data.set.intervals.proj_Icc | Mathlib porting status

(last sync)

feat(data/set/intervals/proj_Icc): Extending from Ici a (#18795)

Define the Ici and Iic versions of set.proj_Icc/set.Icc_extend. Slightly reorder the lemmas to allow better overall structure.

This is useful for extending convex functions by a junk value.

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
 -/
 import data.set.function
-import data.set.intervals.basic
+import data.set.intervals.ord_connected
 
 /-!
 # Projection of a line onto a closed interval
@@ -14,8 +14,16 @@ import data.set.intervals.basic
 
 Given a linearly ordered type `α`, in this file we define
 
+* `set.proj_Ici (a : α)` to be the map `α → [a, ∞[` sending `]-∞, a]` to `a`,
+  and each point `x ∈ [a, ∞[` to itself;
+* `set.proj_Iic (b : α)` to be the map `α → ]-∞, b[` sending `[b, ∞[` to `b`,
+  and each point `x ∈ ]-∞, b]` to itself;
 * `set.proj_Icc (a b : α) (h : a ≤ b)` to be the map `α → [a, b]` sending `(-∞, a]` to `a`, `[b, ∞)`
   to `b`, and each point `x ∈ [a, b]` to itself;
+* `set.Ici_extend {a : α} (f : Ici a → β)` to be the extension of `f` to `α` defined
+  as `f ∘ proj_Ici a`.
+* `set.Iic_extend {b : α} (f : Iic b → β)` to be the extension of `f` to `α` defined
+  as `f ∘ proj_Iic b`.
 * `set.Icc_extend {a b : α} (h : a ≤ b) (f : Icc a b → β)` to be the extension of `f` to `α` defined
   as `f ∘ proj_Icc a b h`.
 
@@ -28,88 +36,156 @@ open function
 
 namespace set
 
+/-- Projection of `α` to the closed interval `[a, ∞[`. -/
+def proj_Ici (a x : α) : Ici a := ⟨max a x, le_max_left _ _⟩
+
+/-- Projection of `α` to the closed interval `]-∞, b]`. -/
+def proj_Iic (b x : α) : Iic b := ⟨min b x, min_le_left _ _⟩
+
 /-- Projection of `α` to the closed interval `[a, b]`. -/
 def proj_Icc (a b : α) (h : a ≤ b) (x : α) : Icc a b :=
 ⟨max a (min b x), le_max_left _ _, max_le h (min_le_left _ _)⟩
 
 variables {a b : α} (h : a ≤ b) {x : α}
 
+@[norm_cast] lemma coe_proj_Ici (a x : α) : (proj_Ici a x : α) = max a x := rfl
+@[norm_cast] lemma coe_proj_Iic (b x : α) : (proj_Iic b x : α) = min b x := rfl
+@[norm_cast] lemma coe_proj_Icc (a b : α) (h : a ≤ b) (x : α) :
+  (proj_Icc a b h x : α) = max a (min b x) := rfl
+
+lemma proj_Ici_of_le (hx : x ≤ a) : proj_Ici a x = ⟨a, le_rfl⟩ := subtype.ext $ max_eq_left hx
+lemma proj_Iic_of_le (hx : b ≤ x) : proj_Iic b x = ⟨b, le_rfl⟩ := subtype.ext $ min_eq_left hx
+
 lemma proj_Icc_of_le_left (hx : x ≤ a) : proj_Icc a b h x = ⟨a, left_mem_Icc.2 h⟩ :=
 by simp [proj_Icc, hx, hx.trans h]
 
-@[simp] lemma proj_Icc_left : proj_Icc a b h a = ⟨a, left_mem_Icc.2 h⟩ :=
-proj_Icc_of_le_left h le_rfl
-
 lemma proj_Icc_of_right_le (hx : b ≤ x) : proj_Icc a b h x = ⟨b, right_mem_Icc.2 h⟩ :=
 by simp [proj_Icc, hx, h]
 
+@[simp] lemma proj_Ici_self (a : α) : proj_Ici a a = ⟨a, le_rfl⟩ := proj_Ici_of_le le_rfl
+@[simp] lemma proj_Iic_self (b : α) : proj_Iic b b = ⟨b, le_rfl⟩ := proj_Iic_of_le le_rfl
+
+@[simp] lemma proj_Icc_left : proj_Icc a b h a = ⟨a, left_mem_Icc.2 h⟩ :=
+proj_Icc_of_le_left h le_rfl
+
 @[simp] lemma proj_Icc_right : proj_Icc a b h b = ⟨b, right_mem_Icc.2 h⟩ :=
 proj_Icc_of_right_le h le_rfl
 
+lemma proj_Ici_eq_self : proj_Ici a x = ⟨a, le_rfl⟩ ↔ x ≤ a := by simp [proj_Ici, subtype.ext_iff]
+lemma proj_Iic_eq_self : proj_Iic b x = ⟨b, le_rfl⟩ ↔ b ≤ x := by simp [proj_Iic, subtype.ext_iff]
+
 lemma proj_Icc_eq_left (h : a < b) : proj_Icc a b h.le x = ⟨a, left_mem_Icc.mpr h.le⟩ ↔ x ≤ a :=
-begin
-  refine ⟨λ h', _, proj_Icc_of_le_left _⟩,
-  simp_rw [subtype.ext_iff_val, proj_Icc, max_eq_left_iff, min_le_iff, h.not_le, false_or] at h',
-  exact h'
-end
+by simp [proj_Icc, subtype.ext_iff, h.not_le]
 
 lemma proj_Icc_eq_right (h : a < b) : proj_Icc a b h.le x = ⟨b, right_mem_Icc.mpr h.le⟩ ↔ b ≤ x :=
-begin
-  refine ⟨λ h', _, proj_Icc_of_right_le _⟩,
-  simp_rw [subtype.ext_iff_val, proj_Icc] at h',
-  have := ((max_choice _ _).resolve_left (by simp [h.ne', h'])).symm.trans h',
-  exact min_eq_left_iff.mp this
-end
+by simp [proj_Icc, subtype.ext_iff, max_min_distrib_left, h.le, h.not_le]
 
+lemma proj_Ici_of_mem (hx : x ∈ Ici a) : proj_Ici a x = ⟨x, hx⟩ := by simpa [proj_Ici]
+lemma proj_Iic_of_mem (hx : x ∈ Iic b) : proj_Iic b x = ⟨x, hx⟩ := by simpa [proj_Iic]
 lemma proj_Icc_of_mem (hx : x ∈ Icc a b) : proj_Icc a b h x = ⟨x, hx⟩ :=
 by simp [proj_Icc, hx.1, hx.2]
 
+@[simp] lemma proj_Ici_coe (x : Ici a) : proj_Ici a x = x := by { cases x, apply proj_Ici_of_mem }
+@[simp] lemma proj_Iic_coe (x : Iic b) : proj_Iic b x = x := by { cases x, apply proj_Iic_of_mem }
 @[simp] lemma proj_Icc_coe (x : Icc a b) : proj_Icc a b h x = x :=
 by { cases x, apply proj_Icc_of_mem }
 
+lemma proj_Ici_surj_on : surj_on (proj_Ici a) (Ici a) univ := λ x _, ⟨x, x.2, proj_Ici_coe x⟩
+lemma proj_Iic_surj_on : surj_on (proj_Iic b) (Iic b) univ := λ x _, ⟨x, x.2, proj_Iic_coe x⟩
 lemma proj_Icc_surj_on : surj_on (proj_Icc a b h) (Icc a b) univ :=
 λ x _, ⟨x, x.2, proj_Icc_coe h x⟩
 
-lemma proj_Icc_surjective : surjective (proj_Icc a b h) :=
-λ x, ⟨x, proj_Icc_coe h x⟩
+lemma proj_Ici_surjective : surjective (proj_Ici a) := λ x, ⟨x, proj_Ici_coe x⟩
+lemma proj_Iic_surjective : surjective (proj_Iic b) := λ x, ⟨x, proj_Iic_coe x⟩
+lemma proj_Icc_surjective : surjective (proj_Icc a b h) := λ x, ⟨x, proj_Icc_coe h x⟩
 
-@[simp] lemma range_proj_Icc : range (proj_Icc a b h) = univ :=
-(proj_Icc_surjective h).range_eq
+@[simp] lemma range_proj_Ici : range (proj_Ici a) = univ := proj_Ici_surjective.range_eq
+@[simp] lemma range_proj_Iic : range (proj_Iic a) = univ := proj_Iic_surjective.range_eq
+@[simp] lemma range_proj_Icc : range (proj_Icc a b h) = univ := (proj_Icc_surjective h).range_eq
 
+lemma monotone_proj_Ici : monotone (proj_Ici a) := λ x y, max_le_max le_rfl
+lemma monotone_proj_Iic : monotone (proj_Iic a) := λ x y, min_le_min le_rfl
 lemma monotone_proj_Icc : monotone (proj_Icc a b h) :=
 λ x y hxy, max_le_max le_rfl $ min_le_min le_rfl hxy
 
+lemma strict_mono_on_proj_Ici : strict_mono_on (proj_Ici a) (Ici a) :=
+λ x hx y hy hxy, by simpa only [proj_Ici_of_mem, hx, hy]
+lemma strict_mono_on_proj_Iic : strict_mono_on (proj_Iic b) (Iic b) :=
+λ x hx y hy hxy, by simpa only [proj_Iic_of_mem, hx, hy]
 lemma strict_mono_on_proj_Icc : strict_mono_on (proj_Icc a b h) (Icc a b) :=
 λ x hx y hy hxy, by simpa only [proj_Icc_of_mem, hx, hy]
 
+/-- Extend a function `[a, ∞[ → β` to a map `α → β`. -/
+def Ici_extend (f : Ici a → β) : α → β := f ∘ proj_Ici a
+
+/-- Extend a function `]-∞, b] → β` to a map `α → β`. -/
+def Iic_extend (f : Iic b → β) : α → β := f ∘ proj_Iic b
+
 /-- Extend a function `[a, b] → β` to a map `α → β`. -/
 def Icc_extend {a b : α} (h : a ≤ b) (f : Icc a b → β) : α → β :=
 f ∘ proj_Icc a b h
 
+@[simp] lemma Ici_extend_apply (f : Ici a → β) (x : α) :
+  Ici_extend f x = f ⟨max a x, le_max_left _ _⟩ := rfl
+@[simp] lemma Iic_extend_apply (f : Iic b → β) (x : α) :
+  Iic_extend f x = f ⟨min b x, min_le_left _ _⟩ := rfl
+lemma Icc_extend_apply (h : a ≤ b) (f : Icc a b → β) (x : α) :
+  Icc_extend h f x = f ⟨max a (min b x), le_max_left _ _, max_le h (min_le_left _ _)⟩ := rfl
+
+@[simp] lemma range_Ici_extend (f : Ici a → β) : range (Ici_extend f) = range f :=
+by simp only [Ici_extend, range_comp f, range_proj_Ici, range_id']
+
+@[simp] lemma range_Iic_extend (f : Iic b → β) : range (Iic_extend f) = range f :=
+by simp only [Iic_extend, range_comp f, range_proj_Iic, range_id']
+
 @[simp] lemma Icc_extend_range (f : Icc a b → β) :
   range (Icc_extend h f) = range f :=
 by simp only [Icc_extend, range_comp f, range_proj_Icc, range_id']
 
+lemma Ici_extend_of_le (f : Ici a → β) (hx : x ≤ a) : Ici_extend f x = f ⟨a, le_rfl⟩ :=
+congr_arg f $ proj_Ici_of_le hx
+
+lemma Iic_extend_of_le (f : Iic b → β) (hx : b ≤ x) : Iic_extend f x = f ⟨b, le_rfl⟩ :=
+congr_arg f $ proj_Iic_of_le hx
+
 lemma Icc_extend_of_le_left (f : Icc a b → β) (hx : x ≤ a) :
   Icc_extend h f x = f ⟨a, left_mem_Icc.2 h⟩ :=
 congr_arg f $ proj_Icc_of_le_left h hx
 
-@[simp] lemma Icc_extend_left (f : Icc a b → β) :
-  Icc_extend h f a = f ⟨a, left_mem_Icc.2 h⟩ :=
-Icc_extend_of_le_left h f le_rfl
-
 lemma Icc_extend_of_right_le (f : Icc a b → β) (hx : b ≤ x) :
   Icc_extend h f x = f ⟨b, right_mem_Icc.2 h⟩ :=
 congr_arg f $ proj_Icc_of_right_le h hx
 
+@[simp] lemma Ici_extend_self (f : Ici a → β) : Ici_extend f a = f ⟨a, le_rfl⟩ :=
+Ici_extend_of_le f le_rfl
+
+@[simp] lemma Iic_extend_self (f : Iic b → β) : Iic_extend f b = f ⟨b, le_rfl⟩ :=
+Iic_extend_of_le f le_rfl
+
+@[simp] lemma Icc_extend_left (f : Icc a b → β) :
+  Icc_extend h f a = f ⟨a, left_mem_Icc.2 h⟩ :=
+Icc_extend_of_le_left h f le_rfl
+
 @[simp] lemma Icc_extend_right (f : Icc a b → β) :
   Icc_extend h f b = f ⟨b, right_mem_Icc.2 h⟩ :=
 Icc_extend_of_right_le h f le_rfl
 
+lemma Ici_extend_of_mem (f : Ici a → β) (hx : x ∈ Ici a) : Ici_extend f x = f ⟨x, hx⟩ :=
+congr_arg f $ proj_Ici_of_mem hx
+
+lemma Iic_extend_of_mem (f : Iic b → β) (hx : x ∈ Iic b) : Iic_extend f x = f ⟨x, hx⟩ :=
+congr_arg f $ proj_Iic_of_mem hx
+
 lemma Icc_extend_of_mem (f : Icc a b → β) (hx : x ∈ Icc a b) :
   Icc_extend h f x = f ⟨x, hx⟩ :=
 congr_arg f $ proj_Icc_of_mem h hx
 
+@[simp] lemma Ici_extend_coe (f : Ici a → β) (x : Ici a) : Ici_extend f x = f x :=
+congr_arg f $ proj_Ici_coe x
+
+@[simp] lemma Iic_extend_coe (f : Iic b → β) (x : Iic b) : Iic_extend f x = f x :=
+congr_arg f $ proj_Iic_coe x
+
 @[simp] lemma Icc_extend_coe (f : Icc a b → β) (x : Icc a b) :
   Icc_extend h f x = f x :=
 congr_arg f $ proj_Icc_coe h x
@@ -132,11 +208,37 @@ end set
 
 open set
 
-variables [preorder β] {a b : α} (h : a ≤ b) {f : Icc a b → β}
+variables [preorder β] {s t : set α} {a b : α} (h : a ≤ b) {f : Icc a b → β}
+
+protected lemma monotone.Ici_extend {f : Ici a → β} (hf : monotone f) : monotone (Ici_extend f) :=
+hf.comp monotone_proj_Ici
+
+protected lemma monotone.Iic_extend {f : Iic b → β} (hf : monotone f) : monotone (Iic_extend f) :=
+hf.comp monotone_proj_Iic
 
-lemma monotone.Icc_extend (hf : monotone f) : monotone (Icc_extend h f) :=
+protected lemma monotone.Icc_extend (hf : monotone f) : monotone (Icc_extend h f) :=
 hf.comp $ monotone_proj_Icc h
 
+lemma strict_mono.strict_mono_on_Ici_extend {f : Ici a → β} (hf : strict_mono f) :
+  strict_mono_on (Ici_extend f) (Ici a) :=
+hf.comp_strict_mono_on strict_mono_on_proj_Ici
+
+lemma strict_mono.strict_mono_on_Iic_extend {f : Iic b → β} (hf : strict_mono f) :
+  strict_mono_on (Iic_extend f) (Iic b) :=
+hf.comp_strict_mono_on strict_mono_on_proj_Iic
+
 lemma strict_mono.strict_mono_on_Icc_extend (hf : strict_mono f) :
   strict_mono_on (Icc_extend h f) (Icc a b) :=
 hf.comp_strict_mono_on (strict_mono_on_proj_Icc h)
+
+protected lemma set.ord_connected.Ici_extend {s : set (Ici a)} (hs : s.ord_connected) :
+  {x | Ici_extend (∈ s) x}.ord_connected :=
+⟨λ x hx y hy z hz, hs.out hx hy ⟨max_le_max le_rfl hz.1, max_le_max le_rfl hz.2⟩⟩
+
+protected lemma set.ord_connected.Iic_extend {s : set (Iic b)} (hs : s.ord_connected) :
+  {x | Iic_extend (∈ s) x}.ord_connected :=
+⟨λ x hx y hy z hz, hs.out hx hy ⟨min_le_min le_rfl hz.1, min_le_min le_rfl hz.2⟩⟩
+
+protected lemma set.ord_connected.restrict (hs : s.ord_connected) :
+  {x | restrict t (∈ s) x}.ord_connected :=
+⟨λ x hx y hy z hz, hs.out hx hy hz⟩

feat(analysis/calculus/bump_function_inner): add real.smooth_transition.proj_Icc (#19097)

Also add real.smooth_transition.continuous_at.

From the sphere eversion project

Diff

@@ -114,6 +114,20 @@ congr_arg f $ proj_Icc_of_mem h hx
   Icc_extend h f x = f x :=
 congr_arg f $ proj_Icc_coe h x
 
+/-- If `f : α → β` is a constant both on $(-∞, a]$ and on $[b, +∞)$, then the extension of this
+function from $[a, b]$ to the whole line is equal to the original function. -/
+lemma Icc_extend_eq_self (f : α → β) (ha : ∀ x < a, f x = f a) (hb : ∀ x, b < x → f x = f b) :
+  Icc_extend h (f ∘ coe) = f :=
+begin
+  ext x,
+  cases lt_or_le x a with hxa hax,
+  { simp [Icc_extend_of_le_left _ _ hxa.le, ha x hxa] },
+  { cases le_or_lt x b with hxb hbx,
+    { lift x to Icc a b using ⟨hax, hxb⟩,
+      rw [Icc_extend_coe] },
+    { simp [Icc_extend_of_right_le _ _ hbx.le, hb x hbx] } }
+end
+
 end set
 
 open set

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-26-08

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

ab3b6a0f

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
 -/
 import Data.Set.Function
-import Data.Set.Intervals.OrdConnected
+import Order.Interval.Set.OrdConnected
 
 #align_import data.set.intervals.proj_Icc from "leanprover-community/mathlib"@"4e24c4bfcff371c71f7ba22050308aa17815626c"

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) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
 -/
-import Mathbin.Data.Set.Function
-import Mathbin.Data.Set.Intervals.OrdConnected
+import Data.Set.Function
+import Data.Set.Intervals.OrdConnected
 
 #align_import data.set.intervals.proj_Icc from "leanprover-community/mathlib"@"4e24c4bfcff371c71f7ba22050308aa17815626c"

bump to nightly-2023-09-08-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

2aec253b

Diff

@@ -312,11 +312,11 @@ theorem IicExtend_apply (f : Iic b → β) (x : α) : IicExtend f x = f ⟨min b
 #align set.Iic_extend_apply Set.IicExtend_apply
 -/
 
-#print Set.iccExtend_apply /-
-theorem iccExtend_apply (h : a ≤ b) (f : Icc a b → β) (x : α) :
+#print Set.IccExtend_apply /-
+theorem IccExtend_apply (h : a ≤ b) (f : Icc a b → β) (x : α) :
     IccExtend h f x = f ⟨max a (min b x), le_max_left _ _, max_le h (min_le_left _ _)⟩ :=
   rfl
-#align set.Icc_extend_apply Set.iccExtend_apply
+#align set.Icc_extend_apply Set.IccExtend_apply
 -/
 
 #print Set.range_IciExtend /-

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) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
-
-! This file was ported from Lean 3 source module data.set.intervals.proj_Icc
-! leanprover-community/mathlib commit 4e24c4bfcff371c71f7ba22050308aa17815626c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Set.Function
 import Mathbin.Data.Set.Intervals.OrdConnected
 
+#align_import data.set.intervals.proj_Icc from "leanprover-community/mathlib"@"4e24c4bfcff371c71f7ba22050308aa17815626c"
+
 /-!
 # Projection of a line onto a closed interval

bump to nightly-2023-07-16-17

mathlib commit https://github.com/leanprover-community/mathlib/commit/2fe465deb81bcd7ccafa065bb686888a82f15372

6db63fa6

Diff

@@ -42,15 +42,19 @@ open Function
 
 namespace Set
 
+#print Set.projIci /-
 /-- Projection of `α` to the closed interval `[a, ∞[`. -/
 def projIci (a x : α) : Ici a :=
   ⟨max a x, le_max_left _ _⟩
 #align set.proj_Ici Set.projIci
+-/
 
+#print Set.projIic /-
 /-- Projection of `α` to the closed interval `]-∞, b]`. -/
 def projIic (b x : α) : Iic b :=
   ⟨min b x, min_le_left _ _⟩
 #align set.proj_Iic Set.projIic
+-/
 
 #print Set.projIcc /-
 /-- Projection of `α` to the closed interval `[a, b]`. -/
@@ -61,28 +65,38 @@ def projIcc (a b : α) (h : a ≤ b) (x : α) : Icc a b :=
 
 variable {a b : α} (h : a ≤ b) {x : α}
 
+#print Set.coe_projIci /-
 @[norm_cast]
 theorem coe_projIci (a x : α) : (projIci a x : α) = max a x :=
   rfl
 #align set.coe_proj_Ici Set.coe_projIci
+-/
 
+#print Set.coe_projIic /-
 @[norm_cast]
 theorem coe_projIic (b x : α) : (projIic b x : α) = min b x :=
   rfl
 #align set.coe_proj_Iic Set.coe_projIic
+-/
 
+#print Set.coe_projIcc /-
 @[norm_cast]
 theorem coe_projIcc (a b : α) (h : a ≤ b) (x : α) : (projIcc a b h x : α) = max a (min b x) :=
   rfl
 #align set.coe_proj_Icc Set.coe_projIcc
+-/
 
+#print Set.projIci_of_le /-
 theorem projIci_of_le (hx : x ≤ a) : projIci a x = ⟨a, le_rfl⟩ :=
   Subtype.ext <| max_eq_left hx
 #align set.proj_Ici_of_le Set.projIci_of_le
+-/
 
+#print Set.projIic_of_le /-
 theorem projIic_of_le (hx : b ≤ x) : projIic b x = ⟨b, le_rfl⟩ :=
   Subtype.ext <| min_eq_left hx
 #align set.proj_Iic_of_le Set.projIic_of_le
+-/
 
 #print Set.projIcc_of_le_left /-
 theorem projIcc_of_le_left (hx : x ≤ a) : projIcc a b h x = ⟨a, left_mem_Icc.2 h⟩ := by
@@ -96,15 +110,19 @@ theorem projIcc_of_right_le (hx : b ≤ x) : projIcc a b h x = ⟨b, right_mem_I
 #align set.proj_Icc_of_right_le Set.projIcc_of_right_le
 -/
 
+#print Set.projIci_self /-
 @[simp]
 theorem projIci_self (a : α) : projIci a a = ⟨a, le_rfl⟩ :=
   projIci_of_le le_rfl
 #align set.proj_Ici_self Set.projIci_self
+-/
 
+#print Set.projIic_self /-
 @[simp]
 theorem projIic_self (b : α) : projIic b b = ⟨b, le_rfl⟩ :=
   projIic_of_le le_rfl
 #align set.proj_Iic_self Set.projIic_self
+-/
 
 #print Set.projIcc_left /-
 @[simp]
@@ -120,11 +138,15 @@ theorem projIcc_right : projIcc a b h b = ⟨b, right_mem_Icc.2 h⟩ :=
 #align set.proj_Icc_right Set.projIcc_right
 -/
 
+#print Set.projIci_eq_self /-
 theorem projIci_eq_self : projIci a x = ⟨a, le_rfl⟩ ↔ x ≤ a := by simp [proj_Ici, Subtype.ext_iff]
 #align set.proj_Ici_eq_self Set.projIci_eq_self
+-/
 
+#print Set.projIic_eq_self /-
 theorem projIic_eq_self : projIic b x = ⟨b, le_rfl⟩ ↔ b ≤ x := by simp [proj_Iic, Subtype.ext_iff]
 #align set.proj_Iic_eq_self Set.projIic_eq_self
+-/
 
 #print Set.projIcc_eq_left /-
 theorem projIcc_eq_left (h : a < b) : projIcc a b h.le x = ⟨a, left_mem_Icc.mpr h.le⟩ ↔ x ≤ a := by
@@ -138,11 +160,15 @@ theorem projIcc_eq_right (h : a < b) : projIcc a b h.le x = ⟨b, right_mem_Icc.
 #align set.proj_Icc_eq_right Set.projIcc_eq_right
 -/
 
+#print Set.projIci_of_mem /-
 theorem projIci_of_mem (hx : x ∈ Ici a) : projIci a x = ⟨x, hx⟩ := by simpa [proj_Ici]
 #align set.proj_Ici_of_mem Set.projIci_of_mem
+-/
 
+#print Set.projIic_of_mem /-
 theorem projIic_of_mem (hx : x ∈ Iic b) : projIic b x = ⟨x, hx⟩ := by simpa [proj_Iic]
 #align set.proj_Iic_of_mem Set.projIic_of_mem
+-/
 
 #print Set.projIcc_of_mem /-
 theorem projIcc_of_mem (hx : x ∈ Icc a b) : projIcc a b h x = ⟨x, hx⟩ := by
@@ -150,13 +176,17 @@ theorem projIcc_of_mem (hx : x ∈ Icc a b) : projIcc a b h x = ⟨x, hx⟩ := b
 #align set.proj_Icc_of_mem Set.projIcc_of_mem
 -/
 
+#print Set.projIci_coe /-
 @[simp]
 theorem projIci_coe (x : Ici a) : projIci a x = x := by cases x; apply proj_Ici_of_mem
 #align set.proj_Ici_coe Set.projIci_coe
+-/
 
+#print Set.projIic_coe /-
 @[simp]
 theorem projIic_coe (x : Iic b) : projIic b x = x := by cases x; apply proj_Iic_of_mem
 #align set.proj_Iic_coe Set.projIic_coe
+-/
 
 #print Set.projIcc_val /-
 @[simp]
@@ -164,11 +194,15 @@ theorem projIcc_val (x : Icc a b) : projIcc a b h x = x := by cases x; apply pro
 #align set.proj_Icc_coe Set.projIcc_val
 -/
 
+#print Set.projIci_surjOn /-
 theorem projIci_surjOn : SurjOn (projIci a) (Ici a) univ := fun x _ => ⟨x, x.2, projIci_coe x⟩
 #align set.proj_Ici_surj_on Set.projIci_surjOn
+-/
 
+#print Set.projIic_surjOn /-
 theorem projIic_surjOn : SurjOn (projIic b) (Iic b) univ := fun x _ => ⟨x, x.2, projIic_coe x⟩
 #align set.proj_Iic_surj_on Set.projIic_surjOn
+-/
 
 #print Set.projIcc_surjOn /-
 theorem projIcc_surjOn : SurjOn (projIcc a b h) (Icc a b) univ := fun x _ =>
@@ -176,26 +210,34 @@ theorem projIcc_surjOn : SurjOn (projIcc a b h) (Icc a b) univ := fun x _ =>
 #align set.proj_Icc_surj_on Set.projIcc_surjOn
 -/
 
+#print Set.projIci_surjective /-
 theorem projIci_surjective : Surjective (projIci a) := fun x => ⟨x, projIci_coe x⟩
 #align set.proj_Ici_surjective Set.projIci_surjective
+-/
 
+#print Set.projIic_surjective /-
 theorem projIic_surjective : Surjective (projIic b) := fun x => ⟨x, projIic_coe x⟩
 #align set.proj_Iic_surjective Set.projIic_surjective
+-/
 
 #print Set.projIcc_surjective /-
 theorem projIcc_surjective : Surjective (projIcc a b h) := fun x => ⟨x, projIcc_val h x⟩
 #align set.proj_Icc_surjective Set.projIcc_surjective
 -/
 
+#print Set.range_projIci /-
 @[simp]
 theorem range_projIci : range (projIci a) = univ :=
   projIci_surjective.range_eq
 #align set.range_proj_Ici Set.range_projIci
+-/
 
+#print Set.range_projIic /-
 @[simp]
 theorem range_projIic : range (projIic a) = univ :=
   projIic_surjective.range_eq
 #align set.range_proj_Iic Set.range_projIic
+-/
 
 #print Set.range_projIcc /-
 @[simp]
@@ -204,11 +246,15 @@ theorem range_projIcc : range (projIcc a b h) = univ :=
 #align set.range_proj_Icc Set.range_projIcc
 -/
 
+#print Set.monotone_projIci /-
 theorem monotone_projIci : Monotone (projIci a) := fun x y => max_le_max le_rfl
 #align set.monotone_proj_Ici Set.monotone_projIci
+-/
 
+#print Set.monotone_projIic /-
 theorem monotone_projIic : Monotone (projIic a) := fun x y => min_le_min le_rfl
 #align set.monotone_proj_Iic Set.monotone_projIic
+-/
 
 #print Set.monotone_projIcc /-
 theorem monotone_projIcc : Monotone (projIcc a b h) := fun x y hxy =>
@@ -216,13 +262,17 @@ theorem monotone_projIcc : Monotone (projIcc a b h) := fun x y hxy =>
 #align set.monotone_proj_Icc Set.monotone_projIcc
 -/
 
+#print Set.strictMonoOn_projIci /-
 theorem strictMonoOn_projIci : StrictMonoOn (projIci a) (Ici a) := fun x hx y hy hxy => by
   simpa only [proj_Ici_of_mem, hx, hy]
 #align set.strict_mono_on_proj_Ici Set.strictMonoOn_projIci
+-/
 
+#print Set.strictMonoOn_projIic /-
 theorem strictMonoOn_projIic : StrictMonoOn (projIic b) (Iic b) := fun x hx y hy hxy => by
   simpa only [proj_Iic_of_mem, hx, hy]
 #align set.strict_mono_on_proj_Iic Set.strictMonoOn_projIic
+-/
 
 #print Set.strictMonoOn_projIcc /-
 theorem strictMonoOn_projIcc : StrictMonoOn (projIcc a b h) (Icc a b) := fun x hx y hy hxy => by
@@ -230,15 +280,19 @@ theorem strictMonoOn_projIcc : StrictMonoOn (projIcc a b h) (Icc a b) := fun x h
 #align set.strict_mono_on_proj_Icc Set.strictMonoOn_projIcc
 -/
 
+#print Set.IciExtend /-
 /-- Extend a function `[a, ∞[ → β` to a map `α → β`. -/
-def iciExtend (f : Ici a → β) : α → β :=
+def IciExtend (f : Ici a → β) : α → β :=
   f ∘ projIci a
-#align set.Ici_extend Set.iciExtend
+#align set.Ici_extend Set.IciExtend
+-/
 
+#print Set.IicExtend /-
 /-- Extend a function `]-∞, b] → β` to a map `α → β`. -/
-def iicExtend (f : Iic b → β) : α → β :=
+def IicExtend (f : Iic b → β) : α → β :=
   f ∘ projIic b
-#align set.Iic_extend Set.iicExtend
+#align set.Iic_extend Set.IicExtend
+-/
 
 #print Set.IccExtend /-
 /-- Extend a function `[a, b] → β` to a map `α → β`. -/
@@ -247,30 +301,40 @@ def IccExtend {a b : α} (h : a ≤ b) (f : Icc a b → β) : α → β :=
 #align set.Icc_extend Set.IccExtend
 -/
 
+#print Set.IciExtend_apply /-
 @[simp]
-theorem iciExtend_apply (f : Ici a → β) (x : α) : iciExtend f x = f ⟨max a x, le_max_left _ _⟩ :=
+theorem IciExtend_apply (f : Ici a → β) (x : α) : IciExtend f x = f ⟨max a x, le_max_left _ _⟩ :=
   rfl
-#align set.Ici_extend_apply Set.iciExtend_apply
+#align set.Ici_extend_apply Set.IciExtend_apply
+-/
 
+#print Set.IicExtend_apply /-
 @[simp]
-theorem iicExtend_apply (f : Iic b → β) (x : α) : iicExtend f x = f ⟨min b x, min_le_left _ _⟩ :=
+theorem IicExtend_apply (f : Iic b → β) (x : α) : IicExtend f x = f ⟨min b x, min_le_left _ _⟩ :=
   rfl
-#align set.Iic_extend_apply Set.iicExtend_apply
+#align set.Iic_extend_apply Set.IicExtend_apply
+-/
 
+#print Set.iccExtend_apply /-
 theorem iccExtend_apply (h : a ≤ b) (f : Icc a b → β) (x : α) :
     IccExtend h f x = f ⟨max a (min b x), le_max_left _ _, max_le h (min_le_left _ _)⟩ :=
   rfl
 #align set.Icc_extend_apply Set.iccExtend_apply
+-/
 
+#print Set.range_IciExtend /-
 @[simp]
-theorem range_iciExtend (f : Ici a → β) : range (iciExtend f) = range f := by
+theorem range_IciExtend (f : Ici a → β) : range (IciExtend f) = range f := by
   simp only [Ici_extend, range_comp f, range_proj_Ici, range_id']
-#align set.range_Ici_extend Set.range_iciExtend
+#align set.range_Ici_extend Set.range_IciExtend
+-/
 
+#print Set.range_IicExtend /-
 @[simp]
-theorem range_iicExtend (f : Iic b → β) : range (iicExtend f) = range f := by
+theorem range_IicExtend (f : Iic b → β) : range (IicExtend f) = range f := by
   simp only [Iic_extend, range_comp f, range_proj_Iic, range_id']
-#align set.range_Iic_extend Set.range_iicExtend
+#align set.range_Iic_extend Set.range_IicExtend
+-/
 
 #print Set.IccExtend_range /-
 @[simp]
@@ -279,13 +343,17 @@ theorem IccExtend_range (f : Icc a b → β) : range (IccExtend h f) = range f :
 #align set.Icc_extend_range Set.IccExtend_range
 -/
 
-theorem iciExtend_of_le (f : Ici a → β) (hx : x ≤ a) : iciExtend f x = f ⟨a, le_rfl⟩ :=
+#print Set.IciExtend_of_le /-
+theorem IciExtend_of_le (f : Ici a → β) (hx : x ≤ a) : IciExtend f x = f ⟨a, le_rfl⟩ :=
   congr_arg f <| projIci_of_le hx
-#align set.Ici_extend_of_le Set.iciExtend_of_le
+#align set.Ici_extend_of_le Set.IciExtend_of_le
+-/
 
-theorem iicExtend_of_le (f : Iic b → β) (hx : b ≤ x) : iicExtend f x = f ⟨b, le_rfl⟩ :=
+#print Set.IicExtend_of_le /-
+theorem IicExtend_of_le (f : Iic b → β) (hx : b ≤ x) : IicExtend f x = f ⟨b, le_rfl⟩ :=
   congr_arg f <| projIic_of_le hx
-#align set.Iic_extend_of_le Set.iicExtend_of_le
+#align set.Iic_extend_of_le Set.IicExtend_of_le
+-/
 
 #print Set.IccExtend_of_le_left /-
 theorem IccExtend_of_le_left (f : Icc a b → β) (hx : x ≤ a) :
@@ -301,15 +369,19 @@ theorem IccExtend_of_right_le (f : Icc a b → β) (hx : b ≤ x) :
 #align set.Icc_extend_of_right_le Set.IccExtend_of_right_le
 -/
 
+#print Set.IciExtend_self /-
 @[simp]
-theorem iciExtend_self (f : Ici a → β) : iciExtend f a = f ⟨a, le_rfl⟩ :=
-  iciExtend_of_le f le_rfl
-#align set.Ici_extend_self Set.iciExtend_self
+theorem IciExtend_self (f : Ici a → β) : IciExtend f a = f ⟨a, le_rfl⟩ :=
+  IciExtend_of_le f le_rfl
+#align set.Ici_extend_self Set.IciExtend_self
+-/
 
+#print Set.IicExtend_self /-
 @[simp]
-theorem iicExtend_self (f : Iic b → β) : iicExtend f b = f ⟨b, le_rfl⟩ :=
-  iicExtend_of_le f le_rfl
-#align set.Iic_extend_self Set.iicExtend_self
+theorem IicExtend_self (f : Iic b → β) : IicExtend f b = f ⟨b, le_rfl⟩ :=
+  IicExtend_of_le f le_rfl
+#align set.Iic_extend_self Set.IicExtend_self
+-/
 
 #print Set.IccExtend_left /-
 @[simp]
@@ -325,13 +397,17 @@ theorem IccExtend_right (f : Icc a b → β) : IccExtend h f b = f ⟨b, right_m
 #align set.Icc_extend_right Set.IccExtend_right
 -/
 
-theorem iciExtend_of_mem (f : Ici a → β) (hx : x ∈ Ici a) : iciExtend f x = f ⟨x, hx⟩ :=
+#print Set.IciExtend_of_mem /-
+theorem IciExtend_of_mem (f : Ici a → β) (hx : x ∈ Ici a) : IciExtend f x = f ⟨x, hx⟩ :=
   congr_arg f <| projIci_of_mem hx
-#align set.Ici_extend_of_mem Set.iciExtend_of_mem
+#align set.Ici_extend_of_mem Set.IciExtend_of_mem
+-/
 
-theorem iicExtend_of_mem (f : Iic b → β) (hx : x ∈ Iic b) : iicExtend f x = f ⟨x, hx⟩ :=
+#print Set.IicExtend_of_mem /-
+theorem IicExtend_of_mem (f : Iic b → β) (hx : x ∈ Iic b) : IicExtend f x = f ⟨x, hx⟩ :=
   congr_arg f <| projIic_of_mem hx
-#align set.Iic_extend_of_mem Set.iicExtend_of_mem
+#align set.Iic_extend_of_mem Set.IicExtend_of_mem
+-/
 
 #print Set.IccExtend_of_mem /-
 theorem IccExtend_of_mem (f : Icc a b → β) (hx : x ∈ Icc a b) : IccExtend h f x = f ⟨x, hx⟩ :=
@@ -339,15 +415,19 @@ theorem IccExtend_of_mem (f : Icc a b → β) (hx : x ∈ Icc a b) : IccExtend h
 #align set.Icc_extend_of_mem Set.IccExtend_of_mem
 -/
 
+#print Set.IciExtend_coe /-
 @[simp]
-theorem iciExtend_coe (f : Ici a → β) (x : Ici a) : iciExtend f x = f x :=
+theorem IciExtend_coe (f : Ici a → β) (x : Ici a) : IciExtend f x = f x :=
   congr_arg f <| projIci_coe x
-#align set.Ici_extend_coe Set.iciExtend_coe
+#align set.Ici_extend_coe Set.IciExtend_coe
+-/
 
+#print Set.IicExtend_coe /-
 @[simp]
-theorem iicExtend_coe (f : Iic b → β) (x : Iic b) : iicExtend f x = f x :=
+theorem IicExtend_coe (f : Iic b → β) (x : Iic b) : IicExtend f x = f x :=
   congr_arg f <| projIic_coe x
-#align set.Iic_extend_coe Set.iicExtend_coe
+#align set.Iic_extend_coe Set.IicExtend_coe
+-/
 
 #print Set.IccExtend_val /-
 @[simp]
@@ -377,13 +457,17 @@ open Set
 
 variable [Preorder β] {s t : Set α} {a b : α} (h : a ≤ b) {f : Icc a b → β}
 
-protected theorem Monotone.iciExtend {f : Ici a → β} (hf : Monotone f) : Monotone (iciExtend f) :=
+#print Monotone.IciExtend /-
+protected theorem Monotone.IciExtend {f : Ici a → β} (hf : Monotone f) : Monotone (IciExtend f) :=
   hf.comp monotone_projIci
-#align monotone.Ici_extend Monotone.iciExtend
+#align monotone.Ici_extend Monotone.IciExtend
+-/
 
-protected theorem Monotone.iicExtend {f : Iic b → β} (hf : Monotone f) : Monotone (iicExtend f) :=
+#print Monotone.IicExtend /-
+protected theorem Monotone.IicExtend {f : Iic b → β} (hf : Monotone f) : Monotone (IicExtend f) :=
   hf.comp monotone_projIic
-#align monotone.Iic_extend Monotone.iicExtend
+#align monotone.Iic_extend Monotone.IicExtend
+-/
 
 #print Monotone.IccExtend /-
 protected theorem Monotone.IccExtend (hf : Monotone f) : Monotone (IccExtend h f) :=
@@ -391,15 +475,19 @@ protected theorem Monotone.IccExtend (hf : Monotone f) : Monotone (IccExtend h f
 #align monotone.Icc_extend Monotone.IccExtend
 -/
 
-theorem StrictMono.strictMonoOn_iciExtend {f : Ici a → β} (hf : StrictMono f) :
-    StrictMonoOn (iciExtend f) (Ici a) :=
+#print StrictMono.strictMonoOn_IciExtend /-
+theorem StrictMono.strictMonoOn_IciExtend {f : Ici a → β} (hf : StrictMono f) :
+    StrictMonoOn (IciExtend f) (Ici a) :=
   hf.comp_strictMonoOn strictMonoOn_projIci
-#align strict_mono.strict_mono_on_Ici_extend StrictMono.strictMonoOn_iciExtend
+#align strict_mono.strict_mono_on_Ici_extend StrictMono.strictMonoOn_IciExtend
+-/
 
-theorem StrictMono.strictMonoOn_iicExtend {f : Iic b → β} (hf : StrictMono f) :
-    StrictMonoOn (iicExtend f) (Iic b) :=
+#print StrictMono.strictMonoOn_IicExtend /-
+theorem StrictMono.strictMonoOn_IicExtend {f : Iic b → β} (hf : StrictMono f) :
+    StrictMonoOn (IicExtend f) (Iic b) :=
   hf.comp_strictMonoOn strictMonoOn_projIic
-#align strict_mono.strict_mono_on_Iic_extend StrictMono.strictMonoOn_iicExtend
+#align strict_mono.strict_mono_on_Iic_extend StrictMono.strictMonoOn_IicExtend
+-/
 
 #print StrictMono.strictMonoOn_IccExtend /-
 theorem StrictMono.strictMonoOn_IccExtend (hf : StrictMono f) :
@@ -408,18 +496,24 @@ theorem StrictMono.strictMonoOn_IccExtend (hf : StrictMono f) :
 #align strict_mono.strict_mono_on_Icc_extend StrictMono.strictMonoOn_IccExtend
 -/
 
-protected theorem Set.OrdConnected.iciExtend {s : Set (Ici a)} (hs : s.OrdConnected) :
-    {x | iciExtend (· ∈ s) x}.OrdConnected :=
+#print Set.OrdConnected.IciExtend /-
+protected theorem Set.OrdConnected.IciExtend {s : Set (Ici a)} (hs : s.OrdConnected) :
+    {x | IciExtend (· ∈ s) x}.OrdConnected :=
   ⟨fun x hx y hy z hz => hs.out hx hy ⟨max_le_max le_rfl hz.1, max_le_max le_rfl hz.2⟩⟩
-#align set.ord_connected.Ici_extend Set.OrdConnected.iciExtend
+#align set.ord_connected.Ici_extend Set.OrdConnected.IciExtend
+-/
 
-protected theorem Set.OrdConnected.iicExtend {s : Set (Iic b)} (hs : s.OrdConnected) :
-    {x | iicExtend (· ∈ s) x}.OrdConnected :=
+#print Set.OrdConnected.IicExtend /-
+protected theorem Set.OrdConnected.IicExtend {s : Set (Iic b)} (hs : s.OrdConnected) :
+    {x | IicExtend (· ∈ s) x}.OrdConnected :=
   ⟨fun x hx y hy z hz => hs.out hx hy ⟨min_le_min le_rfl hz.1, min_le_min le_rfl hz.2⟩⟩
-#align set.ord_connected.Iic_extend Set.OrdConnected.iicExtend
+#align set.ord_connected.Iic_extend Set.OrdConnected.IicExtend
+-/
 
+#print Set.OrdConnected.restrict /-
 protected theorem Set.OrdConnected.restrict (hs : s.OrdConnected) :
     {x | restrict t (· ∈ s) x}.OrdConnected :=
   ⟨fun x hx y hy z hz => hs.out hx hy hz⟩
 #align set.ord_connected.restrict Set.OrdConnected.restrict
+-/

bump to nightly-2023-07-12-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/4e24c4bfcff371c71f7ba22050308aa17815626c

403fa41d

Diff

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
 
 ! This file was ported from Lean 3 source module data.set.intervals.proj_Icc
-! leanprover-community/mathlib commit 42e9a1fd3a99e10f82830349ba7f4f10e8961c2a
+! leanprover-community/mathlib commit 4e24c4bfcff371c71f7ba22050308aa17815626c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Data.Set.Function
-import Mathbin.Data.Set.Intervals.Basic
+import Mathbin.Data.Set.Intervals.OrdConnected
 
 /-!
 # Projection of a line onto a closed interval
@@ -19,8 +19,16 @@ import Mathbin.Data.Set.Intervals.Basic
 
 Given a linearly ordered type `α`, in this file we define
 
+* `set.proj_Ici (a : α)` to be the map `α → [a, ∞[` sending `]-∞, a]` to `a`,
+  and each point `x ∈ [a, ∞[` to itself;
+* `set.proj_Iic (b : α)` to be the map `α → ]-∞, b[` sending `[b, ∞[` to `b`,
+  and each point `x ∈ ]-∞, b]` to itself;
 * `set.proj_Icc (a b : α) (h : a ≤ b)` to be the map `α → [a, b]` sending `(-∞, a]` to `a`, `[b, ∞)`
   to `b`, and each point `x ∈ [a, b]` to itself;
+* `set.Ici_extend {a : α} (f : Ici a → β)` to be the extension of `f` to `α` defined
+  as `f ∘ proj_Ici a`.
+* `set.Iic_extend {b : α} (f : Iic b → β)` to be the extension of `f` to `α` defined
+  as `f ∘ proj_Iic b`.
 * `set.Icc_extend {a b : α} (h : a ≤ b) (f : Icc a b → β)` to be the extension of `f` to `α` defined
   as `f ∘ proj_Icc a b h`.
 
@@ -34,6 +42,16 @@ open Function
 
 namespace Set
 
+/-- Projection of `α` to the closed interval `[a, ∞[`. -/
+def projIci (a x : α) : Ici a :=
+  ⟨max a x, le_max_left _ _⟩
+#align set.proj_Ici Set.projIci
+
+/-- Projection of `α` to the closed interval `]-∞, b]`. -/
+def projIic (b x : α) : Iic b :=
+  ⟨min b x, min_le_left _ _⟩
+#align set.proj_Iic Set.projIic
+
 #print Set.projIcc /-
 /-- Projection of `α` to the closed interval `[a, b]`. -/
 def projIcc (a b : α) (h : a ≤ b) (x : α) : Icc a b :=
@@ -43,12 +61,51 @@ def projIcc (a b : α) (h : a ≤ b) (x : α) : Icc a b :=
 
 variable {a b : α} (h : a ≤ b) {x : α}
 
+@[norm_cast]
+theorem coe_projIci (a x : α) : (projIci a x : α) = max a x :=
+  rfl
+#align set.coe_proj_Ici Set.coe_projIci
+
+@[norm_cast]
+theorem coe_projIic (b x : α) : (projIic b x : α) = min b x :=
+  rfl
+#align set.coe_proj_Iic Set.coe_projIic
+
+@[norm_cast]
+theorem coe_projIcc (a b : α) (h : a ≤ b) (x : α) : (projIcc a b h x : α) = max a (min b x) :=
+  rfl
+#align set.coe_proj_Icc Set.coe_projIcc
+
+theorem projIci_of_le (hx : x ≤ a) : projIci a x = ⟨a, le_rfl⟩ :=
+  Subtype.ext <| max_eq_left hx
+#align set.proj_Ici_of_le Set.projIci_of_le
+
+theorem projIic_of_le (hx : b ≤ x) : projIic b x = ⟨b, le_rfl⟩ :=
+  Subtype.ext <| min_eq_left hx
+#align set.proj_Iic_of_le Set.projIic_of_le
+
 #print Set.projIcc_of_le_left /-
 theorem projIcc_of_le_left (hx : x ≤ a) : projIcc a b h x = ⟨a, left_mem_Icc.2 h⟩ := by
   simp [proj_Icc, hx, hx.trans h]
 #align set.proj_Icc_of_le_left Set.projIcc_of_le_left
 -/
 
+#print Set.projIcc_of_right_le /-
+theorem projIcc_of_right_le (hx : b ≤ x) : projIcc a b h x = ⟨b, right_mem_Icc.2 h⟩ := by
+  simp [proj_Icc, hx, h]
+#align set.proj_Icc_of_right_le Set.projIcc_of_right_le
+-/
+
+@[simp]
+theorem projIci_self (a : α) : projIci a a = ⟨a, le_rfl⟩ :=
+  projIci_of_le le_rfl
+#align set.proj_Ici_self Set.projIci_self
+
+@[simp]
+theorem projIic_self (b : α) : projIic b b = ⟨b, le_rfl⟩ :=
+  projIic_of_le le_rfl
+#align set.proj_Iic_self Set.projIic_self
+
 #print Set.projIcc_left /-
 @[simp]
 theorem projIcc_left : projIcc a b h a = ⟨a, left_mem_Icc.2 h⟩ :=
@@ -56,12 +113,6 @@ theorem projIcc_left : projIcc a b h a = ⟨a, left_mem_Icc.2 h⟩ :=
 #align set.proj_Icc_left Set.projIcc_left
 -/
 
-#print Set.projIcc_of_right_le /-
-theorem projIcc_of_right_le (hx : b ≤ x) : projIcc a b h x = ⟨b, right_mem_Icc.2 h⟩ := by
-  simp [proj_Icc, hx, h]
-#align set.proj_Icc_of_right_le Set.projIcc_of_right_le
--/
-
 #print Set.projIcc_right /-
 @[simp]
 theorem projIcc_right : projIcc a b h b = ⟨b, right_mem_Icc.2 h⟩ :=
@@ -69,48 +120,83 @@ theorem projIcc_right : projIcc a b h b = ⟨b, right_mem_Icc.2 h⟩ :=
 #align set.proj_Icc_right Set.projIcc_right
 -/
 
+theorem projIci_eq_self : projIci a x = ⟨a, le_rfl⟩ ↔ x ≤ a := by simp [proj_Ici, Subtype.ext_iff]
+#align set.proj_Ici_eq_self Set.projIci_eq_self
+
+theorem projIic_eq_self : projIic b x = ⟨b, le_rfl⟩ ↔ b ≤ x := by simp [proj_Iic, Subtype.ext_iff]
+#align set.proj_Iic_eq_self Set.projIic_eq_self
+
 #print Set.projIcc_eq_left /-
-theorem projIcc_eq_left (h : a < b) : projIcc a b h.le x = ⟨a, left_mem_Icc.mpr h.le⟩ ↔ x ≤ a :=
-  by
-  refine' ⟨fun h' => _, proj_Icc_of_le_left _⟩
-  simp_rw [Subtype.ext_iff_val, proj_Icc, max_eq_left_iff, min_le_iff, h.not_le, false_or_iff] at h' 
-  exact h'
+theorem projIcc_eq_left (h : a < b) : projIcc a b h.le x = ⟨a, left_mem_Icc.mpr h.le⟩ ↔ x ≤ a := by
+  simp [proj_Icc, Subtype.ext_iff, h.not_le]
 #align set.proj_Icc_eq_left Set.projIcc_eq_left
 -/
 
 #print Set.projIcc_eq_right /-
 theorem projIcc_eq_right (h : a < b) : projIcc a b h.le x = ⟨b, right_mem_Icc.mpr h.le⟩ ↔ b ≤ x :=
-  by
-  refine' ⟨fun h' => _, proj_Icc_of_right_le _⟩
-  simp_rw [Subtype.ext_iff_val, proj_Icc] at h' 
-  have := ((max_choice _ _).resolve_left (by simp [h.ne', h'])).symm.trans h'
-  exact min_eq_left_iff.mp this
+  by simp [proj_Icc, Subtype.ext_iff, max_min_distrib_left, h.le, h.not_le]
 #align set.proj_Icc_eq_right Set.projIcc_eq_right
 -/
 
+theorem projIci_of_mem (hx : x ∈ Ici a) : projIci a x = ⟨x, hx⟩ := by simpa [proj_Ici]
+#align set.proj_Ici_of_mem Set.projIci_of_mem
+
+theorem projIic_of_mem (hx : x ∈ Iic b) : projIic b x = ⟨x, hx⟩ := by simpa [proj_Iic]
+#align set.proj_Iic_of_mem Set.projIic_of_mem
+
 #print Set.projIcc_of_mem /-
 theorem projIcc_of_mem (hx : x ∈ Icc a b) : projIcc a b h x = ⟨x, hx⟩ := by
   simp [proj_Icc, hx.1, hx.2]
 #align set.proj_Icc_of_mem Set.projIcc_of_mem
 -/
 
+@[simp]
+theorem projIci_coe (x : Ici a) : projIci a x = x := by cases x; apply proj_Ici_of_mem
+#align set.proj_Ici_coe Set.projIci_coe
+
+@[simp]
+theorem projIic_coe (x : Iic b) : projIic b x = x := by cases x; apply proj_Iic_of_mem
+#align set.proj_Iic_coe Set.projIic_coe
+
 #print Set.projIcc_val /-
 @[simp]
 theorem projIcc_val (x : Icc a b) : projIcc a b h x = x := by cases x; apply proj_Icc_of_mem
 #align set.proj_Icc_coe Set.projIcc_val
 -/
 
+theorem projIci_surjOn : SurjOn (projIci a) (Ici a) univ := fun x _ => ⟨x, x.2, projIci_coe x⟩
+#align set.proj_Ici_surj_on Set.projIci_surjOn
+
+theorem projIic_surjOn : SurjOn (projIic b) (Iic b) univ := fun x _ => ⟨x, x.2, projIic_coe x⟩
+#align set.proj_Iic_surj_on Set.projIic_surjOn
+
 #print Set.projIcc_surjOn /-
 theorem projIcc_surjOn : SurjOn (projIcc a b h) (Icc a b) univ := fun x _ =>
   ⟨x, x.2, projIcc_val h x⟩
 #align set.proj_Icc_surj_on Set.projIcc_surjOn
 -/
 
+theorem projIci_surjective : Surjective (projIci a) := fun x => ⟨x, projIci_coe x⟩
+#align set.proj_Ici_surjective Set.projIci_surjective
+
+theorem projIic_surjective : Surjective (projIic b) := fun x => ⟨x, projIic_coe x⟩
+#align set.proj_Iic_surjective Set.projIic_surjective
+
 #print Set.projIcc_surjective /-
 theorem projIcc_surjective : Surjective (projIcc a b h) := fun x => ⟨x, projIcc_val h x⟩
 #align set.proj_Icc_surjective Set.projIcc_surjective
 -/
 
+@[simp]
+theorem range_projIci : range (projIci a) = univ :=
+  projIci_surjective.range_eq
+#align set.range_proj_Ici Set.range_projIci
+
+@[simp]
+theorem range_projIic : range (projIic a) = univ :=
+  projIic_surjective.range_eq
+#align set.range_proj_Iic Set.range_projIic
+
 #print Set.range_projIcc /-
 @[simp]
 theorem range_projIcc : range (projIcc a b h) = univ :=
@@ -118,18 +204,42 @@ theorem range_projIcc : range (projIcc a b h) = univ :=
 #align set.range_proj_Icc Set.range_projIcc
 -/
 
+theorem monotone_projIci : Monotone (projIci a) := fun x y => max_le_max le_rfl
+#align set.monotone_proj_Ici Set.monotone_projIci
+
+theorem monotone_projIic : Monotone (projIic a) := fun x y => min_le_min le_rfl
+#align set.monotone_proj_Iic Set.monotone_projIic
+
 #print Set.monotone_projIcc /-
 theorem monotone_projIcc : Monotone (projIcc a b h) := fun x y hxy =>
   max_le_max le_rfl <| min_le_min le_rfl hxy
 #align set.monotone_proj_Icc Set.monotone_projIcc
 -/
 
+theorem strictMonoOn_projIci : StrictMonoOn (projIci a) (Ici a) := fun x hx y hy hxy => by
+  simpa only [proj_Ici_of_mem, hx, hy]
+#align set.strict_mono_on_proj_Ici Set.strictMonoOn_projIci
+
+theorem strictMonoOn_projIic : StrictMonoOn (projIic b) (Iic b) := fun x hx y hy hxy => by
+  simpa only [proj_Iic_of_mem, hx, hy]
+#align set.strict_mono_on_proj_Iic Set.strictMonoOn_projIic
+
 #print Set.strictMonoOn_projIcc /-
 theorem strictMonoOn_projIcc : StrictMonoOn (projIcc a b h) (Icc a b) := fun x hx y hy hxy => by
   simpa only [proj_Icc_of_mem, hx, hy]
 #align set.strict_mono_on_proj_Icc Set.strictMonoOn_projIcc
 -/
 
+/-- Extend a function `[a, ∞[ → β` to a map `α → β`. -/
+def iciExtend (f : Ici a → β) : α → β :=
+  f ∘ projIci a
+#align set.Ici_extend Set.iciExtend
+
+/-- Extend a function `]-∞, b] → β` to a map `α → β`. -/
+def iicExtend (f : Iic b → β) : α → β :=
+  f ∘ projIic b
+#align set.Iic_extend Set.iicExtend
+
 #print Set.IccExtend /-
 /-- Extend a function `[a, b] → β` to a map `α → β`. -/
 def IccExtend {a b : α} (h : a ≤ b) (f : Icc a b → β) : α → β :=
@@ -137,6 +247,31 @@ def IccExtend {a b : α} (h : a ≤ b) (f : Icc a b → β) : α → β :=
 #align set.Icc_extend Set.IccExtend
 -/
 
+@[simp]
+theorem iciExtend_apply (f : Ici a → β) (x : α) : iciExtend f x = f ⟨max a x, le_max_left _ _⟩ :=
+  rfl
+#align set.Ici_extend_apply Set.iciExtend_apply
+
+@[simp]
+theorem iicExtend_apply (f : Iic b → β) (x : α) : iicExtend f x = f ⟨min b x, min_le_left _ _⟩ :=
+  rfl
+#align set.Iic_extend_apply Set.iicExtend_apply
+
+theorem iccExtend_apply (h : a ≤ b) (f : Icc a b → β) (x : α) :
+    IccExtend h f x = f ⟨max a (min b x), le_max_left _ _, max_le h (min_le_left _ _)⟩ :=
+  rfl
+#align set.Icc_extend_apply Set.iccExtend_apply
+
+@[simp]
+theorem range_iciExtend (f : Ici a → β) : range (iciExtend f) = range f := by
+  simp only [Ici_extend, range_comp f, range_proj_Ici, range_id']
+#align set.range_Ici_extend Set.range_iciExtend
+
+@[simp]
+theorem range_iicExtend (f : Iic b → β) : range (iicExtend f) = range f := by
+  simp only [Iic_extend, range_comp f, range_proj_Iic, range_id']
+#align set.range_Iic_extend Set.range_iicExtend
+
 #print Set.IccExtend_range /-
 @[simp]
 theorem IccExtend_range (f : Icc a b → β) : range (IccExtend h f) = range f := by
@@ -144,6 +279,14 @@ theorem IccExtend_range (f : Icc a b → β) : range (IccExtend h f) = range f :
 #align set.Icc_extend_range Set.IccExtend_range
 -/
 
+theorem iciExtend_of_le (f : Ici a → β) (hx : x ≤ a) : iciExtend f x = f ⟨a, le_rfl⟩ :=
+  congr_arg f <| projIci_of_le hx
+#align set.Ici_extend_of_le Set.iciExtend_of_le
+
+theorem iicExtend_of_le (f : Iic b → β) (hx : b ≤ x) : iicExtend f x = f ⟨b, le_rfl⟩ :=
+  congr_arg f <| projIic_of_le hx
+#align set.Iic_extend_of_le Set.iicExtend_of_le
+
 #print Set.IccExtend_of_le_left /-
 theorem IccExtend_of_le_left (f : Icc a b → β) (hx : x ≤ a) :
     IccExtend h f x = f ⟨a, left_mem_Icc.2 h⟩ :=
@@ -151,13 +294,6 @@ theorem IccExtend_of_le_left (f : Icc a b → β) (hx : x ≤ a) :
 #align set.Icc_extend_of_le_left Set.IccExtend_of_le_left
 -/
 
-#print Set.IccExtend_left /-
-@[simp]
-theorem IccExtend_left (f : Icc a b → β) : IccExtend h f a = f ⟨a, left_mem_Icc.2 h⟩ :=
-  IccExtend_of_le_left h f le_rfl
-#align set.Icc_extend_left Set.IccExtend_left
--/
-
 #print Set.IccExtend_of_right_le /-
 theorem IccExtend_of_right_le (f : Icc a b → β) (hx : b ≤ x) :
     IccExtend h f x = f ⟨b, right_mem_Icc.2 h⟩ :=
@@ -165,6 +301,23 @@ theorem IccExtend_of_right_le (f : Icc a b → β) (hx : b ≤ x) :
 #align set.Icc_extend_of_right_le Set.IccExtend_of_right_le
 -/
 
+@[simp]
+theorem iciExtend_self (f : Ici a → β) : iciExtend f a = f ⟨a, le_rfl⟩ :=
+  iciExtend_of_le f le_rfl
+#align set.Ici_extend_self Set.iciExtend_self
+
+@[simp]
+theorem iicExtend_self (f : Iic b → β) : iicExtend f b = f ⟨b, le_rfl⟩ :=
+  iicExtend_of_le f le_rfl
+#align set.Iic_extend_self Set.iicExtend_self
+
+#print Set.IccExtend_left /-
+@[simp]
+theorem IccExtend_left (f : Icc a b → β) : IccExtend h f a = f ⟨a, left_mem_Icc.2 h⟩ :=
+  IccExtend_of_le_left h f le_rfl
+#align set.Icc_extend_left Set.IccExtend_left
+-/
+
 #print Set.IccExtend_right /-
 @[simp]
 theorem IccExtend_right (f : Icc a b → β) : IccExtend h f b = f ⟨b, right_mem_Icc.2 h⟩ :=
@@ -172,12 +325,30 @@ theorem IccExtend_right (f : Icc a b → β) : IccExtend h f b = f ⟨b, right_m
 #align set.Icc_extend_right Set.IccExtend_right
 -/
 
+theorem iciExtend_of_mem (f : Ici a → β) (hx : x ∈ Ici a) : iciExtend f x = f ⟨x, hx⟩ :=
+  congr_arg f <| projIci_of_mem hx
+#align set.Ici_extend_of_mem Set.iciExtend_of_mem
+
+theorem iicExtend_of_mem (f : Iic b → β) (hx : x ∈ Iic b) : iicExtend f x = f ⟨x, hx⟩ :=
+  congr_arg f <| projIic_of_mem hx
+#align set.Iic_extend_of_mem Set.iicExtend_of_mem
+
 #print Set.IccExtend_of_mem /-
 theorem IccExtend_of_mem (f : Icc a b → β) (hx : x ∈ Icc a b) : IccExtend h f x = f ⟨x, hx⟩ :=
   congr_arg f <| projIcc_of_mem h hx
 #align set.Icc_extend_of_mem Set.IccExtend_of_mem
 -/
 
+@[simp]
+theorem iciExtend_coe (f : Ici a → β) (x : Ici a) : iciExtend f x = f x :=
+  congr_arg f <| projIci_coe x
+#align set.Ici_extend_coe Set.iciExtend_coe
+
+@[simp]
+theorem iicExtend_coe (f : Iic b → β) (x : Iic b) : iicExtend f x = f x :=
+  congr_arg f <| projIic_coe x
+#align set.Iic_extend_coe Set.iicExtend_coe
+
 #print Set.IccExtend_val /-
 @[simp]
 theorem IccExtend_val (f : Icc a b → β) (x : Icc a b) : IccExtend h f x = f x :=
@@ -204,14 +375,32 @@ end Set
 
 open Set
 
-variable [Preorder β] {a b : α} (h : a ≤ b) {f : Icc a b → β}
+variable [Preorder β] {s t : Set α} {a b : α} (h : a ≤ b) {f : Icc a b → β}
+
+protected theorem Monotone.iciExtend {f : Ici a → β} (hf : Monotone f) : Monotone (iciExtend f) :=
+  hf.comp monotone_projIci
+#align monotone.Ici_extend Monotone.iciExtend
+
+protected theorem Monotone.iicExtend {f : Iic b → β} (hf : Monotone f) : Monotone (iicExtend f) :=
+  hf.comp monotone_projIic
+#align monotone.Iic_extend Monotone.iicExtend
 
 #print Monotone.IccExtend /-
-theorem Monotone.IccExtend (hf : Monotone f) : Monotone (IccExtend h f) :=
+protected theorem Monotone.IccExtend (hf : Monotone f) : Monotone (IccExtend h f) :=
   hf.comp <| monotone_projIcc h
 #align monotone.Icc_extend Monotone.IccExtend
 -/
 
+theorem StrictMono.strictMonoOn_iciExtend {f : Ici a → β} (hf : StrictMono f) :
+    StrictMonoOn (iciExtend f) (Ici a) :=
+  hf.comp_strictMonoOn strictMonoOn_projIci
+#align strict_mono.strict_mono_on_Ici_extend StrictMono.strictMonoOn_iciExtend
+
+theorem StrictMono.strictMonoOn_iicExtend {f : Iic b → β} (hf : StrictMono f) :
+    StrictMonoOn (iicExtend f) (Iic b) :=
+  hf.comp_strictMonoOn strictMonoOn_projIic
+#align strict_mono.strict_mono_on_Iic_extend StrictMono.strictMonoOn_iicExtend
+
 #print StrictMono.strictMonoOn_IccExtend /-
 theorem StrictMono.strictMonoOn_IccExtend (hf : StrictMono f) :
     StrictMonoOn (IccExtend h f) (Icc a b) :=
@@ -219,3 +408,18 @@ theorem StrictMono.strictMonoOn_IccExtend (hf : StrictMono f) :
 #align strict_mono.strict_mono_on_Icc_extend StrictMono.strictMonoOn_IccExtend
 -/
 
+protected theorem Set.OrdConnected.iciExtend {s : Set (Ici a)} (hs : s.OrdConnected) :
+    {x | iciExtend (· ∈ s) x}.OrdConnected :=
+  ⟨fun x hx y hy z hz => hs.out hx hy ⟨max_le_max le_rfl hz.1, max_le_max le_rfl hz.2⟩⟩
+#align set.ord_connected.Ici_extend Set.OrdConnected.iciExtend
+
+protected theorem Set.OrdConnected.iicExtend {s : Set (Iic b)} (hs : s.OrdConnected) :
+    {x | iicExtend (· ∈ s) x}.OrdConnected :=
+  ⟨fun x hx y hy z hz => hs.out hx hy ⟨min_le_min le_rfl hz.1, min_le_min le_rfl hz.2⟩⟩
+#align set.ord_connected.Iic_extend Set.OrdConnected.iicExtend
+
+protected theorem Set.OrdConnected.restrict (hs : s.OrdConnected) :
+    {x | restrict t (· ∈ s) x}.OrdConnected :=
+  ⟨fun x hx y hy z hz => hs.out hx hy hz⟩
+#align set.ord_connected.restrict Set.OrdConnected.restrict
+

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -137,40 +137,55 @@ def IccExtend {a b : α} (h : a ≤ b) (f : Icc a b → β) : α → β :=
 #align set.Icc_extend Set.IccExtend
 -/
 
+#print Set.IccExtend_range /-
 @[simp]
 theorem IccExtend_range (f : Icc a b → β) : range (IccExtend h f) = range f := by
   simp only [Icc_extend, range_comp f, range_proj_Icc, range_id']
 #align set.Icc_extend_range Set.IccExtend_range
+-/
 
+#print Set.IccExtend_of_le_left /-
 theorem IccExtend_of_le_left (f : Icc a b → β) (hx : x ≤ a) :
     IccExtend h f x = f ⟨a, left_mem_Icc.2 h⟩ :=
   congr_arg f <| projIcc_of_le_left h hx
 #align set.Icc_extend_of_le_left Set.IccExtend_of_le_left
+-/
 
+#print Set.IccExtend_left /-
 @[simp]
 theorem IccExtend_left (f : Icc a b → β) : IccExtend h f a = f ⟨a, left_mem_Icc.2 h⟩ :=
   IccExtend_of_le_left h f le_rfl
 #align set.Icc_extend_left Set.IccExtend_left
+-/
 
+#print Set.IccExtend_of_right_le /-
 theorem IccExtend_of_right_le (f : Icc a b → β) (hx : b ≤ x) :
     IccExtend h f x = f ⟨b, right_mem_Icc.2 h⟩ :=
   congr_arg f <| projIcc_of_right_le h hx
 #align set.Icc_extend_of_right_le Set.IccExtend_of_right_le
+-/
 
+#print Set.IccExtend_right /-
 @[simp]
 theorem IccExtend_right (f : Icc a b → β) : IccExtend h f b = f ⟨b, right_mem_Icc.2 h⟩ :=
   IccExtend_of_right_le h f le_rfl
 #align set.Icc_extend_right Set.IccExtend_right
+-/
 
+#print Set.IccExtend_of_mem /-
 theorem IccExtend_of_mem (f : Icc a b → β) (hx : x ∈ Icc a b) : IccExtend h f x = f ⟨x, hx⟩ :=
   congr_arg f <| projIcc_of_mem h hx
 #align set.Icc_extend_of_mem Set.IccExtend_of_mem
+-/
 
+#print Set.IccExtend_val /-
 @[simp]
 theorem IccExtend_val (f : Icc a b → β) (x : Icc a b) : IccExtend h f x = f x :=
   congr_arg f <| projIcc_val h x
 #align set.Icc_extend_coe Set.IccExtend_val
+-/
 
+#print Set.IccExtend_eq_self /-
 /-- If `f : α → β` is a constant both on $(-∞, a]$ and on $[b, +∞)$, then the extension of this
 function from $[a, b]$ to the whole line is equal to the original function. -/
 theorem IccExtend_eq_self (f : α → β) (ha : ∀ x < a, f x = f a) (hb : ∀ x, b < x → f x = f b) :
@@ -183,6 +198,7 @@ theorem IccExtend_eq_self (f : α → β) (ha : ∀ x < a, f x = f a) (hb : ∀
       rw [Icc_extend_coe]
     · simp [Icc_extend_of_right_le _ _ hbx.le, hb x hbx]
 #align set.Icc_extend_eq_self Set.IccExtend_eq_self
+-/
 
 end Set
 
@@ -190,12 +206,16 @@ open Set
 
 variable [Preorder β] {a b : α} (h : a ≤ b) {f : Icc a b → β}
 
+#print Monotone.IccExtend /-
 theorem Monotone.IccExtend (hf : Monotone f) : Monotone (IccExtend h f) :=
   hf.comp <| monotone_projIcc h
 #align monotone.Icc_extend Monotone.IccExtend
+-/
 
+#print StrictMono.strictMonoOn_IccExtend /-
 theorem StrictMono.strictMonoOn_IccExtend (hf : StrictMono f) :
     StrictMonoOn (IccExtend h f) (Icc a b) :=
   hf.comp_strictMonoOn (strictMonoOn_projIcc h)
 #align strict_mono.strict_mono_on_Icc_extend StrictMono.strictMonoOn_IccExtend
+-/

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -73,7 +73,7 @@ theorem projIcc_right : projIcc a b h b = ⟨b, right_mem_Icc.2 h⟩ :=
 theorem projIcc_eq_left (h : a < b) : projIcc a b h.le x = ⟨a, left_mem_Icc.mpr h.le⟩ ↔ x ≤ a :=
   by
   refine' ⟨fun h' => _, proj_Icc_of_le_left _⟩
-  simp_rw [Subtype.ext_iff_val, proj_Icc, max_eq_left_iff, min_le_iff, h.not_le, false_or_iff] at h'
+  simp_rw [Subtype.ext_iff_val, proj_Icc, max_eq_left_iff, min_le_iff, h.not_le, false_or_iff] at h' 
   exact h'
 #align set.proj_Icc_eq_left Set.projIcc_eq_left
 -/
@@ -82,7 +82,7 @@ theorem projIcc_eq_left (h : a < b) : projIcc a b h.le x = ⟨a, left_mem_Icc.mp
 theorem projIcc_eq_right (h : a < b) : projIcc a b h.le x = ⟨b, right_mem_Icc.mpr h.le⟩ ↔ b ≤ x :=
   by
   refine' ⟨fun h' => _, proj_Icc_of_right_le _⟩
-  simp_rw [Subtype.ext_iff_val, proj_Icc] at h'
+  simp_rw [Subtype.ext_iff_val, proj_Icc] at h' 
   have := ((max_choice _ _).resolve_left (by simp [h.ne', h'])).symm.trans h'
   exact min_eq_left_iff.mp this
 #align set.proj_Icc_eq_right Set.projIcc_eq_right

bump to nightly-2023-05-29-00

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

f7040f5d

Diff

@@ -167,13 +167,13 @@ theorem IccExtend_of_mem (f : Icc a b → β) (hx : x ∈ Icc a b) : IccExtend h
 #align set.Icc_extend_of_mem Set.IccExtend_of_mem
 
 @[simp]
-theorem Icc_extend_coe (f : Icc a b → β) (x : Icc a b) : IccExtend h f x = f x :=
+theorem IccExtend_val (f : Icc a b → β) (x : Icc a b) : IccExtend h f x = f x :=
   congr_arg f <| projIcc_val h x
-#align set.Icc_extend_coe Set.Icc_extend_coe
+#align set.Icc_extend_coe Set.IccExtend_val
 
 /-- If `f : α → β` is a constant both on $(-∞, a]$ and on $[b, +∞)$, then the extension of this
 function from $[a, b]$ to the whole line is equal to the original function. -/
-theorem iccExtend_eq_self (f : α → β) (ha : ∀ x < a, f x = f a) (hb : ∀ x, b < x → f x = f b) :
+theorem IccExtend_eq_self (f : α → β) (ha : ∀ x < a, f x = f a) (hb : ∀ x, b < x → f x = f b) :
     IccExtend h (f ∘ coe) = f := by
   ext x
   cases' lt_or_le x a with hxa hax
@@ -182,7 +182,7 @@ theorem iccExtend_eq_self (f : α → β) (ha : ∀ x < a, f x = f a) (hb : ∀
     · lift x to Icc a b using ⟨hax, hxb⟩
       rw [Icc_extend_coe]
     · simp [Icc_extend_of_right_le _ _ hbx.le, hb x hbx]
-#align set.Icc_extend_eq_self Set.iccExtend_eq_self
+#align set.Icc_extend_eq_self Set.IccExtend_eq_self
 
 end Set

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -34,38 +34,51 @@ open Function
 
 namespace Set
 
+#print Set.projIcc /-
 /-- Projection of `α` to the closed interval `[a, b]`. -/
 def projIcc (a b : α) (h : a ≤ b) (x : α) : Icc a b :=
   ⟨max a (min b x), le_max_left _ _, max_le h (min_le_left _ _)⟩
 #align set.proj_Icc Set.projIcc
+-/
 
 variable {a b : α} (h : a ≤ b) {x : α}
 
+#print Set.projIcc_of_le_left /-
 theorem projIcc_of_le_left (hx : x ≤ a) : projIcc a b h x = ⟨a, left_mem_Icc.2 h⟩ := by
   simp [proj_Icc, hx, hx.trans h]
 #align set.proj_Icc_of_le_left Set.projIcc_of_le_left
+-/
 
+#print Set.projIcc_left /-
 @[simp]
 theorem projIcc_left : projIcc a b h a = ⟨a, left_mem_Icc.2 h⟩ :=
   projIcc_of_le_left h le_rfl
 #align set.proj_Icc_left Set.projIcc_left
+-/
 
+#print Set.projIcc_of_right_le /-
 theorem projIcc_of_right_le (hx : b ≤ x) : projIcc a b h x = ⟨b, right_mem_Icc.2 h⟩ := by
   simp [proj_Icc, hx, h]
 #align set.proj_Icc_of_right_le Set.projIcc_of_right_le
+-/
 
+#print Set.projIcc_right /-
 @[simp]
 theorem projIcc_right : projIcc a b h b = ⟨b, right_mem_Icc.2 h⟩ :=
   projIcc_of_right_le h le_rfl
 #align set.proj_Icc_right Set.projIcc_right
+-/
 
+#print Set.projIcc_eq_left /-
 theorem projIcc_eq_left (h : a < b) : projIcc a b h.le x = ⟨a, left_mem_Icc.mpr h.le⟩ ↔ x ≤ a :=
   by
   refine' ⟨fun h' => _, proj_Icc_of_le_left _⟩
   simp_rw [Subtype.ext_iff_val, proj_Icc, max_eq_left_iff, min_le_iff, h.not_le, false_or_iff] at h'
   exact h'
 #align set.proj_Icc_eq_left Set.projIcc_eq_left
+-/
 
+#print Set.projIcc_eq_right /-
 theorem projIcc_eq_right (h : a < b) : projIcc a b h.le x = ⟨b, right_mem_Icc.mpr h.le⟩ ↔ b ≤ x :=
   by
   refine' ⟨fun h' => _, proj_Icc_of_right_le _⟩
@@ -73,39 +86,56 @@ theorem projIcc_eq_right (h : a < b) : projIcc a b h.le x = ⟨b, right_mem_Icc.
   have := ((max_choice _ _).resolve_left (by simp [h.ne', h'])).symm.trans h'
   exact min_eq_left_iff.mp this
 #align set.proj_Icc_eq_right Set.projIcc_eq_right
+-/
 
+#print Set.projIcc_of_mem /-
 theorem projIcc_of_mem (hx : x ∈ Icc a b) : projIcc a b h x = ⟨x, hx⟩ := by
   simp [proj_Icc, hx.1, hx.2]
 #align set.proj_Icc_of_mem Set.projIcc_of_mem
+-/
 
+#print Set.projIcc_val /-
 @[simp]
 theorem projIcc_val (x : Icc a b) : projIcc a b h x = x := by cases x; apply proj_Icc_of_mem
 #align set.proj_Icc_coe Set.projIcc_val
+-/
 
+#print Set.projIcc_surjOn /-
 theorem projIcc_surjOn : SurjOn (projIcc a b h) (Icc a b) univ := fun x _ =>
   ⟨x, x.2, projIcc_val h x⟩
 #align set.proj_Icc_surj_on Set.projIcc_surjOn
+-/
 
+#print Set.projIcc_surjective /-
 theorem projIcc_surjective : Surjective (projIcc a b h) := fun x => ⟨x, projIcc_val h x⟩
 #align set.proj_Icc_surjective Set.projIcc_surjective
+-/
 
+#print Set.range_projIcc /-
 @[simp]
 theorem range_projIcc : range (projIcc a b h) = univ :=
   (projIcc_surjective h).range_eq
 #align set.range_proj_Icc Set.range_projIcc
+-/
 
+#print Set.monotone_projIcc /-
 theorem monotone_projIcc : Monotone (projIcc a b h) := fun x y hxy =>
   max_le_max le_rfl <| min_le_min le_rfl hxy
 #align set.monotone_proj_Icc Set.monotone_projIcc
+-/
 
+#print Set.strictMonoOn_projIcc /-
 theorem strictMonoOn_projIcc : StrictMonoOn (projIcc a b h) (Icc a b) := fun x hx y hy hxy => by
   simpa only [proj_Icc_of_mem, hx, hy]
 #align set.strict_mono_on_proj_Icc Set.strictMonoOn_projIcc
+-/
 
+#print Set.IccExtend /-
 /-- Extend a function `[a, b] → β` to a map `α → β`. -/
 def IccExtend {a b : α} (h : a ≤ b) (f : Icc a b → β) : α → β :=
   f ∘ projIcc a b h
 #align set.Icc_extend Set.IccExtend
+-/
 
 @[simp]
 theorem IccExtend_range (f : Icc a b → β) : range (IccExtend h f) = range f := by

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -34,12 +34,6 @@ open Function
 
 namespace Set
 
-/- warning: set.proj_Icc -> Set.projIcc is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] (a : α) (b : α), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b) -> α -> (Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b))
-Case conversion may be inaccurate. Consider using '#align set.proj_Icc Set.projIccₓ'. -/
 /-- Projection of `α` to the closed interval `[a, b]`. -/
 def projIcc (a b : α) (h : a ≤ b) (x : α) : Icc a b :=
   ⟨max a (min b x), le_max_left _ _, max_le h (min_le_left _ _)⟩
@@ -47,54 +41,24 @@ def projIcc (a b : α) (h : a ≤ b) (x : α) : Icc a b :=
 
 variable {a b : α} (h : a ≤ b) {x : α}
 
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 theorem projIcc_of_le_left (hx : x ≤ a) : projIcc a b h x = ⟨a, left_mem_Icc.2 h⟩ := by
   simp [proj_Icc, hx, hx.trans h]
 #align set.proj_Icc_of_le_left Set.projIcc_of_le_left
 
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 @[simp]
 theorem projIcc_left : projIcc a b h a = ⟨a, left_mem_Icc.2 h⟩ :=
   projIcc_of_le_left h le_rfl
 #align set.proj_Icc_left Set.projIcc_left
 
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 theorem projIcc_of_right_le (hx : b ≤ x) : projIcc a b h x = ⟨b, right_mem_Icc.2 h⟩ := by
   simp [proj_Icc, hx, h]
 #align set.proj_Icc_of_right_le Set.projIcc_of_right_le
 
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 @[simp]
 theorem projIcc_right : projIcc a b h b = ⟨b, right_mem_Icc.2 h⟩ :=
   projIcc_of_right_le h le_rfl
 #align set.proj_Icc_right Set.projIcc_right
 
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 theorem projIcc_eq_left (h : a < b) : projIcc a b h.le x = ⟨a, left_mem_Icc.mpr h.le⟩ ↔ x ≤ a :=
   by
   refine' ⟨fun h' => _, proj_Icc_of_le_left _⟩
@@ -102,12 +66,6 @@ theorem projIcc_eq_left (h : a < b) : projIcc a b h.le x = ⟨a, left_mem_Icc.mp
   exact h'
 #align set.proj_Icc_eq_left Set.projIcc_eq_left
 
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 theorem projIcc_eq_right (h : a < b) : projIcc a b h.le x = ⟨b, right_mem_Icc.mpr h.le⟩ ↔ b ≤ x :=
   by
   refine' ⟨fun h' => _, proj_Icc_of_right_le _⟩
@@ -116,158 +74,68 @@ theorem projIcc_eq_right (h : a < b) : projIcc a b h.le x = ⟨b, right_mem_Icc.
   exact min_eq_left_iff.mp this
 #align set.proj_Icc_eq_right Set.projIcc_eq_right
 
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 theorem projIcc_of_mem (hx : x ∈ Icc a b) : projIcc a b h x = ⟨x, hx⟩ := by
   simp [proj_Icc, hx.1, hx.2]
 #align set.proj_Icc_of_mem Set.projIcc_of_mem
 
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 @[simp]
 theorem projIcc_val (x : Icc a b) : projIcc a b h x = x := by cases x; apply proj_Icc_of_mem
 #align set.proj_Icc_coe Set.projIcc_val
 
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 theorem projIcc_surjOn : SurjOn (projIcc a b h) (Icc a b) univ := fun x _ =>
   ⟨x, x.2, projIcc_val h x⟩
 #align set.proj_Icc_surj_on Set.projIcc_surjOn
 
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 theorem projIcc_surjective : Surjective (projIcc a b h) := fun x => ⟨x, projIcc_val h x⟩
 #align set.proj_Icc_surjective Set.projIcc_surjective
 
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 @[simp]
 theorem range_projIcc : range (projIcc a b h) = univ :=
   (projIcc_surjective h).range_eq
 #align set.range_proj_Icc Set.range_projIcc
 
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 theorem monotone_projIcc : Monotone (projIcc a b h) := fun x y hxy =>
   max_le_max le_rfl <| min_le_min le_rfl hxy
 #align set.monotone_proj_Icc Set.monotone_projIcc
 
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 theorem strictMonoOn_projIcc : StrictMonoOn (projIcc a b h) (Icc a b) := fun x hx y hy hxy => by
   simpa only [proj_Icc_of_mem, hx, hy]
 #align set.strict_mono_on_proj_Icc Set.strictMonoOn_projIcc
 
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 /-- Extend a function `[a, b] → β` to a map `α → β`. -/
 def IccExtend {a b : α} (h : a ≤ b) (f : Icc a b → β) : α → β :=
   f ∘ projIcc a b h
 #align set.Icc_extend Set.IccExtend
 
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 @[simp]
 theorem IccExtend_range (f : Icc a b → β) : range (IccExtend h f) = range f := by
   simp only [Icc_extend, range_comp f, range_proj_Icc, range_id']
 #align set.Icc_extend_range Set.IccExtend_range
 
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 theorem IccExtend_of_le_left (f : Icc a b → β) (hx : x ≤ a) :
     IccExtend h f x = f ⟨a, left_mem_Icc.2 h⟩ :=
   congr_arg f <| projIcc_of_le_left h hx
 #align set.Icc_extend_of_le_left Set.IccExtend_of_le_left
 
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 @[simp]
 theorem IccExtend_left (f : Icc a b → β) : IccExtend h f a = f ⟨a, left_mem_Icc.2 h⟩ :=
   IccExtend_of_le_left h f le_rfl
 #align set.Icc_extend_left Set.IccExtend_left
 
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 theorem IccExtend_of_right_le (f : Icc a b → β) (hx : b ≤ x) :
     IccExtend h f x = f ⟨b, right_mem_Icc.2 h⟩ :=
   congr_arg f <| projIcc_of_right_le h hx
 #align set.Icc_extend_of_right_le Set.IccExtend_of_right_le
 
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 @[simp]
 theorem IccExtend_right (f : Icc a b → β) : IccExtend h f b = f ⟨b, right_mem_Icc.2 h⟩ :=
   IccExtend_of_right_le h f le_rfl
 #align set.Icc_extend_right Set.IccExtend_right
 
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 theorem IccExtend_of_mem (f : Icc a b → β) (hx : x ∈ Icc a b) : IccExtend h f x = f ⟨x, hx⟩ :=
   congr_arg f <| projIcc_of_mem h hx
 #align set.Icc_extend_of_mem Set.IccExtend_of_mem
 
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-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] {a : α} {b : α} (h : LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) a b) (f : (Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) -> β) (x : Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)), Eq.{succ u1} β (Set.IccExtend.{u2, u1} α β _inst_1 a b h f (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) x)) (f x)
-Case conversion may be inaccurate. Consider using '#align set.Icc_extend_coe Set.Icc_extend_coeₓ'. -/
 @[simp]
 theorem Icc_extend_coe (f : Icc a b → β) (x : Icc a b) : IccExtend h f x = f x :=
   congr_arg f <| projIcc_val h x
@@ -292,22 +160,10 @@ open Set
 
 variable [Preorder β] {a b : α} (h : a ≤ b) {f : Icc a b → β}
 
-/- warning: monotone.Icc_extend -> Monotone.IccExtend is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Preorder.{u2} β] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) {f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β}, (Monotone.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) β (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b))) _inst_2 f) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 (Set.IccExtend.{u1, u2} α β _inst_1 a b h f))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align monotone.Icc_extend Monotone.IccExtendₓ'. -/
 theorem Monotone.IccExtend (hf : Monotone f) : Monotone (IccExtend h f) :=
   hf.comp <| monotone_projIcc h
 #align monotone.Icc_extend Monotone.IccExtend
 
-/- warning: strict_mono.strict_mono_on_Icc_extend -> StrictMono.strictMonoOn_IccExtend is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Preorder.{u2} β] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) {f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β}, (StrictMono.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) β (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b))) _inst_2 f) -> (StrictMonoOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 (Set.IccExtend.{u1, u2} α β _inst_1 a b h f) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b))
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-Case conversion may be inaccurate. Consider using '#align strict_mono.strict_mono_on_Icc_extend StrictMono.strictMonoOn_IccExtendₓ'. -/
 theorem StrictMono.strictMonoOn_IccExtend (hf : StrictMono f) :
     StrictMonoOn (IccExtend h f) (Icc a b) :=
   hf.comp_strictMonoOn (strictMonoOn_projIcc h)

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -133,10 +133,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b) (x : Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)), Eq.{succ u1} (Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) (Set.projIcc.{u1} α _inst_1 a b h (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) x)) x
 Case conversion may be inaccurate. Consider using '#align set.proj_Icc_coe Set.projIcc_valₓ'. -/
 @[simp]
-theorem projIcc_val (x : Icc a b) : projIcc a b h x = x :=
-  by
-  cases x
-  apply proj_Icc_of_mem
+theorem projIcc_val (x : Icc a b) : projIcc a b h x = x := by cases x; apply proj_Icc_of_mem
 #align set.proj_Icc_coe Set.projIcc_val
 
 /- warning: set.proj_Icc_surj_on -> Set.projIcc_surjOn is a dubious translation:

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
 
 ! This file was ported from Lean 3 source module data.set.intervals.proj_Icc
-! leanprover-community/mathlib commit c3291da49cfa65f0d43b094750541c0731edc932
+! leanprover-community/mathlib commit 42e9a1fd3a99e10f82830349ba7f4f10e8961c2a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -276,6 +276,19 @@ theorem Icc_extend_coe (f : Icc a b → β) (x : Icc a b) : IccExtend h f x = f
   congr_arg f <| projIcc_val h x
 #align set.Icc_extend_coe Set.Icc_extend_coe
 
+/-- If `f : α → β` is a constant both on $(-∞, a]$ and on $[b, +∞)$, then the extension of this
+function from $[a, b]$ to the whole line is equal to the original function. -/
+theorem iccExtend_eq_self (f : α → β) (ha : ∀ x < a, f x = f a) (hb : ∀ x, b < x → f x = f b) :
+    IccExtend h (f ∘ coe) = f := by
+  ext x
+  cases' lt_or_le x a with hxa hax
+  · simp [Icc_extend_of_le_left _ _ hxa.le, ha x hxa]
+  · cases' le_or_lt x b with hxb hbx
+    · lift x to Icc a b using ⟨hax, hxb⟩
+      rw [Icc_extend_coe]
+    · simp [Icc_extend_of_right_le _ _ hbx.le, hb x hbx]
+#align set.Icc_extend_eq_self Set.iccExtend_eq_self
+
 end Set
 
 open Set

c3291da4

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -34,51 +34,80 @@ open Function
 
 namespace Set
 
-#print Set.projIcc /-
+/- warning: set.proj_Icc -> Set.projIcc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] (a : α) (b : α), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) -> α -> (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] (a : α) (b : α), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b) -> α -> (Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b))
+Case conversion may be inaccurate. Consider using '#align set.proj_Icc Set.projIccₓ'. -/
 /-- Projection of `α` to the closed interval `[a, b]`. -/
 def projIcc (a b : α) (h : a ≤ b) (x : α) : Icc a b :=
   ⟨max a (min b x), le_max_left _ _, max_le h (min_le_left _ _)⟩
 #align set.proj_Icc Set.projIcc
--/
 
 variable {a b : α} (h : a ≤ b) {x : α}
 
-#print Set.projIcc_of_le_left /-
+/- warning: set.proj_Icc_of_le_left -> Set.projIcc_of_le_left is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) {x : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) x a) -> (Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (Set.projIcc.{u1} α _inst_1 a b h x) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) a (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (Set.left_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) h)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b) {x : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) x a) -> (Eq.{succ u1} (Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) (Set.projIcc.{u1} α _inst_1 a b h x) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) a (Iff.mpr (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b) (Set.left_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b) h)))
+Case conversion may be inaccurate. Consider using '#align set.proj_Icc_of_le_left Set.projIcc_of_le_leftₓ'. -/
 theorem projIcc_of_le_left (hx : x ≤ a) : projIcc a b h x = ⟨a, left_mem_Icc.2 h⟩ := by
   simp [proj_Icc, hx, hx.trans h]
 #align set.proj_Icc_of_le_left Set.projIcc_of_le_left
--/
 
-#print Set.projIcc_left /-
+/- warning: set.proj_Icc_left -> Set.projIcc_left is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (Set.projIcc.{u1} α _inst_1 a b h a) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) a (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (Set.left_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) h))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b), Eq.{succ u1} (Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) (Set.projIcc.{u1} α _inst_1 a b h a) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) a (Iff.mpr (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b) (Set.left_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b) h))
+Case conversion may be inaccurate. Consider using '#align set.proj_Icc_left Set.projIcc_leftₓ'. -/
 @[simp]
 theorem projIcc_left : projIcc a b h a = ⟨a, left_mem_Icc.2 h⟩ :=
   projIcc_of_le_left h le_rfl
 #align set.proj_Icc_left Set.projIcc_left
--/
 
-#print Set.projIcc_of_right_le /-
+/- warning: set.proj_Icc_of_right_le -> Set.projIcc_of_right_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) {x : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) b x) -> (Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (Set.projIcc.{u1} α _inst_1 a b h x) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) b (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (Set.right_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) h)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b) {x : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) b x) -> (Eq.{succ u1} (Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) (Set.projIcc.{u1} α _inst_1 a b h x) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) b (Iff.mpr (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b) (Set.right_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b) h)))
+Case conversion may be inaccurate. Consider using '#align set.proj_Icc_of_right_le Set.projIcc_of_right_leₓ'. -/
 theorem projIcc_of_right_le (hx : b ≤ x) : projIcc a b h x = ⟨b, right_mem_Icc.2 h⟩ := by
   simp [proj_Icc, hx, h]
 #align set.proj_Icc_of_right_le Set.projIcc_of_right_le
--/
 
-#print Set.projIcc_right /-
+/- warning: set.proj_Icc_right -> Set.projIcc_right is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (Set.projIcc.{u1} α _inst_1 a b h b) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) b (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (Set.right_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) h))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b), Eq.{succ u1} (Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) (Set.projIcc.{u1} α _inst_1 a b h b) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) b (Iff.mpr (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b) (Set.right_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b) h))
+Case conversion may be inaccurate. Consider using '#align set.proj_Icc_right Set.projIcc_rightₓ'. -/
 @[simp]
 theorem projIcc_right : projIcc a b h b = ⟨b, right_mem_Icc.2 h⟩ :=
   projIcc_of_right_le h le_rfl
 #align set.proj_Icc_right Set.projIcc_right
--/
 
-#print Set.projIcc_eq_left /-
+/- warning: set.proj_Icc_eq_left -> Set.projIcc_eq_left is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} {x : α} (h : LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b), Iff (Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (Set.projIcc.{u1} α _inst_1 a b (LT.lt.le.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b h) x) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) a (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (Set.left_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) (LT.lt.le.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b h)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) x a)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align set.proj_Icc_eq_left Set.projIcc_eq_leftₓ'. -/
 theorem projIcc_eq_left (h : a < b) : projIcc a b h.le x = ⟨a, left_mem_Icc.mpr h.le⟩ ↔ x ≤ a :=
   by
   refine' ⟨fun h' => _, proj_Icc_of_le_left _⟩
   simp_rw [Subtype.ext_iff_val, proj_Icc, max_eq_left_iff, min_le_iff, h.not_le, false_or_iff] at h'
   exact h'
 #align set.proj_Icc_eq_left Set.projIcc_eq_left
--/
 
-#print Set.projIcc_eq_right /-
+/- warning: set.proj_Icc_eq_right -> Set.projIcc_eq_right is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} {x : α} (h : LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b), Iff (Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (Set.projIcc.{u1} α _inst_1 a b (LT.lt.le.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b h) x) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) b (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (Set.right_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) (LT.lt.le.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b h)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) b x)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align set.proj_Icc_eq_right Set.projIcc_eq_rightₓ'. -/
 theorem projIcc_eq_right (h : a < b) : projIcc a b h.le x = ⟨b, right_mem_Icc.mpr h.le⟩ ↔ b ≤ x :=
   by
   refine' ⟨fun h' => _, proj_Icc_of_right_le _⟩
@@ -86,63 +115,94 @@ theorem projIcc_eq_right (h : a < b) : projIcc a b h.le x = ⟨b, right_mem_Icc.
   have := ((max_choice _ _).resolve_left (by simp [h.ne', h'])).symm.trans h'
   exact min_eq_left_iff.mp this
 #align set.proj_Icc_eq_right Set.projIcc_eq_right
--/
 
-#print Set.projIcc_of_mem /-
+/- warning: set.proj_Icc_of_mem -> Set.projIcc_of_mem is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align set.proj_Icc_of_mem Set.projIcc_of_memₓ'. -/
 theorem projIcc_of_mem (hx : x ∈ Icc a b) : projIcc a b h x = ⟨x, hx⟩ := by
   simp [proj_Icc, hx.1, hx.2]
 #align set.proj_Icc_of_mem Set.projIcc_of_mem
--/
 
-#print Set.projIcc_val /-
+/- warning: set.proj_Icc_coe -> Set.projIcc_val is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align set.proj_Icc_coe Set.projIcc_valₓ'. -/
 @[simp]
 theorem projIcc_val (x : Icc a b) : projIcc a b h x = x :=
   by
   cases x
   apply proj_Icc_of_mem
 #align set.proj_Icc_coe Set.projIcc_val
--/
 
-#print Set.projIcc_surjOn /-
+/- warning: set.proj_Icc_surj_on -> Set.projIcc_surjOn is a dubious translation:
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+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b), Set.SurjOn.{u1, u1} α (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (Set.projIcc.{u1} α _inst_1 a b h) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) (Set.univ.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align set.proj_Icc_surj_on Set.projIcc_surjOnₓ'. -/
 theorem projIcc_surjOn : SurjOn (projIcc a b h) (Icc a b) univ := fun x _ =>
   ⟨x, x.2, projIcc_val h x⟩
 #align set.proj_Icc_surj_on Set.projIcc_surjOn
--/
 
-#print Set.projIcc_surjective /-
+/- warning: set.proj_Icc_surjective -> Set.projIcc_surjective is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b), Function.Surjective.{succ u1, succ u1} α (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (Set.projIcc.{u1} α _inst_1 a b h)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b), Function.Surjective.{succ u1, succ u1} α (Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) (Set.projIcc.{u1} α _inst_1 a b h)
+Case conversion may be inaccurate. Consider using '#align set.proj_Icc_surjective Set.projIcc_surjectiveₓ'. -/
 theorem projIcc_surjective : Surjective (projIcc a b h) := fun x => ⟨x, projIcc_val h x⟩
 #align set.proj_Icc_surjective Set.projIcc_surjective
--/
 
-#print Set.range_projIcc /-
+/- warning: set.range_proj_Icc -> Set.range_projIcc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b), Eq.{succ u1} (Set.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b))) (Set.range.{u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) α (Set.projIcc.{u1} α _inst_1 a b h)) (Set.univ.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b), Eq.{succ u1} (Set.{u1} (Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b))) (Set.range.{u1, succ u1} (Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) α (Set.projIcc.{u1} α _inst_1 a b h)) (Set.univ.{u1} (Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)))
+Case conversion may be inaccurate. Consider using '#align set.range_proj_Icc Set.range_projIccₓ'. -/
 @[simp]
 theorem range_projIcc : range (projIcc a b h) = univ :=
   (projIcc_surjective h).range_eq
 #align set.range_proj_Icc Set.range_projIcc
--/
 
-#print Set.monotone_projIcc /-
+/- warning: set.monotone_proj_Icc -> Set.monotone_projIcc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b), Monotone.{u1, u1} α (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b))) (Set.projIcc.{u1} α _inst_1 a b h)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b), Monotone.{u1, u1} α (Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b))) (Set.projIcc.{u1} α _inst_1 a b h)
+Case conversion may be inaccurate. Consider using '#align set.monotone_proj_Icc Set.monotone_projIccₓ'. -/
 theorem monotone_projIcc : Monotone (projIcc a b h) := fun x y hxy =>
   max_le_max le_rfl <| min_le_min le_rfl hxy
 #align set.monotone_proj_Icc Set.monotone_projIcc
--/
 
-#print Set.strictMonoOn_projIcc /-
+/- warning: set.strict_mono_on_proj_Icc -> Set.strictMonoOn_projIcc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b), StrictMonoOn.{u1, u1} α (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b))) (Set.projIcc.{u1} α _inst_1 a b h) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b), StrictMonoOn.{u1, u1} α (Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b))) (Set.projIcc.{u1} α _inst_1 a b h) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)
+Case conversion may be inaccurate. Consider using '#align set.strict_mono_on_proj_Icc Set.strictMonoOn_projIccₓ'. -/
 theorem strictMonoOn_projIcc : StrictMonoOn (projIcc a b h) (Icc a b) := fun x hx y hy hxy => by
   simpa only [proj_Icc_of_mem, hx, hy]
 #align set.strict_mono_on_proj_Icc Set.strictMonoOn_projIcc
--/
 
-#print Set.IccExtend /-
+/- warning: set.Icc_extend -> Set.IccExtend is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) -> ((coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β) -> α -> β
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) a b) -> ((Set.Elem.{u1} α (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) a b)) -> β) -> α -> β
+Case conversion may be inaccurate. Consider using '#align set.Icc_extend Set.IccExtendₓ'. -/
 /-- Extend a function `[a, b] → β` to a map `α → β`. -/
 def IccExtend {a b : α} (h : a ≤ b) (f : Icc a b → β) : α → β :=
   f ∘ projIcc a b h
 #align set.Icc_extend Set.IccExtend
--/
 
 /- warning: set.Icc_extend_range -> Set.IccExtend_range is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β), Eq.{succ u2} (Set.{u2} β) (Set.range.{u2, succ u1} β α (Set.IccExtend.{u1, u2} α β _inst_1 a b h f)) (Set.range.{u2, succ u1} β (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) f)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β), Eq.{succ u2} (Set.{u2} β) (Set.range.{u2, succ u1} β α (Set.IccExtend.{u1, u2} α β _inst_1 a b h f)) (Set.range.{u2, succ u1} β (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) f)
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] {a : α} {b : α} (h : LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) a b) (f : (Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) -> β), Eq.{succ u1} (Set.{u1} β) (Set.range.{u1, succ u2} β α (Set.IccExtend.{u2, u1} α β _inst_1 a b h f)) (Set.range.{u1, succ u2} β (Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) f)
 Case conversion may be inaccurate. Consider using '#align set.Icc_extend_range Set.IccExtend_rangeₓ'. -/
@@ -153,7 +213,7 @@ theorem IccExtend_range (f : Icc a b → β) : range (IccExtend h f) = range f :
 
 /- warning: set.Icc_extend_of_le_left -> Set.IccExtend_of_le_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) {x : α} (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) x a) -> (Eq.{succ u2} β (Set.IccExtend.{u1, u2} α β _inst_1 a b h f x) (f (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) a (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (Set.left_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) h))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) {x : α} (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) x a) -> (Eq.{succ u2} β (Set.IccExtend.{u1, u2} α β _inst_1 a b h f x) (f (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) a (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (Set.left_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) h))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] {a : α} {b : α} (h : LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) a b) {x : α} (f : (Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) -> β), (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) x a) -> (Eq.{succ u1} β (Set.IccExtend.{u2, u1} α β _inst_1 a b h f x) (f (Subtype.mk.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) a (Iff.mpr (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) a b) (Set.left_mem_Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b) h))))
 Case conversion may be inaccurate. Consider using '#align set.Icc_extend_of_le_left Set.IccExtend_of_le_leftₓ'. -/
@@ -164,7 +224,7 @@ theorem IccExtend_of_le_left (f : Icc a b → β) (hx : x ≤ a) :
 
 /- warning: set.Icc_extend_left -> Set.IccExtend_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β), Eq.{succ u2} β (Set.IccExtend.{u1, u2} α β _inst_1 a b h f a) (f (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) a (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (Set.left_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) h)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β), Eq.{succ u2} β (Set.IccExtend.{u1, u2} α β _inst_1 a b h f a) (f (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) a (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (Set.left_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) h)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] {a : α} {b : α} (h : LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) a b) (f : (Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) -> β), Eq.{succ u1} β (Set.IccExtend.{u2, u1} α β _inst_1 a b h f a) (f (Subtype.mk.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) a (Iff.mpr (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) a b) (Set.left_mem_Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b) h)))
 Case conversion may be inaccurate. Consider using '#align set.Icc_extend_left Set.IccExtend_leftₓ'. -/
@@ -175,7 +235,7 @@ theorem IccExtend_left (f : Icc a b → β) : IccExtend h f a = f ⟨a, left_mem
 
 /- warning: set.Icc_extend_of_right_le -> Set.IccExtend_of_right_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) {x : α} (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) b x) -> (Eq.{succ u2} β (Set.IccExtend.{u1, u2} α β _inst_1 a b h f x) (f (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) b (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (Set.right_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) h))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) {x : α} (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) b x) -> (Eq.{succ u2} β (Set.IccExtend.{u1, u2} α β _inst_1 a b h f x) (f (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) b (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (Set.right_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) h))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] {a : α} {b : α} (h : LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) a b) {x : α} (f : (Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) -> β), (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) b x) -> (Eq.{succ u1} β (Set.IccExtend.{u2, u1} α β _inst_1 a b h f x) (f (Subtype.mk.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) b (Iff.mpr (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) b (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) a b) (Set.right_mem_Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b) h))))
 Case conversion may be inaccurate. Consider using '#align set.Icc_extend_of_right_le Set.IccExtend_of_right_leₓ'. -/
@@ -186,7 +246,7 @@ theorem IccExtend_of_right_le (f : Icc a b → β) (hx : b ≤ x) :
 
 /- warning: set.Icc_extend_right -> Set.IccExtend_right is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β), Eq.{succ u2} β (Set.IccExtend.{u1, u2} α β _inst_1 a b h f b) (f (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) b (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (Set.right_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) h)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β), Eq.{succ u2} β (Set.IccExtend.{u1, u2} α β _inst_1 a b h f b) (f (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) b (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (Set.right_mem_Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b) h)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] {a : α} {b : α} (h : LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) a b) (f : (Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) -> β), Eq.{succ u1} β (Set.IccExtend.{u2, u1} α β _inst_1 a b h f b) (f (Subtype.mk.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) b (Iff.mpr (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) b (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) a b) (Set.right_mem_Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b) h)))
 Case conversion may be inaccurate. Consider using '#align set.Icc_extend_right Set.IccExtend_rightₓ'. -/
@@ -197,7 +257,7 @@ theorem IccExtend_right (f : Icc a b → β) : IccExtend h f b = f ⟨b, right_m
 
 /- warning: set.Icc_extend_of_mem -> Set.IccExtend_of_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) {x : α} (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β) (hx : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)), Eq.{succ u2} β (Set.IccExtend.{u1, u2} α β _inst_1 a b h f x) (f (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) x hx))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) {x : α} (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β) (hx : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)), Eq.{succ u2} β (Set.IccExtend.{u1, u2} α β _inst_1 a b h f x) (f (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) x hx))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] {a : α} {b : α} (h : LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) a b) {x : α} (f : (Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) -> β) (hx : Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)), Eq.{succ u1} β (Set.IccExtend.{u2, u1} α β _inst_1 a b h f x) (f (Subtype.mk.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) x hx))
 Case conversion may be inaccurate. Consider using '#align set.Icc_extend_of_mem Set.IccExtend_of_memₓ'. -/
@@ -207,7 +267,7 @@ theorem IccExtend_of_mem (f : Icc a b → β) (hx : x ∈ Icc a b) : IccExtend h
 
 /- warning: set.Icc_extend_coe -> Set.Icc_extend_coe is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β) (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)), Eq.{succ u2} β (Set.IccExtend.{u1, u2} α β _inst_1 a b h f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)))))) x)) (f x)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β) (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)), Eq.{succ u2} β (Set.IccExtend.{u1, u2} α β _inst_1 a b h f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)))))) x)) (f x)
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] {a : α} {b : α} (h : LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) a b) (f : (Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) -> β) (x : Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)), Eq.{succ u1} β (Set.IccExtend.{u2, u1} α β _inst_1 a b h f (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) x)) (f x)
 Case conversion may be inaccurate. Consider using '#align set.Icc_extend_coe Set.Icc_extend_coeₓ'. -/
@@ -224,7 +284,7 @@ variable [Preorder β] {a b : α} (h : a ≤ b) {f : Icc a b → β}
 
 /- warning: monotone.Icc_extend -> Monotone.IccExtend is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Preorder.{u2} β] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) {f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β}, (Monotone.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) β (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b))) _inst_2 f) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 (Set.IccExtend.{u1, u2} α β _inst_1 a b h f))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Preorder.{u2} β] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) {f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β}, (Monotone.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) β (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b))) _inst_2 f) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 (Set.IccExtend.{u1, u2} α β _inst_1 a b h f))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : Preorder.{u1} β] {a : α} {b : α} (h : LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) a b) {f : (Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) -> β}, (Monotone.{u2, u1} (Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) β (Subtype.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b))) _inst_2 f) -> (Monotone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) _inst_2 (Set.IccExtend.{u2, u1} α β _inst_1 a b h f))
 Case conversion may be inaccurate. Consider using '#align monotone.Icc_extend Monotone.IccExtendₓ'. -/
@@ -234,7 +294,7 @@ theorem Monotone.IccExtend (hf : Monotone f) : Monotone (IccExtend h f) :=
 
 /- warning: strict_mono.strict_mono_on_Icc_extend -> StrictMono.strictMonoOn_IccExtend is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Preorder.{u2} β] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) {f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β}, (StrictMono.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) β (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b))) _inst_2 f) -> (StrictMonoOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 (Set.IccExtend.{u1, u2} α β _inst_1 a b h f) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Preorder.{u2} β] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) a b) {f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) -> β}, (StrictMono.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b)) β (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b))) _inst_2 f) -> (StrictMonoOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 (Set.IccExtend.{u1, u2} α β _inst_1 a b h f) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a b))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : Preorder.{u1} β] {a : α} {b : α} (h : LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) a b) {f : (Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) -> β}, (StrictMono.{u2, u1} (Set.Elem.{u2} α (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b)) β (Subtype.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b))) _inst_2 f) -> (StrictMonoOn.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) _inst_2 (Set.IccExtend.{u2, u1} α β _inst_1 a b h f) (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a b))
 Case conversion may be inaccurate. Consider using '#align strict_mono.strict_mono_on_Icc_extend StrictMono.strictMonoOn_IccExtendₓ'. -/

c3291da4

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore: Move intervals (#11765)

Move Set.Ixx, Finset.Ixx, Multiset.Ixx together under two different folders:

Order.Interval for their definition and basic properties
Algebra.Order.Interval for their algebraic properties

Move the definitions of Multiset.Ixx to what is now Order.Interval.Multiset. I believe we could just delete this file in a later PR as nothing uses it (and I already had doubts when defining Multiset.Ixx three years ago).

Move the algebraic results out of what is now Order.Interval.Finset.Basic to a new file Algebra.Order.Interval.Finset.Basic.

c7fa7063

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
 -/
 import Mathlib.Data.Set.Function
-import Mathlib.Data.Set.Intervals.OrdConnected
+import Mathlib.Order.Interval.Set.OrdConnected
 
 #align_import data.set.intervals.proj_Icc from "leanprover-community/mathlib"@"4e24c4bfcff371c71f7ba22050308aa17815626c"

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

See Zulip thread for the discussion.

9f6d3388

Diff

@@ -63,10 +63,10 @@ theorem coe_projIic (b x : α) : (projIic b x : α) = min b x := rfl
 theorem coe_projIcc (a b : α) (h : a ≤ b) (x : α) : (projIcc a b h x : α) = max a (min b x) := rfl
 #align set.coe_proj_Icc Set.coe_projIcc
 
-theorem projIci_of_le (hx : x ≤ a) : projIci a x = ⟨a, le_rfl⟩ := Subtype.ext $ max_eq_left hx
+theorem projIci_of_le (hx : x ≤ a) : projIci a x = ⟨a, le_rfl⟩ := Subtype.ext <| max_eq_left hx
 #align set.proj_Ici_of_le Set.projIci_of_le
 
-theorem projIic_of_le (hx : b ≤ x) : projIic b x = ⟨b, le_rfl⟩ := Subtype.ext $ min_eq_left hx
+theorem projIic_of_le (hx : b ≤ x) : projIic b x = ⟨b, le_rfl⟩ := Subtype.ext <| min_eq_left hx
 #align set.proj_Iic_of_le Set.projIic_of_le
 
 theorem projIcc_of_le_left (hx : x ≤ a) : projIcc a b h x = ⟨a, left_mem_Icc.2 h⟩ := by
@@ -231,11 +231,11 @@ theorem IccExtend_range (f : Icc a b → β) : range (IccExtend h f) = range f :
 #align set.Icc_extend_range Set.IccExtend_range
 
 theorem IciExtend_of_le (f : Ici a → β) (hx : x ≤ a) : IciExtend f x = f ⟨a, le_rfl⟩ :=
-  congr_arg f $ projIci_of_le hx
+  congr_arg f <| projIci_of_le hx
 #align set.Ici_extend_of_le Set.IciExtend_of_le
 
 theorem IicExtend_of_le (f : Iic b → β) (hx : b ≤ x) : IicExtend f x = f ⟨b, le_rfl⟩ :=
-  congr_arg f $ projIic_of_le hx
+  congr_arg f <| projIic_of_le hx
 #align set.Iic_extend_of_le Set.IicExtend_of_le
 
 theorem IccExtend_of_le_left (f : Icc a b → β) (hx : x ≤ a) :
@@ -245,7 +245,7 @@ theorem IccExtend_of_le_left (f : Icc a b → β) (hx : x ≤ a) :
 
 theorem IccExtend_of_right_le (f : Icc a b → β) (hx : b ≤ x) :
     IccExtend h f x = f ⟨b, right_mem_Icc.2 h⟩ :=
-  congr_arg f $ projIcc_of_right_le h hx
+  congr_arg f <| projIcc_of_right_le h hx
 #align set.Icc_extend_of_right_le Set.IccExtend_of_right_le
 
 @[simp]
@@ -269,11 +269,11 @@ theorem IccExtend_right (f : Icc a b → β) : IccExtend h f b = f ⟨b, right_m
 #align set.Icc_extend_right Set.IccExtend_right
 
 theorem IciExtend_of_mem (f : Ici a → β) (hx : x ∈ Ici a) : IciExtend f x = f ⟨x, hx⟩ :=
-  congr_arg f $ projIci_of_mem hx
+  congr_arg f <| projIci_of_mem hx
 #align set.Ici_extend_of_mem Set.IciExtend_of_mem
 
 theorem IicExtend_of_mem (f : Iic b → β) (hx : x ∈ Iic b) : IicExtend f x = f ⟨x, hx⟩ :=
-  congr_arg f $ projIic_of_mem hx
+  congr_arg f <| projIic_of_mem hx
 #align set.Iic_extend_of_mem Set.IicExtend_of_mem
 
 theorem IccExtend_of_mem (f : Icc a b → β) (hx : x ∈ Icc a b) : IccExtend h f x = f ⟨x, hx⟩ :=
@@ -282,12 +282,12 @@ theorem IccExtend_of_mem (f : Icc a b → β) (hx : x ∈ Icc a b) : IccExtend h
 
 @[simp]
 theorem IciExtend_coe (f : Ici a → β) (x : Ici a) : IciExtend f x = f x :=
-  congr_arg f $ projIci_coe x
+  congr_arg f <| projIci_coe x
 #align set.Ici_extend_coe Set.IciExtend_coe
 
 @[simp]
 theorem IicExtend_coe (f : Iic b → β) (x : Iic b) : IicExtend f x = f x :=
-  congr_arg f $ projIic_coe x
+  congr_arg f <| projIic_coe x
 #align set.Iic_extend_coe Set.IicExtend_coe
 
 @[simp]

chore: remove uses of 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.

3fca282c

Diff

@@ -302,7 +302,7 @@ theorem IccExtend_eq_self (f : α → β) (ha : ∀ x < a, f x = f a) (hb : ∀
   ext x
   cases' lt_or_le x a with hxa hax
   · simp [IccExtend_of_le_left _ _ hxa.le, ha x hxa]
-  · cases' le_or_lt x b with hxb hbx
+  · rcases le_or_lt x b with hxb | hbx
     · lift x to Icc a b using ⟨hax, hxb⟩
       rw [IccExtend_val, comp_apply]
     · simp [IccExtend_of_right_le _ _ hbx.le, hb x hbx]

chore: tidy various files (#6924)

3ebc913e

Diff

@@ -211,9 +211,9 @@ theorem IicExtend_apply (f : Iic b → β) (x : α) : IicExtend f x = f ⟨min b
   rfl
 #align set.Iic_extend_apply Set.IicExtend_apply
 
-theorem iccExtend_apply (h : a ≤ b) (f : Icc a b → β) (x : α) :
+theorem IccExtend_apply (h : a ≤ b) (f : Icc a b → β) (x : α) :
     IccExtend h f x = f ⟨max a (min b x), le_max_left _ _, max_le h (min_le_left _ _)⟩ := rfl
-#align set.Icc_extend_apply Set.iccExtend_apply
+#align set.Icc_extend_apply Set.IccExtend_apply
 
 @[simp]
 theorem range_IciExtend (f : Ici a → β) : range (IciExtend f) = range f := by

chore: cleanup a few porting notes and friends relating to alias (#6790)

After the new alias command we can now do protected alias
alias at some point broke dot notation by unfolding (see #1022) this was fixed in #1058 but the library was not fixed up there

45e55c3f

Diff

@@ -163,7 +163,7 @@ theorem range_projIic : range (projIic a) = univ := projIic_surjective.range_eq
 
 @[simp]
 theorem range_projIcc : range (projIcc a b h) = univ :=
-  Function.Surjective.range_eq (projIcc_surjective h)
+  (projIcc_surjective h).range_eq
 #align set.range_proj_Icc Set.range_projIcc
 
 theorem monotone_projIci : Monotone (projIci a) := fun _ _ => max_le_max le_rfl

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

@@ -30,7 +30,7 @@ We also prove some trivial properties of these maps.
 -/
 
 
-variable {α β : Type _} [LinearOrder α]
+variable {α β : Type*} [LinearOrder α]
 
 open Function

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) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
-
-! This file was ported from Lean 3 source module data.set.intervals.proj_Icc
-! leanprover-community/mathlib commit 4e24c4bfcff371c71f7ba22050308aa17815626c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Set.Function
 import Mathlib.Data.Set.Intervals.OrdConnected
 
+#align_import data.set.intervals.proj_Icc from "leanprover-community/mathlib"@"4e24c4bfcff371c71f7ba22050308aa17815626c"
+
 /-!
 # Projection of a line onto a closed interval

https://github.com/leanprover-community/mathlib/pull/18795

feat: Extending from Ici a (#5829)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

bbde7ac2

Diff

@@ -4,22 +4,30 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
 
 ! This file was ported from Lean 3 source module data.set.intervals.proj_Icc
-! leanprover-community/mathlib commit 42e9a1fd3a99e10f82830349ba7f4f10e8961c2a
+! leanprover-community/mathlib commit 4e24c4bfcff371c71f7ba22050308aa17815626c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathlib.Data.Set.Function
-import Mathlib.Data.Set.Intervals.Basic
+import Mathlib.Data.Set.Intervals.OrdConnected
 
 /-!
 # Projection of a line onto a closed interval
 
 Given a linearly ordered type `α`, in this file we define
 
+* `Set.projIci (a : α)` to be the map `α → [a, ∞)` sending `(-∞, a]` to `a`, and each point
+   `x ∈ [a, ∞)` to itself;
+* `Set.projIic (b : α)` to be the map `α → (-∞, b[` sending `[b, ∞)` to `b`, and each point
+   `x ∈ (-∞, b]` to itself;
 * `Set.projIcc (a b : α) (h : a ≤ b)` to be the map `α → [a, b]` sending `(-∞, a]` to `a`, `[b, ∞)`
   to `b`, and each point `x ∈ [a, b]` to itself;
 * `Set.IccExtend {a b : α} (h : a ≤ b) (f : Icc a b → β)` to be the extension of `f` to `α` defined
   as `f ∘ projIcc a b h`.
+* `Set.IciExtend {a : α} (f : Ici a → β)` to be the extension of `f` to `α` defined
+  as `f ∘ projIci a`.
+* `Set.IicExtend {b : α} (f : Iic b → β)` to be the extension of `f` to `α` defined
+  as `f ∘ projIic b`.
 
 We also prove some trivial properties of these maps.
 -/
@@ -31,6 +39,14 @@ open Function
 
 namespace Set
 
+/-- Projection of `α` to the closed interval `[a, ∞)`. -/
+def projIci (a x : α) : Ici a := ⟨max a x, le_max_left _ _⟩
+#align set.proj_Ici Set.projIci
+
+/-- Projection of `α` to the closed interval `(-∞, b]`. -/
+def projIic (b x : α) : Iic b := ⟨min b x, min_le_left _ _⟩
+#align set.proj_Iic Set.projIic
+
 /-- Projection of `α` to the closed interval `[a, b]`. -/
 def projIcc (a b : α) (h : a ≤ b) (x : α) : Icc a b :=
   ⟨max a (min b x), le_max_left _ _, max_le h (min_le_left _ _)⟩
@@ -38,102 +54,245 @@ def projIcc (a b : α) (h : a ≤ b) (x : α) : Icc a b :=
 
 variable {a b : α} (h : a ≤ b) {x : α}
 
+@[norm_cast]
+theorem coe_projIci (a x : α) : (projIci a x : α) = max a x := rfl
+#align set.coe_proj_Ici Set.coe_projIci
+
+@[norm_cast]
+theorem coe_projIic (b x : α) : (projIic b x : α) = min b x := rfl
+#align set.coe_proj_Iic Set.coe_projIic
+
+@[norm_cast]
+theorem coe_projIcc (a b : α) (h : a ≤ b) (x : α) : (projIcc a b h x : α) = max a (min b x) := rfl
+#align set.coe_proj_Icc Set.coe_projIcc
+
+theorem projIci_of_le (hx : x ≤ a) : projIci a x = ⟨a, le_rfl⟩ := Subtype.ext $ max_eq_left hx
+#align set.proj_Ici_of_le Set.projIci_of_le
+
+theorem projIic_of_le (hx : b ≤ x) : projIic b x = ⟨b, le_rfl⟩ := Subtype.ext $ min_eq_left hx
+#align set.proj_Iic_of_le Set.projIic_of_le
+
 theorem projIcc_of_le_left (hx : x ≤ a) : projIcc a b h x = ⟨a, left_mem_Icc.2 h⟩ := by
   simp [projIcc, hx, hx.trans h]
 #align set.proj_Icc_of_le_left Set.projIcc_of_le_left
 
-@[simp]
-theorem projIcc_left : projIcc a b h a = ⟨a, left_mem_Icc.2 h⟩ :=
-  projIcc_of_le_left h le_rfl
-#align set.proj_Icc_left Set.projIcc_left
 
 theorem projIcc_of_right_le (hx : b ≤ x) : projIcc a b h x = ⟨b, right_mem_Icc.2 h⟩ := by
   simp [projIcc, hx, h]
 #align set.proj_Icc_of_right_le Set.projIcc_of_right_le
 
+@[simp]
+theorem projIci_self (a : α) : projIci a a = ⟨a, le_rfl⟩ := projIci_of_le le_rfl
+#align set.proj_Ici_self Set.projIci_self
+
+@[simp]
+theorem projIic_self (b : α) : projIic b b = ⟨b, le_rfl⟩ := projIic_of_le le_rfl
+#align set.proj_Iic_self Set.projIic_self
+
+@[simp]
+theorem projIcc_left : projIcc a b h a = ⟨a, left_mem_Icc.2 h⟩ :=
+  projIcc_of_le_left h le_rfl
+#align set.proj_Icc_left Set.projIcc_left
+
 @[simp]
 theorem projIcc_right : projIcc a b h b = ⟨b, right_mem_Icc.2 h⟩ :=
   projIcc_of_right_le h le_rfl
 #align set.proj_Icc_right Set.projIcc_right
 
+theorem projIci_eq_self : projIci a x = ⟨a, le_rfl⟩ ↔ x ≤ a := by simp [projIci, Subtype.ext_iff]
+#align set.proj_Ici_eq_self Set.projIci_eq_self
+
+theorem projIic_eq_self : projIic b x = ⟨b, le_rfl⟩ ↔ b ≤ x := by simp [projIic, Subtype.ext_iff]
+#align set.proj_Iic_eq_self Set.projIic_eq_self
+
 theorem projIcc_eq_left (h : a < b) : projIcc a b h.le x = ⟨a, left_mem_Icc.mpr h.le⟩ ↔ x ≤ a := by
-  refine' ⟨fun h' => _, projIcc_of_le_left _⟩
-  simp_rw [Subtype.ext_iff_val, projIcc, max_eq_left_iff, min_le_iff, h.not_le, false_or_iff] at h'
-  exact h'
+  simp [projIcc, Subtype.ext_iff, h.not_le]
 #align set.proj_Icc_eq_left Set.projIcc_eq_left
 
-theorem projIcc_eq_right (h : a < b) :
-    projIcc a b h.le x = ⟨b, right_mem_Icc.mpr h.le⟩ ↔ b ≤ x := by
-  refine' ⟨fun h' => _, projIcc_of_right_le _⟩
-  simp_rw [Subtype.ext_iff_val, projIcc] at h'
-  have := ((max_choice _ _).resolve_left (by simp [h.ne', h'])).symm.trans h'
-  exact min_eq_left_iff.mp this
+theorem projIcc_eq_right (h : a < b) : projIcc a b h.le x = ⟨b, right_mem_Icc.2 h.le⟩ ↔ b ≤ x := by
+  simp [projIcc, Subtype.ext_iff, max_min_distrib_left, h.le, h.not_le]
 #align set.proj_Icc_eq_right Set.projIcc_eq_right
 
+theorem projIci_of_mem (hx : x ∈ Ici a) : projIci a x = ⟨x, hx⟩ := by simpa [projIci]
+#align set.proj_Ici_of_mem Set.projIci_of_mem
+
+theorem projIic_of_mem (hx : x ∈ Iic b) : projIic b x = ⟨x, hx⟩ := by simpa [projIic]
+#align set.proj_Iic_of_mem Set.projIic_of_mem
+
 theorem projIcc_of_mem (hx : x ∈ Icc a b) : projIcc a b h x = ⟨x, hx⟩ := by
   simp [projIcc, hx.1, hx.2]
 #align set.proj_Icc_of_mem Set.projIcc_of_mem
 
+@[simp]
+theorem projIci_coe (x : Ici a) : projIci a x = x := by cases x; apply projIci_of_mem
+#align set.proj_Ici_coe Set.projIci_coe
+
+@[simp]
+theorem projIic_coe (x : Iic b) : projIic b x = x := by cases x; apply projIic_of_mem
+#align set.proj_Iic_coe Set.projIic_coe
+
 @[simp]
 theorem projIcc_val (x : Icc a b) : projIcc a b h x = x := by
   cases x
   apply projIcc_of_mem
 #align set.proj_Icc_coe Set.projIcc_val
 
+theorem projIci_surjOn : SurjOn (projIci a) (Ici a) univ := fun x _ => ⟨x, x.2, projIci_coe x⟩
+#align set.proj_Ici_surj_on Set.projIci_surjOn
+
+theorem projIic_surjOn : SurjOn (projIic b) (Iic b) univ := fun x _ => ⟨x, x.2, projIic_coe x⟩
+#align set.proj_Iic_surj_on Set.projIic_surjOn
+
 theorem projIcc_surjOn : SurjOn (projIcc a b h) (Icc a b) univ := fun x _ =>
   ⟨x, x.2, projIcc_val h x⟩
 #align set.proj_Icc_surj_on Set.projIcc_surjOn
 
+theorem projIci_surjective : Surjective (projIci a) := fun x => ⟨x, projIci_coe x⟩
+#align set.proj_Ici_surjective Set.projIci_surjective
+
+theorem projIic_surjective : Surjective (projIic b) := fun x => ⟨x, projIic_coe x⟩
+#align set.proj_Iic_surjective Set.projIic_surjective
+
 theorem projIcc_surjective : Surjective (projIcc a b h) := fun x => ⟨x, projIcc_val h x⟩
 #align set.proj_Icc_surjective Set.projIcc_surjective
 
+@[simp]
+theorem range_projIci : range (projIci a) = univ := projIci_surjective.range_eq
+#align set.range_proj_Ici Set.range_projIci
+
+@[simp]
+theorem range_projIic : range (projIic a) = univ := projIic_surjective.range_eq
+#align set.range_proj_Iic Set.range_projIic
+
 @[simp]
 theorem range_projIcc : range (projIcc a b h) = univ :=
   Function.Surjective.range_eq (projIcc_surjective h)
 #align set.range_proj_Icc Set.range_projIcc
 
+theorem monotone_projIci : Monotone (projIci a) := fun _ _ => max_le_max le_rfl
+#align set.monotone_proj_Ici Set.monotone_projIci
+
+theorem monotone_projIic : Monotone (projIic a) := fun _ _ => min_le_min le_rfl
+#align set.monotone_proj_Iic Set.monotone_projIic
+
 theorem monotone_projIcc : Monotone (projIcc a b h) := fun _ _ hxy =>
   max_le_max le_rfl <| min_le_min le_rfl hxy
 #align set.monotone_proj_Icc Set.monotone_projIcc
 
+theorem strictMonoOn_projIci : StrictMonoOn (projIci a) (Ici a) := fun x hx y hy hxy => by
+  simpa only [projIci_of_mem, hx, hy]
+#align set.strict_mono_on_proj_Ici Set.strictMonoOn_projIci
+
+theorem strictMonoOn_projIic : StrictMonoOn (projIic b) (Iic b) := fun x hx y hy hxy => by
+  simpa only [projIic_of_mem, hx, hy]
+#align set.strict_mono_on_proj_Iic Set.strictMonoOn_projIic
+
 theorem strictMonoOn_projIcc : StrictMonoOn (projIcc a b h) (Icc a b) := fun x hx y hy hxy => by
   simpa only [projIcc_of_mem, hx, hy]
 #align set.strict_mono_on_proj_Icc Set.strictMonoOn_projIcc
 
+/-- Extend a function `[a, ∞) → β` to a map `α → β`. -/
+def IciExtend (f : Ici a → β) : α → β :=
+  f ∘ projIci a
+#align set.Ici_extend Set.IciExtend
+
+/-- Extend a function `(-∞, b] → β` to a map `α → β`. -/
+def IicExtend (f : Iic b → β) : α → β :=
+  f ∘ projIic b
+#align set.Iic_extend Set.IicExtend
+
 /-- Extend a function `[a, b] → β` to a map `α → β`. -/
 def IccExtend {a b : α} (h : a ≤ b) (f : Icc a b → β) : α → β :=
   f ∘ projIcc a b h
 #align set.Icc_extend Set.IccExtend
 
+theorem IciExtend_apply (f : Ici a → β) (x : α) : IciExtend f x = f ⟨max a x, le_max_left _ _⟩ :=
+  rfl
+#align set.Ici_extend_apply Set.IciExtend_apply
+
+theorem IicExtend_apply (f : Iic b → β) (x : α) : IicExtend f x = f ⟨min b x, min_le_left _ _⟩ :=
+  rfl
+#align set.Iic_extend_apply Set.IicExtend_apply
+
+theorem iccExtend_apply (h : a ≤ b) (f : Icc a b → β) (x : α) :
+    IccExtend h f x = f ⟨max a (min b x), le_max_left _ _, max_le h (min_le_left _ _)⟩ := rfl
+#align set.Icc_extend_apply Set.iccExtend_apply
+
+@[simp]
+theorem range_IciExtend (f : Ici a → β) : range (IciExtend f) = range f := by
+  simp only [IciExtend, range_comp f, range_projIci, range_id', image_univ]
+#align set.range_Ici_extend Set.range_IciExtend
+
+@[simp]
+theorem range_IicExtend (f : Iic b → β) : range (IicExtend f) = range f := by
+  simp only [IicExtend, range_comp f, range_projIic, range_id', image_univ]
+#align set.range_Iic_extend Set.range_IicExtend
+
 @[simp]
 theorem IccExtend_range (f : Icc a b → β) : range (IccExtend h f) = range f := by
   simp only [IccExtend, range_comp f, range_projIcc, image_univ]
 #align set.Icc_extend_range Set.IccExtend_range
 
+theorem IciExtend_of_le (f : Ici a → β) (hx : x ≤ a) : IciExtend f x = f ⟨a, le_rfl⟩ :=
+  congr_arg f $ projIci_of_le hx
+#align set.Ici_extend_of_le Set.IciExtend_of_le
+
+theorem IicExtend_of_le (f : Iic b → β) (hx : b ≤ x) : IicExtend f x = f ⟨b, le_rfl⟩ :=
+  congr_arg f $ projIic_of_le hx
+#align set.Iic_extend_of_le Set.IicExtend_of_le
+
 theorem IccExtend_of_le_left (f : Icc a b → β) (hx : x ≤ a) :
     IccExtend h f x = f ⟨a, left_mem_Icc.2 h⟩ :=
   congr_arg f <| projIcc_of_le_left h hx
 #align set.Icc_extend_of_le_left Set.IccExtend_of_le_left
 
+theorem IccExtend_of_right_le (f : Icc a b → β) (hx : b ≤ x) :
+    IccExtend h f x = f ⟨b, right_mem_Icc.2 h⟩ :=
+  congr_arg f $ projIcc_of_right_le h hx
+#align set.Icc_extend_of_right_le Set.IccExtend_of_right_le
+
+@[simp]
+theorem IciExtend_self (f : Ici a → β) : IciExtend f a = f ⟨a, le_rfl⟩ :=
+  IciExtend_of_le f le_rfl
+#align set.Ici_extend_self Set.IciExtend_self
+
+@[simp]
+theorem IicExtend_self (f : Iic b → β) : IicExtend f b = f ⟨b, le_rfl⟩ :=
+  IicExtend_of_le f le_rfl
+#align set.Iic_extend_self Set.IicExtend_self
+
 @[simp]
 theorem IccExtend_left (f : Icc a b → β) : IccExtend h f a = f ⟨a, left_mem_Icc.2 h⟩ :=
   IccExtend_of_le_left h f le_rfl
 #align set.Icc_extend_left Set.IccExtend_left
 
-theorem IccExtend_of_right_le (f : Icc a b → β) (hx : b ≤ x) :
-    IccExtend h f x = f ⟨b, right_mem_Icc.2 h⟩ :=
-  congr_arg f <| projIcc_of_right_le h hx
-#align set.Icc_extend_of_right_le Set.IccExtend_of_right_le
-
 @[simp]
 theorem IccExtend_right (f : Icc a b → β) : IccExtend h f b = f ⟨b, right_mem_Icc.2 h⟩ :=
   IccExtend_of_right_le h f le_rfl
 #align set.Icc_extend_right Set.IccExtend_right
 
+theorem IciExtend_of_mem (f : Ici a → β) (hx : x ∈ Ici a) : IciExtend f x = f ⟨x, hx⟩ :=
+  congr_arg f $ projIci_of_mem hx
+#align set.Ici_extend_of_mem Set.IciExtend_of_mem
+
+theorem IicExtend_of_mem (f : Iic b → β) (hx : x ∈ Iic b) : IicExtend f x = f ⟨x, hx⟩ :=
+  congr_arg f $ projIic_of_mem hx
+#align set.Iic_extend_of_mem Set.IicExtend_of_mem
+
 theorem IccExtend_of_mem (f : Icc a b → β) (hx : x ∈ Icc a b) : IccExtend h f x = f ⟨x, hx⟩ :=
   congr_arg f <| projIcc_of_mem h hx
 #align set.Icc_extend_of_mem Set.IccExtend_of_mem
 
+@[simp]
+theorem IciExtend_coe (f : Ici a → β) (x : Ici a) : IciExtend f x = f x :=
+  congr_arg f $ projIci_coe x
+#align set.Ici_extend_coe Set.IciExtend_coe
+
+@[simp]
+theorem IicExtend_coe (f : Iic b → β) (x : Iic b) : IicExtend f x = f x :=
+  congr_arg f $ projIic_coe x
+#align set.Iic_extend_coe Set.IicExtend_coe
+
 @[simp]
 theorem IccExtend_val (f : Icc a b → β) (x : Icc a b) : IccExtend h f x = f x :=
   congr_arg f <| projIcc_val h x
@@ -156,13 +315,46 @@ end Set
 
 open Set
 
-variable [Preorder β] {a b : α} (h : a ≤ b) {f : Icc a b → β}
+variable [Preorder β] {s t : Set α} {a b : α} (h : a ≤ b) {f : Icc a b → β}
+
+protected theorem Monotone.IciExtend {f : Ici a → β} (hf : Monotone f) : Monotone (IciExtend f) :=
+  hf.comp monotone_projIci
+#align monotone.Ici_extend Monotone.IciExtend
 
-theorem Monotone.IccExtend (hf : Monotone f) : Monotone (IccExtend h f) :=
+protected theorem Monotone.IicExtend {f : Iic b → β} (hf : Monotone f) : Monotone (IicExtend f) :=
+  hf.comp monotone_projIic
+#align monotone.Iic_extend Monotone.IicExtend
+
+protected theorem Monotone.IccExtend (hf : Monotone f) : Monotone (IccExtend h f) :=
   hf.comp <| monotone_projIcc h
 #align monotone.Icc_extend Monotone.IccExtend
 
+theorem StrictMono.strictMonoOn_IciExtend {f : Ici a → β} (hf : StrictMono f) :
+    StrictMonoOn (IciExtend f) (Ici a) :=
+  hf.comp_strictMonoOn strictMonoOn_projIci
+#align strict_mono.strict_mono_on_Ici_extend StrictMono.strictMonoOn_IciExtend
+
+theorem StrictMono.strictMonoOn_IicExtend {f : Iic b → β} (hf : StrictMono f) :
+    StrictMonoOn (IicExtend f) (Iic b) :=
+  hf.comp_strictMonoOn strictMonoOn_projIic
+#align strict_mono.strict_mono_on_Iic_extend StrictMono.strictMonoOn_IicExtend
+
 theorem StrictMono.strictMonoOn_IccExtend (hf : StrictMono f) :
     StrictMonoOn (IccExtend h f) (Icc a b) :=
   hf.comp_strictMonoOn (strictMonoOn_projIcc h)
 #align strict_mono.strict_mono_on_Icc_extend StrictMono.strictMonoOn_IccExtend
+
+protected theorem Set.OrdConnected.IciExtend {s : Set (Ici a)} (hs : s.OrdConnected) :
+    {x | IciExtend (· ∈ s) x}.OrdConnected :=
+  ⟨fun _ hx _ hy _ hz => hs.out hx hy ⟨max_le_max le_rfl hz.1, max_le_max le_rfl hz.2⟩⟩
+#align set.ord_connected.Ici_extend Set.OrdConnected.IciExtend
+
+protected theorem Set.OrdConnected.IicExtend {s : Set (Iic b)} (hs : s.OrdConnected) :
+    {x | IicExtend (· ∈ s) x}.OrdConnected :=
+  ⟨fun _ hx _ hy _ hz => hs.out hx hy ⟨min_le_min le_rfl hz.1, min_le_min le_rfl hz.2⟩⟩
+#align set.ord_connected.Iic_extend Set.OrdConnected.IicExtend
+
+protected theorem Set.OrdConnected.restrict (hs : s.OrdConnected) :
+    {x | restrict t (· ∈ s) x}.OrdConnected :=
+  ⟨fun _ hx _ hy _ hz => hs.out hx hy hz⟩
+#align set.ord_connected.restrict Set.OrdConnected.restrict

feat: add Set.IccExtend_eq_self (#4454)

Partial forward-port of leanprover-community/mathlib#19097 Also rename Set.Icc_extend_coe to Set.IccExtend_val.

0f5133e2

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
 
 ! This file was ported from Lean 3 source module data.set.intervals.proj_Icc
-! leanprover-community/mathlib commit aba57d4d3dae35460225919dcd82fe91355162f9
+! leanprover-community/mathlib commit 42e9a1fd3a99e10f82830349ba7f4f10e8961c2a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -135,9 +135,22 @@ theorem IccExtend_of_mem (f : Icc a b → β) (hx : x ∈ Icc a b) : IccExtend h
 #align set.Icc_extend_of_mem Set.IccExtend_of_mem
 
 @[simp]
-theorem Icc_extend_coe (f : Icc a b → β) (x : Icc a b) : IccExtend h f x = f x :=
+theorem IccExtend_val (f : Icc a b → β) (x : Icc a b) : IccExtend h f x = f x :=
   congr_arg f <| projIcc_val h x
-#align set.Icc_extend_coe Set.Icc_extend_coe
+#align set.Icc_extend_coe Set.IccExtend_val
+
+/-- If `f : α → β` is a constant both on $(-∞, a]$ and on $[b, +∞)$, then the extension of this
+function from $[a, b]$ to the whole line is equal to the original function. -/
+theorem IccExtend_eq_self (f : α → β) (ha : ∀ x < a, f x = f a) (hb : ∀ x, b < x → f x = f b) :
+    IccExtend h (f ∘ (↑)) = f := by
+  ext x
+  cases' lt_or_le x a with hxa hax
+  · simp [IccExtend_of_le_left _ _ hxa.le, ha x hxa]
+  · cases' le_or_lt x b with hxb hbx
+    · lift x to Icc a b using ⟨hax, hxb⟩
+      rw [IccExtend_val, comp_apply]
+    · simp [IccExtend_of_right_le _ _ hbx.le, hb x hbx]
+#align set.Icc_extend_eq_self Set.IccExtend_eq_self
 
 end Set

chore: format by line breaks with long lines (#1529)

This was done semi-automatically with some regular expressions in vim in contrast to the fully automatic https://github.com/leanprover-community/mathlib4/pull/1523.

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

1050066f

Diff

@@ -62,8 +62,8 @@ theorem projIcc_eq_left (h : a < b) : projIcc a b h.le x = ⟨a, left_mem_Icc.mp
   exact h'
 #align set.proj_Icc_eq_left Set.projIcc_eq_left
 
-theorem projIcc_eq_right (h : a < b) : projIcc a b h.le x = ⟨b, right_mem_Icc.mpr h.le⟩ ↔ b ≤ x :=
-  by
+theorem projIcc_eq_right (h : a < b) :
+    projIcc a b h.le x = ⟨b, right_mem_Icc.mpr h.le⟩ ↔ b ≤ x := by
   refine' ⟨fun h' => _, projIcc_of_right_le _⟩
   simp_rw [Subtype.ext_iff_val, projIcc] at h'
   have := ((max_choice _ _).resolve_left (by simp [h.ne', h'])).symm.trans h'

chore: tidy various files (#1086)

4e2a7237

Diff

@@ -19,7 +19,7 @@ Given a linearly ordered type `α`, in this file we define
 * `Set.projIcc (a b : α) (h : a ≤ b)` to be the map `α → [a, b]` sending `(-∞, a]` to `a`, `[b, ∞)`
   to `b`, and each point `x ∈ [a, b]` to itself;
 * `Set.IccExtend {a b : α} (h : a ≤ b) (f : Icc a b → β)` to be the extension of `f` to `α` defined
-  as `f ∘ proj_Icc a b h`.
+  as `f ∘ projIcc a b h`.
 
 We also prove some trivial properties of these maps.
 -/
@@ -47,13 +47,13 @@ theorem projIcc_left : projIcc a b h a = ⟨a, left_mem_Icc.2 h⟩ :=
   projIcc_of_le_left h le_rfl
 #align set.proj_Icc_left Set.projIcc_left
 
-theorem proj_Icc_of_right_le (hx : b ≤ x) : projIcc a b h x = ⟨b, right_mem_Icc.2 h⟩ := by
+theorem projIcc_of_right_le (hx : b ≤ x) : projIcc a b h x = ⟨b, right_mem_Icc.2 h⟩ := by
   simp [projIcc, hx, h]
-#align set.proj_Icc_of_right_le Set.proj_Icc_of_right_le
+#align set.proj_Icc_of_right_le Set.projIcc_of_right_le
 
 @[simp]
 theorem projIcc_right : projIcc a b h b = ⟨b, right_mem_Icc.2 h⟩ :=
-  proj_Icc_of_right_le h le_rfl
+  projIcc_of_right_le h le_rfl
 #align set.proj_Icc_right Set.projIcc_right
 
 theorem projIcc_eq_left (h : a < b) : projIcc a b h.le x = ⟨a, left_mem_Icc.mpr h.le⟩ ↔ x ≤ a := by
@@ -64,7 +64,7 @@ theorem projIcc_eq_left (h : a < b) : projIcc a b h.le x = ⟨a, left_mem_Icc.mp
 
 theorem projIcc_eq_right (h : a < b) : projIcc a b h.le x = ⟨b, right_mem_Icc.mpr h.le⟩ ↔ b ≤ x :=
   by
-  refine' ⟨fun h' => _, proj_Icc_of_right_le _⟩
+  refine' ⟨fun h' => _, projIcc_of_right_le _⟩
   simp_rw [Subtype.ext_iff_val, projIcc] at h'
   have := ((max_choice _ _).resolve_left (by simp [h.ne', h'])).symm.trans h'
   exact min_eq_left_iff.mp this
@@ -122,7 +122,7 @@ theorem IccExtend_left (f : Icc a b → β) : IccExtend h f a = f ⟨a, left_mem
 
 theorem IccExtend_of_right_le (f : Icc a b → β) (hx : b ≤ x) :
     IccExtend h f x = f ⟨b, right_mem_Icc.2 h⟩ :=
-  congr_arg f <| proj_Icc_of_right_le h hx
+  congr_arg f <| projIcc_of_right_le h hx
 #align set.Icc_extend_of_right_le Set.IccExtend_of_right_le
 
 @[simp]

feat port:Data.Set.Intervals.ProjIcc (#1051)