topology.continuous_function.weierstrass

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

17ef379e

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

36938f77

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -74,12 +74,12 @@ theorem polynomialFunctions_closure_eq_top (a b : ℝ) :
     -- Thus we take the statement of the Weierstrass approximation theorem for `[0,1]`,
     have p := polynomialFunctions_closure_eq_top'
     -- and pullback both sides, obtaining an equation between subalgebras of `C([a,b], ℝ)`.
-    apply_fun fun s => s.comap W at p 
-    simp only [Algebra.comap_top] at p 
+    apply_fun fun s => s.comap W at p
+    simp only [Algebra.comap_top] at p
     -- Since the pullback operation is continuous, it commutes with taking `topological_closure`,
-    rw [Subalgebra.topologicalClosure_comap_homeomorph _ W W' w] at p 
+    rw [Subalgebra.topologicalClosure_comap_homeomorph _ W W' w] at p
     -- and precomposing with an affine map takes polynomial functions to polynomial functions.
-    rw [polynomialFunctions.comap_compRightAlgHom_iccHomeoI] at p 
+    rw [polynomialFunctions.comap_compRightAlgHom_iccHomeoI] at p
     -- 🎉
     exact p
   · -- Otherwise, `b ≤ a`, and the interval is a subsingleton,
@@ -117,9 +117,9 @@ theorem exists_polynomial_near_continuousMap (a b : ℝ) (f : C(Set.Icc a b, ℝ
     (pos : 0 < ε) : ∃ p : ℝ[X], ‖p.toContinuousMapOn _ - f‖ < ε :=
   by
   have w := mem_closure_iff_frequently.mp (continuousMap_mem_polynomialFunctions_closure _ _ f)
-  rw [metric.nhds_basis_ball.frequently_iff] at w 
+  rw [metric.nhds_basis_ball.frequently_iff] at w
   obtain ⟨-, H, ⟨m, ⟨-, rfl⟩⟩⟩ := w ε Pos
-  rw [Metric.mem_ball, dist_eq_norm] at H 
+  rw [Metric.mem_ball, dist_eq_norm] at H
   exact ⟨m, H⟩
 #align exists_polynomial_near_continuous_map exists_polynomial_near_continuousMap
 -/
@@ -138,7 +138,7 @@ theorem exists_polynomial_near_of_continuousOn (a b : ℝ) (f : ℝ → ℝ)
   let f' : C(Set.Icc a b, ℝ) := ⟨fun x => f x, continuous_on_iff_continuous_restrict.mp c⟩
   obtain ⟨p, b⟩ := exists_polynomial_near_continuousMap a b f' ε Pos
   use p
-  rw [norm_lt_iff _ Pos] at b 
+  rw [norm_lt_iff _ Pos] at b
   intro x m
   exact b ⟨x, m⟩
 #align exists_polynomial_near_of_continuous_on exists_polynomial_near_of_continuousOn

36938f77

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.Analysis.SpecialFunctions.Bernstein
-import Mathbin.Topology.Algebra.Algebra
+import Analysis.SpecialFunctions.Bernstein
+import Topology.Algebra.Algebra
 
 #align_import topology.continuous_function.weierstrass from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"

36938f77

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module topology.continuous_function.weierstrass
-! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.SpecialFunctions.Bernstein
 import Mathbin.Topology.Algebra.Algebra
 
+#align_import topology.continuous_function.weierstrass from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
+
 /-!
 # The Weierstrass approximation theorem for continuous functions on `[a,b]`

36938f77

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -32,6 +32,7 @@ open ContinuousMap Filter
 
 open scoped unitInterval
 
+#print polynomialFunctions_closure_eq_top' /-
 /-- The special case of the Weierstrass approximation theorem for the interval `[0,1]`.
 This is just a matter of unravelling definitions and using the Bernstein approximations.
 -/
@@ -50,7 +51,9 @@ theorem polynomialFunctions_closure_eq_top' : (polynomialFunctions I).topologica
   dsimp [bernstein, polynomialFunctions]
   simp
 #align polynomial_functions_closure_eq_top' polynomialFunctions_closure_eq_top'
+-/
 
+#print polynomialFunctions_closure_eq_top /-
 /-- The **Weierstrass Approximation Theorem**:
 polynomials functions on `[a, b] ⊆ ℝ` are dense in `C([a,b],ℝ)`
 
@@ -90,7 +93,9 @@ theorem polynomialFunctions_closure_eq_top (a b : ℝ) :
           ((y.2.2.trans (not_lt.mp h)).trans x.2.1)⟩
     apply Subsingleton.elim
 #align polynomial_functions_closure_eq_top polynomialFunctions_closure_eq_top
+-/
 
+#print continuousMap_mem_polynomialFunctions_closure /-
 /-- An alternative statement of Weierstrass' theorem.
 
 Every real-valued continuous function on `[a,b]` is a uniform limit of polynomials.
@@ -101,9 +106,11 @@ theorem continuousMap_mem_polynomialFunctions_closure (a b : ℝ) (f : C(Set.Icc
   rw [polynomialFunctions_closure_eq_top _ _]
   simp
 #align continuous_map_mem_polynomial_functions_closure continuousMap_mem_polynomialFunctions_closure
+-/
 
 open scoped Polynomial
 
+#print exists_polynomial_near_continuousMap /-
 /-- An alternative statement of Weierstrass' theorem,
 for those who like their epsilons.
 
@@ -118,7 +125,9 @@ theorem exists_polynomial_near_continuousMap (a b : ℝ) (f : C(Set.Icc a b, ℝ
   rw [Metric.mem_ball, dist_eq_norm] at H 
   exact ⟨m, H⟩
 #align exists_polynomial_near_continuous_map exists_polynomial_near_continuousMap
+-/
 
+#print exists_polynomial_near_of_continuousOn /-
 /-- Another alternative statement of Weierstrass's theorem,
 for those who like epsilons, but not bundled continuous functions.
 
@@ -136,4 +145,5 @@ theorem exists_polynomial_near_of_continuousOn (a b : ℝ) (f : ℝ → ℝ)
   intro x m
   exact b ⟨x, m⟩
 #align exists_polynomial_near_of_continuous_on exists_polynomial_near_of_continuousOn
+-/

36938f77

bump to nightly-2023-06-07-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

831e78ce

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module topology.continuous_function.weierstrass
-! leanprover-community/mathlib commit 17ef379e997badd73e5eabb4d38f11919ab3c4b3
+! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Topology.Algebra.Algebra
 /-!
 # The Weierstrass approximation theorem for continuous functions on `[a,b]`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We've already proved the Weierstrass approximation theorem
 in the sense that we've shown that the Bernstein approximations
 to a continuous function on `[0,1]` converge uniformly.

17ef379e

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -71,7 +71,7 @@ theorem polynomialFunctions_closure_eq_top (a b : ℝ) :
     -- Thus we take the statement of the Weierstrass approximation theorem for `[0,1]`,
     have p := polynomialFunctions_closure_eq_top'
     -- and pullback both sides, obtaining an equation between subalgebras of `C([a,b], ℝ)`.
-    apply_fun fun s => s.comap W  at p 
+    apply_fun fun s => s.comap W at p 
     simp only [Algebra.comap_top] at p 
     -- Since the pullback operation is continuous, it commutes with taking `topological_closure`,
     rw [Subalgebra.topologicalClosure_comap_homeomorph _ W W' w] at p

17ef379e

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -71,12 +71,12 @@ theorem polynomialFunctions_closure_eq_top (a b : ℝ) :
     -- Thus we take the statement of the Weierstrass approximation theorem for `[0,1]`,
     have p := polynomialFunctions_closure_eq_top'
     -- and pullback both sides, obtaining an equation between subalgebras of `C([a,b], ℝ)`.
-    apply_fun fun s => s.comap W  at p
-    simp only [Algebra.comap_top] at p
+    apply_fun fun s => s.comap W  at p 
+    simp only [Algebra.comap_top] at p 
     -- Since the pullback operation is continuous, it commutes with taking `topological_closure`,
-    rw [Subalgebra.topologicalClosure_comap_homeomorph _ W W' w] at p
+    rw [Subalgebra.topologicalClosure_comap_homeomorph _ W W' w] at p 
     -- and precomposing with an affine map takes polynomial functions to polynomial functions.
-    rw [polynomialFunctions.comap_compRightAlgHom_iccHomeoI] at p
+    rw [polynomialFunctions.comap_compRightAlgHom_iccHomeoI] at p 
     -- 🎉
     exact p
   · -- Otherwise, `b ≤ a`, and the interval is a subsingleton,
@@ -110,9 +110,9 @@ theorem exists_polynomial_near_continuousMap (a b : ℝ) (f : C(Set.Icc a b, ℝ
     (pos : 0 < ε) : ∃ p : ℝ[X], ‖p.toContinuousMapOn _ - f‖ < ε :=
   by
   have w := mem_closure_iff_frequently.mp (continuousMap_mem_polynomialFunctions_closure _ _ f)
-  rw [metric.nhds_basis_ball.frequently_iff] at w
+  rw [metric.nhds_basis_ball.frequently_iff] at w 
   obtain ⟨-, H, ⟨m, ⟨-, rfl⟩⟩⟩ := w ε Pos
-  rw [Metric.mem_ball, dist_eq_norm] at H
+  rw [Metric.mem_ball, dist_eq_norm] at H 
   exact ⟨m, H⟩
 #align exists_polynomial_near_continuous_map exists_polynomial_near_continuousMap
 
@@ -129,7 +129,7 @@ theorem exists_polynomial_near_of_continuousOn (a b : ℝ) (f : ℝ → ℝ)
   let f' : C(Set.Icc a b, ℝ) := ⟨fun x => f x, continuous_on_iff_continuous_restrict.mp c⟩
   obtain ⟨p, b⟩ := exists_polynomial_near_continuousMap a b f' ε Pos
   use p
-  rw [norm_lt_iff _ Pos] at b
+  rw [norm_lt_iff _ Pos] at b 
   intro x m
   exact b ⟨x, m⟩
 #align exists_polynomial_near_of_continuous_on exists_polynomial_near_of_continuousOn

17ef379e

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -27,7 +27,7 @@ and then, by precomposing with suitable affine functions,
 
 open ContinuousMap Filter
 
-open unitInterval
+open scoped unitInterval
 
 /-- The special case of the Weierstrass approximation theorem for the interval `[0,1]`.
 This is just a matter of unravelling definitions and using the Bernstein approximations.
@@ -99,7 +99,7 @@ theorem continuousMap_mem_polynomialFunctions_closure (a b : ℝ) (f : C(Set.Icc
   simp
 #align continuous_map_mem_polynomial_functions_closure continuousMap_mem_polynomialFunctions_closure
 
-open Polynomial
+open scoped Polynomial
 
 /-- An alternative statement of Weierstrass' theorem,
 for those who like their epsilons.

17ef379e

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

17ef379e

golf: replace some apply foo.mpr by rw [foo] (#11515)

Sometimes, that line can be golfed into the next line. Inspired by a comment of @loefflerd; any decisions are my own.

fa3a2fdc

Diff

@@ -30,7 +30,7 @@ open scoped unitInterval
 This is just a matter of unravelling definitions and using the Bernstein approximations.
 -/
 theorem polynomialFunctions_closure_eq_top' : (polynomialFunctions I).topologicalClosure = ⊤ := by
-  apply eq_top_iff.mpr
+  rw [eq_top_iff]
   rintro f -
   refine' Filter.Frequently.mem_closure _
   refine' Filter.Tendsto.frequently (bernsteinApproximation_uniform f) _

17ef379e

chore(*): replace $ with <| (#9319)

See Zulip thread for the discussion.

9f6d3388

Diff

@@ -75,7 +75,7 @@ theorem polynomialFunctions_closure_eq_top (a b : ℝ) :
     -- 🎉
     exact p
   · -- Otherwise, `b ≤ a`, and the interval is a subsingleton,
-    have : Subsingleton (Set.Icc a b) := (Set.subsingleton_coe _).mpr $ Set.subsingleton_Icc_of_ge h
+    have : Subsingleton (Set.Icc a b) := (Set.subsingleton_Icc_of_ge h).coe_sort
     apply Subsingleton.elim
 #align polynomial_functions_closure_eq_top polynomialFunctions_closure_eq_top

17ef379e

feat: basic set lemmas (#6010)

3b24f007

Diff

@@ -53,7 +53,7 @@ so we may as well get this done first.)
 -/
 theorem polynomialFunctions_closure_eq_top (a b : ℝ) :
     (polynomialFunctions (Set.Icc a b)).topologicalClosure = ⊤ := by
-  by_cases h : a < b
+  cases' lt_or_le a b with h h
   -- (Otherwise it's easy; we'll deal with that later.)
   · -- We can pullback continuous functions on `[a,b]` to continuous functions on `[0,1]`,
     -- by precomposing with an affine map.
@@ -75,11 +75,7 @@ theorem polynomialFunctions_closure_eq_top (a b : ℝ) :
     -- 🎉
     exact p
   · -- Otherwise, `b ≤ a`, and the interval is a subsingleton,
-    -- so all subalgebras are the same anyway.
-    haveI : Subsingleton (Set.Icc a b) :=
-      ⟨fun x y =>
-        le_antisymm ((x.2.2.trans (not_lt.mp h)).trans y.2.1)
-          ((y.2.2.trans (not_lt.mp h)).trans x.2.1)⟩
+    have : Subsingleton (Set.Icc a b) := (Set.subsingleton_coe _).mpr $ Set.subsingleton_Icc_of_ge h
     apply Subsingleton.elim
 #align polynomial_functions_closure_eq_top polynomialFunctions_closure_eq_top

17ef379e

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module topology.continuous_function.weierstrass
-! leanprover-community/mathlib commit 17ef379e997badd73e5eabb4d38f11919ab3c4b3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.SpecialFunctions.Bernstein
 import Mathlib.Topology.Algebra.Algebra
 
+#align_import topology.continuous_function.weierstrass from "leanprover-community/mathlib"@"17ef379e997badd73e5eabb4d38f11919ab3c4b3"
+
 /-!
 # The Weierstrass approximation theorem for continuous functions on `[a,b]`

17ef379e

feat: port Topology.ContinuousFunction.Weierstrass (#4698)

cab32c98

`topology.continuous_function.weierstrass` ⟷ `Mathlib.Topology.ContinuousFunction.Weierstrass`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 734

topology.continuous_function.weierstrass ⟷ Mathlib.Topology.ContinuousFunction.Weierstrass

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 734

`topology.continuous_function.weierstrass` ⟷ `Mathlib.Topology.ContinuousFunction.Weierstrass`