simp_rw [sqrt_eq_rpow]
   convert @log_div_self_rpow_antitone_on (1 / 2) (by norm_num)
   norm_num
 #align real.log_div_sqrt_antitone_on Real.log_div_sqrt_antitoneOn
+-/
 
 end Real
 

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

@@ -60,7 +60,6 @@ theorem log_div_self_antitoneOn : AntitoneOn (fun x : ℝ => log x / x) {x | exp
     _ ≤ y / x - 1 := (log_le_sub_one_of_pos (div_pos y_pos x_pos))
     _ ≤ log x * (y / x - 1) := (le_mul_of_one_le_left hyx hlogx)
     _ = log x / x * y - log x := by ring
-    
 #align real.log_div_self_antitone_on Real.log_div_self_antitoneOn
 
 theorem log_div_self_rpow_antitoneOn {a : ℝ} (ha : 0 < a) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -35,7 +35,7 @@ namespace Real
 
 variable {x y : ℝ}
 
-theorem log_mul_self_monotoneOn : MonotoneOn (fun x : ℝ => log x * x) { x | 1 ≤ x } :=
+theorem log_mul_self_monotoneOn : MonotoneOn (fun x : ℝ => log x * x) {x | 1 ≤ x} :=
   by
   -- TODO: can be strengthened to exp (-1) ≤ x
   simp only [MonotoneOn, mem_set_of_eq]
@@ -46,7 +46,7 @@ theorem log_mul_self_monotoneOn : MonotoneOn (fun x : ℝ => log x * x) { x | 1
   rwa [le_log_iff_exp_le y_pos, Real.exp_zero]
 #align real.log_mul_self_monotone_on Real.log_mul_self_monotoneOn
 
-theorem log_div_self_antitoneOn : AntitoneOn (fun x : ℝ => log x / x) { x | exp 1 ≤ x } :=
+theorem log_div_self_antitoneOn : AntitoneOn (fun x : ℝ => log x / x) {x | exp 1 ≤ x} :=
   by
   simp only [AntitoneOn, mem_set_of_eq]
   intro x hex y hey hxy
@@ -64,7 +64,7 @@ theorem log_div_self_antitoneOn : AntitoneOn (fun x : ℝ => log x / x) { x | ex
 #align real.log_div_self_antitone_on Real.log_div_self_antitoneOn
 
 theorem log_div_self_rpow_antitoneOn {a : ℝ} (ha : 0 < a) :
-    AntitoneOn (fun x : ℝ => log x / x ^ a) { x | exp (1 / a) ≤ x } :=
+    AntitoneOn (fun x : ℝ => log x / x ^ a) {x | exp (1 / a) ≤ x} :=
   by
   simp only [AntitoneOn, mem_set_of_eq]
   intro x hex y hey hxy
@@ -93,10 +93,10 @@ theorem log_div_self_rpow_antitoneOn {a : ℝ} (ha : 0 < a) :
     exact rpow_le_rpow x_nonneg hxy (le_of_lt ha)
 #align real.log_div_self_rpow_antitone_on Real.log_div_self_rpow_antitoneOn
 
-theorem log_div_sqrt_antitoneOn : AntitoneOn (fun x : ℝ => log x / sqrt x) { x | exp 2 ≤ x } :=
+theorem log_div_sqrt_antitoneOn : AntitoneOn (fun x : ℝ => log x / sqrt x) {x | exp 2 ≤ x} :=
   by
   simp_rw [sqrt_eq_rpow]
-  convert@log_div_self_rpow_antitone_on (1 / 2) (by norm_num)
+  convert @log_div_self_rpow_antitone_on (1 / 2) (by norm_num)
   norm_num
 #align real.log_div_sqrt_antitone_on Real.log_div_sqrt_antitoneOn
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -27,7 +27,7 @@ logarithm, tonality
 
 open Set Filter Function
 
-open Topology
+open scoped Topology
 
 noncomputable section
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -35,12 +35,6 @@ namespace Real
 
 variable {x y : ℝ}
 
-/- warning: real.log_mul_self_monotone_on -> Real.log_mul_self_monotoneOn is a dubious translation:
-lean 3 declaration is
-  MonotoneOn.{0, 0} Real Real Real.preorder Real.preorder (fun (x : Real) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Real.log x) x) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) x))
-but is expected to have type
-  MonotoneOn.{0, 0} Real Real Real.instPreorderReal Real.instPreorderReal (fun (x : Real) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.log x) x) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) x))
-Case conversion may be inaccurate. Consider using '#align real.log_mul_self_monotone_on Real.log_mul_self_monotoneOnₓ'. -/
 theorem log_mul_self_monotoneOn : MonotoneOn (fun x : ℝ => log x * x) { x | 1 ≤ x } :=
   by
   -- TODO: can be strengthened to exp (-1) ≤ x
@@ -52,12 +46,6 @@ theorem log_mul_self_monotoneOn : MonotoneOn (fun x : ℝ => log x * x) { x | 1
   rwa [le_log_iff_exp_le y_pos, Real.exp_zero]
 #align real.log_mul_self_monotone_on Real.log_mul_self_monotoneOn
 
-/- warning: real.log_div_self_antitone_on -> Real.log_div_self_antitoneOn is a dubious translation:
-lean 3 declaration is
-  AntitoneOn.{0, 0} Real Real Real.preorder Real.preorder (fun (x : Real) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Real.log x) x) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.hasLe (Real.exp (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) x))
-but is expected to have type
-  AntitoneOn.{0, 0} Real Real Real.instPreorderReal Real.instPreorderReal (fun (x : Real) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Real.log x) x) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.instLEReal (Real.exp (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) x))
-Case conversion may be inaccurate. Consider using '#align real.log_div_self_antitone_on Real.log_div_self_antitoneOnₓ'. -/
 theorem log_div_self_antitoneOn : AntitoneOn (fun x : ℝ => log x / x) { x | exp 1 ≤ x } :=
   by
   simp only [AntitoneOn, mem_set_of_eq]
@@ -75,12 +63,6 @@ theorem log_div_self_antitoneOn : AntitoneOn (fun x : ℝ => log x / x) { x | ex
     
 #align real.log_div_self_antitone_on Real.log_div_self_antitoneOn
 
-/- warning: real.log_div_self_rpow_antitone_on -> Real.log_div_self_rpow_antitoneOn is a dubious translation:
-lean 3 declaration is
-  forall {a : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) a) -> (AntitoneOn.{0, 0} Real Real Real.preorder Real.preorder (fun (x : Real) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Real.log x) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) x a)) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.hasLe (Real.exp (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) a)) x)))
-but is expected to have type
-  forall {a : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) a) -> (AntitoneOn.{0, 0} Real Real Real.instPreorderReal Real.instPreorderReal (fun (x : Real) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Real.log x) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) x a)) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.instLEReal (Real.exp (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) a)) x)))
-Case conversion may be inaccurate. Consider using '#align real.log_div_self_rpow_antitone_on Real.log_div_self_rpow_antitoneOnₓ'. -/
 theorem log_div_self_rpow_antitoneOn {a : ℝ} (ha : 0 < a) :
     AntitoneOn (fun x : ℝ => log x / x ^ a) { x | exp (1 / a) ≤ x } :=
   by
@@ -111,12 +93,6 @@ theorem log_div_self_rpow_antitoneOn {a : ℝ} (ha : 0 < a) :
     exact rpow_le_rpow x_nonneg hxy (le_of_lt ha)
 #align real.log_div_self_rpow_antitone_on Real.log_div_self_rpow_antitoneOn
 
-/- warning: real.log_div_sqrt_antitone_on -> Real.log_div_sqrt_antitoneOn is a dubious translation:
-lean 3 declaration is
-  AntitoneOn.{0, 0} Real Real Real.preorder Real.preorder (fun (x : Real) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Real.log x) (Real.sqrt x)) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.hasLe (Real.exp (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) x))
-but is expected to have type
-  AntitoneOn.{0, 0} Real Real Real.instPreorderReal Real.instPreorderReal (fun (x : Real) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Real.log x) (Real.sqrt x)) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.instLEReal (Real.exp (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) x))
-Case conversion may be inaccurate. Consider using '#align real.log_div_sqrt_antitone_on Real.log_div_sqrt_antitoneOnₓ'. -/
 theorem log_div_sqrt_antitoneOn : AntitoneOn (fun x : ℝ => log x / sqrt x) { x | exp 2 ≤ x } :=
   by
   simp_rw [sqrt_eq_rpow]

mathlib commit https://github.com/leanprover-community/mathlib/commit/1b0a28e1c93409dbf6d69526863cd9984ef652ce

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bolton Bailey
 
 ! This file was ported from Lean 3 source module analysis.special_functions.log.monotone
-! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
+! leanprover-community/mathlib commit 1b0a28e1c93409dbf6d69526863cd9984ef652ce
 ! 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
 /-!
 # Logarithm Tonality
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we describe the tonality of the logarithm function when multiplied by functions of the
 form `x ^ a`.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed

@@ -32,6 +32,12 @@ namespace Real
 
 variable {x y : ℝ}
 
+/- warning: real.log_mul_self_monotone_on -> Real.log_mul_self_monotoneOn is a dubious translation:
+lean 3 declaration is
+  MonotoneOn.{0, 0} Real Real Real.preorder Real.preorder (fun (x : Real) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Real.log x) x) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) x))
+but is expected to have type
+  MonotoneOn.{0, 0} Real Real Real.instPreorderReal Real.instPreorderReal (fun (x : Real) => HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.log x) x) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) x))
+Case conversion may be inaccurate. Consider using '#align real.log_mul_self_monotone_on Real.log_mul_self_monotoneOnₓ'. -/
 theorem log_mul_self_monotoneOn : MonotoneOn (fun x : ℝ => log x * x) { x | 1 ≤ x } :=
   by
   -- TODO: can be strengthened to exp (-1) ≤ x
@@ -43,6 +49,12 @@ theorem log_mul_self_monotoneOn : MonotoneOn (fun x : ℝ => log x * x) { x | 1
   rwa [le_log_iff_exp_le y_pos, Real.exp_zero]
 #align real.log_mul_self_monotone_on Real.log_mul_self_monotoneOn
 
+/- warning: real.log_div_self_antitone_on -> Real.log_div_self_antitoneOn is a dubious translation:
+lean 3 declaration is
+  AntitoneOn.{0, 0} Real Real Real.preorder Real.preorder (fun (x : Real) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Real.log x) x) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.hasLe (Real.exp (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) x))
+but is expected to have type
+  AntitoneOn.{0, 0} Real Real Real.instPreorderReal Real.instPreorderReal (fun (x : Real) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Real.log x) x) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.instLEReal (Real.exp (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) x))
+Case conversion may be inaccurate. Consider using '#align real.log_div_self_antitone_on Real.log_div_self_antitoneOnₓ'. -/
 theorem log_div_self_antitoneOn : AntitoneOn (fun x : ℝ => log x / x) { x | exp 1 ≤ x } :=
   by
   simp only [AntitoneOn, mem_set_of_eq]
@@ -60,6 +72,12 @@ theorem log_div_self_antitoneOn : AntitoneOn (fun x : ℝ => log x / x) { x | ex
     
 #align real.log_div_self_antitone_on Real.log_div_self_antitoneOn
 
+/- warning: real.log_div_self_rpow_antitone_on -> Real.log_div_self_rpow_antitoneOn is a dubious translation:
+lean 3 declaration is
+  forall {a : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) a) -> (AntitoneOn.{0, 0} Real Real Real.preorder Real.preorder (fun (x : Real) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Real.log x) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.hasPow) x a)) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.hasLe (Real.exp (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) a)) x)))
+but is expected to have type
+  forall {a : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) a) -> (AntitoneOn.{0, 0} Real Real Real.instPreorderReal Real.instPreorderReal (fun (x : Real) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Real.log x) (HPow.hPow.{0, 0, 0} Real Real Real (instHPow.{0, 0} Real Real Real.instPowReal) x a)) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.instLEReal (Real.exp (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) a)) x)))
+Case conversion may be inaccurate. Consider using '#align real.log_div_self_rpow_antitone_on Real.log_div_self_rpow_antitoneOnₓ'. -/
 theorem log_div_self_rpow_antitoneOn {a : ℝ} (ha : 0 < a) :
     AntitoneOn (fun x : ℝ => log x / x ^ a) { x | exp (1 / a) ≤ x } :=
   by
@@ -90,6 +108,12 @@ theorem log_div_self_rpow_antitoneOn {a : ℝ} (ha : 0 < a) :
     exact rpow_le_rpow x_nonneg hxy (le_of_lt ha)
 #align real.log_div_self_rpow_antitone_on Real.log_div_self_rpow_antitoneOn
 
+/- warning: real.log_div_sqrt_antitone_on -> Real.log_div_sqrt_antitoneOn is a dubious translation:
+lean 3 declaration is
+  AntitoneOn.{0, 0} Real Real Real.preorder Real.preorder (fun (x : Real) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Real.log x) (Real.sqrt x)) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.hasLe (Real.exp (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) x))
+but is expected to have type
+  AntitoneOn.{0, 0} Real Real Real.instPreorderReal Real.instPreorderReal (fun (x : Real) => HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Real.log x) (Real.sqrt x)) (setOf.{0} Real (fun (x : Real) => LE.le.{0} Real Real.instLEReal (Real.exp (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) x))
+Case conversion may be inaccurate. Consider using '#align real.log_div_sqrt_antitone_on Real.log_div_sqrt_antitoneOnₓ'. -/
 theorem log_div_sqrt_antitoneOn : AntitoneOn (fun x : ℝ => log x / sqrt x) { x | exp 2 ≤ x } :=
   by
   simp_rw [sqrt_eq_rpow]

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -4,11 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bolton Bailey
 
 ! This file was ported from Lean 3 source module analysis.special_functions.log.monotone
-! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
+! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Analysis.SpecialFunctions.Pow
+import Mathbin.Analysis.SpecialFunctions.Pow.Real
 
 /-!
 # Logarithm Tonality

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -4,11 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bolton Bailey
 
 ! This file was ported from Lean 3 source module analysis.special_functions.log.monotone
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Analysis.SpecialFunctions.Log.Basic
 import Mathbin.Analysis.SpecialFunctions.Pow
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -94,7 +94,7 @@ theorem log_div_self_rpow_antitoneOn {a : ℝ} (ha : 0 < a) :
 theorem log_div_sqrt_antitoneOn : AntitoneOn (fun x : ℝ => log x / sqrt x) { x | exp 2 ≤ x } :=
   by
   simp_rw [sqrt_eq_rpow]
-  convert @log_div_self_rpow_antitone_on (1 / 2) (by norm_num)
+  convert@log_div_self_rpow_antitone_on (1 / 2) (by norm_num)
   norm_num
 #align real.log_div_sqrt_antitone_on Real.log_div_sqrt_antitoneOn
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -55,8 +55,8 @@ theorem log_div_self_antitoneOn : AntitoneOn (fun x : ℝ => log x / x) { x | ex
   rw [div_le_iff y_pos, ← sub_le_sub_iff_right (log x)]
   calc
     log y - log x = log (y / x) := by rw [log_div y_pos.ne' x_pos.ne']
-    _ ≤ y / x - 1 := log_le_sub_one_of_pos (div_pos y_pos x_pos)
-    _ ≤ log x * (y / x - 1) := le_mul_of_one_le_left hyx hlogx
+    _ ≤ y / x - 1 := (log_le_sub_one_of_pos (div_pos y_pos x_pos))
+    _ ≤ log x * (y / x - 1) := (le_mul_of_one_le_left hyx hlogx)
     _ = log x / x * y - log x := by ring
     
 #align real.log_div_self_antitone_on Real.log_div_self_antitoneOn

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -48,8 +48,8 @@ theorem log_div_self_antitoneOn : AntitoneOn (fun x : ℝ => log x / x) { x | ex
   rw [div_le_iff y_pos, ← sub_le_sub_iff_right (log x)]
   calc
     log y - log x = log (y / x) := by rw [log_div y_pos.ne' x_pos.ne']
-    _ ≤ y / x - 1 := (log_le_sub_one_of_pos (div_pos y_pos x_pos))
-    _ ≤ log x * (y / x - 1) := (le_mul_of_one_le_left hyx hlogx)
+    _ ≤ y / x - 1 := log_le_sub_one_of_pos (div_pos y_pos x_pos)
+    _ ≤ log x * (y / x - 1) := le_mul_of_one_le_left hyx hlogx
     _ = log x / x * y - log x := by ring
 #align real.log_div_self_antitone_on Real.log_div_self_antitoneOn
 

This adds the notation √r for Real.sqrt r. The precedence is such that √x⁻¹ is parsed as √(x⁻¹); not because this is particularly desirable, but because it's the default and the choice doesn't really matter.

This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing x.sqrt as that PR does.

While perhaps claiming √ for Real.sqrt is greedy; it:

• Is far more common thatn NNReal.sqrt and Nat.sqrt
• Is far more interesting to mathlib than sqrt on Float
• Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types.
• Will be replaced by a more general typeclass in a future PR.

Zulip

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -82,7 +82,7 @@ theorem log_div_self_rpow_antitoneOn {a : ℝ} (ha : 0 < a) :
     gcongr
 #align real.log_div_self_rpow_antitone_on Real.log_div_self_rpow_antitoneOn
 
-theorem log_div_sqrt_antitoneOn : AntitoneOn (fun x : ℝ => log x / sqrt x) { x | exp 2 ≤ x } := by
+theorem log_div_sqrt_antitoneOn : AntitoneOn (fun x : ℝ => log x / √x) { x | exp 2 ≤ x } := by
   simp_rw [sqrt_eq_rpow]
   convert @log_div_self_rpow_antitoneOn (1 / 2) (by norm_num)
   norm_num

Following on from previous gcongr golfing PRs #4702 and #4784.

This is a replacement for #7901: this round of golfs, first introduced there, there exposed some performance issues in gcongr, hopefully fixed by #8731, and I am opening a new PR so that the performance can be checked against current master rather than master at the time of #7901.

@@ -33,9 +33,8 @@ theorem log_mul_self_monotoneOn : MonotoneOn (fun x : ℝ => log x * x) { x | 1
   -- TODO: can be strengthened to exp (-1) ≤ x
   simp only [MonotoneOn, mem_setOf_eq]
   intro x hex y hey hxy
-  have x_pos : 0 < x := lt_of_lt_of_le zero_lt_one hex
   have y_pos : 0 < y := lt_of_lt_of_le zero_lt_one hey
-  refine' mul_le_mul ((log_le_log x_pos y_pos).mpr hxy) hxy (le_of_lt x_pos) _
+  gcongr
   rwa [le_log_iff_exp_le y_pos, Real.exp_zero]
 #align real.log_mul_self_monotone_on Real.log_mul_self_monotoneOn
 
@@ -80,7 +79,7 @@ theorem log_div_self_rpow_antitoneOn {a : ℝ} (ha : 0 < a) :
       simp only [Real.exp_eq_exp]
       field_simp [(ne_of_lt ha).symm]
       exact le_of_lt (exp_pos (1 / a))
-    exact rpow_le_rpow x_nonneg hxy (le_of_lt ha)
+    gcongr
 #align real.log_div_self_rpow_antitone_on Real.log_div_self_rpow_antitoneOn
 
 theorem log_div_sqrt_antitoneOn : AntitoneOn (fun x : ℝ => log x / sqrt x) { x | exp 2 ≤ x } := by

• 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 Bolton Bailey. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bolton Bailey
-
-! This file was ported from Lean 3 source module analysis.special_functions.log.monotone
-! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
-! 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 analysis.special_functions.log.monotone from "leanprover-community/mathlib"@"0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8"
+
 /-!
 # Logarithm Tonality