analysis.analytic.radius_liminf
⟷
Mathlib.Analysis.Analytic.RadiusLiminf
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.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -47,7 +47,7 @@ theorem radius_eq_liminf : p.radius = liminf (fun n => 1 / (‖p n‖₊ ^ (1 /
rw [one_div, ENNReal.le_inv_iff_mul_le, ← ENNReal.coe_mul, ENNReal.coe_le_one_iff, one_div, ←
NNReal.rpow_one r, ← mul_inv_cancel this.ne', NNReal.rpow_mul, ← NNReal.mul_rpow, ←
NNReal.one_rpow n⁻¹, NNReal.rpow_le_rpow_iff (inv_pos.2 this), mul_comm,
- NNReal.rpow_nat_cast]
+ NNReal.rpow_natCast]
apply le_antisymm <;> refine' ENNReal.le_of_forall_nnreal_lt fun r hr => _
· rcases((TFAE_exists_lt_isLittleO_pow (fun n => ‖p n‖ * r ^ n) 1).out 1 7).1
(p.is_o_of_lt_radius hr) with ⟨a, ha, H⟩
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Analysis.Analytic.Basic
-import Analysis.SpecialFunctions.Pow.Nnreal
+import Analysis.SpecialFunctions.Pow.NNReal
#align_import analysis.analytic.radius_liminf from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Mathbin.Analysis.Analytic.Basic
-import Mathbin.Analysis.SpecialFunctions.Pow.Nnreal
+import Analysis.Analytic.Basic
+import Analysis.SpecialFunctions.Pow.Nnreal
#align_import analysis.analytic.radius_liminf from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.analytic.radius_liminf
-! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Analysis.Analytic.Basic
import Mathbin.Analysis.SpecialFunctions.Pow.Nnreal
+#align_import analysis.analytic.radius_liminf from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
+
/-!
# Representation of `formal_multilinear_series.radius` as a `liminf`
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -34,6 +34,7 @@ namespace FormalMultilinearSeries
variable (p : FormalMultilinearSeries 𝕜 E F)
+#print FormalMultilinearSeries.radius_eq_liminf /-
/-- The radius of a formal multilinear series is equal to
$\liminf_{n\to\infty} \frac{1}{\sqrt[n]{‖p n‖}}$. The actual statement uses `ℝ≥0` and some
coercions. -/
@@ -62,6 +63,7 @@ theorem radius_eq_liminf : p.radius = liminf (fun n => 1 / (‖p n‖₊ ^ (1 /
refine' (eventually_lt_of_lt_liminf hr).mp ((eventually_gt_at_top 0).mono fun n hn₀ hn => _)
simpa using NNReal.coe_le_coe.2 ((this _ hn₀).1 hn.le)
#align formal_multilinear_series.radius_eq_liminf FormalMultilinearSeries.radius_eq_liminf
+-/
end FormalMultilinearSeries
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
! This file was ported from Lean 3 source module analysis.analytic.radius_liminf
-! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
+! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.SpecialFunctions.Pow.Nnreal
/-!
# Representation of `formal_multilinear_series.radius` as a `liminf`
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
In this file we prove that the radius of convergence of a `formal_multilinear_series` is equal to
$\liminf_{n\to\infty} \frac{1}{\sqrt[n]{‖p n‖}}$. This lemma can't go to `basic.lean` because this
would create a circular dependency once we redefine `exp` using `formal_multilinear_series`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -23,7 +23,7 @@ would create a circular dependency once we redefine `exp` using `formal_multilin
variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _} [NormedAddCommGroup E]
[NormedSpace 𝕜 E] {F : Type _} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
-open Topology Classical BigOperators NNReal ENNReal
+open scoped Topology Classical BigOperators NNReal ENNReal
open Filter Asymptotics
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
! This file was ported from Lean 3 source module analysis.analytic.radius_liminf
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! 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.Analytic.Basic
-import Mathbin.Analysis.SpecialFunctions.Pow
+import Mathbin.Analysis.SpecialFunctions.Pow.Nnreal
/-!
# Representation of `formal_multilinear_series.radius` as a `liminf`
mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1
@@ -48,7 +48,7 @@ theorem radius_eq_liminf : p.radius = liminf (fun n => 1 / (‖p n‖₊ ^ (1 /
NNReal.one_rpow n⁻¹, NNReal.rpow_le_rpow_iff (inv_pos.2 this), mul_comm,
NNReal.rpow_nat_cast]
apply le_antisymm <;> refine' ENNReal.le_of_forall_nnreal_lt fun r hr => _
- · rcases((tFAE_exists_lt_isLittleO_pow (fun n => ‖p n‖ * r ^ n) 1).out 1 7).1
+ · rcases((TFAE_exists_lt_isLittleO_pow (fun n => ‖p n‖ * r ^ n) 1).out 1 7).1
(p.is_o_of_lt_radius hr) with ⟨a, ha, H⟩
refine' le_Liminf_of_le (by infer_param) (eventually_map.2 <| _)
refine'
mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65
@@ -48,7 +48,7 @@ theorem radius_eq_liminf : p.radius = liminf (fun n => 1 / (‖p n‖₊ ^ (1 /
NNReal.one_rpow n⁻¹, NNReal.rpow_le_rpow_iff (inv_pos.2 this), mul_comm,
NNReal.rpow_nat_cast]
apply le_antisymm <;> refine' ENNReal.le_of_forall_nnreal_lt fun r hr => _
- · rcases((tFAE_exists_lt_isOCat_pow (fun n => ‖p n‖ * r ^ n) 1).out 1 7).1
+ · rcases((tFAE_exists_lt_isLittleO_pow (fun n => ‖p n‖ * r ^ n) 1).out 1 7).1
(p.is_o_of_lt_radius hr) with ⟨a, ha, H⟩
refine' le_Liminf_of_le (by infer_param) (eventually_map.2 <| _)
refine'
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -23,7 +23,7 @@ would create a circular dependency once we redefine `exp` using `formal_multilin
variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _} [NormedAddCommGroup E]
[NormedSpace 𝕜 E] {F : Type _} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
-open Topology Classical BigOperators NNReal Ennreal
+open Topology Classical BigOperators NNReal ENNReal
open Filter Asymptotics
@@ -43,11 +43,11 @@ theorem radius_eq_liminf : p.radius = liminf (fun n => 1 / (‖p n‖₊ ^ (1 /
intro r n hn
have : 0 < (n : ℝ) := Nat.cast_pos.2 hn
conv_lhs =>
- rw [one_div, Ennreal.le_inv_iff_mul_le, ← Ennreal.coe_mul, Ennreal.coe_le_one_iff, one_div, ←
+ rw [one_div, ENNReal.le_inv_iff_mul_le, ← ENNReal.coe_mul, ENNReal.coe_le_one_iff, one_div, ←
NNReal.rpow_one r, ← mul_inv_cancel this.ne', NNReal.rpow_mul, ← NNReal.mul_rpow, ←
NNReal.one_rpow n⁻¹, NNReal.rpow_le_rpow_iff (inv_pos.2 this), mul_comm,
NNReal.rpow_nat_cast]
- apply le_antisymm <;> refine' Ennreal.le_of_forall_nNReal_lt fun r hr => _
+ apply le_antisymm <;> refine' ENNReal.le_of_forall_nnreal_lt fun r hr => _
· rcases((tFAE_exists_lt_isOCat_pow (fun n => ‖p n‖ * r ^ n) 1).out 1 7).1
(p.is_o_of_lt_radius hr) with ⟨a, ha, H⟩
refine' le_Liminf_of_le (by infer_param) (eventually_map.2 <| _)
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
nat_cast
/int_cast
/rat_cast
to natCast
/intCast
/ratCast
(#11486)
Now that I am defining NNRat.cast
, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast
/intCast
/ratCast
over nat_cast
/int_cast
/rat_cast
, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.
@@ -44,7 +44,7 @@ theorem radius_eq_liminf :
rw [one_div, ENNReal.le_inv_iff_mul_le, ← ENNReal.coe_mul, ENNReal.coe_le_one_iff, one_div, ←
NNReal.rpow_one r, ← mul_inv_cancel this.ne', NNReal.rpow_mul, ← NNReal.mul_rpow, ←
NNReal.one_rpow n⁻¹, NNReal.rpow_le_rpow_iff (inv_pos.2 this), mul_comm,
- NNReal.rpow_nat_cast]
+ NNReal.rpow_natCast]
apply le_antisymm <;> refine' ENNReal.le_of_forall_nnreal_lt fun r hr => _
· have := ((TFAE_exists_lt_isLittleO_pow (fun n => ‖p n‖ * r ^ n) 1).out 1 7).1
(p.isLittleO_of_lt_radius hr)
Homogenises porting notes via capitalisation and addition of whitespace.
It makes the following changes:
@@ -34,7 +34,7 @@ $\liminf_{n\to\infty} \frac{1}{\sqrt[n]{‖p n‖}}$. The actual statement uses
coercions. -/
theorem radius_eq_liminf :
p.radius = liminf (fun n => (1 / (‖p n‖₊ ^ (1 / (n : ℝ)) : ℝ≥0) : ℝ≥0∞)) atTop := by
- -- porting note: added type ascription to make elaborated statement match Lean 3 version
+ -- Porting note: added type ascription to make elaborated statement match Lean 3 version
have :
∀ (r : ℝ≥0) {n : ℕ},
0 < n → ((r : ℝ≥0∞) ≤ 1 / ↑(‖p n‖₊ ^ (1 / (n : ℝ))) ↔ ‖p n‖₊ * r ^ n ≤ 1) := by
@@ -51,7 +51,7 @@ theorem radius_eq_liminf :
obtain ⟨a, ha, H⟩ := this
apply le_liminf_of_le
· infer_param
- · rw [←eventually_map]
+ · rw [← eventually_map]
refine'
H.mp ((eventually_gt_atTop 0).mono fun n hn₀ hn => (this _ hn₀).2 (NNReal.coe_le_coe.1 _))
push_cast
This is the supremum of
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.
In particular this includes adjustments for the Lean PRs
We can get rid of all the
local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)
macros across Mathlib (and in any projects that want to write natural number powers of reals).
Changes the default behaviour of simp
to (config := {decide := false})
. This makes simp
(and consequentially norm_num
) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp
or norm_num
to decide
or rfl
, or adding (config := {decide := true})
.
This changed the behaviour of simp
so that simp [f]
will only unfold "fully applied" occurrences of f
. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true })
. We may in future add a syntax for this, e.g. simp [!f]
; please provide feedback! In the meantime, we have made the following changes:
(config := { unfoldPartialApp := true })
in some places, to recover the old behaviour@[eqns]
to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp
and Function.flip
.This change in Lean may require further changes down the line (e.g. adding the !f
syntax, and/or upstreaming the special treatment for Function.comp
and Function.flip
, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!
Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>
@@ -27,8 +27,6 @@ open Filter Asymptotics
namespace FormalMultilinearSeries
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
variable (p : FormalMultilinearSeries 𝕜 E F)
/-- The radius of a formal multilinear series is equal to
@@ -35,7 +35,7 @@ variable (p : FormalMultilinearSeries 𝕜 E F)
$\liminf_{n\to\infty} \frac{1}{\sqrt[n]{‖p n‖}}$. The actual statement uses `ℝ≥0` and some
coercions. -/
theorem radius_eq_liminf :
- p.radius = liminf (fun n => (1 / (‖p n‖₊ ^ (1 / (n : ℝ)) : ℝ≥0) : ℝ≥0∞)) atTop := by
+ p.radius = liminf (fun n => (1 / (‖p n‖₊ ^ (1 / (n : ℝ)) : ℝ≥0) : ℝ≥0∞)) atTop := by
-- porting note: added type ascription to make elaborated statement match Lean 3 version
have :
∀ (r : ℝ≥0) {n : ℕ},
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -18,8 +18,8 @@ because this would create a circular dependency once we redefine `exp` using
-/
-variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _} [NormedAddCommGroup E]
- [NormedSpace 𝕜 E] {F : Type _} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
+variable {𝕜 : Type*} [NontriviallyNormedField 𝕜] {E : Type*} [NormedAddCommGroup E]
+ [NormedSpace 𝕜 E] {F : Type*} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
open scoped Topology Classical BigOperators NNReal ENNReal
@@ -27,8 +27,7 @@ open Filter Asymptotics
namespace FormalMultilinearSeries
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y)
--- porting note: see lean4#2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
variable (p : FormalMultilinearSeries 𝕜 E F)
@@ -2,15 +2,12 @@
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.analytic.radius_liminf
-! 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.Analytic.Basic
import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
+#align_import analysis.analytic.radius_liminf from "leanprover-community/mathlib"@"0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8"
+
/-!
# Representation of `FormalMultilinearSeries.radius` as a `liminf`
The unported dependencies are
algebra.order.module
init.core
linear_algebra.free_module.finite.rank
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
linear_algebra.free_module.rank
algebra.order.monoid.cancel.basic
init.data.list.default
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file