analysis.hofer | 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

f2ce6086

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

19cb3751

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -52,7 +52,7 @@ theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ)
   replace H :
     ∀ k : ℕ, ∀ x', d x' x ≤ 2 * ε ∧ 2 ^ k * ϕ x ≤ ϕ x' → ∃ y, d x' y ≤ ε / 2 ^ k ∧ 2 * ϕ x' < ϕ y
   · intro k x'
-    push_neg at H 
+    push_neg at H
     simpa [reformulation] using H (ε / 2 ^ k) (by simp [ε_pos]) x' (by simp [ε_pos.le, one_le_two])
   clear reformulation
   haveI : Nonempty X := ⟨x⟩
@@ -107,7 +107,7 @@ theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ)
   have lim_top : tendsto (ϕ ∘ u) at_top at_top :=
     by
     let v n := (ϕ ∘ u) (n + 1)
-    suffices tendsto v at_top at_top by rwa [tendsto_add_at_top_iff_nat] at this 
+    suffices tendsto v at_top at_top by rwa [tendsto_add_at_top_iff_nat] at this
     have hv₀ : 0 < v 0 := by
       have : 0 ≤ ϕ (u 0) := nonneg x
       calc

19cb3751

bump to nightly-2024-01-13-06

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

31733180

Diff

@@ -30,13 +30,11 @@ open Filter Finset
 
 local notation "d" => dist
 
-#print pos_div_pow_pos /-
 @[simp]
 theorem pos_div_pow_pos {α : Type _} [LinearOrderedSemifield α] {a b : α} (ha : 0 < a) (hb : 0 < b)
     (k : ℕ) : 0 < a / b ^ k :=
   div_pos ha (pow_pos hb k)
 #align pos_div_pow_pos pos_div_pow_pos
--/
 
 #print hofer /-
 theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (ε_pos : 0 < ε)

19cb3751

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2020 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
 -/
-import Mathbin.Analysis.SpecificLimits.Basic
+import Analysis.SpecificLimits.Basic
 
 #align_import analysis.hofer from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"

19cb3751

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
-
-! This file was ported from Lean 3 source module analysis.hofer
-! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.SpecificLimits.Basic
 
+#align_import analysis.hofer from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
+
 /-!
 # Hofer's lemma

19cb3751

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -31,15 +31,17 @@ open scoped Classical Topology BigOperators
 
 open Filter Finset
 
--- mathport name: exprd
 local notation "d" => dist
 
+#print pos_div_pow_pos /-
 @[simp]
 theorem pos_div_pow_pos {α : Type _} [LinearOrderedSemifield α] {a b : α} (ha : 0 < a) (hb : 0 < b)
     (k : ℕ) : 0 < a / b ^ k :=
   div_pos ha (pow_pos hb k)
 #align pos_div_pow_pos pos_div_pow_pos
+-/
 
+#print hofer /-
 theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (ε_pos : 0 < ε)
     {ϕ : X → ℝ} (cont : Continuous ϕ) (nonneg : ∀ y, 0 ≤ ϕ y) :
     ∃ ε' > 0,
@@ -123,4 +125,5 @@ theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ)
   -- So we have our contradiction!
   exact not_tendsto_atTop_of_tendsto_nhds limUnder lim_top
 #align hofer hofer
+-/

19cb3751

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -91,7 +91,6 @@ theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ)
         _ = ∑ i in r, (1 / 2) ^ i * ε := by congr with i; field_simp
         _ = (∑ i in r, (1 / 2) ^ i) * ε := finset.sum_mul.symm
         _ ≤ 2 * ε := mul_le_mul_of_nonneg_right (sum_geometric_two_le _) (le_of_lt ε_pos)
-        
     have B : 2 ^ (n + 1) * ϕ x ≤ ϕ (u (n + 1)) :=
       by
       refine' @geom_le (ϕ ∘ u) _ zero_le_two (n + 1) fun m hm => _
@@ -117,7 +116,6 @@ theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ)
       calc
         0 ≤ 2 * ϕ (u 0) := by linarith
         _ < ϕ (u (0 + 1)) := key₂ 0
-        
     apply tendsto_atTop_of_geom_le hv₀ one_lt_two
     exact fun n => (key₂ (n + 1)).le
   -- But ϕ ∘ u also needs to go to ϕ(y)

19cb3751

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -55,7 +55,7 @@ theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ)
   replace H :
     ∀ k : ℕ, ∀ x', d x' x ≤ 2 * ε ∧ 2 ^ k * ϕ x ≤ ϕ x' → ∃ y, d x' y ≤ ε / 2 ^ k ∧ 2 * ϕ x' < ϕ y
   · intro k x'
-    push_neg  at H 
+    push_neg at H 
     simpa [reformulation] using H (ε / 2 ^ k) (by simp [ε_pos]) x' (by simp [ε_pos.le, one_le_two])
   clear reformulation
   haveI : Nonempty X := ⟨x⟩

19cb3751

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -55,7 +55,7 @@ theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ)
   replace H :
     ∀ k : ℕ, ∀ x', d x' x ≤ 2 * ε ∧ 2 ^ k * ϕ x ≤ ϕ x' → ∃ y, d x' y ≤ ε / 2 ^ k ∧ 2 * ϕ x' < ϕ y
   · intro k x'
-    push_neg  at H
+    push_neg  at H 
     simpa [reformulation] using H (ε / 2 ^ k) (by simp [ε_pos]) x' (by simp [ε_pos.le, one_le_two])
   clear reformulation
   haveI : Nonempty X := ⟨x⟩
@@ -111,7 +111,7 @@ theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ)
   have lim_top : tendsto (ϕ ∘ u) at_top at_top :=
     by
     let v n := (ϕ ∘ u) (n + 1)
-    suffices tendsto v at_top at_top by rwa [tendsto_add_at_top_iff_nat] at this
+    suffices tendsto v at_top at_top by rwa [tendsto_add_at_top_iff_nat] at this 
     have hv₀ : 0 < v 0 := by
       have : 0 ≤ ϕ (u 0) := nonneg x
       calc

19cb3751

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -27,7 +27,7 @@ example of a proof needing to construct a sequence by induction in the middle of
 -/
 
 
-open Classical Topology BigOperators
+open scoped Classical Topology BigOperators
 
 open Filter Finset

19cb3751

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -34,24 +34,12 @@ open Filter Finset
 -- mathport name: exprd
 local notation "d" => dist
 
-/- warning: pos_div_pow_pos -> pos_div_pow_pos is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align pos_div_pow_pos pos_div_pow_posₓ'. -/
 @[simp]
 theorem pos_div_pow_pos {α : Type _} [LinearOrderedSemifield α] {a b : α} (ha : 0 < a) (hb : 0 < b)
     (k : ℕ) : 0 < a / b ^ k :=
   div_pos ha (pow_pos hb k)
 #align pos_div_pow_pos pos_div_pow_pos
 
-/- warning: hofer -> hofer is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : MetricSpace.{u1} X] [_inst_2 : CompleteSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1))] (x : X) (ε : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (forall {ϕ : X -> Real}, (Continuous.{u1, 0} X Real (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ϕ) -> (forall (y : X), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (ϕ y)) -> (Exists.{1} Real (fun (ε' : Real) => Exists.{0} (GT.gt.{0} Real Real.hasLt ε' (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (fun (H : GT.gt.{0} Real Real.hasLt ε' (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) => Exists.{succ u1} X (fun (x' : X) => And (LE.le.{0} Real Real.hasLe ε' ε) (And (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} X (PseudoMetricSpace.toHasDist.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1)) x' x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) ε)) (And (LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ε (ϕ x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ε' (ϕ x'))) (forall (y : X), (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} X (PseudoMetricSpace.toHasDist.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1)) x' y) ε') -> (LE.le.{0} Real Real.hasLe (ϕ y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (ϕ x')))))))))))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : MetricSpace.{u1} X] [_inst_2 : CompleteSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1))] (x : X) (ε : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (forall {ϕ : X -> Real}, (Continuous.{u1, 0} X Real (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ϕ) -> (forall (y : X), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (ϕ y)) -> (Exists.{1} Real (fun (ε' : Real) => And (GT.gt.{0} Real Real.instLTReal ε' (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Exists.{succ u1} X (fun (x' : X) => And (LE.le.{0} Real Real.instLEReal ε' ε) (And (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} X (PseudoMetricSpace.toDist.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1)) x' x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) ε)) (And (LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) ε (ϕ x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) ε' (ϕ x'))) (forall (y : X), (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} X (PseudoMetricSpace.toDist.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1)) x' y) ε') -> (LE.le.{0} Real Real.instLEReal (ϕ y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (ϕ x')))))))))))
-Case conversion may be inaccurate. Consider using '#align hofer hoferₓ'. -/
 theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (ε_pos : 0 < ε)
     {ϕ : X → ℝ} (cont : Continuous ϕ) (nonneg : ∀ y, 0 ≤ ϕ y) :
     ∃ ε' > 0,

19cb3751

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -100,9 +100,7 @@ theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ)
         d (u 0) (u (n + 1)) ≤ ∑ i in r, d (u i) (u <| i + 1) := dist_le_range_sum_dist u (n + 1)
         _ ≤ ∑ i in r, ε / 2 ^ i :=
           (sum_le_sum fun i i_in => (IH i <| nat.lt_succ_iff.mp <| finset.mem_range.mp i_in).1)
-        _ = ∑ i in r, (1 / 2) ^ i * ε := by
-          congr with i
-          field_simp
+        _ = ∑ i in r, (1 / 2) ^ i * ε := by congr with i; field_simp
         _ = (∑ i in r, (1 / 2) ^ i) * ε := finset.sum_mul.symm
         _ ≤ 2 * ε := mul_le_mul_of_nonneg_right (sum_geometric_two_le _) (le_of_lt ε_pos)

19cb3751

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -36,7 +36,7 @@ local notation "d" => dist
 
 /- warning: pos_div_pow_pos -> pos_div_pow_pos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedSemifield.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))))) b) -> (forall (k : Nat), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (GroupWithZero.toDivInvMonoid.{u1} α (DivisionSemiring.toGroupWithZero.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))) a (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))))) b k)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedSemifield.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))))) b) -> (forall (k : Nat), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (GroupWithZero.toDivInvMonoid.{u1} α (DivisionSemiring.toGroupWithZero.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))) a (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))))) b k)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedSemifield.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedSemiring.toPartialOrder.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedSemiring.toPartialOrder.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))) b) -> (forall (k : Nat), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedSemiring.toPartialOrder.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedSemifield.toDiv.{u1} α _inst_1)) a (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))))) b k)))
 Case conversion may be inaccurate. Consider using '#align pos_div_pow_pos pos_div_pow_posₓ'. -/

19cb3751

bump to nightly-2023-04-09-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/284fdd2962e67d2932fa3a79ce19fcf92d38e228

32290448

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
 
 ! This file was ported from Lean 3 source module analysis.hofer
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
 ! 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.SpecificLimits.Basic
 /-!
 # Hofer's lemma
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This is an elementary lemma about complete metric spaces. It is motivated by an
 application to the bubbling-off analysis for holomorphic curves in symplectic topology.
 We are *very* far away from having these applications, but the proof here is a nice

f2ce6086

bump to nightly-2023-04-07-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9

d07496b3

Diff

@@ -31,12 +31,24 @@ open Filter Finset
 -- mathport name: exprd
 local notation "d" => dist
 
+/- warning: pos_div_pow_pos -> pos_div_pow_pos is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedSemifield.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))))) b) -> (forall (k : Nat), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (GroupWithZero.toDivInvMonoid.{u1} α (DivisionSemiring.toGroupWithZero.{u1} α (Semifield.toDivisionSemiring.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))) a (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))))) b k)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedSemifield.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedSemiring.toPartialOrder.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedSemiring.toPartialOrder.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))) b) -> (forall (k : Nat), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedSemiring.toPartialOrder.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α _inst_1)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedSemifield.toDiv.{u1} α _inst_1)) a (HPow.hPow.{u1, 0, u1} α Nat α (instHPow.{u1, 0} α Nat (Monoid.Pow.{u1} α (MonoidWithZero.toMonoid.{u1} α (Semiring.toMonoidWithZero.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))))) b k)))
+Case conversion may be inaccurate. Consider using '#align pos_div_pow_pos pos_div_pow_posₓ'. -/
 @[simp]
 theorem pos_div_pow_pos {α : Type _} [LinearOrderedSemifield α] {a b : α} (ha : 0 < a) (hb : 0 < b)
     (k : ℕ) : 0 < a / b ^ k :=
   div_pos ha (pow_pos hb k)
 #align pos_div_pow_pos pos_div_pow_pos
 
+/- warning: hofer -> hofer is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : MetricSpace.{u1} X] [_inst_2 : CompleteSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1))] (x : X) (ε : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (forall {ϕ : X -> Real}, (Continuous.{u1, 0} X Real (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ϕ) -> (forall (y : X), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (ϕ y)) -> (Exists.{1} Real (fun (ε' : Real) => Exists.{0} (GT.gt.{0} Real Real.hasLt ε' (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (fun (H : GT.gt.{0} Real Real.hasLt ε' (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) => Exists.{succ u1} X (fun (x' : X) => And (LE.le.{0} Real Real.hasLe ε' ε) (And (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} X (PseudoMetricSpace.toHasDist.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1)) x' x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) ε)) (And (LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ε (ϕ x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ε' (ϕ x'))) (forall (y : X), (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} X (PseudoMetricSpace.toHasDist.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1)) x' y) ε') -> (LE.le.{0} Real Real.hasLe (ϕ y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (ϕ x')))))))))))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : MetricSpace.{u1} X] [_inst_2 : CompleteSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1))] (x : X) (ε : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (forall {ϕ : X -> Real}, (Continuous.{u1, 0} X Real (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) ϕ) -> (forall (y : X), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (ϕ y)) -> (Exists.{1} Real (fun (ε' : Real) => And (GT.gt.{0} Real Real.instLTReal ε' (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Exists.{succ u1} X (fun (x' : X) => And (LE.le.{0} Real Real.instLEReal ε' ε) (And (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} X (PseudoMetricSpace.toDist.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1)) x' x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) ε)) (And (LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) ε (ϕ x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) ε' (ϕ x'))) (forall (y : X), (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} X (PseudoMetricSpace.toDist.{u1} X (MetricSpace.toPseudoMetricSpace.{u1} X _inst_1)) x' y) ε') -> (LE.le.{0} Real Real.instLEReal (ϕ y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (ϕ x')))))))))))
+Case conversion may be inaccurate. Consider using '#align hofer hoferₓ'. -/
 theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (ε_pos : 0 < ε)
     {ϕ : X → ℝ} (cont : Continuous ϕ) (nonneg : ∀ y, 0 ≤ ϕ y) :
     ∃ ε' > 0,

f2ce6086

bump to nightly-2023-03-01-20

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

20cadee0

Diff

@@ -84,7 +84,7 @@ theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ)
       calc
         d (u 0) (u (n + 1)) ≤ ∑ i in r, d (u i) (u <| i + 1) := dist_le_range_sum_dist u (n + 1)
         _ ≤ ∑ i in r, ε / 2 ^ i :=
-          sum_le_sum fun i i_in => (IH i <| nat.lt_succ_iff.mp <| finset.mem_range.mp i_in).1
+          (sum_le_sum fun i i_in => (IH i <| nat.lt_succ_iff.mp <| finset.mem_range.mp i_in).1)
         _ = ∑ i in r, (1 / 2) ^ i * ε := by
           congr with i
           field_simp

f2ce6086

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

f2ce6086

chore: scope open Classical (#11199)

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

c747be0a

Diff

@@ -21,7 +21,8 @@ example of a proof needing to construct a sequence by induction in the middle of
 -/
 
 
-open Classical Topology BigOperators
+open scoped Classical
+open Topology BigOperators
 
 open Filter Finset

f2ce6086

chore: remove stream-of-conciousness syntax for obtain (#11045)

This covers many instances, but is not exhaustive.

Independently of whether that syntax should be avoided (similar to #10534), I think all these changes are small improvements.

cd23c669

Diff

@@ -86,8 +86,7 @@ theorem hofer {X : Type*} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (
     refine' cauchySeq_of_le_geometric _ ε one_half_lt_one fun n => _
     simpa only [one_div, inv_pow] using key₁ n
   -- So u converges to some y
-  obtain ⟨y, limy⟩ : ∃ y, Tendsto u atTop (𝓝 y)
-  exact CompleteSpace.complete cauchy_u
+  obtain ⟨y, limy⟩ : ∃ y, Tendsto u atTop (𝓝 y) := CompleteSpace.complete cauchy_u
   -- And ϕ ∘ u goes to +∞
   have lim_top : Tendsto (ϕ ∘ u) atTop atTop := by
     let v n := (ϕ ∘ u) (n + 1)

f2ce6086

chore: prepare Lean version bump with explicit simp (#10999)

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

38bce757

Diff

@@ -62,7 +62,7 @@ theorem hofer {X : Type*} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (
   have key : ∀ n, d (u n) (u (n + 1)) ≤ ε / 2 ^ n ∧ 2 * ϕ (u n) < ϕ (u (n + 1)) := by
     intro n
     induction' n using Nat.case_strong_induction_on with n IH
-    · simpa [ε_pos.le] using hu 0
+    · simpa [u, ε_pos.le] using hu 0
     have A : d (u (n + 1)) x ≤ 2 * ε := by
       rw [dist_comm]
       let r := range (n + 1) -- range (n+1) = {0, ..., n}

f2ce6086

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

a13e8040

Diff

@@ -38,9 +38,9 @@ theorem hofer {X : Type*} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (
     rw [div_mul_eq_mul_div, le_div_iff, mul_assoc, mul_le_mul_left ε_pos, mul_comm]
     positivity
   -- Now let's specialize to `ε/2^k`
-  replace H :
-    ∀ k : ℕ, ∀ x', d x' x ≤ 2 * ε ∧ 2 ^ k * ϕ x ≤ ϕ x' → ∃ y, d x' y ≤ ε / 2 ^ k ∧ 2 * ϕ x' < ϕ y
-  · intro k x'
+  replace H : ∀ k : ℕ, ∀ x', d x' x ≤ 2 * ε ∧ 2 ^ k * ϕ x ≤ ϕ x' →
+      ∃ y, d x' y ≤ ε / 2 ^ k ∧ 2 * ϕ x' < ϕ y := by
+    intro k x'
     push_neg at H
     have := H (ε / 2 ^ k) (by positivity) x' (by simp [ε_pos.le, one_le_two])
     simpa [reformulation] using this

f2ce6086

chore: Relocate big operator lemmas (#9383)

A bunch of lemmas in Algebra.BigOperators.Ring were not about rings. This PR moves them along with some lemmas from Data.Fintype.BigOperators to their correct place.

I create a new file with the content from #6605 to avoid importing Fin material in finset files as a result.

From LeanAPAP

b8dc3667

Diff

@@ -27,11 +27,7 @@ open Filter Finset
 
 local notation "d" => dist
 
-@[simp]
-theorem pos_div_pow_pos {α : Type*} [LinearOrderedSemifield α] {a b : α} (ha : 0 < a) (hb : 0 < b)
-    (k : ℕ) : 0 < a / b ^ k :=
-  div_pos ha (pow_pos hb k)
-#align pos_div_pow_pos pos_div_pow_pos
+#noalign pos_div_pow_pos
 
 theorem hofer {X : Type*} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (ε_pos : 0 < ε)
     {ϕ : X → ℝ} (cont : Continuous ϕ) (nonneg : ∀ y, 0 ≤ ϕ y) : ∃ ε' > 0, ∃ x' : X,
@@ -46,7 +42,7 @@ theorem hofer {X : Type*} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (
     ∀ k : ℕ, ∀ x', d x' x ≤ 2 * ε ∧ 2 ^ k * ϕ x ≤ ϕ x' → ∃ y, d x' y ≤ ε / 2 ^ k ∧ 2 * ϕ x' < ϕ y
   · intro k x'
     push_neg at H
-    have := H (ε / 2 ^ k) (by simp [ε_pos]) x' (by simp [ε_pos.le, one_le_two])
+    have := H (ε / 2 ^ k) (by positivity) x' (by simp [ε_pos.le, one_le_two])
     simpa [reformulation] using this
   clear reformulation
   haveI : Nonempty X := ⟨x⟩
@@ -74,10 +70,10 @@ theorem hofer {X : Type*} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (
         d (u 0) (u (n + 1)) ≤ ∑ i in r, d (u i) (u <| i + 1) := dist_le_range_sum_dist u (n + 1)
         _ ≤ ∑ i in r, ε / 2 ^ i :=
           (sum_le_sum fun i i_in => (IH i <| Nat.lt_succ_iff.mp <| Finset.mem_range.mp i_in).1)
-        _ = ∑ i in r, (1 / 2) ^ i * ε := by
+        _ = (∑ i in r, (1 / 2 : ℝ) ^ i) * ε := by
+          rw [Finset.sum_mul]
           congr with i
           field_simp
-        _ = (∑ i in r, ((1 : ℝ) / 2) ^ i) * ε := Finset.sum_mul.symm
         _ ≤ 2 * ε := by gcongr; apply sum_geometric_two_le
     have B : 2 ^ (n + 1) * ϕ x ≤ ϕ (u (n + 1)) := by
       refine' @geom_le (ϕ ∘ u) _ zero_le_two (n + 1) fun m hm => _

f2ce6086

chore(*): golf, mostly using gcongr/positivity (#9546)

b2daba4a

Diff

@@ -66,8 +66,7 @@ theorem hofer {X : Type*} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (
   have key : ∀ n, d (u n) (u (n + 1)) ≤ ε / 2 ^ n ∧ 2 * ϕ (u n) < ϕ (u (n + 1)) := by
     intro n
     induction' n using Nat.case_strong_induction_on with n IH
-    · specialize hu 0
-      simpa [mul_nonneg_iff, zero_le_one, ε_pos.le, le_refl] using hu
+    · simpa [ε_pos.le] using hu 0
     have A : d (u (n + 1)) x ≤ 2 * ε := by
       rw [dist_comm]
       let r := range (n + 1) -- range (n+1) = {0, ..., n}
@@ -98,9 +97,8 @@ theorem hofer {X : Type*} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (
     let v n := (ϕ ∘ u) (n + 1)
     suffices Tendsto v atTop atTop by rwa [tendsto_add_atTop_iff_nat] at this
     have hv₀ : 0 < v 0 := by
-      have : 0 ≤ ϕ (u 0) := nonneg x
       calc
-        0 ≤ 2 * ϕ (u 0) := (mul_nonneg_iff_of_pos_left zero_lt_two).mpr this
+        0 ≤ 2 * ϕ (u 0) := by specialize nonneg x; positivity
         _ < ϕ (u (0 + 1)) := key₂ 0
     apply tendsto_atTop_of_geom_le hv₀ one_lt_two
     exact fun n => (key₂ (n + 1)).le

f2ce6086

feat: 0 ≤ a * b ↔ (0 < a → 0 ≤ b) ∧ (0 < b → 0 ≤ a) (#9219)

I had a slightly logic-heavy argument that was nicely simplified by stating this lemma. Also fix a few lemma names.

From LeanAPAP and LeanCamCombi

23429eb2

Diff

@@ -100,7 +100,7 @@ theorem hofer {X : Type*} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (
     have hv₀ : 0 < v 0 := by
       have : 0 ≤ ϕ (u 0) := nonneg x
       calc
-        0 ≤ 2 * ϕ (u 0) := (zero_le_mul_left zero_lt_two).mpr this
+        0 ≤ 2 * ϕ (u 0) := (mul_nonneg_iff_of_pos_left zero_lt_two).mpr this
         _ < ϕ (u (0 + 1)) := key₂ 0
     apply tendsto_atTop_of_geom_le hv₀ one_lt_two
     exact fun n => (key₂ (n + 1)).le

f2ce6086

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -28,12 +28,12 @@ open Filter Finset
 local notation "d" => dist
 
 @[simp]
-theorem pos_div_pow_pos {α : Type _} [LinearOrderedSemifield α] {a b : α} (ha : 0 < a) (hb : 0 < b)
+theorem pos_div_pow_pos {α : Type*} [LinearOrderedSemifield α] {a b : α} (ha : 0 < a) (hb : 0 < b)
     (k : ℕ) : 0 < a / b ^ k :=
   div_pos ha (pow_pos hb k)
 #align pos_div_pow_pos pos_div_pow_pos
 
-theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (ε_pos : 0 < ε)
+theorem hofer {X : Type*} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ) (ε_pos : 0 < ε)
     {ϕ : X → ℝ} (cont : Continuous ϕ) (nonneg : ∀ y, 0 ≤ ϕ y) : ∃ ε' > 0, ∃ x' : X,
     ε' ≤ ε ∧ d x' x ≤ 2 * ε ∧ ε * ϕ x ≤ ε' * ϕ x' ∧ ∀ y, d x' y ≤ ε' → ϕ y ≤ 2 * ϕ x' := by
   by_contra H

f2ce6086

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

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot
-
-! This file was ported from Lean 3 source module analysis.hofer
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.SpecificLimits.Basic
 
+#align_import analysis.hofer from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Hofer's lemma

f2ce6086

feat: golf using gcongr throughout the library (#4702)

100 sample uses of the new tactic gcongr, added in #3965.

db83690e

Diff

@@ -82,7 +82,7 @@ theorem hofer {X : Type _} [MetricSpace X] [CompleteSpace X] (x : X) (ε : ℝ)
           congr with i
           field_simp
         _ = (∑ i in r, ((1 : ℝ) / 2) ^ i) * ε := Finset.sum_mul.symm
-        _ ≤ 2 * ε := mul_le_mul_of_nonneg_right (sum_geometric_two_le _) (le_of_lt ε_pos)
+        _ ≤ 2 * ε := by gcongr; apply sum_geometric_two_le
     have B : 2 ^ (n + 1) * ϕ x ≤ ϕ (u (n + 1)) := by
       refine' @geom_le (ϕ ∘ u) _ zero_le_two (n + 1) fun m hm => _
       exact (IH _ <| Nat.lt_add_one_iff.1 hm).2.le

f2ce6086

feat: port Analysis.Hofer (#3321)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

a78e52ba

`analysis.hofer` ⟷ `Mathlib.Analysis.Hofer`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 597

analysis.hofer ⟷ Mathlib.Analysis.Hofer

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 597

`analysis.hofer` ⟷ `Mathlib.Analysis.Hofer`