PR contents

(last sync)

chore(*): golf (#18111)

Sets

Add set.maps_to_prod_map_diagonal, set.diagonal_nonempty, and set.diagonal_subset_iff.

Filters

Generalize and rename nhds_eq_comap_uniformity_aux to filter.mem_comap_prod_mk.
Add set.nonempty.principal_ne_bot and filter.comap_id'.
Rename filter.has_basis.comp_of_surjective to filter.has_basis.comp_surjective.

Uniform spaces

Rename monotone_comp_rel to monotone.comp_rel to enable dot notation.
Add nhds_eq_comap_uniformity'.
Use 𝓝ˢ (diagonal γ) instead of ⨆ x, 𝓝 (x, x) in uniform_space_of_compact_t2.
Golf here and there.

Mathlib 4 port

Relevant parts are forward-ported in leanprover-community/mathlib4#1438

Diff

@@ -295,6 +295,9 @@ lemma maps_to_iff_exists_map_subtype : maps_to f s t ↔ ∃ g : s → t, ∀ x
 theorem maps_to' : maps_to f s t ↔ f '' s ⊆ t :=
 image_subset_iff.symm
 
+theorem maps_to_prod_map_diagonal : maps_to (prod.map f f) (diagonal α) (diagonal β) :=
+diagonal_subset_iff.2 $ λ x, rfl
+
 lemma maps_to.subset_preimage {f : α → β} {s : set α} {t : set β} (hf : maps_to f s t) :
   s ⊆ f ⁻¹' t := hf

feat(group_theory/perm/cycle/basic): Cycle on a set (#17899)

Define equiv.perm.is_cycle_on, a predicate for a permutation to be a cycle on a set.

This has two discrepancies with the existing equiv.perm.is_cycle_on (apart from the obvious one that is_cycle_on is restricted to a set):

is_cycle_on forbids fixed points (on s) while is_cycle allows them.
is_cycle forbids the identity while is_cycle_on allows it.

I think the first one isn't so bad given that is_cycle is meant to be used over the entire type (so you can't just rule out fixed points). The second one is more of a worry as I had to case-split on s.subsingleton ∨ s.nontrivial in several is_cycle_on lemmas to derive them from the corresponding is_cycle ones, while of course the is_cycle ones would also have held for a weaker version of is_cycle that allows the identity.

Diff

@@ -1449,6 +1449,12 @@ lemma inv_on : inv_on e e.symm t s :=
 lemma bij_on_image : bij_on e s (e '' s) := (e.injective.inj_on _).bij_on_image
 lemma bij_on_symm_image : bij_on e.symm (e '' s) s := e.bij_on_image.symm e.inv_on
 
+variables {e}
+
+@[simp] lemma bij_on_symm : bij_on e.symm t s ↔ bij_on e s t := bij_on_comm e.symm.inv_on
+
+alias bij_on_symm ↔ _root_.set.bij_on.of_equiv_symm _root_.set.bij_on.equiv_symm
+
 variables [decidable_eq α] {a b : α}
 
 lemma bij_on_swap (ha : a ∈ s) (hb : b ∈ s) : bij_on (swap a b) s s :=

67f36267

feat(data/set/function): ∘ lemmas (#17819)

A few lemmas about inj_on/surj_on/bij_on and ∘.

Diff

@@ -95,7 +95,7 @@ lemma restrict_extend_range (f : α → β) (g : α → γ) (g' : β → γ) :
 by convert restrict_dite _ _
 
 @[simp] lemma restrict_extend_compl_range (f : α → β) (g : α → γ) (g' : β → γ) :
-  (range f)ᶜ.restrict (extend f g g')  = g' ∘ coe :=
+  (range f)ᶜ.restrict (extend f g g') = g' ∘ coe :=
 by convert restrict_dite_compl _ _
 
 lemma range_extend_subset (f : α → β) (g : α → γ) (g' : β → γ) :
@@ -134,7 +134,7 @@ by simp only [injective, subtype.ext_iff, coe_cod_restrict_apply]
 alias injective_cod_restrict ↔ _ _root_.function.injective.cod_restrict
 
 variables {s s₁ s₂ : set α} {t t₁ t₂ : set β} {p : set γ} {f f₁ f₂ f₃ : α → β} {g g₁ g₂ : β → γ}
-  {f' f₁' f₂' : β → α} {g' : γ → β}
+  {f' f₁' f₂' : β → α} {g' : γ → β} {a : α} {b : β}
 
 /-! ### Equality on a set -/
 
@@ -144,6 +144,7 @@ def eq_on (f₁ f₂ : α → β) (s : set α) : Prop :=
 ∀ ⦃x⦄, x ∈ s → f₁ x = f₂ x
 
 @[simp] lemma eq_on_empty (f₁ f₂ : α → β) : eq_on f₁ f₂ ∅ := λ x, false.elim
+@[simp] lemma eq_on_singleton : eq_on f₁ f₂ {a} ↔ f₁ a = f₂ a := by simp [set.eq_on]
 
 @[simp] lemma restrict_eq_restrict_iff : restrict s f₁ = restrict s f₂ ↔ eq_on f₁ f₂ s :=
 restrict_eq_iff
@@ -297,9 +298,8 @@ image_subset_iff.symm
 lemma maps_to.subset_preimage {f : α → β} {s : set α} {t : set β} (hf : maps_to f s t) :
   s ⊆ f ⁻¹' t := hf
 
-@[simp] theorem maps_to_singleton {x : α} : maps_to f {x} t ↔ f x ∈ t := singleton_subset_iff
-
 theorem maps_to_empty (f : α → β) (t : set β) : maps_to f ∅ t := empty_subset _
+@[simp] lemma maps_to_singleton : maps_to f {a} t ↔ f a ∈ t := singleton_subset_iff
 
 theorem maps_to.image_subset (h : maps_to f s t) : f '' s ⊆ t :=
 maps_to'.1 h
@@ -334,6 +334,13 @@ begin
   { simp [nat.iterate, ihn] }
 end
 
+lemma maps_to_of_subsingleton' [subsingleton β] (f : α → β) (h : s.nonempty → t.nonempty) :
+  maps_to f s t :=
+λ a ha, subsingleton.mem_iff_nonempty.2 $ h ⟨a, ha⟩
+
+lemma maps_to_of_subsingleton [subsingleton α] (f : α → α) (s : set α) : maps_to f s s :=
+maps_to_of_subsingleton' _ id
+
 theorem maps_to.mono (hf : maps_to f s₁ t₁) (hs : s₂ ⊆ s₁) (ht : t₁ ⊆ t₂) :
   maps_to f s₂ t₂ :=
 λ x hx, ht (hf $ hs hx)
@@ -381,6 +388,12 @@ theorem maps_to_range (f : α → β) (s : set α) : maps_to f s (range f) :=
   maps_to f (g '' s) t ↔ maps_to (f ∘ g) s t :=
 ⟨λ h c hc, h ⟨c, hc, rfl⟩, λ h d ⟨c, hc⟩, hc.2 ▸ h hc.1⟩
 
+lemma maps_to.comp_left (g : β → γ) (hf : maps_to f s t) : maps_to (g ∘ f) s (g '' t) :=
+λ x hx, ⟨f x, hf hx, rfl⟩
+
+lemma maps_to.comp_right {s : set β} {t : set γ} (hg : maps_to g s t) (f : α → β) :
+  maps_to (g ∘ f) (f ⁻¹' s) t := λ x hx, hg hx
+
 @[simp] lemma maps_univ_to (f : α → β) (s : set β) :
   maps_to f univ s ↔ ∀ a, f a ∈ s :=
 ⟨λ h a, h (mem_univ _), λ h x _, h x⟩
@@ -490,10 +503,20 @@ lemma inj_on_of_injective (h : injective f) (s : set α) : inj_on f s :=
 
 alias inj_on_of_injective ← _root_.function.injective.inj_on
 
+lemma inj_on_id (s : set α) : inj_on id s := injective_id.inj_on _
+
 theorem inj_on.comp (hg : inj_on g t) (hf: inj_on f s) (h : maps_to f s t) :
   inj_on (g ∘ f) s :=
 λ x hx y hy heq, hf hx hy $ hg (h hx) (h hy) heq
 
+lemma inj_on.iterate {f : α → α} {s : set α} (h : inj_on f s) (hf : maps_to f s s) :
+  ∀ n, inj_on (f^[n]) s
+| 0 := inj_on_id _
+| (n + 1) := (inj_on.iterate n).comp h hf
+
+lemma inj_on_of_subsingleton [subsingleton α] (f : α → β) (s : set α) : inj_on f s :=
+(injective_of_subsingleton _).inj_on _
+
 lemma _root_.function.injective.inj_on_range (h : injective (g ∘ f)) : inj_on g (range f) :=
 by { rintros _ ⟨x, rfl⟩ _ ⟨y, rfl⟩ H, exact congr_arg f (h H) }
 
@@ -571,6 +594,8 @@ lemma surj_on_iff_exists_map_subtype :
 
 theorem surj_on_empty (f : α → β) (s : set α) : surj_on f s ∅ := empty_subset _
 
+@[simp] lemma surj_on_singleton : surj_on f s {b} ↔ b ∈ f '' s := singleton_subset_iff
+
 theorem surj_on_image (f : α → β) (s : set α) : surj_on f s (f '' s) := subset.rfl
 
 theorem surj_on.comap_nonempty (h : surj_on f s t) (ht : t.nonempty) : s.nonempty :=
@@ -607,9 +632,29 @@ theorem surj_on.inter (h₁ : surj_on f s₁ t) (h₂ : surj_on f s₂ t) (h : i
   surj_on f (s₁ ∩ s₂) t :=
 inter_self t ▸ h₁.inter_inter h₂ h
 
+lemma surj_on_id (s : set α) : surj_on id s s := by simp [surj_on]
+
 theorem surj_on.comp (hg : surj_on g t p) (hf : surj_on f s t) : surj_on (g ∘ f) s p :=
 subset.trans hg $ subset.trans (image_subset g hf) $ (image_comp g f s) ▸ subset.refl _
 
+lemma surj_on.iterate {f : α → α} {s : set α} (h : surj_on f s s) : ∀ n, surj_on (f^[n]) s s
+| 0 := surj_on_id _
+| (n + 1) := (surj_on.iterate n).comp h
+
+lemma surj_on.comp_left (hf : surj_on f s t) (g : β → γ) : surj_on (g ∘ f) s (g '' t) :=
+by { rw [surj_on, image_comp g f], exact image_subset _ hf }
+
+lemma surj_on.comp_right {s : set β} {t : set γ} (hf : surjective f) (hg : surj_on g s t) :
+  surj_on (g ∘ f) (f ⁻¹' s) t :=
+by rwa [surj_on, image_comp g f, image_preimage_eq _ hf]
+
+lemma surj_on_of_subsingleton' [subsingleton β] (f : α → β) (h : t.nonempty → s.nonempty) :
+  surj_on f s t :=
+λ a ha, subsingleton.mem_iff_nonempty.2 $ (h ⟨a, ha⟩).image _
+
+lemma surj_on_of_subsingleton [subsingleton α] (f : α → α) (s : set α) : surj_on f s s :=
+surj_on_of_subsingleton' _ id
+
 lemma surjective_iff_surj_on_univ : surjective f ↔ surj_on f univ univ :=
 by simp [surjective, surj_on, subset_def]
 
@@ -664,9 +709,11 @@ lemma bij_on.mk (h₁ : maps_to f s t) (h₂ : inj_on f s) (h₃ : surj_on f s t
       bij_on f s t :=
 ⟨h₁, h₂, h₃⟩
 
-lemma bij_on_empty (f : α → β) : bij_on f ∅ ∅ :=
+@[simp] lemma bij_on_empty (f : α → β) : bij_on f ∅ ∅ :=
 ⟨maps_to_empty f ∅, inj_on_empty f, surj_on_empty f ∅⟩
 
+@[simp] lemma bij_on_singleton : bij_on f {a} {b} ↔ f a = b := by simp [bij_on, eq_comm]
+
 lemma bij_on.inter_maps_to (h₁ : bij_on f s₁ t₁) (h₂ : maps_to f s₂ t₂) (h₃ : s₁ ∩ f ⁻¹' t₂ ⊆ s₂) :
   bij_on f (s₁ ∩ s₂) (t₁ ∩ t₂) :=
 ⟨h₁.maps_to.inter_inter h₂, h₁.inj_on.mono $ inter_subset_left _ _,
@@ -703,10 +750,23 @@ lemma bij_on.image_eq (h : bij_on f s t) :
   f '' s = t :=
 h.surj_on.image_eq_of_maps_to h.maps_to
 
+lemma bij_on_id (s : set α) : bij_on id s s := ⟨s.maps_to_id, s.inj_on_id, s.surj_on_id⟩
+
 theorem bij_on.comp (hg : bij_on g t p) (hf : bij_on f s t) : bij_on (g ∘ f) s p :=
 bij_on.mk (hg.maps_to.comp hf.maps_to) (hg.inj_on.comp hf.inj_on hf.maps_to)
   (hg.surj_on.comp hf.surj_on)
 
+lemma bij_on.iterate {f : α → α} {s : set α} (h : bij_on f s s) : ∀ n, bij_on (f^[n]) s s
+| 0 := s.bij_on_id
+| (n + 1) := (bij_on.iterate n).comp h
+
+lemma bij_on_of_subsingleton' [subsingleton α] [subsingleton β] (f : α → β)
+  (h : s.nonempty ↔ t.nonempty) : bij_on f s t :=
+⟨maps_to_of_subsingleton' _ h.1, inj_on_of_subsingleton _ _, surj_on_of_subsingleton' _ h.2⟩
+
+lemma bij_on_of_subsingleton [subsingleton α] (f : α → α) (s : set α) : bij_on f s s :=
+bij_on_of_subsingleton' _ iff.rfl
+
 theorem bij_on.bijective (h : bij_on f s t) : bijective (h.maps_to.restrict f s t) :=
 ⟨λ x y h', subtype.ext $ h.inj_on x.2 y.2 $ subtype.ext_iff.1 h',
   λ ⟨y, hy⟩, let ⟨x, hx, hxy⟩ := h.surj_on hy in ⟨⟨x, hx⟩, subtype.eq hxy⟩⟩
@@ -718,6 +778,8 @@ iff.intro
 (λ h, let ⟨map, inj, surj⟩ := h in
 ⟨iff.mpr injective_iff_inj_on_univ inj, iff.mpr surjective_iff_surj_on_univ surj⟩)
 
+alias bijective_iff_bij_on_univ ↔ _root_.function.bijective.bij_on_univ _
+
 lemma bij_on.compl (hst : bij_on f s t) (hf : bijective f) : bij_on f sᶜ tᶜ :=
 ⟨hst.surj_on.maps_to_compl hf.1, hf.1.inj_on _, hst.maps_to.surj_on_compl hf.2⟩
 
@@ -727,6 +789,9 @@ lemma bij_on.compl (hst : bij_on f s t) (hf : bijective f) : bij_on f sᶜ tᶜ
 def left_inv_on (f' : β → α) (f : α → β) (s : set α) : Prop :=
 ∀ ⦃x⦄, x ∈ s → f' (f x) = x
 
+@[simp] lemma left_inv_on_empty (f' : β → α) (f : α → β) : left_inv_on f' f ∅ := empty_subset _
+@[simp] lemma left_inv_on_singleton : left_inv_on f' f {a} ↔ f' (f a) = a := singleton_subset_iff
+
 lemma left_inv_on.eq_on (h : left_inv_on f' f s) : eq_on (f' ∘ f) id s := h
 
 lemma left_inv_on.eq (h : left_inv_on f' f s) {x} (hx : x ∈ s) : f' (f x) = x := h hx
@@ -752,6 +817,8 @@ theorem left_inv_on.surj_on (h : left_inv_on f' f s) (hf : maps_to f s t) : surj
 theorem left_inv_on.maps_to (h : left_inv_on f' f s) (hf : surj_on f s t) : maps_to f' t s :=
 λ y hy, let ⟨x, hs, hx⟩ := hf hy in by rwa [← hx, h hs]
 
+lemma left_inv_on_id (s : set α) : left_inv_on id id s := λ a _, rfl
+
 theorem left_inv_on.comp
   (hf' : left_inv_on f' f s) (hg' : left_inv_on g' g t) (hf : maps_to f s t) :
   left_inv_on (f' ∘ g') (g ∘ f) s :=
@@ -793,6 +860,9 @@ theorem left_inv_on.image_image' (hf : left_inv_on f' f s) (hs : s₁ ⊆ s) :
 @[reducible] def right_inv_on (f' : β → α) (f : α → β) (t : set β) : Prop :=
 left_inv_on f f' t
 
+@[simp] lemma right_inv_on_empty (f' : β → α) (f : α → β) : right_inv_on f' f ∅ := empty_subset _
+@[simp] lemma right_inv_on_singleton : right_inv_on f' f {b} ↔ f (f' b) = b := singleton_subset_iff
+
 lemma right_inv_on.eq_on (h : right_inv_on f' f t) : eq_on (f ∘ f') id t := h
 
 lemma right_inv_on.eq (h : right_inv_on f' f t) {y} (hy : y ∈ t) : f (f' y) = y := h hy
@@ -815,6 +885,8 @@ hf.surj_on hf'
 theorem right_inv_on.maps_to (h : right_inv_on f' f t) (hf : surj_on f' t s) : maps_to f s t :=
 h.maps_to hf
 
+lemma right_inv_on_id (s : set α) : right_inv_on id id s := λ a _, rfl
+
 theorem right_inv_on.comp (hf : right_inv_on f' f t) (hg : right_inv_on g' g p)
   (g'pt : maps_to g' p t) : right_inv_on (f' ∘ g') (g ∘ f) p :=
 hg.comp hf g'pt
@@ -843,8 +915,19 @@ theorem surj_on.left_inv_on_of_right_inv_on (hf : surj_on f s t) (hf' : right_in
 def inv_on (g : β → α) (f : α → β) (s : set α) (t : set β) : Prop :=
 left_inv_on g f s ∧ right_inv_on g f t
 
+@[simp] lemma inv_on_empty (f' : β → α) (f : α → β) : inv_on f' f ∅ ∅ := by simp [inv_on]
+@[simp] lemma inv_on_singleton : inv_on f' f {a} {b} ↔ f' (f a) = a ∧ f (f' b) = b :=
+by simp [inv_on]
+
 lemma inv_on.symm (h : inv_on f' f s t) : inv_on f f' t s := ⟨h.right, h.left⟩
 
+lemma inv_on_id (s : set α) : inv_on id id s s := ⟨s.left_inv_on_id, s.right_inv_on_id⟩
+
+lemma inv_on.comp (hf : inv_on f' f s t) (hg : inv_on g' g t p) (fst : maps_to f s t)
+  (g'pt : maps_to g' p t) :
+  inv_on (f' ∘ g') (g ∘ f) s p :=
+⟨hf.1.comp hg.1 fst, hf.2.comp hg.2 g'pt⟩
+
 lemma inv_on.mono (h : inv_on f' f s t) (hs : s₁ ⊆ s) (ht : t₁ ⊆ t) : inv_on f' f s₁ t₁ :=
 ⟨h.1.mono hs, h.2.mono ht⟩
 
@@ -855,6 +938,12 @@ theorem inv_on.bij_on (h : inv_on f' f s t) (hf : maps_to f s t) (hf' : maps_to
   bij_on f s t :=
 ⟨hf, h.left.inj_on, h.right.surj_on hf'⟩
 
+lemma bij_on.symm {g : β → α} (h : inv_on f g t s) (hf : bij_on f s t) : bij_on g t s :=
+⟨h.2.maps_to hf.surj_on, h.1.inj_on, h.2.surj_on hf.maps_to⟩
+
+lemma bij_on_comm {g : β → α} (h : inv_on f g t s) : bij_on f s t ↔ bij_on g t s :=
+⟨bij_on.symm h, bij_on.symm h.symm⟩
+
 end set
 
 /-! ### `inv_fun_on` is a left/right inverse -/
@@ -1144,6 +1233,8 @@ by simp
 
 end set
 
+open set
+
 lemma strict_mono_on.inj_on [linear_order α] [preorder β] {f : α → β} {s : set α}
   (H : strict_mono_on f s) :
   s.inj_on f :=
@@ -1311,7 +1402,7 @@ end function
 /-! ### Equivalences, permutations -/
 
 namespace set
-variables {p : β → Prop} [decidable_pred p] {f : α ≃ subtype p} {g : perm α} {s t : set α}
+variables {p : β → Prop} [decidable_pred p] {f : α ≃ subtype p} {g g₁ g₂ : perm α} {s t : set α}
 
 protected lemma maps_to.extend_domain (h : maps_to g s t) :
   maps_to (g.extend_domain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
@@ -1329,4 +1420,39 @@ protected lemma bij_on.extend_domain (h : set.bij_on g s t) :
   bij_on (g.extend_domain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
 ⟨h.maps_to.extend_domain, (g.extend_domain f).injective.inj_on _, h.surj_on.extend_domain⟩
 
+protected lemma left_inv_on.extend_domain (h : left_inv_on g₁ g₂ s) :
+  left_inv_on (g₁.extend_domain f) (g₂.extend_domain f) (coe ∘ f '' s) :=
+by { rintro _ ⟨a, ha, rfl⟩, simp_rw [extend_domain_apply_image, h ha] }
+
+protected lemma right_inv_on.extend_domain (h : right_inv_on g₁ g₂ t) :
+  right_inv_on (g₁.extend_domain f) (g₂.extend_domain f) (coe ∘ f '' t) :=
+by { rintro _ ⟨a, ha, rfl⟩, simp_rw [extend_domain_apply_image, h ha] }
+
+protected lemma inv_on.extend_domain (h : inv_on g₁ g₂ s t) :
+  inv_on (g₁.extend_domain f) (g₂.extend_domain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
+⟨h.1.extend_domain, h.2.extend_domain⟩
+
 end set
+
+namespace equiv
+variables (e : α ≃ β) {s : set α} {t : set β}
+
+lemma bij_on' (h₁ : maps_to e s t) (h₂ : maps_to e.symm t s) : bij_on e s t :=
+⟨h₁, e.injective.inj_on _, λ b hb, ⟨e.symm b, h₂ hb, apply_symm_apply _ _⟩⟩
+
+protected lemma bij_on (h : ∀ a, e a ∈ t ↔ a ∈ s) : bij_on e s t :=
+e.bij_on' (λ a, (h _).2) $ λ b hb, (h _).1 $ by rwa apply_symm_apply
+
+lemma inv_on : inv_on e e.symm t s :=
+⟨e.right_inverse_symm.left_inv_on _, e.left_inverse_symm.left_inv_on _⟩
+
+lemma bij_on_image : bij_on e s (e '' s) := (e.injective.inj_on _).bij_on_image
+lemma bij_on_symm_image : bij_on e.symm (e '' s) s := e.bij_on_image.symm e.inv_on
+
+variables [decidable_eq α] {a b : α}
+
+lemma bij_on_swap (ha : a ∈ s) (hb : b ∈ s) : bij_on (swap a b) s s :=
+(swap a b).bij_on $ λ x, by obtain rfl | hxa := eq_or_ne x a; obtain rfl | hxb := eq_or_ne x b;
+  simp [*, swap_apply_of_ne_of_ne]
+
+end equiv

d1723c04

refactor(group_theory/perm/cycle/basic): Consolidate API (#17898)

Reorganise and complete the cycle API:

Previously, is_cycle was spelling out the definition of same_cycle. Now use it explicitly.
Change binder to semi-implicit in the definition of is_cycle.
Add lemmas and iff aliases.
Golf existing proofs using those (mostly invisible from the diff because git decided I am moving the is_cycle API)
Improve lemma names, mostly for better dot notation.

New lemmas

maps_to.extend_domain
surj_on.extend_domain
bij_on.extend_domain
extend_domain_pow
extend_domain_zpow
same_cycle.rfl
eq.same_cycle
same_cycle.conj
same_cycle_conj
same_cycle_pow_right_iff
same_cycle_zpow_right_iff
same_cycle.pow_left
same_cycle.pow_right
same_cycle.zpow_left
same_cycle.zpow_left
same_cycle.of_pow
same_cycle.of_zpow
same_cycle_subtype_perm
same_cycle.subtype_perm
same_cycle_extend_domain
is_cycle.conj
is_cycle.pow_eq_one_iff'
is_cycle.pow_eq_one_iff''

Renames

order_of_is_cycle → is_cycle.order_of
is_cycle.is_cycle_conj → is_cycle.conj
is_cycle_of_is_cycle_pow → is_cycle.of_pow
is_cycle_of_is_cycle_zpow → is_cycle.of_zpow
same_cycle_cycle → is_cycle_iff_same_cycle
mem_support_pos_pow_iff_of_lt_order_of → support_pow_of_pos_of_lt_order_of and change the statement to talk about unextensionalised finset equality

Diff

@@ -37,7 +37,7 @@ universes u v w x y
 
 variables {α : Type u} {β : Type v} {π : α → Type v} {γ : Type w} {ι : Sort x}
 
-open function
+open equiv equiv.perm function
 
 namespace set
 
@@ -1307,3 +1307,26 @@ lemma antitone_on_of_right_inv_on_of_maps_to
 (monotone_on_of_right_inv_on_of_maps_to hφ.dual_left φψs ψts).dual_right
 
 end function
+
+/-! ### Equivalences, permutations -/
+
+namespace set
+variables {p : β → Prop} [decidable_pred p] {f : α ≃ subtype p} {g : perm α} {s t : set α}
+
+protected lemma maps_to.extend_domain (h : maps_to g s t) :
+  maps_to (g.extend_domain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
+by { rintro _ ⟨a, ha, rfl⟩, exact ⟨_, h ha, by rw extend_domain_apply_image⟩ }
+
+protected lemma surj_on.extend_domain (h : surj_on g s t) :
+  surj_on (g.extend_domain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
+begin
+  rintro _ ⟨a, ha, rfl⟩,
+  obtain ⟨b, hb, rfl⟩ := h ha,
+  exact ⟨_, ⟨_, hb, rfl⟩, by rw extend_domain_apply_image⟩,
+end
+
+protected lemma bij_on.extend_domain (h : set.bij_on g s t) :
+  bij_on (g.extend_domain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
+⟨h.maps_to.extend_domain, (g.extend_domain f).injective.inj_on _, h.surj_on.extend_domain⟩
+
+end set

feat(analysis/bounded_variation): evariation_on of precomposition with monotone/antitone map. (#18001)

Co-authored-by: Rémi Bottinelli <bottine@users.noreply.github.com>

Diff

@@ -1286,4 +1286,21 @@ update_comp_eq_of_not_mem_range' g a h
 
 lemma insert_inj_on (s : set α) : sᶜ.inj_on (λ a, insert a s) := λ a ha b _, (insert_inj ha).1
 
+lemma monotone_on_of_right_inv_on_of_maps_to
+  [partial_order α] [linear_order β] {φ : β → α} {ψ : α → β} {t : set β} {s : set α}
+  (hφ : monotone_on φ t) (φψs : set.right_inv_on ψ φ s) (ψts : set.maps_to ψ s t) :
+  monotone_on ψ s :=
+begin
+  rintro x xs y ys l,
+  rcases le_total (ψ x) (ψ y) with (ψxy|ψyx),
+  { exact ψxy, },
+  { cases le_antisymm l (φψs.eq ys ▸ φψs.eq xs ▸ hφ (ψts ys) (ψts xs) ψyx), refl, },
+end
+
+lemma antitone_on_of_right_inv_on_of_maps_to
+  [partial_order α] [linear_order β] {φ : β → α} {ψ : α → β} {t : set β} {s : set α}
+  (hφ : antitone_on φ t) (φψs : set.right_inv_on ψ φ s) (ψts : set.maps_to ψ s t) :
+  antitone_on ψ s :=
+(monotone_on_of_right_inv_on_of_maps_to hφ.dual_left φψs ψts).dual_right
+
 end function

3d954923

chore(data/set/lattice): move basic lemmas to basic files (#17882)

This PR moves some lemmas in data.set.lattice to data.set.basic, data.set.image, and data.set.function. They are basic enough and do not depend on the set lattice. This also helps #17880 to split data.set.pairwise and reduce the dependency of many files.

mathlib4 PR: https://github.com/leanprover-community/mathlib4/pull/1109

Diff

@@ -411,6 +411,21 @@ begin
     set.preimage_inter, subtype.coe_preimage_self, set.univ_inter],
 end
 
+variables {f} {U : ι → set β}
+
+lemma restrict_preimage_injective (hf : injective f) : injective (t.restrict_preimage f) :=
+λ x y e, subtype.mk.inj_arrow e (λ e, subtype.coe_injective (hf e))
+
+lemma restrict_preimage_surjective (hf : surjective f) : surjective (t.restrict_preimage f) :=
+λ x, ⟨⟨_, (show f (hf x).some ∈ t, from (hf x).some_spec.symm ▸ x.2)⟩, subtype.ext (hf x).some_spec⟩
+
+lemma restrict_preimage_bijective (hf : bijective f) : bijective (t.restrict_preimage f) :=
+⟨t.restrict_preimage_injective hf.1, t.restrict_preimage_surjective hf.2⟩
+
+alias set.restrict_preimage_injective  ← _root_.function.injective.restrict_preimage
+alias set.restrict_preimage_surjective ← _root_.function.surjective.restrict_preimage
+alias set.restrict_preimage_bijective  ← _root_.function.bijective.restrict_preimage
+
 end
 
 /-! ### Injectivity on a set -/
@@ -518,6 +533,25 @@ lemma inj_on.cancel_left (hg : t.inj_on g) (hf₁ : s.maps_to f₁ t) (hf₂ : s
   s.eq_on (g ∘ f₁) (g ∘ f₂) ↔ s.eq_on f₁ f₂ :=
 ⟨λ h, h.cancel_left hg hf₁ hf₂, eq_on.comp_left⟩
 
+lemma inj_on.image_inter {s t u : set α} (hf : u.inj_on f) (hs : s ⊆ u) (ht : t ⊆ u) :
+  f '' (s ∩ t) = f '' s ∩ f '' t :=
+begin
+  apply subset.antisymm (image_inter_subset _ _ _),
+  rintros x ⟨⟨y, ys, hy⟩, ⟨z, zt, hz⟩⟩,
+  have : y = z,
+  { apply hf (hs ys) (ht zt),
+    rwa ← hz at hy },
+  rw ← this at zt,
+  exact ⟨y, ⟨ys, zt⟩, hy⟩,
+end
+
+lemma _root_.disjoint.image {s t u : set α} {f : α → β} (h : disjoint s t) (hf : inj_on f u)
+  (hs : s ⊆ u) (ht : t ⊆ u) : disjoint (f '' s) (f '' t) :=
+begin
+  rw disjoint_iff_inter_eq_empty at h ⊢,
+  rw [← hf.image_inter hs ht, h, image_empty],
+end
+
 /-! ### Surjectivity on a set -/
 
 /-- `f` is surjective from `a` to `b` if `b` is contained in the image of `a`. -/

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-10-08

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

cd0c1af5

Diff

@@ -293,7 +293,7 @@ theorem EqOn.mono (hs : s₁ ⊆ s₂) (hf : EqOn f₁ f₂ s₂) : EqOn f₁ f
 #print Set.eqOn_union /-
 @[simp]
 theorem eqOn_union : EqOn f₁ f₂ (s₁ ∪ s₂) ↔ EqOn f₁ f₂ s₁ ∧ EqOn f₁ f₂ s₂ :=
-  ball_or_left
+  forall₂_or_left
 #align set.eq_on_union Set.eqOn_union
 -/

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -95,7 +95,7 @@ theorem image_restrict (f : α → β) (s t : Set α) : s.restrict f '' (coe ⁻
 #align set.image_restrict Set.image_restrict
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (a «expr ∉ » s) -/
 #print Set.restrict_dite /-
 @[simp]
 theorem restrict_dite {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
@@ -105,7 +105,7 @@ theorem restrict_dite {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s
 #align set.restrict_dite Set.restrict_dite
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (a «expr ∉ » s) -/
 #print Set.restrict_dite_compl /-
 @[simp]
 theorem restrict_dite_compl {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
@@ -1790,7 +1790,7 @@ theorem SurjOn.bijOn_subset [Nonempty α] (h : SurjOn f s t) : BijOn f (invFunOn
 #align set.surj_on.bij_on_subset Set.SurjOn.bijOn_subset
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (s' «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (s' «expr ⊆ » s) -/
 #print Set.surjOn_iff_exists_bijOn_subset /-
 theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _) (_ : s' ⊆ s), BijOn f s' t :=
   by
@@ -1939,7 +1939,7 @@ theorem piecewise_eqOn_compl (f g : α → β) : EqOn (s.piecewise f g) g (sᶜ)
 #align set.piecewise_eq_on_compl Set.piecewise_eqOn_compl
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.piecewise_le /-
 theorem piecewise_le {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g i) (h₂ : ∀ (i) (_ : i ∉ s), f₂ i ≤ g i) :
@@ -1947,7 +1947,7 @@ theorem piecewise_le {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
 #align set.piecewise_le Set.piecewise_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.le_piecewise /-
 theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, g i ≤ f₁ i) (h₂ : ∀ (i) (_ : i ∉ s), g i ≤ f₂ i) :
@@ -1956,7 +1956,7 @@ theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
 #align set.le_piecewise Set.le_piecewise
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.piecewise_le_piecewise /-
 theorem piecewise_le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
     [∀ j, Decidable (j ∈ s)] {f₁ f₂ g₁ g₂ : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g₁ i)
@@ -2073,7 +2073,7 @@ theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪
 #align set.range_piecewise Set.range_piecewise
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (y «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (y «expr ∉ » s) -/
 #print Set.injective_piecewise_iff /-
 theorem injective_piecewise_iff {f g : α → β} :
     Injective (s.piecewise f g) ↔

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -313,7 +313,7 @@ theorem EqOn.comp_left (h : s.EqOn f₁ f₂) : s.EqOn (g ∘ f₁) (g ∘ f₂)
 @[simp]
 theorem eqOn_range {ι : Sort _} {f : ι → α} {g₁ g₂ : α → β} :
     EqOn g₁ g₂ (range f) ↔ g₁ ∘ f = g₂ ∘ f :=
-  forall_range_iff.trans <| funext_iff.symm
+  forall_mem_range.trans <| funext_iff.symm
 #align set.eq_on_range Set.eqOn_range
 -/
 
@@ -993,8 +993,8 @@ theorem InjOn.image_inter {s t u : Set α} (hf : u.InjOn f) (hs : s ⊆ u) (ht :
   rintro x ⟨⟨y, ys, hy⟩, ⟨z, zt, hz⟩⟩
   have : y = z := by
     apply hf (hs ys) (ht zt)
-    rwa [← hz] at hy 
-  rw [← this] at zt 
+    rwa [← hz] at hy
+  rw [← this] at zt
   exact ⟨y, ⟨ys, zt⟩, hy⟩
 #align set.inj_on.image_inter Set.InjOn.image_inter
 -/
@@ -1697,7 +1697,7 @@ noncomputable def invFunOn (f : α → β) (s : Set α) (b : β) : α :=
 
 #print Function.invFunOn_pos /-
 theorem invFunOn_pos (h : ∃ a ∈ s, f a = b) : invFunOn f s b ∈ s ∧ f (invFunOn f s b) = b := by
-  rw [bex_def] at h  <;> rw [inv_fun_on, dif_pos h] <;> exact Classical.choose_spec h
+  rw [bex_def] at h <;> rw [inv_fun_on, dif_pos h] <;> exact Classical.choose_spec h
 #align function.inv_fun_on_pos Function.invFunOn_pos
 -/
 
@@ -1715,7 +1715,7 @@ theorem invFunOn_eq (h : ∃ a ∈ s, f a = b) : f (invFunOn f s b) = b :=
 
 #print Function.invFunOn_neg /-
 theorem invFunOn_neg (h : ¬∃ a ∈ s, f a = b) : invFunOn f s b = Classical.choice ‹Nonempty α› := by
-  rw [bex_def] at h  <;> rw [inv_fun_on, dif_neg h]
+  rw [bex_def] at h <;> rw [inv_fun_on, dif_neg h]
 #align function.inv_fun_on_neg Function.invFunOn_neg
 -/
 
@@ -2209,7 +2209,7 @@ theorem RightInverse.rightInvOn {g : β → α} (h : RightInverse f g) (s : Set
 
 #print Function.LeftInverse.rightInvOn_range /-
 theorem LeftInverse.rightInvOn_range {g : β → α} (h : LeftInverse f g) : RightInvOn f g (range g) :=
-  forall_range_iff.2 fun i => congr_arg g (h i)
+  forall_mem_range.2 fun i => congr_arg g (h i)
 #align function.left_inverse.right_inv_on_range Function.LeftInverse.rightInvOn_range
 -/
 
@@ -2247,7 +2247,7 @@ theorem surjOn_range (h : Semiconj f fa fb) (ha : Surjective fa) : SurjOn fb (ra
 theorem injOn_image (h : Semiconj f fa fb) (ha : InjOn fa s) (hf : InjOn f (fa '' s)) :
     InjOn fb (f '' s) := by
   rintro _ ⟨x, hx, rfl⟩ _ ⟨y, hy, rfl⟩ H
-  simp only [← h.eq] at H 
+  simp only [← h.eq] at H
   exact congr_arg f (ha hx hy <| hf (mem_image_of_mem fa hx) (mem_image_of_mem fa hy) H)
 #align function.semiconj.inj_on_image Function.Semiconj.injOn_image
 -/
@@ -2286,7 +2286,7 @@ theorem injOn_preimage (h : Semiconj f fa fb) {s : Set β} (hb : InjOn fb s)
   by
   intro x hx y hy H
   have := congr_arg f H
-  rw [h.eq, h.eq] at this 
+  rw [h.eq, h.eq] at this
   exact hf hx hy (hb hx hy this)
 #align function.semiconj.inj_on_preimage Function.Semiconj.injOn_preimage
 -/

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -162,7 +162,12 @@ theorem restrict_extend_compl_range (f : α → β) (g : α → γ) (g' : β →
 
 #print Set.range_extend_subset /-
 theorem range_extend_subset (f : α → β) (g : α → γ) (g' : β → γ) :
-    range (extend f g g') ⊆ range g ∪ g' '' range fᶜ := by classical
+    range (extend f g g') ⊆ range g ∪ g' '' range fᶜ := by
+  classical
+  rintro _ ⟨y, rfl⟩
+  rw [extend_def]
+  split_ifs
+  exacts [Or.inl (mem_range_self _), Or.inr (mem_image_of_mem _ h)]
 #align set.range_extend_subset Set.range_extend_subset
 -/

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -162,12 +162,7 @@ theorem restrict_extend_compl_range (f : α → β) (g : α → γ) (g' : β →
 
 #print Set.range_extend_subset /-
 theorem range_extend_subset (f : α → β) (g : α → γ) (g' : β → γ) :
-    range (extend f g g') ⊆ range g ∪ g' '' range fᶜ := by
-  classical
-  rintro _ ⟨y, rfl⟩
-  rw [extend_def]
-  split_ifs
-  exacts [Or.inl (mem_range_self _), Or.inr (mem_image_of_mem _ h)]
+    range (extend f g g') ⊆ range g ∪ g' '' range fᶜ := by classical
 #align set.range_extend_subset Set.range_extend_subset
 -/

bump to nightly-2023-12-26-06

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

c39bd29b

Diff

@@ -685,12 +685,12 @@ theorem mapsTo_range (f : α → β) (s : Set α) : MapsTo f s (range f) :=
 #align set.maps_to_range Set.mapsTo_range
 -/
 
-#print Set.maps_image_to /-
+#print Set.mapsTo_image_iff /-
 @[simp]
-theorem maps_image_to (f : α → β) (g : γ → α) (s : Set γ) (t : Set β) :
+theorem mapsTo_image_iff (f : α → β) (g : γ → α) (s : Set γ) (t : Set β) :
     MapsTo f (g '' s) t ↔ MapsTo (f ∘ g) s t :=
   ⟨fun h c hc => h ⟨c, hc, rfl⟩, fun h d ⟨c, hc⟩ => hc.2 ▸ h hc.1⟩
-#align set.maps_image_to Set.maps_image_to
+#align set.maps_image_to Set.mapsTo_image_iff
 -/
 
 #print Set.MapsTo.comp_left /-

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) 2014 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
 -/
-import Mathbin.Data.Set.Prod
-import Mathbin.Logic.Function.Conjugate
+import Data.Set.Prod
+import Logic.Function.Conjugate
 
 #align_import data.set.function from "leanprover-community/mathlib"@"f974ae84dfc9fea6a036a8f30f09414254e3bc40"
 
@@ -95,7 +95,7 @@ theorem image_restrict (f : α → β) (s t : Set α) : s.restrict f '' (coe ⁻
 #align set.image_restrict Set.image_restrict
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a «expr ∉ » s) -/
 #print Set.restrict_dite /-
 @[simp]
 theorem restrict_dite {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
@@ -105,7 +105,7 @@ theorem restrict_dite {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s
 #align set.restrict_dite Set.restrict_dite
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a «expr ∉ » s) -/
 #print Set.restrict_dite_compl /-
 @[simp]
 theorem restrict_dite_compl {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
@@ -1790,7 +1790,7 @@ theorem SurjOn.bijOn_subset [Nonempty α] (h : SurjOn f s t) : BijOn f (invFunOn
 #align set.surj_on.bij_on_subset Set.SurjOn.bijOn_subset
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (s' «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (s' «expr ⊆ » s) -/
 #print Set.surjOn_iff_exists_bijOn_subset /-
 theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _) (_ : s' ⊆ s), BijOn f s' t :=
   by
@@ -1939,7 +1939,7 @@ theorem piecewise_eqOn_compl (f g : α → β) : EqOn (s.piecewise f g) g (sᶜ)
 #align set.piecewise_eq_on_compl Set.piecewise_eqOn_compl
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.piecewise_le /-
 theorem piecewise_le {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g i) (h₂ : ∀ (i) (_ : i ∉ s), f₂ i ≤ g i) :
@@ -1947,7 +1947,7 @@ theorem piecewise_le {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
 #align set.piecewise_le Set.piecewise_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.le_piecewise /-
 theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, g i ≤ f₁ i) (h₂ : ∀ (i) (_ : i ∉ s), g i ≤ f₂ i) :
@@ -1956,7 +1956,7 @@ theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
 #align set.le_piecewise Set.le_piecewise
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.piecewise_le_piecewise /-
 theorem piecewise_le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
     [∀ j, Decidable (j ∈ s)] {f₁ f₂ g₁ g₂ : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g₁ i)
@@ -2073,7 +2073,7 @@ theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪
 #align set.range_piecewise Set.range_piecewise
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (y «expr ∉ » s) -/
 #print Set.injective_piecewise_iff /-
 theorem injective_piecewise_iff {f g : α → β} :
     Injective (s.piecewise f g) ↔

bump to nightly-2023-08-23-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

f612b9e0

Diff

@@ -212,7 +212,7 @@ theorem injective_codRestrict {f : ι → α} {s : Set α} (h : ∀ x, f x ∈ s
 #align set.injective_cod_restrict Set.injective_codRestrict
 -/
 
-alias injective_cod_restrict ↔ _ _root_.function.injective.cod_restrict
+alias ⟨_, _root_.function.injective.cod_restrict⟩ := injective_cod_restrict
 #align function.injective.cod_restrict Function.Injective.codRestrict
 
 variable {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {p : Set γ} {f f₁ f₂ f₃ : α → β} {g g₁ g₂ : β → γ}
@@ -317,7 +317,7 @@ theorem eqOn_range {ι : Sort _} {f : ι → α} {g₁ g₂ : α → β} :
 #align set.eq_on_range Set.eqOn_range
 -/
 
-alias eq_on_range ↔ eq_on.comp_eq _
+alias ⟨eq_on.comp_eq, _⟩ := eq_on_range
 #align set.eq_on.comp_eq Set.EqOn.comp_eq
 
 /-! ### Congruence lemmas -/
@@ -777,13 +777,13 @@ theorem restrictPreimage_bijective (hf : Bijective f) : Bijective (t.restrictPre
 #align set.restrict_preimage_bijective Set.restrictPreimage_bijective
 -/
 
-alias Set.restrictPreimage_injective ← _root_.function.injective.restrict_preimage
+alias _root_.function.injective.restrict_preimage := Set.restrictPreimage_injective
 #align function.injective.restrict_preimage Function.Injective.restrictPreimage
 
-alias Set.restrictPreimage_surjective ← _root_.function.surjective.restrict_preimage
+alias _root_.function.surjective.restrict_preimage := Set.restrictPreimage_surjective
 #align function.surjective.restrict_preimage Function.Surjective.restrictPreimage
 
-alias Set.restrictPreimage_bijective ← _root_.function.bijective.restrict_preimage
+alias _root_.function.bijective.restrict_preimage := Set.restrictPreimage_bijective
 #align function.bijective.restrict_preimage Function.Bijective.restrictPreimage
 
 end
@@ -830,7 +830,7 @@ theorem InjOn.ne_iff {x y} (h : InjOn f s) (hx : x ∈ s) (hy : y ∈ s) : f x 
 #align set.inj_on.ne_iff Set.InjOn.ne_iff
 -/
 
-alias inj_on.ne_iff ↔ _ inj_on.ne
+alias ⟨_, inj_on.ne⟩ := inj_on.ne_iff
 #align set.inj_on.ne Set.InjOn.ne
 
 #print Set.InjOn.congr /-
@@ -886,7 +886,7 @@ theorem injOn_of_injective (h : Injective f) (s : Set α) : InjOn f s := fun x h
 #align set.inj_on_of_injective Set.injOn_of_injective
 -/
 
-alias inj_on_of_injective ← _root_.function.injective.inj_on
+alias _root_.function.injective.inj_on := inj_on_of_injective
 #align function.injective.inj_on Function.Injective.injOn
 
 #print Set.injOn_id /-
@@ -928,7 +928,7 @@ theorem injOn_iff_injective : InjOn f s ↔ Injective (s.restrict f) :=
 #align set.inj_on_iff_injective Set.injOn_iff_injective
 -/
 
-alias inj_on_iff_injective ↔ inj_on.injective _
+alias ⟨inj_on.injective, _⟩ := inj_on_iff_injective
 #align set.inj_on.injective Set.InjOn.injective
 
 #print Set.MapsTo.restrict_inj /-
@@ -1380,7 +1380,7 @@ theorem bijective_iff_bijOn_univ : Bijective f ↔ BijOn f univ univ :=
 #align set.bijective_iff_bij_on_univ Set.bijective_iff_bijOn_univ
 -/
 
-alias bijective_iff_bij_on_univ ↔ _root_.function.bijective.bij_on_univ _
+alias ⟨_root_.function.bijective.bij_on_univ, _⟩ := bijective_iff_bij_on_univ
 #align function.bijective.bij_on_univ Function.Bijective.bijOn_univ
 
 #print Set.BijOn.compl /-
@@ -2166,7 +2166,7 @@ theorem strictMono_restrict [Preorder α] [Preorder β] {f : α → β} {s : Set
 #align strict_mono_restrict strictMono_restrict
 -/
 
-alias strictMono_restrict ↔ _root_.strict_mono.of_restrict _root_.strict_mono_on.restrict
+alias ⟨_root_.strict_mono.of_restrict, _root_.strict_mono_on.restrict⟩ := strictMono_restrict
 #align strict_mono.of_restrict StrictMono.of_restrict
 #align strict_mono_on.restrict StrictMonoOn.restrict
 
@@ -2433,7 +2433,7 @@ theorem bijOn_symm : BijOn e.symm t s ↔ BijOn e s t :=
 #align equiv.bij_on_symm Equiv.bijOn_symm
 -/
 
-alias bij_on_symm ↔ _root_.set.bij_on.of_equiv_symm _root_.set.bij_on.equiv_symm
+alias ⟨_root_.set.bij_on.of_equiv_symm, _root_.set.bij_on.equiv_symm⟩ := bij_on_symm
 #align set.bij_on.of_equiv_symm Set.BijOn.of_equiv_symm
 #align set.bij_on.equiv_symm Set.BijOn.equiv_symm

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) 2014 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
-
-! This file was ported from Lean 3 source module data.set.function
-! leanprover-community/mathlib commit f974ae84dfc9fea6a036a8f30f09414254e3bc40
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Set.Prod
 import Mathbin.Logic.Function.Conjugate
 
+#align_import data.set.function from "leanprover-community/mathlib"@"f974ae84dfc9fea6a036a8f30f09414254e3bc40"
+
 /-!
 # Functions over sets
 
@@ -98,7 +95,7 @@ theorem image_restrict (f : α → β) (s t : Set α) : s.restrict f '' (coe ⁻
 #align set.image_restrict Set.image_restrict
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
 #print Set.restrict_dite /-
 @[simp]
 theorem restrict_dite {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
@@ -108,7 +105,7 @@ theorem restrict_dite {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s
 #align set.restrict_dite Set.restrict_dite
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
 #print Set.restrict_dite_compl /-
 @[simp]
 theorem restrict_dite_compl {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
@@ -1793,7 +1790,7 @@ theorem SurjOn.bijOn_subset [Nonempty α] (h : SurjOn f s t) : BijOn f (invFunOn
 #align set.surj_on.bij_on_subset Set.SurjOn.bijOn_subset
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (s' «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (s' «expr ⊆ » s) -/
 #print Set.surjOn_iff_exists_bijOn_subset /-
 theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _) (_ : s' ⊆ s), BijOn f s' t :=
   by
@@ -1942,7 +1939,7 @@ theorem piecewise_eqOn_compl (f g : α → β) : EqOn (s.piecewise f g) g (sᶜ)
 #align set.piecewise_eq_on_compl Set.piecewise_eqOn_compl
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.piecewise_le /-
 theorem piecewise_le {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g i) (h₂ : ∀ (i) (_ : i ∉ s), f₂ i ≤ g i) :
@@ -1950,7 +1947,7 @@ theorem piecewise_le {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
 #align set.piecewise_le Set.piecewise_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.le_piecewise /-
 theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, g i ≤ f₁ i) (h₂ : ∀ (i) (_ : i ∉ s), g i ≤ f₂ i) :
@@ -1959,7 +1956,7 @@ theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
 #align set.le_piecewise Set.le_piecewise
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.piecewise_le_piecewise /-
 theorem piecewise_le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
     [∀ j, Decidable (j ∈ s)] {f₁ f₂ g₁ g₂ : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g₁ i)
@@ -2076,7 +2073,7 @@ theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪
 #align set.range_piecewise Set.range_piecewise
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ∉ » s) -/
 #print Set.injective_piecewise_iff /-
 theorem injective_piecewise_iff {f g : α → β} :
     Injective (s.piecewise f g) ↔

bump to nightly-2023-07-07-13

mathlib commit https://github.com/leanprover-community/mathlib/commit/8905e5ed90859939681a725b00f6063e65096d95

569666a8

Diff

@@ -238,9 +238,11 @@ theorem eqOn_empty (f₁ f₂ : α → β) : EqOn f₁ f₂ ∅ := fun x => Fals
 #align set.eq_on_empty Set.eqOn_empty
 -/
 
+#print Set.eqOn_singleton /-
 @[simp]
 theorem eqOn_singleton : EqOn f₁ f₂ {a} ↔ f₁ a = f₂ a := by simp [Set.EqOn]
 #align set.eq_on_singleton Set.eqOn_singleton
+-/
 
 #print Set.restrict_eq_restrict_iff /-
 @[simp]

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -58,83 +58,112 @@ def restrict (s : Set α) (f : ∀ a : α, π a) : ∀ a : s, π a := fun x => f
 #align set.restrict Set.restrict
 -/
 
+#print Set.restrict_eq /-
 theorem restrict_eq (f : α → β) (s : Set α) : s.restrict f = f ∘ coe :=
   rfl
 #align set.restrict_eq Set.restrict_eq
+-/
 
+#print Set.restrict_apply /-
 @[simp]
 theorem restrict_apply (f : α → β) (s : Set α) (x : s) : s.restrict f x = f x :=
   rfl
 #align set.restrict_apply Set.restrict_apply
+-/
 
+#print Set.restrict_eq_iff /-
 theorem restrict_eq_iff {f : ∀ a, π a} {s : Set α} {g : ∀ a : s, π a} :
     restrict s f = g ↔ ∀ (a) (ha : a ∈ s), f a = g ⟨a, ha⟩ :=
   funext_iff.trans Subtype.forall
 #align set.restrict_eq_iff Set.restrict_eq_iff
+-/
 
+#print Set.eq_restrict_iff /-
 theorem eq_restrict_iff {s : Set α} {f : ∀ a : s, π a} {g : ∀ a, π a} :
     f = restrict s g ↔ ∀ (a) (ha : a ∈ s), f ⟨a, ha⟩ = g a :=
   funext_iff.trans Subtype.forall
 #align set.eq_restrict_iff Set.eq_restrict_iff
+-/
 
+#print Set.range_restrict /-
 @[simp]
 theorem range_restrict (f : α → β) (s : Set α) : Set.range (s.restrict f) = f '' s :=
   (range_comp _ _).trans <| congr_arg ((· '' ·) f) Subtype.range_coe
 #align set.range_restrict Set.range_restrict
+-/
 
+#print Set.image_restrict /-
 theorem image_restrict (f : α → β) (s t : Set α) : s.restrict f '' (coe ⁻¹' t) = f '' (t ∩ s) := by
   rw [restrict, image_comp, image_preimage_eq_inter_range, Subtype.range_coe]
 #align set.image_restrict Set.image_restrict
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ∉ » s) -/
+#print Set.restrict_dite /-
 @[simp]
 theorem restrict_dite {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
     (g : ∀ (a) (_ : a ∉ s), β) :
     (s.restrict fun a => if h : a ∈ s then f a h else g a h) = fun a => f a a.2 :=
   funext fun a => dif_pos a.2
 #align set.restrict_dite Set.restrict_dite
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ∉ » s) -/
+#print Set.restrict_dite_compl /-
 @[simp]
 theorem restrict_dite_compl {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
     (g : ∀ (a) (_ : a ∉ s), β) :
     (sᶜ.restrict fun a => if h : a ∈ s then f a h else g a h) = fun a => g a a.2 :=
   funext fun a => dif_neg a.2
 #align set.restrict_dite_compl Set.restrict_dite_compl
+-/
 
+#print Set.restrict_ite /-
 @[simp]
 theorem restrict_ite (f g : α → β) (s : Set α) [∀ x, Decidable (x ∈ s)] :
     (s.restrict fun a => if a ∈ s then f a else g a) = s.restrict f :=
   restrict_dite _ _
 #align set.restrict_ite Set.restrict_ite
+-/
 
+#print Set.restrict_ite_compl /-
 @[simp]
 theorem restrict_ite_compl (f g : α → β) (s : Set α) [∀ x, Decidable (x ∈ s)] :
     (sᶜ.restrict fun a => if a ∈ s then f a else g a) = sᶜ.restrict g :=
   restrict_dite_compl _ _
 #align set.restrict_ite_compl Set.restrict_ite_compl
+-/
 
+#print Set.restrict_piecewise /-
 @[simp]
 theorem restrict_piecewise (f g : α → β) (s : Set α) [∀ x, Decidable (x ∈ s)] :
     s.restrict (piecewise s f g) = s.restrict f :=
   restrict_ite _ _ _
 #align set.restrict_piecewise Set.restrict_piecewise
+-/
 
+#print Set.restrict_piecewise_compl /-
 @[simp]
 theorem restrict_piecewise_compl (f g : α → β) (s : Set α) [∀ x, Decidable (x ∈ s)] :
     sᶜ.restrict (piecewise s f g) = sᶜ.restrict g :=
   restrict_ite_compl _ _ _
 #align set.restrict_piecewise_compl Set.restrict_piecewise_compl
+-/
 
+#print Set.restrict_extend_range /-
 theorem restrict_extend_range (f : α → β) (g : α → γ) (g' : β → γ) :
     (range f).restrict (extend f g g') = fun x => g x.coe_prop.some := by convert restrict_dite _ _
 #align set.restrict_extend_range Set.restrict_extend_range
+-/
 
+#print Set.restrict_extend_compl_range /-
 @[simp]
 theorem restrict_extend_compl_range (f : α → β) (g : α → γ) (g' : β → γ) :
     range fᶜ.restrict (extend f g g') = g' ∘ coe := by convert restrict_dite_compl _ _
 #align set.restrict_extend_compl_range Set.restrict_extend_compl_range
+-/
 
+#print Set.range_extend_subset /-
 theorem range_extend_subset (f : α → β) (g : α → γ) (g' : β → γ) :
     range (extend f g g') ⊆ range g ∪ g' '' range fᶜ := by
   classical
@@ -143,7 +172,9 @@ theorem range_extend_subset (f : α → β) (g : α → γ) (g' : β → γ) :
   split_ifs
   exacts [Or.inl (mem_range_self _), Or.inr (mem_image_of_mem _ h)]
 #align set.range_extend_subset Set.range_extend_subset
+-/
 
+#print Set.range_extend /-
 theorem range_extend {f : α → β} (hf : Injective f) (g : α → γ) (g' : β → γ) :
     range (extend f g g') = range g ∪ g' '' range fᶜ :=
   by
@@ -151,6 +182,7 @@ theorem range_extend {f : α → β} (hf : Injective f) (g : α → γ) (g' : β
   rintro z (⟨x, rfl⟩ | ⟨y, hy, rfl⟩)
   exacts [⟨f x, hf.extend_apply _ _ _⟩, ⟨y, extend_apply' _ _ _ hy⟩]
 #align set.range_extend Set.range_extend
+-/
 
 #print Set.codRestrict /-
 /-- Restrict codomain of a function `f` to a set `s`. Same as `subtype.coind` but this version
@@ -159,23 +191,29 @@ def codRestrict (f : ι → α) (s : Set α) (h : ∀ x, f x ∈ s) : ι → s :
 #align set.cod_restrict Set.codRestrict
 -/
 
+#print Set.val_codRestrict_apply /-
 @[simp]
 theorem val_codRestrict_apply (f : ι → α) (s : Set α) (h : ∀ x, f x ∈ s) (x : ι) :
     (codRestrict f s h x : α) = f x :=
   rfl
 #align set.coe_cod_restrict_apply Set.val_codRestrict_apply
+-/
 
+#print Set.restrict_comp_codRestrict /-
 @[simp]
 theorem restrict_comp_codRestrict {f : ι → α} {g : α → β} {b : Set α} (h : ∀ x, f x ∈ b) :
     b.restrict g ∘ b.codRestrict f h = g ∘ f :=
   rfl
 #align set.restrict_comp_cod_restrict Set.restrict_comp_codRestrict
+-/
 
+#print Set.injective_codRestrict /-
 @[simp]
 theorem injective_codRestrict {f : ι → α} {s : Set α} (h : ∀ x, f x ∈ s) :
     Injective (codRestrict f s h) ↔ Injective f := by
   simp only [injective, Subtype.ext_iff, coe_cod_restrict_apply]
 #align set.injective_cod_restrict Set.injective_codRestrict
+-/
 
 alias injective_cod_restrict ↔ _ _root_.function.injective.cod_restrict
 #align function.injective.cod_restrict Function.Injective.codRestrict
@@ -194,65 +232,91 @@ def EqOn (f₁ f₂ : α → β) (s : Set α) : Prop :=
 #align set.eq_on Set.EqOn
 -/
 
+#print Set.eqOn_empty /-
 @[simp]
 theorem eqOn_empty (f₁ f₂ : α → β) : EqOn f₁ f₂ ∅ := fun x => False.elim
 #align set.eq_on_empty Set.eqOn_empty
+-/
 
 @[simp]
 theorem eqOn_singleton : EqOn f₁ f₂ {a} ↔ f₁ a = f₂ a := by simp [Set.EqOn]
 #align set.eq_on_singleton Set.eqOn_singleton
 
+#print Set.restrict_eq_restrict_iff /-
 @[simp]
 theorem restrict_eq_restrict_iff : restrict s f₁ = restrict s f₂ ↔ EqOn f₁ f₂ s :=
   restrict_eq_iff
 #align set.restrict_eq_restrict_iff Set.restrict_eq_restrict_iff
+-/
 
+#print Set.EqOn.symm /-
 @[symm]
 theorem EqOn.symm (h : EqOn f₁ f₂ s) : EqOn f₂ f₁ s := fun x hx => (h hx).symm
 #align set.eq_on.symm Set.EqOn.symm
+-/
 
+#print Set.eqOn_comm /-
 theorem eqOn_comm : EqOn f₁ f₂ s ↔ EqOn f₂ f₁ s :=
   ⟨EqOn.symm, EqOn.symm⟩
 #align set.eq_on_comm Set.eqOn_comm
+-/
 
+#print Set.eqOn_refl /-
 @[refl]
 theorem eqOn_refl (f : α → β) (s : Set α) : EqOn f f s := fun _ _ => rfl
 #align set.eq_on_refl Set.eqOn_refl
+-/
 
+#print Set.EqOn.trans /-
 @[trans]
 theorem EqOn.trans (h₁ : EqOn f₁ f₂ s) (h₂ : EqOn f₂ f₃ s) : EqOn f₁ f₃ s := fun x hx =>
   (h₁ hx).trans (h₂ hx)
 #align set.eq_on.trans Set.EqOn.trans
+-/
 
+#print Set.EqOn.image_eq /-
 theorem EqOn.image_eq (heq : EqOn f₁ f₂ s) : f₁ '' s = f₂ '' s :=
   image_congr HEq
 #align set.eq_on.image_eq Set.EqOn.image_eq
+-/
 
+#print Set.EqOn.inter_preimage_eq /-
 theorem EqOn.inter_preimage_eq (heq : EqOn f₁ f₂ s) (t : Set β) : s ∩ f₁ ⁻¹' t = s ∩ f₂ ⁻¹' t :=
   ext fun x => and_congr_right_iff.2 fun hx => by rw [mem_preimage, mem_preimage, HEq hx]
 #align set.eq_on.inter_preimage_eq Set.EqOn.inter_preimage_eq
+-/
 
+#print Set.EqOn.mono /-
 theorem EqOn.mono (hs : s₁ ⊆ s₂) (hf : EqOn f₁ f₂ s₂) : EqOn f₁ f₂ s₁ := fun x hx => hf (hs hx)
 #align set.eq_on.mono Set.EqOn.mono
+-/
 
+#print Set.eqOn_union /-
 @[simp]
 theorem eqOn_union : EqOn f₁ f₂ (s₁ ∪ s₂) ↔ EqOn f₁ f₂ s₁ ∧ EqOn f₁ f₂ s₂ :=
   ball_or_left
 #align set.eq_on_union Set.eqOn_union
+-/
 
+#print Set.EqOn.union /-
 theorem EqOn.union (h₁ : EqOn f₁ f₂ s₁) (h₂ : EqOn f₁ f₂ s₂) : EqOn f₁ f₂ (s₁ ∪ s₂) :=
   eqOn_union.2 ⟨h₁, h₂⟩
 #align set.eq_on.union Set.EqOn.union
+-/
 
+#print Set.EqOn.comp_left /-
 theorem EqOn.comp_left (h : s.EqOn f₁ f₂) : s.EqOn (g ∘ f₁) (g ∘ f₂) := fun a ha =>
   congr_arg _ <| h ha
 #align set.eq_on.comp_left Set.EqOn.comp_left
+-/
 
+#print Set.eqOn_range /-
 @[simp]
 theorem eqOn_range {ι : Sort _} {f : ι → α} {g₁ g₂ : α → β} :
     EqOn g₁ g₂ (range f) ↔ g₁ ∘ f = g₂ ∘ f :=
   forall_range_iff.trans <| funext_iff.symm
 #align set.eq_on_range Set.eqOn_range
+-/
 
 alias eq_on_range ↔ eq_on.comp_eq _
 #align set.eq_on.comp_eq Set.EqOn.comp_eq
@@ -264,43 +328,59 @@ section Order
 
 variable [Preorder α] [Preorder β]
 
+#print MonotoneOn.congr /-
 theorem MonotoneOn.congr (h₁ : MonotoneOn f₁ s) (h : s.EqOn f₁ f₂) : MonotoneOn f₂ s :=
   by
   intro a ha b hb hab
   rw [← h ha, ← h hb]
   exact h₁ ha hb hab
 #align monotone_on.congr MonotoneOn.congr
+-/
 
+#print AntitoneOn.congr /-
 theorem AntitoneOn.congr (h₁ : AntitoneOn f₁ s) (h : s.EqOn f₁ f₂) : AntitoneOn f₂ s :=
   h₁.dual_right.congr h
 #align antitone_on.congr AntitoneOn.congr
+-/
 
+#print StrictMonoOn.congr /-
 theorem StrictMonoOn.congr (h₁ : StrictMonoOn f₁ s) (h : s.EqOn f₁ f₂) : StrictMonoOn f₂ s :=
   by
   intro a ha b hb hab
   rw [← h ha, ← h hb]
   exact h₁ ha hb hab
 #align strict_mono_on.congr StrictMonoOn.congr
+-/
 
+#print StrictAntiOn.congr /-
 theorem StrictAntiOn.congr (h₁ : StrictAntiOn f₁ s) (h : s.EqOn f₁ f₂) : StrictAntiOn f₂ s :=
   h₁.dual_right.congr h
 #align strict_anti_on.congr StrictAntiOn.congr
+-/
 
+#print Set.EqOn.congr_monotoneOn /-
 theorem EqOn.congr_monotoneOn (h : s.EqOn f₁ f₂) : MonotoneOn f₁ s ↔ MonotoneOn f₂ s :=
   ⟨fun h₁ => h₁.congr h, fun h₂ => h₂.congr h.symm⟩
 #align set.eq_on.congr_monotone_on Set.EqOn.congr_monotoneOn
+-/
 
+#print Set.EqOn.congr_antitoneOn /-
 theorem EqOn.congr_antitoneOn (h : s.EqOn f₁ f₂) : AntitoneOn f₁ s ↔ AntitoneOn f₂ s :=
   ⟨fun h₁ => h₁.congr h, fun h₂ => h₂.congr h.symm⟩
 #align set.eq_on.congr_antitone_on Set.EqOn.congr_antitoneOn
+-/
 
+#print Set.EqOn.congr_strictMonoOn /-
 theorem EqOn.congr_strictMonoOn (h : s.EqOn f₁ f₂) : StrictMonoOn f₁ s ↔ StrictMonoOn f₂ s :=
   ⟨fun h₁ => h₁.congr h, fun h₂ => h₂.congr h.symm⟩
 #align set.eq_on.congr_strict_mono_on Set.EqOn.congr_strictMonoOn
+-/
 
+#print Set.EqOn.congr_strictAntiOn /-
 theorem EqOn.congr_strictAntiOn (h : s.EqOn f₁ f₂) : StrictAntiOn f₁ s ↔ StrictAntiOn f₂ s :=
   ⟨fun h₁ => h₁.congr h, fun h₂ => h₂.congr h.symm⟩
 #align set.eq_on.congr_strict_anti_on Set.EqOn.congr_strictAntiOn
+-/
 
 end Order
 
@@ -311,37 +391,53 @@ section Mono
 
 variable [Preorder α] [Preorder β]
 
+#print MonotoneOn.mono /-
 theorem MonotoneOn.mono (h : MonotoneOn f s) (h' : s₂ ⊆ s) : MonotoneOn f s₂ := fun x hx y hy =>
   h (h' hx) (h' hy)
 #align monotone_on.mono MonotoneOn.mono
+-/
 
+#print AntitoneOn.mono /-
 theorem AntitoneOn.mono (h : AntitoneOn f s) (h' : s₂ ⊆ s) : AntitoneOn f s₂ := fun x hx y hy =>
   h (h' hx) (h' hy)
 #align antitone_on.mono AntitoneOn.mono
+-/
 
+#print StrictMonoOn.mono /-
 theorem StrictMonoOn.mono (h : StrictMonoOn f s) (h' : s₂ ⊆ s) : StrictMonoOn f s₂ :=
   fun x hx y hy => h (h' hx) (h' hy)
 #align strict_mono_on.mono StrictMonoOn.mono
+-/
 
+#print StrictAntiOn.mono /-
 theorem StrictAntiOn.mono (h : StrictAntiOn f s) (h' : s₂ ⊆ s) : StrictAntiOn f s₂ :=
   fun x hx y hy => h (h' hx) (h' hy)
 #align strict_anti_on.mono StrictAntiOn.mono
+-/
 
+#print MonotoneOn.monotone /-
 protected theorem MonotoneOn.monotone (h : MonotoneOn f s) : Monotone (f ∘ coe : s → β) :=
   fun x y hle => h x.coe_prop y.coe_prop hle
 #align monotone_on.monotone MonotoneOn.monotone
+-/
 
+#print AntitoneOn.monotone /-
 protected theorem AntitoneOn.monotone (h : AntitoneOn f s) : Antitone (f ∘ coe : s → β) :=
   fun x y hle => h x.coe_prop y.coe_prop hle
 #align antitone_on.monotone AntitoneOn.monotone
+-/
 
+#print StrictMonoOn.strictMono /-
 protected theorem StrictMonoOn.strictMono (h : StrictMonoOn f s) : StrictMono (f ∘ coe : s → β) :=
   fun x y hlt => h x.coe_prop y.coe_prop hlt
 #align strict_mono_on.strict_mono StrictMonoOn.strictMono
+-/
 
+#print StrictAntiOn.strictAnti /-
 protected theorem StrictAntiOn.strictAnti (h : StrictAntiOn f s) : StrictAnti (f ∘ coe : s → β) :=
   fun x y hlt => h x.coe_prop y.coe_prop hlt
 #align strict_anti_on.strict_anti StrictAntiOn.strictAnti
+-/
 
 end Mono
 
@@ -363,50 +459,68 @@ def MapsTo.restrict (f : α → β) (s : Set α) (t : Set β) (h : MapsTo f s t)
 #align set.maps_to.restrict Set.MapsTo.restrict
 -/
 
+#print Set.MapsTo.val_restrict_apply /-
 @[simp]
 theorem MapsTo.val_restrict_apply (h : MapsTo f s t) (x : s) : (h.restrict f s t x : β) = f x :=
   rfl
 #align set.maps_to.coe_restrict_apply Set.MapsTo.val_restrict_apply
+-/
 
+#print Set.codRestrict_restrict /-
 /-- Restricting the domain and then the codomain is the same as `maps_to.restrict`. -/
 @[simp]
 theorem codRestrict_restrict (h : ∀ x : s, f x ∈ t) :
     codRestrict (s.restrict f) t h = MapsTo.restrict f s t fun x hx => h ⟨x, hx⟩ :=
   rfl
 #align set.cod_restrict_restrict Set.codRestrict_restrict
+-/
 
+#print Set.MapsTo.restrict_eq_codRestrict /-
 /-- Reverse of `set.cod_restrict_restrict`. -/
 theorem MapsTo.restrict_eq_codRestrict (h : MapsTo f s t) :
     h.restrict f s t = codRestrict (s.restrict f) t fun x => h x.2 :=
   rfl
 #align set.maps_to.restrict_eq_cod_restrict Set.MapsTo.restrict_eq_codRestrict
+-/
 
+#print Set.MapsTo.coe_restrict /-
 theorem MapsTo.coe_restrict (h : Set.MapsTo f s t) : coe ∘ h.restrict f s t = s.restrict f :=
   rfl
 #align set.maps_to.coe_restrict Set.MapsTo.coe_restrict
+-/
 
+#print Set.MapsTo.range_restrict /-
 theorem MapsTo.range_restrict (f : α → β) (s : Set α) (t : Set β) (h : MapsTo f s t) :
     range (h.restrict f s t) = coe ⁻¹' (f '' s) :=
   Set.range_subtype_map f h
 #align set.maps_to.range_restrict Set.MapsTo.range_restrict
+-/
 
+#print Set.mapsTo_iff_exists_map_subtype /-
 theorem mapsTo_iff_exists_map_subtype : MapsTo f s t ↔ ∃ g : s → t, ∀ x : s, f x = g x :=
   ⟨fun h => ⟨h.restrict f s t, fun _ => rfl⟩, fun ⟨g, hg⟩ x hx => by erw [hg ⟨x, hx⟩];
     apply Subtype.coe_prop⟩
 #align set.maps_to_iff_exists_map_subtype Set.mapsTo_iff_exists_map_subtype
+-/
 
+#print Set.mapsTo' /-
 theorem mapsTo' : MapsTo f s t ↔ f '' s ⊆ t :=
   image_subset_iff.symm
 #align set.maps_to' Set.mapsTo'
+-/
 
+#print Set.mapsTo_prod_map_diagonal /-
 theorem mapsTo_prod_map_diagonal : MapsTo (Prod.map f f) (diagonal α) (diagonal β) :=
   diagonal_subset_iff.2 fun x => rfl
 #align set.maps_to_prod_map_diagonal Set.mapsTo_prod_map_diagonal
+-/
 
+#print Set.MapsTo.subset_preimage /-
 theorem MapsTo.subset_preimage {f : α → β} {s : Set α} {t : Set β} (hf : MapsTo f s t) :
     s ⊆ f ⁻¹' t :=
   hf
 #align set.maps_to.subset_preimage Set.MapsTo.subset_preimage
+-/
 
 #print Set.mapsTo_empty /-
 theorem mapsTo_empty (f : α → β) (t : Set β) : MapsTo f ∅ t :=
@@ -414,30 +528,42 @@ theorem mapsTo_empty (f : α → β) (t : Set β) : MapsTo f ∅ t :=
 #align set.maps_to_empty Set.mapsTo_empty
 -/
 
+#print Set.mapsTo_singleton /-
 @[simp]
 theorem mapsTo_singleton : MapsTo f {a} t ↔ f a ∈ t :=
   singleton_subset_iff
 #align set.maps_to_singleton Set.mapsTo_singleton
+-/
 
+#print Set.MapsTo.image_subset /-
 theorem MapsTo.image_subset (h : MapsTo f s t) : f '' s ⊆ t :=
   mapsTo'.1 h
 #align set.maps_to.image_subset Set.MapsTo.image_subset
+-/
 
+#print Set.MapsTo.congr /-
 theorem MapsTo.congr (h₁ : MapsTo f₁ s t) (h : EqOn f₁ f₂ s) : MapsTo f₂ s t := fun x hx =>
   h hx ▸ h₁ hx
 #align set.maps_to.congr Set.MapsTo.congr
+-/
 
+#print Set.EqOn.comp_right /-
 theorem EqOn.comp_right (hg : t.EqOn g₁ g₂) (hf : s.MapsTo f t) : s.EqOn (g₁ ∘ f) (g₂ ∘ f) :=
   fun a ha => hg <| hf ha
 #align set.eq_on.comp_right Set.EqOn.comp_right
+-/
 
+#print Set.EqOn.mapsTo_iff /-
 theorem EqOn.mapsTo_iff (H : EqOn f₁ f₂ s) : MapsTo f₁ s t ↔ MapsTo f₂ s t :=
   ⟨fun h => h.congr H, fun h => h.congr H.symm⟩
 #align set.eq_on.maps_to_iff Set.EqOn.mapsTo_iff
+-/
 
+#print Set.MapsTo.comp /-
 theorem MapsTo.comp (h₁ : MapsTo g t p) (h₂ : MapsTo f s t) : MapsTo (g ∘ f) s p := fun x h =>
   h₁ (h₂ h)
 #align set.maps_to.comp Set.MapsTo.comp
+-/
 
 #print Set.mapsTo_id /-
 theorem mapsTo_id (s : Set α) : MapsTo id s s := fun x => id
@@ -475,27 +601,38 @@ theorem mapsTo_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) :
 #align set.maps_to_of_subsingleton Set.mapsTo_of_subsingleton
 -/
 
+#print Set.MapsTo.mono /-
 theorem MapsTo.mono (hf : MapsTo f s₁ t₁) (hs : s₂ ⊆ s₁) (ht : t₁ ⊆ t₂) : MapsTo f s₂ t₂ :=
   fun x hx => ht (hf <| hs hx)
 #align set.maps_to.mono Set.MapsTo.mono
+-/
 
+#print Set.MapsTo.mono_left /-
 theorem MapsTo.mono_left (hf : MapsTo f s₁ t) (hs : s₂ ⊆ s₁) : MapsTo f s₂ t := fun x hx =>
   hf (hs hx)
 #align set.maps_to.mono_left Set.MapsTo.mono_left
+-/
 
+#print Set.MapsTo.mono_right /-
 theorem MapsTo.mono_right (hf : MapsTo f s t₁) (ht : t₁ ⊆ t₂) : MapsTo f s t₂ := fun x hx =>
   ht (hf hx)
 #align set.maps_to.mono_right Set.MapsTo.mono_right
+-/
 
+#print Set.MapsTo.union_union /-
 theorem MapsTo.union_union (h₁ : MapsTo f s₁ t₁) (h₂ : MapsTo f s₂ t₂) :
     MapsTo f (s₁ ∪ s₂) (t₁ ∪ t₂) := fun x hx =>
   hx.elim (fun hx => Or.inl <| h₁ hx) fun hx => Or.inr <| h₂ hx
 #align set.maps_to.union_union Set.MapsTo.union_union
+-/
 
+#print Set.MapsTo.union /-
 theorem MapsTo.union (h₁ : MapsTo f s₁ t) (h₂ : MapsTo f s₂ t) : MapsTo f (s₁ ∪ s₂) t :=
   union_self t ▸ h₁.union_union h₂
 #align set.maps_to.union Set.MapsTo.union
+-/
 
+#print Set.mapsTo_union /-
 @[simp]
 theorem mapsTo_union : MapsTo f (s₁ ∪ s₂) t ↔ MapsTo f s₁ t ∧ MapsTo f s₂ t :=
   ⟨fun h =>
@@ -503,15 +640,21 @@ theorem mapsTo_union : MapsTo f (s₁ ∪ s₂) t ↔ MapsTo f s₁ t ∧ MapsTo
       h.mono (subset_union_right s₁ s₂) (Subset.refl t)⟩,
     fun h => h.1.union h.2⟩
 #align set.maps_to_union Set.mapsTo_union
+-/
 
+#print Set.MapsTo.inter /-
 theorem MapsTo.inter (h₁ : MapsTo f s t₁) (h₂ : MapsTo f s t₂) : MapsTo f s (t₁ ∩ t₂) := fun x hx =>
   ⟨h₁ hx, h₂ hx⟩
 #align set.maps_to.inter Set.MapsTo.inter
+-/
 
+#print Set.MapsTo.inter_inter /-
 theorem MapsTo.inter_inter (h₁ : MapsTo f s₁ t₁) (h₂ : MapsTo f s₂ t₂) :
     MapsTo f (s₁ ∩ s₂) (t₁ ∩ t₂) := fun x hx => ⟨h₁ hx.1, h₂ hx.2⟩
 #align set.maps_to.inter_inter Set.MapsTo.inter_inter
+-/
 
+#print Set.mapsTo_inter /-
 @[simp]
 theorem mapsTo_inter : MapsTo f s (t₁ ∩ t₂) ↔ MapsTo f s t₁ ∧ MapsTo f s t₂ :=
   ⟨fun h =>
@@ -519,12 +662,17 @@ theorem mapsTo_inter : MapsTo f s (t₁ ∩ t₂) ↔ MapsTo f s t₁ ∧ MapsTo
       h.mono (Subset.refl s) (inter_subset_right t₁ t₂)⟩,
     fun h => h.1.inter h.2⟩
 #align set.maps_to_inter Set.mapsTo_inter
+-/
 
+#print Set.mapsTo_univ /-
 theorem mapsTo_univ (f : α → β) (s : Set α) : MapsTo f s univ := fun x h => trivial
 #align set.maps_to_univ Set.mapsTo_univ
+-/
 
+#print Set.mapsTo_image /-
 theorem mapsTo_image (f : α → β) (s : Set α) : MapsTo f s (f '' s) := by rw [maps_to']
 #align set.maps_to_image Set.mapsTo_image
+-/
 
 #print Set.mapsTo_preimage /-
 theorem mapsTo_preimage (f : α → β) (t : Set β) : MapsTo f (f ⁻¹' t) t :=
@@ -532,9 +680,11 @@ theorem mapsTo_preimage (f : α → β) (t : Set β) : MapsTo f (f ⁻¹' t) t :
 #align set.maps_to_preimage Set.mapsTo_preimage
 -/
 
+#print Set.mapsTo_range /-
 theorem mapsTo_range (f : α → β) (s : Set α) : MapsTo f s (range f) :=
   (mapsTo_image f s).mono (Subset.refl s) (image_subset_range _ _)
 #align set.maps_to_range Set.mapsTo_range
+-/
 
 #print Set.maps_image_to /-
 @[simp]
@@ -544,13 +694,17 @@ theorem maps_image_to (f : α → β) (g : γ → α) (s : Set γ) (t : Set β)
 #align set.maps_image_to Set.maps_image_to
 -/
 
+#print Set.MapsTo.comp_left /-
 theorem MapsTo.comp_left (g : β → γ) (hf : MapsTo f s t) : MapsTo (g ∘ f) s (g '' t) := fun x hx =>
   ⟨f x, hf hx, rfl⟩
 #align set.maps_to.comp_left Set.MapsTo.comp_left
+-/
 
+#print Set.MapsTo.comp_right /-
 theorem MapsTo.comp_right {s : Set β} {t : Set γ} (hg : MapsTo g s t) (f : α → β) :
     MapsTo (g ∘ f) (f ⁻¹' s) t := fun x hx => hg hx
 #align set.maps_to.comp_right Set.MapsTo.comp_right
+-/
 
 #print Set.maps_univ_to /-
 @[simp]
@@ -559,19 +713,25 @@ theorem maps_univ_to (f : α → β) (s : Set β) : MapsTo f univ s ↔ ∀ a, f
 #align set.maps_univ_to Set.maps_univ_to
 -/
 
+#print Set.maps_range_to /-
 @[simp]
 theorem maps_range_to (f : α → β) (g : γ → α) (s : Set β) :
     MapsTo f (range g) s ↔ MapsTo (f ∘ g) univ s := by rw [← image_univ, maps_image_to]
 #align set.maps_range_to Set.maps_range_to
+-/
 
+#print Set.surjective_mapsTo_image_restrict /-
 theorem surjective_mapsTo_image_restrict (f : α → β) (s : Set α) :
     Surjective ((mapsTo_image f s).restrict f s (f '' s)) := fun ⟨y, x, hs, hxy⟩ =>
   ⟨⟨x, hs⟩, Subtype.ext hxy⟩
 #align set.surjective_maps_to_image_restrict Set.surjective_mapsTo_image_restrict
+-/
 
+#print Set.MapsTo.mem_iff /-
 theorem MapsTo.mem_iff (h : MapsTo f s t) (hc : MapsTo f (sᶜ) (tᶜ)) {x} : f x ∈ t ↔ x ∈ s :=
   ⟨fun ht => by_contra fun hs => hc hs ht, fun hx => h hx⟩
 #align set.maps_to.mem_iff Set.MapsTo.mem_iff
+-/
 
 /-! ### Restriction onto preimage -/
 
@@ -599,18 +759,24 @@ theorem range_restrictPreimage : range (t.restrictPreimage f) = coe ⁻¹' range
 
 variable {f} {U : ι → Set β}
 
+#print Set.restrictPreimage_injective /-
 theorem restrictPreimage_injective (hf : Injective f) : Injective (t.restrictPreimage f) :=
   fun x y e => Subtype.mk.injArrow e fun e => Subtype.coe_injective (hf e)
 #align set.restrict_preimage_injective Set.restrictPreimage_injective
+-/
 
+#print Set.restrictPreimage_surjective /-
 theorem restrictPreimage_surjective (hf : Surjective f) : Surjective (t.restrictPreimage f) :=
   fun x =>
   ⟨⟨_, show f (hf x).some ∈ t from (hf x).choose_spec.symm ▸ x.2⟩, Subtype.ext (hf x).choose_spec⟩
 #align set.restrict_preimage_surjective Set.restrictPreimage_surjective
+-/
 
+#print Set.restrictPreimage_bijective /-
 theorem restrictPreimage_bijective (hf : Bijective f) : Bijective (t.restrictPreimage f) :=
   ⟨t.restrictPreimage_injective hf.1, t.restrictPreimage_surjective hf.2⟩
 #align set.restrict_preimage_bijective Set.restrictPreimage_bijective
+-/
 
 alias Set.restrictPreimage_injective ← _root_.function.injective.restrict_preimage
 #align function.injective.restrict_preimage Function.Injective.restrictPreimage
@@ -633,43 +799,60 @@ def InjOn (f : α → β) (s : Set α) : Prop :=
 #align set.inj_on Set.InjOn
 -/
 
+#print Set.Subsingleton.injOn /-
 theorem Subsingleton.injOn (hs : s.Subsingleton) (f : α → β) : InjOn f s := fun x hx y hy h =>
   hs hx hy
 #align set.subsingleton.inj_on Set.Subsingleton.injOn
+-/
 
+#print Set.injOn_empty /-
 @[simp]
 theorem injOn_empty (f : α → β) : InjOn f ∅ :=
   subsingleton_empty.InjOn f
 #align set.inj_on_empty Set.injOn_empty
+-/
 
+#print Set.injOn_singleton /-
 @[simp]
 theorem injOn_singleton (f : α → β) (a : α) : InjOn f {a} :=
   subsingleton_singleton.InjOn f
 #align set.inj_on_singleton Set.injOn_singleton
+-/
 
+#print Set.InjOn.eq_iff /-
 theorem InjOn.eq_iff {x y} (h : InjOn f s) (hx : x ∈ s) (hy : y ∈ s) : f x = f y ↔ x = y :=
   ⟨h hx hy, fun h => h ▸ rfl⟩
 #align set.inj_on.eq_iff Set.InjOn.eq_iff
+-/
 
+#print Set.InjOn.ne_iff /-
 theorem InjOn.ne_iff {x y} (h : InjOn f s) (hx : x ∈ s) (hy : y ∈ s) : f x ≠ f y ↔ x ≠ y :=
   (h.eq_iff hx hy).Not
 #align set.inj_on.ne_iff Set.InjOn.ne_iff
+-/
 
 alias inj_on.ne_iff ↔ _ inj_on.ne
 #align set.inj_on.ne Set.InjOn.ne
 
+#print Set.InjOn.congr /-
 theorem InjOn.congr (h₁ : InjOn f₁ s) (h : EqOn f₁ f₂ s) : InjOn f₂ s := fun x hx y hy =>
   h hx ▸ h hy ▸ h₁ hx hy
 #align set.inj_on.congr Set.InjOn.congr
+-/
 
+#print Set.EqOn.injOn_iff /-
 theorem EqOn.injOn_iff (H : EqOn f₁ f₂ s) : InjOn f₁ s ↔ InjOn f₂ s :=
   ⟨fun h => h.congr H, fun h => h.congr H.symm⟩
 #align set.eq_on.inj_on_iff Set.EqOn.injOn_iff
+-/
 
+#print Set.InjOn.mono /-
 theorem InjOn.mono (h : s₁ ⊆ s₂) (ht : InjOn f s₂) : InjOn f s₁ := fun x hx y hy H =>
   ht (h hx) (h hy) H
 #align set.inj_on.mono Set.InjOn.mono
+-/
 
+#print Set.injOn_union /-
 theorem injOn_union (h : Disjoint s₁ s₂) :
     InjOn f (s₁ ∪ s₂) ↔ InjOn f s₁ ∧ InjOn f s₂ ∧ ∀ x ∈ s₁, ∀ y ∈ s₂, f x ≠ f y :=
   by
@@ -681,7 +864,9 @@ theorem injOn_union (h : Disjoint s₁ s₂) :
     rintro x (hx | hx) y (hy | hy) hxy
     exacts [h₁ hx hy hxy, (h₁₂ _ hx _ hy hxy).elim, (h₁₂ _ hy _ hx hxy.symm).elim, h₂ hx hy hxy]
 #align set.inj_on_union Set.injOn_union
+-/
 
+#print Set.injOn_insert /-
 theorem injOn_insert {f : α → β} {s : Set α} {a : α} (has : a ∉ s) :
     Set.InjOn f (insert a s) ↔ Set.InjOn f s ∧ f a ∉ f '' s :=
   by
@@ -689,13 +874,18 @@ theorem injOn_insert {f : α → β} {s : Set α} {a : α} (has : a ∉ s) :
   rw [← union_singleton, inj_on_union this]
   simp
 #align set.inj_on_insert Set.injOn_insert
+-/
 
+#print Set.injective_iff_injOn_univ /-
 theorem injective_iff_injOn_univ : Injective f ↔ InjOn f univ :=
   ⟨fun h x hx y hy hxy => h hxy, fun h _ _ heq => h trivial trivial HEq⟩
 #align set.injective_iff_inj_on_univ Set.injective_iff_injOn_univ
+-/
 
+#print Set.injOn_of_injective /-
 theorem injOn_of_injective (h : Injective f) (s : Set α) : InjOn f s := fun x hx y hy hxy => h hxy
 #align set.inj_on_of_injective Set.injOn_of_injective
+-/
 
 alias inj_on_of_injective ← _root_.function.injective.inj_on
 #align function.injective.inj_on Function.Injective.injOn
@@ -706,9 +896,11 @@ theorem injOn_id (s : Set α) : InjOn id s :=
 #align set.inj_on_id Set.injOn_id
 -/
 
+#print Set.InjOn.comp /-
 theorem InjOn.comp (hg : InjOn g t) (hf : InjOn f s) (h : MapsTo f s t) : InjOn (g ∘ f) s :=
   fun x hx y hy heq => hf hx hy <| hg (h hx) (h hy) HEq
 #align set.inj_on.comp Set.InjOn.comp
+-/
 
 #print Set.InjOn.iterate /-
 theorem InjOn.iterate {f : α → α} {s : Set α} (h : InjOn f s) (hf : MapsTo f s s) :
@@ -718,25 +910,33 @@ theorem InjOn.iterate {f : α → α} {s : Set α} (h : InjOn f s) (hf : MapsTo
 #align set.inj_on.iterate Set.InjOn.iterate
 -/
 
+#print Set.injOn_of_subsingleton /-
 theorem injOn_of_subsingleton [Subsingleton α] (f : α → β) (s : Set α) : InjOn f s :=
   (injective_of_subsingleton _).InjOn _
 #align set.inj_on_of_subsingleton Set.injOn_of_subsingleton
+-/
 
+#print Function.Injective.injOn_range /-
 theorem Function.Injective.injOn_range (h : Injective (g ∘ f)) : InjOn g (range f) := by
   rintro _ ⟨x, rfl⟩ _ ⟨y, rfl⟩ H; exact congr_arg f (h H)
 #align function.injective.inj_on_range Function.Injective.injOn_range
+-/
 
+#print Set.injOn_iff_injective /-
 theorem injOn_iff_injective : InjOn f s ↔ Injective (s.restrict f) :=
   ⟨fun H a b h => Subtype.eq <| H a.2 b.2 h, fun H a as b bs h =>
     congr_arg Subtype.val <| @H ⟨a, as⟩ ⟨b, bs⟩ h⟩
 #align set.inj_on_iff_injective Set.injOn_iff_injective
+-/
 
 alias inj_on_iff_injective ↔ inj_on.injective _
 #align set.inj_on.injective Set.InjOn.injective
 
+#print Set.MapsTo.restrict_inj /-
 theorem MapsTo.restrict_inj (h : MapsTo f s t) : Injective (h.restrict f s t) ↔ InjOn f s := by
   rw [h.restrict_eq_cod_restrict, injective_cod_restrict, inj_on_iff_injective]
 #align set.maps_to.restrict_inj Set.MapsTo.restrict_inj
+-/
 
 #print Set.exists_injOn_iff_injective /-
 theorem exists_injOn_iff_injective [Nonempty β] :
@@ -752,30 +952,41 @@ theorem injOn_preimage {B : Set (Set β)} (hB : B ⊆ 𝒫 range f) : InjOn (pre
 #align set.inj_on_preimage Set.injOn_preimage
 -/
 
+#print Set.InjOn.mem_of_mem_image /-
 theorem InjOn.mem_of_mem_image {x} (hf : InjOn f s) (hs : s₁ ⊆ s) (h : x ∈ s) (h₁ : f x ∈ f '' s₁) :
     x ∈ s₁ :=
   let ⟨x', h', Eq⟩ := h₁
   hf (hs h') h Eq ▸ h'
 #align set.inj_on.mem_of_mem_image Set.InjOn.mem_of_mem_image
+-/
 
+#print Set.InjOn.mem_image_iff /-
 theorem InjOn.mem_image_iff {x} (hf : InjOn f s) (hs : s₁ ⊆ s) (hx : x ∈ s) :
     f x ∈ f '' s₁ ↔ x ∈ s₁ :=
   ⟨hf.mem_of_mem_image hs hx, mem_image_of_mem f⟩
 #align set.inj_on.mem_image_iff Set.InjOn.mem_image_iff
+-/
 
+#print Set.InjOn.preimage_image_inter /-
 theorem InjOn.preimage_image_inter (hf : InjOn f s) (hs : s₁ ⊆ s) : f ⁻¹' (f '' s₁) ∩ s = s₁ :=
   ext fun x => ⟨fun ⟨h₁, h₂⟩ => hf.mem_of_mem_image hs h₂ h₁, fun h => ⟨mem_image_of_mem _ h, hs h⟩⟩
 #align set.inj_on.preimage_image_inter Set.InjOn.preimage_image_inter
+-/
 
+#print Set.EqOn.cancel_left /-
 theorem EqOn.cancel_left (h : s.EqOn (g ∘ f₁) (g ∘ f₂)) (hg : t.InjOn g) (hf₁ : s.MapsTo f₁ t)
     (hf₂ : s.MapsTo f₂ t) : s.EqOn f₁ f₂ := fun a ha => hg (hf₁ ha) (hf₂ ha) (h ha)
 #align set.eq_on.cancel_left Set.EqOn.cancel_left
+-/
 
+#print Set.InjOn.cancel_left /-
 theorem InjOn.cancel_left (hg : t.InjOn g) (hf₁ : s.MapsTo f₁ t) (hf₂ : s.MapsTo f₂ t) :
     s.EqOn (g ∘ f₁) (g ∘ f₂) ↔ s.EqOn f₁ f₂ :=
   ⟨fun h => h.cancel_left hg hf₁ hf₂, EqOn.comp_left⟩
 #align set.inj_on.cancel_left Set.InjOn.cancel_left
+-/
 
+#print Set.InjOn.image_inter /-
 theorem InjOn.image_inter {s t u : Set α} (hf : u.InjOn f) (hs : s ⊆ u) (ht : t ⊆ u) :
     f '' (s ∩ t) = f '' s ∩ f '' t :=
   by
@@ -787,13 +998,16 @@ theorem InjOn.image_inter {s t u : Set α} (hf : u.InjOn f) (hs : s ⊆ u) (ht :
   rw [← this] at zt 
   exact ⟨y, ⟨ys, zt⟩, hy⟩
 #align set.inj_on.image_inter Set.InjOn.image_inter
+-/
 
+#print Disjoint.image /-
 theorem Disjoint.image {s t u : Set α} {f : α → β} (h : Disjoint s t) (hf : InjOn f u) (hs : s ⊆ u)
     (ht : t ⊆ u) : Disjoint (f '' s) (f '' t) :=
   by
   rw [disjoint_iff_inter_eq_empty] at h ⊢
   rw [← hf.image_inter hs ht, h, image_empty]
 #align disjoint.image Disjoint.image
+-/
 
 /-! ### Surjectivity on a set -/
 
@@ -805,10 +1019,13 @@ def SurjOn (f : α → β) (s : Set α) (t : Set β) : Prop :=
 #align set.surj_on Set.SurjOn
 -/
 
+#print Set.SurjOn.subset_range /-
 theorem SurjOn.subset_range (h : SurjOn f s t) : t ⊆ range f :=
   Subset.trans h <| image_subset_range f s
 #align set.surj_on.subset_range Set.SurjOn.subset_range
+-/
 
+#print Set.surjOn_iff_exists_map_subtype /-
 theorem surjOn_iff_exists_map_subtype :
     SurjOn f s t ↔ ∃ (t' : Set β) (g : s → t'), t ⊆ t' ∧ Surjective g ∧ ∀ x : s, f x = g x :=
   ⟨fun h =>
@@ -817,46 +1034,66 @@ theorem surjOn_iff_exists_map_subtype :
     let ⟨x, hx⟩ := hg ⟨y, htt' hy⟩
     ⟨x, x.2, by rw [hfg, hx, Subtype.coe_mk]⟩⟩
 #align set.surj_on_iff_exists_map_subtype Set.surjOn_iff_exists_map_subtype
+-/
 
+#print Set.surjOn_empty /-
 theorem surjOn_empty (f : α → β) (s : Set α) : SurjOn f s ∅ :=
   empty_subset _
 #align set.surj_on_empty Set.surjOn_empty
+-/
 
+#print Set.surjOn_singleton /-
 @[simp]
 theorem surjOn_singleton : SurjOn f s {b} ↔ b ∈ f '' s :=
   singleton_subset_iff
 #align set.surj_on_singleton Set.surjOn_singleton
+-/
 
+#print Set.surjOn_image /-
 theorem surjOn_image (f : α → β) (s : Set α) : SurjOn f s (f '' s) :=
   Subset.rfl
 #align set.surj_on_image Set.surjOn_image
+-/
 
+#print Set.SurjOn.comap_nonempty /-
 theorem SurjOn.comap_nonempty (h : SurjOn f s t) (ht : t.Nonempty) : s.Nonempty :=
   (ht.mono h).of_image
 #align set.surj_on.comap_nonempty Set.SurjOn.comap_nonempty
+-/
 
+#print Set.SurjOn.congr /-
 theorem SurjOn.congr (h : SurjOn f₁ s t) (H : EqOn f₁ f₂ s) : SurjOn f₂ s t := by
   rwa [surj_on, ← H.image_eq]
 #align set.surj_on.congr Set.SurjOn.congr
+-/
 
+#print Set.EqOn.surjOn_iff /-
 theorem EqOn.surjOn_iff (h : EqOn f₁ f₂ s) : SurjOn f₁ s t ↔ SurjOn f₂ s t :=
   ⟨fun H => H.congr h, fun H => H.congr h.symm⟩
 #align set.eq_on.surj_on_iff Set.EqOn.surjOn_iff
+-/
 
+#print Set.SurjOn.mono /-
 theorem SurjOn.mono (hs : s₁ ⊆ s₂) (ht : t₁ ⊆ t₂) (hf : SurjOn f s₁ t₂) : SurjOn f s₂ t₁ :=
   Subset.trans ht <| Subset.trans hf <| image_subset _ hs
 #align set.surj_on.mono Set.SurjOn.mono
+-/
 
+#print Set.SurjOn.union /-
 theorem SurjOn.union (h₁ : SurjOn f s t₁) (h₂ : SurjOn f s t₂) : SurjOn f s (t₁ ∪ t₂) := fun x hx =>
   hx.elim (fun hx => h₁ hx) fun hx => h₂ hx
 #align set.surj_on.union Set.SurjOn.union
+-/
 
+#print Set.SurjOn.union_union /-
 theorem SurjOn.union_union (h₁ : SurjOn f s₁ t₁) (h₂ : SurjOn f s₂ t₂) :
     SurjOn f (s₁ ∪ s₂) (t₁ ∪ t₂) :=
   (h₁.mono (subset_union_left _ _) (Subset.refl _)).union
     (h₂.mono (subset_union_right _ _) (Subset.refl _))
 #align set.surj_on.union_union Set.SurjOn.union_union
+-/
 
+#print Set.SurjOn.inter_inter /-
 theorem SurjOn.inter_inter (h₁ : SurjOn f s₁ t₁) (h₂ : SurjOn f s₂ t₂) (h : InjOn f (s₁ ∪ s₂)) :
     SurjOn f (s₁ ∩ s₂) (t₁ ∩ t₂) := by
   intro y hy
@@ -865,20 +1102,25 @@ theorem SurjOn.inter_inter (h₁ : SurjOn f s₁ t₁) (h₂ : SurjOn f s₂ t
   obtain rfl : x₁ = x₂ := h (Or.inl hx₁) (Or.inr hx₂) HEq.symm
   exact mem_image_of_mem f ⟨hx₁, hx₂⟩
 #align set.surj_on.inter_inter Set.SurjOn.inter_inter
+-/
 
+#print Set.SurjOn.inter /-
 theorem SurjOn.inter (h₁ : SurjOn f s₁ t) (h₂ : SurjOn f s₂ t) (h : InjOn f (s₁ ∪ s₂)) :
     SurjOn f (s₁ ∩ s₂) t :=
   inter_self t ▸ h₁.inter_inter h₂ h
 #align set.surj_on.inter Set.SurjOn.inter
+-/
 
 #print Set.surjOn_id /-
 theorem surjOn_id (s : Set α) : SurjOn id s s := by simp [surj_on]
 #align set.surj_on_id Set.surjOn_id
 -/
 
+#print Set.SurjOn.comp /-
 theorem SurjOn.comp (hg : SurjOn g t p) (hf : SurjOn f s t) : SurjOn (g ∘ f) s p :=
   Subset.trans hg <| Subset.trans (image_subset g hf) <| image_comp g f s ▸ Subset.refl _
 #align set.surj_on.comp Set.SurjOn.comp
+-/
 
 #print Set.SurjOn.iterate /-
 theorem SurjOn.iterate {f : α → α} {s : Set α} (h : SurjOn f s s) : ∀ n, SurjOn (f^[n]) s s
@@ -887,13 +1129,17 @@ theorem SurjOn.iterate {f : α → α} {s : Set α} (h : SurjOn f s s) : ∀ n,
 #align set.surj_on.iterate Set.SurjOn.iterate
 -/
 
+#print Set.SurjOn.comp_left /-
 theorem SurjOn.comp_left (hf : SurjOn f s t) (g : β → γ) : SurjOn (g ∘ f) s (g '' t) := by
   rw [surj_on, image_comp g f]; exact image_subset _ hf
 #align set.surj_on.comp_left Set.SurjOn.comp_left
+-/
 
+#print Set.SurjOn.comp_right /-
 theorem SurjOn.comp_right {s : Set β} {t : Set γ} (hf : Surjective f) (hg : SurjOn g s t) :
     SurjOn (g ∘ f) (f ⁻¹' s) t := by rwa [surj_on, image_comp g f, image_preimage_eq _ hf]
 #align set.surj_on.comp_right Set.SurjOn.comp_right
+-/
 
 #print Set.surjOn_of_subsingleton' /-
 theorem surjOn_of_subsingleton' [Subsingleton β] (f : α → β) (h : t.Nonempty → s.Nonempty) :
@@ -907,10 +1153,13 @@ theorem surjOn_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) :
 #align set.surj_on_of_subsingleton Set.surjOn_of_subsingleton
 -/
 
+#print Set.surjective_iff_surjOn_univ /-
 theorem surjective_iff_surjOn_univ : Surjective f ↔ SurjOn f univ univ := by
   simp [surjective, surj_on, subset_def]
 #align set.surjective_iff_surj_on_univ Set.surjective_iff_surjOn_univ
+-/
 
+#print Set.surjOn_iff_surjective /-
 theorem surjOn_iff_surjective : SurjOn f s univ ↔ Surjective (s.restrict f) :=
   ⟨fun H b =>
     let ⟨a, as, e⟩ := @H b trivial
@@ -919,10 +1168,13 @@ theorem surjOn_iff_surjective : SurjOn f s univ ↔ Surjective (s.restrict f) :=
     let ⟨⟨a, as⟩, e⟩ := H b
     ⟨a, as, e⟩⟩
 #align set.surj_on_iff_surjective Set.surjOn_iff_surjective
+-/
 
+#print Set.SurjOn.image_eq_of_mapsTo /-
 theorem SurjOn.image_eq_of_mapsTo (h₁ : SurjOn f s t) (h₂ : MapsTo f s t) : f '' s = t :=
   eq_of_subset_of_subset h₂.image_subset h₁
 #align set.surj_on.image_eq_of_maps_to Set.SurjOn.image_eq_of_mapsTo
+-/
 
 #print Set.image_eq_iff_surjOn_mapsTo /-
 theorem image_eq_iff_surjOn_mapsTo : f '' s = t ↔ s.SurjOn f t ∧ s.MapsTo f t :=
@@ -933,31 +1185,41 @@ theorem image_eq_iff_surjOn_mapsTo : f '' s = t ↔ s.SurjOn f t ∧ s.MapsTo f
 #align set.image_eq_iff_surj_on_maps_to Set.image_eq_iff_surjOn_mapsTo
 -/
 
+#print Set.SurjOn.mapsTo_compl /-
 theorem SurjOn.mapsTo_compl (h : SurjOn f s t) (h' : Injective f) : MapsTo f (sᶜ) (tᶜ) :=
   fun x hs ht =>
   let ⟨x', hx', HEq⟩ := h ht
   hs <| h' HEq ▸ hx'
 #align set.surj_on.maps_to_compl Set.SurjOn.mapsTo_compl
+-/
 
+#print Set.MapsTo.surjOn_compl /-
 theorem MapsTo.surjOn_compl (h : MapsTo f s t) (h' : Surjective f) : SurjOn f (sᶜ) (tᶜ) :=
   h'.forall.2 fun x ht => mem_image_of_mem _ fun hs => ht (h hs)
 #align set.maps_to.surj_on_compl Set.MapsTo.surjOn_compl
+-/
 
+#print Set.EqOn.cancel_right /-
 theorem EqOn.cancel_right (hf : s.EqOn (g₁ ∘ f) (g₂ ∘ f)) (hf' : s.SurjOn f t) : t.EqOn g₁ g₂ :=
   by
   intro b hb
   obtain ⟨a, ha, rfl⟩ := hf' hb
   exact hf ha
 #align set.eq_on.cancel_right Set.EqOn.cancel_right
+-/
 
+#print Set.SurjOn.cancel_right /-
 theorem SurjOn.cancel_right (hf : s.SurjOn f t) (hf' : s.MapsTo f t) :
     s.EqOn (g₁ ∘ f) (g₂ ∘ f) ↔ t.EqOn g₁ g₂ :=
   ⟨fun h => h.cancel_right hf, fun h => h.compRight hf'⟩
 #align set.surj_on.cancel_right Set.SurjOn.cancel_right
+-/
 
+#print Set.eqOn_comp_right_iff /-
 theorem eqOn_comp_right_iff : s.EqOn (g₁ ∘ f) (g₂ ∘ f) ↔ (f '' s).EqOn g₁ g₂ :=
   (s.surjOn_image f).cancel_right <| s.mapsTo_image f
 #align set.eq_on_comp_right_iff Set.eqOn_comp_right_iff
+-/
 
 /-! ### Bijectivity -/
 
@@ -969,73 +1231,103 @@ def BijOn (f : α → β) (s : Set α) (t : Set β) : Prop :=
 #align set.bij_on Set.BijOn
 -/
 
+#print Set.BijOn.mapsTo /-
 theorem BijOn.mapsTo (h : BijOn f s t) : MapsTo f s t :=
   h.left
 #align set.bij_on.maps_to Set.BijOn.mapsTo
+-/
 
+#print Set.BijOn.injOn /-
 theorem BijOn.injOn (h : BijOn f s t) : InjOn f s :=
   h.right.left
 #align set.bij_on.inj_on Set.BijOn.injOn
+-/
 
+#print Set.BijOn.surjOn /-
 theorem BijOn.surjOn (h : BijOn f s t) : SurjOn f s t :=
   h.right.right
 #align set.bij_on.surj_on Set.BijOn.surjOn
+-/
 
+#print Set.BijOn.mk /-
 theorem BijOn.mk (h₁ : MapsTo f s t) (h₂ : InjOn f s) (h₃ : SurjOn f s t) : BijOn f s t :=
   ⟨h₁, h₂, h₃⟩
 #align set.bij_on.mk Set.BijOn.mk
+-/
 
+#print Set.bijOn_empty /-
 @[simp]
 theorem bijOn_empty (f : α → β) : BijOn f ∅ ∅ :=
   ⟨mapsTo_empty f ∅, injOn_empty f, surjOn_empty f ∅⟩
 #align set.bij_on_empty Set.bijOn_empty
+-/
 
+#print Set.bijOn_singleton /-
 @[simp]
 theorem bijOn_singleton : BijOn f {a} {b} ↔ f a = b := by simp [bij_on, eq_comm]
 #align set.bij_on_singleton Set.bijOn_singleton
+-/
 
+#print Set.BijOn.inter_mapsTo /-
 theorem BijOn.inter_mapsTo (h₁ : BijOn f s₁ t₁) (h₂ : MapsTo f s₂ t₂) (h₃ : s₁ ∩ f ⁻¹' t₂ ⊆ s₂) :
     BijOn f (s₁ ∩ s₂) (t₁ ∩ t₂) :=
   ⟨h₁.MapsTo.inter_inter h₂, h₁.InjOn.mono <| inter_subset_left _ _, fun y hy =>
     let ⟨x, hx, hxy⟩ := h₁.SurjOn hy.1
     ⟨x, ⟨hx, h₃ ⟨hx, hxy.symm.recOn hy.2⟩⟩, hxy⟩⟩
 #align set.bij_on.inter_maps_to Set.BijOn.inter_mapsTo
+-/
 
+#print Set.MapsTo.inter_bijOn /-
 theorem MapsTo.inter_bijOn (h₁ : MapsTo f s₁ t₁) (h₂ : BijOn f s₂ t₂) (h₃ : s₂ ∩ f ⁻¹' t₁ ⊆ s₁) :
     BijOn f (s₁ ∩ s₂) (t₁ ∩ t₂) :=
   inter_comm s₂ s₁ ▸ inter_comm t₂ t₁ ▸ h₂.inter_mapsTo h₁ h₃
 #align set.maps_to.inter_bij_on Set.MapsTo.inter_bijOn
+-/
 
+#print Set.BijOn.inter /-
 theorem BijOn.inter (h₁ : BijOn f s₁ t₁) (h₂ : BijOn f s₂ t₂) (h : InjOn f (s₁ ∪ s₂)) :
     BijOn f (s₁ ∩ s₂) (t₁ ∩ t₂) :=
   ⟨h₁.MapsTo.inter_inter h₂.MapsTo, h₁.InjOn.mono <| inter_subset_left _ _,
     h₁.SurjOn.inter_inter h₂.SurjOn h⟩
 #align set.bij_on.inter Set.BijOn.inter
+-/
 
+#print Set.BijOn.union /-
 theorem BijOn.union (h₁ : BijOn f s₁ t₁) (h₂ : BijOn f s₂ t₂) (h : InjOn f (s₁ ∪ s₂)) :
     BijOn f (s₁ ∪ s₂) (t₁ ∪ t₂) :=
   ⟨h₁.MapsTo.union_union h₂.MapsTo, h, h₁.SurjOn.union_union h₂.SurjOn⟩
 #align set.bij_on.union Set.BijOn.union
+-/
 
+#print Set.BijOn.subset_range /-
 theorem BijOn.subset_range (h : BijOn f s t) : t ⊆ range f :=
   h.SurjOn.subset_range
 #align set.bij_on.subset_range Set.BijOn.subset_range
+-/
 
+#print Set.InjOn.bijOn_image /-
 theorem InjOn.bijOn_image (h : InjOn f s) : BijOn f s (f '' s) :=
   BijOn.mk (mapsTo_image f s) h (Subset.refl _)
 #align set.inj_on.bij_on_image Set.InjOn.bijOn_image
+-/
 
+#print Set.BijOn.congr /-
 theorem BijOn.congr (h₁ : BijOn f₁ s t) (h : EqOn f₁ f₂ s) : BijOn f₂ s t :=
   BijOn.mk (h₁.MapsTo.congr h) (h₁.InjOn.congr h) (h₁.SurjOn.congr h)
 #align set.bij_on.congr Set.BijOn.congr
+-/
 
+#print Set.EqOn.bijOn_iff /-
 theorem EqOn.bijOn_iff (H : EqOn f₁ f₂ s) : BijOn f₁ s t ↔ BijOn f₂ s t :=
   ⟨fun h => h.congr H, fun h => h.congr H.symm⟩
 #align set.eq_on.bij_on_iff Set.EqOn.bijOn_iff
+-/
 
+#print Set.BijOn.image_eq /-
 theorem BijOn.image_eq (h : BijOn f s t) : f '' s = t :=
   h.SurjOn.image_eq_of_mapsTo h.MapsTo
 #align set.bij_on.image_eq Set.BijOn.image_eq
+-/
 
 #print Set.bijOn_id /-
 theorem bijOn_id (s : Set α) : BijOn id s s :=
@@ -1043,9 +1335,11 @@ theorem bijOn_id (s : Set α) : BijOn id s s :=
 #align set.bij_on_id Set.bijOn_id
 -/
 
+#print Set.BijOn.comp /-
 theorem BijOn.comp (hg : BijOn g t p) (hf : BijOn f s t) : BijOn (g ∘ f) s p :=
   BijOn.mk (hg.MapsTo.comp hf.MapsTo) (hg.InjOn.comp hf.InjOn hf.MapsTo) (hg.SurjOn.comp hf.SurjOn)
 #align set.bij_on.comp Set.BijOn.comp
+-/
 
 #print Set.BijOn.iterate /-
 theorem BijOn.iterate {f : α → α} {s : Set α} (h : BijOn f s s) : ∀ n, BijOn (f^[n]) s s
@@ -1054,10 +1348,12 @@ theorem BijOn.iterate {f : α → α} {s : Set α} (h : BijOn f s s) : ∀ n, Bi
 #align set.bij_on.iterate Set.BijOn.iterate
 -/
 
+#print Set.bijOn_of_subsingleton' /-
 theorem bijOn_of_subsingleton' [Subsingleton α] [Subsingleton β] (f : α → β)
     (h : s.Nonempty ↔ t.Nonempty) : BijOn f s t :=
   ⟨mapsTo_of_subsingleton' _ h.1, injOn_of_subsingleton _ _, surjOn_of_subsingleton' _ h.2⟩
 #align set.bij_on_of_subsingleton' Set.bijOn_of_subsingleton'
+-/
 
 #print Set.bijOn_of_subsingleton /-
 theorem bijOn_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : BijOn f s s :=
@@ -1065,12 +1361,15 @@ theorem bijOn_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : B
 #align set.bij_on_of_subsingleton Set.bijOn_of_subsingleton
 -/
 
+#print Set.BijOn.bijective /-
 theorem BijOn.bijective (h : BijOn f s t) : Bijective (h.MapsTo.restrict f s t) :=
   ⟨fun x y h' => Subtype.ext <| h.InjOn x.2 y.2 <| Subtype.ext_iff.1 h', fun ⟨y, hy⟩ =>
     let ⟨x, hx, hxy⟩ := h.SurjOn hy
     ⟨⟨x, hx⟩, Subtype.eq hxy⟩⟩
 #align set.bij_on.bijective Set.BijOn.bijective
+-/
 
+#print Set.bijective_iff_bijOn_univ /-
 theorem bijective_iff_bijOn_univ : Bijective f ↔ BijOn f univ univ :=
   Iff.intro
     (fun h =>
@@ -1080,13 +1379,16 @@ theorem bijective_iff_bijOn_univ : Bijective f ↔ BijOn f univ univ :=
     let ⟨map, inj, surj⟩ := h
     ⟨Iff.mpr injective_iff_injOn_univ inj, Iff.mpr surjective_iff_surjOn_univ surj⟩
 #align set.bijective_iff_bij_on_univ Set.bijective_iff_bijOn_univ
+-/
 
 alias bijective_iff_bij_on_univ ↔ _root_.function.bijective.bij_on_univ _
 #align function.bijective.bij_on_univ Function.Bijective.bijOn_univ
 
+#print Set.BijOn.compl /-
 theorem BijOn.compl (hst : BijOn f s t) (hf : Bijective f) : BijOn f (sᶜ) (tᶜ) :=
   ⟨hst.SurjOn.mapsTo_compl hf.1, hf.1.InjOn _, hst.MapsTo.surjOn_compl hf.2⟩
 #align set.bij_on.compl Set.BijOn.compl
+-/
 
 /-! ### left inverse -/
 
@@ -1108,76 +1410,102 @@ theorem leftInvOn_singleton : LeftInvOn f' f {a} ↔ f' (f a) = a :=
   singleton_subset_iff
 #align set.left_inv_on_singleton Set.leftInvOn_singleton
 
+#print Set.LeftInvOn.eqOn /-
 theorem LeftInvOn.eqOn (h : LeftInvOn f' f s) : EqOn (f' ∘ f) id s :=
   h
 #align set.left_inv_on.eq_on Set.LeftInvOn.eqOn
+-/
 
+#print Set.LeftInvOn.eq /-
 theorem LeftInvOn.eq (h : LeftInvOn f' f s) {x} (hx : x ∈ s) : f' (f x) = x :=
   h hx
 #align set.left_inv_on.eq Set.LeftInvOn.eq
+-/
 
+#print Set.LeftInvOn.congr_left /-
 theorem LeftInvOn.congr_left (h₁ : LeftInvOn f₁' f s) {t : Set β} (h₁' : MapsTo f s t)
     (heq : EqOn f₁' f₂' t) : LeftInvOn f₂' f s := fun x hx => HEq (h₁' hx) ▸ h₁ hx
 #align set.left_inv_on.congr_left Set.LeftInvOn.congr_left
+-/
 
+#print Set.LeftInvOn.congr_right /-
 theorem LeftInvOn.congr_right (h₁ : LeftInvOn f₁' f₁ s) (heq : EqOn f₁ f₂ s) : LeftInvOn f₁' f₂ s :=
   fun x hx => HEq hx ▸ h₁ hx
 #align set.left_inv_on.congr_right Set.LeftInvOn.congr_right
+-/
 
+#print Set.LeftInvOn.injOn /-
 theorem LeftInvOn.injOn (h : LeftInvOn f₁' f s) : InjOn f s := fun x₁ h₁ x₂ h₂ heq =>
   calc
     x₁ = f₁' (f x₁) := Eq.symm <| h h₁
     _ = f₁' (f x₂) := (congr_arg f₁' HEq)
     _ = x₂ := h h₂
 #align set.left_inv_on.inj_on Set.LeftInvOn.injOn
+-/
 
+#print Set.LeftInvOn.surjOn /-
 theorem LeftInvOn.surjOn (h : LeftInvOn f' f s) (hf : MapsTo f s t) : SurjOn f' t s := fun x hx =>
   ⟨f x, hf hx, h hx⟩
 #align set.left_inv_on.surj_on Set.LeftInvOn.surjOn
+-/
 
+#print Set.LeftInvOn.mapsTo /-
 theorem LeftInvOn.mapsTo (h : LeftInvOn f' f s) (hf : SurjOn f s t) : MapsTo f' t s := fun y hy =>
   by
   let ⟨x, hs, hx⟩ := hf hy
   rwa [← hx, h hs]
 #align set.left_inv_on.maps_to Set.LeftInvOn.mapsTo
+-/
 
 #print Set.leftInvOn_id /-
 theorem leftInvOn_id (s : Set α) : LeftInvOn id id s := fun a _ => rfl
 #align set.left_inv_on_id Set.leftInvOn_id
 -/
 
+#print Set.LeftInvOn.comp /-
 theorem LeftInvOn.comp (hf' : LeftInvOn f' f s) (hg' : LeftInvOn g' g t) (hf : MapsTo f s t) :
     LeftInvOn (f' ∘ g') (g ∘ f) s := fun x h =>
   calc
     (f' ∘ g') ((g ∘ f) x) = f' (f x) := congr_arg f' (hg' (hf h))
     _ = x := hf' h
 #align set.left_inv_on.comp Set.LeftInvOn.comp
+-/
 
+#print Set.LeftInvOn.mono /-
 theorem LeftInvOn.mono (hf : LeftInvOn f' f s) (ht : s₁ ⊆ s) : LeftInvOn f' f s₁ := fun x hx =>
   hf (ht hx)
 #align set.left_inv_on.mono Set.LeftInvOn.mono
+-/
 
+#print Set.LeftInvOn.image_inter' /-
 theorem LeftInvOn.image_inter' (hf : LeftInvOn f' f s) : f '' (s₁ ∩ s) = f' ⁻¹' s₁ ∩ f '' s :=
   by
   apply subset.antisymm
   · rintro _ ⟨x, ⟨h₁, h⟩, rfl⟩; exact ⟨by rwa [mem_preimage, hf h], mem_image_of_mem _ h⟩
   · rintro _ ⟨h₁, ⟨x, h, rfl⟩⟩; exact mem_image_of_mem _ ⟨by rwa [← hf h], h⟩
 #align set.left_inv_on.image_inter' Set.LeftInvOn.image_inter'
+-/
 
+#print Set.LeftInvOn.image_inter /-
 theorem LeftInvOn.image_inter (hf : LeftInvOn f' f s) : f '' (s₁ ∩ s) = f' ⁻¹' (s₁ ∩ s) ∩ f '' s :=
   by
   rw [hf.image_inter']
   refine' subset.antisymm _ (inter_subset_inter_left _ (preimage_mono <| inter_subset_left _ _))
   rintro _ ⟨h₁, x, hx, rfl⟩; exact ⟨⟨h₁, by rwa [hf hx]⟩, mem_image_of_mem _ hx⟩
 #align set.left_inv_on.image_inter Set.LeftInvOn.image_inter
+-/
 
+#print Set.LeftInvOn.image_image /-
 theorem LeftInvOn.image_image (hf : LeftInvOn f' f s) : f' '' (f '' s) = s := by
   rw [image_image, image_congr hf, image_id']
 #align set.left_inv_on.image_image Set.LeftInvOn.image_image
+-/
 
+#print Set.LeftInvOn.image_image' /-
 theorem LeftInvOn.image_image' (hf : LeftInvOn f' f s) (hs : s₁ ⊆ s) : f' '' (f '' s₁) = s₁ :=
   (hf.mono hs).image_image
 #align set.left_inv_on.image_image' Set.LeftInvOn.image_image'
+-/
 
 /-! ### Right inverse -/
 
@@ -1200,66 +1528,90 @@ theorem rightInvOn_singleton : RightInvOn f' f {b} ↔ f (f' b) = b :=
   singleton_subset_iff
 #align set.right_inv_on_singleton Set.rightInvOn_singleton
 
+#print Set.RightInvOn.eqOn /-
 theorem RightInvOn.eqOn (h : RightInvOn f' f t) : EqOn (f ∘ f') id t :=
   h
 #align set.right_inv_on.eq_on Set.RightInvOn.eqOn
+-/
 
+#print Set.RightInvOn.eq /-
 theorem RightInvOn.eq (h : RightInvOn f' f t) {y} (hy : y ∈ t) : f (f' y) = y :=
   h hy
 #align set.right_inv_on.eq Set.RightInvOn.eq
+-/
 
+#print Set.LeftInvOn.rightInvOn_image /-
 theorem LeftInvOn.rightInvOn_image (h : LeftInvOn f' f s) : RightInvOn f' f (f '' s) :=
   fun y ⟨x, hx, Eq⟩ => Eq ▸ congr_arg f <| h.Eq hx
 #align set.left_inv_on.right_inv_on_image Set.LeftInvOn.rightInvOn_image
+-/
 
+#print Set.RightInvOn.congr_left /-
 theorem RightInvOn.congr_left (h₁ : RightInvOn f₁' f t) (heq : EqOn f₁' f₂' t) :
     RightInvOn f₂' f t :=
   h₁.congr_right HEq
 #align set.right_inv_on.congr_left Set.RightInvOn.congr_left
+-/
 
+#print Set.RightInvOn.congr_right /-
 theorem RightInvOn.congr_right (h₁ : RightInvOn f' f₁ t) (hg : MapsTo f' t s) (heq : EqOn f₁ f₂ s) :
     RightInvOn f' f₂ t :=
   LeftInvOn.congr_left h₁ hg HEq
 #align set.right_inv_on.congr_right Set.RightInvOn.congr_right
+-/
 
+#print Set.RightInvOn.surjOn /-
 theorem RightInvOn.surjOn (hf : RightInvOn f' f t) (hf' : MapsTo f' t s) : SurjOn f s t :=
   hf.SurjOn hf'
 #align set.right_inv_on.surj_on Set.RightInvOn.surjOn
+-/
 
+#print Set.RightInvOn.mapsTo /-
 theorem RightInvOn.mapsTo (h : RightInvOn f' f t) (hf : SurjOn f' t s) : MapsTo f s t :=
   h.MapsTo hf
 #align set.right_inv_on.maps_to Set.RightInvOn.mapsTo
+-/
 
 #print Set.rightInvOn_id /-
 theorem rightInvOn_id (s : Set α) : RightInvOn id id s := fun a _ => rfl
 #align set.right_inv_on_id Set.rightInvOn_id
 -/
 
+#print Set.RightInvOn.comp /-
 theorem RightInvOn.comp (hf : RightInvOn f' f t) (hg : RightInvOn g' g p) (g'pt : MapsTo g' p t) :
     RightInvOn (f' ∘ g') (g ∘ f) p :=
   hg.comp hf g'pt
 #align set.right_inv_on.comp Set.RightInvOn.comp
+-/
 
+#print Set.RightInvOn.mono /-
 theorem RightInvOn.mono (hf : RightInvOn f' f t) (ht : t₁ ⊆ t) : RightInvOn f' f t₁ :=
   hf.mono ht
 #align set.right_inv_on.mono Set.RightInvOn.mono
+-/
 
+#print Set.InjOn.rightInvOn_of_leftInvOn /-
 theorem InjOn.rightInvOn_of_leftInvOn (hf : InjOn f s) (hf' : LeftInvOn f f' t) (h₁ : MapsTo f s t)
     (h₂ : MapsTo f' t s) : RightInvOn f f' s := fun x h => hf (h₂ <| h₁ h) h (hf' (h₁ h))
 #align set.inj_on.right_inv_on_of_left_inv_on Set.InjOn.rightInvOn_of_leftInvOn
+-/
 
+#print Set.eqOn_of_leftInvOn_of_rightInvOn /-
 theorem eqOn_of_leftInvOn_of_rightInvOn (h₁ : LeftInvOn f₁' f s) (h₂ : RightInvOn f₂' f t)
     (h : MapsTo f₂' t s) : EqOn f₁' f₂' t := fun y hy =>
   calc
     f₁' y = (f₁' ∘ f ∘ f₂') y := congr_arg f₁' (h₂ hy).symm
     _ = f₂' y := h₁ (h hy)
 #align set.eq_on_of_left_inv_on_of_right_inv_on Set.eqOn_of_leftInvOn_of_rightInvOn
+-/
 
+#print Set.SurjOn.leftInvOn_of_rightInvOn /-
 theorem SurjOn.leftInvOn_of_rightInvOn (hf : SurjOn f s t) (hf' : RightInvOn f f' s) :
     LeftInvOn f f' t := fun y hy => by
   let ⟨x, hx, HEq⟩ := hf hy
   rw [← HEq, hf' hx]
 #align set.surj_on.left_inv_on_of_right_inv_on Set.SurjOn.leftInvOn_of_rightInvOn
+-/
 
 /-! ### Two-side inverses -/
 
@@ -1279,9 +1631,11 @@ theorem invOn_empty (f' : β → α) (f : α → β) : InvOn f' f ∅ ∅ := by
 theorem invOn_singleton : InvOn f' f {a} {b} ↔ f' (f a) = a ∧ f (f' b) = b := by simp [inv_on]
 #align set.inv_on_singleton Set.invOn_singleton
 
+#print Set.InvOn.symm /-
 theorem InvOn.symm (h : InvOn f' f s t) : InvOn f f' t s :=
   ⟨h.right, h.left⟩
 #align set.inv_on.symm Set.InvOn.symm
+-/
 
 #print Set.invOn_id /-
 theorem invOn_id (s : Set α) : InvOn id id s s :=
@@ -1289,21 +1643,27 @@ theorem invOn_id (s : Set α) : InvOn id id s s :=
 #align set.inv_on_id Set.invOn_id
 -/
 
+#print Set.InvOn.comp /-
 theorem InvOn.comp (hf : InvOn f' f s t) (hg : InvOn g' g t p) (fst : MapsTo f s t)
     (g'pt : MapsTo g' p t) : InvOn (f' ∘ g') (g ∘ f) s p :=
   ⟨hf.1.comp hg.1 fst, hf.2.comp hg.2 g'pt⟩
 #align set.inv_on.comp Set.InvOn.comp
+-/
 
+#print Set.InvOn.mono /-
 theorem InvOn.mono (h : InvOn f' f s t) (hs : s₁ ⊆ s) (ht : t₁ ⊆ t) : InvOn f' f s₁ t₁ :=
   ⟨h.1.mono hs, h.2.mono ht⟩
 #align set.inv_on.mono Set.InvOn.mono
+-/
 
+#print Set.InvOn.bijOn /-
 /-- If functions `f'` and `f` are inverse on `s` and `t`, `f` maps `s` into `t`, and `f'` maps `t`
 into `s`, then `f` is a bijection between `s` and `t`. The `maps_to` arguments can be deduced from
 `surj_on` statements using `left_inv_on.maps_to` and `right_inv_on.maps_to`. -/
 theorem InvOn.bijOn (h : InvOn f' f s t) (hf : MapsTo f s t) (hf' : MapsTo f' t s) : BijOn f s t :=
   ⟨hf, h.left.InjOn, h.right.SurjOn hf'⟩
 #align set.inv_on.bij_on Set.InvOn.bijOn
+-/
 
 #print Set.BijOn.symm /-
 theorem BijOn.symm {g : β → α} (h : InvOn f g t s) (hf : BijOn f s t) : BijOn g t s :=
@@ -1336,30 +1696,42 @@ noncomputable def invFunOn (f : α → β) (s : Set α) (b : β) : α :=
 #align function.inv_fun_on Function.invFunOn
 -/
 
+#print Function.invFunOn_pos /-
 theorem invFunOn_pos (h : ∃ a ∈ s, f a = b) : invFunOn f s b ∈ s ∧ f (invFunOn f s b) = b := by
   rw [bex_def] at h  <;> rw [inv_fun_on, dif_pos h] <;> exact Classical.choose_spec h
 #align function.inv_fun_on_pos Function.invFunOn_pos
+-/
 
+#print Function.invFunOn_mem /-
 theorem invFunOn_mem (h : ∃ a ∈ s, f a = b) : invFunOn f s b ∈ s :=
   (invFunOn_pos h).left
 #align function.inv_fun_on_mem Function.invFunOn_mem
+-/
 
+#print Function.invFunOn_eq /-
 theorem invFunOn_eq (h : ∃ a ∈ s, f a = b) : f (invFunOn f s b) = b :=
   (invFunOn_pos h).right
 #align function.inv_fun_on_eq Function.invFunOn_eq
+-/
 
+#print Function.invFunOn_neg /-
 theorem invFunOn_neg (h : ¬∃ a ∈ s, f a = b) : invFunOn f s b = Classical.choice ‹Nonempty α› := by
   rw [bex_def] at h  <;> rw [inv_fun_on, dif_neg h]
 #align function.inv_fun_on_neg Function.invFunOn_neg
+-/
 
+#print Function.invFunOn_apply_mem /-
 @[simp]
 theorem invFunOn_apply_mem (h : a ∈ s) : invFunOn f s (f a) ∈ s :=
   invFunOn_mem ⟨a, h, rfl⟩
 #align function.inv_fun_on_apply_mem Function.invFunOn_apply_mem
+-/
 
+#print Function.invFunOn_apply_eq /-
 theorem invFunOn_apply_eq (h : a ∈ s) : f (invFunOn f s (f a)) = f a :=
   invFunOn_eq ⟨a, h, rfl⟩
 #align function.inv_fun_on_apply_eq Function.invFunOn_apply_eq
+-/
 
 end Function
 
@@ -1369,23 +1741,32 @@ namespace Set
 
 variable {s s₁ s₂ : Set α} {t : Set β} {f : α → β}
 
+#print Set.InjOn.leftInvOn_invFunOn /-
 theorem InjOn.leftInvOn_invFunOn [Nonempty α] (h : InjOn f s) : LeftInvOn (invFunOn f s) f s :=
   fun a ha => h (invFunOn_apply_mem ha) ha (invFunOn_apply_eq ha)
 #align set.inj_on.left_inv_on_inv_fun_on Set.InjOn.leftInvOn_invFunOn
+-/
 
+#print Set.InjOn.invFunOn_image /-
 theorem InjOn.invFunOn_image [Nonempty α] (h : InjOn f s₂) (ht : s₁ ⊆ s₂) :
     invFunOn f s₂ '' (f '' s₁) = s₁ :=
   h.leftInvOn_invFunOn.image_image' ht
 #align set.inj_on.inv_fun_on_image Set.InjOn.invFunOn_image
+-/
 
+#print Set.SurjOn.rightInvOn_invFunOn /-
 theorem SurjOn.rightInvOn_invFunOn [Nonempty α] (h : SurjOn f s t) :
     RightInvOn (invFunOn f s) f t := fun y hy => invFunOn_eq <| mem_image_iff_bex.1 <| h hy
 #align set.surj_on.right_inv_on_inv_fun_on Set.SurjOn.rightInvOn_invFunOn
+-/
 
+#print Set.BijOn.invOn_invFunOn /-
 theorem BijOn.invOn_invFunOn [Nonempty α] (h : BijOn f s t) : InvOn (invFunOn f s) f s t :=
   ⟨h.InjOn.leftInvOn_invFunOn, h.SurjOn.rightInvOn_invFunOn⟩
 #align set.bij_on.inv_on_inv_fun_on Set.BijOn.invOn_invFunOn
+-/
 
+#print Set.SurjOn.invOn_invFunOn /-
 theorem SurjOn.invOn_invFunOn [Nonempty α] (h : SurjOn f s t) :
     InvOn (invFunOn f s) f (invFunOn f s '' t) t :=
   by
@@ -1393,19 +1774,25 @@ theorem SurjOn.invOn_invFunOn [Nonempty α] (h : SurjOn f s t) :
   rintro _ ⟨y, hy, rfl⟩
   rw [h.right_inv_on_inv_fun_on hy]
 #align set.surj_on.inv_on_inv_fun_on Set.SurjOn.invOn_invFunOn
+-/
 
+#print Set.SurjOn.mapsTo_invFunOn /-
 theorem SurjOn.mapsTo_invFunOn [Nonempty α] (h : SurjOn f s t) : MapsTo (invFunOn f s) t s :=
   fun y hy => mem_preimage.2 <| invFunOn_mem <| mem_image_iff_bex.1 <| h hy
 #align set.surj_on.maps_to_inv_fun_on Set.SurjOn.mapsTo_invFunOn
+-/
 
+#print Set.SurjOn.bijOn_subset /-
 theorem SurjOn.bijOn_subset [Nonempty α] (h : SurjOn f s t) : BijOn f (invFunOn f s '' t) t :=
   by
   refine' h.inv_on_inv_fun_on.bij_on _ (maps_to_image _ _)
   rintro _ ⟨y, hy, rfl⟩
   rwa [h.right_inv_on_inv_fun_on hy]
 #align set.surj_on.bij_on_subset Set.SurjOn.bijOn_subset
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (s' «expr ⊆ » s) -/
+#print Set.surjOn_iff_exists_bijOn_subset /-
 theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _) (_ : s' ⊆ s), BijOn f s' t :=
   by
   constructor
@@ -1417,7 +1804,9 @@ theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _) (_ : s' 
   · rintro ⟨s', hs', hfs'⟩
     exact hfs'.surj_on.mono hs' (subset.refl _)
 #align set.surj_on_iff_exists_bij_on_subset Set.surjOn_iff_exists_bijOn_subset
+-/
 
+#print Set.preimage_invFun_of_mem /-
 theorem preimage_invFun_of_mem [n : Nonempty α] {f : α → β} (hf : Injective f) {s : Set α}
     (h : Classical.choice n ∈ s) : invFun f ⁻¹' s = f '' s ∪ range fᶜ :=
   by
@@ -1426,7 +1815,9 @@ theorem preimage_invFun_of_mem [n : Nonempty α] {f : α → β} (hf : Injective
   · simp [left_inverse_inv_fun hf _, hf.mem_set_image]
   · simp [mem_preimage, inv_fun_neg hx, h, hx]
 #align set.preimage_inv_fun_of_mem Set.preimage_invFun_of_mem
+-/
 
+#print Set.preimage_invFun_of_not_mem /-
 theorem preimage_invFun_of_not_mem [n : Nonempty α] {f : α → β} (hf : Injective f) {s : Set α}
     (h : Classical.choice n ∉ s) : invFun f ⁻¹' s = f '' s :=
   by
@@ -1436,6 +1827,7 @@ theorem preimage_invFun_of_not_mem [n : Nonempty α] {f : α → β} (hf : Injec
   · have : x ∉ f '' s := fun h' => hx (image_subset_range _ _ h')
     simp only [mem_preimage, inv_fun_neg hx, h, this]
 #align set.preimage_inv_fun_of_not_mem Set.preimage_invFun_of_not_mem
+-/
 
 end Set
 
@@ -1446,18 +1838,24 @@ namespace Monotone
 
 variable [Preorder α] [Preorder β] {f : α → β}
 
+#print Monotone.restrict /-
 protected theorem restrict (h : Monotone f) (s : Set α) : Monotone (s.restrict f) := fun x y hxy =>
   h hxy
 #align monotone.restrict Monotone.restrict
+-/
 
+#print Monotone.codRestrict /-
 protected theorem codRestrict (h : Monotone f) {s : Set β} (hs : ∀ x, f x ∈ s) :
     Monotone (s.codRestrict f hs) :=
   h
 #align monotone.cod_restrict Monotone.codRestrict
+-/
 
+#print Monotone.rangeFactorization /-
 protected theorem rangeFactorization (h : Monotone f) : Monotone (Set.rangeFactorization f) :=
   h
 #align monotone.range_factorization Monotone.rangeFactorization
+-/
 
 end Monotone
 
@@ -1468,27 +1866,36 @@ namespace Set
 
 variable {δ : α → Sort y} (s : Set α) (f g : ∀ i, δ i)
 
+#print Set.piecewise_empty /-
 @[simp]
 theorem piecewise_empty [∀ i : α, Decidable (i ∈ (∅ : Set α))] : piecewise ∅ f g = g := by ext i;
   simp [piecewise]
 #align set.piecewise_empty Set.piecewise_empty
+-/
 
+#print Set.piecewise_univ /-
 @[simp]
 theorem piecewise_univ [∀ i : α, Decidable (i ∈ (Set.univ : Set α))] : piecewise Set.univ f g = f :=
   by ext i; simp [piecewise]
 #align set.piecewise_univ Set.piecewise_univ
+-/
 
+#print Set.piecewise_insert_self /-
 @[simp]
 theorem piecewise_insert_self {j : α} [∀ i, Decidable (i ∈ insert j s)] :
     (insert j s).piecewise f g j = f j := by simp [piecewise]
 #align set.piecewise_insert_self Set.piecewise_insert_self
+-/
 
 variable [∀ j, Decidable (j ∈ s)]
 
+#print Set.Compl.decidableMem /-
 instance Compl.decidableMem (j : α) : Decidable (j ∈ sᶜ) :=
   Not.decidable
 #align set.compl.decidable_mem Set.Compl.decidableMem
+-/
 
+#print Set.piecewise_insert /-
 theorem piecewise_insert [DecidableEq α] (j : α) [∀ i, Decidable (i ∈ insert j s)] :
     (insert j s).piecewise f g = Function.update (s.piecewise f g) j (f j) :=
   by
@@ -1498,29 +1905,40 @@ theorem piecewise_insert [DecidableEq α] (j : α) [∀ i, Decidable (i ∈ inse
   · rw [h]; simp
   · by_cases h' : i ∈ s <;> simp [h, h']
 #align set.piecewise_insert Set.piecewise_insert
+-/
 
+#print Set.piecewise_eq_of_mem /-
 @[simp]
 theorem piecewise_eq_of_mem {i : α} (hi : i ∈ s) : s.piecewise f g i = f i :=
   if_pos hi
 #align set.piecewise_eq_of_mem Set.piecewise_eq_of_mem
+-/
 
+#print Set.piecewise_eq_of_not_mem /-
 @[simp]
 theorem piecewise_eq_of_not_mem {i : α} (hi : i ∉ s) : s.piecewise f g i = g i :=
   if_neg hi
 #align set.piecewise_eq_of_not_mem Set.piecewise_eq_of_not_mem
+-/
 
+#print Set.piecewise_singleton /-
 theorem piecewise_singleton (x : α) [∀ y, Decidable (y ∈ ({x} : Set α))] [DecidableEq α]
     (f g : α → β) : piecewise {x} f g = Function.update g x (f x) := by ext y; by_cases hy : y = x;
   · subst y; simp; · simp [hy]
 #align set.piecewise_singleton Set.piecewise_singleton
+-/
 
+#print Set.piecewise_eqOn /-
 theorem piecewise_eqOn (f g : α → β) : EqOn (s.piecewise f g) f s := fun _ =>
   piecewise_eq_of_mem _ _ _
 #align set.piecewise_eq_on Set.piecewise_eqOn
+-/
 
+#print Set.piecewise_eqOn_compl /-
 theorem piecewise_eqOn_compl (f g : α → β) : EqOn (s.piecewise f g) g (sᶜ) := fun _ =>
   piecewise_eq_of_not_mem _ _ _
 #align set.piecewise_eq_on_compl Set.piecewise_eqOn_compl
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.piecewise_le /-
@@ -1548,22 +1966,29 @@ theorem piecewise_le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s
 #align set.piecewise_le_piecewise Set.piecewise_le_piecewise
 -/
 
+#print Set.piecewise_insert_of_ne /-
 @[simp]
 theorem piecewise_insert_of_ne {i j : α} (h : i ≠ j) [∀ i, Decidable (i ∈ insert j s)] :
     (insert j s).piecewise f g i = s.piecewise f g i := by simp [piecewise, h]
 #align set.piecewise_insert_of_ne Set.piecewise_insert_of_ne
+-/
 
+#print Set.piecewise_compl /-
 @[simp]
 theorem piecewise_compl [∀ i, Decidable (i ∈ sᶜ)] : sᶜ.piecewise f g = s.piecewise g f :=
   funext fun x => if hx : x ∈ s then by simp [hx] else by simp [hx]
 #align set.piecewise_compl Set.piecewise_compl
+-/
 
+#print Set.piecewise_range_comp /-
 @[simp]
 theorem piecewise_range_comp {ι : Sort _} (f : ι → α) [∀ j, Decidable (j ∈ range f)]
     (g₁ g₂ : α → β) : (range f).piecewise g₁ g₂ ∘ f = g₁ ∘ f :=
   EqOn.comp_eq <| piecewise_eqOn _ _ _
 #align set.piecewise_range_comp Set.piecewise_range_comp
+-/
 
+#print Set.MapsTo.piecewise_ite /-
 theorem MapsTo.piecewise_ite {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {f₁ f₂ : α → β}
     [∀ i, Decidable (i ∈ s)] (h₁ : MapsTo f₁ (s₁ ∩ s) (t₁ ∩ t))
     (h₂ : MapsTo f₂ (s₂ ∩ sᶜ) (t₂ ∩ tᶜ)) : MapsTo (s.piecewise f₁ f₂) (s.ite s₁ s₂) (t.ite t₁ t₂) :=
@@ -1572,23 +1997,30 @@ theorem MapsTo.piecewise_ite {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {f₁
   exacts [(piecewise_eq_on s f₁ f₂).symm.mono (inter_subset_right _ _),
     (piecewise_eq_on_compl s f₁ f₂).symm.mono (inter_subset_right _ _)]
 #align set.maps_to.piecewise_ite Set.MapsTo.piecewise_ite
+-/
 
+#print Set.eqOn_piecewise /-
 theorem eqOn_piecewise {f f' g : α → β} {t} :
     EqOn (s.piecewise f f') g t ↔ EqOn f g (t ∩ s) ∧ EqOn f' g (t ∩ sᶜ) :=
   by
   simp only [eq_on, ← forall_and]
   refine' forall_congr' fun a => _; by_cases a ∈ s <;> simp [*]
 #align set.eq_on_piecewise Set.eqOn_piecewise
+-/
 
+#print Set.EqOn.piecewise_ite' /-
 theorem EqOn.piecewise_ite' {f f' g : α → β} {t t'} (h : EqOn f g (t ∩ s))
     (h' : EqOn f' g (t' ∩ sᶜ)) : EqOn (s.piecewise f f') g (s.ite t t') := by
   simp [eq_on_piecewise, *]
 #align set.eq_on.piecewise_ite' Set.EqOn.piecewise_ite'
+-/
 
+#print Set.EqOn.piecewise_ite /-
 theorem EqOn.piecewise_ite {f f' g : α → β} {t t'} (h : EqOn f g t) (h' : EqOn f' g t') :
     EqOn (s.piecewise f f') g (s.ite t t') :=
   (h.mono (inter_subset_left _ _)).piecewise_ite' s (h'.mono (inter_subset_left _ _))
 #align set.eq_on.piecewise_ite Set.EqOn.piecewise_ite
+-/
 
 #print Set.piecewise_preimage /-
 theorem piecewise_preimage (f g : α → β) (t) : s.piecewise f g ⁻¹' t = s.ite (f ⁻¹' t) (g ⁻¹' t) :=
@@ -1596,41 +2028,54 @@ theorem piecewise_preimage (f g : α → β) (t) : s.piecewise f g ⁻¹' t = s.
 #align set.piecewise_preimage Set.piecewise_preimage
 -/
 
+#print Set.apply_piecewise /-
 theorem apply_piecewise {δ' : α → Sort _} (h : ∀ i, δ i → δ' i) {x : α} :
     h x (s.piecewise f g x) = s.piecewise (fun x => h x (f x)) (fun x => h x (g x)) x := by
   by_cases hx : x ∈ s <;> simp [hx]
 #align set.apply_piecewise Set.apply_piecewise
+-/
 
+#print Set.apply_piecewise₂ /-
 theorem apply_piecewise₂ {δ' δ'' : α → Sort _} (f' g' : ∀ i, δ' i) (h : ∀ i, δ i → δ' i → δ'' i)
     {x : α} :
     h x (s.piecewise f g x) (s.piecewise f' g' x) =
       s.piecewise (fun x => h x (f x) (f' x)) (fun x => h x (g x) (g' x)) x :=
   by by_cases hx : x ∈ s <;> simp [hx]
 #align set.apply_piecewise₂ Set.apply_piecewise₂
+-/
 
+#print Set.piecewise_op /-
 theorem piecewise_op {δ' : α → Sort _} (h : ∀ i, δ i → δ' i) :
     (s.piecewise (fun x => h x (f x)) fun x => h x (g x)) = fun x => h x (s.piecewise f g x) :=
   funext fun x => (apply_piecewise _ _ _ _).symm
 #align set.piecewise_op Set.piecewise_op
+-/
 
+#print Set.piecewise_op₂ /-
 theorem piecewise_op₂ {δ' δ'' : α → Sort _} (f' g' : ∀ i, δ' i) (h : ∀ i, δ i → δ' i → δ'' i) :
     (s.piecewise (fun x => h x (f x) (f' x)) fun x => h x (g x) (g' x)) = fun x =>
       h x (s.piecewise f g x) (s.piecewise f' g' x) :=
   funext fun x => (apply_piecewise₂ _ _ _ _ _ _).symm
 #align set.piecewise_op₂ Set.piecewise_op₂
+-/
 
+#print Set.piecewise_same /-
 @[simp]
 theorem piecewise_same : s.piecewise f f = f := by ext x; by_cases hx : x ∈ s <;> simp [hx]
 #align set.piecewise_same Set.piecewise_same
+-/
 
+#print Set.range_piecewise /-
 theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪ g '' sᶜ :=
   by
   ext y; constructor
   · rintro ⟨x, rfl⟩; by_cases h : x ∈ s <;> [left; right] <;> use x <;> simp [h]
   · rintro (⟨x, hx, rfl⟩ | ⟨x, hx, rfl⟩) <;> use x <;> simp_all
 #align set.range_piecewise Set.range_piecewise
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y «expr ∉ » s) -/
+#print Set.injective_piecewise_iff /-
 theorem injective_piecewise_iff {f g : α → β} :
     Injective (s.piecewise f g) ↔
       InjOn f s ∧ InjOn g (sᶜ) ∧ ∀ x ∈ s, ∀ (y) (_ : y ∉ s), f x ≠ g y :=
@@ -1640,6 +2085,7 @@ theorem injective_piecewise_iff {f g : α → β} :
   refine' and_congr Iff.rfl (and_congr Iff.rfl <| forall₄_congr fun x hx y hy => _)
   rw [piecewise_eq_of_mem s f g hx, piecewise_eq_of_not_mem s f g hy]
 #align set.injective_piecewise_iff Set.injective_piecewise_iff
+-/
 
 #print Set.piecewise_mem_pi /-
 theorem piecewise_mem_pi {δ : α → Type _} {t : Set α} {t' : ∀ i, Set (δ i)} {f g} (hf : f ∈ pi t t')
@@ -1648,6 +2094,7 @@ theorem piecewise_mem_pi {δ : α → Type _} {t : Set α} {t' : ∀ i, Set (δ
 #align set.piecewise_mem_pi Set.piecewise_mem_pi
 -/
 
+#print Set.pi_piecewise /-
 @[simp]
 theorem pi_piecewise {ι : Type _} {α : ι → Type _} (s s' : Set ι) (t t' : ∀ i, Set (α i))
     [∀ x, Decidable (x ∈ s')] : pi s (s'.piecewise t t') = pi (s ∩ s') t ∩ pi (s \ s') t' :=
@@ -1657,60 +2104,79 @@ theorem pi_piecewise {ι : Type _} {α : ι → Type _} (s s' : Set ι) (t t' :
   refine' forall_congr' fun i => _
   by_cases hi : i ∈ s' <;> simp [*]
 #align set.pi_piecewise Set.pi_piecewise
+-/
 
+#print Set.univ_pi_piecewise_univ /-
 theorem univ_pi_piecewise_univ {ι : Type _} {α : ι → Type _} (s : Set ι) (t : ∀ i, Set (α i))
     [∀ x, Decidable (x ∈ s)] : pi univ (s.piecewise t fun _ => univ) = pi s t := by simp
 #align set.univ_pi_piecewise Set.univ_pi_piecewise_univ
+-/
 
 end Set
 
 open Set
 
+#print StrictMonoOn.injOn /-
 theorem StrictMonoOn.injOn [LinearOrder α] [Preorder β] {f : α → β} {s : Set α}
     (H : StrictMonoOn f s) : s.InjOn f := fun x hx y hy hxy =>
   show Ordering.eq.Compares x y from (H.Compares hx hy).1 hxy
 #align strict_mono_on.inj_on StrictMonoOn.injOn
+-/
 
+#print StrictAntiOn.injOn /-
 theorem StrictAntiOn.injOn [LinearOrder α] [Preorder β] {f : α → β} {s : Set α}
     (H : StrictAntiOn f s) : s.InjOn f :=
   @StrictMonoOn.injOn α βᵒᵈ _ _ f s H
 #align strict_anti_on.inj_on StrictAntiOn.injOn
+-/
 
+#print StrictMonoOn.comp /-
 theorem StrictMonoOn.comp [Preorder α] [Preorder β] [Preorder γ] {g : β → γ} {f : α → β} {s : Set α}
     {t : Set β} (hg : StrictMonoOn g t) (hf : StrictMonoOn f s) (hs : Set.MapsTo f s t) :
     StrictMonoOn (g ∘ f) s := fun x hx y hy hxy => hg (hs hx) (hs hy) <| hf hx hy hxy
 #align strict_mono_on.comp StrictMonoOn.comp
+-/
 
+#print StrictMonoOn.comp_strictAntiOn /-
 theorem StrictMonoOn.comp_strictAntiOn [Preorder α] [Preorder β] [Preorder γ] {g : β → γ}
     {f : α → β} {s : Set α} {t : Set β} (hg : StrictMonoOn g t) (hf : StrictAntiOn f s)
     (hs : Set.MapsTo f s t) : StrictAntiOn (g ∘ f) s := fun x hx y hy hxy =>
   hg (hs hy) (hs hx) <| hf hx hy hxy
 #align strict_mono_on.comp_strict_anti_on StrictMonoOn.comp_strictAntiOn
+-/
 
+#print StrictAntiOn.comp /-
 theorem StrictAntiOn.comp [Preorder α] [Preorder β] [Preorder γ] {g : β → γ} {f : α → β} {s : Set α}
     {t : Set β} (hg : StrictAntiOn g t) (hf : StrictAntiOn f s) (hs : Set.MapsTo f s t) :
     StrictMonoOn (g ∘ f) s := fun x hx y hy hxy => hg (hs hy) (hs hx) <| hf hx hy hxy
 #align strict_anti_on.comp StrictAntiOn.comp
+-/
 
+#print StrictAntiOn.comp_strictMonoOn /-
 theorem StrictAntiOn.comp_strictMonoOn [Preorder α] [Preorder β] [Preorder γ] {g : β → γ}
     {f : α → β} {s : Set α} {t : Set β} (hg : StrictAntiOn g t) (hf : StrictMonoOn f s)
     (hs : Set.MapsTo f s t) : StrictAntiOn (g ∘ f) s := fun x hx y hy hxy =>
   hg (hs hx) (hs hy) <| hf hx hy hxy
 #align strict_anti_on.comp_strict_mono_on StrictAntiOn.comp_strictMonoOn
+-/
 
+#print strictMono_restrict /-
 @[simp]
 theorem strictMono_restrict [Preorder α] [Preorder β] {f : α → β} {s : Set α} :
     StrictMono (s.restrict f) ↔ StrictMonoOn f s := by simp [Set.restrict, StrictMono, StrictMonoOn]
 #align strict_mono_restrict strictMono_restrict
+-/
 
 alias strictMono_restrict ↔ _root_.strict_mono.of_restrict _root_.strict_mono_on.restrict
 #align strict_mono.of_restrict StrictMono.of_restrict
 #align strict_mono_on.restrict StrictMonoOn.restrict
 
+#print StrictMono.codRestrict /-
 theorem StrictMono.codRestrict [Preorder α] [Preorder β] {f : α → β} (hf : StrictMono f) {s : Set β}
     (hs : ∀ x, f x ∈ s) : StrictMono (Set.codRestrict f s hs) :=
   hf
 #align strict_mono.cod_restrict StrictMono.codRestrict
+-/
 
 namespace Function
 
@@ -1718,13 +2184,17 @@ open Set
 
 variable {fa : α → α} {fb : β → β} {f : α → β} {g : β → γ} {s t : Set α}
 
+#print Function.Injective.comp_injOn /-
 theorem Injective.comp_injOn (hg : Injective g) (hf : s.InjOn f) : s.InjOn (g ∘ f) :=
   (hg.InjOn univ).comp hf (mapsTo_univ _ _)
 #align function.injective.comp_inj_on Function.Injective.comp_injOn
+-/
 
+#print Function.Surjective.surjOn /-
 theorem Surjective.surjOn (hf : Surjective f) (s : Set β) : SurjOn f univ s :=
   (surjective_iff_surjOn_univ.1 hf).mono (Subset.refl _) (subset_univ _)
 #align function.surjective.surj_on Function.Surjective.surjOn
+-/
 
 #print Function.LeftInverse.leftInvOn /-
 theorem LeftInverse.leftInvOn {g : β → α} (h : LeftInverse f g) (s : Set β) : LeftInvOn f g s :=
@@ -1746,14 +2216,19 @@ theorem LeftInverse.rightInvOn_range {g : β → α} (h : LeftInverse f g) : Rig
 
 namespace Semiconj
 
+#print Function.Semiconj.mapsTo_image /-
 theorem mapsTo_image (h : Semiconj f fa fb) (ha : MapsTo fa s t) : MapsTo fb (f '' s) (f '' t) :=
   fun y ⟨x, hx, hy⟩ => hy ▸ ⟨fa x, ha hx, h x⟩
 #align function.semiconj.maps_to_image Function.Semiconj.mapsTo_image
+-/
 
+#print Function.Semiconj.mapsTo_range /-
 theorem mapsTo_range (h : Semiconj f fa fb) : MapsTo fb (range f) (range f) := fun y ⟨x, hy⟩ =>
   hy ▸ ⟨fa x, h x⟩
 #align function.semiconj.maps_to_range Function.Semiconj.mapsTo_range
+-/
 
+#print Function.Semiconj.surjOn_image /-
 theorem surjOn_image (h : Semiconj f fa fb) (ha : SurjOn fa s t) : SurjOn fb (f '' s) (f '' t) :=
   by
   rintro y ⟨x, hxt, rfl⟩
@@ -1761,38 +2236,52 @@ theorem surjOn_image (h : Semiconj f fa fb) (ha : SurjOn fa s t) : SurjOn fb (f
   rw [h x]
   exact mem_image_of_mem _ (mem_image_of_mem _ hxs)
 #align function.semiconj.surj_on_image Function.Semiconj.surjOn_image
+-/
 
+#print Function.Semiconj.surjOn_range /-
 theorem surjOn_range (h : Semiconj f fa fb) (ha : Surjective fa) : SurjOn fb (range f) (range f) :=
   by rw [← image_univ]; exact h.surj_on_image (ha.surj_on univ)
 #align function.semiconj.surj_on_range Function.Semiconj.surjOn_range
+-/
 
+#print Function.Semiconj.injOn_image /-
 theorem injOn_image (h : Semiconj f fa fb) (ha : InjOn fa s) (hf : InjOn f (fa '' s)) :
     InjOn fb (f '' s) := by
   rintro _ ⟨x, hx, rfl⟩ _ ⟨y, hy, rfl⟩ H
   simp only [← h.eq] at H 
   exact congr_arg f (ha hx hy <| hf (mem_image_of_mem fa hx) (mem_image_of_mem fa hy) H)
 #align function.semiconj.inj_on_image Function.Semiconj.injOn_image
+-/
 
+#print Function.Semiconj.injOn_range /-
 theorem injOn_range (h : Semiconj f fa fb) (ha : Injective fa) (hf : InjOn f (range fa)) :
     InjOn fb (range f) := by rw [← image_univ] at *; exact h.inj_on_image (ha.inj_on univ) hf
 #align function.semiconj.inj_on_range Function.Semiconj.injOn_range
+-/
 
+#print Function.Semiconj.bijOn_image /-
 theorem bijOn_image (h : Semiconj f fa fb) (ha : BijOn fa s t) (hf : InjOn f t) :
     BijOn fb (f '' s) (f '' t) :=
   ⟨h.mapsTo_image ha.MapsTo, h.injOn_image ha.InjOn (ha.image_eq.symm ▸ hf),
     h.surjOn_image ha.SurjOn⟩
 #align function.semiconj.bij_on_image Function.Semiconj.bijOn_image
+-/
 
+#print Function.Semiconj.bijOn_range /-
 theorem bijOn_range (h : Semiconj f fa fb) (ha : Bijective fa) (hf : Injective f) :
     BijOn fb (range f) (range f) := by
   rw [← image_univ]
   exact h.bij_on_image (bijective_iff_bij_on_univ.1 ha) (hf.inj_on univ)
 #align function.semiconj.bij_on_range Function.Semiconj.bijOn_range
+-/
 
+#print Function.Semiconj.mapsTo_preimage /-
 theorem mapsTo_preimage (h : Semiconj f fa fb) {s t : Set β} (hb : MapsTo fb s t) :
     MapsTo fa (f ⁻¹' s) (f ⁻¹' t) := fun x hx => by simp only [mem_preimage, h x, hb hx]
 #align function.semiconj.maps_to_preimage Function.Semiconj.mapsTo_preimage
+-/
 
+#print Function.Semiconj.injOn_preimage /-
 theorem injOn_preimage (h : Semiconj f fa fb) {s : Set β} (hb : InjOn fb s)
     (hf : InjOn f (f ⁻¹' s)) : InjOn fa (f ⁻¹' s) :=
   by
@@ -1801,24 +2290,32 @@ theorem injOn_preimage (h : Semiconj f fa fb) {s : Set β} (hb : InjOn fb s)
   rw [h.eq, h.eq] at this 
   exact hf hx hy (hb hx hy this)
 #align function.semiconj.inj_on_preimage Function.Semiconj.injOn_preimage
+-/
 
 end Semiconj
 
+#print Function.update_comp_eq_of_not_mem_range' /-
 theorem update_comp_eq_of_not_mem_range' {α β : Sort _} {γ : β → Sort _} [DecidableEq β]
     (g : ∀ b, γ b) {f : α → β} {i : β} (a : γ i) (h : i ∉ Set.range f) :
     (fun j => (Function.update g i a) (f j)) = fun j => g (f j) :=
   update_comp_eq_of_forall_ne' _ _ fun x hx => h ⟨x, hx⟩
 #align function.update_comp_eq_of_not_mem_range' Function.update_comp_eq_of_not_mem_range'
+-/
 
+#print Function.update_comp_eq_of_not_mem_range /-
 /-- Non-dependent version of `function.update_comp_eq_of_not_mem_range'` -/
 theorem update_comp_eq_of_not_mem_range {α β γ : Sort _} [DecidableEq β] (g : β → γ) {f : α → β}
     {i : β} (a : γ) (h : i ∉ Set.range f) : Function.update g i a ∘ f = g ∘ f :=
   update_comp_eq_of_not_mem_range' g a h
 #align function.update_comp_eq_of_not_mem_range Function.update_comp_eq_of_not_mem_range
+-/
 
+#print Function.insert_injOn /-
 theorem insert_injOn (s : Set α) : sᶜ.InjOn fun a => insert a s := fun a ha b _ => (insert_inj ha).1
 #align function.insert_inj_on Function.insert_injOn
+-/
 
+#print Function.monotoneOn_of_rightInvOn_of_mapsTo /-
 theorem monotoneOn_of_rightInvOn_of_mapsTo [PartialOrder α] [LinearOrder β] {φ : β → α} {ψ : α → β}
     {t : Set β} {s : Set α} (hφ : MonotoneOn φ t) (φψs : Set.RightInvOn ψ φ s)
     (ψts : Set.MapsTo ψ s t) : MonotoneOn ψ s :=
@@ -1828,12 +2325,15 @@ theorem monotoneOn_of_rightInvOn_of_mapsTo [PartialOrder α] [LinearOrder β] {
   · exact ψxy
   · cases le_antisymm l (φψs.eq ys ▸ φψs.eq xs ▸ hφ (ψts ys) (ψts xs) ψyx); rfl
 #align function.monotone_on_of_right_inv_on_of_maps_to Function.monotoneOn_of_rightInvOn_of_mapsTo
+-/
 
+#print Function.antitoneOn_of_rightInvOn_of_mapsTo /-
 theorem antitoneOn_of_rightInvOn_of_mapsTo [PartialOrder α] [LinearOrder β] {φ : β → α} {ψ : α → β}
     {t : Set β} {s : Set α} (hφ : AntitoneOn φ t) (φψs : Set.RightInvOn ψ φ s)
     (ψts : Set.MapsTo ψ s t) : AntitoneOn ψ s :=
   (monotoneOn_of_rightInvOn_of_mapsTo hφ.dual_left φψs ψts).dual_right
 #align function.antitone_on_of_right_inv_on_of_maps_to Function.antitoneOn_of_rightInvOn_of_mapsTo
+-/
 
 end Function
 
@@ -1844,11 +2344,14 @@ namespace Set
 
 variable {p : β → Prop} [DecidablePred p] {f : α ≃ Subtype p} {g g₁ g₂ : Perm α} {s t : Set α}
 
+#print Set.MapsTo.extendDomain /-
 protected theorem MapsTo.extendDomain (h : MapsTo g s t) :
     MapsTo (g.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) := by rintro _ ⟨a, ha, rfl⟩;
   exact ⟨_, h ha, by rw [extend_domain_apply_image]⟩
 #align set.maps_to.extend_domain Set.MapsTo.extendDomain
+-/
 
+#print Set.SurjOn.extendDomain /-
 protected theorem SurjOn.extendDomain (h : SurjOn g s t) :
     SurjOn (g.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
   by
@@ -1856,26 +2359,35 @@ protected theorem SurjOn.extendDomain (h : SurjOn g s t) :
   obtain ⟨b, hb, rfl⟩ := h ha
   exact ⟨_, ⟨_, hb, rfl⟩, by rw [extend_domain_apply_image]⟩
 #align set.surj_on.extend_domain Set.SurjOn.extendDomain
+-/
 
+#print Set.BijOn.extendDomain /-
 protected theorem BijOn.extendDomain (h : Set.BijOn g s t) :
     BijOn (g.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
   ⟨h.MapsTo.extendDomain, (g.extendDomain f).Injective.InjOn _, h.SurjOn.extendDomain⟩
 #align set.bij_on.extend_domain Set.BijOn.extendDomain
+-/
 
+#print Set.LeftInvOn.extendDomain /-
 protected theorem LeftInvOn.extendDomain (h : LeftInvOn g₁ g₂ s) :
     LeftInvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' s) := by rintro _ ⟨a, ha, rfl⟩;
   simp_rw [extend_domain_apply_image, h ha]
 #align set.left_inv_on.extend_domain Set.LeftInvOn.extendDomain
+-/
 
+#print Set.RightInvOn.extendDomain /-
 protected theorem RightInvOn.extendDomain (h : RightInvOn g₁ g₂ t) :
     RightInvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' t) := by rintro _ ⟨a, ha, rfl⟩;
   simp_rw [extend_domain_apply_image, h ha]
 #align set.right_inv_on.extend_domain Set.RightInvOn.extendDomain
+-/
 
+#print Set.InvOn.extendDomain /-
 protected theorem InvOn.extendDomain (h : InvOn g₁ g₂ s t) :
     InvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
   ⟨h.1.extendDomain, h.2.extendDomain⟩
 #align set.inv_on.extend_domain Set.InvOn.extendDomain
+-/
 
 end Set
 
@@ -1883,9 +2395,11 @@ namespace Equiv
 
 variable (e : α ≃ β) {s : Set α} {t : Set β}
 
+#print Equiv.bijOn' /-
 theorem bijOn' (h₁ : MapsTo e s t) (h₂ : MapsTo e.symm t s) : BijOn e s t :=
   ⟨h₁, e.Injective.InjOn _, fun b hb => ⟨e.symm b, h₂ hb, apply_symm_apply _ _⟩⟩
 #align equiv.bij_on' Equiv.bijOn'
+-/
 
 #print Equiv.bijOn /-
 protected theorem bijOn (h : ∀ a, e a ∈ t ↔ a ∈ s) : BijOn e s t :=
@@ -1899,9 +2413,11 @@ theorem invOn : InvOn e e.symm t s :=
 #align equiv.inv_on Equiv.invOn
 -/
 
+#print Equiv.bijOn_image /-
 theorem bijOn_image : BijOn e s (e '' s) :=
   (e.Injective.InjOn _).bijOn_image
 #align equiv.bij_on_image Equiv.bijOn_image
+-/
 
 #print Equiv.bijOn_symm_image /-
 theorem bijOn_symm_image : BijOn e.symm (e '' s) s :=

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -1129,7 +1129,6 @@ theorem LeftInvOn.injOn (h : LeftInvOn f₁' f s) : InjOn f s := fun x₁ h₁ x
     x₁ = f₁' (f x₁) := Eq.symm <| h h₁
     _ = f₁' (f x₂) := (congr_arg f₁' HEq)
     _ = x₂ := h h₂
-    
 #align set.left_inv_on.inj_on Set.LeftInvOn.injOn
 
 theorem LeftInvOn.surjOn (h : LeftInvOn f' f s) (hf : MapsTo f s t) : SurjOn f' t s := fun x hx =>
@@ -1152,7 +1151,6 @@ theorem LeftInvOn.comp (hf' : LeftInvOn f' f s) (hg' : LeftInvOn g' g t) (hf : M
   calc
     (f' ∘ g') ((g ∘ f) x) = f' (f x) := congr_arg f' (hg' (hf h))
     _ = x := hf' h
-    
 #align set.left_inv_on.comp Set.LeftInvOn.comp
 
 theorem LeftInvOn.mono (hf : LeftInvOn f' f s) (ht : s₁ ⊆ s) : LeftInvOn f' f s₁ := fun x hx =>
@@ -1255,7 +1253,6 @@ theorem eqOn_of_leftInvOn_of_rightInvOn (h₁ : LeftInvOn f₁' f s) (h₂ : Rig
   calc
     f₁' y = (f₁' ∘ f ∘ f₂') y := congr_arg f₁' (h₂ hy).symm
     _ = f₂' y := h₁ (h hy)
-    
 #align set.eq_on_of_left_inv_on_of_right_inv_on Set.eqOn_of_leftInvOn_of_rightInvOn
 
 theorem SurjOn.leftInvOn_of_rightInvOn (hf : SurjOn f s t) (hf' : RightInvOn f f' s) :

bump to nightly-2023-06-08-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

d3cfe2e3

Diff

@@ -86,7 +86,7 @@ theorem image_restrict (f : α → β) (s t : Set α) : s.restrict f '' (coe ⁻
   rw [restrict, image_comp, image_preimage_eq_inter_range, Subtype.range_coe]
 #align set.image_restrict Set.image_restrict
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ∉ » s) -/
 @[simp]
 theorem restrict_dite {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
     (g : ∀ (a) (_ : a ∉ s), β) :
@@ -94,7 +94,7 @@ theorem restrict_dite {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s
   funext fun a => dif_pos a.2
 #align set.restrict_dite Set.restrict_dite
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ∉ » s) -/
 @[simp]
 theorem restrict_dite_compl {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
     (g : ∀ (a) (_ : a ∉ s), β) :
@@ -1408,7 +1408,7 @@ theorem SurjOn.bijOn_subset [Nonempty α] (h : SurjOn f s t) : BijOn f (invFunOn
   rwa [h.right_inv_on_inv_fun_on hy]
 #align set.surj_on.bij_on_subset Set.SurjOn.bijOn_subset
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (s' «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (s' «expr ⊆ » s) -/
 theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _) (_ : s' ⊆ s), BijOn f s' t :=
   by
   constructor
@@ -1525,7 +1525,7 @@ theorem piecewise_eqOn_compl (f g : α → β) : EqOn (s.piecewise f g) g (sᶜ)
   piecewise_eq_of_not_mem _ _ _
 #align set.piecewise_eq_on_compl Set.piecewise_eqOn_compl
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.piecewise_le /-
 theorem piecewise_le {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g i) (h₂ : ∀ (i) (_ : i ∉ s), f₂ i ≤ g i) :
@@ -1533,7 +1533,7 @@ theorem piecewise_le {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
 #align set.piecewise_le Set.piecewise_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.le_piecewise /-
 theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, g i ≤ f₁ i) (h₂ : ∀ (i) (_ : i ∉ s), g i ≤ f₂ i) :
@@ -1542,7 +1542,7 @@ theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
 #align set.le_piecewise Set.le_piecewise
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.piecewise_le_piecewise /-
 theorem piecewise_le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
     [∀ j, Decidable (j ∈ s)] {f₁ f₂ g₁ g₂ : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g₁ i)
@@ -1633,7 +1633,7 @@ theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪
   · rintro (⟨x, hx, rfl⟩ | ⟨x, hx, rfl⟩) <;> use x <;> simp_all
 #align set.range_piecewise Set.range_piecewise
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y «expr ∉ » s) -/
 theorem injective_piecewise_iff {f g : α → β} :
     Injective (s.piecewise f g) ↔
       InjOn f s ∧ InjOn g (sᶜ) ∧ ∀ x ∈ s, ∀ (y) (_ : y ∉ s), f x ≠ g y :=

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -138,10 +138,10 @@ theorem restrict_extend_compl_range (f : α → β) (g : α → γ) (g' : β →
 theorem range_extend_subset (f : α → β) (g : α → γ) (g' : β → γ) :
     range (extend f g g') ⊆ range g ∪ g' '' range fᶜ := by
   classical
-    rintro _ ⟨y, rfl⟩
-    rw [extend_def]
-    split_ifs
-    exacts [Or.inl (mem_range_self _), Or.inr (mem_image_of_mem _ h)]
+  rintro _ ⟨y, rfl⟩
+  rw [extend_def]
+  split_ifs
+  exacts [Or.inl (mem_range_self _), Or.inr (mem_image_of_mem _ h)]
 #align set.range_extend_subset Set.range_extend_subset
 
 theorem range_extend {f : α → β} (hf : Injective f) (g : α → γ) (g' : β → γ) :

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -141,7 +141,7 @@ theorem range_extend_subset (f : α → β) (g : α → γ) (g' : β → γ) :
     rintro _ ⟨y, rfl⟩
     rw [extend_def]
     split_ifs
-    exacts[Or.inl (mem_range_self _), Or.inr (mem_image_of_mem _ h)]
+    exacts [Or.inl (mem_range_self _), Or.inr (mem_image_of_mem _ h)]
 #align set.range_extend_subset Set.range_extend_subset
 
 theorem range_extend {f : α → β} (hf : Injective f) (g : α → γ) (g' : β → γ) :
@@ -149,7 +149,7 @@ theorem range_extend {f : α → β} (hf : Injective f) (g : α → γ) (g' : β
   by
   refine' (range_extend_subset _ _ _).antisymm _
   rintro z (⟨x, rfl⟩ | ⟨y, hy, rfl⟩)
-  exacts[⟨f x, hf.extend_apply _ _ _⟩, ⟨y, extend_apply' _ _ _ hy⟩]
+  exacts [⟨f x, hf.extend_apply _ _ _⟩, ⟨y, extend_apply' _ _ _ hy⟩]
 #align set.range_extend Set.range_extend
 
 #print Set.codRestrict /-
@@ -679,7 +679,7 @@ theorem injOn_union (h : Disjoint s₁ s₂) :
     exact h.le_bot ⟨hx, hy⟩
   · rintro ⟨h₁, h₂, h₁₂⟩
     rintro x (hx | hx) y (hy | hy) hxy
-    exacts[h₁ hx hy hxy, (h₁₂ _ hx _ hy hxy).elim, (h₁₂ _ hy _ hx hxy.symm).elim, h₂ hx hy hxy]
+    exacts [h₁ hx hy hxy, (h₁₂ _ hx _ hy hxy).elim, (h₁₂ _ hy _ hx hxy.symm).elim, h₂ hx hy hxy]
 #align set.inj_on_union Set.injOn_union
 
 theorem injOn_insert {f : α → β} {s : Set α} {a : α} (has : a ∉ s) :
@@ -783,15 +783,15 @@ theorem InjOn.image_inter {s t u : Set α} (hf : u.InjOn f) (hs : s ⊆ u) (ht :
   rintro x ⟨⟨y, ys, hy⟩, ⟨z, zt, hz⟩⟩
   have : y = z := by
     apply hf (hs ys) (ht zt)
-    rwa [← hz] at hy
-  rw [← this] at zt
+    rwa [← hz] at hy 
+  rw [← this] at zt 
   exact ⟨y, ⟨ys, zt⟩, hy⟩
 #align set.inj_on.image_inter Set.InjOn.image_inter
 
 theorem Disjoint.image {s t u : Set α} {f : α → β} (h : Disjoint s t) (hf : InjOn f u) (hs : s ⊆ u)
     (ht : t ⊆ u) : Disjoint (f '' s) (f '' t) :=
   by
-  rw [disjoint_iff_inter_eq_empty] at h⊢
+  rw [disjoint_iff_inter_eq_empty] at h ⊢
   rw [← hf.image_inter hs ht, h, image_empty]
 #align disjoint.image Disjoint.image
 
@@ -810,7 +810,7 @@ theorem SurjOn.subset_range (h : SurjOn f s t) : t ⊆ range f :=
 #align set.surj_on.subset_range Set.SurjOn.subset_range
 
 theorem surjOn_iff_exists_map_subtype :
-    SurjOn f s t ↔ ∃ (t' : Set β)(g : s → t'), t ⊆ t' ∧ Surjective g ∧ ∀ x : s, f x = g x :=
+    SurjOn f s t ↔ ∃ (t' : Set β) (g : s → t'), t ⊆ t' ∧ Surjective g ∧ ∀ x : s, f x = g x :=
   ⟨fun h =>
     ⟨_, (mapsTo_image f s).restrict f s _, h, surjective_mapsTo_image_restrict _ _, fun _ => rfl⟩,
     fun ⟨t', g, htt', hg, hfg⟩ y hy =>
@@ -1340,7 +1340,7 @@ noncomputable def invFunOn (f : α → β) (s : Set α) (b : β) : α :=
 -/
 
 theorem invFunOn_pos (h : ∃ a ∈ s, f a = b) : invFunOn f s b ∈ s ∧ f (invFunOn f s b) = b := by
-  rw [bex_def] at h <;> rw [inv_fun_on, dif_pos h] <;> exact Classical.choose_spec h
+  rw [bex_def] at h  <;> rw [inv_fun_on, dif_pos h] <;> exact Classical.choose_spec h
 #align function.inv_fun_on_pos Function.invFunOn_pos
 
 theorem invFunOn_mem (h : ∃ a ∈ s, f a = b) : invFunOn f s b ∈ s :=
@@ -1352,7 +1352,7 @@ theorem invFunOn_eq (h : ∃ a ∈ s, f a = b) : f (invFunOn f s b) = b :=
 #align function.inv_fun_on_eq Function.invFunOn_eq
 
 theorem invFunOn_neg (h : ¬∃ a ∈ s, f a = b) : invFunOn f s b = Classical.choice ‹Nonempty α› := by
-  rw [bex_def] at h <;> rw [inv_fun_on, dif_neg h]
+  rw [bex_def] at h  <;> rw [inv_fun_on, dif_neg h]
 #align function.inv_fun_on_neg Function.invFunOn_neg
 
 @[simp]
@@ -1409,7 +1409,7 @@ theorem SurjOn.bijOn_subset [Nonempty α] (h : SurjOn f s t) : BijOn f (invFunOn
 #align set.surj_on.bij_on_subset Set.SurjOn.bijOn_subset
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (s' «expr ⊆ » s) -/
-theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _)(_ : s' ⊆ s), BijOn f s' t :=
+theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _) (_ : s' ⊆ s), BijOn f s' t :=
   by
   constructor
   · rcases eq_empty_or_nonempty t with (rfl | ht)
@@ -1572,7 +1572,7 @@ theorem MapsTo.piecewise_ite {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {f₁
     (h₂ : MapsTo f₂ (s₂ ∩ sᶜ) (t₂ ∩ tᶜ)) : MapsTo (s.piecewise f₁ f₂) (s.ite s₁ s₂) (t.ite t₁ t₂) :=
   by
   refine' (h₁.congr _).union_union (h₂.congr _)
-  exacts[(piecewise_eq_on s f₁ f₂).symm.mono (inter_subset_right _ _),
+  exacts [(piecewise_eq_on s f₁ f₂).symm.mono (inter_subset_right _ _),
     (piecewise_eq_on_compl s f₁ f₂).symm.mono (inter_subset_right _ _)]
 #align set.maps_to.piecewise_ite Set.MapsTo.piecewise_ite
 
@@ -1629,7 +1629,7 @@ theorem piecewise_same : s.piecewise f f = f := by ext x; by_cases hx : x ∈ s
 theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪ g '' sᶜ :=
   by
   ext y; constructor
-  · rintro ⟨x, rfl⟩; by_cases h : x ∈ s <;> [left;right] <;> use x <;> simp [h]
+  · rintro ⟨x, rfl⟩; by_cases h : x ∈ s <;> [left; right] <;> use x <;> simp [h]
   · rintro (⟨x, hx, rfl⟩ | ⟨x, hx, rfl⟩) <;> use x <;> simp_all
 #align set.range_piecewise Set.range_piecewise
 
@@ -1772,7 +1772,7 @@ theorem surjOn_range (h : Semiconj f fa fb) (ha : Surjective fa) : SurjOn fb (ra
 theorem injOn_image (h : Semiconj f fa fb) (ha : InjOn fa s) (hf : InjOn f (fa '' s)) :
     InjOn fb (f '' s) := by
   rintro _ ⟨x, hx, rfl⟩ _ ⟨y, hy, rfl⟩ H
-  simp only [← h.eq] at H
+  simp only [← h.eq] at H 
   exact congr_arg f (ha hx hy <| hf (mem_image_of_mem fa hx) (mem_image_of_mem fa hy) H)
 #align function.semiconj.inj_on_image Function.Semiconj.injOn_image
 
@@ -1801,7 +1801,7 @@ theorem injOn_preimage (h : Semiconj f fa fb) {s : Set β} (hb : InjOn fb s)
   by
   intro x hx y hy H
   have := congr_arg f H
-  rw [h.eq, h.eq] at this
+  rw [h.eq, h.eq] at this 
   exact hf hx hy (hb hx hy this)
 #align function.semiconj.inj_on_preimage Function.Semiconj.injOn_preimage

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -1526,24 +1526,30 @@ theorem piecewise_eqOn_compl (f g : α → β) : EqOn (s.piecewise f g) g (sᶜ)
 #align set.piecewise_eq_on_compl Set.piecewise_eqOn_compl
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
+#print Set.piecewise_le /-
 theorem piecewise_le {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g i) (h₂ : ∀ (i) (_ : i ∉ s), f₂ i ≤ g i) :
     s.piecewise f₁ f₂ ≤ g := fun i => if h : i ∈ s then by simp [*] else by simp [*]
 #align set.piecewise_le Set.piecewise_le
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
+#print Set.le_piecewise /-
 theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, g i ≤ f₁ i) (h₂ : ∀ (i) (_ : i ∉ s), g i ≤ f₂ i) :
     g ≤ s.piecewise f₁ f₂ :=
   @piecewise_le α (fun i => (δ i)ᵒᵈ) _ s _ _ _ _ h₁ h₂
 #align set.le_piecewise Set.le_piecewise
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
+#print Set.piecewise_le_piecewise /-
 theorem piecewise_le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
     [∀ j, Decidable (j ∈ s)] {f₁ f₂ g₁ g₂ : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g₁ i)
     (h₂ : ∀ (i) (_ : i ∉ s), f₂ i ≤ g₂ i) : s.piecewise f₁ f₂ ≤ s.piecewise g₁ g₂ := by
   apply piecewise_le <;> intros <;> simp [*]
 #align set.piecewise_le_piecewise Set.piecewise_le_piecewise
+-/
 
 @[simp]
 theorem piecewise_insert_of_ne {i j : α} (h : i ≠ j) [∀ i, Decidable (i ∈ insert j s)] :

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -58,76 +58,34 @@ def restrict (s : Set α) (f : ∀ a : α, π a) : ∀ a : s, π a := fun x => f
 #align set.restrict Set.restrict
 -/
 
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 theorem restrict_eq (f : α → β) (s : Set α) : s.restrict f = f ∘ coe :=
   rfl
 #align set.restrict_eq Set.restrict_eq
 
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 @[simp]
 theorem restrict_apply (f : α → β) (s : Set α) (x : s) : s.restrict f x = f x :=
   rfl
 #align set.restrict_apply Set.restrict_apply
 
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 theorem restrict_eq_iff {f : ∀ a, π a} {s : Set α} {g : ∀ a : s, π a} :
     restrict s f = g ↔ ∀ (a) (ha : a ∈ s), f a = g ⟨a, ha⟩ :=
   funext_iff.trans Subtype.forall
 #align set.restrict_eq_iff Set.restrict_eq_iff
 
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 theorem eq_restrict_iff {s : Set α} {f : ∀ a : s, π a} {g : ∀ a, π a} :
     f = restrict s g ↔ ∀ (a) (ha : a ∈ s), f ⟨a, ha⟩ = g a :=
   funext_iff.trans Subtype.forall
 #align set.eq_restrict_iff Set.eq_restrict_iff
 
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 @[simp]
 theorem range_restrict (f : α → β) (s : Set α) : Set.range (s.restrict f) = f '' s :=
   (range_comp _ _).trans <| congr_arg ((· '' ·) f) Subtype.range_coe
 #align set.range_restrict Set.range_restrict
 
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 theorem image_restrict (f : α → β) (s t : Set α) : s.restrict f '' (coe ⁻¹' t) = f '' (t ∩ s) := by
   rw [restrict, image_comp, image_preimage_eq_inter_range, Subtype.range_coe]
 #align set.image_restrict Set.image_restrict
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
 @[simp]
 theorem restrict_dite {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
@@ -136,12 +94,6 @@ theorem restrict_dite {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s
   funext fun a => dif_pos a.2
 #align set.restrict_dite Set.restrict_dite
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
 @[simp]
 theorem restrict_dite_compl {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
@@ -150,81 +102,39 @@ theorem restrict_dite_compl {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a
   funext fun a => dif_neg a.2
 #align set.restrict_dite_compl Set.restrict_dite_compl
 
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 @[simp]
 theorem restrict_ite (f g : α → β) (s : Set α) [∀ x, Decidable (x ∈ s)] :
     (s.restrict fun a => if a ∈ s then f a else g a) = s.restrict f :=
   restrict_dite _ _
 #align set.restrict_ite Set.restrict_ite
 
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 @[simp]
 theorem restrict_ite_compl (f g : α → β) (s : Set α) [∀ x, Decidable (x ∈ s)] :
     (sᶜ.restrict fun a => if a ∈ s then f a else g a) = sᶜ.restrict g :=
   restrict_dite_compl _ _
 #align set.restrict_ite_compl Set.restrict_ite_compl
 
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 @[simp]
 theorem restrict_piecewise (f g : α → β) (s : Set α) [∀ x, Decidable (x ∈ s)] :
     s.restrict (piecewise s f g) = s.restrict f :=
   restrict_ite _ _ _
 #align set.restrict_piecewise Set.restrict_piecewise
 
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 @[simp]
 theorem restrict_piecewise_compl (f g : α → β) (s : Set α) [∀ x, Decidable (x ∈ s)] :
     sᶜ.restrict (piecewise s f g) = sᶜ.restrict g :=
   restrict_ite_compl _ _ _
 #align set.restrict_piecewise_compl Set.restrict_piecewise_compl
 
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 theorem restrict_extend_range (f : α → β) (g : α → γ) (g' : β → γ) :
     (range f).restrict (extend f g g') = fun x => g x.coe_prop.some := by convert restrict_dite _ _
 #align set.restrict_extend_range Set.restrict_extend_range
 
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 @[simp]
 theorem restrict_extend_compl_range (f : α → β) (g : α → γ) (g' : β → γ) :
     range fᶜ.restrict (extend f g g') = g' ∘ coe := by convert restrict_dite_compl _ _
 #align set.restrict_extend_compl_range Set.restrict_extend_compl_range
 
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 theorem range_extend_subset (f : α → β) (g : α → γ) (g' : β → γ) :
     range (extend f g g') ⊆ range g ∪ g' '' range fᶜ := by
   classical
@@ -234,12 +144,6 @@ theorem range_extend_subset (f : α → β) (g : α → γ) (g' : β → γ) :
     exacts[Or.inl (mem_range_self _), Or.inr (mem_image_of_mem _ h)]
 #align set.range_extend_subset Set.range_extend_subset
 
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 theorem range_extend {f : α → β} (hf : Injective f) (g : α → γ) (g' : β → γ) :
     range (extend f g g') = range g ∪ g' '' range fᶜ :=
   by
@@ -255,48 +159,24 @@ def codRestrict (f : ι → α) (s : Set α) (h : ∀ x, f x ∈ s) : ι → s :
 #align set.cod_restrict Set.codRestrict
 -/
 
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 @[simp]
 theorem val_codRestrict_apply (f : ι → α) (s : Set α) (h : ∀ x, f x ∈ s) (x : ι) :
     (codRestrict f s h x : α) = f x :=
   rfl
 #align set.coe_cod_restrict_apply Set.val_codRestrict_apply
 
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 @[simp]
 theorem restrict_comp_codRestrict {f : ι → α} {g : α → β} {b : Set α} (h : ∀ x, f x ∈ b) :
     b.restrict g ∘ b.codRestrict f h = g ∘ f :=
   rfl
 #align set.restrict_comp_cod_restrict Set.restrict_comp_codRestrict
 
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 @[simp]
 theorem injective_codRestrict {f : ι → α} {s : Set α} (h : ∀ x, f x ∈ s) :
     Injective (codRestrict f s h) ↔ Injective f := by
   simp only [injective, Subtype.ext_iff, coe_cod_restrict_apply]
 #align set.injective_cod_restrict Set.injective_codRestrict
 
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 alias injective_cod_restrict ↔ _ _root_.function.injective.cod_restrict
 #align function.injective.cod_restrict Function.Injective.codRestrict
 
@@ -314,12 +194,6 @@ def EqOn (f₁ f₂ : α → β) (s : Set α) : Prop :=
 #align set.eq_on Set.EqOn
 -/
 
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 @[simp]
 theorem eqOn_empty (f₁ f₂ : α → β) : EqOn f₁ f₂ ∅ := fun x => False.elim
 #align set.eq_on_empty Set.eqOn_empty
@@ -328,136 +202,58 @@ theorem eqOn_empty (f₁ f₂ : α → β) : EqOn f₁ f₂ ∅ := fun x => Fals
 theorem eqOn_singleton : EqOn f₁ f₂ {a} ↔ f₁ a = f₂ a := by simp [Set.EqOn]
 #align set.eq_on_singleton Set.eqOn_singleton
 
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 @[simp]
 theorem restrict_eq_restrict_iff : restrict s f₁ = restrict s f₂ ↔ EqOn f₁ f₂ s :=
   restrict_eq_iff
 #align set.restrict_eq_restrict_iff Set.restrict_eq_restrict_iff
 
-/- warning: set.eq_on.symm -> Set.EqOn.symm is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.eq_on.symm Set.EqOn.symmₓ'. -/
 @[symm]
 theorem EqOn.symm (h : EqOn f₁ f₂ s) : EqOn f₂ f₁ s := fun x hx => (h hx).symm
 #align set.eq_on.symm Set.EqOn.symm
 
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-Case conversion may be inaccurate. Consider using '#align set.eq_on_comm Set.eqOn_commₓ'. -/
 theorem eqOn_comm : EqOn f₁ f₂ s ↔ EqOn f₂ f₁ s :=
   ⟨EqOn.symm, EqOn.symm⟩
 #align set.eq_on_comm Set.eqOn_comm
 
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.eq_on_refl Set.eqOn_reflₓ'. -/
 @[refl]
 theorem eqOn_refl (f : α → β) (s : Set α) : EqOn f f s := fun _ _ => rfl
 #align set.eq_on_refl Set.eqOn_refl
 
-/- warning: set.eq_on.trans -> Set.EqOn.trans is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.eq_on.trans Set.EqOn.transₓ'. -/
 @[trans]
 theorem EqOn.trans (h₁ : EqOn f₁ f₂ s) (h₂ : EqOn f₂ f₃ s) : EqOn f₁ f₃ s := fun x hx =>
   (h₁ hx).trans (h₂ hx)
 #align set.eq_on.trans Set.EqOn.trans
 
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-Case conversion may be inaccurate. Consider using '#align set.eq_on.image_eq Set.EqOn.image_eqₓ'. -/
 theorem EqOn.image_eq (heq : EqOn f₁ f₂ s) : f₁ '' s = f₂ '' s :=
   image_congr HEq
 #align set.eq_on.image_eq Set.EqOn.image_eq
 
-/- warning: set.eq_on.inter_preimage_eq -> Set.EqOn.inter_preimage_eq is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.eq_on.inter_preimage_eq Set.EqOn.inter_preimage_eqₓ'. -/
 theorem EqOn.inter_preimage_eq (heq : EqOn f₁ f₂ s) (t : Set β) : s ∩ f₁ ⁻¹' t = s ∩ f₂ ⁻¹' t :=
   ext fun x => and_congr_right_iff.2 fun hx => by rw [mem_preimage, mem_preimage, HEq hx]
 #align set.eq_on.inter_preimage_eq Set.EqOn.inter_preimage_eq
 
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-Case conversion may be inaccurate. Consider using '#align set.eq_on.mono Set.EqOn.monoₓ'. -/
 theorem EqOn.mono (hs : s₁ ⊆ s₂) (hf : EqOn f₁ f₂ s₂) : EqOn f₁ f₂ s₁ := fun x hx => hf (hs hx)
 #align set.eq_on.mono Set.EqOn.mono
 
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-Case conversion may be inaccurate. Consider using '#align set.eq_on_union Set.eqOn_unionₓ'. -/
 @[simp]
 theorem eqOn_union : EqOn f₁ f₂ (s₁ ∪ s₂) ↔ EqOn f₁ f₂ s₁ ∧ EqOn f₁ f₂ s₂ :=
   ball_or_left
 #align set.eq_on_union Set.eqOn_union
 
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.eq_on.union Set.EqOn.unionₓ'. -/
 theorem EqOn.union (h₁ : EqOn f₁ f₂ s₁) (h₂ : EqOn f₁ f₂ s₂) : EqOn f₁ f₂ (s₁ ∪ s₂) :=
   eqOn_union.2 ⟨h₁, h₂⟩
 #align set.eq_on.union Set.EqOn.union
 
-/- warning: set.eq_on.comp_left -> Set.EqOn.comp_left is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.eq_on.comp_left Set.EqOn.comp_leftₓ'. -/
 theorem EqOn.comp_left (h : s.EqOn f₁ f₂) : s.EqOn (g ∘ f₁) (g ∘ f₂) := fun a ha =>
   congr_arg _ <| h ha
 #align set.eq_on.comp_left Set.EqOn.comp_left
 
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-Case conversion may be inaccurate. Consider using '#align set.eq_on_range Set.eqOn_rangeₓ'. -/
 @[simp]
 theorem eqOn_range {ι : Sort _} {f : ι → α} {g₁ g₂ : α → β} :
     EqOn g₁ g₂ (range f) ↔ g₁ ∘ f = g₂ ∘ f :=
   forall_range_iff.trans <| funext_iff.symm
 #align set.eq_on_range Set.eqOn_range
 
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-Case conversion may be inaccurate. Consider using '#align set.eq_on.comp_eq Set.EqOn.comp_eqₓ'. -/
 alias eq_on_range ↔ eq_on.comp_eq _
 #align set.eq_on.comp_eq Set.EqOn.comp_eq
 
@@ -468,12 +264,6 @@ section Order
 
 variable [Preorder α] [Preorder β]
 
-/- warning: monotone_on.congr -> MonotoneOn.congr is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align monotone_on.congr MonotoneOn.congrₓ'. -/
 theorem MonotoneOn.congr (h₁ : MonotoneOn f₁ s) (h : s.EqOn f₁ f₂) : MonotoneOn f₂ s :=
   by
   intro a ha b hb hab
@@ -481,22 +271,10 @@ theorem MonotoneOn.congr (h₁ : MonotoneOn f₁ s) (h : s.EqOn f₁ f₂) : Mon
   exact h₁ ha hb hab
 #align monotone_on.congr MonotoneOn.congr
 
-/- warning: antitone_on.congr -> AntitoneOn.congr is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align antitone_on.congr AntitoneOn.congrₓ'. -/
 theorem AntitoneOn.congr (h₁ : AntitoneOn f₁ s) (h : s.EqOn f₁ f₂) : AntitoneOn f₂ s :=
   h₁.dual_right.congr h
 #align antitone_on.congr AntitoneOn.congr
 
-/- warning: strict_mono_on.congr -> StrictMonoOn.congr is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align strict_mono_on.congr StrictMonoOn.congrₓ'. -/
 theorem StrictMonoOn.congr (h₁ : StrictMonoOn f₁ s) (h : s.EqOn f₁ f₂) : StrictMonoOn f₂ s :=
   by
   intro a ha b hb hab
@@ -504,52 +282,22 @@ theorem StrictMonoOn.congr (h₁ : StrictMonoOn f₁ s) (h : s.EqOn f₁ f₂) :
   exact h₁ ha hb hab
 #align strict_mono_on.congr StrictMonoOn.congr
 
-/- warning: strict_anti_on.congr -> StrictAntiOn.congr is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align strict_anti_on.congr StrictAntiOn.congrₓ'. -/
 theorem StrictAntiOn.congr (h₁ : StrictAntiOn f₁ s) (h : s.EqOn f₁ f₂) : StrictAntiOn f₂ s :=
   h₁.dual_right.congr h
 #align strict_anti_on.congr StrictAntiOn.congr
 
-/- warning: set.eq_on.congr_monotone_on -> Set.EqOn.congr_monotoneOn is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.eq_on.congr_monotone_on Set.EqOn.congr_monotoneOnₓ'. -/
 theorem EqOn.congr_monotoneOn (h : s.EqOn f₁ f₂) : MonotoneOn f₁ s ↔ MonotoneOn f₂ s :=
   ⟨fun h₁ => h₁.congr h, fun h₂ => h₂.congr h.symm⟩
 #align set.eq_on.congr_monotone_on Set.EqOn.congr_monotoneOn
 
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 theorem EqOn.congr_antitoneOn (h : s.EqOn f₁ f₂) : AntitoneOn f₁ s ↔ AntitoneOn f₂ s :=
   ⟨fun h₁ => h₁.congr h, fun h₂ => h₂.congr h.symm⟩
 #align set.eq_on.congr_antitone_on Set.EqOn.congr_antitoneOn
 
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 theorem EqOn.congr_strictMonoOn (h : s.EqOn f₁ f₂) : StrictMonoOn f₁ s ↔ StrictMonoOn f₂ s :=
   ⟨fun h₁ => h₁.congr h, fun h₂ => h₂.congr h.symm⟩
 #align set.eq_on.congr_strict_mono_on Set.EqOn.congr_strictMonoOn
 
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 theorem EqOn.congr_strictAntiOn (h : s.EqOn f₁ f₂) : StrictAntiOn f₁ s ↔ StrictAntiOn f₂ s :=
   ⟨fun h₁ => h₁.congr h, fun h₂ => h₂.congr h.symm⟩
 #align set.eq_on.congr_strict_anti_on Set.EqOn.congr_strictAntiOn
@@ -563,82 +311,34 @@ section Mono
 
 variable [Preorder α] [Preorder β]
 
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 theorem MonotoneOn.mono (h : MonotoneOn f s) (h' : s₂ ⊆ s) : MonotoneOn f s₂ := fun x hx y hy =>
   h (h' hx) (h' hy)
 #align monotone_on.mono MonotoneOn.mono
 
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 theorem AntitoneOn.mono (h : AntitoneOn f s) (h' : s₂ ⊆ s) : AntitoneOn f s₂ := fun x hx y hy =>
   h (h' hx) (h' hy)
 #align antitone_on.mono AntitoneOn.mono
 
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 theorem StrictMonoOn.mono (h : StrictMonoOn f s) (h' : s₂ ⊆ s) : StrictMonoOn f s₂ :=
   fun x hx y hy => h (h' hx) (h' hy)
 #align strict_mono_on.mono StrictMonoOn.mono
 
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 theorem StrictAntiOn.mono (h : StrictAntiOn f s) (h' : s₂ ⊆ s) : StrictAntiOn f s₂ :=
   fun x hx y hy => h (h' hx) (h' hy)
 #align strict_anti_on.mono StrictAntiOn.mono
 
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 protected theorem MonotoneOn.monotone (h : MonotoneOn f s) : Monotone (f ∘ coe : s → β) :=
   fun x y hle => h x.coe_prop y.coe_prop hle
 #align monotone_on.monotone MonotoneOn.monotone
 
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 protected theorem AntitoneOn.monotone (h : AntitoneOn f s) : Antitone (f ∘ coe : s → β) :=
   fun x y hle => h x.coe_prop y.coe_prop hle
 #align antitone_on.monotone AntitoneOn.monotone
 
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 protected theorem StrictMonoOn.strictMono (h : StrictMonoOn f s) : StrictMono (f ∘ coe : s → β) :=
   fun x y hlt => h x.coe_prop y.coe_prop hlt
 #align strict_mono_on.strict_mono StrictMonoOn.strictMono
 
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 protected theorem StrictAntiOn.strictAnti (h : StrictAntiOn f s) : StrictAnti (f ∘ coe : s → β) :=
   fun x y hlt => h x.coe_prop y.coe_prop hlt
 #align strict_anti_on.strict_anti StrictAntiOn.strictAnti
@@ -663,23 +363,11 @@ def MapsTo.restrict (f : α → β) (s : Set α) (t : Set β) (h : MapsTo f s t)
 #align set.maps_to.restrict Set.MapsTo.restrict
 -/
 
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 @[simp]
 theorem MapsTo.val_restrict_apply (h : MapsTo f s t) (x : s) : (h.restrict f s t x : β) = f x :=
   rfl
 #align set.maps_to.coe_restrict_apply Set.MapsTo.val_restrict_apply
 
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 /-- Restricting the domain and then the codomain is the same as `maps_to.restrict`. -/
 @[simp]
 theorem codRestrict_restrict (h : ∀ x : s, f x ∈ t) :
@@ -687,76 +375,34 @@ theorem codRestrict_restrict (h : ∀ x : s, f x ∈ t) :
   rfl
 #align set.cod_restrict_restrict Set.codRestrict_restrict
 
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 /-- Reverse of `set.cod_restrict_restrict`. -/
 theorem MapsTo.restrict_eq_codRestrict (h : MapsTo f s t) :
     h.restrict f s t = codRestrict (s.restrict f) t fun x => h x.2 :=
   rfl
 #align set.maps_to.restrict_eq_cod_restrict Set.MapsTo.restrict_eq_codRestrict
 
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 theorem MapsTo.coe_restrict (h : Set.MapsTo f s t) : coe ∘ h.restrict f s t = s.restrict f :=
   rfl
 #align set.maps_to.coe_restrict Set.MapsTo.coe_restrict
 
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 theorem MapsTo.range_restrict (f : α → β) (s : Set α) (t : Set β) (h : MapsTo f s t) :
     range (h.restrict f s t) = coe ⁻¹' (f '' s) :=
   Set.range_subtype_map f h
 #align set.maps_to.range_restrict Set.MapsTo.range_restrict
 
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 theorem mapsTo_iff_exists_map_subtype : MapsTo f s t ↔ ∃ g : s → t, ∀ x : s, f x = g x :=
   ⟨fun h => ⟨h.restrict f s t, fun _ => rfl⟩, fun ⟨g, hg⟩ x hx => by erw [hg ⟨x, hx⟩];
     apply Subtype.coe_prop⟩
 #align set.maps_to_iff_exists_map_subtype Set.mapsTo_iff_exists_map_subtype
 
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 theorem mapsTo' : MapsTo f s t ↔ f '' s ⊆ t :=
   image_subset_iff.symm
 #align set.maps_to' Set.mapsTo'
 
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-Case conversion may be inaccurate. Consider using '#align set.maps_to_prod_map_diagonal Set.mapsTo_prod_map_diagonalₓ'. -/
 theorem mapsTo_prod_map_diagonal : MapsTo (Prod.map f f) (diagonal α) (diagonal β) :=
   diagonal_subset_iff.2 fun x => rfl
 #align set.maps_to_prod_map_diagonal Set.mapsTo_prod_map_diagonal
 
-/- warning: set.maps_to.subset_preimage -> Set.MapsTo.subset_preimage is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {f : α -> β} {s : Set.{u1} α} {t : Set.{u2} β}, (Set.MapsTo.{u1, u2} α β f s t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.preimage.{u1, u2} α β f t))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.maps_to.subset_preimage Set.MapsTo.subset_preimageₓ'. -/
 theorem MapsTo.subset_preimage {f : α → β} {s : Set α} {t : Set β} (hf : MapsTo f s t) :
     s ⊆ f ⁻¹' t :=
   hf
@@ -768,63 +414,27 @@ theorem mapsTo_empty (f : α → β) (t : Set β) : MapsTo f ∅ t :=
 #align set.maps_to_empty Set.mapsTo_empty
 -/
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.maps_to_singleton Set.mapsTo_singletonₓ'. -/
 @[simp]
 theorem mapsTo_singleton : MapsTo f {a} t ↔ f a ∈ t :=
   singleton_subset_iff
 #align set.maps_to_singleton Set.mapsTo_singleton
 
-/- warning: set.maps_to.image_subset -> Set.MapsTo.image_subset is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.maps_to.image_subset Set.MapsTo.image_subsetₓ'. -/
 theorem MapsTo.image_subset (h : MapsTo f s t) : f '' s ⊆ t :=
   mapsTo'.1 h
 #align set.maps_to.image_subset Set.MapsTo.image_subset
 
-/- warning: set.maps_to.congr -> Set.MapsTo.congr 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.maps_to.congr Set.MapsTo.congrₓ'. -/
 theorem MapsTo.congr (h₁ : MapsTo f₁ s t) (h : EqOn f₁ f₂ s) : MapsTo f₂ s t := fun x hx =>
   h hx ▸ h₁ hx
 #align set.maps_to.congr Set.MapsTo.congr
 
-/- warning: set.eq_on.comp_right -> Set.EqOn.comp_right is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.eq_on.comp_right Set.EqOn.comp_rightₓ'. -/
 theorem EqOn.comp_right (hg : t.EqOn g₁ g₂) (hf : s.MapsTo f t) : s.EqOn (g₁ ∘ f) (g₂ ∘ f) :=
   fun a ha => hg <| hf ha
 #align set.eq_on.comp_right Set.EqOn.comp_right
 
-/- warning: set.eq_on.maps_to_iff -> Set.EqOn.mapsTo_iff is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} {t : Set.{u2} β} {f₁ : α -> β} {f₂ : α -> β}, (Set.EqOn.{u1, u2} α β f₁ f₂ s) -> (Iff (Set.MapsTo.{u1, u2} α β f₁ s t) (Set.MapsTo.{u1, u2} α β f₂ s t))
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-Case conversion may be inaccurate. Consider using '#align set.eq_on.maps_to_iff Set.EqOn.mapsTo_iffₓ'. -/
 theorem EqOn.mapsTo_iff (H : EqOn f₁ f₂ s) : MapsTo f₁ s t ↔ MapsTo f₂ s t :=
   ⟨fun h => h.congr H, fun h => h.congr H.symm⟩
 #align set.eq_on.maps_to_iff Set.EqOn.mapsTo_iff
 
-/- warning: set.maps_to.comp -> Set.MapsTo.comp is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.maps_to.comp Set.MapsTo.compₓ'. -/
 theorem MapsTo.comp (h₁ : MapsTo g t p) (h₂ : MapsTo f s t) : MapsTo (g ∘ f) s p := fun x h =>
   h₁ (h₂ h)
 #align set.maps_to.comp Set.MapsTo.comp
@@ -865,63 +475,27 @@ theorem mapsTo_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) :
 #align set.maps_to_of_subsingleton Set.mapsTo_of_subsingleton
 -/
 
-/- warning: set.maps_to.mono -> Set.MapsTo.mono is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.maps_to.mono Set.MapsTo.monoₓ'. -/
 theorem MapsTo.mono (hf : MapsTo f s₁ t₁) (hs : s₂ ⊆ s₁) (ht : t₁ ⊆ t₂) : MapsTo f s₂ t₂ :=
   fun x hx => ht (hf <| hs hx)
 #align set.maps_to.mono Set.MapsTo.mono
 
-/- warning: set.maps_to.mono_left -> Set.MapsTo.mono_left 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.maps_to.mono_left Set.MapsTo.mono_leftₓ'. -/
 theorem MapsTo.mono_left (hf : MapsTo f s₁ t) (hs : s₂ ⊆ s₁) : MapsTo f s₂ t := fun x hx =>
   hf (hs hx)
 #align set.maps_to.mono_left Set.MapsTo.mono_left
 
-/- warning: set.maps_to.mono_right -> Set.MapsTo.mono_right is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.maps_to.mono_right Set.MapsTo.mono_rightₓ'. -/
 theorem MapsTo.mono_right (hf : MapsTo f s t₁) (ht : t₁ ⊆ t₂) : MapsTo f s t₂ := fun x hx =>
   ht (hf hx)
 #align set.maps_to.mono_right Set.MapsTo.mono_right
 
-/- warning: set.maps_to.union_union -> Set.MapsTo.union_union is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.maps_to.union_union Set.MapsTo.union_unionₓ'. -/
 theorem MapsTo.union_union (h₁ : MapsTo f s₁ t₁) (h₂ : MapsTo f s₂ t₂) :
     MapsTo f (s₁ ∪ s₂) (t₁ ∪ t₂) := fun x hx =>
   hx.elim (fun hx => Or.inl <| h₁ hx) fun hx => Or.inr <| h₂ hx
 #align set.maps_to.union_union Set.MapsTo.union_union
 
-/- warning: set.maps_to.union -> Set.MapsTo.union is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.maps_to.union Set.MapsTo.unionₓ'. -/
 theorem MapsTo.union (h₁ : MapsTo f s₁ t) (h₂ : MapsTo f s₂ t) : MapsTo f (s₁ ∪ s₂) t :=
   union_self t ▸ h₁.union_union h₂
 #align set.maps_to.union Set.MapsTo.union
 
-/- warning: set.maps_to_union -> Set.mapsTo_union is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.maps_to_union Set.mapsTo_unionₓ'. -/
 @[simp]
 theorem mapsTo_union : MapsTo f (s₁ ∪ s₂) t ↔ MapsTo f s₁ t ∧ MapsTo f s₂ t :=
   ⟨fun h =>
@@ -930,32 +504,14 @@ theorem mapsTo_union : MapsTo f (s₁ ∪ s₂) t ↔ MapsTo f s₁ t ∧ MapsTo
     fun h => h.1.union h.2⟩
 #align set.maps_to_union Set.mapsTo_union
 
-/- warning: set.maps_to.inter -> Set.MapsTo.inter 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.maps_to.inter Set.MapsTo.interₓ'. -/
 theorem MapsTo.inter (h₁ : MapsTo f s t₁) (h₂ : MapsTo f s t₂) : MapsTo f s (t₁ ∩ t₂) := fun x hx =>
   ⟨h₁ hx, h₂ hx⟩
 #align set.maps_to.inter Set.MapsTo.inter
 
-/- warning: set.maps_to.inter_inter -> Set.MapsTo.inter_inter is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.maps_to.inter_inter Set.MapsTo.inter_interₓ'. -/
 theorem MapsTo.inter_inter (h₁ : MapsTo f s₁ t₁) (h₂ : MapsTo f s₂ t₂) :
     MapsTo f (s₁ ∩ s₂) (t₁ ∩ t₂) := fun x hx => ⟨h₁ hx.1, h₂ hx.2⟩
 #align set.maps_to.inter_inter Set.MapsTo.inter_inter
 
-/- warning: set.maps_to_inter -> Set.mapsTo_inter is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.maps_to_inter Set.mapsTo_interₓ'. -/
 @[simp]
 theorem mapsTo_inter : MapsTo f s (t₁ ∩ t₂) ↔ MapsTo f s t₁ ∧ MapsTo f s t₂ :=
   ⟨fun h =>
@@ -964,21 +520,9 @@ theorem mapsTo_inter : MapsTo f s (t₁ ∩ t₂) ↔ MapsTo f s t₁ ∧ MapsTo
     fun h => h.1.inter h.2⟩
 #align set.maps_to_inter Set.mapsTo_inter
 
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 theorem mapsTo_univ (f : α → β) (s : Set α) : MapsTo f s univ := fun x h => trivial
 #align set.maps_to_univ Set.mapsTo_univ
 
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-Case conversion may be inaccurate. Consider using '#align set.maps_to_image Set.mapsTo_imageₓ'. -/
 theorem mapsTo_image (f : α → β) (s : Set α) : MapsTo f s (f '' s) := by rw [maps_to']
 #align set.maps_to_image Set.mapsTo_image
 
@@ -988,12 +532,6 @@ theorem mapsTo_preimage (f : α → β) (t : Set β) : MapsTo f (f ⁻¹' t) t :
 #align set.maps_to_preimage Set.mapsTo_preimage
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.maps_to_range Set.mapsTo_rangeₓ'. -/
 theorem mapsTo_range (f : α → β) (s : Set α) : MapsTo f s (range f) :=
   (mapsTo_image f s).mono (Subset.refl s) (image_subset_range _ _)
 #align set.maps_to_range Set.mapsTo_range
@@ -1006,22 +544,10 @@ theorem maps_image_to (f : α → β) (g : γ → α) (s : Set γ) (t : Set β)
 #align set.maps_image_to Set.maps_image_to
 -/
 
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 theorem MapsTo.comp_left (g : β → γ) (hf : MapsTo f s t) : MapsTo (g ∘ f) s (g '' t) := fun x hx =>
   ⟨f x, hf hx, rfl⟩
 #align set.maps_to.comp_left Set.MapsTo.comp_left
 
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-Case conversion may be inaccurate. Consider using '#align set.maps_to.comp_right Set.MapsTo.comp_rightₓ'. -/
 theorem MapsTo.comp_right {s : Set β} {t : Set γ} (hg : MapsTo g s t) (f : α → β) :
     MapsTo (g ∘ f) (f ⁻¹' s) t := fun x hx => hg hx
 #align set.maps_to.comp_right Set.MapsTo.comp_right
@@ -1033,34 +559,16 @@ theorem maps_univ_to (f : α → β) (s : Set β) : MapsTo f univ s ↔ ∀ a, f
 #align set.maps_univ_to Set.maps_univ_to
 -/
 
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 @[simp]
 theorem maps_range_to (f : α → β) (g : γ → α) (s : Set β) :
     MapsTo f (range g) s ↔ MapsTo (f ∘ g) univ s := by rw [← image_univ, maps_image_to]
 #align set.maps_range_to Set.maps_range_to
 
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 theorem surjective_mapsTo_image_restrict (f : α → β) (s : Set α) :
     Surjective ((mapsTo_image f s).restrict f s (f '' s)) := fun ⟨y, x, hs, hxy⟩ =>
   ⟨⟨x, hs⟩, Subtype.ext hxy⟩
 #align set.surjective_maps_to_image_restrict Set.surjective_mapsTo_image_restrict
 
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 theorem MapsTo.mem_iff (h : MapsTo f s t) (hc : MapsTo f (sᶜ) (tᶜ)) {x} : f x ∈ t ↔ x ∈ s :=
   ⟨fun ht => by_contra fun hs => hc hs ht, fun hx => h hx⟩
 #align set.maps_to.mem_iff Set.MapsTo.mem_iff
@@ -1091,61 +599,25 @@ theorem range_restrictPreimage : range (t.restrictPreimage f) = coe ⁻¹' range
 
 variable {f} {U : ι → Set β}
 
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 theorem restrictPreimage_injective (hf : Injective f) : Injective (t.restrictPreimage f) :=
   fun x y e => Subtype.mk.injArrow e fun e => Subtype.coe_injective (hf e)
 #align set.restrict_preimage_injective Set.restrictPreimage_injective
 
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 theorem restrictPreimage_surjective (hf : Surjective f) : Surjective (t.restrictPreimage f) :=
   fun x =>
   ⟨⟨_, show f (hf x).some ∈ t from (hf x).choose_spec.symm ▸ x.2⟩, Subtype.ext (hf x).choose_spec⟩
 #align set.restrict_preimage_surjective Set.restrictPreimage_surjective
 
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 theorem restrictPreimage_bijective (hf : Bijective f) : Bijective (t.restrictPreimage f) :=
   ⟨t.restrictPreimage_injective hf.1, t.restrictPreimage_surjective hf.2⟩
 #align set.restrict_preimage_bijective Set.restrictPreimage_bijective
 
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 alias Set.restrictPreimage_injective ← _root_.function.injective.restrict_preimage
 #align function.injective.restrict_preimage Function.Injective.restrictPreimage
 
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 alias Set.restrictPreimage_surjective ← _root_.function.surjective.restrict_preimage
 #align function.surjective.restrict_preimage Function.Surjective.restrictPreimage
 
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 alias Set.restrictPreimage_bijective ← _root_.function.bijective.restrict_preimage
 #align function.bijective.restrict_preimage Function.Bijective.restrictPreimage
 
@@ -1161,103 +633,43 @@ def InjOn (f : α → β) (s : Set α) : Prop :=
 #align set.inj_on Set.InjOn
 -/
 
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 theorem Subsingleton.injOn (hs : s.Subsingleton) (f : α → β) : InjOn f s := fun x hx y hy h =>
   hs hx hy
 #align set.subsingleton.inj_on Set.Subsingleton.injOn
 
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 @[simp]
 theorem injOn_empty (f : α → β) : InjOn f ∅ :=
   subsingleton_empty.InjOn f
 #align set.inj_on_empty Set.injOn_empty
 
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-Case conversion may be inaccurate. Consider using '#align set.inj_on_singleton Set.injOn_singletonₓ'. -/
 @[simp]
 theorem injOn_singleton (f : α → β) (a : α) : InjOn f {a} :=
   subsingleton_singleton.InjOn f
 #align set.inj_on_singleton Set.injOn_singleton
 
-/- warning: set.inj_on.eq_iff -> Set.InjOn.eq_iff is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.inj_on.eq_iff Set.InjOn.eq_iffₓ'. -/
 theorem InjOn.eq_iff {x y} (h : InjOn f s) (hx : x ∈ s) (hy : y ∈ s) : f x = f y ↔ x = y :=
   ⟨h hx hy, fun h => h ▸ rfl⟩
 #align set.inj_on.eq_iff Set.InjOn.eq_iff
 
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-Case conversion may be inaccurate. Consider using '#align set.inj_on.ne_iff Set.InjOn.ne_iffₓ'. -/
 theorem InjOn.ne_iff {x y} (h : InjOn f s) (hx : x ∈ s) (hy : y ∈ s) : f x ≠ f y ↔ x ≠ y :=
   (h.eq_iff hx hy).Not
 #align set.inj_on.ne_iff Set.InjOn.ne_iff
 
-/- warning: set.inj_on.ne -> Set.InjOn.ne is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inj_on.ne Set.InjOn.neₓ'. -/
 alias inj_on.ne_iff ↔ _ inj_on.ne
 #align set.inj_on.ne Set.InjOn.ne
 
-/- warning: set.inj_on.congr -> Set.InjOn.congr is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inj_on.congr Set.InjOn.congrₓ'. -/
 theorem InjOn.congr (h₁ : InjOn f₁ s) (h : EqOn f₁ f₂ s) : InjOn f₂ s := fun x hx y hy =>
   h hx ▸ h hy ▸ h₁ hx hy
 #align set.inj_on.congr Set.InjOn.congr
 
-/- warning: set.eq_on.inj_on_iff -> Set.EqOn.injOn_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.eq_on.inj_on_iff Set.EqOn.injOn_iffₓ'. -/
 theorem EqOn.injOn_iff (H : EqOn f₁ f₂ s) : InjOn f₁ s ↔ InjOn f₂ s :=
   ⟨fun h => h.congr H, fun h => h.congr H.symm⟩
 #align set.eq_on.inj_on_iff Set.EqOn.injOn_iff
 
-/- warning: set.inj_on.mono -> Set.InjOn.mono is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inj_on.mono Set.InjOn.monoₓ'. -/
 theorem InjOn.mono (h : s₁ ⊆ s₂) (ht : InjOn f s₂) : InjOn f s₁ := fun x hx y hy H =>
   ht (h hx) (h hy) H
 #align set.inj_on.mono Set.InjOn.mono
 
-/- warning: set.inj_on_union -> Set.injOn_union is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} {s₁ : Set.{u1} α} {s₂ : Set.{u1} α} {f : α -> β}, (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s₁ s₂) -> (Iff (Set.InjOn.{u1, u2} α β f (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s₁ s₂)) (And (Set.InjOn.{u1, u2} α β f s₁) (And (Set.InjOn.{u1, u2} α β f s₂) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s₁) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s₂) -> (Ne.{succ u2} β (f x) (f y)))))))
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-Case conversion may be inaccurate. Consider using '#align set.inj_on_union Set.injOn_unionₓ'. -/
 theorem injOn_union (h : Disjoint s₁ s₂) :
     InjOn f (s₁ ∪ s₂) ↔ InjOn f s₁ ∧ InjOn f s₂ ∧ ∀ x ∈ s₁, ∀ y ∈ s₂, f x ≠ f y :=
   by
@@ -1270,12 +682,6 @@ theorem injOn_union (h : Disjoint s₁ s₂) :
     exacts[h₁ hx hy hxy, (h₁₂ _ hx _ hy hxy).elim, (h₁₂ _ hy _ hx hxy.symm).elim, h₂ hx hy hxy]
 #align set.inj_on_union Set.injOn_union
 
-/- warning: set.inj_on_insert -> Set.injOn_insert is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inj_on_insert Set.injOn_insertₓ'. -/
 theorem injOn_insert {f : α → β} {s : Set α} {a : α} (has : a ∉ s) :
     Set.InjOn f (insert a s) ↔ Set.InjOn f s ∧ f a ∉ f '' s :=
   by
@@ -1284,31 +690,13 @@ theorem injOn_insert {f : α → β} {s : Set α} {a : α} (has : a ∉ s) :
   simp
 #align set.inj_on_insert Set.injOn_insert
 
-/- warning: set.injective_iff_inj_on_univ -> Set.injective_iff_injOn_univ is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.injective_iff_inj_on_univ Set.injective_iff_injOn_univₓ'. -/
 theorem injective_iff_injOn_univ : Injective f ↔ InjOn f univ :=
   ⟨fun h x hx y hy hxy => h hxy, fun h _ _ heq => h trivial trivial HEq⟩
 #align set.injective_iff_inj_on_univ Set.injective_iff_injOn_univ
 
-/- warning: set.inj_on_of_injective -> Set.injOn_of_injective is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inj_on_of_injective Set.injOn_of_injectiveₓ'. -/
 theorem injOn_of_injective (h : Injective f) (s : Set α) : InjOn f s := fun x hx y hy hxy => h hxy
 #align set.inj_on_of_injective Set.injOn_of_injective
 
-/- warning: function.injective.inj_on -> Function.Injective.injOn is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align function.injective.inj_on Function.Injective.injOnₓ'. -/
 alias inj_on_of_injective ← _root_.function.injective.inj_on
 #align function.injective.inj_on Function.Injective.injOn
 
@@ -1318,12 +706,6 @@ theorem injOn_id (s : Set α) : InjOn id s :=
 #align set.inj_on_id Set.injOn_id
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.inj_on.comp Set.InjOn.compₓ'. -/
 theorem InjOn.comp (hg : InjOn g t) (hf : InjOn f s) (h : MapsTo f s t) : InjOn (g ∘ f) s :=
   fun x hx y hy heq => hf hx hy <| hg (h hx) (h hy) HEq
 #align set.inj_on.comp Set.InjOn.comp
@@ -1336,52 +718,22 @@ theorem InjOn.iterate {f : α → α} {s : Set α} (h : InjOn f s) (hf : MapsTo
 #align set.inj_on.iterate Set.InjOn.iterate
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.inj_on_of_subsingleton Set.injOn_of_subsingletonₓ'. -/
 theorem injOn_of_subsingleton [Subsingleton α] (f : α → β) (s : Set α) : InjOn f s :=
   (injective_of_subsingleton _).InjOn _
 #align set.inj_on_of_subsingleton Set.injOn_of_subsingleton
 
-/- warning: function.injective.inj_on_range -> Function.Injective.injOn_range is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align function.injective.inj_on_range Function.Injective.injOn_rangeₓ'. -/
 theorem Function.Injective.injOn_range (h : Injective (g ∘ f)) : InjOn g (range f) := by
   rintro _ ⟨x, rfl⟩ _ ⟨y, rfl⟩ H; exact congr_arg f (h H)
 #align function.injective.inj_on_range Function.Injective.injOn_range
 
-/- warning: set.inj_on_iff_injective -> Set.injOn_iff_injective is a dubious translation:
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 theorem injOn_iff_injective : InjOn f s ↔ Injective (s.restrict f) :=
   ⟨fun H a b h => Subtype.eq <| H a.2 b.2 h, fun H a as b bs h =>
     congr_arg Subtype.val <| @H ⟨a, as⟩ ⟨b, bs⟩ h⟩
 #align set.inj_on_iff_injective Set.injOn_iff_injective
 
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 alias inj_on_iff_injective ↔ inj_on.injective _
 #align set.inj_on.injective Set.InjOn.injective
 
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 theorem MapsTo.restrict_inj (h : MapsTo f s t) : Injective (h.restrict f s t) ↔ InjOn f s := by
   rw [h.restrict_eq_cod_restrict, injective_cod_restrict, inj_on_iff_injective]
 #align set.maps_to.restrict_inj Set.MapsTo.restrict_inj
@@ -1400,66 +752,30 @@ theorem injOn_preimage {B : Set (Set β)} (hB : B ⊆ 𝒫 range f) : InjOn (pre
 #align set.inj_on_preimage Set.injOn_preimage
 -/
 
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 theorem InjOn.mem_of_mem_image {x} (hf : InjOn f s) (hs : s₁ ⊆ s) (h : x ∈ s) (h₁ : f x ∈ f '' s₁) :
     x ∈ s₁ :=
   let ⟨x', h', Eq⟩ := h₁
   hf (hs h') h Eq ▸ h'
 #align set.inj_on.mem_of_mem_image Set.InjOn.mem_of_mem_image
 
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 theorem InjOn.mem_image_iff {x} (hf : InjOn f s) (hs : s₁ ⊆ s) (hx : x ∈ s) :
     f x ∈ f '' s₁ ↔ x ∈ s₁ :=
   ⟨hf.mem_of_mem_image hs hx, mem_image_of_mem f⟩
 #align set.inj_on.mem_image_iff Set.InjOn.mem_image_iff
 
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 theorem InjOn.preimage_image_inter (hf : InjOn f s) (hs : s₁ ⊆ s) : f ⁻¹' (f '' s₁) ∩ s = s₁ :=
   ext fun x => ⟨fun ⟨h₁, h₂⟩ => hf.mem_of_mem_image hs h₂ h₁, fun h => ⟨mem_image_of_mem _ h, hs h⟩⟩
 #align set.inj_on.preimage_image_inter Set.InjOn.preimage_image_inter
 
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 theorem EqOn.cancel_left (h : s.EqOn (g ∘ f₁) (g ∘ f₂)) (hg : t.InjOn g) (hf₁ : s.MapsTo f₁ t)
     (hf₂ : s.MapsTo f₂ t) : s.EqOn f₁ f₂ := fun a ha => hg (hf₁ ha) (hf₂ ha) (h ha)
 #align set.eq_on.cancel_left Set.EqOn.cancel_left
 
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 theorem InjOn.cancel_left (hg : t.InjOn g) (hf₁ : s.MapsTo f₁ t) (hf₂ : s.MapsTo f₂ t) :
     s.EqOn (g ∘ f₁) (g ∘ f₂) ↔ s.EqOn f₁ f₂ :=
   ⟨fun h => h.cancel_left hg hf₁ hf₂, EqOn.comp_left⟩
 #align set.inj_on.cancel_left Set.InjOn.cancel_left
 
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 theorem InjOn.image_inter {s t u : Set α} (hf : u.InjOn f) (hs : s ⊆ u) (ht : t ⊆ u) :
     f '' (s ∩ t) = f '' s ∩ f '' t :=
   by
@@ -1472,12 +788,6 @@ theorem InjOn.image_inter {s t u : Set α} (hf : u.InjOn f) (hs : s ⊆ u) (ht :
   exact ⟨y, ⟨ys, zt⟩, hy⟩
 #align set.inj_on.image_inter Set.InjOn.image_inter
 
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-Case conversion may be inaccurate. Consider using '#align disjoint.image Disjoint.imageₓ'. -/
 theorem Disjoint.image {s t u : Set α} {f : α → β} (h : Disjoint s t) (hf : InjOn f u) (hs : s ⊆ u)
     (ht : t ⊆ u) : Disjoint (f '' s) (f '' t) :=
   by
@@ -1495,22 +805,10 @@ def SurjOn (f : α → β) (s : Set α) (t : Set β) : Prop :=
 #align set.surj_on Set.SurjOn
 -/
 
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 theorem SurjOn.subset_range (h : SurjOn f s t) : t ⊆ range f :=
   Subset.trans h <| image_subset_range f s
 #align set.surj_on.subset_range Set.SurjOn.subset_range
 
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 theorem surjOn_iff_exists_map_subtype :
     SurjOn f s t ↔ ∃ (t' : Set β)(g : s → t'), t ⊆ t' ∧ Surjective g ∧ ∀ x : s, f x = g x :=
   ⟨fun h =>
@@ -1520,105 +818,45 @@ theorem surjOn_iff_exists_map_subtype :
     ⟨x, x.2, by rw [hfg, hx, Subtype.coe_mk]⟩⟩
 #align set.surj_on_iff_exists_map_subtype Set.surjOn_iff_exists_map_subtype
 
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 theorem surjOn_empty (f : α → β) (s : Set α) : SurjOn f s ∅ :=
   empty_subset _
 #align set.surj_on_empty Set.surjOn_empty
 
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 @[simp]
 theorem surjOn_singleton : SurjOn f s {b} ↔ b ∈ f '' s :=
   singleton_subset_iff
 #align set.surj_on_singleton Set.surjOn_singleton
 
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 theorem surjOn_image (f : α → β) (s : Set α) : SurjOn f s (f '' s) :=
   Subset.rfl
 #align set.surj_on_image Set.surjOn_image
 
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 theorem SurjOn.comap_nonempty (h : SurjOn f s t) (ht : t.Nonempty) : s.Nonempty :=
   (ht.mono h).of_image
 #align set.surj_on.comap_nonempty Set.SurjOn.comap_nonempty
 
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 theorem SurjOn.congr (h : SurjOn f₁ s t) (H : EqOn f₁ f₂ s) : SurjOn f₂ s t := by
   rwa [surj_on, ← H.image_eq]
 #align set.surj_on.congr Set.SurjOn.congr
 
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 theorem EqOn.surjOn_iff (h : EqOn f₁ f₂ s) : SurjOn f₁ s t ↔ SurjOn f₂ s t :=
   ⟨fun H => H.congr h, fun H => H.congr h.symm⟩
 #align set.eq_on.surj_on_iff Set.EqOn.surjOn_iff
 
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 theorem SurjOn.mono (hs : s₁ ⊆ s₂) (ht : t₁ ⊆ t₂) (hf : SurjOn f s₁ t₂) : SurjOn f s₂ t₁ :=
   Subset.trans ht <| Subset.trans hf <| image_subset _ hs
 #align set.surj_on.mono Set.SurjOn.mono
 
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 theorem SurjOn.union (h₁ : SurjOn f s t₁) (h₂ : SurjOn f s t₂) : SurjOn f s (t₁ ∪ t₂) := fun x hx =>
   hx.elim (fun hx => h₁ hx) fun hx => h₂ hx
 #align set.surj_on.union Set.SurjOn.union
 
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 theorem SurjOn.union_union (h₁ : SurjOn f s₁ t₁) (h₂ : SurjOn f s₂ t₂) :
     SurjOn f (s₁ ∪ s₂) (t₁ ∪ t₂) :=
   (h₁.mono (subset_union_left _ _) (Subset.refl _)).union
     (h₂.mono (subset_union_right _ _) (Subset.refl _))
 #align set.surj_on.union_union Set.SurjOn.union_union
 
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 theorem SurjOn.inter_inter (h₁ : SurjOn f s₁ t₁) (h₂ : SurjOn f s₂ t₂) (h : InjOn f (s₁ ∪ s₂)) :
     SurjOn f (s₁ ∩ s₂) (t₁ ∩ t₂) := by
   intro y hy
@@ -1628,12 +866,6 @@ theorem SurjOn.inter_inter (h₁ : SurjOn f s₁ t₁) (h₂ : SurjOn f s₂ t
   exact mem_image_of_mem f ⟨hx₁, hx₂⟩
 #align set.surj_on.inter_inter Set.SurjOn.inter_inter
 
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 theorem SurjOn.inter (h₁ : SurjOn f s₁ t) (h₂ : SurjOn f s₂ t) (h : InjOn f (s₁ ∪ s₂)) :
     SurjOn f (s₁ ∩ s₂) t :=
   inter_self t ▸ h₁.inter_inter h₂ h
@@ -1644,12 +876,6 @@ theorem surjOn_id (s : Set α) : SurjOn id s s := by simp [surj_on]
 #align set.surj_on_id Set.surjOn_id
 -/
 
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 theorem SurjOn.comp (hg : SurjOn g t p) (hf : SurjOn f s t) : SurjOn (g ∘ f) s p :=
   Subset.trans hg <| Subset.trans (image_subset g hf) <| image_comp g f s ▸ Subset.refl _
 #align set.surj_on.comp Set.SurjOn.comp
@@ -1661,22 +887,10 @@ theorem SurjOn.iterate {f : α → α} {s : Set α} (h : SurjOn f s s) : ∀ n,
 #align set.surj_on.iterate Set.SurjOn.iterate
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.surj_on.comp_left Set.SurjOn.comp_leftₓ'. -/
 theorem SurjOn.comp_left (hf : SurjOn f s t) (g : β → γ) : SurjOn (g ∘ f) s (g '' t) := by
   rw [surj_on, image_comp g f]; exact image_subset _ hf
 #align set.surj_on.comp_left Set.SurjOn.comp_left
 
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-Case conversion may be inaccurate. Consider using '#align set.surj_on.comp_right Set.SurjOn.comp_rightₓ'. -/
 theorem SurjOn.comp_right {s : Set β} {t : Set γ} (hf : Surjective f) (hg : SurjOn g s t) :
     SurjOn (g ∘ f) (f ⁻¹' s) t := by rwa [surj_on, image_comp g f, image_preimage_eq _ hf]
 #align set.surj_on.comp_right Set.SurjOn.comp_right
@@ -1693,22 +907,10 @@ theorem surjOn_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) :
 #align set.surj_on_of_subsingleton Set.surjOn_of_subsingleton
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.surjective_iff_surj_on_univ Set.surjective_iff_surjOn_univₓ'. -/
 theorem surjective_iff_surjOn_univ : Surjective f ↔ SurjOn f univ univ := by
   simp [surjective, surj_on, subset_def]
 #align set.surjective_iff_surj_on_univ Set.surjective_iff_surjOn_univ
 
-/- warning: set.surj_on_iff_surjective -> Set.surjOn_iff_surjective is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.surj_on_iff_surjective Set.surjOn_iff_surjectiveₓ'. -/
 theorem surjOn_iff_surjective : SurjOn f s univ ↔ Surjective (s.restrict f) :=
   ⟨fun H b =>
     let ⟨a, as, e⟩ := @H b trivial
@@ -1718,12 +920,6 @@ theorem surjOn_iff_surjective : SurjOn f s univ ↔ Surjective (s.restrict f) :=
     ⟨a, as, e⟩⟩
 #align set.surj_on_iff_surjective Set.surjOn_iff_surjective
 
-/- warning: set.surj_on.image_eq_of_maps_to -> Set.SurjOn.image_eq_of_mapsTo is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.surj_on.image_eq_of_maps_to Set.SurjOn.image_eq_of_mapsToₓ'. -/
 theorem SurjOn.image_eq_of_mapsTo (h₁ : SurjOn f s t) (h₂ : MapsTo f s t) : f '' s = t :=
   eq_of_subset_of_subset h₂.image_subset h₁
 #align set.surj_on.image_eq_of_maps_to Set.SurjOn.image_eq_of_mapsTo
@@ -1737,34 +933,16 @@ theorem image_eq_iff_surjOn_mapsTo : f '' s = t ↔ s.SurjOn f t ∧ s.MapsTo f
 #align set.image_eq_iff_surj_on_maps_to Set.image_eq_iff_surjOn_mapsTo
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.surj_on.maps_to_compl Set.SurjOn.mapsTo_complₓ'. -/
 theorem SurjOn.mapsTo_compl (h : SurjOn f s t) (h' : Injective f) : MapsTo f (sᶜ) (tᶜ) :=
   fun x hs ht =>
   let ⟨x', hx', HEq⟩ := h ht
   hs <| h' HEq ▸ hx'
 #align set.surj_on.maps_to_compl Set.SurjOn.mapsTo_compl
 
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-Case conversion may be inaccurate. Consider using '#align set.maps_to.surj_on_compl Set.MapsTo.surjOn_complₓ'. -/
 theorem MapsTo.surjOn_compl (h : MapsTo f s t) (h' : Surjective f) : SurjOn f (sᶜ) (tᶜ) :=
   h'.forall.2 fun x ht => mem_image_of_mem _ fun hs => ht (h hs)
 #align set.maps_to.surj_on_compl Set.MapsTo.surjOn_compl
 
-/- warning: set.eq_on.cancel_right -> Set.EqOn.cancel_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} {s : Set.{u1} α} {t : Set.{u2} β} {f : α -> β} {g₁ : β -> γ} {g₂ : β -> γ}, (Set.EqOn.{u1, u3} α γ (Function.comp.{succ u1, succ u2, succ u3} α β γ g₁ f) (Function.comp.{succ u1, succ u2, succ u3} α β γ g₂ f) s) -> (Set.SurjOn.{u1, u2} α β f s t) -> (Set.EqOn.{u2, u3} β γ g₁ g₂ t)
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-Case conversion may be inaccurate. Consider using '#align set.eq_on.cancel_right Set.EqOn.cancel_rightₓ'. -/
 theorem EqOn.cancel_right (hf : s.EqOn (g₁ ∘ f) (g₂ ∘ f)) (hf' : s.SurjOn f t) : t.EqOn g₁ g₂ :=
   by
   intro b hb
@@ -1772,23 +950,11 @@ theorem EqOn.cancel_right (hf : s.EqOn (g₁ ∘ f) (g₂ ∘ f)) (hf' : s.SurjO
   exact hf ha
 #align set.eq_on.cancel_right Set.EqOn.cancel_right
 
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-Case conversion may be inaccurate. Consider using '#align set.surj_on.cancel_right Set.SurjOn.cancel_rightₓ'. -/
 theorem SurjOn.cancel_right (hf : s.SurjOn f t) (hf' : s.MapsTo f t) :
     s.EqOn (g₁ ∘ f) (g₂ ∘ f) ↔ t.EqOn g₁ g₂ :=
   ⟨fun h => h.cancel_right hf, fun h => h.compRight hf'⟩
 #align set.surj_on.cancel_right Set.SurjOn.cancel_right
 
-/- warning: set.eq_on_comp_right_iff -> Set.eqOn_comp_right_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.eq_on_comp_right_iff Set.eqOn_comp_right_iffₓ'. -/
 theorem eqOn_comp_right_iff : s.EqOn (g₁ ∘ f) (g₂ ∘ f) ↔ (f '' s).EqOn g₁ g₂ :=
   (s.surjOn_image f).cancel_right <| s.mapsTo_image f
 #align set.eq_on_comp_right_iff Set.eqOn_comp_right_iff
@@ -1803,73 +969,31 @@ def BijOn (f : α → β) (s : Set α) (t : Set β) : Prop :=
 #align set.bij_on Set.BijOn
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.bij_on.maps_to Set.BijOn.mapsToₓ'. -/
 theorem BijOn.mapsTo (h : BijOn f s t) : MapsTo f s t :=
   h.left
 #align set.bij_on.maps_to Set.BijOn.mapsTo
 
-/- warning: set.bij_on.inj_on -> Set.BijOn.injOn is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.bij_on.inj_on Set.BijOn.injOnₓ'. -/
 theorem BijOn.injOn (h : BijOn f s t) : InjOn f s :=
   h.right.left
 #align set.bij_on.inj_on Set.BijOn.injOn
 
-/- warning: set.bij_on.surj_on -> Set.BijOn.surjOn 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.bij_on.surj_on Set.BijOn.surjOnₓ'. -/
 theorem BijOn.surjOn (h : BijOn f s t) : SurjOn f s t :=
   h.right.right
 #align set.bij_on.surj_on Set.BijOn.surjOn
 
-/- warning: set.bij_on.mk -> Set.BijOn.mk 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.bij_on.mk Set.BijOn.mkₓ'. -/
 theorem BijOn.mk (h₁ : MapsTo f s t) (h₂ : InjOn f s) (h₃ : SurjOn f s t) : BijOn f s t :=
   ⟨h₁, h₂, h₃⟩
 #align set.bij_on.mk Set.BijOn.mk
 
-/- warning: set.bij_on_empty -> Set.bijOn_empty is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β), Set.BijOn.{u1, u2} α β f (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α)) (EmptyCollection.emptyCollection.{u2} (Set.{u2} β) (Set.hasEmptyc.{u2} β))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.bij_on_empty Set.bijOn_emptyₓ'. -/
 @[simp]
 theorem bijOn_empty (f : α → β) : BijOn f ∅ ∅ :=
   ⟨mapsTo_empty f ∅, injOn_empty f, surjOn_empty f ∅⟩
 #align set.bij_on_empty Set.bijOn_empty
 
-/- warning: set.bij_on_singleton -> Set.bijOn_singleton 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.bij_on_singleton Set.bijOn_singletonₓ'. -/
 @[simp]
 theorem bijOn_singleton : BijOn f {a} {b} ↔ f a = b := by simp [bij_on, eq_comm]
 #align set.bij_on_singleton Set.bijOn_singleton
 
-/- warning: set.bij_on.inter_maps_to -> Set.BijOn.inter_mapsTo is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.bij_on.inter_maps_to Set.BijOn.inter_mapsToₓ'. -/
 theorem BijOn.inter_mapsTo (h₁ : BijOn f s₁ t₁) (h₂ : MapsTo f s₂ t₂) (h₃ : s₁ ∩ f ⁻¹' t₂ ⊆ s₂) :
     BijOn f (s₁ ∩ s₂) (t₁ ∩ t₂) :=
   ⟨h₁.MapsTo.inter_inter h₂, h₁.InjOn.mono <| inter_subset_left _ _, fun y hy =>
@@ -1877,86 +1001,38 @@ theorem BijOn.inter_mapsTo (h₁ : BijOn f s₁ t₁) (h₂ : MapsTo f s₂ t₂
     ⟨x, ⟨hx, h₃ ⟨hx, hxy.symm.recOn hy.2⟩⟩, hxy⟩⟩
 #align set.bij_on.inter_maps_to Set.BijOn.inter_mapsTo
 
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-Case conversion may be inaccurate. Consider using '#align set.maps_to.inter_bij_on Set.MapsTo.inter_bijOnₓ'. -/
 theorem MapsTo.inter_bijOn (h₁ : MapsTo f s₁ t₁) (h₂ : BijOn f s₂ t₂) (h₃ : s₂ ∩ f ⁻¹' t₁ ⊆ s₁) :
     BijOn f (s₁ ∩ s₂) (t₁ ∩ t₂) :=
   inter_comm s₂ s₁ ▸ inter_comm t₂ t₁ ▸ h₂.inter_mapsTo h₁ h₃
 #align set.maps_to.inter_bij_on Set.MapsTo.inter_bijOn
 
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-Case conversion may be inaccurate. Consider using '#align set.bij_on.inter Set.BijOn.interₓ'. -/
 theorem BijOn.inter (h₁ : BijOn f s₁ t₁) (h₂ : BijOn f s₂ t₂) (h : InjOn f (s₁ ∪ s₂)) :
     BijOn f (s₁ ∩ s₂) (t₁ ∩ t₂) :=
   ⟨h₁.MapsTo.inter_inter h₂.MapsTo, h₁.InjOn.mono <| inter_subset_left _ _,
     h₁.SurjOn.inter_inter h₂.SurjOn h⟩
 #align set.bij_on.inter Set.BijOn.inter
 
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-Case conversion may be inaccurate. Consider using '#align set.bij_on.union Set.BijOn.unionₓ'. -/
 theorem BijOn.union (h₁ : BijOn f s₁ t₁) (h₂ : BijOn f s₂ t₂) (h : InjOn f (s₁ ∪ s₂)) :
     BijOn f (s₁ ∪ s₂) (t₁ ∪ t₂) :=
   ⟨h₁.MapsTo.union_union h₂.MapsTo, h, h₁.SurjOn.union_union h₂.SurjOn⟩
 #align set.bij_on.union Set.BijOn.union
 
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.bij_on.subset_range Set.BijOn.subset_rangeₓ'. -/
 theorem BijOn.subset_range (h : BijOn f s t) : t ⊆ range f :=
   h.SurjOn.subset_range
 #align set.bij_on.subset_range Set.BijOn.subset_range
 
-/- warning: set.inj_on.bij_on_image -> Set.InjOn.bijOn_image is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} {f : α -> β}, (Set.InjOn.{u1, u2} α β f s) -> (Set.BijOn.{u1, u2} α β f s (Set.image.{u1, u2} α β f s))
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-Case conversion may be inaccurate. Consider using '#align set.inj_on.bij_on_image Set.InjOn.bijOn_imageₓ'. -/
 theorem InjOn.bijOn_image (h : InjOn f s) : BijOn f s (f '' s) :=
   BijOn.mk (mapsTo_image f s) h (Subset.refl _)
 #align set.inj_on.bij_on_image Set.InjOn.bijOn_image
 
-/- warning: set.bij_on.congr -> Set.BijOn.congr is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} {t : Set.{u2} β} {f₁ : α -> β} {f₂ : α -> β}, (Set.BijOn.{u1, u2} α β f₁ s t) -> (Set.EqOn.{u1, u2} α β f₁ f₂ s) -> (Set.BijOn.{u1, u2} α β f₂ s t)
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-Case conversion may be inaccurate. Consider using '#align set.bij_on.congr Set.BijOn.congrₓ'. -/
 theorem BijOn.congr (h₁ : BijOn f₁ s t) (h : EqOn f₁ f₂ s) : BijOn f₂ s t :=
   BijOn.mk (h₁.MapsTo.congr h) (h₁.InjOn.congr h) (h₁.SurjOn.congr h)
 #align set.bij_on.congr Set.BijOn.congr
 
-/- warning: set.eq_on.bij_on_iff -> Set.EqOn.bijOn_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} {t : Set.{u2} β} {f₁ : α -> β} {f₂ : α -> β}, (Set.EqOn.{u1, u2} α β f₁ f₂ s) -> (Iff (Set.BijOn.{u1, u2} α β f₁ s t) (Set.BijOn.{u1, u2} α β f₂ s t))
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-Case conversion may be inaccurate. Consider using '#align set.eq_on.bij_on_iff Set.EqOn.bijOn_iffₓ'. -/
 theorem EqOn.bijOn_iff (H : EqOn f₁ f₂ s) : BijOn f₁ s t ↔ BijOn f₂ s t :=
   ⟨fun h => h.congr H, fun h => h.congr H.symm⟩
 #align set.eq_on.bij_on_iff Set.EqOn.bijOn_iff
 
-/- warning: set.bij_on.image_eq -> Set.BijOn.image_eq is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} {t : Set.{u2} β} {f : α -> β}, (Set.BijOn.{u1, u2} α β f s t) -> (Eq.{succ u2} (Set.{u2} β) (Set.image.{u1, u2} α β f s) t)
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-Case conversion may be inaccurate. Consider using '#align set.bij_on.image_eq Set.BijOn.image_eqₓ'. -/
 theorem BijOn.image_eq (h : BijOn f s t) : f '' s = t :=
   h.SurjOn.image_eq_of_mapsTo h.MapsTo
 #align set.bij_on.image_eq Set.BijOn.image_eq
@@ -1967,12 +1043,6 @@ theorem bijOn_id (s : Set α) : BijOn id s s :=
 #align set.bij_on_id Set.bijOn_id
 -/
 
-/- warning: set.bij_on.comp -> Set.BijOn.comp is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.bij_on.comp Set.BijOn.compₓ'. -/
 theorem BijOn.comp (hg : BijOn g t p) (hf : BijOn f s t) : BijOn (g ∘ f) s p :=
   BijOn.mk (hg.MapsTo.comp hf.MapsTo) (hg.InjOn.comp hf.InjOn hf.MapsTo) (hg.SurjOn.comp hf.SurjOn)
 #align set.bij_on.comp Set.BijOn.comp
@@ -1984,12 +1054,6 @@ theorem BijOn.iterate {f : α → α} {s : Set α} (h : BijOn f s s) : ∀ n, Bi
 #align set.bij_on.iterate Set.BijOn.iterate
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.bij_on_of_subsingleton' Set.bijOn_of_subsingleton'ₓ'. -/
 theorem bijOn_of_subsingleton' [Subsingleton α] [Subsingleton β] (f : α → β)
     (h : s.Nonempty ↔ t.Nonempty) : BijOn f s t :=
   ⟨mapsTo_of_subsingleton' _ h.1, injOn_of_subsingleton _ _, surjOn_of_subsingleton' _ h.2⟩
@@ -2001,24 +1065,12 @@ theorem bijOn_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : B
 #align set.bij_on_of_subsingleton Set.bijOn_of_subsingleton
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.bij_on.bijective Set.BijOn.bijectiveₓ'. -/
 theorem BijOn.bijective (h : BijOn f s t) : Bijective (h.MapsTo.restrict f s t) :=
   ⟨fun x y h' => Subtype.ext <| h.InjOn x.2 y.2 <| Subtype.ext_iff.1 h', fun ⟨y, hy⟩ =>
     let ⟨x, hx, hxy⟩ := h.SurjOn hy
     ⟨⟨x, hx⟩, Subtype.eq hxy⟩⟩
 #align set.bij_on.bijective Set.BijOn.bijective
 
-/- warning: set.bijective_iff_bij_on_univ -> Set.bijective_iff_bijOn_univ is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} {f : α -> β}, Iff (Function.Bijective.{succ u1, succ u2} α β f) (Set.BijOn.{u1, u2} α β f (Set.univ.{u1} α) (Set.univ.{u2} β))
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-Case conversion may be inaccurate. Consider using '#align set.bijective_iff_bij_on_univ Set.bijective_iff_bijOn_univₓ'. -/
 theorem bijective_iff_bijOn_univ : Bijective f ↔ BijOn f univ univ :=
   Iff.intro
     (fun h =>
@@ -2029,21 +1081,9 @@ theorem bijective_iff_bijOn_univ : Bijective f ↔ BijOn f univ univ :=
     ⟨Iff.mpr injective_iff_injOn_univ inj, Iff.mpr surjective_iff_surjOn_univ surj⟩
 #align set.bijective_iff_bij_on_univ Set.bijective_iff_bijOn_univ
 
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-Case conversion may be inaccurate. Consider using '#align function.bijective.bij_on_univ Function.Bijective.bijOn_univₓ'. -/
 alias bijective_iff_bij_on_univ ↔ _root_.function.bijective.bij_on_univ _
 #align function.bijective.bij_on_univ Function.Bijective.bijOn_univ
 
-/- warning: set.bij_on.compl -> Set.BijOn.compl is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.bij_on.compl Set.BijOn.complₓ'. -/
 theorem BijOn.compl (hst : BijOn f s t) (hf : Bijective f) : BijOn f (sᶜ) (tᶜ) :=
   ⟨hst.SurjOn.mapsTo_compl hf.1, hf.1.InjOn _, hst.MapsTo.surjOn_compl hf.2⟩
 #align set.bij_on.compl Set.BijOn.compl
@@ -2068,52 +1108,22 @@ theorem leftInvOn_singleton : LeftInvOn f' f {a} ↔ f' (f a) = a :=
   singleton_subset_iff
 #align set.left_inv_on_singleton Set.leftInvOn_singleton
 
-/- warning: set.left_inv_on.eq_on -> Set.LeftInvOn.eqOn 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.left_inv_on.eq_on Set.LeftInvOn.eqOnₓ'. -/
 theorem LeftInvOn.eqOn (h : LeftInvOn f' f s) : EqOn (f' ∘ f) id s :=
   h
 #align set.left_inv_on.eq_on Set.LeftInvOn.eqOn
 
-/- warning: set.left_inv_on.eq -> Set.LeftInvOn.eq is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.left_inv_on.eq Set.LeftInvOn.eqₓ'. -/
 theorem LeftInvOn.eq (h : LeftInvOn f' f s) {x} (hx : x ∈ s) : f' (f x) = x :=
   h hx
 #align set.left_inv_on.eq Set.LeftInvOn.eq
 
-/- warning: set.left_inv_on.congr_left -> Set.LeftInvOn.congr_left is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.left_inv_on.congr_left Set.LeftInvOn.congr_leftₓ'. -/
 theorem LeftInvOn.congr_left (h₁ : LeftInvOn f₁' f s) {t : Set β} (h₁' : MapsTo f s t)
     (heq : EqOn f₁' f₂' t) : LeftInvOn f₂' f s := fun x hx => HEq (h₁' hx) ▸ h₁ hx
 #align set.left_inv_on.congr_left Set.LeftInvOn.congr_left
 
-/- warning: set.left_inv_on.congr_right -> Set.LeftInvOn.congr_right is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} {f₁ : α -> β} {f₂ : α -> β} {f₁' : β -> α}, (Set.LeftInvOn.{u1, u2} α β f₁' f₁ s) -> (Set.EqOn.{u1, u2} α β f₁ f₂ s) -> (Set.LeftInvOn.{u1, u2} α β f₁' f₂ s)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.left_inv_on.congr_right Set.LeftInvOn.congr_rightₓ'. -/
 theorem LeftInvOn.congr_right (h₁ : LeftInvOn f₁' f₁ s) (heq : EqOn f₁ f₂ s) : LeftInvOn f₁' f₂ s :=
   fun x hx => HEq hx ▸ h₁ hx
 #align set.left_inv_on.congr_right Set.LeftInvOn.congr_right
 
-/- warning: set.left_inv_on.inj_on -> Set.LeftInvOn.injOn is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} {f : α -> β} {f₁' : β -> α}, (Set.LeftInvOn.{u1, u2} α β f₁' f s) -> (Set.InjOn.{u1, u2} α β f s)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.left_inv_on.inj_on Set.LeftInvOn.injOnₓ'. -/
 theorem LeftInvOn.injOn (h : LeftInvOn f₁' f s) : InjOn f s := fun x₁ h₁ x₂ h₂ heq =>
   calc
     x₁ = f₁' (f x₁) := Eq.symm <| h h₁
@@ -2122,22 +1132,10 @@ theorem LeftInvOn.injOn (h : LeftInvOn f₁' f s) : InjOn f s := fun x₁ h₁ x
     
 #align set.left_inv_on.inj_on Set.LeftInvOn.injOn
 
-/- warning: set.left_inv_on.surj_on -> Set.LeftInvOn.surjOn 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.left_inv_on.surj_on Set.LeftInvOn.surjOnₓ'. -/
 theorem LeftInvOn.surjOn (h : LeftInvOn f' f s) (hf : MapsTo f s t) : SurjOn f' t s := fun x hx =>
   ⟨f x, hf hx, h hx⟩
 #align set.left_inv_on.surj_on Set.LeftInvOn.surjOn
 
-/- warning: set.left_inv_on.maps_to -> Set.LeftInvOn.mapsTo 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.left_inv_on.maps_to Set.LeftInvOn.mapsToₓ'. -/
 theorem LeftInvOn.mapsTo (h : LeftInvOn f' f s) (hf : SurjOn f s t) : MapsTo f' t s := fun y hy =>
   by
   let ⟨x, hs, hx⟩ := hf hy
@@ -2149,12 +1147,6 @@ theorem leftInvOn_id (s : Set α) : LeftInvOn id id s := fun a _ => rfl
 #align set.left_inv_on_id Set.leftInvOn_id
 -/
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.left_inv_on.comp Set.LeftInvOn.compₓ'. -/
 theorem LeftInvOn.comp (hf' : LeftInvOn f' f s) (hg' : LeftInvOn g' g t) (hf : MapsTo f s t) :
     LeftInvOn (f' ∘ g') (g ∘ f) s := fun x h =>
   calc
@@ -2163,22 +1155,10 @@ theorem LeftInvOn.comp (hf' : LeftInvOn f' f s) (hg' : LeftInvOn g' g t) (hf : M
     
 #align set.left_inv_on.comp Set.LeftInvOn.comp
 
-/- warning: set.left_inv_on.mono -> Set.LeftInvOn.mono is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.left_inv_on.mono Set.LeftInvOn.monoₓ'. -/
 theorem LeftInvOn.mono (hf : LeftInvOn f' f s) (ht : s₁ ⊆ s) : LeftInvOn f' f s₁ := fun x hx =>
   hf (ht hx)
 #align set.left_inv_on.mono Set.LeftInvOn.mono
 
-/- warning: set.left_inv_on.image_inter' -> Set.LeftInvOn.image_inter' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.left_inv_on.image_inter' Set.LeftInvOn.image_inter'ₓ'. -/
 theorem LeftInvOn.image_inter' (hf : LeftInvOn f' f s) : f '' (s₁ ∩ s) = f' ⁻¹' s₁ ∩ f '' s :=
   by
   apply subset.antisymm
@@ -2186,12 +1166,6 @@ theorem LeftInvOn.image_inter' (hf : LeftInvOn f' f s) : f '' (s₁ ∩ s) = f'
   · rintro _ ⟨h₁, ⟨x, h, rfl⟩⟩; exact mem_image_of_mem _ ⟨by rwa [← hf h], h⟩
 #align set.left_inv_on.image_inter' Set.LeftInvOn.image_inter'
 
-/- warning: set.left_inv_on.image_inter -> Set.LeftInvOn.image_inter is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.left_inv_on.image_inter Set.LeftInvOn.image_interₓ'. -/
 theorem LeftInvOn.image_inter (hf : LeftInvOn f' f s) : f '' (s₁ ∩ s) = f' ⁻¹' (s₁ ∩ s) ∩ f '' s :=
   by
   rw [hf.image_inter']
@@ -2199,22 +1173,10 @@ theorem LeftInvOn.image_inter (hf : LeftInvOn f' f s) : f '' (s₁ ∩ s) = f' 
   rintro _ ⟨h₁, x, hx, rfl⟩; exact ⟨⟨h₁, by rwa [hf hx]⟩, mem_image_of_mem _ hx⟩
 #align set.left_inv_on.image_inter Set.LeftInvOn.image_inter
 
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-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.left_inv_on.image_image Set.LeftInvOn.image_imageₓ'. -/
 theorem LeftInvOn.image_image (hf : LeftInvOn f' f s) : f' '' (f '' s) = s := by
   rw [image_image, image_congr hf, image_id']
 #align set.left_inv_on.image_image Set.LeftInvOn.image_image
 
-/- warning: set.left_inv_on.image_image' -> Set.LeftInvOn.image_image' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} {s₁ : Set.{u1} α} {f : α -> β} {f' : β -> α}, (Set.LeftInvOn.{u1, u2} α β f' f s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s₁ s) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u2, u1} β α f' (Set.image.{u1, u2} α β f s₁)) s₁)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.left_inv_on.image_image' Set.LeftInvOn.image_image'ₓ'. -/
 theorem LeftInvOn.image_image' (hf : LeftInvOn f' f s) (hs : s₁ ⊆ s) : f' '' (f '' s₁) = s₁ :=
   (hf.mono hs).image_image
 #align set.left_inv_on.image_image' Set.LeftInvOn.image_image'
@@ -2240,74 +1202,32 @@ theorem rightInvOn_singleton : RightInvOn f' f {b} ↔ f (f' b) = b :=
   singleton_subset_iff
 #align set.right_inv_on_singleton Set.rightInvOn_singleton
 
-/- warning: set.right_inv_on.eq_on -> Set.RightInvOn.eqOn is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {t : Set.{u2} β} {f : α -> β} {f' : β -> α}, (Set.RightInvOn.{u1, u2} α β f' f t) -> (Set.EqOn.{u2, u2} β β (Function.comp.{succ u2, succ u1, succ u2} β α β f f') (id.{succ u2} β) t)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.right_inv_on.eq_on Set.RightInvOn.eqOnₓ'. -/
 theorem RightInvOn.eqOn (h : RightInvOn f' f t) : EqOn (f ∘ f') id t :=
   h
 #align set.right_inv_on.eq_on Set.RightInvOn.eqOn
 
-/- warning: set.right_inv_on.eq -> Set.RightInvOn.eq is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {t : Set.{u2} β} {f : α -> β} {f' : β -> α}, (Set.RightInvOn.{u1, u2} α β f' f t) -> (forall {y : β}, (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y t) -> (Eq.{succ u2} β (f (f' y)) y))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.right_inv_on.eq Set.RightInvOn.eqₓ'. -/
 theorem RightInvOn.eq (h : RightInvOn f' f t) {y} (hy : y ∈ t) : f (f' y) = y :=
   h hy
 #align set.right_inv_on.eq Set.RightInvOn.eq
 
-/- warning: set.left_inv_on.right_inv_on_image -> Set.LeftInvOn.rightInvOn_image is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} {f : α -> β} {f' : β -> α}, (Set.LeftInvOn.{u1, u2} α β f' f s) -> (Set.RightInvOn.{u1, u2} α β f' f (Set.image.{u1, u2} α β f s))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.left_inv_on.right_inv_on_image Set.LeftInvOn.rightInvOn_imageₓ'. -/
 theorem LeftInvOn.rightInvOn_image (h : LeftInvOn f' f s) : RightInvOn f' f (f '' s) :=
   fun y ⟨x, hx, Eq⟩ => Eq ▸ congr_arg f <| h.Eq hx
 #align set.left_inv_on.right_inv_on_image Set.LeftInvOn.rightInvOn_image
 
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-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {t : Set.{u2} β} {f : α -> β} {f₁' : β -> α} {f₂' : β -> α}, (Set.RightInvOn.{u1, u2} α β f₁' f t) -> (Set.EqOn.{u2, u1} β α f₁' f₂' t) -> (Set.RightInvOn.{u1, u2} α β f₂' f t)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.right_inv_on.congr_left Set.RightInvOn.congr_leftₓ'. -/
 theorem RightInvOn.congr_left (h₁ : RightInvOn f₁' f t) (heq : EqOn f₁' f₂' t) :
     RightInvOn f₂' f t :=
   h₁.congr_right HEq
 #align set.right_inv_on.congr_left Set.RightInvOn.congr_left
 
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-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} {t : Set.{u2} β} {f₁ : α -> β} {f₂ : α -> β} {f' : β -> α}, (Set.RightInvOn.{u1, u2} α β f' f₁ t) -> (Set.MapsTo.{u2, u1} β α f' t s) -> (Set.EqOn.{u1, u2} α β f₁ f₂ s) -> (Set.RightInvOn.{u1, u2} α β f' f₂ t)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.right_inv_on.congr_right Set.RightInvOn.congr_rightₓ'. -/
 theorem RightInvOn.congr_right (h₁ : RightInvOn f' f₁ t) (hg : MapsTo f' t s) (heq : EqOn f₁ f₂ s) :
     RightInvOn f' f₂ t :=
   LeftInvOn.congr_left h₁ hg HEq
 #align set.right_inv_on.congr_right Set.RightInvOn.congr_right
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.right_inv_on.surj_on Set.RightInvOn.surjOnₓ'. -/
 theorem RightInvOn.surjOn (hf : RightInvOn f' f t) (hf' : MapsTo f' t s) : SurjOn f s t :=
   hf.SurjOn hf'
 #align set.right_inv_on.surj_on Set.RightInvOn.surjOn
 
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-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.right_inv_on.maps_to Set.RightInvOn.mapsToₓ'. -/
 theorem RightInvOn.mapsTo (h : RightInvOn f' f t) (hf : SurjOn f' t s) : MapsTo f s t :=
   h.MapsTo hf
 #align set.right_inv_on.maps_to Set.RightInvOn.mapsTo
@@ -2317,43 +1237,19 @@ theorem rightInvOn_id (s : Set α) : RightInvOn id id s := fun a _ => rfl
 #align set.right_inv_on_id Set.rightInvOn_id
 -/
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.right_inv_on.comp Set.RightInvOn.compₓ'. -/
 theorem RightInvOn.comp (hf : RightInvOn f' f t) (hg : RightInvOn g' g p) (g'pt : MapsTo g' p t) :
     RightInvOn (f' ∘ g') (g ∘ f) p :=
   hg.comp hf g'pt
 #align set.right_inv_on.comp Set.RightInvOn.comp
 
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-Case conversion may be inaccurate. Consider using '#align set.right_inv_on.mono Set.RightInvOn.monoₓ'. -/
 theorem RightInvOn.mono (hf : RightInvOn f' f t) (ht : t₁ ⊆ t) : RightInvOn f' f t₁ :=
   hf.mono ht
 #align set.right_inv_on.mono Set.RightInvOn.mono
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.inj_on.right_inv_on_of_left_inv_on Set.InjOn.rightInvOn_of_leftInvOnₓ'. -/
 theorem InjOn.rightInvOn_of_leftInvOn (hf : InjOn f s) (hf' : LeftInvOn f f' t) (h₁ : MapsTo f s t)
     (h₂ : MapsTo f' t s) : RightInvOn f f' s := fun x h => hf (h₂ <| h₁ h) h (hf' (h₁ h))
 #align set.inj_on.right_inv_on_of_left_inv_on Set.InjOn.rightInvOn_of_leftInvOn
 
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.eq_on_of_left_inv_on_of_right_inv_on Set.eqOn_of_leftInvOn_of_rightInvOnₓ'. -/
 theorem eqOn_of_leftInvOn_of_rightInvOn (h₁ : LeftInvOn f₁' f s) (h₂ : RightInvOn f₂' f t)
     (h : MapsTo f₂' t s) : EqOn f₁' f₂' t := fun y hy =>
   calc
@@ -2362,12 +1258,6 @@ theorem eqOn_of_leftInvOn_of_rightInvOn (h₁ : LeftInvOn f₁' f s) (h₂ : Rig
     
 #align set.eq_on_of_left_inv_on_of_right_inv_on Set.eqOn_of_leftInvOn_of_rightInvOn
 
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-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.surj_on.left_inv_on_of_right_inv_on Set.SurjOn.leftInvOn_of_rightInvOnₓ'. -/
 theorem SurjOn.leftInvOn_of_rightInvOn (hf : SurjOn f s t) (hf' : RightInvOn f f' s) :
     LeftInvOn f f' t := fun y hy => by
   let ⟨x, hx, HEq⟩ := hf hy
@@ -2392,12 +1282,6 @@ theorem invOn_empty (f' : β → α) (f : α → β) : InvOn f' f ∅ ∅ := by
 theorem invOn_singleton : InvOn f' f {a} {b} ↔ f' (f a) = a ∧ f (f' b) = b := by simp [inv_on]
 #align set.inv_on_singleton Set.invOn_singleton
 
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-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.inv_on.symm Set.InvOn.symmₓ'. -/
 theorem InvOn.symm (h : InvOn f' f s t) : InvOn f f' t s :=
   ⟨h.right, h.left⟩
 #align set.inv_on.symm Set.InvOn.symm
@@ -2408,33 +1292,15 @@ theorem invOn_id (s : Set α) : InvOn id id s s :=
 #align set.inv_on_id Set.invOn_id
 -/
 
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-Case conversion may be inaccurate. Consider using '#align set.inv_on.comp Set.InvOn.compₓ'. -/
 theorem InvOn.comp (hf : InvOn f' f s t) (hg : InvOn g' g t p) (fst : MapsTo f s t)
     (g'pt : MapsTo g' p t) : InvOn (f' ∘ g') (g ∘ f) s p :=
   ⟨hf.1.comp hg.1 fst, hf.2.comp hg.2 g'pt⟩
 #align set.inv_on.comp Set.InvOn.comp
 
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-Case conversion may be inaccurate. Consider using '#align set.inv_on.mono Set.InvOn.monoₓ'. -/
 theorem InvOn.mono (h : InvOn f' f s t) (hs : s₁ ⊆ s) (ht : t₁ ⊆ t) : InvOn f' f s₁ t₁ :=
   ⟨h.1.mono hs, h.2.mono ht⟩
 #align set.inv_on.mono Set.InvOn.mono
 
-/- warning: set.inv_on.bij_on -> Set.InvOn.bijOn 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.inv_on.bij_on Set.InvOn.bijOnₓ'. -/
 /-- If functions `f'` and `f` are inverse on `s` and `t`, `f` maps `s` into `t`, and `f'` maps `t`
 into `s`, then `f` is a bijection between `s` and `t`. The `maps_to` arguments can be deduced from
 `surj_on` statements using `left_inv_on.maps_to` and `right_inv_on.maps_to`. -/
@@ -2473,63 +1339,27 @@ noncomputable def invFunOn (f : α → β) (s : Set α) (b : β) : α :=
 #align function.inv_fun_on Function.invFunOn
 -/
 
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 theorem invFunOn_pos (h : ∃ a ∈ s, f a = b) : invFunOn f s b ∈ s ∧ f (invFunOn f s b) = b := by
   rw [bex_def] at h <;> rw [inv_fun_on, dif_pos h] <;> exact Classical.choose_spec h
 #align function.inv_fun_on_pos Function.invFunOn_pos
 
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 theorem invFunOn_mem (h : ∃ a ∈ s, f a = b) : invFunOn f s b ∈ s :=
   (invFunOn_pos h).left
 #align function.inv_fun_on_mem Function.invFunOn_mem
 
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 theorem invFunOn_eq (h : ∃ a ∈ s, f a = b) : f (invFunOn f s b) = b :=
   (invFunOn_pos h).right
 #align function.inv_fun_on_eq Function.invFunOn_eq
 
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 theorem invFunOn_neg (h : ¬∃ a ∈ s, f a = b) : invFunOn f s b = Classical.choice ‹Nonempty α› := by
   rw [bex_def] at h <;> rw [inv_fun_on, dif_neg h]
 #align function.inv_fun_on_neg Function.invFunOn_neg
 
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 @[simp]
 theorem invFunOn_apply_mem (h : a ∈ s) : invFunOn f s (f a) ∈ s :=
   invFunOn_mem ⟨a, h, rfl⟩
 #align function.inv_fun_on_apply_mem Function.invFunOn_apply_mem
 
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 theorem invFunOn_apply_eq (h : a ∈ s) : f (invFunOn f s (f a)) = f a :=
   invFunOn_eq ⟨a, h, rfl⟩
 #align function.inv_fun_on_apply_eq Function.invFunOn_apply_eq
@@ -2542,53 +1372,23 @@ namespace Set
 
 variable {s s₁ s₂ : Set α} {t : Set β} {f : α → β}
 
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 theorem InjOn.leftInvOn_invFunOn [Nonempty α] (h : InjOn f s) : LeftInvOn (invFunOn f s) f s :=
   fun a ha => h (invFunOn_apply_mem ha) ha (invFunOn_apply_eq ha)
 #align set.inj_on.left_inv_on_inv_fun_on Set.InjOn.leftInvOn_invFunOn
 
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 theorem InjOn.invFunOn_image [Nonempty α] (h : InjOn f s₂) (ht : s₁ ⊆ s₂) :
     invFunOn f s₂ '' (f '' s₁) = s₁ :=
   h.leftInvOn_invFunOn.image_image' ht
 #align set.inj_on.inv_fun_on_image Set.InjOn.invFunOn_image
 
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 theorem SurjOn.rightInvOn_invFunOn [Nonempty α] (h : SurjOn f s t) :
     RightInvOn (invFunOn f s) f t := fun y hy => invFunOn_eq <| mem_image_iff_bex.1 <| h hy
 #align set.surj_on.right_inv_on_inv_fun_on Set.SurjOn.rightInvOn_invFunOn
 
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 theorem BijOn.invOn_invFunOn [Nonempty α] (h : BijOn f s t) : InvOn (invFunOn f s) f s t :=
   ⟨h.InjOn.leftInvOn_invFunOn, h.SurjOn.rightInvOn_invFunOn⟩
 #align set.bij_on.inv_on_inv_fun_on Set.BijOn.invOn_invFunOn
 
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 theorem SurjOn.invOn_invFunOn [Nonempty α] (h : SurjOn f s t) :
     InvOn (invFunOn f s) f (invFunOn f s '' t) t :=
   by
@@ -2597,22 +1397,10 @@ theorem SurjOn.invOn_invFunOn [Nonempty α] (h : SurjOn f s t) :
   rw [h.right_inv_on_inv_fun_on hy]
 #align set.surj_on.inv_on_inv_fun_on Set.SurjOn.invOn_invFunOn
 
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-Case conversion may be inaccurate. Consider using '#align set.surj_on.maps_to_inv_fun_on Set.SurjOn.mapsTo_invFunOnₓ'. -/
 theorem SurjOn.mapsTo_invFunOn [Nonempty α] (h : SurjOn f s t) : MapsTo (invFunOn f s) t s :=
   fun y hy => mem_preimage.2 <| invFunOn_mem <| mem_image_iff_bex.1 <| h hy
 #align set.surj_on.maps_to_inv_fun_on Set.SurjOn.mapsTo_invFunOn
 
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 theorem SurjOn.bijOn_subset [Nonempty α] (h : SurjOn f s t) : BijOn f (invFunOn f s '' t) t :=
   by
   refine' h.inv_on_inv_fun_on.bij_on _ (maps_to_image _ _)
@@ -2620,12 +1408,6 @@ theorem SurjOn.bijOn_subset [Nonempty α] (h : SurjOn f s t) : BijOn f (invFunOn
   rwa [h.right_inv_on_inv_fun_on hy]
 #align set.surj_on.bij_on_subset Set.SurjOn.bijOn_subset
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (s' «expr ⊆ » s) -/
 theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _)(_ : s' ⊆ s), BijOn f s' t :=
   by
@@ -2639,12 +1421,6 @@ theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _)(_ : s' 
     exact hfs'.surj_on.mono hs' (subset.refl _)
 #align set.surj_on_iff_exists_bij_on_subset Set.surjOn_iff_exists_bijOn_subset
 
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 theorem preimage_invFun_of_mem [n : Nonempty α] {f : α → β} (hf : Injective f) {s : Set α}
     (h : Classical.choice n ∈ s) : invFun f ⁻¹' s = f '' s ∪ range fᶜ :=
   by
@@ -2654,12 +1430,6 @@ theorem preimage_invFun_of_mem [n : Nonempty α] {f : α → β} (hf : Injective
   · simp [mem_preimage, inv_fun_neg hx, h, hx]
 #align set.preimage_inv_fun_of_mem Set.preimage_invFun_of_mem
 
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 theorem preimage_invFun_of_not_mem [n : Nonempty α] {f : α → β} (hf : Injective f) {s : Set α}
     (h : Classical.choice n ∉ s) : invFun f ⁻¹' s = f '' s :=
   by
@@ -2679,33 +1449,15 @@ namespace Monotone
 
 variable [Preorder α] [Preorder β] {f : α → β}
 
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 protected theorem restrict (h : Monotone f) (s : Set α) : Monotone (s.restrict f) := fun x y hxy =>
   h hxy
 #align monotone.restrict Monotone.restrict
 
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 protected theorem codRestrict (h : Monotone f) {s : Set β} (hs : ∀ x, f x ∈ s) :
     Monotone (s.codRestrict f hs) :=
   h
 #align monotone.cod_restrict Monotone.codRestrict
 
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 protected theorem rangeFactorization (h : Monotone f) : Monotone (Set.rangeFactorization f) :=
   h
 #align monotone.range_factorization Monotone.rangeFactorization
@@ -2719,34 +1471,16 @@ namespace Set
 
 variable {δ : α → Sort y} (s : Set α) (f g : ∀ i, δ i)
 
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 @[simp]
 theorem piecewise_empty [∀ i : α, Decidable (i ∈ (∅ : Set α))] : piecewise ∅ f g = g := by ext i;
   simp [piecewise]
 #align set.piecewise_empty Set.piecewise_empty
 
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 @[simp]
 theorem piecewise_univ [∀ i : α, Decidable (i ∈ (Set.univ : Set α))] : piecewise Set.univ f g = f :=
   by ext i; simp [piecewise]
 #align set.piecewise_univ Set.piecewise_univ
 
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 @[simp]
 theorem piecewise_insert_self {j : α} [∀ i, Decidable (i ∈ insert j s)] :
     (insert j s).piecewise f g j = f j := by simp [piecewise]
@@ -2754,22 +1488,10 @@ theorem piecewise_insert_self {j : α} [∀ i, Decidable (i ∈ insert j s)] :
 
 variable [∀ j, Decidable (j ∈ s)]
 
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 instance Compl.decidableMem (j : α) : Decidable (j ∈ sᶜ) :=
   Not.decidable
 #align set.compl.decidable_mem Set.Compl.decidableMem
 
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 theorem piecewise_insert [DecidableEq α] (j : α) [∀ i, Decidable (i ∈ insert j s)] :
     (insert j s).piecewise f g = Function.update (s.piecewise f g) j (f j) :=
   by
@@ -2780,77 +1502,35 @@ theorem piecewise_insert [DecidableEq α] (j : α) [∀ i, Decidable (i ∈ inse
   · by_cases h' : i ∈ s <;> simp [h, h']
 #align set.piecewise_insert Set.piecewise_insert
 
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 @[simp]
 theorem piecewise_eq_of_mem {i : α} (hi : i ∈ s) : s.piecewise f g i = f i :=
   if_pos hi
 #align set.piecewise_eq_of_mem Set.piecewise_eq_of_mem
 
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 @[simp]
 theorem piecewise_eq_of_not_mem {i : α} (hi : i ∉ s) : s.piecewise f g i = g i :=
   if_neg hi
 #align set.piecewise_eq_of_not_mem Set.piecewise_eq_of_not_mem
 
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 theorem piecewise_singleton (x : α) [∀ y, Decidable (y ∈ ({x} : Set α))] [DecidableEq α]
     (f g : α → β) : piecewise {x} f g = Function.update g x (f x) := by ext y; by_cases hy : y = x;
   · subst y; simp; · simp [hy]
 #align set.piecewise_singleton Set.piecewise_singleton
 
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 theorem piecewise_eqOn (f g : α → β) : EqOn (s.piecewise f g) f s := fun _ =>
   piecewise_eq_of_mem _ _ _
 #align set.piecewise_eq_on Set.piecewise_eqOn
 
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 theorem piecewise_eqOn_compl (f g : α → β) : EqOn (s.piecewise f g) g (sᶜ) := fun _ =>
   piecewise_eq_of_not_mem _ _ _
 #align set.piecewise_eq_on_compl Set.piecewise_eqOn_compl
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
 theorem piecewise_le {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g i) (h₂ : ∀ (i) (_ : i ∉ s), f₂ i ≤ g i) :
     s.piecewise f₁ f₂ ≤ g := fun i => if h : i ∈ s then by simp [*] else by simp [*]
 #align set.piecewise_le Set.piecewise_le
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
 theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, g i ≤ f₁ i) (h₂ : ∀ (i) (_ : i ∉ s), g i ≤ f₂ i) :
@@ -2858,12 +1538,6 @@ theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
   @piecewise_le α (fun i => (δ i)ᵒᵈ) _ s _ _ _ _ h₁ h₂
 #align set.le_piecewise Set.le_piecewise
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
 theorem piecewise_le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
     [∀ j, Decidable (j ∈ s)] {f₁ f₂ g₁ g₂ : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g₁ i)
@@ -2871,46 +1545,22 @@ theorem piecewise_le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s
   apply piecewise_le <;> intros <;> simp [*]
 #align set.piecewise_le_piecewise Set.piecewise_le_piecewise
 
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 @[simp]
 theorem piecewise_insert_of_ne {i j : α} (h : i ≠ j) [∀ i, Decidable (i ∈ insert j s)] :
     (insert j s).piecewise f g i = s.piecewise f g i := by simp [piecewise, h]
 #align set.piecewise_insert_of_ne Set.piecewise_insert_of_ne
 
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 @[simp]
 theorem piecewise_compl [∀ i, Decidable (i ∈ sᶜ)] : sᶜ.piecewise f g = s.piecewise g f :=
   funext fun x => if hx : x ∈ s then by simp [hx] else by simp [hx]
 #align set.piecewise_compl Set.piecewise_compl
 
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 @[simp]
 theorem piecewise_range_comp {ι : Sort _} (f : ι → α) [∀ j, Decidable (j ∈ range f)]
     (g₁ g₂ : α → β) : (range f).piecewise g₁ g₂ ∘ f = g₁ ∘ f :=
   EqOn.comp_eq <| piecewise_eqOn _ _ _
 #align set.piecewise_range_comp Set.piecewise_range_comp
 
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-Case conversion may be inaccurate. Consider using '#align set.maps_to.piecewise_ite Set.MapsTo.piecewise_iteₓ'. -/
 theorem MapsTo.piecewise_ite {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {f₁ f₂ : α → β}
     [∀ i, Decidable (i ∈ s)] (h₁ : MapsTo f₁ (s₁ ∩ s) (t₁ ∩ t))
     (h₂ : MapsTo f₂ (s₂ ∩ sᶜ) (t₂ ∩ tᶜ)) : MapsTo (s.piecewise f₁ f₂) (s.ite s₁ s₂) (t.ite t₁ t₂) :=
@@ -2920,12 +1570,6 @@ theorem MapsTo.piecewise_ite {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {f₁
     (piecewise_eq_on_compl s f₁ f₂).symm.mono (inter_subset_right _ _)]
 #align set.maps_to.piecewise_ite Set.MapsTo.piecewise_ite
 
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 theorem eqOn_piecewise {f f' g : α → β} {t} :
     EqOn (s.piecewise f f') g t ↔ EqOn f g (t ∩ s) ∧ EqOn f' g (t ∩ sᶜ) :=
   by
@@ -2933,23 +1577,11 @@ theorem eqOn_piecewise {f f' g : α → β} {t} :
   refine' forall_congr' fun a => _; by_cases a ∈ s <;> simp [*]
 #align set.eq_on_piecewise Set.eqOn_piecewise
 
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 theorem EqOn.piecewise_ite' {f f' g : α → β} {t t'} (h : EqOn f g (t ∩ s))
     (h' : EqOn f' g (t' ∩ sᶜ)) : EqOn (s.piecewise f f') g (s.ite t t') := by
   simp [eq_on_piecewise, *]
 #align set.eq_on.piecewise_ite' Set.EqOn.piecewise_ite'
 
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 theorem EqOn.piecewise_ite {f f' g : α → β} {t t'} (h : EqOn f g t) (h' : EqOn f' g t') :
     EqOn (s.piecewise f f') g (s.ite t t') :=
   (h.mono (inter_subset_left _ _)).piecewise_ite' s (h'.mono (inter_subset_left _ _))
@@ -2961,23 +1593,11 @@ theorem piecewise_preimage (f g : α → β) (t) : s.piecewise f g ⁻¹' t = s.
 #align set.piecewise_preimage Set.piecewise_preimage
 -/
 
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 theorem apply_piecewise {δ' : α → Sort _} (h : ∀ i, δ i → δ' i) {x : α} :
     h x (s.piecewise f g x) = s.piecewise (fun x => h x (f x)) (fun x => h x (g x)) x := by
   by_cases hx : x ∈ s <;> simp [hx]
 #align set.apply_piecewise Set.apply_piecewise
 
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 theorem apply_piecewise₂ {δ' δ'' : α → Sort _} (f' g' : ∀ i, δ' i) (h : ∀ i, δ i → δ' i → δ'' i)
     {x : α} :
     h x (s.piecewise f g x) (s.piecewise f' g' x) =
@@ -2985,45 +1605,21 @@ theorem apply_piecewise₂ {δ' δ'' : α → Sort _} (f' g' : ∀ i, δ' i) (h
   by by_cases hx : x ∈ s <;> simp [hx]
 #align set.apply_piecewise₂ Set.apply_piecewise₂
 
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 theorem piecewise_op {δ' : α → Sort _} (h : ∀ i, δ i → δ' i) :
     (s.piecewise (fun x => h x (f x)) fun x => h x (g x)) = fun x => h x (s.piecewise f g x) :=
   funext fun x => (apply_piecewise _ _ _ _).symm
 #align set.piecewise_op Set.piecewise_op
 
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 theorem piecewise_op₂ {δ' δ'' : α → Sort _} (f' g' : ∀ i, δ' i) (h : ∀ i, δ i → δ' i → δ'' i) :
     (s.piecewise (fun x => h x (f x) (f' x)) fun x => h x (g x) (g' x)) = fun x =>
       h x (s.piecewise f g x) (s.piecewise f' g' x) :=
   funext fun x => (apply_piecewise₂ _ _ _ _ _ _).symm
 #align set.piecewise_op₂ Set.piecewise_op₂
 
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 @[simp]
 theorem piecewise_same : s.piecewise f f = f := by ext x; by_cases hx : x ∈ s <;> simp [hx]
 #align set.piecewise_same Set.piecewise_same
 
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 theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪ g '' sᶜ :=
   by
   ext y; constructor
@@ -3031,12 +1627,6 @@ theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪
   · rintro (⟨x, hx, rfl⟩ | ⟨x, hx, rfl⟩) <;> use x <;> simp_all
 #align set.range_piecewise Set.range_piecewise
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ∉ » s) -/
 theorem injective_piecewise_iff {f g : α → β} :
     Injective (s.piecewise f g) ↔
@@ -3055,12 +1645,6 @@ theorem piecewise_mem_pi {δ : α → Type _} {t : Set α} {t' : ∀ i, Set (δ
 #align set.piecewise_mem_pi Set.piecewise_mem_pi
 -/
 
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 @[simp]
 theorem pi_piecewise {ι : Type _} {α : ι → Type _} (s s' : Set ι) (t t' : ∀ i, Set (α i))
     [∀ x, Decidable (x ∈ s')] : pi s (s'.piecewise t t') = pi (s ∩ s') t ∩ pi (s \ s') t' :=
@@ -3071,12 +1655,6 @@ theorem pi_piecewise {ι : Type _} {α : ι → Type _} (s s' : Set ι) (t t' :
   by_cases hi : i ∈ s' <;> simp [*]
 #align set.pi_piecewise Set.pi_piecewise
 
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 theorem univ_pi_piecewise_univ {ι : Type _} {α : ι → Type _} (s : Set ι) (t : ∀ i, Set (α i))
     [∀ x, Decidable (x ∈ s)] : pi univ (s.piecewise t fun _ => univ) = pi s t := by simp
 #align set.univ_pi_piecewise Set.univ_pi_piecewise_univ
@@ -3085,107 +1663,47 @@ end Set
 
 open Set
 
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 theorem StrictMonoOn.injOn [LinearOrder α] [Preorder β] {f : α → β} {s : Set α}
     (H : StrictMonoOn f s) : s.InjOn f := fun x hx y hy hxy =>
   show Ordering.eq.Compares x y from (H.Compares hx hy).1 hxy
 #align strict_mono_on.inj_on StrictMonoOn.injOn
 
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 theorem StrictAntiOn.injOn [LinearOrder α] [Preorder β] {f : α → β} {s : Set α}
     (H : StrictAntiOn f s) : s.InjOn f :=
   @StrictMonoOn.injOn α βᵒᵈ _ _ f s H
 #align strict_anti_on.inj_on StrictAntiOn.injOn
 
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 theorem StrictMonoOn.comp [Preorder α] [Preorder β] [Preorder γ] {g : β → γ} {f : α → β} {s : Set α}
     {t : Set β} (hg : StrictMonoOn g t) (hf : StrictMonoOn f s) (hs : Set.MapsTo f s t) :
     StrictMonoOn (g ∘ f) s := fun x hx y hy hxy => hg (hs hx) (hs hy) <| hf hx hy hxy
 #align strict_mono_on.comp StrictMonoOn.comp
 
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 theorem StrictMonoOn.comp_strictAntiOn [Preorder α] [Preorder β] [Preorder γ] {g : β → γ}
     {f : α → β} {s : Set α} {t : Set β} (hg : StrictMonoOn g t) (hf : StrictAntiOn f s)
     (hs : Set.MapsTo f s t) : StrictAntiOn (g ∘ f) s := fun x hx y hy hxy =>
   hg (hs hy) (hs hx) <| hf hx hy hxy
 #align strict_mono_on.comp_strict_anti_on StrictMonoOn.comp_strictAntiOn
 
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 theorem StrictAntiOn.comp [Preorder α] [Preorder β] [Preorder γ] {g : β → γ} {f : α → β} {s : Set α}
     {t : Set β} (hg : StrictAntiOn g t) (hf : StrictAntiOn f s) (hs : Set.MapsTo f s t) :
     StrictMonoOn (g ∘ f) s := fun x hx y hy hxy => hg (hs hy) (hs hx) <| hf hx hy hxy
 #align strict_anti_on.comp StrictAntiOn.comp
 
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 theorem StrictAntiOn.comp_strictMonoOn [Preorder α] [Preorder β] [Preorder γ] {g : β → γ}
     {f : α → β} {s : Set α} {t : Set β} (hg : StrictAntiOn g t) (hf : StrictMonoOn f s)
     (hs : Set.MapsTo f s t) : StrictAntiOn (g ∘ f) s := fun x hx y hy hxy =>
   hg (hs hx) (hs hy) <| hf hx hy hxy
 #align strict_anti_on.comp_strict_mono_on StrictAntiOn.comp_strictMonoOn
 
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 @[simp]
 theorem strictMono_restrict [Preorder α] [Preorder β] {f : α → β} {s : Set α} :
     StrictMono (s.restrict f) ↔ StrictMonoOn f s := by simp [Set.restrict, StrictMono, StrictMonoOn]
 #align strict_mono_restrict strictMono_restrict
 
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 alias strictMono_restrict ↔ _root_.strict_mono.of_restrict _root_.strict_mono_on.restrict
 #align strict_mono.of_restrict StrictMono.of_restrict
 #align strict_mono_on.restrict StrictMonoOn.restrict
 
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 theorem StrictMono.codRestrict [Preorder α] [Preorder β] {f : α → β} (hf : StrictMono f) {s : Set β}
     (hs : ∀ x, f x ∈ s) : StrictMono (Set.codRestrict f s hs) :=
   hf
@@ -3197,22 +1715,10 @@ open Set
 
 variable {fa : α → α} {fb : β → β} {f : α → β} {g : β → γ} {s t : Set α}
 
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 theorem Injective.comp_injOn (hg : Injective g) (hf : s.InjOn f) : s.InjOn (g ∘ f) :=
   (hg.InjOn univ).comp hf (mapsTo_univ _ _)
 #align function.injective.comp_inj_on Function.Injective.comp_injOn
 
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 theorem Surjective.surjOn (hf : Surjective f) (s : Set β) : SurjOn f univ s :=
   (surjective_iff_surjOn_univ.1 hf).mono (Subset.refl _) (subset_univ _)
 #align function.surjective.surj_on Function.Surjective.surjOn
@@ -3237,32 +1743,14 @@ theorem LeftInverse.rightInvOn_range {g : β → α} (h : LeftInverse f g) : Rig
 
 namespace Semiconj
 
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 theorem mapsTo_image (h : Semiconj f fa fb) (ha : MapsTo fa s t) : MapsTo fb (f '' s) (f '' t) :=
   fun y ⟨x, hx, hy⟩ => hy ▸ ⟨fa x, ha hx, h x⟩
 #align function.semiconj.maps_to_image Function.Semiconj.mapsTo_image
 
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 theorem mapsTo_range (h : Semiconj f fa fb) : MapsTo fb (range f) (range f) := fun y ⟨x, hy⟩ =>
   hy ▸ ⟨fa x, h x⟩
 #align function.semiconj.maps_to_range Function.Semiconj.mapsTo_range
 
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 theorem surjOn_image (h : Semiconj f fa fb) (ha : SurjOn fa s t) : SurjOn fb (f '' s) (f '' t) :=
   by
   rintro y ⟨x, hxt, rfl⟩
@@ -3271,22 +1759,10 @@ theorem surjOn_image (h : Semiconj f fa fb) (ha : SurjOn fa s t) : SurjOn fb (f
   exact mem_image_of_mem _ (mem_image_of_mem _ hxs)
 #align function.semiconj.surj_on_image Function.Semiconj.surjOn_image
 
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 theorem surjOn_range (h : Semiconj f fa fb) (ha : Surjective fa) : SurjOn fb (range f) (range f) :=
   by rw [← image_univ]; exact h.surj_on_image (ha.surj_on univ)
 #align function.semiconj.surj_on_range Function.Semiconj.surjOn_range
 
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 theorem injOn_image (h : Semiconj f fa fb) (ha : InjOn fa s) (hf : InjOn f (fa '' s)) :
     InjOn fb (f '' s) := by
   rintro _ ⟨x, hx, rfl⟩ _ ⟨y, hy, rfl⟩ H
@@ -3294,56 +1770,26 @@ theorem injOn_image (h : Semiconj f fa fb) (ha : InjOn fa s) (hf : InjOn f (fa '
   exact congr_arg f (ha hx hy <| hf (mem_image_of_mem fa hx) (mem_image_of_mem fa hy) H)
 #align function.semiconj.inj_on_image Function.Semiconj.injOn_image
 
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 theorem injOn_range (h : Semiconj f fa fb) (ha : Injective fa) (hf : InjOn f (range fa)) :
     InjOn fb (range f) := by rw [← image_univ] at *; exact h.inj_on_image (ha.inj_on univ) hf
 #align function.semiconj.inj_on_range Function.Semiconj.injOn_range
 
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 theorem bijOn_image (h : Semiconj f fa fb) (ha : BijOn fa s t) (hf : InjOn f t) :
     BijOn fb (f '' s) (f '' t) :=
   ⟨h.mapsTo_image ha.MapsTo, h.injOn_image ha.InjOn (ha.image_eq.symm ▸ hf),
     h.surjOn_image ha.SurjOn⟩
 #align function.semiconj.bij_on_image Function.Semiconj.bijOn_image
 
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 theorem bijOn_range (h : Semiconj f fa fb) (ha : Bijective fa) (hf : Injective f) :
     BijOn fb (range f) (range f) := by
   rw [← image_univ]
   exact h.bij_on_image (bijective_iff_bij_on_univ.1 ha) (hf.inj_on univ)
 #align function.semiconj.bij_on_range Function.Semiconj.bijOn_range
 
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 theorem mapsTo_preimage (h : Semiconj f fa fb) {s t : Set β} (hb : MapsTo fb s t) :
     MapsTo fa (f ⁻¹' s) (f ⁻¹' t) := fun x hx => by simp only [mem_preimage, h x, hb hx]
 #align function.semiconj.maps_to_preimage Function.Semiconj.mapsTo_preimage
 
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 theorem injOn_preimage (h : Semiconj f fa fb) {s : Set β} (hb : InjOn fb s)
     (hf : InjOn f (f ⁻¹' s)) : InjOn fa (f ⁻¹' s) :=
   by
@@ -3355,45 +1801,21 @@ theorem injOn_preimage (h : Semiconj f fa fb) {s : Set β} (hb : InjOn fb s)
 
 end Semiconj
 
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 theorem update_comp_eq_of_not_mem_range' {α β : Sort _} {γ : β → Sort _} [DecidableEq β]
     (g : ∀ b, γ b) {f : α → β} {i : β} (a : γ i) (h : i ∉ Set.range f) :
     (fun j => (Function.update g i a) (f j)) = fun j => g (f j) :=
   update_comp_eq_of_forall_ne' _ _ fun x hx => h ⟨x, hx⟩
 #align function.update_comp_eq_of_not_mem_range' Function.update_comp_eq_of_not_mem_range'
 
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 /-- Non-dependent version of `function.update_comp_eq_of_not_mem_range'` -/
 theorem update_comp_eq_of_not_mem_range {α β γ : Sort _} [DecidableEq β] (g : β → γ) {f : α → β}
     {i : β} (a : γ) (h : i ∉ Set.range f) : Function.update g i a ∘ f = g ∘ f :=
   update_comp_eq_of_not_mem_range' g a h
 #align function.update_comp_eq_of_not_mem_range Function.update_comp_eq_of_not_mem_range
 
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 theorem insert_injOn (s : Set α) : sᶜ.InjOn fun a => insert a s := fun a ha b _ => (insert_inj ha).1
 #align function.insert_inj_on Function.insert_injOn
 
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 theorem monotoneOn_of_rightInvOn_of_mapsTo [PartialOrder α] [LinearOrder β] {φ : β → α} {ψ : α → β}
     {t : Set β} {s : Set α} (hφ : MonotoneOn φ t) (φψs : Set.RightInvOn ψ φ s)
     (ψts : Set.MapsTo ψ s t) : MonotoneOn ψ s :=
@@ -3404,12 +1826,6 @@ theorem monotoneOn_of_rightInvOn_of_mapsTo [PartialOrder α] [LinearOrder β] {
   · cases le_antisymm l (φψs.eq ys ▸ φψs.eq xs ▸ hφ (ψts ys) (ψts xs) ψyx); rfl
 #align function.monotone_on_of_right_inv_on_of_maps_to Function.monotoneOn_of_rightInvOn_of_mapsTo
 
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 theorem antitoneOn_of_rightInvOn_of_mapsTo [PartialOrder α] [LinearOrder β] {φ : β → α} {ψ : α → β}
     {t : Set β} {s : Set α} (hφ : AntitoneOn φ t) (φψs : Set.RightInvOn ψ φ s)
     (ψts : Set.MapsTo ψ s t) : AntitoneOn ψ s :=
@@ -3425,23 +1841,11 @@ namespace Set
 
 variable {p : β → Prop} [DecidablePred p] {f : α ≃ Subtype p} {g g₁ g₂ : Perm α} {s t : Set α}
 
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 protected theorem MapsTo.extendDomain (h : MapsTo g s t) :
     MapsTo (g.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) := by rintro _ ⟨a, ha, rfl⟩;
   exact ⟨_, h ha, by rw [extend_domain_apply_image]⟩
 #align set.maps_to.extend_domain Set.MapsTo.extendDomain
 
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 protected theorem SurjOn.extendDomain (h : SurjOn g s t) :
     SurjOn (g.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
   by
@@ -3450,45 +1854,21 @@ protected theorem SurjOn.extendDomain (h : SurjOn g s t) :
   exact ⟨_, ⟨_, hb, rfl⟩, by rw [extend_domain_apply_image]⟩
 #align set.surj_on.extend_domain Set.SurjOn.extendDomain
 
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 protected theorem BijOn.extendDomain (h : Set.BijOn g s t) :
     BijOn (g.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
   ⟨h.MapsTo.extendDomain, (g.extendDomain f).Injective.InjOn _, h.SurjOn.extendDomain⟩
 #align set.bij_on.extend_domain Set.BijOn.extendDomain
 
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 protected theorem LeftInvOn.extendDomain (h : LeftInvOn g₁ g₂ s) :
     LeftInvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' s) := by rintro _ ⟨a, ha, rfl⟩;
   simp_rw [extend_domain_apply_image, h ha]
 #align set.left_inv_on.extend_domain Set.LeftInvOn.extendDomain
 
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 protected theorem RightInvOn.extendDomain (h : RightInvOn g₁ g₂ t) :
     RightInvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' t) := by rintro _ ⟨a, ha, rfl⟩;
   simp_rw [extend_domain_apply_image, h ha]
 #align set.right_inv_on.extend_domain Set.RightInvOn.extendDomain
 
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-Case conversion may be inaccurate. Consider using '#align set.inv_on.extend_domain Set.InvOn.extendDomainₓ'. -/
 protected theorem InvOn.extendDomain (h : InvOn g₁ g₂ s t) :
     InvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
   ⟨h.1.extendDomain, h.2.extendDomain⟩
@@ -3500,12 +1880,6 @@ namespace Equiv
 
 variable (e : α ≃ β) {s : Set α} {t : Set β}
 
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-Case conversion may be inaccurate. Consider using '#align equiv.bij_on' Equiv.bijOn'ₓ'. -/
 theorem bijOn' (h₁ : MapsTo e s t) (h₂ : MapsTo e.symm t s) : BijOn e s t :=
   ⟨h₁, e.Injective.InjOn _, fun b hb => ⟨e.symm b, h₂ hb, apply_symm_apply _ _⟩⟩
 #align equiv.bij_on' Equiv.bijOn'
@@ -3522,12 +1896,6 @@ theorem invOn : InvOn e e.symm t s :=
 #align equiv.inv_on Equiv.invOn
 -/
 
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-Case conversion may be inaccurate. Consider using '#align equiv.bij_on_image Equiv.bijOn_imageₓ'. -/
 theorem bijOn_image : BijOn e s (e '' s) :=
   (e.Injective.InjOn _).bijOn_image
 #align equiv.bij_on_image Equiv.bijOn_image

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -727,9 +727,7 @@ but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {s : Set.{u2} α} {t : Set.{u1} β} {f : α -> β}, Iff (Set.MapsTo.{u2, u1} α β f s t) (Exists.{max (succ u2) (succ u1)} ((Set.Elem.{u2} α s) -> (Set.Elem.{u1} β t)) (fun (g : (Set.Elem.{u2} α s) -> (Set.Elem.{u1} β t)) => forall (x : Set.Elem.{u2} α s), Eq.{succ u1} β (f (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (Subtype.val.{succ u1} β (fun (x : β) => Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x t) (g x))))
 Case conversion may be inaccurate. Consider using '#align set.maps_to_iff_exists_map_subtype Set.mapsTo_iff_exists_map_subtypeₓ'. -/
 theorem mapsTo_iff_exists_map_subtype : MapsTo f s t ↔ ∃ g : s → t, ∀ x : s, f x = g x :=
-  ⟨fun h => ⟨h.restrict f s t, fun _ => rfl⟩, fun ⟨g, hg⟩ x hx =>
-    by
-    erw [hg ⟨x, hx⟩]
+  ⟨fun h => ⟨h.restrict f s t, fun _ => rfl⟩, fun ⟨g, hg⟩ x hx => by erw [hg ⟨x, hx⟩];
     apply Subtype.coe_prop⟩
 #align set.maps_to_iff_exists_map_subtype Set.mapsTo_iff_exists_map_subtype
 
@@ -1265,8 +1263,7 @@ theorem injOn_union (h : Disjoint s₁ s₂) :
   by
   refine' ⟨fun H => ⟨H.mono <| subset_union_left _ _, H.mono <| subset_union_right _ _, _⟩, _⟩
   · intro x hx y hy hxy
-    obtain rfl : x = y
-    exact H (Or.inl hx) (Or.inr hy) hxy
+    obtain rfl : x = y; exact H (Or.inl hx) (Or.inr hy) hxy
     exact h.le_bot ⟨hx, hy⟩
   · rintro ⟨h₁, h₂, h₁₂⟩
     rintro x (hx | hx) y (hy | hy) hxy
@@ -1355,10 +1352,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} {f : α -> β} {g : β -> γ}, (Function.Injective.{succ u3, succ u2} α γ (Function.comp.{succ u3, succ u1, succ u2} α β γ g f)) -> (Set.InjOn.{u1, u2} β γ g (Set.range.{u1, succ u3} β α f))
 Case conversion may be inaccurate. Consider using '#align function.injective.inj_on_range Function.Injective.injOn_rangeₓ'. -/
-theorem Function.Injective.injOn_range (h : Injective (g ∘ f)) : InjOn g (range f) :=
-  by
-  rintro _ ⟨x, rfl⟩ _ ⟨y, rfl⟩ H
-  exact congr_arg f (h H)
+theorem Function.Injective.injOn_range (h : Injective (g ∘ f)) : InjOn g (range f) := by
+  rintro _ ⟨x, rfl⟩ _ ⟨y, rfl⟩ H; exact congr_arg f (h H)
 #align function.injective.inj_on_range Function.Injective.injOn_range
 
 /- warning: set.inj_on_iff_injective -> Set.injOn_iff_injective is a dubious translation:
@@ -1394,9 +1389,7 @@ theorem MapsTo.restrict_inj (h : MapsTo f s t) : Injective (h.restrict f s t) 
 #print Set.exists_injOn_iff_injective /-
 theorem exists_injOn_iff_injective [Nonempty β] :
     (∃ f : α → β, InjOn f s) ↔ ∃ f : s → β, Injective f :=
-  ⟨fun ⟨f, hf⟩ => ⟨_, hf.Injective⟩, fun ⟨f, hf⟩ =>
-    by
-    lift f to α → β using trivial
+  ⟨fun ⟨f, hf⟩ => ⟨_, hf.Injective⟩, fun ⟨f, hf⟩ => by lift f to α → β using trivial;
     exact ⟨f, inj_on_iff_injective.2 hf⟩⟩
 #align set.exists_inj_on_iff_injective Set.exists_injOn_iff_injective
 -/
@@ -1674,10 +1667,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} {s : Set.{u3} α} {t : Set.{u2} β} {f : α -> β}, (Set.SurjOn.{u3, u2} α β f s t) -> (forall (g : β -> γ), Set.SurjOn.{u3, u1} α γ (Function.comp.{succ u3, succ u2, succ u1} α β γ g f) s (Set.image.{u2, u1} β γ g t))
 Case conversion may be inaccurate. Consider using '#align set.surj_on.comp_left Set.SurjOn.comp_leftₓ'. -/
-theorem SurjOn.comp_left (hf : SurjOn f s t) (g : β → γ) : SurjOn (g ∘ f) s (g '' t) :=
-  by
-  rw [surj_on, image_comp g f]
-  exact image_subset _ hf
+theorem SurjOn.comp_left (hf : SurjOn f s t) (g : β → γ) : SurjOn (g ∘ f) s (g '' t) := by
+  rw [surj_on, image_comp g f]; exact image_subset _ hf
 #align set.surj_on.comp_left Set.SurjOn.comp_left
 
 /- warning: set.surj_on.comp_right -> Set.SurjOn.comp_right is a dubious translation:
@@ -2191,10 +2182,8 @@ Case conversion may be inaccurate. Consider using '#align set.left_inv_on.image_
 theorem LeftInvOn.image_inter' (hf : LeftInvOn f' f s) : f '' (s₁ ∩ s) = f' ⁻¹' s₁ ∩ f '' s :=
   by
   apply subset.antisymm
-  · rintro _ ⟨x, ⟨h₁, h⟩, rfl⟩
-    exact ⟨by rwa [mem_preimage, hf h], mem_image_of_mem _ h⟩
-  · rintro _ ⟨h₁, ⟨x, h, rfl⟩⟩
-    exact mem_image_of_mem _ ⟨by rwa [← hf h], h⟩
+  · rintro _ ⟨x, ⟨h₁, h⟩, rfl⟩; exact ⟨by rwa [mem_preimage, hf h], mem_image_of_mem _ h⟩
+  · rintro _ ⟨h₁, ⟨x, h, rfl⟩⟩; exact mem_image_of_mem _ ⟨by rwa [← hf h], h⟩
 #align set.left_inv_on.image_inter' Set.LeftInvOn.image_inter'
 
 /- warning: set.left_inv_on.image_inter -> Set.LeftInvOn.image_inter is a dubious translation:
@@ -2737,9 +2726,7 @@ but is expected to have type
   forall {α : Type.{u2}} {δ : α -> Sort.{u1}} (f : forall (i : α), δ i) (g : forall (i : α), δ i) [_inst_1 : forall (i : α), Decidable (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) i (EmptyCollection.emptyCollection.{u2} (Set.{u2} α) (Set.instEmptyCollectionSet.{u2} α)))], Eq.{imax (succ u2) u1} (forall (i : α), δ i) (Set.piecewise.{u2, u1} α (fun (i : α) => δ i) (EmptyCollection.emptyCollection.{u2} (Set.{u2} α) (Set.instEmptyCollectionSet.{u2} α)) f g (fun (j : α) => _inst_1 j)) g
 Case conversion may be inaccurate. Consider using '#align set.piecewise_empty Set.piecewise_emptyₓ'. -/
 @[simp]
-theorem piecewise_empty [∀ i : α, Decidable (i ∈ (∅ : Set α))] : piecewise ∅ f g = g :=
-  by
-  ext i
+theorem piecewise_empty [∀ i : α, Decidable (i ∈ (∅ : Set α))] : piecewise ∅ f g = g := by ext i;
   simp [piecewise]
 #align set.piecewise_empty Set.piecewise_empty
 
@@ -2751,9 +2738,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align set.piecewise_univ Set.piecewise_univₓ'. -/
 @[simp]
 theorem piecewise_univ [∀ i : α, Decidable (i ∈ (Set.univ : Set α))] : piecewise Set.univ f g = f :=
-  by
-  ext i
-  simp [piecewise]
+  by ext i; simp [piecewise]
 #align set.piecewise_univ Set.piecewise_univ
 
 /- warning: set.piecewise_insert_self -> Set.piecewise_insert_self is a dubious translation:
@@ -2791,8 +2776,7 @@ theorem piecewise_insert [DecidableEq α] (j : α) [∀ i, Decidable (i ∈ inse
   simp [piecewise]
   ext i
   by_cases h : i = j
-  · rw [h]
-    simp
+  · rw [h]; simp
   · by_cases h' : i ∈ s <;> simp [h, h']
 #align set.piecewise_insert Set.piecewise_insert
 
@@ -2825,13 +2809,8 @@ but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} (x : α) [_inst_2 : forall (y : α), Decidable (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) y (Singleton.singleton.{u2, u2} α (Set.{u2} α) (Set.instSingletonSet.{u2} α) x))] [_inst_3 : DecidableEq.{succ u2} α] (f : α -> β) (g : α -> β), Eq.{max (succ u2) (succ u1)} (α -> β) (Set.piecewise.{u2, succ u1} α (fun (ᾰ : α) => β) (Singleton.singleton.{u2, u2} α (Set.{u2} α) (Set.instSingletonSet.{u2} α) x) f g (fun (j : α) => _inst_2 j)) (Function.update.{succ u2, succ u1} α (fun (i : α) => β) (fun (a : α) (b : α) => _inst_3 a b) g x (f x))
 Case conversion may be inaccurate. Consider using '#align set.piecewise_singleton Set.piecewise_singletonₓ'. -/
 theorem piecewise_singleton (x : α) [∀ y, Decidable (y ∈ ({x} : Set α))] [DecidableEq α]
-    (f g : α → β) : piecewise {x} f g = Function.update g x (f x) :=
-  by
-  ext y
-  by_cases hy : y = x
-  · subst y
-    simp
-  · simp [hy]
+    (f g : α → β) : piecewise {x} f g = Function.update g x (f x) := by ext y; by_cases hy : y = x;
+  · subst y; simp; · simp [hy]
 #align set.piecewise_singleton Set.piecewise_singleton
 
 /- warning: set.piecewise_eq_on -> Set.piecewise_eqOn is a dubious translation:
@@ -3036,10 +3015,7 @@ but is expected to have type
   forall {α : Type.{u2}} {δ : α -> Sort.{u1}} (s : Set.{u2} α) (f : forall (i : α), δ i) [_inst_1 : forall (j : α), Decidable (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) j s)], Eq.{imax (succ u2) u1} (forall (i : α), δ i) (Set.piecewise.{u2, u1} α (fun (i : α) => δ i) s f f (fun (j : α) => _inst_1 j)) f
 Case conversion may be inaccurate. Consider using '#align set.piecewise_same Set.piecewise_sameₓ'. -/
 @[simp]
-theorem piecewise_same : s.piecewise f f = f :=
-  by
-  ext x
-  by_cases hx : x ∈ s <;> simp [hx]
+theorem piecewise_same : s.piecewise f f = f := by ext x; by_cases hx : x ∈ s <;> simp [hx]
 #align set.piecewise_same Set.piecewise_same
 
 /- warning: set.range_piecewise -> Set.range_piecewise is a dubious translation:
@@ -3051,8 +3027,7 @@ Case conversion may be inaccurate. Consider using '#align set.range_piecewise Se
 theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪ g '' sᶜ :=
   by
   ext y; constructor
-  · rintro ⟨x, rfl⟩
-    by_cases h : x ∈ s <;> [left;right] <;> use x <;> simp [h]
+  · rintro ⟨x, rfl⟩; by_cases h : x ∈ s <;> [left;right] <;> use x <;> simp [h]
   · rintro (⟨x, hx, rfl⟩ | ⟨x, hx, rfl⟩) <;> use x <;> simp_all
 #align set.range_piecewise Set.range_piecewise
 
@@ -3075,9 +3050,7 @@ theorem injective_piecewise_iff {f g : α → β} :
 
 #print Set.piecewise_mem_pi /-
 theorem piecewise_mem_pi {δ : α → Type _} {t : Set α} {t' : ∀ i, Set (δ i)} {f g} (hf : f ∈ pi t t')
-    (hg : g ∈ pi t t') : s.piecewise f g ∈ pi t t' :=
-  by
-  intro i ht
+    (hg : g ∈ pi t t') : s.piecewise f g ∈ pi t t' := by intro i ht;
   by_cases hs : i ∈ s <;> simp [hf i ht, hg i ht, hs]
 #align set.piecewise_mem_pi Set.piecewise_mem_pi
 -/
@@ -3305,9 +3278,7 @@ but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {fa : α -> α} {fb : β -> β} {f : α -> β}, (Function.Semiconj.{u2, u1} α β f fa fb) -> (Function.Surjective.{succ u2, succ u2} α α fa) -> (Set.SurjOn.{u1, u1} β β fb (Set.range.{u1, succ u2} β α f) (Set.range.{u1, succ u2} β α f))
 Case conversion may be inaccurate. Consider using '#align function.semiconj.surj_on_range Function.Semiconj.surjOn_rangeₓ'. -/
 theorem surjOn_range (h : Semiconj f fa fb) (ha : Surjective fa) : SurjOn fb (range f) (range f) :=
-  by
-  rw [← image_univ]
-  exact h.surj_on_image (ha.surj_on univ)
+  by rw [← image_univ]; exact h.surj_on_image (ha.surj_on univ)
 #align function.semiconj.surj_on_range Function.Semiconj.surjOn_range
 
 /- warning: function.semiconj.inj_on_image -> Function.Semiconj.injOn_image is a dubious translation:
@@ -3330,9 +3301,7 @@ but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {fa : α -> α} {fb : β -> β} {f : α -> β}, (Function.Semiconj.{u2, u1} α β f fa fb) -> (Function.Injective.{succ u2, succ u2} α α fa) -> (Set.InjOn.{u2, u1} α β f (Set.range.{u2, succ u2} α α fa)) -> (Set.InjOn.{u1, u1} β β fb (Set.range.{u1, succ u2} β α f))
 Case conversion may be inaccurate. Consider using '#align function.semiconj.inj_on_range Function.Semiconj.injOn_rangeₓ'. -/
 theorem injOn_range (h : Semiconj f fa fb) (ha : Injective fa) (hf : InjOn f (range fa)) :
-    InjOn fb (range f) := by
-  rw [← image_univ] at *
-  exact h.inj_on_image (ha.inj_on univ) hf
+    InjOn fb (range f) := by rw [← image_univ] at *; exact h.inj_on_image (ha.inj_on univ) hf
 #align function.semiconj.inj_on_range Function.Semiconj.injOn_range
 
 /- warning: function.semiconj.bij_on_image -> Function.Semiconj.bijOn_image is a dubious translation:
@@ -3432,8 +3401,7 @@ theorem monotoneOn_of_rightInvOn_of_mapsTo [PartialOrder α] [LinearOrder β] {
   rintro x xs y ys l
   rcases le_total (ψ x) (ψ y) with (ψxy | ψyx)
   · exact ψxy
-  · cases le_antisymm l (φψs.eq ys ▸ φψs.eq xs ▸ hφ (ψts ys) (ψts xs) ψyx)
-    rfl
+  · cases le_antisymm l (φψs.eq ys ▸ φψs.eq xs ▸ hφ (ψts ys) (ψts xs) ψyx); rfl
 #align function.monotone_on_of_right_inv_on_of_maps_to Function.monotoneOn_of_rightInvOn_of_mapsTo
 
 /- warning: function.antitone_on_of_right_inv_on_of_maps_to -> Function.antitoneOn_of_rightInvOn_of_mapsTo is a dubious translation:
@@ -3464,9 +3432,7 @@ but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.MapsTo.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g) s t) -> (Set.MapsTo.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
 Case conversion may be inaccurate. Consider using '#align set.maps_to.extend_domain Set.MapsTo.extendDomainₓ'. -/
 protected theorem MapsTo.extendDomain (h : MapsTo g s t) :
-    MapsTo (g.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
-  by
-  rintro _ ⟨a, ha, rfl⟩
+    MapsTo (g.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) := by rintro _ ⟨a, ha, rfl⟩;
   exact ⟨_, h ha, by rw [extend_domain_apply_image]⟩
 #align set.maps_to.extend_domain Set.MapsTo.extendDomain
 
@@ -3502,9 +3468,7 @@ but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g₁ : Equiv.Perm.{succ u2} α} {g₂ : Equiv.Perm.{succ u2} α} {s : Set.{u2} α}, (Set.LeftInvOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₁) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₂) s) -> (Set.LeftInvOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₁ p (fun (a : β) => _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s))
 Case conversion may be inaccurate. Consider using '#align set.left_inv_on.extend_domain Set.LeftInvOn.extendDomainₓ'. -/
 protected theorem LeftInvOn.extendDomain (h : LeftInvOn g₁ g₂ s) :
-    LeftInvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' s) :=
-  by
-  rintro _ ⟨a, ha, rfl⟩
+    LeftInvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' s) := by rintro _ ⟨a, ha, rfl⟩;
   simp_rw [extend_domain_apply_image, h ha]
 #align set.left_inv_on.extend_domain Set.LeftInvOn.extendDomain
 
@@ -3515,9 +3479,7 @@ but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g₁ : Equiv.Perm.{succ u2} α} {g₂ : Equiv.Perm.{succ u2} α} {t : Set.{u2} α}, (Set.RightInvOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₁) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₂) t) -> (Set.RightInvOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₁ p (fun (a : β) => _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
 Case conversion may be inaccurate. Consider using '#align set.right_inv_on.extend_domain Set.RightInvOn.extendDomainₓ'. -/
 protected theorem RightInvOn.extendDomain (h : RightInvOn g₁ g₂ t) :
-    RightInvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' t) :=
-  by
-  rintro _ ⟨a, ha, rfl⟩
+    RightInvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' t) := by rintro _ ⟨a, ha, rfl⟩;
   simp_rw [extend_domain_apply_image, h ha]
 #align set.right_inv_on.extend_domain Set.RightInvOn.extendDomain

bump to nightly-2023-05-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

fbc7b476

Diff

@@ -3052,7 +3052,7 @@ theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪
   by
   ext y; constructor
   · rintro ⟨x, rfl⟩
-    by_cases h : x ∈ s <;> [left, right] <;> use x <;> simp [h]
+    by_cases h : x ∈ s <;> [left;right] <;> use x <;> simp [h]
   · rintro (⟨x, hx, rfl⟩ | ⟨x, hx, rfl⟩) <;> use x <;> simp_all
 #align set.range_piecewise Set.range_piecewise

bump to nightly-2023-05-19-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

a31df521

Diff

@@ -3461,7 +3461,7 @@ variable {p : β → Prop} [DecidablePred p] {f : α ≃ Subtype p} {g g₁ g₂
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u2} β p] {f : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)} {g : Equiv.Perm.{succ u1} α} {s : Set.{u1} α} {t : Set.{u1} α}, (Set.MapsTo.{u1, u1} α α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g) s t) -> (Set.MapsTo.{u2, u2} β β (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) s) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) t))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.MapsTo.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g) s t) -> (Set.MapsTo.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
+  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.MapsTo.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g) s t) -> (Set.MapsTo.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
 Case conversion may be inaccurate. Consider using '#align set.maps_to.extend_domain Set.MapsTo.extendDomainₓ'. -/
 protected theorem MapsTo.extendDomain (h : MapsTo g s t) :
     MapsTo (g.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
@@ -3474,7 +3474,7 @@ protected theorem MapsTo.extendDomain (h : MapsTo g s t) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u2} β p] {f : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)} {g : Equiv.Perm.{succ u1} α} {s : Set.{u1} α} {t : Set.{u1} α}, (Set.SurjOn.{u1, u1} α α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g) s t) -> (Set.SurjOn.{u2, u2} β β (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) s) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) t))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.SurjOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g) s t) -> (Set.SurjOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
+  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.SurjOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g) s t) -> (Set.SurjOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
 Case conversion may be inaccurate. Consider using '#align set.surj_on.extend_domain Set.SurjOn.extendDomainₓ'. -/
 protected theorem SurjOn.extendDomain (h : SurjOn g s t) :
     SurjOn (g.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
@@ -3488,7 +3488,7 @@ protected theorem SurjOn.extendDomain (h : SurjOn g s t) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u2} β p] {f : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)} {g : Equiv.Perm.{succ u1} α} {s : Set.{u1} α} {t : Set.{u1} α}, (Set.BijOn.{u1, u1} α α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g) s t) -> (Set.BijOn.{u2, u2} β β (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) s) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) t))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.BijOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g) s t) -> (Set.BijOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
+  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.BijOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g) s t) -> (Set.BijOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
 Case conversion may be inaccurate. Consider using '#align set.bij_on.extend_domain Set.BijOn.extendDomainₓ'. -/
 protected theorem BijOn.extendDomain (h : Set.BijOn g s t) :
     BijOn (g.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
@@ -3499,7 +3499,7 @@ protected theorem BijOn.extendDomain (h : Set.BijOn g s t) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u2} β p] {f : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)} {g₁ : Equiv.Perm.{succ u1} α} {g₂ : Equiv.Perm.{succ u1} α} {s : Set.{u1} α}, (Set.LeftInvOn.{u1, u1} α α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g₁) (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g₂) s) -> (Set.LeftInvOn.{u2, u2} β β (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g₁ p (fun (a : β) => _inst_1 a) f)) (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g₁ : Equiv.Perm.{succ u2} α} {g₂ : Equiv.Perm.{succ u2} α} {s : Set.{u2} α}, (Set.LeftInvOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₁) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₂) s) -> (Set.LeftInvOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₁ p (fun (a : β) => _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s))
+  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g₁ : Equiv.Perm.{succ u2} α} {g₂ : Equiv.Perm.{succ u2} α} {s : Set.{u2} α}, (Set.LeftInvOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₁) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₂) s) -> (Set.LeftInvOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₁ p (fun (a : β) => _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s))
 Case conversion may be inaccurate. Consider using '#align set.left_inv_on.extend_domain Set.LeftInvOn.extendDomainₓ'. -/
 protected theorem LeftInvOn.extendDomain (h : LeftInvOn g₁ g₂ s) :
     LeftInvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' s) :=
@@ -3512,7 +3512,7 @@ protected theorem LeftInvOn.extendDomain (h : LeftInvOn g₁ g₂ s) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u2} β p] {f : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)} {g₁ : Equiv.Perm.{succ u1} α} {g₂ : Equiv.Perm.{succ u1} α} {t : Set.{u1} α}, (Set.RightInvOn.{u1, u1} α α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g₁) (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g₂) t) -> (Set.RightInvOn.{u2, u2} β β (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g₁ p (fun (a : β) => _inst_1 a) f)) (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) t))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g₁ : Equiv.Perm.{succ u2} α} {g₂ : Equiv.Perm.{succ u2} α} {t : Set.{u2} α}, (Set.RightInvOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₁) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₂) t) -> (Set.RightInvOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₁ p (fun (a : β) => _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
+  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g₁ : Equiv.Perm.{succ u2} α} {g₂ : Equiv.Perm.{succ u2} α} {t : Set.{u2} α}, (Set.RightInvOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₁) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₂) t) -> (Set.RightInvOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₁ p (fun (a : β) => _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
 Case conversion may be inaccurate. Consider using '#align set.right_inv_on.extend_domain Set.RightInvOn.extendDomainₓ'. -/
 protected theorem RightInvOn.extendDomain (h : RightInvOn g₁ g₂ t) :
     RightInvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' t) :=
@@ -3525,7 +3525,7 @@ protected theorem RightInvOn.extendDomain (h : RightInvOn g₁ g₂ t) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u2} β p] {f : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)} {g₁ : Equiv.Perm.{succ u1} α} {g₂ : Equiv.Perm.{succ u1} α} {s : Set.{u1} α} {t : Set.{u1} α}, (Set.InvOn.{u1, u1} α α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g₁) (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g₂) s t) -> (Set.InvOn.{u2, u2} β β (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g₁ p (fun (a : β) => _inst_1 a) f)) (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) s) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) t))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g₁ : Equiv.Perm.{succ u2} α} {g₂ : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.InvOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₁) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₂) s t) -> (Set.InvOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₁ p (fun (a : β) => _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
+  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g₁ : Equiv.Perm.{succ u2} α} {g₂ : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.InvOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₁) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₂) s t) -> (Set.InvOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₁ p (fun (a : β) => _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
 Case conversion may be inaccurate. Consider using '#align set.inv_on.extend_domain Set.InvOn.extendDomainₓ'. -/
 protected theorem InvOn.extendDomain (h : InvOn g₁ g₂ s t) :
     InvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
@@ -3542,7 +3542,7 @@ variable (e : α ≃ β) {s : Set α} {t : Set β}
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (e : Equiv.{succ u1, succ u2} α β) {s : Set.{u1} α} {t : Set.{u2} β}, (Set.MapsTo.{u1, u2} α β (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) e) s t) -> (Set.MapsTo.{u2, u1} β α (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} β α) (fun (_x : Equiv.{succ u2, succ u1} β α) => β -> α) (Equiv.hasCoeToFun.{succ u2, succ u1} β α) (Equiv.symm.{succ u1, succ u2} α β e)) t s) -> (Set.BijOn.{u1, u2} α β (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) e) s t)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (e : Equiv.{succ u2, succ u1} α β) {s : Set.{u2} α} {t : Set.{u1} β}, (Set.MapsTo.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s t) -> (Set.MapsTo.{u1, u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Equiv.{succ u1, succ u2} β α) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u2} β α) (Equiv.symm.{succ u2, succ u1} α β e)) t s) -> (Set.BijOn.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s t)
+  forall {α : Type.{u2}} {β : Type.{u1}} (e : Equiv.{succ u2, succ u1} α β) {s : Set.{u2} α} {t : Set.{u1} β}, (Set.MapsTo.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s t) -> (Set.MapsTo.{u1, u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Equiv.{succ u1, succ u2} β α) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u2} β α) (Equiv.symm.{succ u2, succ u1} α β e)) t s) -> (Set.BijOn.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s t)
 Case conversion may be inaccurate. Consider using '#align equiv.bij_on' Equiv.bijOn'ₓ'. -/
 theorem bijOn' (h₁ : MapsTo e s t) (h₂ : MapsTo e.symm t s) : BijOn e s t :=
   ⟨h₁, e.Injective.InjOn _, fun b hb => ⟨e.symm b, h₂ hb, apply_symm_apply _ _⟩⟩
@@ -3564,7 +3564,7 @@ theorem invOn : InvOn e e.symm t s :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (e : Equiv.{succ u1, succ u2} α β) {s : Set.{u1} α}, Set.BijOn.{u1, u2} α β (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) e) s (Set.image.{u1, u2} α β (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) e) s)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (e : Equiv.{succ u2, succ u1} α β) {s : Set.{u2} α}, Set.BijOn.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s)
+  forall {α : Type.{u2}} {β : Type.{u1}} (e : Equiv.{succ u2, succ u1} α β) {s : Set.{u2} α}, Set.BijOn.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s)
 Case conversion may be inaccurate. Consider using '#align equiv.bij_on_image Equiv.bijOn_imageₓ'. -/
 theorem bijOn_image : BijOn e s (e '' s) :=
   (e.Injective.InjOn _).bijOn_image

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -2854,31 +2854,43 @@ theorem piecewise_eqOn_compl (f g : α → β) : EqOn (s.piecewise f g) g (sᶜ)
   piecewise_eq_of_not_mem _ _ _
 #align set.piecewise_eq_on_compl Set.piecewise_eqOn_compl
 
+/- warning: set.piecewise_le -> Set.piecewise_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {δ : α -> Type.{u2}} [_inst_2 : forall (i : α), Preorder.{u2} (δ i)] {s : Set.{u1} α} [_inst_3 : forall (j : α), Decidable (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) j s)] {f₁ : forall (i : α), δ i} {f₂ : forall (i : α), δ i} {g : forall (i : α), δ i}, (forall (i : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) i s) -> (LE.le.{u2} (δ i) (Preorder.toHasLe.{u2} (δ i) (_inst_2 i)) (f₁ i) (g i))) -> (forall (i : α), (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) i s)) -> (LE.le.{u2} (δ i) (Preorder.toHasLe.{u2} (δ i) (_inst_2 i)) (f₂ i) (g i))) -> (LE.le.{max u1 u2} (forall (i : α), δ i) (Pi.hasLe.{u1, u2} α (fun (i : α) => δ i) (fun (i : α) => Preorder.toHasLe.{u2} (δ i) (_inst_2 i))) (Set.piecewise.{u1, succ u2} α (fun (i : α) => δ i) s f₁ f₂ (fun (j : α) => _inst_3 j)) g)
+but is expected to have type
+  forall {α : Type.{u1}} {δ : α -> Type.{u2}} [_inst_2 : forall (i : α), Preorder.{u2} (δ i)] {s : Set.{u1} α} [_inst_3 : forall (j : α), Decidable (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) j s)] {f₁ : forall (i : α), δ i} {f₂ : forall (i : α), δ i} {g : forall (i : α), δ i}, (forall (i : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) i s) -> (LE.le.{u2} (δ i) (Preorder.toLE.{u2} (δ i) (_inst_2 i)) (f₁ i) (g i))) -> (forall (i : α), (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) i s)) -> (LE.le.{u2} (δ i) (Preorder.toLE.{u2} (δ i) (_inst_2 i)) (f₂ i) (g i))) -> (LE.le.{max u1 u2} (forall (i : α), δ i) (Pi.hasLe.{u1, u2} α (fun (i : α) => δ i) (fun (i : α) => Preorder.toLE.{u2} (δ i) (_inst_2 i))) (Set.piecewise.{u1, succ u2} α (fun (i : α) => δ i) s f₁ f₂ (fun (j : α) => _inst_3 j)) g)
+Case conversion may be inaccurate. Consider using '#align set.piecewise_le Set.piecewise_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
-#print Set.piecewise_le /-
 theorem piecewise_le {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g i) (h₂ : ∀ (i) (_ : i ∉ s), f₂ i ≤ g i) :
     s.piecewise f₁ f₂ ≤ g := fun i => if h : i ∈ s then by simp [*] else by simp [*]
 #align set.piecewise_le Set.piecewise_le
--/
 
+/- warning: set.le_piecewise -> Set.le_piecewise is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {δ : α -> Type.{u2}} [_inst_2 : forall (i : α), Preorder.{u2} (δ i)] {s : Set.{u1} α} [_inst_3 : forall (j : α), Decidable (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) j s)] {f₁ : forall (i : α), δ i} {f₂ : forall (i : α), δ i} {g : forall (i : α), δ i}, (forall (i : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) i s) -> (LE.le.{u2} (δ i) (Preorder.toHasLe.{u2} (δ i) (_inst_2 i)) (g i) (f₁ i))) -> (forall (i : α), (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) i s)) -> (LE.le.{u2} (δ i) (Preorder.toHasLe.{u2} (δ i) (_inst_2 i)) (g i) (f₂ i))) -> (LE.le.{max u1 u2} (forall (i : α), δ i) (Pi.hasLe.{u1, u2} α (fun (i : α) => δ i) (fun (i : α) => Preorder.toHasLe.{u2} (δ i) (_inst_2 i))) g (Set.piecewise.{u1, succ u2} α (fun (i : α) => δ i) s f₁ f₂ (fun (j : α) => _inst_3 j)))
+but is expected to have type
+  forall {α : Type.{u1}} {δ : α -> Type.{u2}} [_inst_2 : forall (i : α), Preorder.{u2} (δ i)] {s : Set.{u1} α} [_inst_3 : forall (j : α), Decidable (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) j s)] {f₁ : forall (i : α), δ i} {f₂ : forall (i : α), δ i} {g : forall (i : α), δ i}, (forall (i : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) i s) -> (LE.le.{u2} (δ i) (Preorder.toLE.{u2} (δ i) (_inst_2 i)) (g i) (f₁ i))) -> (forall (i : α), (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) i s)) -> (LE.le.{u2} (δ i) (Preorder.toLE.{u2} (δ i) (_inst_2 i)) (g i) (f₂ i))) -> (LE.le.{max u1 u2} (forall (i : α), δ i) (Pi.hasLe.{u1, u2} α (fun (i : α) => δ i) (fun (i : α) => Preorder.toLE.{u2} (δ i) (_inst_2 i))) g (Set.piecewise.{u1, succ u2} α (fun (i : α) => δ i) s f₁ f₂ (fun (j : α) => _inst_3 j)))
+Case conversion may be inaccurate. Consider using '#align set.le_piecewise Set.le_piecewiseₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
-#print Set.le_piecewise /-
 theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, g i ≤ f₁ i) (h₂ : ∀ (i) (_ : i ∉ s), g i ≤ f₂ i) :
     g ≤ s.piecewise f₁ f₂ :=
   @piecewise_le α (fun i => (δ i)ᵒᵈ) _ s _ _ _ _ h₁ h₂
 #align set.le_piecewise Set.le_piecewise
--/
 
+/- warning: set.piecewise_le_piecewise -> Set.piecewise_le_piecewise is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {δ : α -> Type.{u2}} [_inst_2 : forall (i : α), Preorder.{u2} (δ i)] {s : Set.{u1} α} [_inst_3 : forall (j : α), Decidable (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) j s)] {f₁ : forall (i : α), δ i} {f₂ : forall (i : α), δ i} {g₁ : forall (i : α), δ i} {g₂ : forall (i : α), δ i}, (forall (i : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) i s) -> (LE.le.{u2} (δ i) (Preorder.toHasLe.{u2} (δ i) (_inst_2 i)) (f₁ i) (g₁ i))) -> (forall (i : α), (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) i s)) -> (LE.le.{u2} (δ i) (Preorder.toHasLe.{u2} (δ i) (_inst_2 i)) (f₂ i) (g₂ i))) -> (LE.le.{max u1 u2} (forall (i : α), δ i) (Pi.hasLe.{u1, u2} α (fun (i : α) => δ i) (fun (i : α) => Preorder.toHasLe.{u2} (δ i) (_inst_2 i))) (Set.piecewise.{u1, succ u2} α (fun (i : α) => δ i) s f₁ f₂ (fun (j : α) => _inst_3 j)) (Set.piecewise.{u1, succ u2} α (fun (i : α) => δ i) s g₁ g₂ (fun (j : α) => _inst_3 j)))
+but is expected to have type
+  forall {α : Type.{u1}} {δ : α -> Type.{u2}} [_inst_2 : forall (i : α), Preorder.{u2} (δ i)] {s : Set.{u1} α} [_inst_3 : forall (j : α), Decidable (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) j s)] {f₁ : forall (i : α), δ i} {f₂ : forall (i : α), δ i} {g₁ : forall (i : α), δ i} {g₂ : forall (i : α), δ i}, (forall (i : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) i s) -> (LE.le.{u2} (δ i) (Preorder.toLE.{u2} (δ i) (_inst_2 i)) (f₁ i) (g₁ i))) -> (forall (i : α), (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) i s)) -> (LE.le.{u2} (δ i) (Preorder.toLE.{u2} (δ i) (_inst_2 i)) (f₂ i) (g₂ i))) -> (LE.le.{max u1 u2} (forall (i : α), δ i) (Pi.hasLe.{u1, u2} α (fun (i : α) => δ i) (fun (i : α) => Preorder.toLE.{u2} (δ i) (_inst_2 i))) (Set.piecewise.{u1, succ u2} α (fun (i : α) => δ i) s f₁ f₂ (fun (j : α) => _inst_3 j)) (Set.piecewise.{u1, succ u2} α (fun (i : α) => δ i) s g₁ g₂ (fun (j : α) => _inst_3 j)))
+Case conversion may be inaccurate. Consider using '#align set.piecewise_le_piecewise Set.piecewise_le_piecewiseₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
-#print Set.piecewise_le_piecewise /-
 theorem piecewise_le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
     [∀ j, Decidable (j ∈ s)] {f₁ f₂ g₁ g₂ : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g₁ i)
     (h₂ : ∀ (i) (_ : i ∉ s), f₂ i ≤ g₂ i) : s.piecewise f₁ f₂ ≤ s.piecewise g₁ g₂ := by
   apply piecewise_le <;> intros <;> simp [*]
 #align set.piecewise_le_piecewise Set.piecewise_le_piecewise
--/
 
 /- warning: set.piecewise_insert_of_ne -> Set.piecewise_insert_of_ne is a dubious translation:
 lean 3 declaration is

bump to nightly-2023-04-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

ff662d55

Diff

@@ -2474,7 +2474,7 @@ namespace Function
 
 variable [Nonempty α] {s : Set α} {f : α → β} {a : α} {b : β}
 
-attribute [local instance] Classical.propDecidable
+attribute [local instance 10] Classical.propDecidable
 
 #print Function.invFunOn /-
 /-- Construct the inverse for a function `f` on domain `s`. This function is a right inverse of `f`

bump to nightly-2023-03-11-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

a8ee822f

Diff

@@ -3449,7 +3449,7 @@ variable {p : β → Prop} [DecidablePred p] {f : α ≃ Subtype p} {g g₁ g₂
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u2} β p] {f : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)} {g : Equiv.Perm.{succ u1} α} {s : Set.{u1} α} {t : Set.{u1} α}, (Set.MapsTo.{u1, u1} α α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g) s t) -> (Set.MapsTo.{u2, u2} β β (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) s) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) t))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.MapsTo.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g) s t) -> (Set.MapsTo.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
+  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.MapsTo.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g) s t) -> (Set.MapsTo.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
 Case conversion may be inaccurate. Consider using '#align set.maps_to.extend_domain Set.MapsTo.extendDomainₓ'. -/
 protected theorem MapsTo.extendDomain (h : MapsTo g s t) :
     MapsTo (g.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
@@ -3462,7 +3462,7 @@ protected theorem MapsTo.extendDomain (h : MapsTo g s t) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u2} β p] {f : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)} {g : Equiv.Perm.{succ u1} α} {s : Set.{u1} α} {t : Set.{u1} α}, (Set.SurjOn.{u1, u1} α α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g) s t) -> (Set.SurjOn.{u2, u2} β β (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) s) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) t))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.SurjOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g) s t) -> (Set.SurjOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
+  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.SurjOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g) s t) -> (Set.SurjOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
 Case conversion may be inaccurate. Consider using '#align set.surj_on.extend_domain Set.SurjOn.extendDomainₓ'. -/
 protected theorem SurjOn.extendDomain (h : SurjOn g s t) :
     SurjOn (g.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
@@ -3476,7 +3476,7 @@ protected theorem SurjOn.extendDomain (h : SurjOn g s t) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u2} β p] {f : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)} {g : Equiv.Perm.{succ u1} α} {s : Set.{u1} α} {t : Set.{u1} α}, (Set.BijOn.{u1, u1} α α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g) s t) -> (Set.BijOn.{u2, u2} β β (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) s) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) t))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.BijOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g) s t) -> (Set.BijOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
+  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.BijOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g) s t) -> (Set.BijOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
 Case conversion may be inaccurate. Consider using '#align set.bij_on.extend_domain Set.BijOn.extendDomainₓ'. -/
 protected theorem BijOn.extendDomain (h : Set.BijOn g s t) :
     BijOn (g.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
@@ -3487,7 +3487,7 @@ protected theorem BijOn.extendDomain (h : Set.BijOn g s t) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u2} β p] {f : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)} {g₁ : Equiv.Perm.{succ u1} α} {g₂ : Equiv.Perm.{succ u1} α} {s : Set.{u1} α}, (Set.LeftInvOn.{u1, u1} α α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g₁) (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g₂) s) -> (Set.LeftInvOn.{u2, u2} β β (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g₁ p (fun (a : β) => _inst_1 a) f)) (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g₁ : Equiv.Perm.{succ u2} α} {g₂ : Equiv.Perm.{succ u2} α} {s : Set.{u2} α}, (Set.LeftInvOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₁) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₂) s) -> (Set.LeftInvOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₁ p (fun (a : β) => _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s))
+  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g₁ : Equiv.Perm.{succ u2} α} {g₂ : Equiv.Perm.{succ u2} α} {s : Set.{u2} α}, (Set.LeftInvOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₁) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₂) s) -> (Set.LeftInvOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₁ p (fun (a : β) => _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s))
 Case conversion may be inaccurate. Consider using '#align set.left_inv_on.extend_domain Set.LeftInvOn.extendDomainₓ'. -/
 protected theorem LeftInvOn.extendDomain (h : LeftInvOn g₁ g₂ s) :
     LeftInvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' s) :=
@@ -3500,7 +3500,7 @@ protected theorem LeftInvOn.extendDomain (h : LeftInvOn g₁ g₂ s) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u2} β p] {f : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)} {g₁ : Equiv.Perm.{succ u1} α} {g₂ : Equiv.Perm.{succ u1} α} {t : Set.{u1} α}, (Set.RightInvOn.{u1, u1} α α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g₁) (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g₂) t) -> (Set.RightInvOn.{u2, u2} β β (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g₁ p (fun (a : β) => _inst_1 a) f)) (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) t))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g₁ : Equiv.Perm.{succ u2} α} {g₂ : Equiv.Perm.{succ u2} α} {t : Set.{u2} α}, (Set.RightInvOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₁) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₂) t) -> (Set.RightInvOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₁ p (fun (a : β) => _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
+  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g₁ : Equiv.Perm.{succ u2} α} {g₂ : Equiv.Perm.{succ u2} α} {t : Set.{u2} α}, (Set.RightInvOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₁) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₂) t) -> (Set.RightInvOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₁ p (fun (a : β) => _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
 Case conversion may be inaccurate. Consider using '#align set.right_inv_on.extend_domain Set.RightInvOn.extendDomainₓ'. -/
 protected theorem RightInvOn.extendDomain (h : RightInvOn g₁ g₂ t) :
     RightInvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' t) :=
@@ -3513,7 +3513,7 @@ protected theorem RightInvOn.extendDomain (h : RightInvOn g₁ g₂ t) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u2} β p] {f : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)} {g₁ : Equiv.Perm.{succ u1} α} {g₂ : Equiv.Perm.{succ u1} α} {s : Set.{u1} α} {t : Set.{u1} α}, (Set.InvOn.{u1, u1} α α (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g₁) (coeFn.{succ u1, succ u1} (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.{succ u1, succ u1} α α) => α -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} α α) g₂) s t) -> (Set.InvOn.{u2, u2} β β (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g₁ p (fun (a : β) => _inst_1 a) f)) (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} β) (fun (_x : Equiv.{succ u2, succ u2} β β) => β -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} β β) (Equiv.Perm.extendDomain.{u1, u2} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) s) (Set.image.{u1, u2} α β (Function.comp.{succ u1, succ u2, succ u2} α (Subtype.{succ u2} β p) β ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} β p) β (HasLiftT.mk.{succ u2, succ u2} (Subtype.{succ u2} β p) β (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeBase.{succ u2, succ u2} (Subtype.{succ u2} β p) β (coeSubtype.{succ u2} β (fun (x : β) => p x)))))) (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) (fun (_x : Equiv.{succ u1, succ u2} α (Subtype.{succ u2} β p)) => α -> (Subtype.{succ u2} β p)) (Equiv.hasCoeToFun.{succ u1, succ u2} α (Subtype.{succ u2} β p)) f)) t))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g₁ : Equiv.Perm.{succ u2} α} {g₂ : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.InvOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₁) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₂) s t) -> (Set.InvOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₁ p (fun (a : β) => _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
+  forall {α : Type.{u2}} {β : Type.{u1}} {p : β -> Prop} [_inst_1 : DecidablePred.{succ u1} β p] {f : Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)} {g₁ : Equiv.Perm.{succ u2} α} {g₂ : Equiv.Perm.{succ u2} α} {s : Set.{u2} α} {t : Set.{u2} α}, (Set.InvOn.{u2, u2} α α (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₁) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.Perm.{succ u2} α) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α α) g₂) s t) -> (Set.InvOn.{u1, u1} β β (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₁ p (fun (a : β) => _inst_1 a) f)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} β) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β β) (Equiv.Perm.extendDomain.{u2, u1} α β g₂ p (fun (a : β) => _inst_1 a) f)) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) s) (Set.image.{u2, u1} α β (Function.comp.{succ u2, succ u1, succ u1} α (Subtype.{succ u1} β p) β (Subtype.val.{succ u1} β p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => Subtype.{succ u1} β p) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α (Subtype.{succ u1} β p)) f)) t))
 Case conversion may be inaccurate. Consider using '#align set.inv_on.extend_domain Set.InvOn.extendDomainₓ'. -/
 protected theorem InvOn.extendDomain (h : InvOn g₁ g₂ s t) :
     InvOn (g₁.extendDomain f) (g₂.extendDomain f) (coe ∘ f '' s) (coe ∘ f '' t) :=
@@ -3530,7 +3530,7 @@ variable (e : α ≃ β) {s : Set α} {t : Set β}
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (e : Equiv.{succ u1, succ u2} α β) {s : Set.{u1} α} {t : Set.{u2} β}, (Set.MapsTo.{u1, u2} α β (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) e) s t) -> (Set.MapsTo.{u2, u1} β α (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} β α) (fun (_x : Equiv.{succ u2, succ u1} β α) => β -> α) (Equiv.hasCoeToFun.{succ u2, succ u1} β α) (Equiv.symm.{succ u1, succ u2} α β e)) t s) -> (Set.BijOn.{u1, u2} α β (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) e) s t)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (e : Equiv.{succ u2, succ u1} α β) {s : Set.{u2} α} {t : Set.{u1} β}, (Set.MapsTo.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s t) -> (Set.MapsTo.{u1, u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Equiv.{succ u1, succ u2} β α) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u2} β α) (Equiv.symm.{succ u2, succ u1} α β e)) t s) -> (Set.BijOn.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s t)
+  forall {α : Type.{u2}} {β : Type.{u1}} (e : Equiv.{succ u2, succ u1} α β) {s : Set.{u2} α} {t : Set.{u1} β}, (Set.MapsTo.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s t) -> (Set.MapsTo.{u1, u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Equiv.{succ u1, succ u2} β α) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u2} β α) (Equiv.symm.{succ u2, succ u1} α β e)) t s) -> (Set.BijOn.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s t)
 Case conversion may be inaccurate. Consider using '#align equiv.bij_on' Equiv.bijOn'ₓ'. -/
 theorem bijOn' (h₁ : MapsTo e s t) (h₂ : MapsTo e.symm t s) : BijOn e s t :=
   ⟨h₁, e.Injective.InjOn _, fun b hb => ⟨e.symm b, h₂ hb, apply_symm_apply _ _⟩⟩
@@ -3552,7 +3552,7 @@ theorem invOn : InvOn e e.symm t s :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (e : Equiv.{succ u1, succ u2} α β) {s : Set.{u1} α}, Set.BijOn.{u1, u2} α β (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) e) s (Set.image.{u1, u2} α β (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) e) s)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (e : Equiv.{succ u2, succ u1} α β) {s : Set.{u2} α}, Set.BijOn.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s)
+  forall {α : Type.{u2}} {β : Type.{u1}} (e : Equiv.{succ u2, succ u1} α β) {s : Set.{u2} α}, Set.BijOn.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) e) s)
 Case conversion may be inaccurate. Consider using '#align equiv.bij_on_image Equiv.bijOn_imageₓ'. -/
 theorem bijOn_image : BijOn e s (e '' s) :=
   (e.Injective.InjOn _).bijOn_image

bump to nightly-2023-03-01-20

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

20cadee0

Diff

@@ -128,7 +128,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {s : Set.{u2} α} [_inst_1 : forall (x : α), Decidable (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s)] (f : forall (a : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a s) -> β) (g : forall (a : α), (Not (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a s)) -> β), Eq.{max (succ u2) (succ u1)} ((Set.Elem.{u2} α s) -> β) (Set.restrict.{u2, u1} α (fun (a : α) => β) s (fun (a : α) => dite.{succ u1} β (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a s) (_inst_1 a) (fun (h : Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a s) => f a h) (fun (h : Not (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a s)) => g a h))) (fun (a : Set.Elem.{u2} α s) => f (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) a) (Subtype.property.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) a))
 Case conversion may be inaccurate. Consider using '#align set.restrict_dite Set.restrict_diteₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
 @[simp]
 theorem restrict_dite {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
     (g : ∀ (a) (_ : a ∉ s), β) :
@@ -142,7 +142,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {s : Set.{u2} α} [_inst_1 : forall (x : α), Decidable (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s)] (f : forall (a : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a s) -> β) (g : forall (a : α), (Not (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a s)) -> β), Eq.{max (succ u2) (succ u1)} ((Set.Elem.{u2} α (HasCompl.compl.{u2} (Set.{u2} α) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} α) (Set.instBooleanAlgebraSet.{u2} α)) s)) -> β) (Set.restrict.{u2, u1} α (fun (a : α) => β) (HasCompl.compl.{u2} (Set.{u2} α) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} α) (Set.instBooleanAlgebraSet.{u2} α)) s) (fun (a : α) => dite.{succ u1} β (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a s) (_inst_1 a) (fun (h : Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a s) => f a h) (fun (h : Not (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a s)) => g a h))) (fun (a : Set.Elem.{u2} α (HasCompl.compl.{u2} (Set.{u2} α) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} α) (Set.instBooleanAlgebraSet.{u2} α)) s)) => g (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (HasCompl.compl.{u2} (Set.{u2} α) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} α) (Set.instBooleanAlgebraSet.{u2} α)) s)) a) (Subtype.property.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (HasCompl.compl.{u2} (Set.{u2} α) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} α) (Set.instBooleanAlgebraSet.{u2} α)) s)) a))
 Case conversion may be inaccurate. Consider using '#align set.restrict_dite_compl Set.restrict_dite_complₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (a «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ∉ » s) -/
 @[simp]
 theorem restrict_dite_compl {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
     (g : ∀ (a) (_ : a ∉ s), β) :
@@ -2126,7 +2126,7 @@ Case conversion may be inaccurate. Consider using '#align set.left_inv_on.inj_on
 theorem LeftInvOn.injOn (h : LeftInvOn f₁' f s) : InjOn f s := fun x₁ h₁ x₂ h₂ heq =>
   calc
     x₁ = f₁' (f x₁) := Eq.symm <| h h₁
-    _ = f₁' (f x₂) := congr_arg f₁' HEq
+    _ = f₁' (f x₂) := (congr_arg f₁' HEq)
     _ = x₂ := h h₂
     
 #align set.left_inv_on.inj_on Set.LeftInvOn.injOn
@@ -2637,7 +2637,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {s : Set.{u2} α} {t : Set.{u1} β} {f : α -> β}, Iff (Set.SurjOn.{u2, u1} α β f s t) (Exists.{succ u2} (Set.{u2} α) (fun (s' : Set.{u2} α) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) s' s) (fun (H : HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) s' s) => Set.BijOn.{u2, u1} α β f s' t)))
 Case conversion may be inaccurate. Consider using '#align set.surj_on_iff_exists_bij_on_subset Set.surjOn_iff_exists_bijOn_subsetₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (s' «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (s' «expr ⊆ » s) -/
 theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _)(_ : s' ⊆ s), BijOn f s' t :=
   by
   constructor
@@ -2854,7 +2854,7 @@ theorem piecewise_eqOn_compl (f g : α → β) : EqOn (s.piecewise f g) g (sᶜ)
   piecewise_eq_of_not_mem _ _ _
 #align set.piecewise_eq_on_compl Set.piecewise_eqOn_compl
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.piecewise_le /-
 theorem piecewise_le {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g i) (h₂ : ∀ (i) (_ : i ∉ s), f₂ i ≤ g i) :
@@ -2862,7 +2862,7 @@ theorem piecewise_le {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
 #align set.piecewise_le Set.piecewise_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.le_piecewise /-
 theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, g i ≤ f₁ i) (h₂ : ∀ (i) (_ : i ∉ s), g i ≤ f₂ i) :
@@ -2871,7 +2871,7 @@ theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
 #align set.le_piecewise Set.le_piecewise
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (i «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (i «expr ∉ » s) -/
 #print Set.piecewise_le_piecewise /-
 theorem piecewise_le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
     [∀ j, Decidable (j ∈ s)] {f₁ f₂ g₁ g₂ : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g₁ i)
@@ -3050,7 +3050,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} (s : Set.{u2} α) [_inst_1 : forall (j : α), Decidable (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) j s)] {f : α -> β} {g : α -> β}, Iff (Function.Injective.{succ u2, succ u1} α β (Set.piecewise.{u2, succ u1} α (fun (ᾰ : α) => β) s f g (fun (j : α) => _inst_1 j))) (And (Set.InjOn.{u2, u1} α β f s) (And (Set.InjOn.{u2, u1} α β g (HasCompl.compl.{u2} (Set.{u2} α) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} α) (Set.instBooleanAlgebraSet.{u2} α)) s)) (forall (x : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) -> (forall (y : α), (Not (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) y s)) -> (Ne.{succ u1} β (f x) (g y))))))
 Case conversion may be inaccurate. Consider using '#align set.injective_piecewise_iff Set.injective_piecewise_iffₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (y «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ∉ » s) -/
 theorem injective_piecewise_iff {f g : α → β} :
     Injective (s.piecewise f g) ↔
       InjOn f s ∧ InjOn g (sᶜ) ∧ ∀ x ∈ s, ∀ (y) (_ : y ∉ s), f x ≠ g y :=

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore(Data/Set/Function): add sections to group related material (#11675)

delay on open statement until actually needed
note that two lemmas seem mis-placed
use some namespaces

6201c942

Diff

@@ -40,7 +40,7 @@ open Equiv Equiv.Perm Function
 namespace Set
 
 /-! ### Restrict -/
-
+section restrict
 
 /-- Restrict domain of a function `f` to a set `s`. Same as `Subtype.restrict` but this version
 takes an argument `↥s` instead of `Subtype s`. -/
@@ -169,10 +169,13 @@ theorem injective_codRestrict {f : ι → α} {s : Set α} (h : ∀ x, f x ∈ s
 alias ⟨_, _root_.Function.Injective.codRestrict⟩ := injective_codRestrict
 #align function.injective.cod_restrict Function.Injective.codRestrict
 
-variable {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {p : Set γ} {f f₁ f₂ f₃ : α → β} {g g₁ g₂ : β → γ}
-  {f' f₁' f₂' : β → α} {g' : γ → β} {a : α} {b : β}
+end restrict
 
 /-! ### Equality on a set -/
+section equality
+
+variable {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {p : Set γ} {f f₁ f₂ f₃ : α → β} {g g₁ g₂ : β → γ}
+  {f' f₁' f₂' : β → α} {g' : γ → β} {a : α} {b : β}
 
 @[simp]
 theorem eqOn_empty (f₁ f₂ : α → β) : EqOn f₁ f₂ ∅ := fun _ => False.elim
@@ -251,12 +254,12 @@ theorem eqOn_range {ι : Sort*} {f : ι → α} {g₁ g₂ : α → β} :
 alias ⟨EqOn.comp_eq, _⟩ := eqOn_range
 #align set.eq_on.comp_eq Set.EqOn.comp_eq
 
-/-! ### Congruence lemmas -/
-
+end equality
 
+/-! ### Congruence lemmas for monotonicity and antitonicity -/
 section Order
 
-variable [Preorder α] [Preorder β]
+variable {s : Set α} {f₁ f₂ : α → β} [Preorder α] [Preorder β]
 
 theorem _root_.MonotoneOn.congr (h₁ : MonotoneOn f₁ s) (h : s.EqOn f₁ f₂) : MonotoneOn f₂ s := by
   intro a ha b hb hab
@@ -297,12 +300,10 @@ theorem EqOn.congr_strictAntiOn (h : s.EqOn f₁ f₂) : StrictAntiOn f₁ s ↔
 
 end Order
 
-/-! ### Mono lemmas-/
-
-
+/-! ### Monotonicity lemmas-/
 section Mono
 
-variable [Preorder α] [Preorder β]
+variable {s s₁ s₂ : Set α} {f f₁ f₂ : α → β} [Preorder α] [Preorder β]
 
 theorem _root_.MonotoneOn.mono (h : MonotoneOn f s) (h' : s₂ ⊆ s) : MonotoneOn f s₂ :=
   fun _ hx _ hy => h (h' hx) (h' hy)
@@ -342,7 +343,10 @@ protected theorem _root_.StrictAntiOn.strictAnti (h : StrictAntiOn f s) :
 
 end Mono
 
-/-! ### maps to -/
+variable {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {p : Set γ} {f f₁ f₂ f₃ : α → β} {g g₁ g₂ : β → γ}
+  {f' f₁' f₂' : β → α} {g' : γ → β} {a : α} {b : β}
+
+section MapsTo
 
 theorem MapsTo.restrict_commutes (f : α → β) (s : Set α) (t : Set β) (h : MapsTo f s t) :
     Subtype.val ∘ h.restrict f s t = f ∘ Subtype.val :=
@@ -557,25 +561,26 @@ theorem MapsTo.mem_iff (h : MapsTo f s t) (hc : MapsTo f sᶜ tᶜ) {x} : f x 
   ⟨fun ht => by_contra fun hs => hc hs ht, fun hx => h hx⟩
 #align set.maps_to.mem_iff Set.MapsTo.mem_iff
 
-/-! ### Restriction onto preimage -/
-
+end MapsTo
 
+/-! ### Restriction onto preimage -/
 section
 
-variable (t f)
+variable (t)
 
-variable (s) in
+variable (f s) in
 theorem image_restrictPreimage :
     t.restrictPreimage f '' (Subtype.val ⁻¹' s) = Subtype.val ⁻¹' (f '' s) := by
   delta Set.restrictPreimage
   rw [← (Subtype.coe_injective).image_injective.eq_iff, ← image_comp, MapsTo.restrict_commutes,
     image_comp, Subtype.image_preimage_coe, Subtype.image_preimage_coe, image_preimage_inter]
 
+variable (f) in
 theorem range_restrictPreimage : range (t.restrictPreimage f) = Subtype.val ⁻¹' range f := by
   simp only [← image_univ, ← image_restrictPreimage, preimage_univ]
 #align set.range_restrict_preimage Set.range_restrictPreimage
 
-variable {f} {U : ι → Set β}
+variable {U : ι → Set β}
 
 lemma restrictPreimage_injective (hf : Injective f) : Injective (t.restrictPreimage f) :=
   fun _ _ e => Subtype.coe_injective <| hf <| Subtype.mk.inj e
@@ -599,6 +604,7 @@ alias _root_.Function.Bijective.restrictPreimage := Set.restrictPreimage_bijecti
 end
 
 /-! ### Injectivity on a set -/
+section injOn
 
 theorem Subsingleton.injOn (hs : s.Subsingleton) (f : α → β) : InjOn f s := fun _ hx _ hy _ =>
   hs hx hy
@@ -754,12 +760,17 @@ lemma InjOn.image_inter {s t u : Set α} (hf : u.InjOn f) (hs : s ⊆ u) (ht : t
   exact ⟨y, ⟨ys, zt⟩, hy⟩
 #align set.inj_on.image_inter Set.InjOn.image_inter
 
+end injOn
+
+-- TODO: can this move to a better place?
 theorem _root_.Disjoint.image {s t u : Set α} {f : α → β} (h : Disjoint s t) (hf : u.InjOn f)
     (hs : s ⊆ u) (ht : t ⊆ u) : Disjoint (f '' s) (f '' t) := by
   rw [disjoint_iff_inter_eq_empty] at h ⊢
   rw [← hf.image_inter hs ht, h, image_empty]
 #align disjoint.image Disjoint.image
 
+section graphOn
+
 @[simp] lemma graphOn_empty (f : α → β) : graphOn f ∅ = ∅ := image_empty _
 
 @[simp]
@@ -797,7 +808,10 @@ lemma exists_eq_graphOn [Nonempty β] {s : Set (α × β)} :
   .trans ⟨fun ⟨f, t, hs⟩ ↦ ⟨f, by rw [hs, image_fst_graphOn]⟩, fun ⟨f, hf⟩ ↦ ⟨f, _, hf⟩⟩
     exists_eq_graphOn_image_fst
 
+end graphOn
+
 /-! ### Surjectivity on a set -/
+section surjOn
 
 theorem SurjOn.subset_range (h : SurjOn f s t) : t ⊆ range f :=
   Subset.trans h <| image_subset_range f s
@@ -956,7 +970,10 @@ theorem eqOn_comp_right_iff : s.EqOn (g₁ ∘ f) (g₂ ∘ f) ↔ (f '' s).EqOn
   (s.surjOn_image f).cancel_right <| s.mapsTo_image f
 #align set.eq_on_comp_right_iff Set.eqOn_comp_right_iff
 
+end surjOn
+
 /-! ### Bijectivity -/
+section bijOn
 
 theorem BijOn.mapsTo (h : BijOn f s t) : MapsTo f s t :=
   h.left
@@ -1072,56 +1089,59 @@ theorem BijOn.compl (hst : BijOn f s t) (hf : Bijective f) : BijOn f sᶜ tᶜ :
   ⟨hst.surjOn.mapsTo_compl hf.1, hf.1.injOn _, hst.mapsTo.surjOn_compl hf.2⟩
 #align set.bij_on.compl Set.BijOn.compl
 
+end bijOn
+
 /-! ### left inverse -/
+namespace LeftInvOn
 
-theorem LeftInvOn.eqOn (h : LeftInvOn f' f s) : EqOn (f' ∘ f) id s :=
+theorem eqOn (h : LeftInvOn f' f s) : EqOn (f' ∘ f) id s :=
   h
 #align set.left_inv_on.eq_on Set.LeftInvOn.eqOn
 
-theorem LeftInvOn.eq (h : LeftInvOn f' f s) {x} (hx : x ∈ s) : f' (f x) = x :=
+theorem eq (h : LeftInvOn f' f s) {x} (hx : x ∈ s) : f' (f x) = x :=
   h hx
 #align set.left_inv_on.eq Set.LeftInvOn.eq
 
-theorem LeftInvOn.congr_left (h₁ : LeftInvOn f₁' f s) {t : Set β} (h₁' : MapsTo f s t)
+theorem congr_left (h₁ : LeftInvOn f₁' f s) {t : Set β} (h₁' : MapsTo f s t)
     (heq : EqOn f₁' f₂' t) : LeftInvOn f₂' f s := fun _ hx => heq (h₁' hx) ▸ h₁ hx
 #align set.left_inv_on.congr_left Set.LeftInvOn.congr_left
 
-theorem LeftInvOn.congr_right (h₁ : LeftInvOn f₁' f₁ s) (heq : EqOn f₁ f₂ s) : LeftInvOn f₁' f₂ s :=
+theorem congr_right (h₁ : LeftInvOn f₁' f₁ s) (heq : EqOn f₁ f₂ s) : LeftInvOn f₁' f₂ s :=
   fun _ hx => heq hx ▸ h₁ hx
 #align set.left_inv_on.congr_right Set.LeftInvOn.congr_right
 
-theorem LeftInvOn.injOn (h : LeftInvOn f₁' f s) : InjOn f s := fun x₁ h₁ x₂ h₂ heq =>
+theorem injOn (h : LeftInvOn f₁' f s) : InjOn f s := fun x₁ h₁ x₂ h₂ heq =>
   calc
     x₁ = f₁' (f x₁) := Eq.symm <| h h₁
     _ = f₁' (f x₂) := congr_arg f₁' heq
     _ = x₂ := h h₂
 #align set.left_inv_on.inj_on Set.LeftInvOn.injOn
 
-theorem LeftInvOn.surjOn (h : LeftInvOn f' f s) (hf : MapsTo f s t) : SurjOn f' t s := fun x hx =>
+theorem surjOn (h : LeftInvOn f' f s) (hf : MapsTo f s t) : SurjOn f' t s := fun x hx =>
   ⟨f x, hf hx, h hx⟩
 #align set.left_inv_on.surj_on Set.LeftInvOn.surjOn
 
-theorem LeftInvOn.mapsTo (h : LeftInvOn f' f s) (hf : SurjOn f s t) :
+theorem mapsTo (h : LeftInvOn f' f s) (hf : SurjOn f s t) :
     MapsTo f' t s := fun y hy => by
   let ⟨x, hs, hx⟩ := hf hy
   rwa [← hx, h hs]
 #align set.left_inv_on.maps_to Set.LeftInvOn.mapsTo
 
-lemma leftInvOn_id (s : Set α) : LeftInvOn id id s := fun _ _ ↦ rfl
+lemma _root_.Set.leftInvOn_id (s : Set α) : LeftInvOn id id s := fun _ _ ↦ rfl
 #align set.left_inv_on_id Set.leftInvOn_id
 
-theorem LeftInvOn.comp (hf' : LeftInvOn f' f s) (hg' : LeftInvOn g' g t) (hf : MapsTo f s t) :
+theorem comp (hf' : LeftInvOn f' f s) (hg' : LeftInvOn g' g t) (hf : MapsTo f s t) :
     LeftInvOn (f' ∘ g') (g ∘ f) s := fun x h =>
   calc
     (f' ∘ g') ((g ∘ f) x) = f' (f x) := congr_arg f' (hg' (hf h))
     _ = x := hf' h
 #align set.left_inv_on.comp Set.LeftInvOn.comp
 
-theorem LeftInvOn.mono (hf : LeftInvOn f' f s) (ht : s₁ ⊆ s) : LeftInvOn f' f s₁ := fun _ hx =>
+theorem mono (hf : LeftInvOn f' f s) (ht : s₁ ⊆ s) : LeftInvOn f' f s₁ := fun _ hx =>
   hf (ht hx)
 #align set.left_inv_on.mono Set.LeftInvOn.mono
 
-theorem LeftInvOn.image_inter' (hf : LeftInvOn f' f s) : f '' (s₁ ∩ s) = f' ⁻¹' s₁ ∩ f '' s := by
+theorem image_inter' (hf : LeftInvOn f' f s) : f '' (s₁ ∩ s) = f' ⁻¹' s₁ ∩ f '' s := by
   apply Subset.antisymm
   · rintro _ ⟨x, ⟨h₁, h⟩, rfl⟩
     exact ⟨by rwa [mem_preimage, hf h], mem_image_of_mem _ h⟩
@@ -1129,64 +1149,69 @@ theorem LeftInvOn.image_inter' (hf : LeftInvOn f' f s) : f '' (s₁ ∩ s) = f'
     exact mem_image_of_mem _ ⟨by rwa [← hf h], h⟩
 #align set.left_inv_on.image_inter' Set.LeftInvOn.image_inter'
 
-theorem LeftInvOn.image_inter (hf : LeftInvOn f' f s) :
+theorem image_inter (hf : LeftInvOn f' f s) :
     f '' (s₁ ∩ s) = f' ⁻¹' (s₁ ∩ s) ∩ f '' s := by
   rw [hf.image_inter']
   refine' Subset.antisymm _ (inter_subset_inter_left _ (preimage_mono <| inter_subset_left _ _))
   rintro _ ⟨h₁, x, hx, rfl⟩; exact ⟨⟨h₁, by rwa [hf hx]⟩, mem_image_of_mem _ hx⟩
 #align set.left_inv_on.image_inter Set.LeftInvOn.image_inter
 
-theorem LeftInvOn.image_image (hf : LeftInvOn f' f s) : f' '' (f '' s) = s := by
+theorem image_image (hf : LeftInvOn f' f s) : f' '' (f '' s) = s := by
   rw [Set.image_image, image_congr hf, image_id']
 #align set.left_inv_on.image_image Set.LeftInvOn.image_image
 
-theorem LeftInvOn.image_image' (hf : LeftInvOn f' f s) (hs : s₁ ⊆ s) : f' '' (f '' s₁) = s₁ :=
+theorem image_image' (hf : LeftInvOn f' f s) (hs : s₁ ⊆ s) : f' '' (f '' s₁) = s₁ :=
   (hf.mono hs).image_image
 #align set.left_inv_on.image_image' Set.LeftInvOn.image_image'
 
+end LeftInvOn
+
 /-! ### Right inverse -/
+section RightInvOn
+namespace RightInvOn
 
-theorem RightInvOn.eqOn (h : RightInvOn f' f t) : EqOn (f ∘ f') id t :=
+theorem eqOn (h : RightInvOn f' f t) : EqOn (f ∘ f') id t :=
   h
 #align set.right_inv_on.eq_on Set.RightInvOn.eqOn
 
-theorem RightInvOn.eq (h : RightInvOn f' f t) {y} (hy : y ∈ t) : f (f' y) = y :=
+theorem eq (h : RightInvOn f' f t) {y} (hy : y ∈ t) : f (f' y) = y :=
   h hy
 #align set.right_inv_on.eq Set.RightInvOn.eq
 
-theorem LeftInvOn.rightInvOn_image (h : LeftInvOn f' f s) : RightInvOn f' f (f '' s) :=
+theorem _root_.Set.LeftInvOn.rightInvOn_image (h : LeftInvOn f' f s) : RightInvOn f' f (f '' s) :=
   fun _y ⟨_x, hx, heq⟩ => heq ▸ (congr_arg f <| h.eq hx)
 #align set.left_inv_on.right_inv_on_image Set.LeftInvOn.rightInvOn_image
 
-theorem RightInvOn.congr_left (h₁ : RightInvOn f₁' f t) (heq : EqOn f₁' f₂' t) :
+theorem congr_left (h₁ : RightInvOn f₁' f t) (heq : EqOn f₁' f₂' t) :
     RightInvOn f₂' f t :=
   h₁.congr_right heq
 #align set.right_inv_on.congr_left Set.RightInvOn.congr_left
 
-theorem RightInvOn.congr_right (h₁ : RightInvOn f' f₁ t) (hg : MapsTo f' t s) (heq : EqOn f₁ f₂ s) :
+theorem congr_right (h₁ : RightInvOn f' f₁ t) (hg : MapsTo f' t s) (heq : EqOn f₁ f₂ s) :
     RightInvOn f' f₂ t :=
   LeftInvOn.congr_left h₁ hg heq
 #align set.right_inv_on.congr_right Set.RightInvOn.congr_right
 
-theorem RightInvOn.surjOn (hf : RightInvOn f' f t) (hf' : MapsTo f' t s) : SurjOn f s t :=
+theorem surjOn (hf : RightInvOn f' f t) (hf' : MapsTo f' t s) : SurjOn f s t :=
   LeftInvOn.surjOn hf hf'
 #align set.right_inv_on.surj_on Set.RightInvOn.surjOn
 
-theorem RightInvOn.mapsTo (h : RightInvOn f' f t) (hf : SurjOn f' t s) : MapsTo f s t :=
+theorem mapsTo (h : RightInvOn f' f t) (hf : SurjOn f' t s) : MapsTo f s t :=
   LeftInvOn.mapsTo h hf
 #align set.right_inv_on.maps_to Set.RightInvOn.mapsTo
 
-lemma rightInvOn_id (s : Set α) : RightInvOn id id s := fun _ _ ↦ rfl
+lemma _root_.Set.rightInvOn_id (s : Set α) : RightInvOn id id s := fun _ _ ↦ rfl
 #align set.right_inv_on_id Set.rightInvOn_id
 
-theorem RightInvOn.comp (hf : RightInvOn f' f t) (hg : RightInvOn g' g p) (g'pt : MapsTo g' p t) :
+theorem comp (hf : RightInvOn f' f t) (hg : RightInvOn g' g p) (g'pt : MapsTo g' p t) :
     RightInvOn (f' ∘ g') (g ∘ f) p :=
   LeftInvOn.comp hg hf g'pt
 #align set.right_inv_on.comp Set.RightInvOn.comp
 
-theorem RightInvOn.mono (hf : RightInvOn f' f t) (ht : t₁ ⊆ t) : RightInvOn f' f t₁ :=
+theorem mono (hf : RightInvOn f' f t) (ht : t₁ ⊆ t) : RightInvOn f' f t₁ :=
   LeftInvOn.mono hf ht
 #align set.right_inv_on.mono Set.RightInvOn.mono
+end RightInvOn
 
 theorem InjOn.rightInvOn_of_leftInvOn (hf : InjOn f s) (hf' : LeftInvOn f f' t)
     (h₁ : MapsTo f s t) (h₂ : MapsTo f' t s) : RightInvOn f f' s := fun _ h =>
@@ -1206,38 +1231,41 @@ theorem SurjOn.leftInvOn_of_rightInvOn (hf : SurjOn f s t) (hf' : RightInvOn f f
   rw [← heq, hf' hx]
 #align set.surj_on.left_inv_on_of_right_inv_on Set.SurjOn.leftInvOn_of_rightInvOn
 
+end RightInvOn
+
 /-! ### Two-side inverses -/
+namespace InvOn
 
-lemma invOn_id (s : Set α) : InvOn id id s s := ⟨s.leftInvOn_id, s.rightInvOn_id⟩
+lemma _root_.Set.invOn_id (s : Set α) : InvOn id id s s := ⟨s.leftInvOn_id, s.rightInvOn_id⟩
 #align set.inv_on_id Set.invOn_id
 
-lemma InvOn.comp (hf : InvOn f' f s t) (hg : InvOn g' g t p) (fst : MapsTo f s t)
+lemma comp (hf : InvOn f' f s t) (hg : InvOn g' g t p) (fst : MapsTo f s t)
     (g'pt : MapsTo g' p t) :
     InvOn (f' ∘ g') (g ∘ f) s p :=
   ⟨hf.1.comp hg.1 fst, hf.2.comp hg.2 g'pt⟩
 #align set.inv_on.comp Set.InvOn.comp
 
 @[symm]
-theorem InvOn.symm (h : InvOn f' f s t) : InvOn f f' t s :=
+theorem symm (h : InvOn f' f s t) : InvOn f f' t s :=
   ⟨h.right, h.left⟩
 #align set.inv_on.symm Set.InvOn.symm
 
-theorem InvOn.mono (h : InvOn f' f s t) (hs : s₁ ⊆ s) (ht : t₁ ⊆ t) : InvOn f' f s₁ t₁ :=
+theorem mono (h : InvOn f' f s t) (hs : s₁ ⊆ s) (ht : t₁ ⊆ t) : InvOn f' f s₁ t₁ :=
   ⟨h.1.mono hs, h.2.mono ht⟩
 #align set.inv_on.mono Set.InvOn.mono
 
 /-- If functions `f'` and `f` are inverse on `s` and `t`, `f` maps `s` into `t`, and `f'` maps `t`
 into `s`, then `f` is a bijection between `s` and `t`. The `mapsTo` arguments can be deduced from
 `surjOn` statements using `LeftInvOn.mapsTo` and `RightInvOn.mapsTo`. -/
-theorem InvOn.bijOn (h : InvOn f' f s t) (hf : MapsTo f s t) (hf' : MapsTo f' t s) : BijOn f s t :=
+theorem bijOn (h : InvOn f' f s t) (hf : MapsTo f s t) (hf' : MapsTo f' t s) : BijOn f s t :=
   ⟨hf, h.left.injOn, h.right.surjOn hf'⟩
 #align set.inv_on.bij_on Set.InvOn.bijOn
 
+end InvOn
+
 end Set
 
 /-! ### `invFunOn` is a left/right inverse -/
-
-
 namespace Function
 
 variable [Nonempty α] {s : Set α} {f : α → β} {a : α} {b : β}
@@ -1395,8 +1423,6 @@ lemma bijOn_comm {g : β → α} (h : InvOn f g t s) : BijOn f s t ↔ BijOn g t
 end Set
 
 /-! ### Monotone -/
-
-
 namespace Monotone
 
 variable [Preorder α] [Preorder β] {f : α → β}
@@ -1417,8 +1443,6 @@ protected theorem rangeFactorization (h : Monotone f) : Monotone (Set.rangeFacto
 end Monotone
 
 /-! ### Piecewise defined function -/
-
-
 namespace Set
 
 variable {δ : α → Sort*} (s : Set α) (f g : ∀ i, δ i)
@@ -1443,6 +1467,7 @@ theorem piecewise_insert_self {j : α} [∀ i, Decidable (i ∈ insert j s)] :
 
 variable [∀ j, Decidable (j ∈ s)]
 
+-- TODO: move!
 instance Compl.decidableMem (j : α) : Decidable (j ∈ sᶜ) :=
   instDecidableNot
 #align set.compl.decidable_mem Set.Compl.decidableMem
@@ -1582,7 +1607,6 @@ theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪
   · rintro (⟨x, hx, rfl⟩ | ⟨x, hx, rfl⟩) <;> use x <;> simp_all
 #align set.range_piecewise Set.range_piecewise
 
-
 theorem injective_piecewise_iff {f g : α → β} :
     Injective (s.piecewise f g) ↔
       InjOn f s ∧ InjOn g sᶜ ∧ ∀ x ∈ s, ∀ y ∉ s, f x ≠ g y := by
@@ -1615,7 +1639,7 @@ theorem univ_pi_piecewise_univ {ι : Type*} {α : ι → Type*} (s : Set ι) (t
 
 end Set
 
-open Set
+section strictMono
 
 theorem StrictMonoOn.injOn [LinearOrder α] [Preorder β] {f : α → β} {s : Set α}
     (H : StrictMonoOn f s) : s.InjOn f := fun x hx y hy hxy =>
@@ -1663,6 +1687,8 @@ theorem StrictMono.codRestrict [Preorder α] [Preorder β] {f : α → β} (hf :
   hf
 #align strict_mono.cod_restrict StrictMono.codRestrict
 
+end strictMono
+
 namespace Function
 
 open Set
@@ -1789,8 +1815,8 @@ theorem antitoneOn_of_rightInvOn_of_mapsTo [PartialOrder α] [LinearOrder β]
 end Function
 
 /-! ### Equivalences, permutations -/
-
 namespace Set
+
 variable {p : β → Prop} [DecidablePred p] {f : α ≃ Subtype p} {g g₁ g₂ : Perm α} {s t : Set α}
 
 protected lemma MapsTo.extendDomain (h : MapsTo g s t) :
@@ -1828,6 +1854,8 @@ protected lemma InvOn.extendDomain (h : InvOn g₁ g₂ s t) :
 end Set
 
 namespace Equiv
+open Set
+
 variable (e : α ≃ β) {s : Set α} {t : Set β}
 
 lemma bijOn' (h₁ : MapsTo e s t) (h₂ : MapsTo e.symm t s) : BijOn e s t :=

chore: remove more bex and ball from lemma names (#11615)

Follow-up to #10816.

Remaining places containing such lemmas are

Option.bex_ne_none and Option.ball_ne_none: defined in Lean core
Nat.decidableBallLT and Nat.decidableBallLE: defined in Lean core
bef_def is still used in a number of places and could be renamed
BAll.imp_{left,right}, BEx.imp_{left,right}, BEx.intro and BEx.elim

I only audited the first ~150 lemmas mentioning "ball"; too many lemmas named after Metric.ball/openBall/closedBall.

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

7b7bbd73

Diff

@@ -231,7 +231,7 @@ theorem EqOn.mono (hs : s₁ ⊆ s₂) (hf : EqOn f₁ f₂ s₂) : EqOn f₁ f
 
 @[simp]
 theorem eqOn_union : EqOn f₁ f₂ (s₁ ∪ s₂) ↔ EqOn f₁ f₂ s₁ ∧ EqOn f₁ f₂ s₂ :=
-  ball_or_left
+  forall₂_or_left
 #align set.eq_on_union Set.eqOn_union
 
 theorem EqOn.union (h₁ : EqOn f₁ f₂ s₁) (h₂ : EqOn f₁ f₂ s₂) : EqOn f₁ f₂ (s₁ ∪ s₂) :=

feat: add image_restrictPreimage (#11640)

add the theorem image_restrictPreimage; use it to simplify the proof of Set.restrictPreimage_isClosedMap
add the equivalent for open maps Set.restrictPreimage_isOpenMap.
delete IsClosedMap.restrictPreimage, which duplicates Set.restrictPreimage_isClosedMap

Co-authored-by: BGuillemet <115193742+BGuillemet@users.noreply.github.com>

68ab53e5

Diff

@@ -564,10 +564,15 @@ section
 
 variable (t f)
 
-theorem range_restrictPreimage : range (t.restrictPreimage f) = Subtype.val ⁻¹' range f := by
+variable (s) in
+theorem image_restrictPreimage :
+    t.restrictPreimage f '' (Subtype.val ⁻¹' s) = Subtype.val ⁻¹' (f '' s) := by
   delta Set.restrictPreimage
-  rw [MapsTo.range_restrict, Set.image_preimage_eq_inter_range, Set.preimage_inter,
-    Subtype.coe_preimage_self, Set.univ_inter]
+  rw [← (Subtype.coe_injective).image_injective.eq_iff, ← image_comp, MapsTo.restrict_commutes,
+    image_comp, Subtype.image_preimage_coe, Subtype.image_preimage_coe, image_preimage_inter]
+
+theorem range_restrictPreimage : range (t.restrictPreimage f) = Subtype.val ⁻¹' range f := by
+  simp only [← image_univ, ← image_restrictPreimage, preimage_univ]
 #align set.range_restrict_preimage Set.range_restrictPreimage
 
 variable {f} {U : ι → Set β}

chore: classify new lemma porting notes (#11217)

Classifies by adding issue number #10756 to porting notes claiming anything semantically equivalent to:

"new lemma"
"added lemma"

68df7d0d

Diff

@@ -1599,7 +1599,7 @@ theorem pi_piecewise {ι : Type*} {α : ι → Type*} (s s' : Set ι) (t t' : 
   pi_if _ _ _
 #align set.pi_piecewise Set.pi_piecewise
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 theorem univ_pi_piecewise {ι : Type*} {α : ι → Type*} (s : Set ι) (t t' : ∀ i, Set (α i))
     [∀ x, Decidable (x ∈ s)] : pi univ (s.piecewise t t') = pi s t ∩ pi sᶜ t' := by
   simp [compl_eq_univ_diff]

chore: Remove ball and bex from lemma names (#10816)

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

c697e040

Diff

@@ -245,7 +245,7 @@ theorem EqOn.comp_left (h : s.EqOn f₁ f₂) : s.EqOn (g ∘ f₁) (g ∘ f₂)
 @[simp]
 theorem eqOn_range {ι : Sort*} {f : ι → α} {g₁ g₂ : α → β} :
     EqOn g₁ g₂ (range f) ↔ g₁ ∘ f = g₂ ∘ f :=
-  forall_range_iff.trans <| funext_iff.symm
+  forall_mem_range.trans <| funext_iff.symm
 #align set.eq_on_range Set.eqOn_range
 
 alias ⟨EqOn.comp_eq, _⟩ := eqOn_range
@@ -541,7 +541,7 @@ theorem maps_univ_to (f : α → β) (s : Set β) : MapsTo f univ s ↔ ∀ a, f
 
 @[simp]
 lemma mapsTo_range_iff {g : ι → α} : MapsTo f (range g) t ↔ ∀ i, f (g i) ∈ t :=
-  forall_range_iff
+  forall_mem_range
 
 @[deprecated mapsTo_range_iff]
 theorem maps_range_to (f : α → β) (g : γ → α) (s : Set β) :
@@ -672,7 +672,7 @@ theorem InjOn.comp (hg : InjOn g t) (hf : InjOn f s) (h : MapsTo f s t) : InjOn
 #align set.inj_on.comp Set.InjOn.comp
 
 lemma InjOn.image_of_comp (h : InjOn (g ∘ f) s) : InjOn g (f '' s) :=
-  ball_image_iff.2 fun _x hx ↦ ball_image_iff.2 fun _y hy heq ↦ congr_arg f <| h hx hy heq
+  forall_mem_image.2 fun _x hx ↦ forall_mem_image.2 fun _y hy heq ↦ congr_arg f <| h hx hy heq
 
 lemma InjOn.iterate {f : α → α} {s : Set α} (h : InjOn f s) (hf : MapsTo f s s) :
     ∀ n, InjOn f^[n] s
@@ -780,12 +780,12 @@ lemma exists_eq_graphOn_image_fst [Nonempty β] {s : Set (α × β)} :
   · rintro ⟨f, hf⟩
     rw [hf]
     exact InjOn.image_of_comp <| injOn_id _
-  · have : ∀ x ∈ Prod.fst '' s, ∃ y, (x, y) ∈ s := ball_image_iff.2 fun (x, y) h ↦ ⟨y, h⟩
+  · have : ∀ x ∈ Prod.fst '' s, ∃ y, (x, y) ∈ s := forall_mem_image.2 fun (x, y) h ↦ ⟨y, h⟩
     choose! f hf using this
-    rw [ball_image_iff] at hf
+    rw [forall_mem_image] at hf
     use f
     rw [graphOn, image_image, EqOn.image_eq_self]
-    exact fun x hx ↦ h (hf x hx) hx rfl
+    exact fun x hx ↦ h (hf hx) hx rfl
 
 lemma exists_eq_graphOn [Nonempty β] {s : Set (α × β)} :
     (∃ f t, s = graphOn f t) ↔ InjOn Prod.fst s :=
@@ -1682,7 +1682,7 @@ theorem RightInverse.rightInvOn {g : β → α} (h : RightInverse f g) (s : Set
 
 theorem LeftInverse.rightInvOn_range {g : β → α} (h : LeftInverse f g) :
     RightInvOn f g (range g) :=
-  forall_range_iff.2 fun i => congr_arg g (h i)
+  forall_mem_range.2 fun i => congr_arg g (h i)
 #align function.left_inverse.right_inv_on_range Function.LeftInverse.rightInvOn_range
 
 namespace Semiconj

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -711,7 +711,7 @@ theorem exists_injOn_iff_injective [Nonempty β] :
 
 theorem injOn_preimage {B : Set (Set β)} (hB : B ⊆ 𝒫 range f) : InjOn (preimage f) B :=
   fun s hs t ht hst => (preimage_eq_preimage' (@hB s hs) (@hB t ht)).1 hst
--- porting note: is there a semi-implicit variable problem with `⊆`?
+-- Porting note: is there a semi-implicit variable problem with `⊆`?
 #align set.inj_on_preimage Set.injOn_preimage
 
 theorem InjOn.mem_of_mem_image {x} (hf : InjOn f s) (hs : s₁ ⊆ s) (h : x ∈ s) (h₁ : f x ∈ f '' s₁) :
@@ -858,7 +858,7 @@ theorem SurjOn.inter (h₁ : SurjOn f s₁ t) (h₂ : SurjOn f s₂ t) (h : InjO
   inter_self t ▸ h₁.inter_inter h₂ h
 #align set.surj_on.inter Set.SurjOn.inter
 
---porting note: Why does `simp` not call `refl` by itself?
+-- Porting note: Why does `simp` not call `refl` by itself?
 lemma surjOn_id (s : Set α) : SurjOn id s s := by simp [SurjOn, subset_rfl]
 #align set.surj_on_id Set.surjOn_id
 
@@ -1599,7 +1599,7 @@ theorem pi_piecewise {ι : Type*} {α : ι → Type*} (s s' : Set ι) (t t' : 
   pi_if _ _ _
 #align set.pi_piecewise Set.pi_piecewise
 
--- porting note: new lemma
+-- Porting note: new lemma
 theorem univ_pi_piecewise {ι : Type*} {α : ι → Type*} (s : Set ι) (t t' : ∀ i, Set (α i))
     [∀ x, Decidable (x ∈ s)] : pi univ (s.piecewise t t') = pi s t ∩ pi sᶜ t' := by
   simp [compl_eq_univ_diff]

feat: Add SurjOn.image_preimage (#10342)

12f566f0

Diff

@@ -923,6 +923,9 @@ theorem image_eq_iff_surjOn_mapsTo : f '' s = t ↔ s.SurjOn f t ∧ s.MapsTo f
   exact ⟨s.surjOn_image f, s.mapsTo_image f⟩
 #align set.image_eq_iff_surj_on_maps_to Set.image_eq_iff_surjOn_mapsTo
 
+lemma SurjOn.image_preimage (h : Set.SurjOn f s t) (ht : t₁ ⊆ t) : f '' (f ⁻¹' t₁) = t₁ :=
+  image_preimage_eq_iff.2 fun _ hx ↦ mem_range_of_mem_image f s <| h <| ht hx
+
 theorem SurjOn.mapsTo_compl (h : SurjOn f s t) (h' : Injective f) : MapsTo f sᶜ tᶜ :=
   fun _ hs ht =>
   let ⟨_, hx', HEq⟩ := h ht

feat: Injectivity on {a, b} (#10212)

From LeanAPAP

7af47e01

Diff

@@ -608,6 +608,8 @@ theorem injOn_singleton (f : α → β) (a : α) : InjOn f {a} :=
   subsingleton_singleton.injOn f
 #align set.inj_on_singleton Set.injOn_singleton
 
+@[simp] lemma injOn_pair {b : α} : InjOn f {a, b} ↔ f a = f b → a = b := by unfold InjOn; aesop
+
 theorem InjOn.eq_iff {x y} (h : InjOn f s) (hx : x ∈ s) (hy : y ∈ s) : f x = f y ↔ x = y :=
   ⟨h hx hy, fun h => h ▸ rfl⟩
 #align set.inj_on.eq_iff Set.InjOn.eq_iff

chore(Data/Set): move definitions to a new file (#9737)

This and other similar PRs will help us reduce import dependencies and improve parallel compilation in the future.

9fb36425

Diff

@@ -174,13 +174,6 @@ variable {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {p : Set γ} {f f₁ f₂
 
 /-! ### Equality on a set -/
 
-
-/-- Two functions `f₁ f₂ : α → β` are equal on `s`
-  if `f₁ x = f₂ x` for all `x ∈ s`. -/
-def EqOn (f₁ f₂ : α → β) (s : Set α) : Prop :=
-  ∀ ⦃x⦄, x ∈ s → f₁ x = f₂ x
-#align set.eq_on Set.EqOn
-
 @[simp]
 theorem eqOn_empty (f₁ f₂ : α → β) : EqOn f₁ f₂ ∅ := fun _ => False.elim
 #align set.eq_on_empty Set.eqOn_empty
@@ -351,18 +344,6 @@ end Mono
 
 /-! ### maps to -/
 
-
-/-- `MapsTo f a b` means that the image of `a` is contained in `b`. -/
-def MapsTo (f : α → β) (s : Set α) (t : Set β) : Prop :=
-  ∀ ⦃x⦄, x ∈ s → f x ∈ t
-#align set.maps_to Set.MapsTo
-
-/-- Given a map `f` sending `s : Set α` into `t : Set β`, restrict domain of `f` to `s`
-and the codomain to `t`. Same as `Subtype.map`. -/
-def MapsTo.restrict (f : α → β) (s : Set α) (t : Set β) (h : MapsTo f s t) : s → t :=
-  Subtype.map f h
-#align set.maps_to.restrict Set.MapsTo.restrict
-
 theorem MapsTo.restrict_commutes (f : α → β) (s : Set α) (t : Set β) (h : MapsTo f s t) :
     Subtype.val ∘ h.restrict f s t = f ∘ Subtype.val :=
   rfl
@@ -526,13 +507,6 @@ theorem mapsTo_inter : MapsTo f s (t₁ ∩ t₂) ↔ MapsTo f s t₁ ∧ MapsTo
 theorem mapsTo_univ (f : α → β) (s : Set α) : MapsTo f s univ := fun _ _ => trivial
 #align set.maps_to_univ Set.mapsTo_univ
 
-theorem mapsTo_image (f : α → β) (s : Set α) : MapsTo f s (f '' s) := by rw [mapsTo']
-#align set.maps_to_image Set.mapsTo_image
-
-theorem mapsTo_preimage (f : α → β) (t : Set β) : MapsTo f (f ⁻¹' t) t :=
-  Subset.refl _
-#align set.maps_to_preimage Set.mapsTo_preimage
-
 theorem mapsTo_range (f : α → β) (s : Set α) : MapsTo f s (range f) :=
   (mapsTo_image f s).mono (Subset.refl s) (image_subset_range _ _)
 #align set.maps_to_range Set.mapsTo_range
@@ -590,13 +564,6 @@ section
 
 variable (t f)
 
-/-- The restriction of a function onto the preimage of a set. -/
-@[simps!]
-def restrictPreimage : f ⁻¹' t → t :=
-  (Set.mapsTo_preimage f t).restrict _ _ _
-#align set.restrict_preimage Set.restrictPreimage
-#align set.restrict_preimage_coe Set.restrictPreimage_coe
-
 theorem range_restrictPreimage : range (t.restrictPreimage f) = Subtype.val ⁻¹' range f := by
   delta Set.restrictPreimage
   rw [MapsTo.range_restrict, Set.image_preimage_eq_inter_range, Set.preimage_inter,
@@ -628,12 +595,6 @@ end
 
 /-! ### Injectivity on a set -/
 
-
-/-- `f` is injective on `a` if the restriction of `f` to `a` is injective. -/
-def InjOn (f : α → β) (s : Set α) : Prop :=
-  ∀ ⦃x₁ : α⦄, x₁ ∈ s → ∀ ⦃x₂ : α⦄, x₂ ∈ s → f x₁ = f x₂ → x₁ = x₂
-#align set.inj_on Set.InjOn
-
 theorem Subsingleton.injOn (hs : s.Subsingleton) (f : α → β) : InjOn f s := fun _ hx _ hy _ =>
   hs hx hy
 #align set.subsingleton.inj_on Set.Subsingleton.injOn
@@ -792,9 +753,6 @@ theorem _root_.Disjoint.image {s t u : Set α} {f : α → β} (h : Disjoint s t
   rw [← hf.image_inter hs ht, h, image_empty]
 #align disjoint.image Disjoint.image
 
-/-- The graph of a function `f : α → β` on a set `s`. -/
-def graphOn (f : α → β) (s : Set α) : Set (α × β) := (fun x ↦ (x, f x)) '' s
-
 @[simp] lemma graphOn_empty (f : α → β) : graphOn f ∅ = ∅ := image_empty _
 
 @[simp]
@@ -834,11 +792,6 @@ lemma exists_eq_graphOn [Nonempty β] {s : Set (α × β)} :
 
 /-! ### Surjectivity on a set -/
 
-/-- `f` is surjective from `a` to `b` if `b` is contained in the image of `a`. -/
-def SurjOn (f : α → β) (s : Set α) (t : Set β) : Prop :=
-  t ⊆ f '' s
-#align set.surj_on Set.SurjOn
-
 theorem SurjOn.subset_range (h : SurjOn f s t) : t ⊆ range f :=
   Subset.trans h <| image_subset_range f s
 #align set.surj_on.subset_range Set.SurjOn.subset_range
@@ -995,12 +948,6 @@ theorem eqOn_comp_right_iff : s.EqOn (g₁ ∘ f) (g₂ ∘ f) ↔ (f '' s).EqOn
 
 /-! ### Bijectivity -/
 
-
-/-- `f` is bijective from `s` to `t` if `f` is injective on `s` and `f '' s = t`. -/
-def BijOn (f : α → β) (s : Set α) (t : Set β) : Prop :=
-  MapsTo f s t ∧ InjOn f s ∧ SurjOn f s t
-#align set.bij_on Set.BijOn
-
 theorem BijOn.mapsTo (h : BijOn f s t) : MapsTo f s t :=
   h.left
 #align set.bij_on.maps_to Set.BijOn.mapsTo
@@ -1117,12 +1064,6 @@ theorem BijOn.compl (hst : BijOn f s t) (hf : Bijective f) : BijOn f sᶜ tᶜ :
 
 /-! ### left inverse -/
 
-
-/-- `g` is a left inverse to `f` on `a` means that `g (f x) = x` for all `x ∈ a`. -/
-def LeftInvOn (f' : β → α) (f : α → β) (s : Set α) : Prop :=
-  ∀ ⦃x⦄, x ∈ s → f' (f x) = x
-#align set.left_inv_on Set.LeftInvOn
-
 theorem LeftInvOn.eqOn (h : LeftInvOn f' f s) : EqOn (f' ∘ f) id s :=
   h
 #align set.left_inv_on.eq_on Set.LeftInvOn.eqOn
@@ -1195,13 +1136,6 @@ theorem LeftInvOn.image_image' (hf : LeftInvOn f' f s) (hs : s₁ ⊆ s) : f' ''
 
 /-! ### Right inverse -/
 
-
-/-- `g` is a right inverse to `f` on `b` if `f (g x) = x` for all `x ∈ b`. -/
-@[reducible]
-def RightInvOn (f' : β → α) (f : α → β) (t : Set β) : Prop :=
-  LeftInvOn f f' t
-#align set.right_inv_on Set.RightInvOn
-
 theorem RightInvOn.eqOn (h : RightInvOn f' f t) : EqOn (f ∘ f') id t :=
   h
 #align set.right_inv_on.eq_on Set.RightInvOn.eqOn
@@ -1264,12 +1198,6 @@ theorem SurjOn.leftInvOn_of_rightInvOn (hf : SurjOn f s t) (hf' : RightInvOn f f
 
 /-! ### Two-side inverses -/
 
-
-/-- `g` is an inverse to `f` viewed as a map from `a` to `b` -/
-def InvOn (g : β → α) (f : α → β) (s : Set α) (t : Set β) : Prop :=
-  LeftInvOn g f s ∧ RightInvOn g f t
-#align set.inv_on Set.InvOn
-
 lemma invOn_id (s : Set α) : InvOn id id s s := ⟨s.leftInvOn_id, s.rightInvOn_id⟩
 #align set.inv_on_id Set.invOn_id

feat: injective continuous linear map with closed range is a continuous linear equivalence (#9756)

Added analogue of LinearEquiv.ofInjective but for ContinuousLinearEquiv on Banach spaces.

Added analogue of LinearMap.rangeRestrict but for ContinuousLinearMap.

Also I updated a docstring that had the old name of a theorem.

Co-authored-by: Jireh Loreaux <loreaujy@gmail.com>

c8766486

Diff

@@ -1307,7 +1307,7 @@ variable [Nonempty α] {s : Set α} {f : α → β} {a : α} {b : β}
 attribute [local instance] Classical.propDecidable
 
 /-- Construct the inverse for a function `f` on domain `s`. This function is a right inverse of `f`
-on `f '' s`. For a computable version, see `Function.Injective.inv_of_mem_range`. -/
+on `f '' s`. For a computable version, see `Function.Embedding.invOfMemRange`. -/
 noncomputable def invFunOn (f : α → β) (s : Set α) (b : β) : α :=
   if h : ∃ a, a ∈ s ∧ f a = b then Classical.choose h else Classical.choice ‹Nonempty α›
 #align function.inv_fun_on Function.invFunOn

feat(Set/Function): define Set.graphOn (#9497)

Also prove that s : Set (α × β) is a graph of a function on a set if and only if Prod.fst is injective on s.

869c0233

Diff

@@ -708,6 +708,9 @@ theorem InjOn.comp (hg : InjOn g t) (hf : InjOn f s) (h : MapsTo f s t) : InjOn
   fun _ hx _ hy heq => hf hx hy <| hg (h hx) (h hy) heq
 #align set.inj_on.comp Set.InjOn.comp
 
+lemma InjOn.image_of_comp (h : InjOn (g ∘ f) s) : InjOn g (f '' s) :=
+  ball_image_iff.2 fun _x hx ↦ ball_image_iff.2 fun _y hy heq ↦ congr_arg f <| h hx hy heq
+
 lemma InjOn.iterate {f : α → α} {s : Set α} (h : InjOn f s) (hf : MapsTo f s s) :
     ∀ n, InjOn f^[n] s
   | 0 => injOn_id _
@@ -789,8 +792,47 @@ theorem _root_.Disjoint.image {s t u : Set α} {f : α → β} (h : Disjoint s t
   rw [← hf.image_inter hs ht, h, image_empty]
 #align disjoint.image Disjoint.image
 
-/-! ### Surjectivity on a set -/
+/-- The graph of a function `f : α → β` on a set `s`. -/
+def graphOn (f : α → β) (s : Set α) : Set (α × β) := (fun x ↦ (x, f x)) '' s
+
+@[simp] lemma graphOn_empty (f : α → β) : graphOn f ∅ = ∅ := image_empty _
+
+@[simp]
+lemma graphOn_union (f : α → β) (s t : Set α) : graphOn f (s ∪ t) = graphOn f s ∪ graphOn f t :=
+  image_union ..
+
+@[simp]
+lemma graphOn_singleton (f : α → β) (x : α) : graphOn f {x} = {(x, f x)} :=
+  image_singleton ..
+
+@[simp]
+lemma graphOn_insert (f : α → β) (x : α) (s : Set α) :
+    graphOn f (insert x s) = insert (x, f x) (graphOn f s) :=
+  image_insert_eq ..
 
+@[simp]
+lemma image_fst_graphOn (f : α → β) (s : Set α) : Prod.fst '' graphOn f s = s := by
+  simp [graphOn, image_image]
+
+lemma exists_eq_graphOn_image_fst [Nonempty β] {s : Set (α × β)} :
+    (∃ f : α → β, s = graphOn f (Prod.fst '' s)) ↔ InjOn Prod.fst s := by
+  refine ⟨?_, fun h ↦ ?_⟩
+  · rintro ⟨f, hf⟩
+    rw [hf]
+    exact InjOn.image_of_comp <| injOn_id _
+  · have : ∀ x ∈ Prod.fst '' s, ∃ y, (x, y) ∈ s := ball_image_iff.2 fun (x, y) h ↦ ⟨y, h⟩
+    choose! f hf using this
+    rw [ball_image_iff] at hf
+    use f
+    rw [graphOn, image_image, EqOn.image_eq_self]
+    exact fun x hx ↦ h (hf x hx) hx rfl
+
+lemma exists_eq_graphOn [Nonempty β] {s : Set (α × β)} :
+    (∃ f t, s = graphOn f t) ↔ InjOn Prod.fst s :=
+  .trans ⟨fun ⟨f, t, hs⟩ ↦ ⟨f, by rw [hs, image_fst_graphOn]⟩, fun ⟨f, hf⟩ ↦ ⟨f, _, hf⟩⟩
+    exists_eq_graphOn_image_fst
+
+/-! ### Surjectivity on a set -/
 
 /-- `f` is surjective from `a` to `b` if `b` is contained in the image of `a`. -/
 def SurjOn (f : α → β) (s : Set α) (t : Set β) : Prop :=

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

See Zulip thread for the discussion.

9f6d3388

Diff

@@ -471,7 +471,7 @@ theorem MapsTo.iterate_restrict {f : α → α} {s : Set α} (h : MapsTo f s s)
 
 lemma mapsTo_of_subsingleton' [Subsingleton β] (f : α → β) (h : s.Nonempty → t.Nonempty) :
     MapsTo f s t :=
-  fun a ha ↦ Subsingleton.mem_iff_nonempty.2 $ h ⟨a, ha⟩
+  fun a ha ↦ Subsingleton.mem_iff_nonempty.2 <| h ⟨a, ha⟩
 #align set.maps_to_of_subsingleton' Set.mapsTo_of_subsingleton'
 
 lemma mapsTo_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : MapsTo f s s :=
@@ -885,7 +885,7 @@ lemma SurjOn.comp_right {s : Set β} {t : Set γ} (hf : Surjective f) (hg : Surj
 
 lemma surjOn_of_subsingleton' [Subsingleton β] (f : α → β) (h : t.Nonempty → s.Nonempty) :
     SurjOn f s t :=
-  fun _ ha ↦ Subsingleton.mem_iff_nonempty.2 $ (h ⟨_, ha⟩).image _
+  fun _ ha ↦ Subsingleton.mem_iff_nonempty.2 <| (h ⟨_, ha⟩).image _
 #align set.surj_on_of_subsingleton' Set.surjOn_of_subsingleton'
 
 lemma surjOn_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : SurjOn f s s :=
@@ -1855,7 +1855,7 @@ lemma bijOn' (h₁ : MapsTo e s t) (h₂ : MapsTo e.symm t s) : BijOn e s t :=
 #align equiv.bij_on' Equiv.bijOn'
 
 protected lemma bijOn (h : ∀ a, e a ∈ t ↔ a ∈ s) : BijOn e s t :=
-  e.bijOn' (fun a ↦ (h _).2) fun b hb ↦ (h _).1 $ by rwa [apply_symm_apply]
+  e.bijOn' (fun a ↦ (h _).2) fun b hb ↦ (h _).1 <| by rwa [apply_symm_apply]
 #align equiv.bij_on Equiv.bijOn
 
 lemma invOn : InvOn e e.symm t s :=

chore(Set/Function): don't use Sort _ (#9478)

Use Sort* or Type* instead. Also slightly golf 1 proof.

cd6e906e

Diff

@@ -683,8 +683,7 @@ theorem injOn_union (h : Disjoint s₁ s₂) :
 
 theorem injOn_insert {f : α → β} {s : Set α} {a : α} (has : a ∉ s) :
     Set.InjOn f (insert a s) ↔ Set.InjOn f s ∧ f a ∉ f '' s := by
-  have : Disjoint s {a} := disjoint_iff_inf_le.mpr fun x ⟨hxs, (hxa : x = a)⟩ => has (hxa ▸ hxs)
-  rw [← union_singleton, injOn_union this]
+  rw [← union_singleton, injOn_union (disjoint_singleton_right.2 has)]
   simp
 #align set.inj_on_insert Set.injOn_insert
 
@@ -1773,15 +1772,15 @@ theorem injOn_preimage (h : Semiconj f fa fb) {s : Set β} (hb : InjOn fb s)
 
 end Semiconj
 
-theorem update_comp_eq_of_not_mem_range' {α β : Sort _} {γ : β → Sort*} [DecidableEq β]
+theorem update_comp_eq_of_not_mem_range' {α : Sort*} {β : Type*} {γ : β → Sort*} [DecidableEq β]
     (g : ∀ b, γ b) {f : α → β} {i : β} (a : γ i) (h : i ∉ Set.range f) :
-    (fun j => (Function.update g i a) (f j)) = fun j => g (f j) :=
+    (fun j => update g i a (f j)) = fun j => g (f j) :=
   (update_comp_eq_of_forall_ne' _ _) fun x hx => h ⟨x, hx⟩
 #align function.update_comp_eq_of_not_mem_range' Function.update_comp_eq_of_not_mem_range'
 
 /-- Non-dependent version of `Function.update_comp_eq_of_not_mem_range'` -/
-theorem update_comp_eq_of_not_mem_range {α β γ : Sort _} [DecidableEq β] (g : β → γ) {f : α → β}
-    {i : β} (a : γ) (h : i ∉ Set.range f) : Function.update g i a ∘ f = g ∘ f :=
+theorem update_comp_eq_of_not_mem_range {α : Sort*} {β : Type*} {γ : Sort*} [DecidableEq β]
+    (g : β → γ) {f : α → β} {i : β} (a : γ) (h : i ∉ Set.range f) : update g i a ∘ f = g ∘ f :=
   update_comp_eq_of_not_mem_range' g a h
 #align function.update_comp_eq_of_not_mem_range Function.update_comp_eq_of_not_mem_range
 
@@ -1789,7 +1788,7 @@ theorem insert_injOn (s : Set α) : sᶜ.InjOn fun a => insert a s := fun _a ha
   (insert_inj ha).1
 #align function.insert_inj_on Function.insert_injOn
 
-theorem monotoneOn_of_rightInvOn_of_mapsTo {α β : Sort _} [PartialOrder α] [LinearOrder β]
+theorem monotoneOn_of_rightInvOn_of_mapsTo {α β : Type*} [PartialOrder α] [LinearOrder β]
     {φ : β → α} {ψ : α → β} {t : Set β} {s : Set α} (hφ : MonotoneOn φ t)
     (φψs : Set.RightInvOn ψ φ s) (ψts : Set.MapsTo ψ s t) : MonotoneOn ψ s := by
   rintro x xs y ys l
@@ -1801,7 +1800,7 @@ theorem monotoneOn_of_rightInvOn_of_mapsTo {α β : Sort _} [PartialOrder α] [L
     exact le_refl _
 #align function.monotone_on_of_right_inv_on_of_maps_to Function.monotoneOn_of_rightInvOn_of_mapsTo
 
-theorem antitoneOn_of_rightInvOn_of_mapsTo {α β : Sort _} [PartialOrder α] [LinearOrder β]
+theorem antitoneOn_of_rightInvOn_of_mapsTo [PartialOrder α] [LinearOrder β]
     {φ : β → α} {ψ : α → β} {t : Set β} {s : Set α} (hφ : AntitoneOn φ t)
     (φψs : Set.RightInvOn ψ φ s) (ψts : Set.MapsTo ψ s t) : AntitoneOn ψ s :=
   (monotoneOn_of_rightInvOn_of_mapsTo hφ.dual_left φψs ψts).dual_right

chore(*): drop $/<| before fun (#9361)

Subset of #9319

3694e27d

Diff

@@ -411,7 +411,7 @@ theorem mapsTo' : MapsTo f s t ↔ f '' s ⊆ t :=
 #align set.maps_to' Set.mapsTo'
 
 theorem mapsTo_prod_map_diagonal : MapsTo (Prod.map f f) (diagonal α) (diagonal β) :=
-  diagonal_subset_iff.2 <| fun _ => rfl
+  diagonal_subset_iff.2 fun _ => rfl
 #align set.maps_to_prod_map_diagonal Set.mapsTo_prod_map_diagonal
 
 theorem MapsTo.subset_preimage {f : α → β} {s : Set α} {t : Set β} (hf : MapsTo f s t) :
@@ -1856,7 +1856,7 @@ lemma bijOn' (h₁ : MapsTo e s t) (h₂ : MapsTo e.symm t s) : BijOn e s t :=
 #align equiv.bij_on' Equiv.bijOn'
 
 protected lemma bijOn (h : ∀ a, e a ∈ t ↔ a ∈ s) : BijOn e s t :=
-  e.bijOn' (fun a ↦ (h _).2) $ fun b hb ↦ (h _).1 $ by rwa [apply_symm_apply]
+  e.bijOn' (fun a ↦ (h _).2) fun b hb ↦ (h _).1 $ by rwa [apply_symm_apply]
 #align equiv.bij_on Equiv.bijOn
 
 lemma invOn : InvOn e e.symm t s :=
@@ -1880,7 +1880,7 @@ alias ⟨_root_.Set.BijOn.of_equiv_symm, _root_.Set.BijOn.equiv_symm⟩ := bijOn
 variable [DecidableEq α] {a b : α}
 
 lemma bijOn_swap (ha : a ∈ s) (hb : b ∈ s) : BijOn (swap a b) s s :=
-  (swap a b).bijOn $ fun x ↦ by
+  (swap a b).bijOn fun x ↦ by
     obtain rfl | hxa := eq_or_ne x a <;>
     obtain rfl | hxb := eq_or_ne x b <;>
     simp [*, swap_apply_of_ne_of_ne]

chore(Data/Set/Function): rename some lemmas (#9257)

Set.maps_image_to → Set.mapsTo_image_iff;
Set.maps_univ_to → Set.mapsTo_univ_iff;
Set.maps_range_to → Set.mapsTo_range_iff.

In all cases, use implicit arguments instead of explicit arguments. In the last case, also generalize from Type* to Sort* and replace the RHS with its simp-normal form.

Old lemmas stay there but are now deprecated.

8919646c

Diff

@@ -538,10 +538,15 @@ theorem mapsTo_range (f : α → β) (s : Set α) : MapsTo f s (range f) :=
 #align set.maps_to_range Set.mapsTo_range
 
 @[simp]
-theorem maps_image_to (f : α → β) (g : γ → α) (s : Set γ) (t : Set β) :
+theorem mapsTo_image_iff {f : α → β} {g : γ → α} {s : Set γ} {t : Set β} :
     MapsTo f (g '' s) t ↔ MapsTo (f ∘ g) s t :=
   ⟨fun h c hc => h ⟨c, hc, rfl⟩, fun h _ ⟨_, hc⟩ => hc.2 ▸ h hc.1⟩
-#align set.maps_image_to Set.maps_image_to
+#align set.maps_image_to Set.mapsTo_image_iff
+
+@[deprecated]
+lemma maps_image_to (f : α → β) (g : γ → α) (s : Set γ) (t : Set β) :
+    MapsTo f (g '' s) t ↔ MapsTo (f ∘ g) s t :=
+  mapsTo_image_iff
 
 lemma MapsTo.comp_left (g : β → γ) (hf : MapsTo f s t) : MapsTo (g ∘ f) s (g '' t) :=
   fun x hx ↦ ⟨f x, hf hx, rfl⟩
@@ -552,13 +557,21 @@ lemma MapsTo.comp_right {s : Set β} {t : Set γ} (hg : MapsTo g s t) (f : α 
 #align set.maps_to.comp_right Set.MapsTo.comp_right
 
 @[simp]
-theorem maps_univ_to (f : α → β) (s : Set β) : MapsTo f univ s ↔ ∀ a, f a ∈ s :=
+lemma mapsTo_univ_iff : MapsTo f univ t ↔ ∀ x, f x ∈ t :=
   ⟨fun h _ => h (mem_univ _), fun h x _ => h x⟩
+
+@[deprecated]
+theorem maps_univ_to (f : α → β) (s : Set β) : MapsTo f univ s ↔ ∀ a, f a ∈ s :=
+  mapsTo_univ_iff
 #align set.maps_univ_to Set.maps_univ_to
 
 @[simp]
+lemma mapsTo_range_iff {g : ι → α} : MapsTo f (range g) t ↔ ∀ i, f (g i) ∈ t :=
+  forall_range_iff
+
+@[deprecated mapsTo_range_iff]
 theorem maps_range_to (f : α → β) (g : γ → α) (s : Set β) :
-    MapsTo f (range g) s ↔ MapsTo (f ∘ g) univ s := by rw [← image_univ, maps_image_to]
+    MapsTo f (range g) s ↔ MapsTo (f ∘ g) univ s := by rw [← image_univ, mapsTo_image_iff]
 #align set.maps_range_to Set.maps_range_to
 
 theorem surjective_mapsTo_image_restrict (f : α → β) (s : Set α) :

chore(*): use ∃ x ∈ s, _ instead of ∃ (x) (_ : x ∈ s), _ (#9184)

Search for [∀∃].*(_ and manually replace some occurrences with more readable versions. In case of ∀, the new expressions are defeq to the old ones. In case of ∃, they differ by exists_prop.

In some rare cases, golf proofs that needed fixing.

14c72960

Diff

@@ -78,14 +78,14 @@ theorem image_restrict (f : α → β) (s t : Set α) :
 
 @[simp]
 theorem restrict_dite {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
-    (g : ∀ (a) (_ : a ∉ s), β) :
+    (g : ∀ a ∉ s, β) :
     (s.restrict fun a => if h : a ∈ s then f a h else g a h) = (fun a : s => f a a.2) :=
   funext fun a => dif_pos a.2
 #align set.restrict_dite Set.restrict_dite
 
 @[simp]
 theorem restrict_dite_compl {s : Set α} [∀ x, Decidable (x ∈ s)] (f : ∀ a ∈ s, β)
-    (g : ∀ (a) (_ : a ∉ s), β) :
+    (g : ∀ a ∉ s, β) :
     (sᶜ.restrict fun a => if h : a ∈ s then f a h else g a h) = (fun a : (sᶜ : Set α) => g a a.2) :=
   funext fun a => dif_neg a.2
 #align set.restrict_dite_compl Set.restrict_dite_compl
@@ -1493,19 +1493,19 @@ theorem piecewise_eqOn_compl (f g : α → β) : EqOn (s.piecewise f g) g sᶜ :
 #align set.piecewise_eq_on_compl Set.piecewise_eqOn_compl
 
 theorem piecewise_le {δ : α → Type*} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
-    {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g i) (h₂ : ∀ (i) (_ : i ∉ s), f₂ i ≤ g i) :
+    {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g i) (h₂ : ∀ i ∉ s, f₂ i ≤ g i) :
     s.piecewise f₁ f₂ ≤ g := fun i => if h : i ∈ s then by simp [*] else by simp [*]
 #align set.piecewise_le Set.piecewise_le
 
 theorem le_piecewise {δ : α → Type*} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
-    {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, g i ≤ f₁ i) (h₂ : ∀ (i) (_ : i ∉ s), g i ≤ f₂ i) :
+    {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, g i ≤ f₁ i) (h₂ : ∀ i ∉ s, g i ≤ f₂ i) :
     g ≤ s.piecewise f₁ f₂ :=
   @piecewise_le α (fun i => (δ i)ᵒᵈ) _ s _ _ _ _ h₁ h₂
 #align set.le_piecewise Set.le_piecewise
 
 theorem piecewise_le_piecewise {δ : α → Type*} [∀ i, Preorder (δ i)] {s : Set α}
     [∀ j, Decidable (j ∈ s)] {f₁ f₂ g₁ g₂ : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g₁ i)
-    (h₂ : ∀ (i) (_ : i ∉ s), f₂ i ≤ g₂ i) : s.piecewise f₁ f₂ ≤ s.piecewise g₁ g₂ := by
+    (h₂ : ∀ i ∉ s, f₂ i ≤ g₂ i) : s.piecewise f₁ f₂ ≤ s.piecewise g₁ g₂ := by
   apply piecewise_le <;> intros <;> simp [*]
 #align set.piecewise_le_piecewise Set.piecewise_le_piecewise
 
@@ -1593,7 +1593,7 @@ theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪
 
 theorem injective_piecewise_iff {f g : α → β} :
     Injective (s.piecewise f g) ↔
-      InjOn f s ∧ InjOn g sᶜ ∧ ∀ x ∈ s, ∀ (y) (_ : y ∉ s), f x ≠ g y := by
+      InjOn f s ∧ InjOn g sᶜ ∧ ∀ x ∈ s, ∀ y ∉ s, f x ≠ g y := by
   rw [injective_iff_injOn_univ, ← union_compl_self s, injOn_union (@disjoint_compl_right _ _ s),
     (piecewise_eqOn s f g).injOn_iff, (piecewise_eqOn_compl s f g).injOn_iff]
   refine' and_congr Iff.rfl (and_congr Iff.rfl <| forall₄_congr fun x hx y hy => _)

feat(Data/Set/Function): add MapsTo.map_nonempty (#9093)

Extracted from #8160.

Co-authored-by: grunweg <grunweg@posteo.de>

a369b3d6

Diff

@@ -428,6 +428,10 @@ theorem mapsTo_empty (f : α → β) (t : Set β) : MapsTo f ∅ t :=
   empty_subset _
 #align set.maps_to_empty Set.mapsTo_empty
 
+/-- If `f` maps `s` to `t` and `s` is non-empty, `t` is non-empty. -/
+theorem MapsTo.nonempty (h : MapsTo f s t) (hs : s.Nonempty) : t.Nonempty :=
+  (hs.image f).mono (mapsTo'.mp h)
+
 theorem MapsTo.image_subset (h : MapsTo f s t) : f '' s ⊆ t :=
   mapsTo'.1 h
 #align set.maps_to.image_subset Set.MapsTo.image_subset

feat: supporting lemmas for defining root systems (#8980)

A collection of loosely-related lemmas, split out from other work in the hopes of simplifying review.

e8acc5ce

Diff

@@ -372,6 +372,11 @@ theorem MapsTo.val_restrict_apply (h : MapsTo f s t) (x : s) : (h.restrict f s t
   rfl
 #align set.maps_to.coe_restrict_apply Set.MapsTo.val_restrict_apply
 
+theorem MapsTo.coe_iterate_restrict {f : α → α} (h : MapsTo f s s) (x : s) (k : ℕ) :
+    h.restrict^[k] x = f^[k] x := by
+  induction' k with k ih; · simp
+  simp only [iterate_succ', comp_apply, val_restrict_apply, ih]
+
 /-- Restricting the domain and then the codomain is the same as `MapsTo.restrict`. -/
 @[simp]
 theorem codRestrict_restrict (h : ∀ x : s, f x ∈ t) :
@@ -1004,6 +1009,10 @@ theorem BijOn.image_eq (h : BijOn f s t) : f '' s = t :=
   h.surjOn.image_eq_of_mapsTo h.mapsTo
 #align set.bij_on.image_eq Set.BijOn.image_eq
 
+lemma _root_.Equiv.image_eq_iff_bijOn (e : α ≃ β) : e '' s = t ↔ BijOn e s t :=
+  ⟨fun h ↦ ⟨(mapsTo_image e s).mono_right h.subset, e.injective.injOn _, h ▸ surjOn_image e s⟩,
+  BijOn.image_eq⟩
+
 lemma bijOn_id (s : Set α) : BijOn id s s := ⟨s.mapsTo_id, s.injOn_id, s.surjOn_id⟩
 #align set.bij_on_id Set.bijOn_id

chore: Replace (· op ·) a by (a op ·) (#8843)

I used the regex $\(· (.) ·$ (.)\), replacing with ($2 $1 ·).

d14658b4

Diff

@@ -68,7 +68,7 @@ theorem eq_restrict_iff {s : Set α} {f : ∀ a : s, π a} {g : ∀ a, π a} :
 
 @[simp]
 theorem range_restrict (f : α → β) (s : Set α) : Set.range (s.restrict f) = f '' s :=
-  (range_comp _ _).trans <| congr_arg ((· '' ·) f) Subtype.range_coe
+  (range_comp _ _).trans <| congr_arg (f '' ·) Subtype.range_coe
 #align set.range_restrict Set.range_restrict
 
 theorem image_restrict (f : α → β) (s t : Set α) :

chore: space after ← (#8178)

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

5fb9beab

Diff

@@ -1302,7 +1302,7 @@ theorem injOn_iff_invFunOn_image_image_eq_self [Nonempty α] :
 theorem _root_.Function.invFunOn_injOn_image [Nonempty α] (f : α → β) (s : Set α) :
     Set.InjOn (invFunOn f s) (f '' s) := by
   rintro _ ⟨x, hx, rfl⟩ _ ⟨x', hx', rfl⟩ he
-  rw [←invFunOn_apply_eq (f := f) hx, he, invFunOn_apply_eq (f := f) hx']
+  rw [← invFunOn_apply_eq (f := f) hx, he, invFunOn_apply_eq (f := f) hx']
 
 theorem _root_.Function.invFunOn_image_image_subset [Nonempty α] (f : α → β) (s : Set α) :
     (invFunOn f s) '' (f '' s) ⊆ s := by

chore: bump to v4.3.0-rc2 (#8366)

PR contents

This is the supremum of

#8284
#8056
#8023
#8332
#8226 (already approved)
#7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

switching to using explicit lemmas that have the intended level of application
(config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

40b64f79

Diff

@@ -1444,7 +1444,7 @@ instance Compl.decidableMem (j : α) : Decidable (j ∈ sᶜ) :=
 
 theorem piecewise_insert [DecidableEq α] (j : α) [∀ i, Decidable (i ∈ insert j s)] :
     (insert j s).piecewise f g = Function.update (s.piecewise f g) j (f j) := by
-  simp only [piecewise, mem_insert_iff]
+  simp (config := { unfoldPartialApp := true }) only [piecewise, mem_insert_iff]
   ext i
   by_cases h : i = j
   · rw [h]

feat: two missing injOn lemmas (#8303)

508efdc9

Diff

@@ -1333,7 +1333,7 @@ theorem SurjOn.bijOn_subset [Nonempty α] (h : SurjOn f s t) : BijOn f (invFunOn
   rwa [h.rightInvOn_invFunOn hy]
 #align set.surj_on.bij_on_subset Set.SurjOn.bijOn_subset
 
-theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _) (_ : s' ⊆ s), BijOn f s' t := by
+theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ s' ⊆ s, BijOn f s' t := by
   constructor
   · rcases eq_empty_or_nonempty t with (rfl | ht)
     · exact fun _ => ⟨∅, empty_subset _, bijOn_empty f⟩
@@ -1344,6 +1344,23 @@ theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _) (_ : s' 
     exact hfs'.surjOn.mono hs' (Subset.refl _)
 #align set.surj_on_iff_exists_bij_on_subset Set.surjOn_iff_exists_bijOn_subset
 
+alias ⟨SurjOn.exists_bijOn_subset, _⟩ := Set.surjOn_iff_exists_bijOn_subset
+
+variable (f s)
+
+lemma exists_subset_bijOn : ∃ s' ⊆ s, BijOn f s' (f '' s) :=
+  surjOn_iff_exists_bijOn_subset.mp (surjOn_image f s)
+
+lemma exists_image_eq_and_injOn : ∃ u, f '' u =  f '' s ∧ InjOn f u :=
+  let ⟨u, _, hfu⟩ := exists_subset_bijOn s f
+  ⟨u, hfu.image_eq, hfu.injOn⟩
+
+variable {f s}
+
+lemma exists_image_eq_injOn_of_subset_range (ht : t ⊆ range f) :
+    ∃ s, f '' s = t ∧ InjOn f s :=
+  image_preimage_eq_of_subset ht ▸ exists_image_eq_and_injOn _ _
+
 theorem preimage_invFun_of_mem [n : Nonempty α] {f : α → β} (hf : Injective f) {s : Set α}
     (h : Classical.choice n ∈ s) : invFun f ⁻¹' s = f '' s ∪ (range f)ᶜ := by
   ext x

chore: tidy various files (#8175)

11572f18

Diff

@@ -190,6 +190,10 @@ theorem eqOn_singleton : Set.EqOn f₁ f₂ {a} ↔ f₁ a = f₂ a := by
   simp [Set.EqOn]
 #align set.eq_on_singleton Set.eqOn_singleton
 
+@[simp]
+theorem eqOn_univ (f₁ f₂ : α → β) : EqOn f₁ f₂ univ ↔ f₁ = f₂ := by
+  simp [EqOn, funext_iff]
+
 @[simp]
 theorem restrict_eq_restrict_iff : restrict s f₁ = restrict s f₂ ↔ EqOn f₁ f₂ s :=
   restrict_eq_iff

feat: miscellaneous lemmas about local homeomorphisms (#8062)

variant of extend_left_inv', stated in terms of images (instead of point-wise)
variant of map_source', stated for images of subsets (instead of point-wise)
a local homeomorphism and its inverse are open on its source

Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>

a1f33eb2

Diff

@@ -221,6 +221,10 @@ theorem EqOn.image_eq (heq : EqOn f₁ f₂ s) : f₁ '' s = f₂ '' s :=
   image_congr heq
 #align set.eq_on.image_eq Set.EqOn.image_eq
 
+/-- Variant of `EqOn.image_eq`, for one function being the identity. -/
+theorem EqOn.image_eq_self {f : α → α} (h : Set.EqOn f id s) : f '' s = s := by
+  rw [h.image_eq, image_id]
+
 theorem EqOn.inter_preimage_eq (heq : EqOn f₁ f₂ s) (t : Set β) : s ∩ f₁ ⁻¹' t = s ∩ f₂ ⁻¹' t :=
   ext fun x => and_congr_right_iff.2 fun hx => by rw [mem_preimage, mem_preimage, heq hx]
 #align set.eq_on.inter_preimage_eq Set.EqOn.inter_preimage_eq

feat: miscellaneous linear algebra lemmas (#8157)

ccd15763

Diff

@@ -876,6 +876,17 @@ theorem surjOn_iff_surjective : SurjOn f s univ ↔ Surjective (s.restrict f) :=
     ⟨a, as, e⟩⟩
 #align set.surj_on_iff_surjective Set.surjOn_iff_surjective
 
+@[simp]
+theorem MapsTo.restrict_surjective_iff (h : MapsTo f s t) :
+    Surjective (MapsTo.restrict _ _ _ h) ↔ SurjOn f s t := by
+  refine ⟨fun h' b hb ↦ ?_, fun h' ⟨b, hb⟩ ↦ ?_⟩
+  · obtain ⟨⟨a, ha⟩, ha'⟩ := h' ⟨b, hb⟩
+    replace ha' : f a = b := by simpa [Subtype.ext_iff] using ha'
+    rw [← ha']
+    exact mem_image_of_mem f ha
+  · obtain ⟨a, ha, rfl⟩ := h' hb
+    exact ⟨⟨a, ha⟩, rfl⟩
+
 theorem SurjOn.image_eq_of_mapsTo (h₁ : SurjOn f s t) (h₂ : MapsTo f s t) : f '' s = t :=
   eq_of_subset_of_subset h₂.image_subset h₁
 #align set.surj_on.image_eq_of_maps_to Set.SurjOn.image_eq_of_mapsTo

chore: remove nonterminal simp (#7580)

Removes nonterminal simps on lines looking like simp [...]

6fc8e6ec

Diff

@@ -1408,7 +1408,7 @@ instance Compl.decidableMem (j : α) : Decidable (j ∈ sᶜ) :=
 
 theorem piecewise_insert [DecidableEq α] (j : α) [∀ i, Decidable (i ∈ insert j s)] :
     (insert j s).piecewise f g = Function.update (s.piecewise f g) j (f j) := by
-  simp [piecewise]
+  simp only [piecewise, mem_insert_iff]
   ext i
   by_cases h : i = j
   · rw [h]

chore: remove invalid trans argument on EqOn.trans (#7285)

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

b85546bf

Diff

@@ -203,11 +203,16 @@ theorem eqOn_comm : EqOn f₁ f₂ s ↔ EqOn f₂ f₁ s :=
   ⟨EqOn.symm, EqOn.symm⟩
 #align set.eq_on_comm Set.eqOn_comm
 
--- porting note: can't add `@[refl]` for some reason
+-- This can not be tagged as `@[refl]` with the current argument order.
+-- See note below at `EqOn.trans`.
 theorem eqOn_refl (f : α → β) (s : Set α) : EqOn f f s := fun _ _ => rfl
 #align set.eq_on_refl Set.eqOn_refl
 
-@[trans]
+-- Note: this was formerly tagged with `@[trans]`, and although the `trans` attribute accepted it
+-- the `trans` tactic could not use it.
+-- An update to the trans tactic coming in mathlib4#7014 will reject this attribute.
+-- It can be restored by changing the argument order from `EqOn f₁ f₂ s` to `EqOn s f₁ f₂`.
+-- This change will be made separately: [zulip](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Reordering.20arguments.20of.20.60Set.2EEqOn.60/near/390467581).
 theorem EqOn.trans (h₁ : EqOn f₁ f₂ s) (h₂ : EqOn f₂ f₃ s) : EqOn f₁ f₃ s := fun _ hx =>
   (h₁ hx).trans (h₂ hx)
 #align set.eq_on.trans Set.EqOn.trans

chore: only four spaces for subsequent lines (#7286)

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

0c7d6fa5

Diff

@@ -526,7 +526,7 @@ lemma MapsTo.comp_left (g : β → γ) (hf : MapsTo f s t) : MapsTo (g ∘ f) s
 #align set.maps_to.comp_left Set.MapsTo.comp_left
 
 lemma MapsTo.comp_right {s : Set β} {t : Set γ} (hg : MapsTo g s t) (f : α → β) :
-  MapsTo (g ∘ f) (f ⁻¹' s) t := fun _ hx ↦ hg hx
+    MapsTo (g ∘ f) (f ⁻¹' s) t := fun _ hx ↦ hg hx
 #align set.maps_to.comp_right Set.MapsTo.comp_right
 
 @[simp]

chore: tidy various files (#7132)

7eb27432

Diff

@@ -1264,7 +1264,7 @@ theorem InjOn.invFunOn_image [Nonempty α] (h : InjOn f s₂) (ht : s₁ ⊆ s
   h.leftInvOn_invFunOn.image_image' ht
 #align set.inj_on.inv_fun_on_image Set.InjOn.invFunOn_image
 
-theorem _root_.Function.LeftInvOn_invFunOn_of_subset_image_image [Nonempty α]
+theorem _root_.Function.leftInvOn_invFunOn_of_subset_image_image [Nonempty α]
     (h : s ⊆ (invFunOn f s) '' (f '' s)) : LeftInvOn (invFunOn f s) f s :=
   fun x hx ↦ by
     obtain ⟨-, ⟨x, hx', rfl⟩, rfl⟩ := h hx
@@ -1273,7 +1273,7 @@ theorem _root_.Function.LeftInvOn_invFunOn_of_subset_image_image [Nonempty α]
 theorem injOn_iff_invFunOn_image_image_eq_self [Nonempty α] :
     InjOn f s ↔ (invFunOn f s) '' (f '' s) = s :=
   ⟨fun h ↦ h.invFunOn_image Subset.rfl, fun h ↦
-    (Function.LeftInvOn_invFunOn_of_subset_image_image h.symm.subset).injOn⟩
+    (Function.leftInvOn_invFunOn_of_subset_image_image h.symm.subset).injOn⟩
 
 theorem _root_.Function.invFunOn_injOn_image [Nonempty α] (f : α → β) (s : Set α) :
     Set.InjOn (invFunOn f s) (f '' s) := 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

@@ -1737,8 +1737,7 @@ theorem monotoneOn_of_rightInvOn_of_mapsTo {α β : Sort _} [PartialOrder α] [L
 theorem antitoneOn_of_rightInvOn_of_mapsTo {α β : Sort _} [PartialOrder α] [LinearOrder β]
     {φ : β → α} {ψ : α → β} {t : Set β} {s : Set α} (hφ : AntitoneOn φ t)
     (φψs : Set.RightInvOn ψ φ s) (ψts : Set.MapsTo ψ s t) : AntitoneOn ψ s :=
-  MonotoneOn.dual_right (monotoneOn_of_rightInvOn_of_mapsTo (AntitoneOn.dual_left hφ) φψs ψts)
--- Porting note: dot notation for `*.dual_*` didn't work
+  (monotoneOn_of_rightInvOn_of_mapsTo hφ.dual_left φψs ψts).dual_right
 #align function.antitone_on_of_right_inv_on_of_maps_to Function.antitoneOn_of_rightInvOn_of_mapsTo
 
 end Function

feat: patch for new alias command (#6172)

19e0ba92

Diff

@@ -166,7 +166,7 @@ theorem injective_codRestrict {f : ι → α} {s : Set α} (h : ∀ x, f x ∈ s
   simp only [Injective, Subtype.ext_iff, val_codRestrict_apply]
 #align set.injective_cod_restrict Set.injective_codRestrict
 
-alias injective_codRestrict ↔ _ _root_.Function.Injective.codRestrict
+alias ⟨_, _root_.Function.Injective.codRestrict⟩ := injective_codRestrict
 #align function.injective.cod_restrict Function.Injective.codRestrict
 
 variable {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {p : Set γ} {f f₁ f₂ f₃ : α → β} {g g₁ g₂ : β → γ}
@@ -242,7 +242,7 @@ theorem eqOn_range {ι : Sort*} {f : ι → α} {g₁ g₂ : α → β} :
   forall_range_iff.trans <| funext_iff.symm
 #align set.eq_on_range Set.eqOn_range
 
-alias eqOn_range ↔ EqOn.comp_eq _
+alias ⟨EqOn.comp_eq, _⟩ := eqOn_range
 #align set.eq_on.comp_eq Set.EqOn.comp_eq
 
 /-! ### Congruence lemmas -/
@@ -582,9 +582,9 @@ lemma restrictPreimage_bijective (hf : Bijective f) : Bijective (t.restrictPreim
   ⟨t.restrictPreimage_injective hf.1, t.restrictPreimage_surjective hf.2⟩
 #align set.restrict_preimage_bijective Set.restrictPreimage_bijective
 
-alias Set.restrictPreimage_injective  ← _root_.Function.Injective.restrictPreimage
-alias Set.restrictPreimage_surjective ← _root_.Function.Surjective.restrictPreimage
-alias Set.restrictPreimage_bijective  ← _root_.Function.Bijective.restrictPreimage
+alias _root_.Function.Injective.restrictPreimage := Set.restrictPreimage_injective
+alias _root_.Function.Surjective.restrictPreimage := Set.restrictPreimage_surjective
+alias _root_.Function.Bijective.restrictPreimage := Set.restrictPreimage_bijective
 #align function.bijective.restrict_preimage Function.Bijective.restrictPreimage
 #align function.surjective.restrict_preimage Function.Surjective.restrictPreimage
 #align function.injective.restrict_preimage Function.Injective.restrictPreimage
@@ -620,7 +620,7 @@ theorem InjOn.ne_iff {x y} (h : InjOn f s) (hx : x ∈ s) (hy : y ∈ s) : f x 
   (h.eq_iff hx hy).not
 #align set.inj_on.ne_iff Set.InjOn.ne_iff
 
-alias InjOn.ne_iff ↔ _ InjOn.ne
+alias ⟨_, InjOn.ne⟩ := InjOn.ne_iff
 #align set.inj_on.ne Set.InjOn.ne
 
 theorem InjOn.congr (h₁ : InjOn f₁ s) (h : EqOn f₁ f₂ s) : InjOn f₂ s := fun _ hx _ hy =>
@@ -660,7 +660,7 @@ theorem injective_iff_injOn_univ : Injective f ↔ InjOn f univ :=
 theorem injOn_of_injective (h : Injective f) (s : Set α) : InjOn f s := fun _ _ _ _ hxy => h hxy
 #align set.inj_on_of_injective Set.injOn_of_injective
 
-alias injOn_of_injective ← _root_.Function.Injective.injOn
+alias _root_.Function.Injective.injOn := injOn_of_injective
 #align function.injective.inj_on Function.Injective.injOn
 
 -- A specialization of `injOn_of_injective` for `Subtype.val`.
@@ -694,7 +694,7 @@ theorem injOn_iff_injective : InjOn f s ↔ Injective (s.restrict f) :=
     congr_arg Subtype.val <| @H ⟨a, as⟩ ⟨b, bs⟩ h⟩
 #align set.inj_on_iff_injective Set.injOn_iff_injective
 
-alias Set.injOn_iff_injective ↔ InjOn.injective _
+alias ⟨InjOn.injective, _⟩ := Set.injOn_iff_injective
 #align set.inj_on.injective Set.InjOn.injective
 
 theorem MapsTo.restrict_inj (h : MapsTo f s t) : Injective (h.restrict f s t) ↔ InjOn f s := by
@@ -1017,7 +1017,7 @@ theorem bijective_iff_bijOn_univ : Bijective f ↔ BijOn f univ univ :=
     ⟨Iff.mpr injective_iff_injOn_univ inj, Iff.mpr surjective_iff_surjOn_univ surj⟩
 #align set.bijective_iff_bij_on_univ Set.bijective_iff_bijOn_univ
 
-alias bijective_iff_bijOn_univ ↔ _root_.Function.Bijective.bijOn_univ _
+alias ⟨_root_.Function.Bijective.bijOn_univ, _⟩ := bijective_iff_bijOn_univ
 #align function.bijective.bij_on_univ Function.Bijective.bijOn_univ
 
 theorem BijOn.compl (hst : BijOn f s t) (hf : Bijective f) : BijOn f sᶜ tᶜ :=
@@ -1608,7 +1608,7 @@ theorem strictMono_restrict [Preorder α] [Preorder β] {f : α → β} {s : Set
     StrictMono (s.restrict f) ↔ StrictMonoOn f s := by simp [Set.restrict, StrictMono, StrictMonoOn]
 #align strict_mono_restrict strictMono_restrict
 
-alias strictMono_restrict ↔ _root_.StrictMono.of_restrict _root_.StrictMonoOn.restrict
+alias ⟨_root_.StrictMono.of_restrict, _root_.StrictMonoOn.restrict⟩ := strictMono_restrict
 #align strict_mono.of_restrict StrictMono.of_restrict
 #align strict_mono_on.restrict StrictMonoOn.restrict
 
@@ -1807,7 +1807,7 @@ variable {e}
 @[simp] lemma bijOn_symm : BijOn e.symm t s ↔ BijOn e s t := bijOn_comm e.symm.invOn
 #align equiv.bij_on_symm Equiv.bijOn_symm
 
-alias bijOn_symm ↔ _root_.Set.BijOn.of_equiv_symm _root_.Set.BijOn.equiv_symm
+alias ⟨_root_.Set.BijOn.of_equiv_symm, _root_.Set.BijOn.equiv_symm⟩ := bijOn_symm
 #align set.bij_on.of_equiv_symm Set.BijOn.of_equiv_symm
 #align set.bij_on.equiv_symm Set.BijOn.equiv_symm

feat: add some symm attributes throughout the library (#6708)

Also add a couple of refl and trans attributes

20d6b8e6

Diff

@@ -1188,6 +1188,7 @@ lemma InvOn.comp (hf : InvOn f' f s t) (hg : InvOn g' g t p) (fst : MapsTo f s t
   ⟨hf.1.comp hg.1 fst, hf.2.comp hg.2 g'pt⟩
 #align set.inv_on.comp Set.InvOn.comp
 
+@[symm]
 theorem InvOn.symm (h : InvOn f' f s t) : InvOn f f' t s :=
   ⟨h.right, h.left⟩
 #align set.inv_on.symm Set.InvOn.symm

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

@@ -33,7 +33,7 @@ import Mathlib.Logic.Function.Conjugate
   and the codomain to `t`.
 -/
 
-variable {α β γ : Type _} {ι : Sort _} {π : α → Type _}
+variable {α β γ : Type*} {ι : Sort*} {π : α → Type*}
 
 open Equiv Equiv.Perm Function
 
@@ -237,7 +237,7 @@ theorem EqOn.comp_left (h : s.EqOn f₁ f₂) : s.EqOn (g ∘ f₁) (g ∘ f₂)
 #align set.eq_on.comp_left Set.EqOn.comp_left
 
 @[simp]
-theorem eqOn_range {ι : Sort _} {f : ι → α} {g₁ g₂ : α → β} :
+theorem eqOn_range {ι : Sort*} {f : ι → α} {g₁ g₂ : α → β} :
     EqOn g₁ g₂ (range f) ↔ g₁ ∘ f = g₂ ∘ f :=
   forall_range_iff.trans <| funext_iff.symm
 #align set.eq_on_range Set.eqOn_range
@@ -1374,7 +1374,7 @@ end Monotone
 
 namespace Set
 
-variable {δ : α → Sort _} (s : Set α) (f g : ∀ i, δ i)
+variable {δ : α → Sort*} (s : Set α) (f g : ∀ i, δ i)
 
 @[simp]
 theorem piecewise_empty [∀ i : α, Decidable (i ∈ (∅ : Set α))] : piecewise ∅ f g = g := by
@@ -1437,18 +1437,18 @@ theorem piecewise_eqOn_compl (f g : α → β) : EqOn (s.piecewise f g) g sᶜ :
   piecewise_eq_of_not_mem _ _ _
 #align set.piecewise_eq_on_compl Set.piecewise_eqOn_compl
 
-theorem piecewise_le {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
+theorem piecewise_le {δ : α → Type*} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g i) (h₂ : ∀ (i) (_ : i ∉ s), f₂ i ≤ g i) :
     s.piecewise f₁ f₂ ≤ g := fun i => if h : i ∈ s then by simp [*] else by simp [*]
 #align set.piecewise_le Set.piecewise_le
 
-theorem le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
+theorem le_piecewise {δ : α → Type*} [∀ i, Preorder (δ i)] {s : Set α} [∀ j, Decidable (j ∈ s)]
     {f₁ f₂ g : ∀ i, δ i} (h₁ : ∀ i ∈ s, g i ≤ f₁ i) (h₂ : ∀ (i) (_ : i ∉ s), g i ≤ f₂ i) :
     g ≤ s.piecewise f₁ f₂ :=
   @piecewise_le α (fun i => (δ i)ᵒᵈ) _ s _ _ _ _ h₁ h₂
 #align set.le_piecewise Set.le_piecewise
 
-theorem piecewise_le_piecewise {δ : α → Type _} [∀ i, Preorder (δ i)] {s : Set α}
+theorem piecewise_le_piecewise {δ : α → Type*} [∀ i, Preorder (δ i)] {s : Set α}
     [∀ j, Decidable (j ∈ s)] {f₁ f₂ g₁ g₂ : ∀ i, δ i} (h₁ : ∀ i ∈ s, f₁ i ≤ g₁ i)
     (h₂ : ∀ (i) (_ : i ∉ s), f₂ i ≤ g₂ i) : s.piecewise f₁ f₂ ≤ s.piecewise g₁ g₂ := by
   apply piecewise_le <;> intros <;> simp [*]
@@ -1465,7 +1465,7 @@ theorem piecewise_compl [∀ i, Decidable (i ∈ sᶜ)] : sᶜ.piecewise f g = s
 #align set.piecewise_compl Set.piecewise_compl
 
 @[simp]
-theorem piecewise_range_comp {ι : Sort _} (f : ι → α) [∀ j, Decidable (j ∈ range f)]
+theorem piecewise_range_comp {ι : Sort*} (f : ι → α) [∀ j, Decidable (j ∈ range f)]
     (g₁ g₂ : α → β) : (range f).piecewise g₁ g₂ ∘ f = g₁ ∘ f :=
   (piecewise_eqOn ..).comp_eq
 #align set.piecewise_range_comp Set.piecewise_range_comp
@@ -1499,24 +1499,24 @@ theorem piecewise_preimage (f g : α → β) (t) : s.piecewise f g ⁻¹' t = s.
   ext fun x => by by_cases x ∈ s <;> simp [*, Set.ite]
 #align set.piecewise_preimage Set.piecewise_preimage
 
-theorem apply_piecewise {δ' : α → Sort _} (h : ∀ i, δ i → δ' i) {x : α} :
+theorem apply_piecewise {δ' : α → Sort*} (h : ∀ i, δ i → δ' i) {x : α} :
     h x (s.piecewise f g x) = s.piecewise (fun x => h x (f x)) (fun x => h x (g x)) x := by
   by_cases hx : x ∈ s <;> simp [hx]
 #align set.apply_piecewise Set.apply_piecewise
 
-theorem apply_piecewise₂ {δ' δ'' : α → Sort _} (f' g' : ∀ i, δ' i) (h : ∀ i, δ i → δ' i → δ'' i)
+theorem apply_piecewise₂ {δ' δ'' : α → Sort*} (f' g' : ∀ i, δ' i) (h : ∀ i, δ i → δ' i → δ'' i)
     {x : α} :
     h x (s.piecewise f g x) (s.piecewise f' g' x) =
       s.piecewise (fun x => h x (f x) (f' x)) (fun x => h x (g x) (g' x)) x :=
   by by_cases hx : x ∈ s <;> simp [hx]
 #align set.apply_piecewise₂ Set.apply_piecewise₂
 
-theorem piecewise_op {δ' : α → Sort _} (h : ∀ i, δ i → δ' i) :
+theorem piecewise_op {δ' : α → Sort*} (h : ∀ i, δ i → δ' i) :
     (s.piecewise (fun x => h x (f x)) fun x => h x (g x)) = fun x => h x (s.piecewise f g x) :=
   funext fun _ => (apply_piecewise _ _ _ _).symm
 #align set.piecewise_op Set.piecewise_op
 
-theorem piecewise_op₂ {δ' δ'' : α → Sort _} (f' g' : ∀ i, δ' i) (h : ∀ i, δ i → δ' i → δ'' i) :
+theorem piecewise_op₂ {δ' δ'' : α → Sort*} (f' g' : ∀ i, δ' i) (h : ∀ i, δ i → δ' i → δ'' i) :
     (s.piecewise (fun x => h x (f x) (f' x)) fun x => h x (g x) (g' x)) = fun x =>
       h x (s.piecewise f g x) (s.piecewise f' g' x) :=
   funext fun _ => (apply_piecewise₂ _ _ _ _ _ _).symm
@@ -1545,24 +1545,24 @@ theorem injective_piecewise_iff {f g : α → β} :
   rw [piecewise_eq_of_mem s f g hx, piecewise_eq_of_not_mem s f g hy]
 #align set.injective_piecewise_iff Set.injective_piecewise_iff
 
-theorem piecewise_mem_pi {δ : α → Type _} {t : Set α} {t' : ∀ i, Set (δ i)} {f g} (hf : f ∈ pi t t')
+theorem piecewise_mem_pi {δ : α → Type*} {t : Set α} {t' : ∀ i, Set (δ i)} {f g} (hf : f ∈ pi t t')
     (hg : g ∈ pi t t') : s.piecewise f g ∈ pi t t' := by
   intro i ht
   by_cases hs : i ∈ s <;> simp [hf i ht, hg i ht, hs]
 #align set.piecewise_mem_pi Set.piecewise_mem_pi
 
 @[simp]
-theorem pi_piecewise {ι : Type _} {α : ι → Type _} (s s' : Set ι) (t t' : ∀ i, Set (α i))
+theorem pi_piecewise {ι : Type*} {α : ι → Type*} (s s' : Set ι) (t t' : ∀ i, Set (α i))
     [∀ x, Decidable (x ∈ s')] : pi s (s'.piecewise t t') = pi (s ∩ s') t ∩ pi (s \ s') t' :=
   pi_if _ _ _
 #align set.pi_piecewise Set.pi_piecewise
 
 -- porting note: new lemma
-theorem univ_pi_piecewise {ι : Type _} {α : ι → Type _} (s : Set ι) (t t' : ∀ i, Set (α i))
+theorem univ_pi_piecewise {ι : Type*} {α : ι → Type*} (s : Set ι) (t t' : ∀ i, Set (α i))
     [∀ x, Decidable (x ∈ s)] : pi univ (s.piecewise t t') = pi s t ∩ pi sᶜ t' := by
   simp [compl_eq_univ_diff]
 
-theorem univ_pi_piecewise_univ {ι : Type _} {α : ι → Type _} (s : Set ι) (t : ∀ i, Set (α i))
+theorem univ_pi_piecewise_univ {ι : Type*} {α : ι → Type*} (s : Set ι) (t : ∀ i, Set (α i))
     [∀ x, Decidable (x ∈ s)] : pi univ (s.piecewise t fun _ => univ) = pi s t := by simp
 #align set.univ_pi_piecewise Set.univ_pi_piecewise_univ
 
@@ -1705,7 +1705,7 @@ theorem injOn_preimage (h : Semiconj f fa fb) {s : Set β} (hb : InjOn fb s)
 
 end Semiconj
 
-theorem update_comp_eq_of_not_mem_range' {α β : Sort _} {γ : β → Sort _} [DecidableEq β]
+theorem update_comp_eq_of_not_mem_range' {α β : Sort _} {γ : β → Sort*} [DecidableEq β]
     (g : ∀ b, γ b) {f : α → β} {i : β} (a : γ i) (h : i ∉ Set.range f) :
     (fun j => (Function.update g i a) (f j)) = fun j => g (f j) :=
   (update_comp_eq_of_forall_ne' _ _) fun x hx => h ⟨x, hx⟩

feat: add instances for intervals (#5957)

Don't mind at all if anyone would like to push refactors or golfs. My main requirement from this PR is that

import Mathlib

example : WellFoundedLT { x : ℕ // x ≤ 37 }ᵒᵈ := inferInstance

works out of the box.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Matthew Robert Ballard <matt@mrb.email> Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jz Pan <acme_pjz@hotmail.com> Co-authored-by: Thomas Browning <tb65536@uw.edu> Co-authored-by: Oliver Nash <github@olivernash.org> Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Anatole Dedecker <anatolededecker@gmail.com> Co-authored-by: Matthew Robert Ballard <k.buzzard@imperial.ac.uk> Co-authored-by: Peter Nelson <71660771+apnelson1@users.noreply.github.com> Co-authored-by: Rémy Degenne <remydegenne@gmail.com> Co-authored-by: MohanadAhmed <m.a.m.elhassan@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: damiano <adomani@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com> Co-authored-by: Rémy Degenne <Remydegenne@gmail.com> Co-authored-by: Jon Eugster <eugster.jon@gmail.com> Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk>

50ce43f7

Diff

@@ -663,6 +663,10 @@ theorem injOn_of_injective (h : Injective f) (s : Set α) : InjOn f s := fun _ _
 alias injOn_of_injective ← _root_.Function.Injective.injOn
 #align function.injective.inj_on Function.Injective.injOn
 
+-- A specialization of `injOn_of_injective` for `Subtype.val`.
+theorem injOn_subtype_val {s : Set { x // p x }} : Set.InjOn Subtype.val s :=
+  Subtype.coe_injective.injOn s
+
 lemma injOn_id (s : Set α) : InjOn id s := injective_id.injOn _
 #align set.inj_on_id Set.injOn_id

feat(Data.Set.Ncard): enat set cardinality (#5908)

This PR is a second attempt at defining the cardinality of a set as extended natural number, with a function encard. The implementation involves a refactor, where the existingncard function is redefined in terms of encard. This shortens a lot of proofs, reduces reliance on the Finset API, and allows for a potential future refactor where ncard is removed if it is decided to be redundant.

Co-authored-by: Jireh Loreaux <loreaujy@gmail.com>

444b9f33

Diff

@@ -1259,6 +1259,26 @@ theorem InjOn.invFunOn_image [Nonempty α] (h : InjOn f s₂) (ht : s₁ ⊆ s
   h.leftInvOn_invFunOn.image_image' ht
 #align set.inj_on.inv_fun_on_image Set.InjOn.invFunOn_image
 
+theorem _root_.Function.LeftInvOn_invFunOn_of_subset_image_image [Nonempty α]
+    (h : s ⊆ (invFunOn f s) '' (f '' s)) : LeftInvOn (invFunOn f s) f s :=
+  fun x hx ↦ by
+    obtain ⟨-, ⟨x, hx', rfl⟩, rfl⟩ := h hx
+    rw [invFunOn_apply_eq (f := f) hx']
+
+theorem injOn_iff_invFunOn_image_image_eq_self [Nonempty α] :
+    InjOn f s ↔ (invFunOn f s) '' (f '' s) = s :=
+  ⟨fun h ↦ h.invFunOn_image Subset.rfl, fun h ↦
+    (Function.LeftInvOn_invFunOn_of_subset_image_image h.symm.subset).injOn⟩
+
+theorem _root_.Function.invFunOn_injOn_image [Nonempty α] (f : α → β) (s : Set α) :
+    Set.InjOn (invFunOn f s) (f '' s) := by
+  rintro _ ⟨x, hx, rfl⟩ _ ⟨x', hx', rfl⟩ he
+  rw [←invFunOn_apply_eq (f := f) hx, he, invFunOn_apply_eq (f := f) hx']
+
+theorem _root_.Function.invFunOn_image_image_subset [Nonempty α] (f : α → β) (s : Set α) :
+    (invFunOn f s) '' (f '' s) ⊆ s := by
+  rintro _ ⟨_, ⟨x,hx,rfl⟩, rfl⟩; exact invFunOn_apply_mem hx
+
 theorem SurjOn.rightInvOn_invFunOn [Nonempty α] (h : SurjOn f s t) :
     RightInvOn (invFunOn f s) f t := fun _y hy => invFunOn_eq <| h hy
 #align set.surj_on.right_inv_on_inv_fun_on Set.SurjOn.rightInvOn_invFunOn

chore: tidy various files (#6158)

0bcfc2d2

Diff

@@ -448,8 +448,8 @@ theorem MapsTo.iterate_restrict {f : α → α} {s : Set α} (h : MapsTo f s s)
 #align set.maps_to.iterate_restrict Set.MapsTo.iterate_restrict
 
 lemma mapsTo_of_subsingleton' [Subsingleton β] (f : α → β) (h : s.Nonempty → t.Nonempty) :
-  MapsTo f s t :=
-fun a ha ↦ Subsingleton.mem_iff_nonempty.2 $ h ⟨a, ha⟩
+    MapsTo f s t :=
+  fun a ha ↦ Subsingleton.mem_iff_nonempty.2 $ h ⟨a, ha⟩
 #align set.maps_to_of_subsingleton' Set.mapsTo_of_subsingleton'
 
 lemma mapsTo_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : MapsTo f s s :=
@@ -671,9 +671,9 @@ theorem InjOn.comp (hg : InjOn g t) (hf : InjOn f s) (h : MapsTo f s t) : InjOn
 #align set.inj_on.comp Set.InjOn.comp
 
 lemma InjOn.iterate {f : α → α} {s : Set α} (h : InjOn f s) (hf : MapsTo f s s) :
-  ∀ n, InjOn f^[n] s
-| 0 => injOn_id _
-| (n + 1) => (h.iterate hf n).comp h hf
+    ∀ n, InjOn f^[n] s
+  | 0 => injOn_id _
+  | (n + 1) => (h.iterate hf n).comp h hf
 #align set.inj_on.iterate Set.InjOn.iterate
 
 lemma injOn_of_subsingleton [Subsingleton α] (f : α → β) (s : Set α) : InjOn f s :=
@@ -841,13 +841,13 @@ lemma SurjOn.comp_left (hf : SurjOn f s t) (g : β → γ) : SurjOn (g ∘ f) s
 #align set.surj_on.comp_left Set.SurjOn.comp_left
 
 lemma SurjOn.comp_right {s : Set β} {t : Set γ} (hf : Surjective f) (hg : SurjOn g s t) :
-  SurjOn (g ∘ f) (f ⁻¹' s) t :=
-by rwa [SurjOn, image_comp g f, image_preimage_eq _ hf]
+    SurjOn (g ∘ f) (f ⁻¹' s) t := by
+  rwa [SurjOn, image_comp g f, image_preimage_eq _ hf]
 #align set.surj_on.comp_right Set.SurjOn.comp_right
 
 lemma surjOn_of_subsingleton' [Subsingleton β] (f : α → β) (h : t.Nonempty → s.Nonempty) :
-  SurjOn f s t :=
-fun _ ha ↦ Subsingleton.mem_iff_nonempty.2 $ (h ⟨_, ha⟩).image _
+    SurjOn f s t :=
+  fun _ ha ↦ Subsingleton.mem_iff_nonempty.2 $ (h ⟨_, ha⟩).image _
 #align set.surj_on_of_subsingleton' Set.surjOn_of_subsingleton'
 
 lemma surjOn_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : SurjOn f s s :=
@@ -989,8 +989,8 @@ lemma BijOn.iterate {f : α → α} {s : Set α} (h : BijOn f s s) : ∀ n, BijO
 #align set.bij_on.iterate Set.BijOn.iterate
 
 lemma bijOn_of_subsingleton' [Subsingleton α] [Subsingleton β] (f : α → β)
-  (h : s.Nonempty ↔ t.Nonempty) : BijOn f s t :=
-⟨mapsTo_of_subsingleton' _ h.1, injOn_of_subsingleton _ _, surjOn_of_subsingleton' _ h.2⟩
+    (h : s.Nonempty ↔ t.Nonempty) : BijOn f s t :=
+  ⟨mapsTo_of_subsingleton' _ h.1, injOn_of_subsingleton _ _, surjOn_of_subsingleton' _ h.2⟩
 #align set.bij_on_of_subsingleton' Set.bijOn_of_subsingleton'
 
 lemma bijOn_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : BijOn f s s :=
@@ -1179,9 +1179,9 @@ lemma invOn_id (s : Set α) : InvOn id id s s := ⟨s.leftInvOn_id, s.rightInvOn
 #align set.inv_on_id Set.invOn_id
 
 lemma InvOn.comp (hf : InvOn f' f s t) (hg : InvOn g' g t p) (fst : MapsTo f s t)
-  (g'pt : MapsTo g' p t) :
-  InvOn (f' ∘ g') (g ∘ f) s p :=
-⟨hf.1.comp hg.1 fst, hf.2.comp hg.2 g'pt⟩
+    (g'pt : MapsTo g' p t) :
+    InvOn (f' ∘ g') (g ∘ f) s p :=
+  ⟨hf.1.comp hg.1 fst, hf.2.comp hg.2 g'pt⟩
 #align set.inv_on.comp Set.InvOn.comp
 
 theorem InvOn.symm (h : InvOn f' f s t) : InvOn f f' t s :=
@@ -1724,35 +1724,35 @@ namespace Set
 variable {p : β → Prop} [DecidablePred p] {f : α ≃ Subtype p} {g g₁ g₂ : Perm α} {s t : Set α}
 
 protected lemma MapsTo.extendDomain (h : MapsTo g s t) :
-  MapsTo (g.extendDomain f) ((↑) ∘ f '' s) ((↑) ∘ f '' t) := by
+    MapsTo (g.extendDomain f) ((↑) ∘ f '' s) ((↑) ∘ f '' t) := by
   rintro _ ⟨a, ha, rfl⟩; exact ⟨_, h ha, by simp_rw [Function.comp_apply, extendDomain_apply_image]⟩
 #align set.maps_to.extend_domain Set.MapsTo.extendDomain
 
 protected lemma SurjOn.extendDomain (h : SurjOn g s t) :
-  SurjOn (g.extendDomain f) ((↑) ∘ f '' s) ((↑) ∘ f '' t) := by
+    SurjOn (g.extendDomain f) ((↑) ∘ f '' s) ((↑) ∘ f '' t) := by
   rintro _ ⟨a, ha, rfl⟩
   obtain ⟨b, hb, rfl⟩ := h ha
   exact ⟨_, ⟨_, hb, rfl⟩, by simp_rw [Function.comp_apply, extendDomain_apply_image]⟩
 #align set.surj_on.extend_domain Set.SurjOn.extendDomain
 
 protected lemma BijOn.extendDomain (h : BijOn g s t) :
-  BijOn (g.extendDomain f) ((↑) ∘ f '' s) ((↑) ∘ f '' t) :=
-⟨h.mapsTo.extendDomain, (g.extendDomain f).injective.injOn _, h.surjOn.extendDomain⟩
+    BijOn (g.extendDomain f) ((↑) ∘ f '' s) ((↑) ∘ f '' t) :=
+  ⟨h.mapsTo.extendDomain, (g.extendDomain f).injective.injOn _, h.surjOn.extendDomain⟩
 #align set.bij_on.extend_domain Set.BijOn.extendDomain
 
 protected lemma LeftInvOn.extendDomain (h : LeftInvOn g₁ g₂ s) :
-  LeftInvOn (g₁.extendDomain f) (g₂.extendDomain f) ((↑) ∘ f '' s) := by
+    LeftInvOn (g₁.extendDomain f) (g₂.extendDomain f) ((↑) ∘ f '' s) := by
   rintro _ ⟨a, ha, rfl⟩; simp_rw [Function.comp_apply, extendDomain_apply_image, h ha]
 #align set.left_inv_on.extend_domain Set.LeftInvOn.extendDomain
 
 protected lemma RightInvOn.extendDomain (h : RightInvOn g₁ g₂ t) :
-  RightInvOn (g₁.extendDomain f) (g₂.extendDomain f) ((↑) ∘ f '' t) := by
+    RightInvOn (g₁.extendDomain f) (g₂.extendDomain f) ((↑) ∘ f '' t) := by
   rintro _ ⟨a, ha, rfl⟩; simp_rw [Function.comp_apply, extendDomain_apply_image, h ha]
 #align set.right_inv_on.extend_domain Set.RightInvOn.extendDomain
 
 protected lemma InvOn.extendDomain (h : InvOn g₁ g₂ s t) :
-  InvOn (g₁.extendDomain f) (g₂.extendDomain f) ((↑) ∘ f '' s) ((↑) ∘ f '' t) :=
-⟨h.1.extendDomain, h.2.extendDomain⟩
+    InvOn (g₁.extendDomain f) (g₂.extendDomain f) ((↑) ∘ f '' s) ((↑) ∘ f '' t) :=
+  ⟨h.1.extendDomain, h.2.extendDomain⟩
 #align set.inv_on.extend_domain Set.InvOn.extendDomain
 
 end Set
@@ -1789,8 +1789,10 @@ alias bijOn_symm ↔ _root_.Set.BijOn.of_equiv_symm _root_.Set.BijOn.equiv_symm
 variable [DecidableEq α] {a b : α}
 
 lemma bijOn_swap (ha : a ∈ s) (hb : b ∈ s) : BijOn (swap a b) s s :=
-  (swap a b).bijOn $ fun x ↦ by obtain rfl | hxa := eq_or_ne x a <;>
-    obtain rfl | hxb := eq_or_ne x b <;> simp [*, swap_apply_of_ne_of_ne]
+  (swap a b).bijOn $ fun x ↦ by
+    obtain rfl | hxa := eq_or_ne x a <;>
+    obtain rfl | hxb := eq_or_ne x b <;>
+    simp [*, swap_apply_of_ne_of_ne]
 #align equiv.bij_on_swap Equiv.bijOn_swap
 
 end Equiv

feat(Topology.Constructions): restriction of a closed map (#6013)

88fb181b

Diff

@@ -350,6 +350,10 @@ def MapsTo.restrict (f : α → β) (s : Set α) (t : Set β) (h : MapsTo f s t)
   Subtype.map f h
 #align set.maps_to.restrict Set.MapsTo.restrict
 
+theorem MapsTo.restrict_commutes (f : α → β) (s : Set α) (t : Set β) (h : MapsTo f s t) :
+    Subtype.val ∘ h.restrict f s t = f ∘ Subtype.val :=
+  rfl
+
 @[simp]
 theorem MapsTo.val_restrict_apply (h : MapsTo f s t) (x : s) : (h.restrict f s t x : β) = f x :=
   rfl

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) 2014 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
-
-! This file was ported from Lean 3 source module data.set.function
-! leanprover-community/mathlib commit 996b0ff959da753a555053a480f36e5f264d4207
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Set.Prod
 import Mathlib.Logic.Function.Conjugate
 
+#align_import data.set.function from "leanprover-community/mathlib"@"996b0ff959da753a555053a480f36e5f264d4207"
+
 /-!
 # Functions over sets

fix: restore Set.eqOn_singleton (#5754)

c4bb14cb

Diff

@@ -188,6 +188,11 @@ def EqOn (f₁ f₂ : α → β) (s : Set α) : Prop :=
 theorem eqOn_empty (f₁ f₂ : α → β) : EqOn f₁ f₂ ∅ := fun _ => False.elim
 #align set.eq_on_empty Set.eqOn_empty
 
+@[simp]
+theorem eqOn_singleton : Set.EqOn f₁ f₂ {a} ↔ f₁ a = f₂ a := by
+  simp [Set.EqOn]
+#align set.eq_on_singleton Set.eqOn_singleton
+
 @[simp]
 theorem restrict_eq_restrict_iff : restrict s f₁ = restrict s f₂ ↔ EqOn f₁ f₂ s :=
   restrict_eq_iff

fix: change compl precedence (#5586)

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

4d4f0f25

Diff

@@ -125,13 +125,13 @@ theorem restrict_extend_range (f : α → β) (g : α → γ) (g' : β → γ) :
 
 @[simp]
 theorem restrict_extend_compl_range (f : α → β) (g : α → γ) (g' : β → γ) :
-    range fᶜ.restrict (extend f g g') = g' ∘ Subtype.val := by
+    (range f)ᶜ.restrict (extend f g g') = g' ∘ Subtype.val := by
   classical
   exact restrict_dite_compl _ _
 #align set.restrict_extend_compl_range Set.restrict_extend_compl_range
 
 theorem range_extend_subset (f : α → β) (g : α → γ) (g' : β → γ) :
-    range (extend f g g') ⊆ range g ∪ g' '' range fᶜ := by
+    range (extend f g g') ⊆ range g ∪ g' '' (range f)ᶜ := by
   classical
   rintro _ ⟨y, rfl⟩
   rw [extend_def]
@@ -140,7 +140,7 @@ theorem range_extend_subset (f : α → β) (g : α → γ) (g' : β → γ) :
 #align set.range_extend_subset Set.range_extend_subset
 
 theorem range_extend {f : α → β} (hf : Injective f) (g : α → γ) (g' : β → γ) :
-    range (extend f g g') = range g ∪ g' '' range fᶜ := by
+    range (extend f g g') = range g ∪ g' '' (range f)ᶜ := by
   refine' (range_extend_subset _ _ _).antisymm _
   rintro z (⟨x, rfl⟩ | ⟨y, hy, rfl⟩)
   exacts [⟨f x, hf.extend_apply _ _ _⟩, ⟨y, extend_apply' _ _ _ hy⟩]
@@ -538,7 +538,7 @@ theorem surjective_mapsTo_image_restrict (f : α → β) (s : Set α) :
   ⟨⟨x, hs⟩, Subtype.ext hxy⟩
 #align set.surjective_maps_to_image_restrict Set.surjective_mapsTo_image_restrict
 
-theorem MapsTo.mem_iff (h : MapsTo f s t) (hc : MapsTo f (sᶜ) (tᶜ)) {x} : f x ∈ t ↔ x ∈ s :=
+theorem MapsTo.mem_iff (h : MapsTo f s t) (hc : MapsTo f sᶜ tᶜ) {x} : f x ∈ t ↔ x ∈ s :=
   ⟨fun ht => by_contra fun hs => hc hs ht, fun hx => h hx⟩
 #align set.maps_to.mem_iff Set.MapsTo.mem_iff
 
@@ -871,13 +871,13 @@ theorem image_eq_iff_surjOn_mapsTo : f '' s = t ↔ s.SurjOn f t ∧ s.MapsTo f
   exact ⟨s.surjOn_image f, s.mapsTo_image f⟩
 #align set.image_eq_iff_surj_on_maps_to Set.image_eq_iff_surjOn_mapsTo
 
-theorem SurjOn.mapsTo_compl (h : SurjOn f s t) (h' : Injective f) : MapsTo f (sᶜ) (tᶜ) :=
+theorem SurjOn.mapsTo_compl (h : SurjOn f s t) (h' : Injective f) : MapsTo f sᶜ tᶜ :=
   fun _ hs ht =>
   let ⟨_, hx', HEq⟩ := h ht
   hs <| h' HEq ▸ hx'
 #align set.surj_on.maps_to_compl Set.SurjOn.mapsTo_compl
 
-theorem MapsTo.surjOn_compl (h : MapsTo f s t) (h' : Surjective f) : SurjOn f (sᶜ) (tᶜ) :=
+theorem MapsTo.surjOn_compl (h : MapsTo f s t) (h' : Surjective f) : SurjOn f sᶜ tᶜ :=
   h'.forall.2 fun _ ht => (mem_image_of_mem _) fun hs => ht (h hs)
 #align set.maps_to.surj_on_compl Set.MapsTo.surjOn_compl
 
@@ -1010,7 +1010,7 @@ theorem bijective_iff_bijOn_univ : Bijective f ↔ BijOn f univ univ :=
 alias bijective_iff_bijOn_univ ↔ _root_.Function.Bijective.bijOn_univ _
 #align function.bijective.bij_on_univ Function.Bijective.bijOn_univ
 
-theorem BijOn.compl (hst : BijOn f s t) (hf : Bijective f) : BijOn f (sᶜ) (tᶜ) :=
+theorem BijOn.compl (hst : BijOn f s t) (hf : Bijective f) : BijOn f sᶜ tᶜ :=
   ⟨hst.surjOn.mapsTo_compl hf.1, hf.1.injOn _, hst.mapsTo.surjOn_compl hf.2⟩
 #align set.bij_on.compl Set.BijOn.compl
 
@@ -1290,7 +1290,7 @@ theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _) (_ : s' 
 #align set.surj_on_iff_exists_bij_on_subset Set.surjOn_iff_exists_bijOn_subset
 
 theorem preimage_invFun_of_mem [n : Nonempty α] {f : α → β} (hf : Injective f) {s : Set α}
-    (h : Classical.choice n ∈ s) : invFun f ⁻¹' s = f '' s ∪ range fᶜ := by
+    (h : Classical.choice n ∈ s) : invFun f ⁻¹' s = f '' s ∪ (range f)ᶜ := by
   ext x
   rcases em (x ∈ range f) with (⟨a, rfl⟩ | hx)
   · simp only [mem_preimage, mem_union, mem_compl_iff, mem_range_self, not_true, or_false,
@@ -1403,7 +1403,7 @@ theorem piecewise_eqOn (f g : α → β) : EqOn (s.piecewise f g) f s := fun _ =
   piecewise_eq_of_mem _ _ _
 #align set.piecewise_eq_on Set.piecewise_eqOn
 
-theorem piecewise_eqOn_compl (f g : α → β) : EqOn (s.piecewise f g) g (sᶜ) := fun _ =>
+theorem piecewise_eqOn_compl (f g : α → β) : EqOn (s.piecewise f g) g sᶜ := fun _ =>
   piecewise_eq_of_not_mem _ _ _
 #align set.piecewise_eq_on_compl Set.piecewise_eqOn_compl
 
@@ -1508,7 +1508,7 @@ theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪
 
 theorem injective_piecewise_iff {f g : α → β} :
     Injective (s.piecewise f g) ↔
-      InjOn f s ∧ InjOn g (sᶜ) ∧ ∀ x ∈ s, ∀ (y) (_ : y ∉ s), f x ≠ g y := by
+      InjOn f s ∧ InjOn g sᶜ ∧ ∀ x ∈ s, ∀ (y) (_ : y ∉ s), f x ≠ g y := by
   rw [injective_iff_injOn_univ, ← union_compl_self s, injOn_union (@disjoint_compl_right _ _ s),
     (piecewise_eqOn s f g).injOn_iff, (piecewise_eqOn_compl s f g).injOn_iff]
   refine' and_congr Iff.rfl (and_congr Iff.rfl <| forall₄_congr fun x hx y hy => _)
@@ -1529,7 +1529,7 @@ theorem pi_piecewise {ι : Type _} {α : ι → Type _} (s s' : Set ι) (t t' :
 
 -- porting note: new lemma
 theorem univ_pi_piecewise {ι : Type _} {α : ι → Type _} (s : Set ι) (t t' : ∀ i, Set (α i))
-    [∀ x, Decidable (x ∈ s)] : pi univ (s.piecewise t t') = pi s t ∩ pi (sᶜ) t' := by
+    [∀ x, Decidable (x ∈ s)] : pi univ (s.piecewise t t') = pi s t ∩ pi sᶜ t' := by
   simp [compl_eq_univ_diff]
 
 theorem univ_pi_piecewise_univ {ι : Type _} {α : ι → Type _} (s : Set ι) (t : ∀ i, Set (α i))

fix precedence of Nat.iterate (#5589)

bd2fff86

Diff

@@ -427,13 +427,13 @@ theorem MapsTo.comp (h₁ : MapsTo g t p) (h₂ : MapsTo f s t) : MapsTo (g ∘
 theorem mapsTo_id (s : Set α) : MapsTo id s s := fun _ => id
 #align set.maps_to_id Set.mapsTo_id
 
-theorem MapsTo.iterate {f : α → α} {s : Set α} (h : MapsTo f s s) : ∀ n, MapsTo (f^[n]) s s
+theorem MapsTo.iterate {f : α → α} {s : Set α} (h : MapsTo f s s) : ∀ n, MapsTo f^[n] s s
   | 0 => fun _ => id
   | n + 1 => (MapsTo.iterate h n).comp h
 #align set.maps_to.iterate Set.MapsTo.iterate
 
 theorem MapsTo.iterate_restrict {f : α → α} {s : Set α} (h : MapsTo f s s) (n : ℕ) :
-    h.restrict f s s^[n] = (h.iterate n).restrict _ _ _ := by
+    (h.restrict f s s)^[n] = (h.iterate n).restrict _ _ _ := by
   funext x
   rw [Subtype.ext_iff, MapsTo.val_restrict_apply]
   induction' n with n ihn generalizing x
@@ -665,7 +665,7 @@ theorem InjOn.comp (hg : InjOn g t) (hf : InjOn f s) (h : MapsTo f s t) : InjOn
 #align set.inj_on.comp Set.InjOn.comp
 
 lemma InjOn.iterate {f : α → α} {s : Set α} (h : InjOn f s) (hf : MapsTo f s s) :
-  ∀ n, InjOn (f^[n]) s
+  ∀ n, InjOn f^[n] s
 | 0 => injOn_id _
 | (n + 1) => (h.iterate hf n).comp h hf
 #align set.inj_on.iterate Set.InjOn.iterate
@@ -825,7 +825,7 @@ theorem SurjOn.comp (hg : SurjOn g t p) (hf : SurjOn f s t) : SurjOn (g ∘ f) s
   Subset.trans hg <| Subset.trans (image_subset g hf) <| image_comp g f s ▸ Subset.refl _
 #align set.surj_on.comp Set.SurjOn.comp
 
-lemma SurjOn.iterate {f : α → α} {s : Set α} (h : SurjOn f s s) : ∀ n, SurjOn (f^[n]) s s
+lemma SurjOn.iterate {f : α → α} {s : Set α} (h : SurjOn f s s) : ∀ n, SurjOn f^[n] s s
   | 0 => surjOn_id _
   | (n + 1) => (h.iterate n).comp h
 #align set.surj_on.iterate Set.SurjOn.iterate
@@ -977,7 +977,7 @@ theorem BijOn.comp (hg : BijOn g t p) (hf : BijOn f s t) : BijOn (g ∘ f) s p :
   BijOn.mk (hg.mapsTo.comp hf.mapsTo) (hg.injOn.comp hf.injOn hf.mapsTo) (hg.surjOn.comp hf.surjOn)
 #align set.bij_on.comp Set.BijOn.comp
 
-lemma BijOn.iterate {f : α → α} {s : Set α} (h : BijOn f s s) : ∀ n, BijOn (f^[n]) s s
+lemma BijOn.iterate {f : α → α} {s : Set α} (h : BijOn f s s) : ∀ n, BijOn f^[n] s s
   | 0 => s.bijOn_id
   | (n + 1) => (h.iterate n).comp h
 #align set.bij_on.iterate Set.BijOn.iterate

chore: formatting issues (#4947)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

5068808d

Diff

@@ -447,7 +447,7 @@ fun a ha ↦ Subsingleton.mem_iff_nonempty.2 $ h ⟨a, ha⟩
 #align set.maps_to_of_subsingleton' Set.mapsTo_of_subsingleton'
 
 lemma mapsTo_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : MapsTo f s s :=
-mapsTo_of_subsingleton' _ id
+  mapsTo_of_subsingleton' _ id
 #align set.maps_to_of_subsingleton Set.mapsTo_of_subsingleton
 
 theorem MapsTo.mono (hf : MapsTo f s₁ t₁) (hs : s₂ ⊆ s₁) (ht : t₁ ⊆ t₂) : MapsTo f s₂ t₂ :=
@@ -516,7 +516,7 @@ theorem maps_image_to (f : α → β) (g : γ → α) (s : Set γ) (t : Set β)
 #align set.maps_image_to Set.maps_image_to
 
 lemma MapsTo.comp_left (g : β → γ) (hf : MapsTo f s t) : MapsTo (g ∘ f) s (g '' t) :=
-fun x hx ↦ ⟨f x, hf hx, rfl⟩
+  fun x hx ↦ ⟨f x, hf hx, rfl⟩
 #align set.maps_to.comp_left Set.MapsTo.comp_left
 
 lemma MapsTo.comp_right {s : Set β} {t : Set γ} (hg : MapsTo g s t) (f : α → β) :
@@ -671,7 +671,7 @@ lemma InjOn.iterate {f : α → α} {s : Set α} (h : InjOn f s) (hf : MapsTo f
 #align set.inj_on.iterate Set.InjOn.iterate
 
 lemma injOn_of_subsingleton [Subsingleton α] (f : α → β) (s : Set α) : InjOn f s :=
-(injective_of_subsingleton _).injOn _
+  (injective_of_subsingleton _).injOn _
 #align set.inj_on_of_subsingleton Set.injOn_of_subsingleton
 
 theorem _root_.Function.Injective.injOn_range (h : Injective (g ∘ f)) : InjOn g (range f) := by
@@ -758,7 +758,7 @@ theorem SurjOn.subset_range (h : SurjOn f s t) : t ⊆ range f :=
 #align set.surj_on.subset_range Set.SurjOn.subset_range
 
 theorem surjOn_iff_exists_map_subtype :
-    SurjOn f s t ↔ ∃ (t' : Set β)(g : s → t'), t ⊆ t' ∧ Surjective g ∧ ∀ x : s, f x = g x :=
+    SurjOn f s t ↔ ∃ (t' : Set β) (g : s → t'), t ⊆ t' ∧ Surjective g ∧ ∀ x : s, f x = g x :=
   ⟨fun h =>
     ⟨_, (mapsTo_image f s).restrict f s _, h, surjective_mapsTo_image_restrict _ _, fun _ => rfl⟩,
     fun ⟨t', g, htt', hg, hfg⟩ y hy =>
@@ -826,8 +826,8 @@ theorem SurjOn.comp (hg : SurjOn g t p) (hf : SurjOn f s t) : SurjOn (g ∘ f) s
 #align set.surj_on.comp Set.SurjOn.comp
 
 lemma SurjOn.iterate {f : α → α} {s : Set α} (h : SurjOn f s s) : ∀ n, SurjOn (f^[n]) s s
-| 0 => surjOn_id _
-| (n + 1) => (h.iterate n).comp h
+  | 0 => surjOn_id _
+  | (n + 1) => (h.iterate n).comp h
 #align set.surj_on.iterate Set.SurjOn.iterate
 
 lemma SurjOn.comp_left (hf : SurjOn f s t) (g : β → γ) : SurjOn (g ∘ f) s (g '' t) := by
@@ -845,7 +845,7 @@ fun _ ha ↦ Subsingleton.mem_iff_nonempty.2 $ (h ⟨_, ha⟩).image _
 #align set.surj_on_of_subsingleton' Set.surjOn_of_subsingleton'
 
 lemma surjOn_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : SurjOn f s s :=
-surjOn_of_subsingleton' _ id
+  surjOn_of_subsingleton' _ id
 #align set.surj_on_of_subsingleton Set.surjOn_of_subsingleton
 
 theorem surjective_iff_surjOn_univ : Surjective f ↔ SurjOn f univ univ := by
@@ -978,8 +978,8 @@ theorem BijOn.comp (hg : BijOn g t p) (hf : BijOn f s t) : BijOn (g ∘ f) s p :
 #align set.bij_on.comp Set.BijOn.comp
 
 lemma BijOn.iterate {f : α → α} {s : Set α} (h : BijOn f s s) : ∀ n, BijOn (f^[n]) s s
-| 0 => s.bijOn_id
-| (n + 1) => (h.iterate n).comp h
+  | 0 => s.bijOn_id
+  | (n + 1) => (h.iterate n).comp h
 #align set.bij_on.iterate Set.BijOn.iterate
 
 lemma bijOn_of_subsingleton' [Subsingleton α] [Subsingleton β] (f : α → β)
@@ -988,7 +988,7 @@ lemma bijOn_of_subsingleton' [Subsingleton α] [Subsingleton β] (f : α → β)
 #align set.bij_on_of_subsingleton' Set.bijOn_of_subsingleton'
 
 lemma bijOn_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : BijOn f s s :=
-bijOn_of_subsingleton' _ Iff.rfl
+  bijOn_of_subsingleton' _ Iff.rfl
 #align set.bij_on_of_subsingleton Set.bijOn_of_subsingleton
 
 theorem BijOn.bijective (h : BijOn f s t) : Bijective (h.mapsTo.restrict f s t) :=
@@ -1278,7 +1278,7 @@ theorem SurjOn.bijOn_subset [Nonempty α] (h : SurjOn f s t) : BijOn f (invFunOn
   rwa [h.rightInvOn_invFunOn hy]
 #align set.surj_on.bij_on_subset Set.SurjOn.bijOn_subset
 
-theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _)(_ : s' ⊆ s), BijOn f s' t := by
+theorem surjOn_iff_exists_bijOn_subset : SurjOn f s t ↔ ∃ (s' : _) (_ : s' ⊆ s), BijOn f s' t := by
   constructor
   · rcases eq_empty_or_nonempty t with (rfl | ht)
     · exact fun _ => ⟨∅, empty_subset _, bijOn_empty f⟩
@@ -1308,11 +1308,11 @@ theorem preimage_invFun_of_not_mem [n : Nonempty α] {f : α → β} (hf : Injec
 #align set.preimage_inv_fun_of_not_mem Set.preimage_invFun_of_not_mem
 
 lemma BijOn.symm {g : β → α} (h : InvOn f g t s) (hf : BijOn f s t) : BijOn g t s :=
-⟨h.2.mapsTo hf.surjOn, h.1.injOn, h.2.surjOn hf.mapsTo⟩
+  ⟨h.2.mapsTo hf.surjOn, h.1.injOn, h.2.surjOn hf.mapsTo⟩
 #align set.bij_on.symm Set.BijOn.symm
 
 lemma bijOn_comm {g : β → α} (h : InvOn f g t s) : BijOn f s t ↔ BijOn g t s :=
-⟨BijOn.symm h, BijOn.symm h.symm⟩
+  ⟨BijOn.symm h, BijOn.symm h.symm⟩
 #align set.bij_on_comm Set.bijOn_comm
 
 end Set
@@ -1755,15 +1755,15 @@ namespace Equiv
 variable (e : α ≃ β) {s : Set α} {t : Set β}
 
 lemma bijOn' (h₁ : MapsTo e s t) (h₂ : MapsTo e.symm t s) : BijOn e s t :=
-⟨h₁, e.injective.injOn _, fun b hb ↦ ⟨e.symm b, h₂ hb, apply_symm_apply _ _⟩⟩
+  ⟨h₁, e.injective.injOn _, fun b hb ↦ ⟨e.symm b, h₂ hb, apply_symm_apply _ _⟩⟩
 #align equiv.bij_on' Equiv.bijOn'
 
 protected lemma bijOn (h : ∀ a, e a ∈ t ↔ a ∈ s) : BijOn e s t :=
-e.bijOn' (fun a ↦ (h _).2) $ fun b hb ↦ (h _).1 $ by rwa [apply_symm_apply]
+  e.bijOn' (fun a ↦ (h _).2) $ fun b hb ↦ (h _).1 $ by rwa [apply_symm_apply]
 #align equiv.bij_on Equiv.bijOn
 
 lemma invOn : InvOn e e.symm t s :=
-⟨e.rightInverse_symm.leftInvOn _, e.leftInverse_symm.leftInvOn _⟩
+  ⟨e.rightInverse_symm.leftInvOn _, e.leftInverse_symm.leftInvOn _⟩
 #align equiv.inv_on Equiv.invOn
 
 lemma bijOn_image : BijOn e s (e '' s) := (e.injective.injOn _).bijOn_image
@@ -1783,8 +1783,8 @@ alias bijOn_symm ↔ _root_.Set.BijOn.of_equiv_symm _root_.Set.BijOn.equiv_symm
 variable [DecidableEq α] {a b : α}
 
 lemma bijOn_swap (ha : a ∈ s) (hb : b ∈ s) : BijOn (swap a b) s s :=
-(swap a b).bijOn $ fun x ↦ by obtain rfl | hxa := eq_or_ne x a <;>
-  obtain rfl | hxb := eq_or_ne x b <;> simp [*, swap_apply_of_ne_of_ne]
+  (swap a b).bijOn $ fun x ↦ by obtain rfl | hxa := eq_or_ne x a <;>
+    obtain rfl | hxb := eq_or_ne x b <;> simp [*, swap_apply_of_ne_of_ne]
 #align equiv.bij_on_swap Equiv.bijOn_swap
 
 end Equiv

chore: update std 05-22 (#4248)

The main breaking change is that tac <;> [t1, t2] is now written tac <;> [t1; t2], to avoid clashing with tactics like cases and use that take comma-separated lists.

ac36b28e

Diff

@@ -1501,7 +1501,7 @@ theorem piecewise_same : s.piecewise f f = f := by
 theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪ g '' sᶜ := by
   ext y; constructor
   · rintro ⟨x, rfl⟩
-    by_cases h : x ∈ s <;> [left, right] <;> use x <;> simp [h]
+    by_cases h : x ∈ s <;> [left; right] <;> use x <;> simp [h]
   · rintro (⟨x, hx, rfl⟩ | ⟨x, hx, rfl⟩) <;> use x <;> simp_all
 #align set.range_piecewise Set.range_piecewise

chore: fix #align lines (#3640)

This PR fixes two things:

Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

2b42dc7c

Diff

@@ -1043,7 +1043,6 @@ theorem LeftInvOn.injOn (h : LeftInvOn f₁' f s) : InjOn f s := fun x₁ h₁ x
     x₁ = f₁' (f x₁) := Eq.symm <| h h₁
     _ = f₁' (f x₂) := congr_arg f₁' heq
     _ = x₂ := h h₂
-
 #align set.left_inv_on.inj_on Set.LeftInvOn.injOn
 
 theorem LeftInvOn.surjOn (h : LeftInvOn f' f s) (hf : MapsTo f s t) : SurjOn f' t s := fun x hx =>
@@ -1064,7 +1063,6 @@ theorem LeftInvOn.comp (hf' : LeftInvOn f' f s) (hg' : LeftInvOn g' g t) (hf : M
   calc
     (f' ∘ g') ((g ∘ f) x) = f' (f x) := congr_arg f' (hg' (hf h))
     _ = x := hf' h
-
 #align set.left_inv_on.comp Set.LeftInvOn.comp
 
 theorem LeftInvOn.mono (hf : LeftInvOn f' f s) (ht : s₁ ⊆ s) : LeftInvOn f' f s₁ := fun _ hx =>
@@ -1155,7 +1153,6 @@ theorem eqOn_of_leftInvOn_of_rightInvOn (h₁ : LeftInvOn f₁' f s) (h₂ : Rig
   calc
     f₁' y = (f₁' ∘ f ∘ f₂') y := congr_arg f₁' (h₂ hy).symm
     _ = f₂' y := h₁ (h hy)
-
 #align set.eq_on_of_left_inv_on_of_right_inv_on Set.eqOn_of_leftInvOn_of_rightInvOn
 
 theorem SurjOn.leftInvOn_of_rightInvOn (hf : SurjOn f s t) (hf' : RightInvOn f f' s) :

feat: require @[simps!] if simps runs in expensive mode (#1885)

This does not change the behavior of simps, just raises a linter error if you run simps in a more expensive mode without writing !.
Fixed some incorrect occurrences of to_additive, simps. Will do that systematically in future PR.
Fix port of OmegaCompletePartialOrder.ContinuousHom.ofMono a bit

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

52c04a34

Diff

@@ -550,7 +550,7 @@ section
 variable (t f)
 
 /-- The restriction of a function onto the preimage of a set. -/
-@[simps]
+@[simps!]
 def restrictPreimage : f ⁻¹' t → t :=
   (Set.mapsTo_preimage f t).restrict _ _ _
 #align set.restrict_preimage Set.restrictPreimage

chore: tidy various files (#2056)

a347ef63

Diff

@@ -136,14 +136,14 @@ theorem range_extend_subset (f : α → β) (g : α → γ) (g' : β → γ) :
   rintro _ ⟨y, rfl⟩
   rw [extend_def]
   split_ifs with h
-  exacts[Or.inl (mem_range_self _), Or.inr (mem_image_of_mem _ h)]
+  exacts [Or.inl (mem_range_self _), Or.inr (mem_image_of_mem _ h)]
 #align set.range_extend_subset Set.range_extend_subset
 
 theorem range_extend {f : α → β} (hf : Injective f) (g : α → γ) (g' : β → γ) :
     range (extend f g g') = range g ∪ g' '' range fᶜ := by
   refine' (range_extend_subset _ _ _).antisymm _
   rintro z (⟨x, rfl⟩ | ⟨y, hy, rfl⟩)
-  exacts[⟨f x, hf.extend_apply _ _ _⟩, ⟨y, extend_apply' _ _ _ hy⟩]
+  exacts [⟨f x, hf.extend_apply _ _ _⟩, ⟨y, extend_apply' _ _ _ hy⟩]
 #align set.range_extend Set.range_extend
 
 /-- Restrict codomain of a function `f` to a set `s`. Same as `Subtype.coind` but this version
@@ -240,8 +240,8 @@ theorem eqOn_range {ι : Sort _} {f : ι → α} {g₁ g₂ : α → β} :
   forall_range_iff.trans <| funext_iff.symm
 #align set.eq_on_range Set.eqOn_range
 
-alias eqOn_range ↔ eqOn.comp_eq _
-#align set.eq_on.comp_eq Set.eqOn.comp_eq
+alias eqOn_range ↔ EqOn.comp_eq _
+#align set.eq_on.comp_eq Set.EqOn.comp_eq
 
 /-! ### Congruence lemmas -/
 
@@ -637,7 +637,7 @@ theorem injOn_union (h : Disjoint s₁ s₂) :
     exact h.le_bot ⟨hx, hy⟩
   · rintro ⟨h₁, h₂, h₁₂⟩
     rintro x (hx | hx) y (hy | hy) hxy
-    exacts[h₁ hx hy hxy, (h₁₂ _ hx _ hy hxy).elim, (h₁₂ _ hy _ hx hxy.symm).elim, h₂ hx hy hxy]
+    exacts [h₁ hx hy hxy, (h₁₂ _ hx _ hy hxy).elim, (h₁₂ _ hy _ hx hxy.symm).elim, h₂ hx hy hxy]
 #align set.inj_on_union Set.injOn_union
 
 theorem injOn_insert {f : α → β} {s : Set α} {a : α} (has : a ∉ s) :
@@ -1160,8 +1160,8 @@ theorem eqOn_of_leftInvOn_of_rightInvOn (h₁ : LeftInvOn f₁' f s) (h₂ : Rig
 
 theorem SurjOn.leftInvOn_of_rightInvOn (hf : SurjOn f s t) (hf' : RightInvOn f f' s) :
     LeftInvOn f f' t := fun y hy => by
-  let ⟨x, hx, HEq⟩ := hf hy
-  rw [← HEq, hf' hx]
+  let ⟨x, hx, heq⟩ := hf hy
+  rw [← heq, hf' hx]
 #align set.surj_on.left_inv_on_of_right_inv_on Set.SurjOn.leftInvOn_of_rightInvOn
 
 /-! ### Two-side inverses -/
@@ -1440,7 +1440,7 @@ theorem piecewise_compl [∀ i, Decidable (i ∈ sᶜ)] : sᶜ.piecewise f g = s
 @[simp]
 theorem piecewise_range_comp {ι : Sort _} (f : ι → α) [∀ j, Decidable (j ∈ range f)]
     (g₁ g₂ : α → β) : (range f).piecewise g₁ g₂ ∘ f = g₁ ∘ f :=
-  eqOn.comp_eq <| piecewise_eqOn _ _ _
+  (piecewise_eqOn ..).comp_eq
 #align set.piecewise_range_comp Set.piecewise_range_comp
 
 theorem MapsTo.piecewise_ite {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {f₁ f₂ : α → β}
@@ -1448,7 +1448,7 @@ theorem MapsTo.piecewise_ite {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {f₁
     (h₂ : MapsTo f₂ (s₂ ∩ sᶜ) (t₂ ∩ tᶜ)) :
     MapsTo (s.piecewise f₁ f₂) (s.ite s₁ s₂) (t.ite t₁ t₂) := by
   refine' (h₁.congr _).union_union (h₂.congr _)
-  exacts[(piecewise_eqOn s f₁ f₂).symm.mono (inter_subset_right _ _),
+  exacts [(piecewise_eqOn s f₁ f₂).symm.mono (inter_subset_right _ _),
     (piecewise_eqOn_compl s f₁ f₂).symm.mono (inter_subset_right _ _)]
 #align set.maps_to.piecewise_ite Set.MapsTo.piecewise_ite

Feat: add new Set.univ_pi_piecewise, rename the old lemma to Set.univ_pi_piecewise_univ (#1904)

2f3db46e

Diff

@@ -1526,16 +1526,18 @@ theorem piecewise_mem_pi {δ : α → Type _} {t : Set α} {t' : ∀ i, Set (δ
 
 @[simp]
 theorem pi_piecewise {ι : Type _} {α : ι → Type _} (s s' : Set ι) (t t' : ∀ i, Set (α i))
-    [∀ x, Decidable (x ∈ s')] : pi s (s'.piecewise t t') = pi (s ∩ s') t ∩ pi (s \ s') t' := by
-  ext x
-  simp only [mem_pi, mem_inter_iff, ← forall_and]
-  refine' forall_congr' fun i => _
-  by_cases hi : i ∈ s' <;> simp [*]
+    [∀ x, Decidable (x ∈ s')] : pi s (s'.piecewise t t') = pi (s ∩ s') t ∩ pi (s \ s') t' :=
+  pi_if _ _ _
 #align set.pi_piecewise Set.pi_piecewise
 
-theorem univ_pi_piecewise {ι : Type _} {α : ι → Type _} (s : Set ι) (t : ∀ i, Set (α i))
+-- porting note: new lemma
+theorem univ_pi_piecewise {ι : Type _} {α : ι → Type _} (s : Set ι) (t t' : ∀ i, Set (α i))
+    [∀ x, Decidable (x ∈ s)] : pi univ (s.piecewise t t') = pi s t ∩ pi (sᶜ) t' := by
+  simp [compl_eq_univ_diff]
+
+theorem univ_pi_piecewise_univ {ι : Type _} {α : ι → Type _} (s : Set ι) (t : ∀ i, Set (α i))
     [∀ x, Decidable (x ∈ s)] : pi univ (s.piecewise t fun _ => univ) = pi s t := by simp
-#align set.univ_pi_piecewise Set.univ_pi_piecewise
+#align set.univ_pi_piecewise Set.univ_pi_piecewise_univ
 
 end Set

chore: add missing #align statements (#1902)

This PR is the result of a slight variant on the following "algorithm"

take all mathlib 3 names, remove _ and make all uppercase letters into lowercase
take all mathlib 4 names, remove _ and make all uppercase letters into lowercase
look for matches, and create pairs (original_lean3_name, OriginalLean4Name)
for pairs that do not have an align statement:
- use Lean 4 to lookup the file + position of the Lean 4 name
- add an #align statement just before the next empty line
manually fix some tiny mistakes (e.g., empty lines in proofs might cause the #align statement to have been inserted too early)

b72bb858

Diff

@@ -170,6 +170,7 @@ theorem injective_codRestrict {f : ι → α} {s : Set α} (h : ∀ x, f x ∈ s
 #align set.injective_cod_restrict Set.injective_codRestrict
 
 alias injective_codRestrict ↔ _ _root_.Function.Injective.codRestrict
+#align function.injective.cod_restrict Function.Injective.codRestrict
 
 variable {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {p : Set γ} {f f₁ f₂ f₃ : α → β} {g g₁ g₂ : β → γ}
   {f' f₁' f₂' : β → α} {g' : γ → β} {a : α} {b : β}
@@ -240,6 +241,7 @@ theorem eqOn_range {ι : Sort _} {f : ι → α} {g₁ g₂ : α → β} :
 #align set.eq_on_range Set.eqOn_range
 
 alias eqOn_range ↔ eqOn.comp_eq _
+#align set.eq_on.comp_eq Set.eqOn.comp_eq
 
 /-! ### Congruence lemmas -/
 
@@ -552,6 +554,7 @@ variable (t f)
 def restrictPreimage : f ⁻¹' t → t :=
   (Set.mapsTo_preimage f t).restrict _ _ _
 #align set.restrict_preimage Set.restrictPreimage
+#align set.restrict_preimage_coe Set.restrictPreimage_coe
 
 theorem range_restrictPreimage : range (t.restrictPreimage f) = Subtype.val ⁻¹' range f := by
   delta Set.restrictPreimage
@@ -576,6 +579,9 @@ lemma restrictPreimage_bijective (hf : Bijective f) : Bijective (t.restrictPreim
 alias Set.restrictPreimage_injective  ← _root_.Function.Injective.restrictPreimage
 alias Set.restrictPreimage_surjective ← _root_.Function.Surjective.restrictPreimage
 alias Set.restrictPreimage_bijective  ← _root_.Function.Bijective.restrictPreimage
+#align function.bijective.restrict_preimage Function.Bijective.restrictPreimage
+#align function.surjective.restrict_preimage Function.Surjective.restrictPreimage
+#align function.injective.restrict_preimage Function.Injective.restrictPreimage
 
 end
 
@@ -609,6 +615,7 @@ theorem InjOn.ne_iff {x y} (h : InjOn f s) (hx : x ∈ s) (hy : y ∈ s) : f x 
 #align set.inj_on.ne_iff Set.InjOn.ne_iff
 
 alias InjOn.ne_iff ↔ _ InjOn.ne
+#align set.inj_on.ne Set.InjOn.ne
 
 theorem InjOn.congr (h₁ : InjOn f₁ s) (h : EqOn f₁ f₂ s) : InjOn f₂ s := fun _ hx _ hy =>
   h hx ▸ h hy ▸ h₁ hx hy
@@ -648,6 +655,7 @@ theorem injOn_of_injective (h : Injective f) (s : Set α) : InjOn f s := fun _ _
 #align set.inj_on_of_injective Set.injOn_of_injective
 
 alias injOn_of_injective ← _root_.Function.Injective.injOn
+#align function.injective.inj_on Function.Injective.injOn
 
 lemma injOn_id (s : Set α) : InjOn id s := injective_id.injOn _
 #align set.inj_on_id Set.injOn_id
@@ -677,6 +685,7 @@ theorem injOn_iff_injective : InjOn f s ↔ Injective (s.restrict f) :=
 #align set.inj_on_iff_injective Set.injOn_iff_injective
 
 alias Set.injOn_iff_injective ↔ InjOn.injective _
+#align set.inj_on.injective Set.InjOn.injective
 
 theorem MapsTo.restrict_inj (h : MapsTo f s t) : Injective (h.restrict f s t) ↔ InjOn f s := by
   rw [h.restrict_eq_codRestrict, injective_codRestrict, injOn_iff_injective]
@@ -999,6 +1008,7 @@ theorem bijective_iff_bijOn_univ : Bijective f ↔ BijOn f univ univ :=
 #align set.bijective_iff_bij_on_univ Set.bijective_iff_bijOn_univ
 
 alias bijective_iff_bijOn_univ ↔ _root_.Function.Bijective.bijOn_univ _
+#align function.bijective.bij_on_univ Function.Bijective.bijOn_univ
 
 theorem BijOn.compl (hst : BijOn f s t) (hf : Bijective f) : BijOn f (sᶜ) (tᶜ) :=
   ⟨hst.surjOn.mapsTo_compl hf.1, hf.1.injOn _, hst.mapsTo.surjOn_compl hf.2⟩
@@ -1569,6 +1579,8 @@ theorem strictMono_restrict [Preorder α] [Preorder β] {f : α → β} {s : Set
 #align strict_mono_restrict strictMono_restrict
 
 alias strictMono_restrict ↔ _root_.StrictMono.of_restrict _root_.StrictMonoOn.restrict
+#align strict_mono.of_restrict StrictMono.of_restrict
+#align strict_mono_on.restrict StrictMonoOn.restrict
 
 theorem StrictMono.codRestrict [Preorder α] [Preorder β] {f : α → β} (hf : StrictMono f)
     {s : Set β} (hs : ∀ x, f x ∈ s) : StrictMono (Set.codRestrict f s hs) :=

Feat: add lemmas about Set.diagonal (#1438)

This is a partial forward-port of leanprover-community/mathlib#18111

11d5cd71

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module data.set.function
-! leanprover-community/mathlib commit b86832321b586c6ac23ef8cdef6a7a27e42b13bd
+! leanprover-community/mathlib commit 996b0ff959da753a555053a480f36e5f264d4207
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -384,6 +384,10 @@ theorem mapsTo' : MapsTo f s t ↔ f '' s ⊆ t :=
   image_subset_iff.symm
 #align set.maps_to' Set.mapsTo'
 
+theorem mapsTo_prod_map_diagonal : MapsTo (Prod.map f f) (diagonal α) (diagonal β) :=
+  diagonal_subset_iff.2 <| fun _ => rfl
+#align set.maps_to_prod_map_diagonal Set.mapsTo_prod_map_diagonal
+
 theorem MapsTo.subset_preimage {f : α → β} {s : Set α} {t : Set β} (hf : MapsTo f s t) :
     s ⊆ f ⁻¹' t :=
   hf

chore: fix most phantom #aligns (#1794)

3d3fb046

Diff

@@ -1579,7 +1579,7 @@ variable {fa : α → α} {fb : β → β} {f : α → β} {g : β → γ} {s t
 
 theorem Injective.comp_injOn (hg : Injective g) (hf : s.InjOn f) : s.InjOn (g ∘ f) :=
   (hg.injOn univ).comp hf (mapsTo_univ _ _)
-#align function.injective.comp_injOn Function.Injective.comp_injOn
+#align function.injective.comp_inj_on Function.Injective.comp_injOn
 
 theorem Surjective.surjOn (hf : Surjective f) (s : Set β) : SurjOn f univ s :=
   (surjective_iff_surjOn_univ.1 hf).mono (Subset.refl _) (subset_univ _)

feat: port Data.Finite.Set (#1685)

Port of data.finite.set

Also fixed a blocking variable declaration bug in Data.Set.Function

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

6ac326c7

Diff

@@ -36,7 +36,7 @@ import Mathlib.Logic.Function.Conjugate
   and the codomain to `t`.
 -/
 
-variable {α β γ ι : Type _} {π : α → Type _}
+variable {α β γ : Type _} {ι : Sort _} {π : α → Type _}
 
 open Equiv Equiv.Perm Function

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

@@ -1036,8 +1036,8 @@ theorem LeftInvOn.surjOn (h : LeftInvOn f' f s) (hf : MapsTo f s t) : SurjOn f'
   ⟨f x, hf hx, h hx⟩
 #align set.left_inv_on.surj_on Set.LeftInvOn.surjOn
 
-theorem LeftInvOn.mapsTo (h : LeftInvOn f' f s) (hf : SurjOn f s t) : MapsTo f' t s := fun y hy =>
-  by
+theorem LeftInvOn.mapsTo (h : LeftInvOn f' f s) (hf : SurjOn f s t) :
+    MapsTo f' t s := fun y hy => by
   let ⟨x, hs, hx⟩ := hf hy
   rwa [← hx, h hs]
 #align set.left_inv_on.maps_to Set.LeftInvOn.mapsTo
@@ -1065,8 +1065,8 @@ theorem LeftInvOn.image_inter' (hf : LeftInvOn f' f s) : f '' (s₁ ∩ s) = f'
     exact mem_image_of_mem _ ⟨by rwa [← hf h], h⟩
 #align set.left_inv_on.image_inter' Set.LeftInvOn.image_inter'
 
-theorem LeftInvOn.image_inter (hf : LeftInvOn f' f s) : f '' (s₁ ∩ s) = f' ⁻¹' (s₁ ∩ s) ∩ f '' s :=
-  by
+theorem LeftInvOn.image_inter (hf : LeftInvOn f' f s) :
+    f '' (s₁ ∩ s) = f' ⁻¹' (s₁ ∩ s) ∩ f '' s := by
   rw [hf.image_inter']
   refine' Subset.antisymm _ (inter_subset_inter_left _ (preimage_mono <| inter_subset_left _ _))
   rintro _ ⟨h₁, x, hx, rfl⟩; exact ⟨⟨h₁, by rwa [hf hx]⟩, mem_image_of_mem _ hx⟩
@@ -1342,8 +1342,8 @@ theorem piecewise_empty [∀ i : α, Decidable (i ∈ (∅ : Set α))] : piecewi
 #align set.piecewise_empty Set.piecewise_empty
 
 @[simp]
-theorem piecewise_univ [∀ i : α, Decidable (i ∈ (Set.univ : Set α))] : piecewise Set.univ f g = f :=
-  by
+theorem piecewise_univ [∀ i : α, Decidable (i ∈ (Set.univ : Set α))] :
+    piecewise Set.univ f g = f := by
   ext i
   simp [piecewise]
 #align set.piecewise_univ Set.piecewise_univ
@@ -1431,8 +1431,8 @@ theorem piecewise_range_comp {ι : Sort _} (f : ι → α) [∀ j, Decidable (j
 
 theorem MapsTo.piecewise_ite {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {f₁ f₂ : α → β}
     [∀ i, Decidable (i ∈ s)] (h₁ : MapsTo f₁ (s₁ ∩ s) (t₁ ∩ t))
-    (h₂ : MapsTo f₂ (s₂ ∩ sᶜ) (t₂ ∩ tᶜ)) : MapsTo (s.piecewise f₁ f₂) (s.ite s₁ s₂) (t.ite t₁ t₂) :=
-  by
+    (h₂ : MapsTo f₂ (s₂ ∩ sᶜ) (t₂ ∩ tᶜ)) :
+    MapsTo (s.piecewise f₁ f₂) (s.ite s₁ s₂) (t.ite t₁ t₂) := by
   refine' (h₁.congr _).union_union (h₂.congr _)
   exacts[(piecewise_eqOn s f₁ f₂).symm.mono (inter_subset_right _ _),
     (piecewise_eqOn_compl s f₁ f₂).symm.mono (inter_subset_right _ _)]
@@ -1615,8 +1615,8 @@ theorem surjOn_image (h : Semiconj f fa fb) (ha : SurjOn fa s t) : SurjOn fb (f
   exact mem_image_of_mem _ (mem_image_of_mem _ hxs)
 #align function.semiconj.surj_on_image Function.Semiconj.surjOn_image
 
-theorem surjOn_range (h : Semiconj f fa fb) (ha : Surjective fa) : SurjOn fb (range f) (range f) :=
-  by
+theorem surjOn_range (h : Semiconj f fa fb) (ha : Surjective fa) :
+    SurjOn fb (range f) (range f) := by
   rw [← image_univ]
   exact h.surjOn_image (ha.surjOn univ)
 #align function.semiconj.surj_on_range Function.Semiconj.surjOn_range

chore: format by line breaks (#1523)

During porting, I usually fix the desired format we seem to want for the line breaks around by with

awk '{do {{if (match($0, "^  by$") && length(p) < 98) {p=p " by";} else {if (NR!=1) {print p}; p=$0}}} while (getline == 1) if (getline==0) print p}' Mathlib/File/Im/Working/On.lean

I noticed there are some more files that slipped through.

This pull request is the result of running this command:

grep -lr "^  by\$" Mathlib | xargs -n 1 awk -i inplace '{do {{if (match($0, "^  by$") && length(p) < 98 && not (match(p, "^[ \t]*--"))) {p=p " by";} else {if (NR!=1) {print p}; p=$0}}} while (getline == 1) if (getline==0) print p}'

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

d6d859a7

Diff

@@ -1497,8 +1497,7 @@ theorem range_piecewise (f g : α → β) : range (s.piecewise f g) = f '' s ∪
 
 theorem injective_piecewise_iff {f g : α → β} :
     Injective (s.piecewise f g) ↔
-      InjOn f s ∧ InjOn g (sᶜ) ∧ ∀ x ∈ s, ∀ (y) (_ : y ∉ s), f x ≠ g y :=
-  by
+      InjOn f s ∧ InjOn g (sᶜ) ∧ ∀ x ∈ s, ∀ (y) (_ : y ∉ s), f x ≠ g y := by
   rw [injective_iff_injOn_univ, ← union_compl_self s, injOn_union (@disjoint_compl_right _ _ s),
     (piecewise_eqOn s f g).injOn_iff, (piecewise_eqOn_compl s f g).injOn_iff]
   refine' and_congr Iff.rfl (and_congr Iff.rfl <| forall₄_congr fun x hx y hy => _)
@@ -1609,8 +1608,7 @@ theorem mapsTo_range (h : Semiconj f fa fb) : MapsTo fb (range f) (range f) := f
   hy ▸ ⟨fa x, h x⟩
 #align function.semiconj.maps_to_range Function.Semiconj.mapsTo_range
 
-theorem surjOn_image (h : Semiconj f fa fb) (ha : SurjOn fa s t) : SurjOn fb (f '' s) (f '' t) :=
-  by
+theorem surjOn_image (h : Semiconj f fa fb) (ha : SurjOn fa s t) : SurjOn fb (f '' s) (f '' t) := by
   rintro y ⟨x, hxt, rfl⟩
   rcases ha hxt with ⟨x, hxs, rfl⟩
   rw [h x]

chore: tidy various files (#1595)

6fe10b88

Diff

@@ -994,7 +994,7 @@ theorem bijective_iff_bijOn_univ : Bijective f ↔ BijOn f univ univ :=
     ⟨Iff.mpr injective_iff_injOn_univ inj, Iff.mpr surjective_iff_surjOn_univ surj⟩
 #align set.bijective_iff_bij_on_univ Set.bijective_iff_bijOn_univ
 
-alias bijective_iff_bijOn_univ ↔ _root_.Function.Bijective.bij_on_univ _
+alias bijective_iff_bijOn_univ ↔ _root_.Function.Bijective.bijOn_univ _
 
 theorem BijOn.compl (hst : BijOn f s t) (hf : Bijective f) : BijOn f (sᶜ) (tᶜ) :=
   ⟨hst.surjOn.mapsTo_compl hf.1, hf.1.injOn _, hst.mapsTo.surjOn_compl hf.2⟩

Match https://github.com/leanprover-community/mathlib/pull/17819, https://github.com/leanprover-community/mathlib/pull/17898 and https://github.com/leanprover-community/mathlib/pull/17899

feat: ∘ lemmas (#1347)

aec2f1d4

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module data.set.function
-! leanprover-community/mathlib commit cd9a9326dc14ad6e438e62267c31c66dd680d94e
+! leanprover-community/mathlib commit b86832321b586c6ac23ef8cdef6a7a27e42b13bd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -38,7 +38,7 @@ import Mathlib.Logic.Function.Conjugate
 
 variable {α β γ ι : Type _} {π : α → Type _}
 
-open Function
+open Equiv Equiv.Perm Function
 
 namespace Set
 
@@ -172,7 +172,7 @@ theorem injective_codRestrict {f : ι → α} {s : Set α} (h : ∀ x, f x ∈ s
 alias injective_codRestrict ↔ _ _root_.Function.Injective.codRestrict
 
 variable {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {p : Set γ} {f f₁ f₂ f₃ : α → β} {g g₁ g₂ : β → γ}
-  {f' f₁' f₂' : β → α} {g' : γ → β}
+  {f' f₁' f₂' : β → α} {g' : γ → β} {a : α} {b : β}
 
 /-! ### Equality on a set -/
 
@@ -435,6 +435,15 @@ theorem MapsTo.iterate_restrict {f : α → α} {s : Set α} (h : MapsTo f s s)
   · simp [Nat.iterate, ihn]
 #align set.maps_to.iterate_restrict Set.MapsTo.iterate_restrict
 
+lemma mapsTo_of_subsingleton' [Subsingleton β] (f : α → β) (h : s.Nonempty → t.Nonempty) :
+  MapsTo f s t :=
+fun a ha ↦ Subsingleton.mem_iff_nonempty.2 $ h ⟨a, ha⟩
+#align set.maps_to_of_subsingleton' Set.mapsTo_of_subsingleton'
+
+lemma mapsTo_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : MapsTo f s s :=
+mapsTo_of_subsingleton' _ id
+#align set.maps_to_of_subsingleton Set.mapsTo_of_subsingleton
+
 theorem MapsTo.mono (hf : MapsTo f s₁ t₁) (hs : s₂ ⊆ s₁) (ht : t₁ ⊆ t₂) : MapsTo f s₂ t₂ :=
   fun _ hx => ht (hf <| hs hx)
 #align set.maps_to.mono Set.MapsTo.mono
@@ -500,6 +509,14 @@ theorem maps_image_to (f : α → β) (g : γ → α) (s : Set γ) (t : Set β)
   ⟨fun h c hc => h ⟨c, hc, rfl⟩, fun h _ ⟨_, hc⟩ => hc.2 ▸ h hc.1⟩
 #align set.maps_image_to Set.maps_image_to
 
+lemma MapsTo.comp_left (g : β → γ) (hf : MapsTo f s t) : MapsTo (g ∘ f) s (g '' t) :=
+fun x hx ↦ ⟨f x, hf hx, rfl⟩
+#align set.maps_to.comp_left Set.MapsTo.comp_left
+
+lemma MapsTo.comp_right {s : Set β} {t : Set γ} (hg : MapsTo g s t) (f : α → β) :
+  MapsTo (g ∘ f) (f ⁻¹' s) t := fun _ hx ↦ hg hx
+#align set.maps_to.comp_right Set.MapsTo.comp_right
+
 @[simp]
 theorem maps_univ_to (f : α → β) (s : Set β) : MapsTo f univ s ↔ ∀ a, f a ∈ s :=
   ⟨fun h _ => h (mem_univ _), fun h x _ => h x⟩
@@ -628,10 +645,23 @@ theorem injOn_of_injective (h : Injective f) (s : Set α) : InjOn f s := fun _ _
 
 alias injOn_of_injective ← _root_.Function.Injective.injOn
 
+lemma injOn_id (s : Set α) : InjOn id s := injective_id.injOn _
+#align set.inj_on_id Set.injOn_id
+
 theorem InjOn.comp (hg : InjOn g t) (hf : InjOn f s) (h : MapsTo f s t) : InjOn (g ∘ f) s :=
   fun _ hx _ hy heq => hf hx hy <| hg (h hx) (h hy) heq
 #align set.inj_on.comp Set.InjOn.comp
 
+lemma InjOn.iterate {f : α → α} {s : Set α} (h : InjOn f s) (hf : MapsTo f s s) :
+  ∀ n, InjOn (f^[n]) s
+| 0 => injOn_id _
+| (n + 1) => (h.iterate hf n).comp h hf
+#align set.inj_on.iterate Set.InjOn.iterate
+
+lemma injOn_of_subsingleton [Subsingleton α] (f : α → β) (s : Set α) : InjOn f s :=
+(injective_of_subsingleton _).injOn _
+#align set.inj_on_of_subsingleton Set.injOn_of_subsingleton
+
 theorem _root_.Function.Injective.injOn_range (h : Injective (g ∘ f)) : InjOn g (range f) := by
   rintro _ ⟨x, rfl⟩ _ ⟨y, rfl⟩ H
   exact congr_arg f (h H)
@@ -727,6 +757,9 @@ theorem surjOn_empty (f : α → β) (s : Set α) : SurjOn f s ∅ :=
   empty_subset _
 #align set.surj_on_empty Set.surjOn_empty
 
+@[simp] lemma surjOn_singleton : SurjOn f s {b} ↔ b ∈ f '' s := singleton_subset_iff
+#align set.surj_on_singleton Set.surjOn_singleton
+
 theorem surjOn_image (f : α → β) (s : Set α) : SurjOn f s (f '' s) :=
   Subset.rfl
 #align set.surj_on_image Set.surjOn_image
@@ -771,10 +804,37 @@ theorem SurjOn.inter (h₁ : SurjOn f s₁ t) (h₂ : SurjOn f s₂ t) (h : InjO
   inter_self t ▸ h₁.inter_inter h₂ h
 #align set.surj_on.inter Set.SurjOn.inter
 
+--porting note: Why does `simp` not call `refl` by itself?
+lemma surjOn_id (s : Set α) : SurjOn id s s := by simp [SurjOn, subset_rfl]
+#align set.surj_on_id Set.surjOn_id
+
 theorem SurjOn.comp (hg : SurjOn g t p) (hf : SurjOn f s t) : SurjOn (g ∘ f) s p :=
   Subset.trans hg <| Subset.trans (image_subset g hf) <| image_comp g f s ▸ Subset.refl _
 #align set.surj_on.comp Set.SurjOn.comp
 
+lemma SurjOn.iterate {f : α → α} {s : Set α} (h : SurjOn f s s) : ∀ n, SurjOn (f^[n]) s s
+| 0 => surjOn_id _
+| (n + 1) => (h.iterate n).comp h
+#align set.surj_on.iterate Set.SurjOn.iterate
+
+lemma SurjOn.comp_left (hf : SurjOn f s t) (g : β → γ) : SurjOn (g ∘ f) s (g '' t) := by
+  rw [SurjOn, image_comp g f]; exact image_subset _ hf
+#align set.surj_on.comp_left Set.SurjOn.comp_left
+
+lemma SurjOn.comp_right {s : Set β} {t : Set γ} (hf : Surjective f) (hg : SurjOn g s t) :
+  SurjOn (g ∘ f) (f ⁻¹' s) t :=
+by rwa [SurjOn, image_comp g f, image_preimage_eq _ hf]
+#align set.surj_on.comp_right Set.SurjOn.comp_right
+
+lemma surjOn_of_subsingleton' [Subsingleton β] (f : α → β) (h : t.Nonempty → s.Nonempty) :
+  SurjOn f s t :=
+fun _ ha ↦ Subsingleton.mem_iff_nonempty.2 $ (h ⟨_, ha⟩).image _
+#align set.surj_on_of_subsingleton' Set.surjOn_of_subsingleton'
+
+lemma surjOn_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : SurjOn f s s :=
+surjOn_of_subsingleton' _ id
+#align set.surj_on_of_subsingleton Set.surjOn_of_subsingleton
+
 theorem surjective_iff_surjOn_univ : Surjective f ↔ SurjOn f univ univ := by
   simp [Surjective, SurjOn, subset_def]
 #align set.surjective_iff_surj_on_univ Set.surjective_iff_surjOn_univ
@@ -851,6 +911,9 @@ theorem bijOn_empty (f : α → β) : BijOn f ∅ ∅ :=
   ⟨mapsTo_empty f ∅, injOn_empty f, surjOn_empty f ∅⟩
 #align set.bij_on_empty Set.bijOn_empty
 
+@[simp] lemma bijOn_singleton : BijOn f {a} {b} ↔ f a = b := by simp [BijOn, eq_comm]
+#align set.bij_on_singleton Set.bijOn_singleton
+
 theorem BijOn.inter_mapsTo (h₁ : BijOn f s₁ t₁) (h₂ : MapsTo f s₂ t₂) (h₃ : s₁ ∩ f ⁻¹' t₂ ⊆ s₂) :
     BijOn f (s₁ ∩ s₂) (t₁ ∩ t₂) :=
   ⟨h₁.mapsTo.inter_inter h₂, h₁.injOn.mono <| inter_subset_left _ _, fun _ hy =>
@@ -894,10 +957,27 @@ theorem BijOn.image_eq (h : BijOn f s t) : f '' s = t :=
   h.surjOn.image_eq_of_mapsTo h.mapsTo
 #align set.bij_on.image_eq Set.BijOn.image_eq
 
+lemma bijOn_id (s : Set α) : BijOn id s s := ⟨s.mapsTo_id, s.injOn_id, s.surjOn_id⟩
+#align set.bij_on_id Set.bijOn_id
+
 theorem BijOn.comp (hg : BijOn g t p) (hf : BijOn f s t) : BijOn (g ∘ f) s p :=
   BijOn.mk (hg.mapsTo.comp hf.mapsTo) (hg.injOn.comp hf.injOn hf.mapsTo) (hg.surjOn.comp hf.surjOn)
 #align set.bij_on.comp Set.BijOn.comp
 
+lemma BijOn.iterate {f : α → α} {s : Set α} (h : BijOn f s s) : ∀ n, BijOn (f^[n]) s s
+| 0 => s.bijOn_id
+| (n + 1) => (h.iterate n).comp h
+#align set.bij_on.iterate Set.BijOn.iterate
+
+lemma bijOn_of_subsingleton' [Subsingleton α] [Subsingleton β] (f : α → β)
+  (h : s.Nonempty ↔ t.Nonempty) : BijOn f s t :=
+⟨mapsTo_of_subsingleton' _ h.1, injOn_of_subsingleton _ _, surjOn_of_subsingleton' _ h.2⟩
+#align set.bij_on_of_subsingleton' Set.bijOn_of_subsingleton'
+
+lemma bijOn_of_subsingleton [Subsingleton α] (f : α → α) (s : Set α) : BijOn f s s :=
+bijOn_of_subsingleton' _ Iff.rfl
+#align set.bij_on_of_subsingleton Set.bijOn_of_subsingleton
+
 theorem BijOn.bijective (h : BijOn f s t) : Bijective (h.mapsTo.restrict f s t) :=
   ⟨fun x y h' => Subtype.ext <| h.injOn x.2 y.2 <| Subtype.ext_iff.1 h', fun ⟨_, hy⟩ =>
     let ⟨x, hx, hxy⟩ := h.surjOn hy
@@ -914,6 +994,8 @@ theorem bijective_iff_bijOn_univ : Bijective f ↔ BijOn f univ univ :=
     ⟨Iff.mpr injective_iff_injOn_univ inj, Iff.mpr surjective_iff_surjOn_univ surj⟩
 #align set.bijective_iff_bij_on_univ Set.bijective_iff_bijOn_univ
 
+alias bijective_iff_bijOn_univ ↔ _root_.Function.Bijective.bij_on_univ _
+
 theorem BijOn.compl (hst : BijOn f s t) (hf : Bijective f) : BijOn f (sᶜ) (tᶜ) :=
   ⟨hst.surjOn.mapsTo_compl hf.1, hf.1.injOn _, hst.mapsTo.surjOn_compl hf.2⟩
 #align set.bij_on.compl Set.BijOn.compl
@@ -960,6 +1042,9 @@ theorem LeftInvOn.mapsTo (h : LeftInvOn f' f s) (hf : SurjOn f s t) : MapsTo f'
   rwa [← hx, h hs]
 #align set.left_inv_on.maps_to Set.LeftInvOn.mapsTo
 
+lemma leftInvOn_id (s : Set α) : LeftInvOn id id s := fun _ _ ↦ rfl
+#align set.left_inv_on_id Set.leftInvOn_id
+
 theorem LeftInvOn.comp (hf' : LeftInvOn f' f s) (hg' : LeftInvOn g' g t) (hf : MapsTo f s t) :
     LeftInvOn (f' ∘ g') (g ∘ f) s := fun x h =>
   calc
@@ -1034,6 +1119,9 @@ theorem RightInvOn.mapsTo (h : RightInvOn f' f t) (hf : SurjOn f' t s) : MapsTo
   LeftInvOn.mapsTo h hf
 #align set.right_inv_on.maps_to Set.RightInvOn.mapsTo
 
+lemma rightInvOn_id (s : Set α) : RightInvOn id id s := fun _ _ ↦ rfl
+#align set.right_inv_on_id Set.rightInvOn_id
+
 theorem RightInvOn.comp (hf : RightInvOn f' f t) (hg : RightInvOn g' g p) (g'pt : MapsTo g' p t) :
     RightInvOn (f' ∘ g') (g ∘ f) p :=
   LeftInvOn.comp hg hf g'pt
@@ -1070,6 +1158,15 @@ def InvOn (g : β → α) (f : α → β) (s : Set α) (t : Set β) : Prop :=
   LeftInvOn g f s ∧ RightInvOn g f t
 #align set.inv_on Set.InvOn
 
+lemma invOn_id (s : Set α) : InvOn id id s s := ⟨s.leftInvOn_id, s.rightInvOn_id⟩
+#align set.inv_on_id Set.invOn_id
+
+lemma InvOn.comp (hf : InvOn f' f s t) (hg : InvOn g' g t p) (fst : MapsTo f s t)
+  (g'pt : MapsTo g' p t) :
+  InvOn (f' ∘ g') (g ∘ f) s p :=
+⟨hf.1.comp hg.1 fst, hf.2.comp hg.2 g'pt⟩
+#align set.inv_on.comp Set.InvOn.comp
+
 theorem InvOn.symm (h : InvOn f' f s t) : InvOn f f' t s :=
   ⟨h.right, h.left⟩
 #align set.inv_on.symm Set.InvOn.symm
@@ -1079,8 +1176,8 @@ theorem InvOn.mono (h : InvOn f' f s t) (hs : s₁ ⊆ s) (ht : t₁ ⊆ t) : In
 #align set.inv_on.mono Set.InvOn.mono
 
 /-- If functions `f'` and `f` are inverse on `s` and `t`, `f` maps `s` into `t`, and `f'` maps `t`
-into `s`, then `f` is a bijection between `s` and `t`. The `maps_to` arguments can be deduced from
-`surj_on` statements using `left_inv_on.maps_to` and `right_inv_on.maps_to`. -/
+into `s`, then `f` is a bijection between `s` and `t`. The `mapsTo` arguments can be deduced from
+`surjOn` statements using `LeftInvOn.mapsTo` and `RightInvOn.mapsTo`. -/
 theorem InvOn.bijOn (h : InvOn f' f s t) (hf : MapsTo f s t) (hf' : MapsTo f' t s) : BijOn f s t :=
   ⟨hf, h.left.injOn, h.right.surjOn hf'⟩
 #align set.inv_on.bij_on Set.InvOn.bijOn
@@ -1199,6 +1296,14 @@ theorem preimage_invFun_of_not_mem [n : Nonempty α] {f : α → β} (hf : Injec
     simp only [mem_preimage, invFun_neg hx, h, this]
 #align set.preimage_inv_fun_of_not_mem Set.preimage_invFun_of_not_mem
 
+lemma BijOn.symm {g : β → α} (h : InvOn f g t s) (hf : BijOn f s t) : BijOn g t s :=
+⟨h.2.mapsTo hf.surjOn, h.1.injOn, h.2.surjOn hf.mapsTo⟩
+#align set.bij_on.symm Set.BijOn.symm
+
+lemma bijOn_comm {g : β → α} (h : InvOn f g t s) : BijOn f s t ↔ BijOn g t s :=
+⟨BijOn.symm h, BijOn.symm h.symm⟩
+#align set.bij_on_comm Set.bijOn_comm
+
 end Set
 
 /-! ### Monotone -/
@@ -1228,7 +1333,7 @@ end Monotone
 
 namespace Set
 
-variable {δ : α → Sort y} (s : Set α) (f g : ∀ i, δ i)
+variable {δ : α → Sort _} (s : Set α) (f g : ∀ i, δ i)
 
 @[simp]
 theorem piecewise_empty [∀ i : α, Decidable (i ∈ (∅ : Set α))] : piecewise ∅ f g = g := by
@@ -1421,6 +1526,8 @@ theorem univ_pi_piecewise {ι : Type _} {α : ι → Type _} (s : Set ι) (t : 
 
 end Set
 
+open Set
+
 theorem StrictMonoOn.injOn [LinearOrder α] [Preorder β] {f : α → β} {s : Set α}
     (H : StrictMonoOn f s) : s.InjOn f := fun x hx y hy hxy =>
   show Ordering.eq.Compares x y from (H.compares hx hy).1 hxy
@@ -1591,3 +1698,80 @@ theorem antitoneOn_of_rightInvOn_of_mapsTo {α β : Sort _} [PartialOrder α] [L
 #align function.antitone_on_of_right_inv_on_of_maps_to Function.antitoneOn_of_rightInvOn_of_mapsTo
 
 end Function
+
+/-! ### Equivalences, permutations -/
+
+namespace Set
+variable {p : β → Prop} [DecidablePred p] {f : α ≃ Subtype p} {g g₁ g₂ : Perm α} {s t : Set α}
+
+protected lemma MapsTo.extendDomain (h : MapsTo g s t) :
+  MapsTo (g.extendDomain f) ((↑) ∘ f '' s) ((↑) ∘ f '' t) := by
+  rintro _ ⟨a, ha, rfl⟩; exact ⟨_, h ha, by simp_rw [Function.comp_apply, extendDomain_apply_image]⟩
+#align set.maps_to.extend_domain Set.MapsTo.extendDomain
+
+protected lemma SurjOn.extendDomain (h : SurjOn g s t) :
+  SurjOn (g.extendDomain f) ((↑) ∘ f '' s) ((↑) ∘ f '' t) := by
+  rintro _ ⟨a, ha, rfl⟩
+  obtain ⟨b, hb, rfl⟩ := h ha
+  exact ⟨_, ⟨_, hb, rfl⟩, by simp_rw [Function.comp_apply, extendDomain_apply_image]⟩
+#align set.surj_on.extend_domain Set.SurjOn.extendDomain
+
+protected lemma BijOn.extendDomain (h : BijOn g s t) :
+  BijOn (g.extendDomain f) ((↑) ∘ f '' s) ((↑) ∘ f '' t) :=
+⟨h.mapsTo.extendDomain, (g.extendDomain f).injective.injOn _, h.surjOn.extendDomain⟩
+#align set.bij_on.extend_domain Set.BijOn.extendDomain
+
+protected lemma LeftInvOn.extendDomain (h : LeftInvOn g₁ g₂ s) :
+  LeftInvOn (g₁.extendDomain f) (g₂.extendDomain f) ((↑) ∘ f '' s) := by
+  rintro _ ⟨a, ha, rfl⟩; simp_rw [Function.comp_apply, extendDomain_apply_image, h ha]
+#align set.left_inv_on.extend_domain Set.LeftInvOn.extendDomain
+
+protected lemma RightInvOn.extendDomain (h : RightInvOn g₁ g₂ t) :
+  RightInvOn (g₁.extendDomain f) (g₂.extendDomain f) ((↑) ∘ f '' t) := by
+  rintro _ ⟨a, ha, rfl⟩; simp_rw [Function.comp_apply, extendDomain_apply_image, h ha]
+#align set.right_inv_on.extend_domain Set.RightInvOn.extendDomain
+
+protected lemma InvOn.extendDomain (h : InvOn g₁ g₂ s t) :
+  InvOn (g₁.extendDomain f) (g₂.extendDomain f) ((↑) ∘ f '' s) ((↑) ∘ f '' t) :=
+⟨h.1.extendDomain, h.2.extendDomain⟩
+#align set.inv_on.extend_domain Set.InvOn.extendDomain
+
+end Set
+
+namespace Equiv
+variable (e : α ≃ β) {s : Set α} {t : Set β}
+
+lemma bijOn' (h₁ : MapsTo e s t) (h₂ : MapsTo e.symm t s) : BijOn e s t :=
+⟨h₁, e.injective.injOn _, fun b hb ↦ ⟨e.symm b, h₂ hb, apply_symm_apply _ _⟩⟩
+#align equiv.bij_on' Equiv.bijOn'
+
+protected lemma bijOn (h : ∀ a, e a ∈ t ↔ a ∈ s) : BijOn e s t :=
+e.bijOn' (fun a ↦ (h _).2) $ fun b hb ↦ (h _).1 $ by rwa [apply_symm_apply]
+#align equiv.bij_on Equiv.bijOn
+
+lemma invOn : InvOn e e.symm t s :=
+⟨e.rightInverse_symm.leftInvOn _, e.leftInverse_symm.leftInvOn _⟩
+#align equiv.inv_on Equiv.invOn
+
+lemma bijOn_image : BijOn e s (e '' s) := (e.injective.injOn _).bijOn_image
+#align equiv.bij_on_image Equiv.bijOn_image
+lemma bijOn_symm_image : BijOn e.symm (e '' s) s := e.bijOn_image.symm e.invOn
+#align equiv.bij_on_symm_image Equiv.bijOn_symm_image
+
+variable {e}
+
+@[simp] lemma bijOn_symm : BijOn e.symm t s ↔ BijOn e s t := bijOn_comm e.symm.invOn
+#align equiv.bij_on_symm Equiv.bijOn_symm
+
+alias bijOn_symm ↔ _root_.Set.BijOn.of_equiv_symm _root_.Set.BijOn.equiv_symm
+#align set.bij_on.of_equiv_symm Set.BijOn.of_equiv_symm
+#align set.bij_on.equiv_symm Set.BijOn.equiv_symm
+
+variable [DecidableEq α] {a b : α}
+
+lemma bijOn_swap (ha : a ∈ s) (hb : b ∈ s) : BijOn (swap a b) s s :=
+(swap a b).bijOn $ fun x ↦ by obtain rfl | hxa := eq_or_ne x a <;>
+  obtain rfl | hxb := eq_or_ne x b <;> simp [*, swap_apply_of_ne_of_ne]
+#align equiv.bij_on_swap Equiv.bijOn_swap
+
+end Equiv

feat: port some CanLift instances, restore lift tactic usage (#1425)

93812b0f

Diff

@@ -649,16 +649,11 @@ theorem MapsTo.restrict_inj (h : MapsTo f s t) : Injective (h.restrict f s t) 
 #align set.maps_to.restrict_inj Set.MapsTo.restrict_inj
 
 theorem exists_injOn_iff_injective [Nonempty β] :
-    (∃ f : α → β, InjOn f s) ↔ ∃ f : s → β, Injective f := by
-  classical
-  refine ⟨fun ⟨f, hf⟩ => ⟨_, hf.injective⟩, fun ⟨f, hf⟩ => ?_⟩
-  refine ⟨fun x => if h : x ∈ s then f ⟨x, h⟩ else _root_.Nonempty.some ‹_›, ?_⟩
-  refine injOn_iff_injective.2 ?_
-  rw [Set.restrict_dite]
-  exact hf
-  -- porting note: TODO: once we have `lift`, replace the above with the original proof
-    --lift f to α → β using trivial
-    --exact ⟨f, inj_on_iff_injective.2 hf⟩⟩
+    (∃ f : α → β, InjOn f s) ↔ ∃ f : s → β, Injective f :=
+  ⟨fun ⟨f, hf⟩ => ⟨_, hf.injective⟩,
+   fun ⟨f, hf⟩ => by
+    lift f to α → β using trivial
+    exact ⟨f, injOn_iff_injective.2 hf⟩⟩
 #align set.exists_inj_on_iff_injective Set.exists_injOn_iff_injective
 
 theorem injOn_preimage {B : Set (Set β)} (hB : B ⊆ 𝒫 range f) : InjOn (preimage f) B :=

chore: remove iff_self from simp only after lean4#1933 (#1406)

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

72b23bd4

Diff

@@ -166,7 +166,7 @@ theorem restrict_comp_codRestrict {f : ι → α} {g : α → β} {b : Set α} (
 @[simp]
 theorem injective_codRestrict {f : ι → α} {s : Set α} (h : ∀ x, f x ∈ s) :
     Injective (codRestrict f s h) ↔ Injective f := by
-  simp only [Injective, Subtype.ext_iff, val_codRestrict_apply, iff_self]
+  simp only [Injective, Subtype.ext_iff, val_codRestrict_apply]
 #align set.injective_cod_restrict Set.injective_codRestrict
 
 alias injective_codRestrict ↔ _ _root_.Function.Injective.codRestrict

https://github.com/leanprover-community/mathlib/pull/18001

chore: Update some synchronization SHAs (#1377)

Note that the SHA for Data.Set.Function has not be bumped to HEAD since some functions introduced in https://github.com/leanprover-community/mathlib/commit/d1723c047a091ae3fca0af8aeab1743e1a898611 are missing.

806541da

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module data.set.function
-! leanprover-community/mathlib commit 3d95492390dc90e34184b13e865f50bc67f30fbb
+! leanprover-community/mathlib commit cd9a9326dc14ad6e438e62267c31c66dd680d94e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

3d954923

feat: Data.Set.Function two lemmas about inverse of mono/antitone maps to sync with mathlib3#18001 (#1222)

a3d8bb76

Diff

@@ -1576,4 +1576,23 @@ theorem insert_injOn (s : Set α) : sᶜ.InjOn fun a => insert a s := fun _a ha
   (insert_inj ha).1
 #align function.insert_inj_on Function.insert_injOn
 
+theorem monotoneOn_of_rightInvOn_of_mapsTo {α β : Sort _} [PartialOrder α] [LinearOrder β]
+    {φ : β → α} {ψ : α → β} {t : Set β} {s : Set α} (hφ : MonotoneOn φ t)
+    (φψs : Set.RightInvOn ψ φ s) (ψts : Set.MapsTo ψ s t) : MonotoneOn ψ s := by
+  rintro x xs y ys l
+  rcases le_total (ψ x) (ψ y) with (ψxy|ψyx)
+  · exact ψxy
+  · have := hφ (ψts ys) (ψts xs) ψyx
+    rw [φψs.eq ys, φψs.eq xs] at this
+    induction le_antisymm l this
+    exact le_refl _
+#align function.monotone_on_of_right_inv_on_of_maps_to Function.monotoneOn_of_rightInvOn_of_mapsTo
+
+theorem antitoneOn_of_rightInvOn_of_mapsTo {α β : Sort _} [PartialOrder α] [LinearOrder β]
+    {φ : β → α} {ψ : α → β} {t : Set β} {s : Set α} (hφ : AntitoneOn φ t)
+    (φψs : Set.RightInvOn ψ φ s) (ψts : Set.MapsTo ψ s t) : AntitoneOn ψ s :=
+  MonotoneOn.dual_right (monotoneOn_of_rightInvOn_of_mapsTo (AntitoneOn.dual_left hφ) φψs ψts)
+-- Porting note: dot notation for `*.dual_*` didn't work
+#align function.antitone_on_of_right_inv_on_of_maps_to Function.antitoneOn_of_rightInvOn_of_mapsTo
+
 end Function

3d954923

chore: move basic lemmas to basic files (#1109)

synchronize with https://github.com/leanprover-community/mathlib/pull/17882

~~Make disjoint_singleton @[simp 1100] because the linter complains it is not in simpNF (because of disjoint_singleton_left and disjoint_singleton_right).~~

Removing simp of disjoint_singleton, making disjoint_singleton_left have a greater priority than disjoint_singleton_right, then disjoint_singleton can be proved by simp.

d90ae095

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module data.set.function
-! leanprover-community/mathlib commit 198161d833f2c01498c39c266b0b3dbe2c7a8c07
+! leanprover-community/mathlib commit 3d95492390dc90e34184b13e865f50bc67f30fbb
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -538,6 +538,24 @@ theorem range_restrictPreimage : range (t.restrictPreimage f) = Subtype.val ⁻
     Subtype.coe_preimage_self, Set.univ_inter]
 #align set.range_restrict_preimage Set.range_restrictPreimage
 
+variable {f} {U : ι → Set β}
+
+lemma restrictPreimage_injective (hf : Injective f) : Injective (t.restrictPreimage f) :=
+  fun _ _ e => Subtype.coe_injective <| hf <| Subtype.mk.inj e
+#align set.restrict_preimage_injective Set.restrictPreimage_injective
+
+lemma restrictPreimage_surjective (hf : Surjective f) : Surjective (t.restrictPreimage f) :=
+  fun x => ⟨⟨_, ((hf x).choose_spec.symm ▸ x.2 : _ ∈ t)⟩, Subtype.ext (hf x).choose_spec⟩
+#align set.restrict_preimage_surjective Set.restrictPreimage_surjective
+
+lemma restrictPreimage_bijective (hf : Bijective f) : Bijective (t.restrictPreimage f) :=
+  ⟨t.restrictPreimage_injective hf.1, t.restrictPreimage_surjective hf.2⟩
+#align set.restrict_preimage_bijective Set.restrictPreimage_bijective
+
+alias Set.restrictPreimage_injective  ← _root_.Function.Injective.restrictPreimage
+alias Set.restrictPreimage_surjective ← _root_.Function.Surjective.restrictPreimage
+alias Set.restrictPreimage_bijective  ← _root_.Function.Bijective.restrictPreimage
+
 end
 
 /-! ### Injectivity on a set -/
@@ -672,6 +690,23 @@ theorem InjOn.cancel_left (hg : t.InjOn g) (hf₁ : s.MapsTo f₁ t) (hf₂ : s.
   ⟨fun h => h.cancel_left hg hf₁ hf₂, EqOn.comp_left⟩
 #align set.inj_on.cancel_left Set.InjOn.cancel_left
 
+lemma InjOn.image_inter {s t u : Set α} (hf : u.InjOn f) (hs : s ⊆ u) (ht : t ⊆ u) :
+    f '' (s ∩ t) = f '' s ∩ f '' t := by
+  apply Subset.antisymm (image_inter_subset _ _ _)
+  intro x ⟨⟨y, ys, hy⟩, ⟨z, zt, hz⟩⟩
+  have : y = z := by
+    apply hf (hs ys) (ht zt)
+    rwa [← hz] at hy
+  rw [← this] at zt
+  exact ⟨y, ⟨ys, zt⟩, hy⟩
+#align set.inj_on.image_inter Set.InjOn.image_inter
+
+theorem _root_.Disjoint.image {s t u : Set α} {f : α → β} (h : Disjoint s t) (hf : u.InjOn f)
+    (hs : s ⊆ u) (ht : t ⊆ u) : Disjoint (f '' s) (f '' t) := by
+  rw [disjoint_iff_inter_eq_empty] at h ⊢
+  rw [← hf.image_inter hs ht, h, image_empty]
+#align disjoint.image Disjoint.image
+
 /-! ### Surjectivity on a set -/

chore: fix casing per naming scheme (#1183)

Fix a lot of wrong casing mostly in the docstrings but also sometimes in def/theorem names. E.g. fin 2 --> Fin 2, add_monoid_hom --> AddMonoidHom

Remove \n from to_additive docstrings that were inserted by mathport.

Move files and directories with Gcd and Smul to GCD and SMul

71723d8b

Diff

@@ -1531,7 +1531,7 @@ theorem update_comp_eq_of_not_mem_range' {α β : Sort _} {γ : β → Sort _} [
   (update_comp_eq_of_forall_ne' _ _) fun x hx => h ⟨x, hx⟩
 #align function.update_comp_eq_of_not_mem_range' Function.update_comp_eq_of_not_mem_range'
 
-/-- Non-dependent version of `function.update_comp_eq_of_not_mem_range'` -/
+/-- Non-dependent version of `Function.update_comp_eq_of_not_mem_range'` -/
 theorem update_comp_eq_of_not_mem_range {α β γ : Sort _} [DecidableEq β] (g : β → γ) {f : α → β}
     {i : β} (a : γ) (h : i ∉ Set.range f) : Function.update g i a ∘ f = g ∘ f :=
   update_comp_eq_of_not_mem_range' g a h

chore: fix names (#1171)

10507fe5

Diff

@@ -169,7 +169,7 @@ theorem injective_codRestrict {f : ι → α} {s : Set α} (h : ∀ x, f x ∈ s
   simp only [Injective, Subtype.ext_iff, val_codRestrict_apply, iff_self]
 #align set.injective_cod_restrict Set.injective_codRestrict
 
-alias injective_codRestrict ↔ _ _root_.function.injective.codRestrict
+alias injective_codRestrict ↔ _ _root_.Function.Injective.codRestrict
 
 variable {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {p : Set γ} {f f₁ f₂ f₃ : α → β} {g g₁ g₂ : β → γ}
   {f' f₁' f₂' : β → α} {g' : γ → β}
@@ -569,7 +569,7 @@ theorem InjOn.ne_iff {x y} (h : InjOn f s) (hx : x ∈ s) (hy : y ∈ s) : f x 
   (h.eq_iff hx hy).not
 #align set.inj_on.ne_iff Set.InjOn.ne_iff
 
-alias InjOn.ne_iff ↔ _ inj_on.ne
+alias InjOn.ne_iff ↔ _ InjOn.ne
 
 theorem InjOn.congr (h₁ : InjOn f₁ s) (h : EqOn f₁ f₂ s) : InjOn f₂ s := fun _ hx _ hy =>
   h hx ▸ h hy ▸ h₁ hx hy
@@ -1428,7 +1428,7 @@ theorem strictMono_restrict [Preorder α] [Preorder β] {f : α → β} {s : Set
     StrictMono (s.restrict f) ↔ StrictMonoOn f s := by simp [Set.restrict, StrictMono, StrictMonoOn]
 #align strict_mono_restrict strictMono_restrict
 
-alias strictMono_restrict ↔ _root_.strictMono.of_restrict _root_.strictMonoOn.restrict
+alias strictMono_restrict ↔ _root_.StrictMono.of_restrict _root_.StrictMonoOn.restrict
 
 theorem StrictMono.codRestrict [Preorder α] [Preorder β] {f : α → β} (hf : StrictMono f)
     {s : Set β} (hs : ∀ x, f x ∈ s) : StrictMono (Set.codRestrict f s hs) :=

chore: update lean4/std4 (#1096)

a9a1f7d7

Diff

@@ -1156,7 +1156,7 @@ theorem preimage_invFun_of_mem [n : Nonempty α] {f : α → β} (hf : Injective
   ext x
   rcases em (x ∈ range f) with (⟨a, rfl⟩ | hx)
   · simp only [mem_preimage, mem_union, mem_compl_iff, mem_range_self, not_true, or_false,
-      leftInverse_invFun hf _, hf.mem_set_image]; rfl
+      leftInverse_invFun hf _, hf.mem_set_image]
   · simp only [mem_preimage, invFun_neg hx, h, hx, mem_union, mem_compl_iff, not_false_iff, or_true]
 #align set.preimage_inv_fun_of_mem Set.preimage_invFun_of_mem

chore: tidy various files (#1086)

4e2a7237

Diff

@@ -31,7 +31,7 @@ import Mathlib.Logic.Function.Conjugate
 ### Functions
 
 * `Set.restrict f s` : restrict the domain of `f` to the set `s`;
-* `Set.cod_restrict f s h` : given `h : ∀ x, f x ∈ s`, restrict the codomain of `f` to the set `s`;
+* `Set.codRestrict f s h` : given `h : ∀ x, f x ∈ s`, restrict the codomain of `f` to the set `s`;
 * `Set.MapsTo.restrict f s t h`: given `h : MapsTo f s t`, restrict the domain of `f` to `s`
   and the codomain to `t`.
 -/
@@ -178,7 +178,7 @@ variable {s s₁ s₂ : Set α} {t t₁ t₂ : Set β} {p : Set γ} {f f₁ f₂
 
 
 /-- Two functions `f₁ f₂ : α → β` are equal on `s`
-  if `f₁ x = f₂ x` for all `x ∈ a`. -/
+  if `f₁ x = f₂ x` for all `x ∈ s`. -/
 def EqOn (f₁ f₂ : α → β) (s : Set α) : Prop :=
   ∀ ⦃x⦄, x ∈ s → f₁ x = f₂ x
 #align set.eq_on Set.EqOn
@@ -587,8 +587,7 @@ theorem injOn_union (h : Disjoint s₁ s₂) :
     InjOn f (s₁ ∪ s₂) ↔ InjOn f s₁ ∧ InjOn f s₂ ∧ ∀ x ∈ s₁, ∀ y ∈ s₂, f x ≠ f y := by
   refine' ⟨fun H => ⟨H.mono <| subset_union_left _ _, H.mono <| subset_union_right _ _, _⟩, _⟩
   · intro x hx y hy hxy
-    obtain rfl : x = y
-    exact H (Or.inl hx) (Or.inr hy) hxy
+    obtain rfl : x = y := H (Or.inl hx) (Or.inr hy) hxy
     exact h.le_bot ⟨hx, hy⟩
   · rintro ⟨h₁, h₂, h₁₂⟩
     rintro x (hx | hx) y (hy | hy) hxy