seminorm_lattice_not_distrib
⟷
Counterexamples.SeminormLatticeNotDistrib
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/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin
-/
-import Mathbin.Analysis.Seminorm
+import Analysis.Seminorm
#align_import seminorm_lattice_not_distrib from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin
-
-! This file was ported from Lean 3 source module seminorm_lattice_not_distrib
-! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Analysis.Seminorm
+#align_import seminorm_lattice_not_distrib from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
/-!
# The lattice of seminorms is not distributive
mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin
! This file was ported from Lean 3 source module seminorm_lattice_not_distrib
-! leanprover-community/mathlib commit 328375597f2c0dd00522d9c2e5a33b6a6128feeb
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.Seminorm
/-!
# The lattice of seminorms is not distributive
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
We provide an example of three seminorms over the ℝ-vector space ℝ×ℝ which don't satisfy the lattice
distributivity property `(p ⊔ q1) ⊓ (p ⊔ q2) ≤ p ⊔ (q1 ⊓ q2)`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0
@@ -72,7 +72,6 @@ theorem not_distrib : ¬(p ⊔ q1) ⊓ (p ⊔ q2) ≤ p ⊔ q1 ⊓ q2 :=
_ = q2 ((1, 1) - x) := rfl
_ ≤ (p ⊔ q2) ((1, 1) - x) := le_sup_right
_ ≤ (p ⊔ q1) x + (p ⊔ q2) ((1, 1) - x) := le_add_of_nonneg_left (map_nonneg _ _)
-
·
calc
4 / 3 = 2 / 3 + (1 - 1 / 3) := by norm_num
@@ -80,7 +79,6 @@ theorem not_distrib : ¬(p ⊔ q1) ⊓ (p ⊔ q2) ≤ p ⊔ q1 ⊓ q2 :=
_ ≤ |x.snd| + |1 - x.fst| := (add_le_add (le_abs_self _) (le_abs_self _))
_ ≤ p x + p ((1, 1) - x) := (add_le_add le_sup_right le_sup_left)
_ ≤ (p ⊔ q1) x + (p ⊔ q2) ((1, 1) - x) := add_le_add le_sup_left le_sup_left
-
·
calc
4 / 3 = 4 * (1 / 3) := by norm_num
@@ -89,7 +87,6 @@ theorem not_distrib : ¬(p ⊔ q1) ⊓ (p ⊔ q2) ≤ p ⊔ q1 ⊓ q2 :=
_ = q1 x := rfl
_ ≤ (p ⊔ q1) x := le_sup_right
_ ≤ (p ⊔ q1) x + (p ⊔ q2) ((1, 1) - x) := le_add_of_nonneg_right (map_nonneg _ _)
-
#align counterexample.seminorm_not_distrib.not_distrib Counterexample.SeminormNotDistrib.not_distrib
end SeminormNotDistrib
mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090
@@ -65,7 +65,7 @@ theorem not_distrib : ¬(p ⊔ q1) ⊓ (p ⊔ q2) ≤ p ⊔ q1 ⊓ q2 := by
_ ≤ 4 * |1 - x.snd| := by gcongr; apply le_abs_self
_ = q2 ((1, 1) - x) := by simp; rfl
_ ≤ (p ⊔ q2) ((1, 1) - x) := le_sup_right
- _ ≤ (p ⊔ q1) x + (p ⊔ q2) ((1, 1) - x) := le_add_of_nonneg_left (map_nonneg _ _)
+ _ ≤ (p ⊔ q1) x + (p ⊔ q2) ((1, 1) - x) := le_add_of_nonneg_left (apply_nonneg _ _)
· calc
4 / 3 = 2 / 3 + (1 - 1 / 3) := by norm_num
_ ≤ x.snd + (1 - x.fst) := by gcongr
@@ -78,7 +78,7 @@ theorem not_distrib : ¬(p ⊔ q1) ⊓ (p ⊔ q2) ≤ p ⊔ q1 ⊓ q2 := by
_ ≤ 4 * |x.fst| := by gcongr; apply le_abs_self
_ = q1 x := rfl
_ ≤ (p ⊔ q1) x := le_sup_right
- _ ≤ (p ⊔ q1) x + (p ⊔ q2) ((1, 1) - x) := le_add_of_nonneg_right (map_nonneg _ _)
+ _ ≤ (p ⊔ q1) x + (p ⊔ q2) ((1, 1) - x) := le_add_of_nonneg_right (apply_nonneg _ _)
#align counterexample.seminorm_not_distrib.not_distrib Counterexample.SeminormNotDistrib.not_distrib
end SeminormNotDistrib
@@ -61,21 +61,21 @@ theorem not_distrib : ¬(p ⊔ q1) ⊓ (p ⊔ q2) ≤ p ⊔ q1 ⊓ q2 := by
· rcases le_or_lt x.snd (2 / 3) with h2 | h2
· calc
4 / 3 = 4 * (1 - 2 / 3) := by norm_num
- _ ≤ 4 * (1 - x.snd) := (mul_le_mul_left zero_lt_four).mpr (sub_le_sub_left h2 _)
- _ ≤ 4 * |1 - x.snd| := (mul_le_mul_left zero_lt_four).mpr (le_abs_self _)
+ _ ≤ 4 * (1 - x.snd) := by gcongr
+ _ ≤ 4 * |1 - x.snd| := by gcongr; apply le_abs_self
_ = q2 ((1, 1) - x) := by simp; rfl
_ ≤ (p ⊔ q2) ((1, 1) - x) := le_sup_right
_ ≤ (p ⊔ q1) x + (p ⊔ q2) ((1, 1) - x) := le_add_of_nonneg_left (map_nonneg _ _)
· calc
4 / 3 = 2 / 3 + (1 - 1 / 3) := by norm_num
- _ ≤ x.snd + (1 - x.fst) := add_le_add (le_of_lt h2) (sub_le_sub_left h1 _)
+ _ ≤ x.snd + (1 - x.fst) := by gcongr
_ ≤ |x.snd| + |1 - x.fst| := add_le_add (le_abs_self _) (le_abs_self _)
_ ≤ p x + p ((1, 1) - x) := by exact add_le_add le_sup_right le_sup_left
_ ≤ (p ⊔ q1) x + (p ⊔ q2) ((1, 1) - x) := add_le_add le_sup_left le_sup_left
· calc
4 / 3 = 4 * (1 / 3) := by norm_num
- _ ≤ 4 * x.fst := (mul_le_mul_left zero_lt_four).mpr (le_of_lt h1)
- _ ≤ 4 * |x.fst| := (mul_le_mul_left zero_lt_four).mpr (le_abs_self _)
+ _ ≤ 4 * x.fst := by gcongr
+ _ ≤ 4 * |x.fst| := by gcongr; apply le_abs_self
_ = q1 x := rfl
_ ≤ (p ⊔ q1) x := le_sup_right
_ ≤ (p ⊔ q1) x + (p ⊔ q2) ((1, 1) - x) := le_add_of_nonneg_right (map_nonneg _ _)
cases'
(#9171)
I literally went through and regex'd some uses of cases'
, replacing them with rcases
; this is meant to be a low effort PR as I hope that tools can do this in the future.
rcases
is an easier replacement than cases
, though with better tools we could in future do a second pass converting simple rcases
added here (and existing ones) to cases
.
@@ -57,8 +57,8 @@ theorem not_distrib : ¬(p ⊔ q1) ⊓ (p ⊔ q2) ≤ p ⊔ q1 ⊓ q2 := by
apply c; nth_rw 1 [← eq_one]
apply le_trans _ (le_sup_inf _)
apply le_ciInf; intro x
- cases' le_or_lt x.fst (1 / 3) with h1 h1
- · cases' le_or_lt x.snd (2 / 3) with h2 h2
+ rcases le_or_lt x.fst (1 / 3) with h1 | h1
+ · rcases le_or_lt x.snd (2 / 3) with h2 | h2
· calc
4 / 3 = 4 * (1 - 2 / 3) := by norm_num
_ ≤ 4 * (1 - x.snd) := (mul_le_mul_left zero_lt_four).mpr (sub_le_sub_left h2 _)
@@ -2,14 +2,11 @@
Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin
-
-! This file was ported from Lean 3 source module seminorm_lattice_not_distrib
-! leanprover-community/mathlib commit 328375597f2c0dd00522d9c2e5a33b6a6128feeb
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Analysis.Seminorm
+#align_import seminorm_lattice_not_distrib from "leanprover-community/mathlib"@"328375597f2c0dd00522d9c2e5a33b6a6128feeb"
+
/-!
# The lattice of seminorms is not distributive
@@ -48,7 +48,7 @@ noncomputable def q2 : Seminorm ℝ (ℝ × ℝ) :=
#align counterexample.seminorm_not_distrib.q2 Counterexample.SeminormNotDistrib.q2
theorem eq_one : (p ⊔ q1 ⊓ q2) (1, 1) = 1 := by
- suffices (⨅ x : ℝ × ℝ, q1 x + q2 (1 - x)) ≤ 1 by simpa
+ suffices ⨅ x : ℝ × ℝ, q1 x + q2 (1 - x) ≤ 1 by simpa
apply ciInf_le_of_le bddBelow_range_add ((0, 1) : ℝ × ℝ); dsimp [q1, q2]
simp only [abs_zero, smul_zero, sub_self, add_zero, zero_le_one]
#align counterexample.seminorm_not_distrib.eq_one Counterexample.SeminormNotDistrib.eq_one
The unported dependencies are
algebra.order.module
init.core
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
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