topology.metric_space.infsep | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

5316314b

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

f4758115

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -52,7 +52,7 @@ section EDist
 
 variable [EDist α] {x y : α} {s t : Set α}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.le_einfsep_iff /-
 theorem le_einfsep_iff {d} :
     d ≤ s.einfsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y := by
@@ -60,7 +60,7 @@ theorem le_einfsep_iff {d} :
 #align set.le_einfsep_iff Set.le_einfsep_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_zero /-
 theorem einfsep_zero :
     s.einfsep = 0 ↔
@@ -69,7 +69,7 @@ theorem einfsep_zero :
 #align set.einfsep_zero Set.einfsep_zero
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_pos /-
 theorem einfsep_pos :
     0 < s.einfsep ↔
@@ -79,7 +79,7 @@ theorem einfsep_pos :
 #align set.einfsep_pos Set.einfsep_pos
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_top /-
 theorem einfsep_top :
     s.einfsep = ∞ ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), edist x y = ∞ := by
@@ -87,7 +87,7 @@ theorem einfsep_top :
 #align set.einfsep_top Set.einfsep_top
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_lt_top /-
 theorem einfsep_lt_top :
     s.einfsep < ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y < ∞ := by
@@ -95,7 +95,7 @@ theorem einfsep_lt_top :
 #align set.einfsep_lt_top Set.einfsep_lt_top
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_ne_top /-
 theorem einfsep_ne_top :
     s.einfsep ≠ ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y ≠ ∞ := by
@@ -103,7 +103,7 @@ theorem einfsep_ne_top :
 #align set.einfsep_ne_top Set.einfsep_ne_top
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_lt_iff /-
 theorem einfsep_lt_iff {d} :
     s.einfsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (h : x ≠ y), edist x y < d := by
@@ -129,7 +129,7 @@ theorem Subsingleton.einfsep (hs : s.Subsingleton) : s.einfsep = ∞ := by rw [e
 #align set.subsingleton.einfsep Set.Subsingleton.einfsep
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.le_einfsep_image_iff /-
 theorem le_einfsep_image_iff {d} {f : β → α} {s : Set β} :
     d ≤ einfsep (f '' s) ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s), f x ≠ f y → d ≤ edist (f x) (f y) :=
@@ -158,7 +158,7 @@ theorem einfsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (h
 #align set.einfsep_le_of_mem_of_edist_le Set.einfsep_le_of_mem_of_edist_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.le_einfsep /-
 theorem le_einfsep {d} (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y) :
     d ≤ s.einfsep :=
@@ -261,7 +261,7 @@ theorem Finset.coe_einfsep [DecidableEq α] {s : Finset α} :
 #align set.finset.coe_einfsep Set.Finset.coe_einfsep
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.einfsep_exists_of_finite /-
 theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y := by
@@ -275,7 +275,7 @@ theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
 #align set.nontrivial.einfsep_exists_of_finite Set.Nontrivial.einfsep_exists_of_finite
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Finite.einfsep_exists_of_nontrivial /-
 theorem Finite.einfsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y :=
@@ -376,7 +376,7 @@ theorem einfsep_ne_top_iff : s.einfsep ≠ ∞ ↔ s.Nontrivial :=
 #align set.einfsep_ne_top_iff Set.einfsep_ne_top_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.le_einfsep_of_forall_dist_le /-
 theorem le_einfsep_of_forall_dist_le {d}
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) :
@@ -403,7 +403,7 @@ theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
 #align set.einfsep_pos_of_finite Set.einfsep_pos_of_finite
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.relatively_discrete_of_finite /-
 theorem relatively_discrete_of_finite [Finite s] :
     ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y := by
@@ -418,7 +418,7 @@ theorem Finite.einfsep_pos (hs : s.Finite) : 0 < s.einfsep :=
 #align set.finite.einfsep_pos Set.Finite.einfsep_pos
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Finite.relatively_discrete /-
 theorem Finite.relatively_discrete (hs : s.Finite) :
     ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
@@ -518,7 +518,7 @@ section PseudoMetricSpace
 
 variable [PseudoMetricSpace α] {x y z : α} {s t : Set α}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.le_infsep_iff /-
 theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
     d ≤ s.infsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y := by
@@ -527,7 +527,7 @@ theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
 #align set.nontrivial.le_infsep_iff Set.Nontrivial.le_infsep_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.infsep_lt_iff /-
 theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
     s.infsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), dist x y < d := by
@@ -535,7 +535,7 @@ theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
 #align set.nontrivial.infsep_lt_iff Set.Nontrivial.infsep_lt_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.le_infsep /-
 theorem Nontrivial.le_infsep {d} (hs : s.Nontrivial)
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) : d ≤ s.infsep :=
@@ -679,7 +679,7 @@ theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs
 #align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_empty
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.infsep_exists_of_finite /-
 theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y := by
@@ -693,7 +693,7 @@ theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
 #align set.nontrivial.infsep_exists_of_finite Set.Nontrivial.infsep_exists_of_finite
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Finite.infsep_exists_of_nontrivial /-
 theorem Finite.infsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y :=

f4758115

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -270,7 +270,7 @@ theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
   simp_rw [einfsep_of_fintype]
   rcases@Finset.exists_mem_eq_inf _ _ _ _ s.off_diag.to_finset (by simpa) (uncurry edist) with
     ⟨_, hxy, hed⟩
-  simp_rw [mem_to_finset] at hxy 
+  simp_rw [mem_to_finset] at hxy
   refine' ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.einfsep_exists_of_finite Set.Nontrivial.einfsep_exists_of_finite
 -/
@@ -326,7 +326,7 @@ theorem le_einfsep_pi_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMet
     c ≤ einfsep (Set.pi univ s) :=
   by
   refine' le_einfsep fun x hx y hy hxy => _
-  rw [mem_univ_pi] at hx hy 
+  rw [mem_univ_pi] at hx hy
   rcases function.ne_iff.mp hxy with ⟨i, hi⟩
   exact le_trans (le_einfsep_iff.1 (h i) _ (hx _) _ (hy _) hi) (edist_le_pi_edist _ _ i)
 #align set.le_einfsep_pi_of_le Set.le_einfsep_pi_of_le
@@ -341,7 +341,7 @@ variable [PseudoMetricSpace α] {s : Set α}
 #print Set.subsingleton_of_einfsep_eq_top /-
 theorem subsingleton_of_einfsep_eq_top (hs : s.einfsep = ∞) : s.Subsingleton :=
   by
-  rw [einfsep_top] at hs 
+  rw [einfsep_top] at hs
   exact fun _ hx _ hy => of_not_not fun hxy => edist_ne_top _ _ (hs _ hx _ hy hxy)
 #align set.subsingleton_of_einfsep_eq_top Set.subsingleton_of_einfsep_eq_top
 -/
@@ -398,7 +398,7 @@ theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
   by_cases hs : s.nontrivial
   · rcases hs.einfsep_exists_of_finite with ⟨x, hx, y, hy, hxy, hxy'⟩
     exact hxy'.symm ▸ edist_pos.2 hxy
-  · rw [not_nontrivial_iff] at hs 
+  · rw [not_nontrivial_iff] at hs
     exact hs.einfsep.symm ▸ WithTop.zero_lt_top
 #align set.einfsep_pos_of_finite Set.einfsep_pos_of_finite
 -/
@@ -474,7 +474,7 @@ theorem Subsingleton.infsep_zero (hs : s.Subsingleton) : s.infsep = 0 := by
 
 #print Set.nontrivial_of_infsep_pos /-
 theorem nontrivial_of_infsep_pos (hs : 0 < s.infsep) : s.Nontrivial := by contrapose hs;
-  rw [not_nontrivial_iff] at hs ; exact hs.infsep_zero ▸ lt_irrefl _
+  rw [not_nontrivial_iff] at hs; exact hs.infsep_zero ▸ lt_irrefl _
 #align set.nontrivial_of_infsep_pos Set.nontrivial_of_infsep_pos
 -/
 
@@ -549,8 +549,8 @@ theorem le_edist_of_le_infsep {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x 
   by
   by_cases hs : s.nontrivial
   · exact hs.le_infsep_iff.1 hd x hx y hy hxy
-  · rw [not_nontrivial_iff] at hs 
-    rw [hs.infsep_zero] at hd 
+  · rw [not_nontrivial_iff] at hs
+    rw [hs.infsep_zero] at hd
     exact le_trans hd dist_nonneg
 #align set.le_edist_of_le_infsep Set.le_edist_of_le_infsep
 -/
@@ -597,7 +597,7 @@ theorem infsep_eq_iInf [Decidable s.Nontrivial] :
   · have hb : BddBelow (uncurry dist '' s.off_diag) :=
       by
       refine' ⟨0, fun d h => _⟩
-      simp_rw [mem_image, Prod.exists, uncurry_apply_pair] at h 
+      simp_rw [mem_image, Prod.exists, uncurry_apply_pair] at h
       rcases h with ⟨_, _, _, rfl⟩
       exact dist_nonneg
     refine' eq_of_forall_le_iff fun _ => _
@@ -622,7 +622,7 @@ theorem infsep_of_fintype [Decidable s.Nontrivial] [DecidableEq α] [Fintype s]
   · refine' eq_of_forall_le_iff fun _ => _
     simp_rw [hs.le_infsep_iff, imp_forall_iff, Finset.le_inf'_iff, mem_to_finset, mem_off_diag,
       Prod.forall, uncurry_apply_pair, and_imp]
-  · rw [not_nontrivial_iff] at hs ; exact hs.infsep_zero
+  · rw [not_nontrivial_iff] at hs; exact hs.infsep_zero
 #align set.infsep_of_fintype Set.infsep_of_fintype
 -/
 
@@ -642,7 +642,7 @@ theorem Finite.infsep [Decidable s.Nontrivial] (hsf : s.Finite) :
   · refine' eq_of_forall_le_iff fun _ => _
     simp_rw [hs.le_infsep_iff, imp_forall_iff, Finset.le_inf'_iff, finite.mem_to_finset,
       mem_off_diag, Prod.forall, uncurry_apply_pair, and_imp]
-  · rw [not_nontrivial_iff] at hs ; exact hs.infsep_zero
+  · rw [not_nontrivial_iff] at hs; exact hs.infsep_zero
 #align set.finite.infsep Set.Finite.infsep
 -/
 
@@ -674,7 +674,7 @@ theorem Finset.coe_infsep_of_offDiag_nonempty [DecidableEq α] {s : Finset α}
 
 #print Finset.coe_infsep_of_offDiag_empty /-
 theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs : s.offDiag = ∅) :
-    (s : Set α).infsep = 0 := by rw [← Finset.not_nonempty_iff_eq_empty] at hs ;
+    (s : Set α).infsep = 0 := by rw [← Finset.not_nonempty_iff_eq_empty] at hs;
   rw [Finset.coe_infsep, dif_neg hs]
 #align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_empty
 -/
@@ -688,7 +688,7 @@ theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
   simp_rw [hs.infsep_of_fintype]
   rcases@Finset.exists_mem_eq_inf' _ _ _ s.off_diag.to_finset (by simpa) (uncurry dist) with
     ⟨_, hxy, hed⟩
-  simp_rw [mem_to_finset] at hxy 
+  simp_rw [mem_to_finset] at hxy
   exact ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.infsep_exists_of_finite Set.Nontrivial.infsep_exists_of_finite
 -/

f4758115

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -264,7 +264,14 @@ theorem Finset.coe_einfsep [DecidableEq α] {s : Finset α} :
 /- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.einfsep_exists_of_finite /-
 theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
-    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y := by classical
+    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y := by
+  classical
+  cases nonempty_fintype s
+  simp_rw [einfsep_of_fintype]
+  rcases@Finset.exists_mem_eq_inf _ _ _ _ s.off_diag.to_finset (by simpa) (uncurry edist) with
+    ⟨_, hxy, hed⟩
+  simp_rw [mem_to_finset] at hxy 
+  refine' ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.einfsep_exists_of_finite Set.Nontrivial.einfsep_exists_of_finite
 -/
 
@@ -602,7 +609,8 @@ theorem infsep_eq_iInf [Decidable s.Nontrivial] :
 
 #print Set.Nontrivial.infsep_eq_iInf /-
 theorem Nontrivial.infsep_eq_iInf (hs : s.Nontrivial) :
-    s.infsep = ⨅ d : s.offDiag, (uncurry dist) (d : α × α) := by classical
+    s.infsep = ⨅ d : s.offDiag, (uncurry dist) (d : α × α) := by
+  classical rw [infsep_eq_infi, if_pos hs]
 #align set.nontrivial.infsep_eq_infi Set.Nontrivial.infsep_eq_iInf
 -/
 
@@ -620,7 +628,8 @@ theorem infsep_of_fintype [Decidable s.Nontrivial] [DecidableEq α] [Fintype s]
 
 #print Set.Nontrivial.infsep_of_fintype /-
 theorem Nontrivial.infsep_of_fintype [DecidableEq α] [Fintype s] (hs : s.Nontrivial) :
-    s.infsep = s.offDiag.toFinset.inf' (by simpa) (uncurry dist) := by classical
+    s.infsep = s.offDiag.toFinset.inf' (by simpa) (uncurry dist) := by
+  classical rw [infsep_of_fintype, dif_pos hs]
 #align set.nontrivial.infsep_of_fintype Set.Nontrivial.infsep_of_fintype
 -/
 
@@ -639,7 +648,8 @@ theorem Finite.infsep [Decidable s.Nontrivial] (hsf : s.Finite) :
 
 #print Set.Finite.infsep_of_nontrivial /-
 theorem Finite.infsep_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
-    s.infsep = hsf.offDiag.toFinset.inf' (by simpa) (uncurry dist) := by classical
+    s.infsep = hsf.offDiag.toFinset.inf' (by simpa) (uncurry dist) := by
+  classical simp_rw [hsf.infsep, dif_pos hs]
 #align set.finite.infsep_of_nontrivial Set.Finite.infsep_of_nontrivial
 -/
 
@@ -672,7 +682,14 @@ theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs
 /- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.infsep_exists_of_finite /-
 theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
-    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y := by classical
+    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y := by
+  classical
+  cases nonempty_fintype s
+  simp_rw [hs.infsep_of_fintype]
+  rcases@Finset.exists_mem_eq_inf' _ _ _ s.off_diag.to_finset (by simpa) (uncurry dist) with
+    ⟨_, hxy, hed⟩
+  simp_rw [mem_to_finset] at hxy 
+  exact ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.infsep_exists_of_finite Set.Nontrivial.infsep_exists_of_finite
 -/

f4758115

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -264,14 +264,7 @@ theorem Finset.coe_einfsep [DecidableEq α] {s : Finset α} :
 /- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.einfsep_exists_of_finite /-
 theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
-    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y := by
-  classical
-  cases nonempty_fintype s
-  simp_rw [einfsep_of_fintype]
-  rcases@Finset.exists_mem_eq_inf _ _ _ _ s.off_diag.to_finset (by simpa) (uncurry edist) with
-    ⟨_, hxy, hed⟩
-  simp_rw [mem_to_finset] at hxy 
-  refine' ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
+    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y := by classical
 #align set.nontrivial.einfsep_exists_of_finite Set.Nontrivial.einfsep_exists_of_finite
 -/
 
@@ -609,8 +602,7 @@ theorem infsep_eq_iInf [Decidable s.Nontrivial] :
 
 #print Set.Nontrivial.infsep_eq_iInf /-
 theorem Nontrivial.infsep_eq_iInf (hs : s.Nontrivial) :
-    s.infsep = ⨅ d : s.offDiag, (uncurry dist) (d : α × α) := by
-  classical rw [infsep_eq_infi, if_pos hs]
+    s.infsep = ⨅ d : s.offDiag, (uncurry dist) (d : α × α) := by classical
 #align set.nontrivial.infsep_eq_infi Set.Nontrivial.infsep_eq_iInf
 -/
 
@@ -628,8 +620,7 @@ theorem infsep_of_fintype [Decidable s.Nontrivial] [DecidableEq α] [Fintype s]
 
 #print Set.Nontrivial.infsep_of_fintype /-
 theorem Nontrivial.infsep_of_fintype [DecidableEq α] [Fintype s] (hs : s.Nontrivial) :
-    s.infsep = s.offDiag.toFinset.inf' (by simpa) (uncurry dist) := by
-  classical rw [infsep_of_fintype, dif_pos hs]
+    s.infsep = s.offDiag.toFinset.inf' (by simpa) (uncurry dist) := by classical
 #align set.nontrivial.infsep_of_fintype Set.Nontrivial.infsep_of_fintype
 -/
 
@@ -648,8 +639,7 @@ theorem Finite.infsep [Decidable s.Nontrivial] (hsf : s.Finite) :
 
 #print Set.Finite.infsep_of_nontrivial /-
 theorem Finite.infsep_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
-    s.infsep = hsf.offDiag.toFinset.inf' (by simpa) (uncurry dist) := by
-  classical simp_rw [hsf.infsep, dif_pos hs]
+    s.infsep = hsf.offDiag.toFinset.inf' (by simpa) (uncurry dist) := by classical
 #align set.finite.infsep_of_nontrivial Set.Finite.infsep_of_nontrivial
 -/
 
@@ -682,14 +672,7 @@ theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs
 /- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.infsep_exists_of_finite /-
 theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
-    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y := by
-  classical
-  cases nonempty_fintype s
-  simp_rw [hs.infsep_of_fintype]
-  rcases@Finset.exists_mem_eq_inf' _ _ _ s.off_diag.to_finset (by simpa) (uncurry dist) with
-    ⟨_, hxy, hed⟩
-  simp_rw [mem_to_finset] at hxy 
-  exact ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
+    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y := by classical
 #align set.nontrivial.infsep_exists_of_finite Set.Nontrivial.infsep_exists_of_finite
 -/

f4758115

bump to nightly-2023-10-21-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

a2dc86f8

Diff

@@ -74,7 +74,8 @@ theorem einfsep_zero :
 theorem einfsep_pos :
     0 < s.einfsep ↔
       ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
-  by rw [pos_iff_ne_zero, Ne.def, einfsep_zero]; simp only [not_forall, not_exists, not_lt]
+  by rw [pos_iff_ne_zero, Ne.def, einfsep_zero];
+  simp only [Classical.not_forall, not_exists, not_lt]
 #align set.einfsep_pos Set.einfsep_pos
 -/

f4758115

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2022 Wrenna Robson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Wrenna Robson
 -/
-import Mathbin.Topology.MetricSpace.Basic
+import Topology.MetricSpace.Basic
 
 #align_import topology.metric_space.infsep from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
 
@@ -52,7 +52,7 @@ section EDist
 
 variable [EDist α] {x y : α} {s t : Set α}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.le_einfsep_iff /-
 theorem le_einfsep_iff {d} :
     d ≤ s.einfsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y := by
@@ -60,7 +60,7 @@ theorem le_einfsep_iff {d} :
 #align set.le_einfsep_iff Set.le_einfsep_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_zero /-
 theorem einfsep_zero :
     s.einfsep = 0 ↔
@@ -69,7 +69,7 @@ theorem einfsep_zero :
 #align set.einfsep_zero Set.einfsep_zero
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_pos /-
 theorem einfsep_pos :
     0 < s.einfsep ↔
@@ -78,7 +78,7 @@ theorem einfsep_pos :
 #align set.einfsep_pos Set.einfsep_pos
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_top /-
 theorem einfsep_top :
     s.einfsep = ∞ ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), edist x y = ∞ := by
@@ -86,7 +86,7 @@ theorem einfsep_top :
 #align set.einfsep_top Set.einfsep_top
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_lt_top /-
 theorem einfsep_lt_top :
     s.einfsep < ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y < ∞ := by
@@ -94,7 +94,7 @@ theorem einfsep_lt_top :
 #align set.einfsep_lt_top Set.einfsep_lt_top
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_ne_top /-
 theorem einfsep_ne_top :
     s.einfsep ≠ ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y ≠ ∞ := by
@@ -102,7 +102,7 @@ theorem einfsep_ne_top :
 #align set.einfsep_ne_top Set.einfsep_ne_top
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_lt_iff /-
 theorem einfsep_lt_iff {d} :
     s.einfsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (h : x ≠ y), edist x y < d := by
@@ -128,7 +128,7 @@ theorem Subsingleton.einfsep (hs : s.Subsingleton) : s.einfsep = ∞ := by rw [e
 #align set.subsingleton.einfsep Set.Subsingleton.einfsep
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.le_einfsep_image_iff /-
 theorem le_einfsep_image_iff {d} {f : β → α} {s : Set β} :
     d ≤ einfsep (f '' s) ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s), f x ≠ f y → d ≤ edist (f x) (f y) :=
@@ -157,7 +157,7 @@ theorem einfsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (h
 #align set.einfsep_le_of_mem_of_edist_le Set.einfsep_le_of_mem_of_edist_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.le_einfsep /-
 theorem le_einfsep {d} (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y) :
     d ≤ s.einfsep :=
@@ -260,7 +260,7 @@ theorem Finset.coe_einfsep [DecidableEq α] {s : Finset α} :
 #align set.finset.coe_einfsep Set.Finset.coe_einfsep
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.einfsep_exists_of_finite /-
 theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y := by
@@ -274,7 +274,7 @@ theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
 #align set.nontrivial.einfsep_exists_of_finite Set.Nontrivial.einfsep_exists_of_finite
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Finite.einfsep_exists_of_nontrivial /-
 theorem Finite.einfsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y :=
@@ -375,7 +375,7 @@ theorem einfsep_ne_top_iff : s.einfsep ≠ ∞ ↔ s.Nontrivial :=
 #align set.einfsep_ne_top_iff Set.einfsep_ne_top_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.le_einfsep_of_forall_dist_le /-
 theorem le_einfsep_of_forall_dist_le {d}
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) :
@@ -402,7 +402,7 @@ theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
 #align set.einfsep_pos_of_finite Set.einfsep_pos_of_finite
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.relatively_discrete_of_finite /-
 theorem relatively_discrete_of_finite [Finite s] :
     ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y := by
@@ -417,7 +417,7 @@ theorem Finite.einfsep_pos (hs : s.Finite) : 0 < s.einfsep :=
 #align set.finite.einfsep_pos Set.Finite.einfsep_pos
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Finite.relatively_discrete /-
 theorem Finite.relatively_discrete (hs : s.Finite) :
     ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
@@ -517,7 +517,7 @@ section PseudoMetricSpace
 
 variable [PseudoMetricSpace α] {x y z : α} {s t : Set α}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.le_infsep_iff /-
 theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
     d ≤ s.infsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y := by
@@ -526,7 +526,7 @@ theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
 #align set.nontrivial.le_infsep_iff Set.Nontrivial.le_infsep_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.infsep_lt_iff /-
 theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
     s.infsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), dist x y < d := by
@@ -534,7 +534,7 @@ theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
 #align set.nontrivial.infsep_lt_iff Set.Nontrivial.infsep_lt_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.le_infsep /-
 theorem Nontrivial.le_infsep {d} (hs : s.Nontrivial)
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) : d ≤ s.infsep :=
@@ -678,7 +678,7 @@ theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs
 #align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_empty
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.infsep_exists_of_finite /-
 theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y := by
@@ -692,7 +692,7 @@ theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
 #align set.nontrivial.infsep_exists_of_finite Set.Nontrivial.infsep_exists_of_finite
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Finite.infsep_exists_of_nontrivial /-
 theorem Finite.infsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y :=

f4758115

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Wrenna Robson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Wrenna Robson
-
-! This file was ported from Lean 3 source module topology.metric_space.infsep
-! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.MetricSpace.Basic
 
+#align_import topology.metric_space.infsep from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
 /-!
 # Infimum separation
 
@@ -55,7 +52,7 @@ section EDist
 
 variable [EDist α] {x y : α} {s t : Set α}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.le_einfsep_iff /-
 theorem le_einfsep_iff {d} :
     d ≤ s.einfsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y := by
@@ -63,7 +60,7 @@ theorem le_einfsep_iff {d} :
 #align set.le_einfsep_iff Set.le_einfsep_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_zero /-
 theorem einfsep_zero :
     s.einfsep = 0 ↔
@@ -72,7 +69,7 @@ theorem einfsep_zero :
 #align set.einfsep_zero Set.einfsep_zero
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_pos /-
 theorem einfsep_pos :
     0 < s.einfsep ↔
@@ -81,7 +78,7 @@ theorem einfsep_pos :
 #align set.einfsep_pos Set.einfsep_pos
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_top /-
 theorem einfsep_top :
     s.einfsep = ∞ ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), edist x y = ∞ := by
@@ -89,7 +86,7 @@ theorem einfsep_top :
 #align set.einfsep_top Set.einfsep_top
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_lt_top /-
 theorem einfsep_lt_top :
     s.einfsep < ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y < ∞ := by
@@ -97,7 +94,7 @@ theorem einfsep_lt_top :
 #align set.einfsep_lt_top Set.einfsep_lt_top
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_ne_top /-
 theorem einfsep_ne_top :
     s.einfsep ≠ ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y ≠ ∞ := by
@@ -105,7 +102,7 @@ theorem einfsep_ne_top :
 #align set.einfsep_ne_top Set.einfsep_ne_top
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.einfsep_lt_iff /-
 theorem einfsep_lt_iff {d} :
     s.einfsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (h : x ≠ y), edist x y < d := by
@@ -131,7 +128,7 @@ theorem Subsingleton.einfsep (hs : s.Subsingleton) : s.einfsep = ∞ := by rw [e
 #align set.subsingleton.einfsep Set.Subsingleton.einfsep
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.le_einfsep_image_iff /-
 theorem le_einfsep_image_iff {d} {f : β → α} {s : Set β} :
     d ≤ einfsep (f '' s) ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s), f x ≠ f y → d ≤ edist (f x) (f y) :=
@@ -160,7 +157,7 @@ theorem einfsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (h
 #align set.einfsep_le_of_mem_of_edist_le Set.einfsep_le_of_mem_of_edist_le
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.le_einfsep /-
 theorem le_einfsep {d} (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y) :
     d ≤ s.einfsep :=
@@ -263,7 +260,7 @@ theorem Finset.coe_einfsep [DecidableEq α] {s : Finset α} :
 #align set.finset.coe_einfsep Set.Finset.coe_einfsep
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.einfsep_exists_of_finite /-
 theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y := by
@@ -277,7 +274,7 @@ theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
 #align set.nontrivial.einfsep_exists_of_finite Set.Nontrivial.einfsep_exists_of_finite
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Finite.einfsep_exists_of_nontrivial /-
 theorem Finite.einfsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y :=
@@ -378,7 +375,7 @@ theorem einfsep_ne_top_iff : s.einfsep ≠ ∞ ↔ s.Nontrivial :=
 #align set.einfsep_ne_top_iff Set.einfsep_ne_top_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.le_einfsep_of_forall_dist_le /-
 theorem le_einfsep_of_forall_dist_le {d}
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) :
@@ -405,7 +402,7 @@ theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
 #align set.einfsep_pos_of_finite Set.einfsep_pos_of_finite
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.relatively_discrete_of_finite /-
 theorem relatively_discrete_of_finite [Finite s] :
     ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y := by
@@ -420,7 +417,7 @@ theorem Finite.einfsep_pos (hs : s.Finite) : 0 < s.einfsep :=
 #align set.finite.einfsep_pos Set.Finite.einfsep_pos
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Finite.relatively_discrete /-
 theorem Finite.relatively_discrete (hs : s.Finite) :
     ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
@@ -520,7 +517,7 @@ section PseudoMetricSpace
 
 variable [PseudoMetricSpace α] {x y z : α} {s t : Set α}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.le_infsep_iff /-
 theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
     d ≤ s.infsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y := by
@@ -529,7 +526,7 @@ theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
 #align set.nontrivial.le_infsep_iff Set.Nontrivial.le_infsep_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.infsep_lt_iff /-
 theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
     s.infsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), dist x y < d := by
@@ -537,7 +534,7 @@ theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
 #align set.nontrivial.infsep_lt_iff Set.Nontrivial.infsep_lt_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.le_infsep /-
 theorem Nontrivial.le_infsep {d} (hs : s.Nontrivial)
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) : d ≤ s.infsep :=
@@ -681,7 +678,7 @@ theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs
 #align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_empty
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.infsep_exists_of_finite /-
 theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y := by
@@ -695,7 +692,7 @@ theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
 #align set.nontrivial.infsep_exists_of_finite Set.Nontrivial.infsep_exists_of_finite
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Finite.infsep_exists_of_nontrivial /-
 theorem Finite.infsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y :=

f4758115

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -56,137 +56,188 @@ section EDist
 variable [EDist α] {x y : α} {s t : Set α}
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.le_einfsep_iff /-
 theorem le_einfsep_iff {d} :
     d ≤ s.einfsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y := by
   simp_rw [einfsep, le_iInf_iff]
 #align set.le_einfsep_iff Set.le_einfsep_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.einfsep_zero /-
 theorem einfsep_zero :
     s.einfsep = 0 ↔
       ∀ (C) (hC : 0 < C), ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y < C :=
   by simp_rw [einfsep, ← bot_eq_zero, iInf_eq_bot, iInf_lt_iff]
 #align set.einfsep_zero Set.einfsep_zero
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.einfsep_pos /-
 theorem einfsep_pos :
     0 < s.einfsep ↔
       ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
   by rw [pos_iff_ne_zero, Ne.def, einfsep_zero]; simp only [not_forall, not_exists, not_lt]
 #align set.einfsep_pos Set.einfsep_pos
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.einfsep_top /-
 theorem einfsep_top :
     s.einfsep = ∞ ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), edist x y = ∞ := by
   simp_rw [einfsep, iInf_eq_top]
 #align set.einfsep_top Set.einfsep_top
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.einfsep_lt_top /-
 theorem einfsep_lt_top :
     s.einfsep < ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y < ∞ := by
   simp_rw [einfsep, iInf_lt_iff]
 #align set.einfsep_lt_top Set.einfsep_lt_top
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.einfsep_ne_top /-
 theorem einfsep_ne_top :
     s.einfsep ≠ ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y ≠ ∞ := by
   simp_rw [← lt_top_iff_ne_top, einfsep_lt_top]
 #align set.einfsep_ne_top Set.einfsep_ne_top
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.einfsep_lt_iff /-
 theorem einfsep_lt_iff {d} :
     s.einfsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (h : x ≠ y), edist x y < d := by
   simp_rw [einfsep, iInf_lt_iff]
 #align set.einfsep_lt_iff Set.einfsep_lt_iff
+-/
 
+#print Set.nontrivial_of_einfsep_lt_top /-
 theorem nontrivial_of_einfsep_lt_top (hs : s.einfsep < ∞) : s.Nontrivial := by
   rcases einfsep_lt_top.1 hs with ⟨_, hx, _, hy, hxy, _⟩; exact ⟨_, hx, _, hy, hxy⟩
 #align set.nontrivial_of_einfsep_lt_top Set.nontrivial_of_einfsep_lt_top
+-/
 
+#print Set.nontrivial_of_einfsep_ne_top /-
 theorem nontrivial_of_einfsep_ne_top (hs : s.einfsep ≠ ∞) : s.Nontrivial :=
   nontrivial_of_einfsep_lt_top (lt_top_iff_ne_top.mpr hs)
 #align set.nontrivial_of_einfsep_ne_top Set.nontrivial_of_einfsep_ne_top
+-/
 
+#print Set.Subsingleton.einfsep /-
 theorem Subsingleton.einfsep (hs : s.Subsingleton) : s.einfsep = ∞ := by rw [einfsep_top];
   exact fun _ hx _ hy hxy => (hxy <| hs hx hy).elim
 #align set.subsingleton.einfsep Set.Subsingleton.einfsep
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.le_einfsep_image_iff /-
 theorem le_einfsep_image_iff {d} {f : β → α} {s : Set β} :
     d ≤ einfsep (f '' s) ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s), f x ≠ f y → d ≤ edist (f x) (f y) :=
   by simp_rw [le_einfsep_iff, ball_image_iff]
 #align set.le_einfsep_image_iff Set.le_einfsep_image_iff
+-/
 
+#print Set.le_edist_of_le_einfsep /-
 theorem le_edist_of_le_einfsep {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y)
     (hd : d ≤ s.einfsep) : d ≤ edist x y :=
   le_einfsep_iff.1 hd x hx y hy hxy
 #align set.le_edist_of_le_einfsep Set.le_edist_of_le_einfsep
+-/
 
+#print Set.einfsep_le_edist_of_mem /-
 theorem einfsep_le_edist_of_mem {x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y) :
     s.einfsep ≤ edist x y :=
   le_edist_of_le_einfsep hx hy hxy le_rfl
 #align set.einfsep_le_edist_of_mem Set.einfsep_le_edist_of_mem
+-/
 
+#print Set.einfsep_le_of_mem_of_edist_le /-
 theorem einfsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y)
     (hxy' : edist x y ≤ d) : s.einfsep ≤ d :=
   le_trans (einfsep_le_edist_of_mem hx hy hxy) hxy'
 #align set.einfsep_le_of_mem_of_edist_le Set.einfsep_le_of_mem_of_edist_le
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.le_einfsep /-
 theorem le_einfsep {d} (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y) :
     d ≤ s.einfsep :=
   le_einfsep_iff.2 h
 #align set.le_einfsep Set.le_einfsep
+-/
 
+#print Set.einfsep_empty /-
 @[simp]
 theorem einfsep_empty : (∅ : Set α).einfsep = ∞ :=
   subsingleton_empty.einfsep
 #align set.einfsep_empty Set.einfsep_empty
+-/
 
+#print Set.einfsep_singleton /-
 @[simp]
 theorem einfsep_singleton : ({x} : Set α).einfsep = ∞ :=
   subsingleton_singleton.einfsep
 #align set.einfsep_singleton Set.einfsep_singleton
+-/
 
+#print Set.einfsep_iUnion_mem_option /-
 theorem einfsep_iUnion_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
     (⋃ i ∈ o, s i).einfsep = ⨅ i ∈ o, (s i).einfsep := by cases o <;> simp
 #align set.einfsep_Union_mem_option Set.einfsep_iUnion_mem_option
+-/
 
+#print Set.einfsep_anti /-
 theorem einfsep_anti (hst : s ⊆ t) : t.einfsep ≤ s.einfsep :=
   le_einfsep fun x hx y hy => einfsep_le_edist_of_mem (hst hx) (hst hy)
 #align set.einfsep_anti Set.einfsep_anti
+-/
 
+#print Set.einfsep_insert_le /-
 theorem einfsep_insert_le : (insert x s).einfsep ≤ ⨅ (y ∈ s) (hxy : x ≠ y), edist x y :=
   by
   simp_rw [le_iInf_iff]
   refine' fun _ hy hxy => einfsep_le_edist_of_mem (mem_insert _ _) (mem_insert_of_mem _ hy) hxy
 #align set.einfsep_insert_le Set.einfsep_insert_le
+-/
 
+#print Set.le_einfsep_pair /-
 theorem le_einfsep_pair : edist x y ⊓ edist y x ≤ ({x, y} : Set α).einfsep :=
   by
   simp_rw [le_einfsep_iff, inf_le_iff, mem_insert_iff, mem_singleton_iff]
   rintro a (rfl | rfl) b (rfl | rfl) hab <;> finish
 #align set.le_einfsep_pair Set.le_einfsep_pair
+-/
 
+#print Set.einfsep_pair_le_left /-
 theorem einfsep_pair_le_left (hxy : x ≠ y) : ({x, y} : Set α).einfsep ≤ edist x y :=
   einfsep_le_edist_of_mem (mem_insert _ _) (mem_insert_of_mem _ (mem_singleton _)) hxy
 #align set.einfsep_pair_le_left Set.einfsep_pair_le_left
+-/
 
+#print Set.einfsep_pair_le_right /-
 theorem einfsep_pair_le_right (hxy : x ≠ y) : ({x, y} : Set α).einfsep ≤ edist y x := by
   rw [pair_comm] <;> exact einfsep_pair_le_left hxy.symm
 #align set.einfsep_pair_le_right Set.einfsep_pair_le_right
+-/
 
+#print Set.einfsep_pair_eq_inf /-
 theorem einfsep_pair_eq_inf (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist x y ⊓ edist y x :=
   le_antisymm (le_inf (einfsep_pair_le_left hxy) (einfsep_pair_le_right hxy)) le_einfsep_pair
 #align set.einfsep_pair_eq_inf Set.einfsep_pair_eq_inf
+-/
 
+#print Set.einfsep_eq_iInf /-
 theorem einfsep_eq_iInf : s.einfsep = ⨅ d : s.offDiag, (uncurry edist) (d : α × α) :=
   by
   refine' eq_of_forall_le_iff fun _ => _
   simp_rw [le_einfsep_iff, le_iInf_iff, imp_forall_iff, SetCoe.forall, Subtype.coe_mk, mem_off_diag,
     Prod.forall, uncurry_apply_pair, and_imp]
 #align set.einfsep_eq_infi Set.einfsep_eq_iInf
+-/
 
+#print Set.einfsep_of_fintype /-
 theorem einfsep_of_fintype [DecidableEq α] [Fintype s] :
     s.einfsep = s.offDiag.toFinset.inf (uncurry edist) :=
   by
@@ -194,18 +245,23 @@ theorem einfsep_of_fintype [DecidableEq α] [Fintype s] :
   simp_rw [le_einfsep_iff, imp_forall_iff, Finset.le_inf_iff, mem_to_finset, mem_off_diag,
     Prod.forall, uncurry_apply_pair, and_imp]
 #align set.einfsep_of_fintype Set.einfsep_of_fintype
+-/
 
+#print Set.Finite.einfsep /-
 theorem Finite.einfsep (hs : s.Finite) : s.einfsep = hs.offDiag.toFinset.inf (uncurry edist) :=
   by
   refine' eq_of_forall_le_iff fun _ => _
   simp_rw [le_einfsep_iff, imp_forall_iff, Finset.le_inf_iff, finite.mem_to_finset, mem_off_diag,
     Prod.forall, uncurry_apply_pair, and_imp]
 #align set.finite.einfsep Set.Finite.einfsep
+-/
 
+#print Set.Finset.coe_einfsep /-
 theorem Finset.coe_einfsep [DecidableEq α] {s : Finset α} :
     (s : Set α).einfsep = s.offDiag.inf (uncurry edist) := by
   simp_rw [einfsep_of_fintype, ← Finset.coe_offDiag, Finset.toFinset_coe]
 #align set.finset.coe_einfsep Set.Finset.coe_einfsep
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.einfsep_exists_of_finite /-
@@ -245,6 +301,7 @@ theorem einfsep_pair (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist x y :=
 #align set.einfsep_pair Set.einfsep_pair
 -/
 
+#print Set.einfsep_insert /-
 theorem einfsep_insert : einfsep (insert x s) = (⨅ (y ∈ s) (hxy : x ≠ y), edist x y) ⊓ s.einfsep :=
   by
   refine' le_antisymm (le_min einfsep_insert_le (einfsep_anti (subset_insert _ _))) _
@@ -255,13 +312,17 @@ theorem einfsep_insert : einfsep (insert x s) = (⨅ (y ∈ s) (hxy : x ≠ y),
   · rw [edist_comm]; exact Or.inl (iInf_le_of_le _ (iInf₂_le hy hyz.symm))
   · exact Or.inr (einfsep_le_edist_of_mem hy hz hyz)
 #align set.einfsep_insert Set.einfsep_insert
+-/
 
+#print Set.einfsep_triple /-
 theorem einfsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
     einfsep ({x, y, z} : Set α) = edist x y ⊓ edist x z ⊓ edist y z := by
   simp_rw [einfsep_insert, iInf_insert, iInf_singleton, einfsep_singleton, inf_top_eq,
     ciInf_pos hxy, ciInf_pos hyz, ciInf_pos hxz]
 #align set.einfsep_triple Set.einfsep_triple
+-/
 
+#print Set.le_einfsep_pi_of_le /-
 theorem le_einfsep_pi_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMetricSpace (π b)]
     {s : ∀ b : β, Set (π b)} {c : ℝ≥0∞} (h : ∀ b, c ≤ einfsep (s b)) :
     c ≤ einfsep (Set.pi univ s) :=
@@ -271,6 +332,7 @@ theorem le_einfsep_pi_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMet
   rcases function.ne_iff.mp hxy with ⟨i, hi⟩
   exact le_trans (le_einfsep_iff.1 (h i) _ (hx _) _ (hy _) hi) (edist_le_pi_edist _ _ i)
 #align set.le_einfsep_pi_of_le Set.le_einfsep_pi_of_le
+-/
 
 end PseudoEMetricSpace
 
@@ -278,38 +340,52 @@ section PseudoMetricSpace
 
 variable [PseudoMetricSpace α] {s : Set α}
 
+#print Set.subsingleton_of_einfsep_eq_top /-
 theorem subsingleton_of_einfsep_eq_top (hs : s.einfsep = ∞) : s.Subsingleton :=
   by
   rw [einfsep_top] at hs 
   exact fun _ hx _ hy => of_not_not fun hxy => edist_ne_top _ _ (hs _ hx _ hy hxy)
 #align set.subsingleton_of_einfsep_eq_top Set.subsingleton_of_einfsep_eq_top
+-/
 
+#print Set.einfsep_eq_top_iff /-
 theorem einfsep_eq_top_iff : s.einfsep = ∞ ↔ s.Subsingleton :=
   ⟨subsingleton_of_einfsep_eq_top, Subsingleton.einfsep⟩
 #align set.einfsep_eq_top_iff Set.einfsep_eq_top_iff
+-/
 
+#print Set.Nontrivial.einfsep_ne_top /-
 theorem Nontrivial.einfsep_ne_top (hs : s.Nontrivial) : s.einfsep ≠ ∞ := by contrapose! hs;
   rw [not_nontrivial_iff]; exact subsingleton_of_einfsep_eq_top hs
 #align set.nontrivial.einfsep_ne_top Set.Nontrivial.einfsep_ne_top
+-/
 
+#print Set.Nontrivial.einfsep_lt_top /-
 theorem Nontrivial.einfsep_lt_top (hs : s.Nontrivial) : s.einfsep < ∞ := by rw [lt_top_iff_ne_top];
   exact hs.einfsep_ne_top
 #align set.nontrivial.einfsep_lt_top Set.Nontrivial.einfsep_lt_top
+-/
 
+#print Set.einfsep_lt_top_iff /-
 theorem einfsep_lt_top_iff : s.einfsep < ∞ ↔ s.Nontrivial :=
   ⟨nontrivial_of_einfsep_lt_top, Nontrivial.einfsep_lt_top⟩
 #align set.einfsep_lt_top_iff Set.einfsep_lt_top_iff
+-/
 
+#print Set.einfsep_ne_top_iff /-
 theorem einfsep_ne_top_iff : s.einfsep ≠ ∞ ↔ s.Nontrivial :=
   ⟨nontrivial_of_einfsep_ne_top, Nontrivial.einfsep_ne_top⟩
 #align set.einfsep_ne_top_iff Set.einfsep_ne_top_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.le_einfsep_of_forall_dist_le /-
 theorem le_einfsep_of_forall_dist_le {d}
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) :
     ENNReal.ofReal d ≤ s.einfsep :=
   le_einfsep fun x hx y hy hxy => (edist_dist x y).symm ▸ ENNReal.ofReal_le_ofReal (h x hx y hy hxy)
 #align set.le_einfsep_of_forall_dist_le Set.le_einfsep_of_forall_dist_le
+-/
 
 end PseudoMetricSpace
 
@@ -317,6 +393,7 @@ section EMetricSpace
 
 variable [EMetricSpace α] {x y z : α} {s t : Set α} {C : ℝ≥0∞} {sC : Set ℝ≥0∞}
 
+#print Set.einfsep_pos_of_finite /-
 theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
   by
   cases nonempty_fintype s
@@ -326,24 +403,31 @@ theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
   · rw [not_nontrivial_iff] at hs 
     exact hs.einfsep.symm ▸ WithTop.zero_lt_top
 #align set.einfsep_pos_of_finite Set.einfsep_pos_of_finite
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.relatively_discrete_of_finite /-
 theorem relatively_discrete_of_finite [Finite s] :
     ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y := by
   rw [← einfsep_pos]; exact einfsep_pos_of_finite
 #align set.relatively_discrete_of_finite Set.relatively_discrete_of_finite
+-/
 
+#print Set.Finite.einfsep_pos /-
 theorem Finite.einfsep_pos (hs : s.Finite) : 0 < s.einfsep :=
   letI := hs.fintype
   einfsep_pos_of_finite
 #align set.finite.einfsep_pos Set.Finite.einfsep_pos
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.Finite.relatively_discrete /-
 theorem Finite.relatively_discrete (hs : s.Finite) :
     ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
   letI := hs.fintype
   relatively_discrete_of_finite
 #align set.finite.relatively_discrete Set.Finite.relatively_discrete
+-/
 
 end EMetricSpace
 
@@ -366,38 +450,54 @@ section EDist
 
 variable [EDist α] {x y : α} {s : Set α}
 
+#print Set.infsep_zero /-
 theorem infsep_zero : s.infsep = 0 ↔ s.einfsep = 0 ∨ s.einfsep = ∞ := by
   rw [infsep, ENNReal.toReal_eq_zero_iff]
 #align set.infsep_zero Set.infsep_zero
+-/
 
+#print Set.infsep_nonneg /-
 theorem infsep_nonneg : 0 ≤ s.infsep :=
   ENNReal.toReal_nonneg
 #align set.infsep_nonneg Set.infsep_nonneg
+-/
 
+#print Set.infsep_pos /-
 theorem infsep_pos : 0 < s.infsep ↔ 0 < s.einfsep ∧ s.einfsep < ∞ := by
   simp_rw [infsep, ENNReal.toReal_pos_iff]
 #align set.infsep_pos Set.infsep_pos
+-/
 
+#print Set.Subsingleton.infsep_zero /-
 theorem Subsingleton.infsep_zero (hs : s.Subsingleton) : s.infsep = 0 := by
   rw [infsep_zero, hs.einfsep]; right; rfl
 #align set.subsingleton.infsep_zero Set.Subsingleton.infsep_zero
+-/
 
+#print Set.nontrivial_of_infsep_pos /-
 theorem nontrivial_of_infsep_pos (hs : 0 < s.infsep) : s.Nontrivial := by contrapose hs;
   rw [not_nontrivial_iff] at hs ; exact hs.infsep_zero ▸ lt_irrefl _
 #align set.nontrivial_of_infsep_pos Set.nontrivial_of_infsep_pos
+-/
 
+#print Set.infsep_empty /-
 theorem infsep_empty : (∅ : Set α).infsep = 0 :=
   subsingleton_empty.infsep_zero
 #align set.infsep_empty Set.infsep_empty
+-/
 
+#print Set.infsep_singleton /-
 theorem infsep_singleton : ({x} : Set α).infsep = 0 :=
   subsingleton_singleton.infsep_zero
 #align set.infsep_singleton Set.infsep_singleton
+-/
 
+#print Set.infsep_pair_le_toReal_inf /-
 theorem infsep_pair_le_toReal_inf (hxy : x ≠ y) :
     ({x, y} : Set α).infsep ≤ (edist x y ⊓ edist y x).toReal := by
   simp_rw [infsep, einfsep_pair_eq_inf hxy]
 #align set.infsep_pair_le_to_real_inf Set.infsep_pair_le_toReal_inf
+-/
 
 end EDist
 
@@ -421,24 +521,31 @@ section PseudoMetricSpace
 variable [PseudoMetricSpace α] {x y z : α} {s t : Set α}
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.Nontrivial.le_infsep_iff /-
 theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
     d ≤ s.infsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y := by
   simp_rw [infsep, ← ENNReal.ofReal_le_iff_le_toReal hs.einfsep_ne_top, le_einfsep_iff, edist_dist,
     ENNReal.ofReal_le_ofReal_iff dist_nonneg]
 #align set.nontrivial.le_infsep_iff Set.Nontrivial.le_infsep_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.Nontrivial.infsep_lt_iff /-
 theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
     s.infsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), dist x y < d := by
   rw [← not_iff_not]; push_neg; exact hs.le_infsep_iff
 #align set.nontrivial.infsep_lt_iff Set.Nontrivial.infsep_lt_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.Nontrivial.le_infsep /-
 theorem Nontrivial.le_infsep {d} (hs : s.Nontrivial)
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) : d ≤ s.infsep :=
   hs.le_infsep_iff.2 h
 #align set.nontrivial.le_infsep Set.Nontrivial.le_infsep
+-/
 
+#print Set.le_edist_of_le_infsep /-
 theorem le_edist_of_le_infsep {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y)
     (hd : d ≤ s.infsep) : d ≤ dist x y :=
   by
@@ -448,15 +555,20 @@ theorem le_edist_of_le_infsep {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x 
     rw [hs.infsep_zero] at hd 
     exact le_trans hd dist_nonneg
 #align set.le_edist_of_le_infsep Set.le_edist_of_le_infsep
+-/
 
+#print Set.infsep_le_dist_of_mem /-
 theorem infsep_le_dist_of_mem (hx : x ∈ s) (hy : y ∈ s) (hxy : x ≠ y) : s.infsep ≤ dist x y :=
   le_edist_of_le_infsep hx hy hxy le_rfl
 #align set.infsep_le_dist_of_mem Set.infsep_le_dist_of_mem
+-/
 
+#print Set.infsep_le_of_mem_of_edist_le /-
 theorem infsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y)
     (hxy' : dist x y ≤ d) : s.infsep ≤ d :=
   le_trans (infsep_le_dist_of_mem hx hy hxy) hxy'
 #align set.infsep_le_of_mem_of_edist_le Set.infsep_le_of_mem_of_edist_le
+-/
 
 #print Set.infsep_pair /-
 theorem infsep_pair : ({x, y} : Set α).infsep = dist x y := by
@@ -464,17 +576,22 @@ theorem infsep_pair : ({x, y} : Set α).infsep = dist x y := by
 #align set.infsep_pair Set.infsep_pair
 -/
 
+#print Set.infsep_triple /-
 theorem infsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
     ({x, y, z} : Set α).infsep = dist x y ⊓ dist x z ⊓ dist y z := by
   simp only [infsep, einfsep_triple hxy hyz hxz, ENNReal.toReal_inf, edist_ne_top x y,
     edist_ne_top x z, edist_ne_top y z, dist_edist, Ne.def, inf_eq_top_iff, and_self_iff,
     not_false_iff]
 #align set.infsep_triple Set.infsep_triple
+-/
 
+#print Set.Nontrivial.infsep_anti /-
 theorem Nontrivial.infsep_anti (hs : s.Nontrivial) (hst : s ⊆ t) : t.infsep ≤ s.infsep :=
   ENNReal.toReal_mono hs.einfsep_ne_top (einfsep_anti hst)
 #align set.nontrivial.infsep_anti Set.Nontrivial.infsep_anti
+-/
 
+#print Set.infsep_eq_iInf /-
 theorem infsep_eq_iInf [Decidable s.Nontrivial] :
     s.infsep = if s.Nontrivial then ⨅ d : s.offDiag, (uncurry dist) (d : α × α) else 0 :=
   by
@@ -490,12 +607,16 @@ theorem infsep_eq_iInf [Decidable s.Nontrivial] :
       mem_off_diag, Prod.forall, uncurry_apply_pair, and_imp]
   · exact (not_nontrivial_iff.mp hs).infsep_zero
 #align set.infsep_eq_infi Set.infsep_eq_iInf
+-/
 
+#print Set.Nontrivial.infsep_eq_iInf /-
 theorem Nontrivial.infsep_eq_iInf (hs : s.Nontrivial) :
     s.infsep = ⨅ d : s.offDiag, (uncurry dist) (d : α × α) := by
   classical rw [infsep_eq_infi, if_pos hs]
 #align set.nontrivial.infsep_eq_infi Set.Nontrivial.infsep_eq_iInf
+-/
 
+#print Set.infsep_of_fintype /-
 theorem infsep_of_fintype [Decidable s.Nontrivial] [DecidableEq α] [Fintype s] :
     s.infsep = if hs : s.Nontrivial then s.offDiag.toFinset.inf' (by simpa) (uncurry dist) else 0 :=
   by
@@ -505,6 +626,7 @@ theorem infsep_of_fintype [Decidable s.Nontrivial] [DecidableEq α] [Fintype s]
       Prod.forall, uncurry_apply_pair, and_imp]
   · rw [not_nontrivial_iff] at hs ; exact hs.infsep_zero
 #align set.infsep_of_fintype Set.infsep_of_fintype
+-/
 
 #print Set.Nontrivial.infsep_of_fintype /-
 theorem Nontrivial.infsep_of_fintype [DecidableEq α] [Fintype s] (hs : s.Nontrivial) :
@@ -513,6 +635,7 @@ theorem Nontrivial.infsep_of_fintype [DecidableEq α] [Fintype s] (hs : s.Nontri
 #align set.nontrivial.infsep_of_fintype Set.Nontrivial.infsep_of_fintype
 -/
 
+#print Set.Finite.infsep /-
 theorem Finite.infsep [Decidable s.Nontrivial] (hsf : s.Finite) :
     s.infsep =
       if hs : s.Nontrivial then hsf.offDiag.toFinset.inf' (by simpa) (uncurry dist) else 0 :=
@@ -523,6 +646,7 @@ theorem Finite.infsep [Decidable s.Nontrivial] (hsf : s.Finite) :
       mem_off_diag, Prod.forall, uncurry_apply_pair, and_imp]
   · rw [not_nontrivial_iff] at hs ; exact hs.infsep_zero
 #align set.finite.infsep Set.Finite.infsep
+-/
 
 #print Set.Finite.infsep_of_nontrivial /-
 theorem Finite.infsep_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
@@ -531,6 +655,7 @@ theorem Finite.infsep_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
 #align set.finite.infsep_of_nontrivial Set.Finite.infsep_of_nontrivial
 -/
 
+#print Finset.coe_infsep /-
 theorem Finset.coe_infsep [DecidableEq α] (s : Finset α) :
     (s : Set α).infsep = if hs : s.offDiag.Nonempty then s.offDiag.inf' hs (uncurry dist) else 0 :=
   by
@@ -540,6 +665,7 @@ theorem Finset.coe_infsep [DecidableEq α] (s : Finset α) :
   · simp_rw [(H.mpr hs).infsep_of_fintype, ← Finset.coe_offDiag, Finset.toFinset_coe]
   · exact (not_nontrivial_iff.mp (H.mp.mt hs)).infsep_zero
 #align finset.coe_infsep Finset.coe_infsep
+-/
 
 #print Finset.coe_infsep_of_offDiag_nonempty /-
 theorem Finset.coe_infsep_of_offDiag_nonempty [DecidableEq α] {s : Finset α}
@@ -548,10 +674,12 @@ theorem Finset.coe_infsep_of_offDiag_nonempty [DecidableEq α] {s : Finset α}
 #align finset.coe_infsep_of_off_diag_nonempty Finset.coe_infsep_of_offDiag_nonempty
 -/
 
+#print Finset.coe_infsep_of_offDiag_empty /-
 theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs : s.offDiag = ∅) :
     (s : Set α).infsep = 0 := by rw [← Finset.not_nonempty_iff_eq_empty] at hs ;
   rw [Finset.coe_infsep, dif_neg hs]
 #align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_empty
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.infsep_exists_of_finite /-
@@ -582,37 +710,49 @@ section MetricSpace
 
 variable [MetricSpace α] {s : Set α}
 
+#print Set.infsep_zero_iff_subsingleton_of_finite /-
 theorem infsep_zero_iff_subsingleton_of_finite [Finite s] : s.infsep = 0 ↔ s.Subsingleton :=
   by
   rw [infsep_zero, einfsep_eq_top_iff, or_iff_right_iff_imp]
   exact fun H => (einfsep_pos_of_finite.ne' H).elim
 #align set.infsep_zero_iff_subsingleton_of_finite Set.infsep_zero_iff_subsingleton_of_finite
+-/
 
+#print Set.infsep_pos_iff_nontrivial_of_finite /-
 theorem infsep_pos_iff_nontrivial_of_finite [Finite s] : 0 < s.infsep ↔ s.Nontrivial :=
   by
   rw [infsep_pos, einfsep_lt_top_iff, and_iff_right_iff_imp]
   exact fun _ => einfsep_pos_of_finite
 #align set.infsep_pos_iff_nontrivial_of_finite Set.infsep_pos_iff_nontrivial_of_finite
+-/
 
+#print Set.Finite.infsep_zero_iff_subsingleton /-
 theorem Finite.infsep_zero_iff_subsingleton (hs : s.Finite) : s.infsep = 0 ↔ s.Subsingleton :=
   letI := hs.fintype
   infsep_zero_iff_subsingleton_of_finite
 #align set.finite.infsep_zero_iff_subsingleton Set.Finite.infsep_zero_iff_subsingleton
+-/
 
+#print Set.Finite.infsep_pos_iff_nontrivial /-
 theorem Finite.infsep_pos_iff_nontrivial (hs : s.Finite) : 0 < s.infsep ↔ s.Nontrivial :=
   letI := hs.fintype
   infsep_pos_iff_nontrivial_of_finite
 #align set.finite.infsep_pos_iff_nontrivial Set.Finite.infsep_pos_iff_nontrivial
+-/
 
+#print Finset.infsep_zero_iff_subsingleton /-
 theorem Finset.infsep_zero_iff_subsingleton (s : Finset α) :
     (s : Set α).infsep = 0 ↔ (s : Set α).Subsingleton :=
   infsep_zero_iff_subsingleton_of_finite
 #align finset.infsep_zero_iff_subsingleton Finset.infsep_zero_iff_subsingleton
+-/
 
+#print Finset.infsep_pos_iff_nontrivial /-
 theorem Finset.infsep_pos_iff_nontrivial (s : Finset α) :
     0 < (s : Set α).infsep ↔ (s : Set α).Nontrivial :=
   infsep_pos_iff_nontrivial_of_finite
 #align finset.infsep_pos_iff_nontrivial Finset.infsep_pos_iff_nontrivial
+-/
 
 end MetricSpace

f4758115

bump to nightly-2023-06-08-23

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

d3cfe2e3

Diff

@@ -55,45 +55,45 @@ section EDist
 
 variable [EDist α] {x y : α} {s t : Set α}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_iff {d} :
     d ≤ s.einfsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y := by
   simp_rw [einfsep, le_iInf_iff]
 #align set.le_einfsep_iff Set.le_einfsep_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_zero :
     s.einfsep = 0 ↔
       ∀ (C) (hC : 0 < C), ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y < C :=
   by simp_rw [einfsep, ← bot_eq_zero, iInf_eq_bot, iInf_lt_iff]
 #align set.einfsep_zero Set.einfsep_zero
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_pos :
     0 < s.einfsep ↔
       ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
   by rw [pos_iff_ne_zero, Ne.def, einfsep_zero]; simp only [not_forall, not_exists, not_lt]
 #align set.einfsep_pos Set.einfsep_pos
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_top :
     s.einfsep = ∞ ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), edist x y = ∞ := by
   simp_rw [einfsep, iInf_eq_top]
 #align set.einfsep_top Set.einfsep_top
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_lt_top :
     s.einfsep < ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y < ∞ := by
   simp_rw [einfsep, iInf_lt_iff]
 #align set.einfsep_lt_top Set.einfsep_lt_top
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_ne_top :
     s.einfsep ≠ ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y ≠ ∞ := by
   simp_rw [← lt_top_iff_ne_top, einfsep_lt_top]
 #align set.einfsep_ne_top Set.einfsep_ne_top
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_lt_iff {d} :
     s.einfsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (h : x ≠ y), edist x y < d := by
   simp_rw [einfsep, iInf_lt_iff]
@@ -111,7 +111,7 @@ theorem Subsingleton.einfsep (hs : s.Subsingleton) : s.einfsep = ∞ := by rw [e
   exact fun _ hx _ hy hxy => (hxy <| hs hx hy).elim
 #align set.subsingleton.einfsep Set.Subsingleton.einfsep
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_image_iff {d} {f : β → α} {s : Set β} :
     d ≤ einfsep (f '' s) ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s), f x ≠ f y → d ≤ edist (f x) (f y) :=
   by simp_rw [le_einfsep_iff, ball_image_iff]
@@ -132,7 +132,7 @@ theorem einfsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (h
   le_trans (einfsep_le_edist_of_mem hx hy hxy) hxy'
 #align set.einfsep_le_of_mem_of_edist_le Set.einfsep_le_of_mem_of_edist_le
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep {d} (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y) :
     d ≤ s.einfsep :=
   le_einfsep_iff.2 h
@@ -207,7 +207,7 @@ theorem Finset.coe_einfsep [DecidableEq α] {s : Finset α} :
   simp_rw [einfsep_of_fintype, ← Finset.coe_offDiag, Finset.toFinset_coe]
 #align set.finset.coe_einfsep Set.Finset.coe_einfsep
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.einfsep_exists_of_finite /-
 theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y := by
@@ -221,7 +221,7 @@ theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
 #align set.nontrivial.einfsep_exists_of_finite Set.Nontrivial.einfsep_exists_of_finite
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Finite.einfsep_exists_of_nontrivial /-
 theorem Finite.einfsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y :=
@@ -304,7 +304,7 @@ theorem einfsep_ne_top_iff : s.einfsep ≠ ∞ ↔ s.Nontrivial :=
   ⟨nontrivial_of_einfsep_ne_top, Nontrivial.einfsep_ne_top⟩
 #align set.einfsep_ne_top_iff Set.einfsep_ne_top_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_of_forall_dist_le {d}
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) :
     ENNReal.ofReal d ≤ s.einfsep :=
@@ -327,7 +327,7 @@ theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
     exact hs.einfsep.symm ▸ WithTop.zero_lt_top
 #align set.einfsep_pos_of_finite Set.einfsep_pos_of_finite
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem relatively_discrete_of_finite [Finite s] :
     ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y := by
   rw [← einfsep_pos]; exact einfsep_pos_of_finite
@@ -338,7 +338,7 @@ theorem Finite.einfsep_pos (hs : s.Finite) : 0 < s.einfsep :=
   einfsep_pos_of_finite
 #align set.finite.einfsep_pos Set.Finite.einfsep_pos
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Finite.relatively_discrete (hs : s.Finite) :
     ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
   letI := hs.fintype
@@ -420,20 +420,20 @@ section PseudoMetricSpace
 
 variable [PseudoMetricSpace α] {x y z : α} {s t : Set α}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
     d ≤ s.infsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y := by
   simp_rw [infsep, ← ENNReal.ofReal_le_iff_le_toReal hs.einfsep_ne_top, le_einfsep_iff, edist_dist,
     ENNReal.ofReal_le_ofReal_iff dist_nonneg]
 #align set.nontrivial.le_infsep_iff Set.Nontrivial.le_infsep_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
     s.infsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), dist x y < d := by
   rw [← not_iff_not]; push_neg; exact hs.le_infsep_iff
 #align set.nontrivial.infsep_lt_iff Set.Nontrivial.infsep_lt_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.le_infsep {d} (hs : s.Nontrivial)
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) : d ≤ s.infsep :=
   hs.le_infsep_iff.2 h
@@ -553,7 +553,7 @@ theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs
   rw [Finset.coe_infsep, dif_neg hs]
 #align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_empty
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.infsep_exists_of_finite /-
 theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y := by
@@ -567,7 +567,7 @@ theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
 #align set.nontrivial.infsep_exists_of_finite Set.Nontrivial.infsep_exists_of_finite
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Finite.infsep_exists_of_nontrivial /-
 theorem Finite.infsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y :=

f4758115

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -212,12 +212,12 @@ theorem Finset.coe_einfsep [DecidableEq α] {s : Finset α} :
 theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y := by
   classical
-    cases nonempty_fintype s
-    simp_rw [einfsep_of_fintype]
-    rcases@Finset.exists_mem_eq_inf _ _ _ _ s.off_diag.to_finset (by simpa) (uncurry edist) with
-      ⟨_, hxy, hed⟩
-    simp_rw [mem_to_finset] at hxy 
-    refine' ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
+  cases nonempty_fintype s
+  simp_rw [einfsep_of_fintype]
+  rcases@Finset.exists_mem_eq_inf _ _ _ _ s.off_diag.to_finset (by simpa) (uncurry edist) with
+    ⟨_, hxy, hed⟩
+  simp_rw [mem_to_finset] at hxy 
+  refine' ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.einfsep_exists_of_finite Set.Nontrivial.einfsep_exists_of_finite
 -/
 
@@ -558,12 +558,12 @@ theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs
 theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y := by
   classical
-    cases nonempty_fintype s
-    simp_rw [hs.infsep_of_fintype]
-    rcases@Finset.exists_mem_eq_inf' _ _ _ s.off_diag.to_finset (by simpa) (uncurry dist) with
-      ⟨_, hxy, hed⟩
-    simp_rw [mem_to_finset] at hxy 
-    exact ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
+  cases nonempty_fintype s
+  simp_rw [hs.infsep_of_fintype]
+  rcases@Finset.exists_mem_eq_inf' _ _ _ s.off_diag.to_finset (by simpa) (uncurry dist) with
+    ⟨_, hxy, hed⟩
+  simp_rw [mem_to_finset] at hxy 
+  exact ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.infsep_exists_of_finite Set.Nontrivial.infsep_exists_of_finite
 -/

f4758115

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -64,14 +64,14 @@ theorem le_einfsep_iff {d} :
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_zero :
     s.einfsep = 0 ↔
-      ∀ (C) (hC : 0 < C), ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), edist x y < C :=
+      ∀ (C) (hC : 0 < C), ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y < C :=
   by simp_rw [einfsep, ← bot_eq_zero, iInf_eq_bot, iInf_lt_iff]
 #align set.einfsep_zero Set.einfsep_zero
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_pos :
     0 < s.einfsep ↔
-      ∃ (C : _)(hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
+      ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
   by rw [pos_iff_ne_zero, Ne.def, einfsep_zero]; simp only [not_forall, not_exists, not_lt]
 #align set.einfsep_pos Set.einfsep_pos
 
@@ -83,19 +83,19 @@ theorem einfsep_top :
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_lt_top :
-    s.einfsep < ∞ ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), edist x y < ∞ := by
+    s.einfsep < ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y < ∞ := by
   simp_rw [einfsep, iInf_lt_iff]
 #align set.einfsep_lt_top Set.einfsep_lt_top
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_ne_top :
-    s.einfsep ≠ ∞ ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), edist x y ≠ ∞ := by
+    s.einfsep ≠ ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), edist x y ≠ ∞ := by
   simp_rw [← lt_top_iff_ne_top, einfsep_lt_top]
 #align set.einfsep_ne_top Set.einfsep_ne_top
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_lt_iff {d} :
-    s.einfsep < d ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(h : x ≠ y), edist x y < d := by
+    s.einfsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (h : x ≠ y), edist x y < d := by
   simp_rw [einfsep, iInf_lt_iff]
 #align set.einfsep_lt_iff Set.einfsep_lt_iff
 
@@ -210,13 +210,13 @@ theorem Finset.coe_einfsep [DecidableEq α] {s : Finset α} :
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.einfsep_exists_of_finite /-
 theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
-    ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), s.einfsep = edist x y := by
+    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y := by
   classical
     cases nonempty_fintype s
     simp_rw [einfsep_of_fintype]
     rcases@Finset.exists_mem_eq_inf _ _ _ _ s.off_diag.to_finset (by simpa) (uncurry edist) with
       ⟨_, hxy, hed⟩
-    simp_rw [mem_to_finset] at hxy
+    simp_rw [mem_to_finset] at hxy 
     refine' ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.einfsep_exists_of_finite Set.Nontrivial.einfsep_exists_of_finite
 -/
@@ -224,7 +224,7 @@ theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Finite.einfsep_exists_of_nontrivial /-
 theorem Finite.einfsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
-    ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), s.einfsep = edist x y :=
+    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.einfsep = edist x y :=
   letI := hsf.fintype
   hs.einfsep_exists_of_finite
 #align set.finite.einfsep_exists_of_nontrivial Set.Finite.einfsep_exists_of_nontrivial
@@ -267,7 +267,7 @@ theorem le_einfsep_pi_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMet
     c ≤ einfsep (Set.pi univ s) :=
   by
   refine' le_einfsep fun x hx y hy hxy => _
-  rw [mem_univ_pi] at hx hy
+  rw [mem_univ_pi] at hx hy 
   rcases function.ne_iff.mp hxy with ⟨i, hi⟩
   exact le_trans (le_einfsep_iff.1 (h i) _ (hx _) _ (hy _) hi) (edist_le_pi_edist _ _ i)
 #align set.le_einfsep_pi_of_le Set.le_einfsep_pi_of_le
@@ -280,7 +280,7 @@ variable [PseudoMetricSpace α] {s : Set α}
 
 theorem subsingleton_of_einfsep_eq_top (hs : s.einfsep = ∞) : s.Subsingleton :=
   by
-  rw [einfsep_top] at hs
+  rw [einfsep_top] at hs 
   exact fun _ hx _ hy => of_not_not fun hxy => edist_ne_top _ _ (hs _ hx _ hy hxy)
 #align set.subsingleton_of_einfsep_eq_top Set.subsingleton_of_einfsep_eq_top
 
@@ -323,13 +323,13 @@ theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
   by_cases hs : s.nontrivial
   · rcases hs.einfsep_exists_of_finite with ⟨x, hx, y, hy, hxy, hxy'⟩
     exact hxy'.symm ▸ edist_pos.2 hxy
-  · rw [not_nontrivial_iff] at hs
+  · rw [not_nontrivial_iff] at hs 
     exact hs.einfsep.symm ▸ WithTop.zero_lt_top
 #align set.einfsep_pos_of_finite Set.einfsep_pos_of_finite
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem relatively_discrete_of_finite [Finite s] :
-    ∃ (C : _)(hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y := by
+    ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y := by
   rw [← einfsep_pos]; exact einfsep_pos_of_finite
 #align set.relatively_discrete_of_finite Set.relatively_discrete_of_finite
 
@@ -340,7 +340,7 @@ theorem Finite.einfsep_pos (hs : s.Finite) : 0 < s.einfsep :=
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Finite.relatively_discrete (hs : s.Finite) :
-    ∃ (C : _)(hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
+    ∃ (C : _) (hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
   letI := hs.fintype
   relatively_discrete_of_finite
 #align set.finite.relatively_discrete Set.Finite.relatively_discrete
@@ -383,7 +383,7 @@ theorem Subsingleton.infsep_zero (hs : s.Subsingleton) : s.infsep = 0 := by
 #align set.subsingleton.infsep_zero Set.Subsingleton.infsep_zero
 
 theorem nontrivial_of_infsep_pos (hs : 0 < s.infsep) : s.Nontrivial := by contrapose hs;
-  rw [not_nontrivial_iff] at hs; exact hs.infsep_zero ▸ lt_irrefl _
+  rw [not_nontrivial_iff] at hs ; exact hs.infsep_zero ▸ lt_irrefl _
 #align set.nontrivial_of_infsep_pos Set.nontrivial_of_infsep_pos
 
 theorem infsep_empty : (∅ : Set α).infsep = 0 :=
@@ -429,7 +429,7 @@ theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
-    s.infsep < d ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), dist x y < d := by
+    s.infsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), dist x y < d := by
   rw [← not_iff_not]; push_neg; exact hs.le_infsep_iff
 #align set.nontrivial.infsep_lt_iff Set.Nontrivial.infsep_lt_iff
 
@@ -444,8 +444,8 @@ theorem le_edist_of_le_infsep {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x 
   by
   by_cases hs : s.nontrivial
   · exact hs.le_infsep_iff.1 hd x hx y hy hxy
-  · rw [not_nontrivial_iff] at hs
-    rw [hs.infsep_zero] at hd
+  · rw [not_nontrivial_iff] at hs 
+    rw [hs.infsep_zero] at hd 
     exact le_trans hd dist_nonneg
 #align set.le_edist_of_le_infsep Set.le_edist_of_le_infsep
 
@@ -482,7 +482,7 @@ theorem infsep_eq_iInf [Decidable s.Nontrivial] :
   · have hb : BddBelow (uncurry dist '' s.off_diag) :=
       by
       refine' ⟨0, fun d h => _⟩
-      simp_rw [mem_image, Prod.exists, uncurry_apply_pair] at h
+      simp_rw [mem_image, Prod.exists, uncurry_apply_pair] at h 
       rcases h with ⟨_, _, _, rfl⟩
       exact dist_nonneg
     refine' eq_of_forall_le_iff fun _ => _
@@ -503,7 +503,7 @@ theorem infsep_of_fintype [Decidable s.Nontrivial] [DecidableEq α] [Fintype s]
   · refine' eq_of_forall_le_iff fun _ => _
     simp_rw [hs.le_infsep_iff, imp_forall_iff, Finset.le_inf'_iff, mem_to_finset, mem_off_diag,
       Prod.forall, uncurry_apply_pair, and_imp]
-  · rw [not_nontrivial_iff] at hs; exact hs.infsep_zero
+  · rw [not_nontrivial_iff] at hs ; exact hs.infsep_zero
 #align set.infsep_of_fintype Set.infsep_of_fintype
 
 #print Set.Nontrivial.infsep_of_fintype /-
@@ -521,7 +521,7 @@ theorem Finite.infsep [Decidable s.Nontrivial] (hsf : s.Finite) :
   · refine' eq_of_forall_le_iff fun _ => _
     simp_rw [hs.le_infsep_iff, imp_forall_iff, Finset.le_inf'_iff, finite.mem_to_finset,
       mem_off_diag, Prod.forall, uncurry_apply_pair, and_imp]
-  · rw [not_nontrivial_iff] at hs; exact hs.infsep_zero
+  · rw [not_nontrivial_iff] at hs ; exact hs.infsep_zero
 #align set.finite.infsep Set.Finite.infsep
 
 #print Set.Finite.infsep_of_nontrivial /-
@@ -549,20 +549,20 @@ theorem Finset.coe_infsep_of_offDiag_nonempty [DecidableEq α] {s : Finset α}
 -/
 
 theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs : s.offDiag = ∅) :
-    (s : Set α).infsep = 0 := by rw [← Finset.not_nonempty_iff_eq_empty] at hs;
+    (s : Set α).infsep = 0 := by rw [← Finset.not_nonempty_iff_eq_empty] at hs ;
   rw [Finset.coe_infsep, dif_neg hs]
 #align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_empty
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.infsep_exists_of_finite /-
 theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
-    ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), s.infsep = dist x y := by
+    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y := by
   classical
     cases nonempty_fintype s
     simp_rw [hs.infsep_of_fintype]
     rcases@Finset.exists_mem_eq_inf' _ _ _ s.off_diag.to_finset (by simpa) (uncurry dist) with
       ⟨_, hxy, hed⟩
-    simp_rw [mem_to_finset] at hxy
+    simp_rw [mem_to_finset] at hxy 
     exact ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.infsep_exists_of_finite Set.Nontrivial.infsep_exists_of_finite
 -/
@@ -570,7 +570,7 @@ theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Finite.infsep_exists_of_nontrivial /-
 theorem Finite.infsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
-    ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), s.infsep = dist x y :=
+    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (hxy : x ≠ y), s.infsep = dist x y :=
   letI := hsf.fintype
   hs.infsep_exists_of_finite
 #align set.finite.infsep_exists_of_nontrivial Set.Finite.infsep_exists_of_nontrivial

f4758115

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -40,7 +40,7 @@ namespace Set
 
 section Einfsep
 
-open ENNReal
+open scoped ENNReal
 
 open Function
 
@@ -351,7 +351,7 @@ end Einfsep
 
 section Infsep
 
-open ENNReal
+open scoped ENNReal
 
 open Set Function

f4758115

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -55,24 +55,12 @@ section EDist
 
 variable [EDist α] {x y : α} {s t : Set α}
 
-/- warning: set.le_einfsep_iff -> Set.le_einfsep_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (Set.einfsep.{u1} α _inst_1 s)) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (EDist.edist.{u1} α _inst_1 x y))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (Set.einfsep.{u1} α _inst_1 s)) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (EDist.edist.{u1} α _inst_1 x y))))
-Case conversion may be inaccurate. Consider using '#align set.le_einfsep_iff Set.le_einfsep_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_iff {d} :
     d ≤ s.einfsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y := by
   simp_rw [einfsep, le_iInf_iff]
 #align set.le_einfsep_iff Set.le_einfsep_iff
 
-/- warning: set.einfsep_zero -> Set.einfsep_zero is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (forall (C : ENNReal), (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) C)))))))
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-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall (C : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α _inst_1 x y) C)))))))
-Case conversion may be inaccurate. Consider using '#align set.einfsep_zero Set.einfsep_zeroₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_zero :
     s.einfsep = 0 ↔
@@ -80,12 +68,6 @@ theorem einfsep_zero :
   by simp_rw [einfsep, ← bot_eq_zero, iInf_eq_bot, iInf_lt_iff]
 #align set.einfsep_zero Set.einfsep_zero
 
-/- warning: set.einfsep_pos -> Set.einfsep_pos is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (Set.einfsep.{u1} α _inst_1 s)) (Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) => forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) C (EDist.edist.{u1} α _inst_1 x y))))))
-Case conversion may be inaccurate. Consider using '#align set.einfsep_pos Set.einfsep_posₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_pos :
     0 < s.einfsep ↔
@@ -93,243 +75,111 @@ theorem einfsep_pos :
   by rw [pos_iff_ne_zero, Ne.def, einfsep_zero]; simp only [not_forall, not_exists, not_lt]
 #align set.einfsep_pos Set.einfsep_pos
 
-/- warning: set.einfsep_top -> Set.einfsep_top is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.einfsep_top Set.einfsep_topₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_top :
     s.einfsep = ∞ ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), edist x y = ∞ := by
   simp_rw [einfsep, iInf_eq_top]
 #align set.einfsep_top Set.einfsep_top
 
-/- warning: set.einfsep_lt_top -> Set.einfsep_lt_top is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.einfsep_lt_top Set.einfsep_lt_topₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_lt_top :
     s.einfsep < ∞ ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), edist x y < ∞ := by
   simp_rw [einfsep, iInf_lt_iff]
 #align set.einfsep_lt_top Set.einfsep_lt_top
 
-/- warning: set.einfsep_ne_top -> Set.einfsep_ne_top is a dubious translation:
-lean 3 declaration is
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_ne_top :
     s.einfsep ≠ ∞ ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), edist x y ≠ ∞ := by
   simp_rw [← lt_top_iff_ne_top, einfsep_lt_top]
 #align set.einfsep_ne_top Set.einfsep_ne_top
 
-/- warning: set.einfsep_lt_iff -> Set.einfsep_lt_iff is a dubious translation:
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_lt_iff {d} :
     s.einfsep < d ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(h : x ≠ y), edist x y < d := by
   simp_rw [einfsep, iInf_lt_iff]
 #align set.einfsep_lt_iff Set.einfsep_lt_iff
 
-/- warning: set.nontrivial_of_einfsep_lt_top -> Set.nontrivial_of_einfsep_lt_top is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.nontrivial_of_einfsep_lt_top Set.nontrivial_of_einfsep_lt_topₓ'. -/
 theorem nontrivial_of_einfsep_lt_top (hs : s.einfsep < ∞) : s.Nontrivial := by
   rcases einfsep_lt_top.1 hs with ⟨_, hx, _, hy, hxy, _⟩; exact ⟨_, hx, _, hy, hxy⟩
 #align set.nontrivial_of_einfsep_lt_top Set.nontrivial_of_einfsep_lt_top
 
-/- warning: set.nontrivial_of_einfsep_ne_top -> Set.nontrivial_of_einfsep_ne_top is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.nontrivial_of_einfsep_ne_top Set.nontrivial_of_einfsep_ne_topₓ'. -/
 theorem nontrivial_of_einfsep_ne_top (hs : s.einfsep ≠ ∞) : s.Nontrivial :=
   nontrivial_of_einfsep_lt_top (lt_top_iff_ne_top.mpr hs)
 #align set.nontrivial_of_einfsep_ne_top Set.nontrivial_of_einfsep_ne_top
 
-/- warning: set.subsingleton.einfsep -> Set.Subsingleton.einfsep is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.subsingleton.einfsep Set.Subsingleton.einfsepₓ'. -/
 theorem Subsingleton.einfsep (hs : s.Subsingleton) : s.einfsep = ∞ := by rw [einfsep_top];
   exact fun _ hx _ hy hxy => (hxy <| hs hx hy).elim
 #align set.subsingleton.einfsep Set.Subsingleton.einfsep
 
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-Case conversion may be inaccurate. Consider using '#align set.le_einfsep_image_iff Set.le_einfsep_image_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_image_iff {d} {f : β → α} {s : Set β} :
     d ≤ einfsep (f '' s) ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s), f x ≠ f y → d ≤ edist (f x) (f y) :=
   by simp_rw [le_einfsep_iff, ball_image_iff]
 #align set.le_einfsep_image_iff Set.le_einfsep_image_iff
 
-/- warning: set.le_edist_of_le_einfsep -> Set.le_edist_of_le_einfsep is a dubious translation:
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 theorem le_edist_of_le_einfsep {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y)
     (hd : d ≤ s.einfsep) : d ≤ edist x y :=
   le_einfsep_iff.1 hd x hx y hy hxy
 #align set.le_edist_of_le_einfsep Set.le_edist_of_le_einfsep
 
-/- warning: set.einfsep_le_edist_of_mem -> Set.einfsep_le_edist_of_mem is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.einfsep_le_edist_of_mem Set.einfsep_le_edist_of_memₓ'. -/
 theorem einfsep_le_edist_of_mem {x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y) :
     s.einfsep ≤ edist x y :=
   le_edist_of_le_einfsep hx hy hxy le_rfl
 #align set.einfsep_le_edist_of_mem Set.einfsep_le_edist_of_mem
 
-/- warning: set.einfsep_le_of_mem_of_edist_le -> Set.einfsep_le_of_mem_of_edist_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.einfsep_le_of_mem_of_edist_le Set.einfsep_le_of_mem_of_edist_leₓ'. -/
 theorem einfsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y)
     (hxy' : edist x y ≤ d) : s.einfsep ≤ d :=
   le_trans (einfsep_le_edist_of_mem hx hy hxy) hxy'
 #align set.einfsep_le_of_mem_of_edist_le Set.einfsep_le_of_mem_of_edist_le
 
-/- warning: set.le_einfsep -> Set.le_einfsep is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.le_einfsep Set.le_einfsepₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep {d} (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y) :
     d ≤ s.einfsep :=
   le_einfsep_iff.2 h
 #align set.le_einfsep Set.le_einfsep
 
-/- warning: set.einfsep_empty -> Set.einfsep_empty is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.einfsep_empty Set.einfsep_emptyₓ'. -/
 @[simp]
 theorem einfsep_empty : (∅ : Set α).einfsep = ∞ :=
   subsingleton_empty.einfsep
 #align set.einfsep_empty Set.einfsep_empty
 
-/- warning: set.einfsep_singleton -> Set.einfsep_singleton is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.einfsep_singleton Set.einfsep_singletonₓ'. -/
 @[simp]
 theorem einfsep_singleton : ({x} : Set α).einfsep = ∞ :=
   subsingleton_singleton.einfsep
 #align set.einfsep_singleton Set.einfsep_singleton
 
-/- warning: set.einfsep_Union_mem_option -> Set.einfsep_iUnion_mem_option is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.einfsep_Union_mem_option Set.einfsep_iUnion_mem_optionₓ'. -/
 theorem einfsep_iUnion_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
     (⋃ i ∈ o, s i).einfsep = ⨅ i ∈ o, (s i).einfsep := by cases o <;> simp
 #align set.einfsep_Union_mem_option Set.einfsep_iUnion_mem_option
 
-/- warning: set.einfsep_anti -> Set.einfsep_anti is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.einfsep_anti Set.einfsep_antiₓ'. -/
 theorem einfsep_anti (hst : s ⊆ t) : t.einfsep ≤ s.einfsep :=
   le_einfsep fun x hx y hy => einfsep_le_edist_of_mem (hst hx) (hst hy)
 #align set.einfsep_anti Set.einfsep_anti
 
-/- warning: set.einfsep_insert_le -> Set.einfsep_insert_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.einfsep_insert_le Set.einfsep_insert_leₓ'. -/
 theorem einfsep_insert_le : (insert x s).einfsep ≤ ⨅ (y ∈ s) (hxy : x ≠ y), edist x y :=
   by
   simp_rw [le_iInf_iff]
   refine' fun _ hy hxy => einfsep_le_edist_of_mem (mem_insert _ _) (mem_insert_of_mem _ hy) hxy
 #align set.einfsep_insert_le Set.einfsep_insert_le
 
-/- warning: set.le_einfsep_pair -> Set.le_einfsep_pair is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.le_einfsep_pair Set.le_einfsep_pairₓ'. -/
 theorem le_einfsep_pair : edist x y ⊓ edist y x ≤ ({x, y} : Set α).einfsep :=
   by
   simp_rw [le_einfsep_iff, inf_le_iff, mem_insert_iff, mem_singleton_iff]
   rintro a (rfl | rfl) b (rfl | rfl) hab <;> finish
 #align set.le_einfsep_pair Set.le_einfsep_pair
 
-/- warning: set.einfsep_pair_le_left -> Set.einfsep_pair_le_left is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.einfsep_pair_le_left Set.einfsep_pair_le_leftₓ'. -/
 theorem einfsep_pair_le_left (hxy : x ≠ y) : ({x, y} : Set α).einfsep ≤ edist x y :=
   einfsep_le_edist_of_mem (mem_insert _ _) (mem_insert_of_mem _ (mem_singleton _)) hxy
 #align set.einfsep_pair_le_left Set.einfsep_pair_le_left
 
-/- warning: set.einfsep_pair_le_right -> Set.einfsep_pair_le_right is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.einfsep_pair_le_right Set.einfsep_pair_le_rightₓ'. -/
 theorem einfsep_pair_le_right (hxy : x ≠ y) : ({x, y} : Set α).einfsep ≤ edist y x := by
   rw [pair_comm] <;> exact einfsep_pair_le_left hxy.symm
 #align set.einfsep_pair_le_right Set.einfsep_pair_le_right
 
-/- warning: set.einfsep_pair_eq_inf -> Set.einfsep_pair_eq_inf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.einfsep_pair_eq_inf Set.einfsep_pair_eq_infₓ'. -/
 theorem einfsep_pair_eq_inf (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist x y ⊓ edist y x :=
   le_antisymm (le_inf (einfsep_pair_le_left hxy) (einfsep_pair_le_right hxy)) le_einfsep_pair
 #align set.einfsep_pair_eq_inf Set.einfsep_pair_eq_inf
 
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 theorem einfsep_eq_iInf : s.einfsep = ⨅ d : s.offDiag, (uncurry edist) (d : α × α) :=
   by
   refine' eq_of_forall_le_iff fun _ => _
@@ -337,12 +187,6 @@ theorem einfsep_eq_iInf : s.einfsep = ⨅ d : s.offDiag, (uncurry edist) (d : α
     Prod.forall, uncurry_apply_pair, and_imp]
 #align set.einfsep_eq_infi Set.einfsep_eq_iInf
 
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 theorem einfsep_of_fintype [DecidableEq α] [Fintype s] :
     s.einfsep = s.offDiag.toFinset.inf (uncurry edist) :=
   by
@@ -351,12 +195,6 @@ theorem einfsep_of_fintype [DecidableEq α] [Fintype s] :
     Prod.forall, uncurry_apply_pair, and_imp]
 #align set.einfsep_of_fintype Set.einfsep_of_fintype
 
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 theorem Finite.einfsep (hs : s.Finite) : s.einfsep = hs.offDiag.toFinset.inf (uncurry edist) :=
   by
   refine' eq_of_forall_le_iff fun _ => _
@@ -364,12 +202,6 @@ theorem Finite.einfsep (hs : s.Finite) : s.einfsep = hs.offDiag.toFinset.inf (un
     Prod.forall, uncurry_apply_pair, and_imp]
 #align set.finite.einfsep Set.Finite.einfsep
 
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 theorem Finset.coe_einfsep [DecidableEq α] {s : Finset α} :
     (s : Set α).einfsep = s.offDiag.inf (uncurry edist) := by
   simp_rw [einfsep_of_fintype, ← Finset.coe_offDiag, Finset.toFinset_coe]
@@ -413,12 +245,6 @@ theorem einfsep_pair (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist x y :=
 #align set.einfsep_pair Set.einfsep_pair
 -/
 
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 theorem einfsep_insert : einfsep (insert x s) = (⨅ (y ∈ s) (hxy : x ≠ y), edist x y) ⊓ s.einfsep :=
   by
   refine' le_antisymm (le_min einfsep_insert_le (einfsep_anti (subset_insert _ _))) _
@@ -430,24 +256,12 @@ theorem einfsep_insert : einfsep (insert x s) = (⨅ (y ∈ s) (hxy : x ≠ y),
   · exact Or.inr (einfsep_le_edist_of_mem hy hz hyz)
 #align set.einfsep_insert Set.einfsep_insert
 
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-Case conversion may be inaccurate. Consider using '#align set.einfsep_triple Set.einfsep_tripleₓ'. -/
 theorem einfsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
     einfsep ({x, y, z} : Set α) = edist x y ⊓ edist x z ⊓ edist y z := by
   simp_rw [einfsep_insert, iInf_insert, iInf_singleton, einfsep_singleton, inf_top_eq,
     ciInf_pos hxy, ciInf_pos hyz, ciInf_pos hxz]
 #align set.einfsep_triple Set.einfsep_triple
 
-/- warning: set.le_einfsep_pi_of_le -> Set.le_einfsep_pi_of_le is a dubious translation:
-lean 3 declaration is
-  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] {s : forall (b : β), Set.{u2} (π b)} {c : ENNReal}, (forall (b : β), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) c (Set.einfsep.{u2} (π b) (PseudoEMetricSpace.toHasEdist.{u2} (π b) (_inst_3 b)) (s b))) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) c (Set.einfsep.{max u1 u2} (forall (i : β), π i) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (forall (i : β), π i) (pseudoEMetricSpacePi.{u1, u2} β (fun (i : β) => π i) _inst_2 (fun (b : β) => _inst_3 b))) (Set.pi.{u1, u2} β (fun (b : β) => π b) (Set.univ.{u1} β) s)))
-but is expected to have type
-  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] {s : forall (b : β), Set.{u2} (π b)} {c : ENNReal}, (forall (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) c (Set.einfsep.{u2} (π b) (PseudoEMetricSpace.toEDist.{u2} (π b) (_inst_3 b)) (s b))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) c (Set.einfsep.{max u2 u1} (forall (i : β), π i) (instEDistForAll.{u1, u2} β (fun (i : β) => π i) _inst_2 (fun (b : β) => PseudoEMetricSpace.toEDist.{u2} (π b) (_inst_3 b))) (Set.pi.{u1, u2} β (fun (b : β) => π b) (Set.univ.{u1} β) s)))
-Case conversion may be inaccurate. Consider using '#align set.le_einfsep_pi_of_le Set.le_einfsep_pi_of_leₓ'. -/
 theorem le_einfsep_pi_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMetricSpace (π b)]
     {s : ∀ b : β, Set (π b)} {c : ℝ≥0∞} (h : ∀ b, c ≤ einfsep (s b)) :
     c ≤ einfsep (Set.pi univ s) :=
@@ -464,74 +278,32 @@ section PseudoMetricSpace
 
 variable [PseudoMetricSpace α] {s : Set α}
 
-/- warning: set.subsingleton_of_einfsep_eq_top -> Set.subsingleton_of_einfsep_eq_top is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Set.Subsingleton.{u1} α s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Set.Subsingleton.{u1} α s)
-Case conversion may be inaccurate. Consider using '#align set.subsingleton_of_einfsep_eq_top Set.subsingleton_of_einfsep_eq_topₓ'. -/
 theorem subsingleton_of_einfsep_eq_top (hs : s.einfsep = ∞) : s.Subsingleton :=
   by
   rw [einfsep_top] at hs
   exact fun _ hx _ hy => of_not_not fun hxy => edist_ne_top _ _ (hs _ hx _ hy hxy)
 #align set.subsingleton_of_einfsep_eq_top Set.subsingleton_of_einfsep_eq_top
 
-/- warning: set.einfsep_eq_top_iff -> Set.einfsep_eq_top_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (Set.Subsingleton.{u1} α s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Set.Subsingleton.{u1} α s)
-Case conversion may be inaccurate. Consider using '#align set.einfsep_eq_top_iff Set.einfsep_eq_top_iffₓ'. -/
 theorem einfsep_eq_top_iff : s.einfsep = ∞ ↔ s.Subsingleton :=
   ⟨subsingleton_of_einfsep_eq_top, Subsingleton.einfsep⟩
 #align set.einfsep_eq_top_iff Set.einfsep_eq_top_iff
 
-/- warning: set.nontrivial.einfsep_ne_top -> Set.Nontrivial.einfsep_ne_top is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (Ne.{1} ENNReal (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (Ne.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))
-Case conversion may be inaccurate. Consider using '#align set.nontrivial.einfsep_ne_top Set.Nontrivial.einfsep_ne_topₓ'. -/
 theorem Nontrivial.einfsep_ne_top (hs : s.Nontrivial) : s.einfsep ≠ ∞ := by contrapose! hs;
   rw [not_nontrivial_iff]; exact subsingleton_of_einfsep_eq_top hs
 #align set.nontrivial.einfsep_ne_top Set.Nontrivial.einfsep_ne_top
 
-/- warning: set.nontrivial.einfsep_lt_top -> Set.Nontrivial.einfsep_lt_top is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))
-Case conversion may be inaccurate. Consider using '#align set.nontrivial.einfsep_lt_top Set.Nontrivial.einfsep_lt_topₓ'. -/
 theorem Nontrivial.einfsep_lt_top (hs : s.Nontrivial) : s.einfsep < ∞ := by rw [lt_top_iff_ne_top];
   exact hs.einfsep_ne_top
 #align set.nontrivial.einfsep_lt_top Set.Nontrivial.einfsep_lt_top
 
-/- warning: set.einfsep_lt_top_iff -> Set.einfsep_lt_top_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (Set.Nontrivial.{u1} α s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Set.Nontrivial.{u1} α s)
-Case conversion may be inaccurate. Consider using '#align set.einfsep_lt_top_iff Set.einfsep_lt_top_iffₓ'. -/
 theorem einfsep_lt_top_iff : s.einfsep < ∞ ↔ s.Nontrivial :=
   ⟨nontrivial_of_einfsep_lt_top, Nontrivial.einfsep_lt_top⟩
 #align set.einfsep_lt_top_iff Set.einfsep_lt_top_iff
 
-/- warning: set.einfsep_ne_top_iff -> Set.einfsep_ne_top_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (Ne.{1} ENNReal (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (Set.Nontrivial.{u1} α s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (Ne.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Set.Nontrivial.{u1} α s)
-Case conversion may be inaccurate. Consider using '#align set.einfsep_ne_top_iff Set.einfsep_ne_top_iffₓ'. -/
 theorem einfsep_ne_top_iff : s.einfsep ≠ ∞ ↔ s.Nontrivial :=
   ⟨nontrivial_of_einfsep_ne_top, Nontrivial.einfsep_ne_top⟩
 #align set.einfsep_ne_top_iff Set.einfsep_ne_top_iff
 
-/- warning: set.le_einfsep_of_forall_dist_le -> Set.le_einfsep_of_forall_dist_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.hasLe d (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) x y)))) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (ENNReal.ofReal d) (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real}, (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.instLEReal d (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) x y)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (ENNReal.ofReal d) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s))
-Case conversion may be inaccurate. Consider using '#align set.le_einfsep_of_forall_dist_le Set.le_einfsep_of_forall_dist_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_of_forall_dist_le {d}
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) :
@@ -545,12 +317,6 @@ section EMetricSpace
 
 variable [EMetricSpace α] {x y z : α} {s t : Set α} {C : ℝ≥0∞} {sC : Set ℝ≥0∞}
 
-/- warning: set.einfsep_pos_of_finite -> Set.einfsep_pos_of_finite is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)], LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (Set.Elem.{u1} α s)], LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s)
-Case conversion may be inaccurate. Consider using '#align set.einfsep_pos_of_finite Set.einfsep_pos_of_finiteₓ'. -/
 theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
   by
   cases nonempty_fintype s
@@ -561,35 +327,17 @@ theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
     exact hs.einfsep.symm ▸ WithTop.zero_lt_top
 #align set.einfsep_pos_of_finite Set.einfsep_pos_of_finite
 
-/- warning: set.relatively_discrete_of_finite -> Set.relatively_discrete_of_finite is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.relatively_discrete_of_finite Set.relatively_discrete_of_finiteₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem relatively_discrete_of_finite [Finite s] :
     ∃ (C : _)(hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y := by
   rw [← einfsep_pos]; exact einfsep_pos_of_finite
 #align set.relatively_discrete_of_finite Set.relatively_discrete_of_finite
 
-/- warning: set.finite.einfsep_pos -> Set.Finite.einfsep_pos is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s))
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-Case conversion may be inaccurate. Consider using '#align set.finite.einfsep_pos Set.Finite.einfsep_posₓ'. -/
 theorem Finite.einfsep_pos (hs : s.Finite) : 0 < s.einfsep :=
   letI := hs.fintype
   einfsep_pos_of_finite
 #align set.finite.einfsep_pos Set.Finite.einfsep_pos
 
-/- warning: set.finite.relatively_discrete -> Set.Finite.relatively_discrete is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.finite.relatively_discrete Set.Finite.relatively_discreteₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Finite.relatively_discrete (hs : s.Finite) :
     ∃ (C : _)(hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
@@ -618,82 +366,34 @@ section EDist
 
 variable [EDist α] {x y : α} {s : Set α}
 
-/- warning: set.infsep_zero -> Set.infsep_zero is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} Real (Set.infsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Or (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} Real (Set.infsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Or (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))))
-Case conversion may be inaccurate. Consider using '#align set.infsep_zero Set.infsep_zeroₓ'. -/
 theorem infsep_zero : s.infsep = 0 ↔ s.einfsep = 0 ∨ s.einfsep = ∞ := by
   rw [infsep, ENNReal.toReal_eq_zero_iff]
 #align set.infsep_zero Set.infsep_zero
 
-/- warning: set.infsep_nonneg -> Set.infsep_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.infsep.{u1} α _inst_1 s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.infsep.{u1} α _inst_1 s)
-Case conversion may be inaccurate. Consider using '#align set.infsep_nonneg Set.infsep_nonnegₓ'. -/
 theorem infsep_nonneg : 0 ≤ s.infsep :=
   ENNReal.toReal_nonneg
 #align set.infsep_nonneg Set.infsep_nonneg
 
-/- warning: set.infsep_pos -> Set.infsep_pos is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.infsep.{u1} α _inst_1 s)) (And (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (Set.einfsep.{u1} α _inst_1 s)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))))
-Case conversion may be inaccurate. Consider using '#align set.infsep_pos Set.infsep_posₓ'. -/
 theorem infsep_pos : 0 < s.infsep ↔ 0 < s.einfsep ∧ s.einfsep < ∞ := by
   simp_rw [infsep, ENNReal.toReal_pos_iff]
 #align set.infsep_pos Set.infsep_pos
 
-/- warning: set.subsingleton.infsep_zero -> Set.Subsingleton.infsep_zero is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (Set.Subsingleton.{u1} α s) -> (Eq.{1} Real (Set.infsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (Set.Subsingleton.{u1} α s) -> (Eq.{1} Real (Set.infsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align set.subsingleton.infsep_zero Set.Subsingleton.infsep_zeroₓ'. -/
 theorem Subsingleton.infsep_zero (hs : s.Subsingleton) : s.infsep = 0 := by
   rw [infsep_zero, hs.einfsep]; right; rfl
 #align set.subsingleton.infsep_zero Set.Subsingleton.infsep_zero
 
-/- warning: set.nontrivial_of_infsep_pos -> Set.nontrivial_of_infsep_pos is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.infsep.{u1} α _inst_1 s)) -> (Set.Nontrivial.{u1} α s)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.nontrivial_of_infsep_pos Set.nontrivial_of_infsep_posₓ'. -/
 theorem nontrivial_of_infsep_pos (hs : 0 < s.infsep) : s.Nontrivial := by contrapose hs;
   rw [not_nontrivial_iff] at hs; exact hs.infsep_zero ▸ lt_irrefl _
 #align set.nontrivial_of_infsep_pos Set.nontrivial_of_infsep_pos
 
-/- warning: set.infsep_empty -> Set.infsep_empty is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α], Eq.{1} Real (Set.infsep.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.infsep_empty Set.infsep_emptyₓ'. -/
 theorem infsep_empty : (∅ : Set α).infsep = 0 :=
   subsingleton_empty.infsep_zero
 #align set.infsep_empty Set.infsep_empty
 
-/- warning: set.infsep_singleton -> Set.infsep_singleton is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α}, Eq.{1} Real (Set.infsep.{u1} α _inst_1 (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) x)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.infsep_singleton Set.infsep_singletonₓ'. -/
 theorem infsep_singleton : ({x} : Set α).infsep = 0 :=
   subsingleton_singleton.infsep_zero
 #align set.infsep_singleton Set.infsep_singleton
 
-/- warning: set.infsep_pair_le_to_real_inf -> Set.infsep_pair_le_toReal_inf 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.infsep_pair_le_to_real_inf Set.infsep_pair_le_toReal_infₓ'. -/
 theorem infsep_pair_le_toReal_inf (hxy : x ≠ y) :
     ({x, y} : Set α).infsep ≤ (edist x y ⊓ edist y x).toReal := by
   simp_rw [infsep, einfsep_pair_eq_inf hxy]
@@ -720,12 +420,6 @@ section PseudoMetricSpace
 
 variable [PseudoMetricSpace α] {x y z : α} {s t : Set α}
 
-/- warning: set.nontrivial.le_infsep_iff -> Set.Nontrivial.le_infsep_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.nontrivial.le_infsep_iff Set.Nontrivial.le_infsep_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
     d ≤ s.infsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y := by
@@ -733,36 +427,18 @@ theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
     ENNReal.ofReal_le_ofReal_iff dist_nonneg]
 #align set.nontrivial.le_infsep_iff Set.Nontrivial.le_infsep_iff
 
-/- warning: set.nontrivial.infsep_lt_iff -> Set.Nontrivial.infsep_lt_iff is a dubious translation:
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
     s.infsep < d ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), dist x y < d := by
   rw [← not_iff_not]; push_neg; exact hs.le_infsep_iff
 #align set.nontrivial.infsep_lt_iff Set.Nontrivial.infsep_lt_iff
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.le_infsep {d} (hs : s.Nontrivial)
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) : d ≤ s.infsep :=
   hs.le_infsep_iff.2 h
 #align set.nontrivial.le_infsep Set.Nontrivial.le_infsep
 
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 theorem le_edist_of_le_infsep {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y)
     (hd : d ≤ s.infsep) : d ≤ dist x y :=
   by
@@ -773,22 +449,10 @@ theorem le_edist_of_le_infsep {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x 
     exact le_trans hd dist_nonneg
 #align set.le_edist_of_le_infsep Set.le_edist_of_le_infsep
 
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 theorem infsep_le_dist_of_mem (hx : x ∈ s) (hy : y ∈ s) (hxy : x ≠ y) : s.infsep ≤ dist x y :=
   le_edist_of_le_infsep hx hy hxy le_rfl
 #align set.infsep_le_dist_of_mem Set.infsep_le_dist_of_mem
 
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 theorem infsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y)
     (hxy' : dist x y ≤ d) : s.infsep ≤ d :=
   le_trans (infsep_le_dist_of_mem hx hy hxy) hxy'
@@ -800,12 +464,6 @@ theorem infsep_pair : ({x, y} : Set α).infsep = dist x y := by
 #align set.infsep_pair Set.infsep_pair
 -/
 
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 theorem infsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
     ({x, y, z} : Set α).infsep = dist x y ⊓ dist x z ⊓ dist y z := by
   simp only [infsep, einfsep_triple hxy hyz hxz, ENNReal.toReal_inf, edist_ne_top x y,
@@ -813,22 +471,10 @@ theorem infsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
     not_false_iff]
 #align set.infsep_triple Set.infsep_triple
 
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 theorem Nontrivial.infsep_anti (hs : s.Nontrivial) (hst : s ⊆ t) : t.infsep ≤ s.infsep :=
   ENNReal.toReal_mono hs.einfsep_ne_top (einfsep_anti hst)
 #align set.nontrivial.infsep_anti Set.Nontrivial.infsep_anti
 
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 theorem infsep_eq_iInf [Decidable s.Nontrivial] :
     s.infsep = if s.Nontrivial then ⨅ d : s.offDiag, (uncurry dist) (d : α × α) else 0 :=
   by
@@ -845,23 +491,11 @@ theorem infsep_eq_iInf [Decidable s.Nontrivial] :
   · exact (not_nontrivial_iff.mp hs).infsep_zero
 #align set.infsep_eq_infi Set.infsep_eq_iInf
 
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 theorem Nontrivial.infsep_eq_iInf (hs : s.Nontrivial) :
     s.infsep = ⨅ d : s.offDiag, (uncurry dist) (d : α × α) := by
   classical rw [infsep_eq_infi, if_pos hs]
 #align set.nontrivial.infsep_eq_infi Set.Nontrivial.infsep_eq_iInf
 
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 theorem infsep_of_fintype [Decidable s.Nontrivial] [DecidableEq α] [Fintype s] :
     s.infsep = if hs : s.Nontrivial then s.offDiag.toFinset.inf' (by simpa) (uncurry dist) else 0 :=
   by
@@ -879,12 +513,6 @@ theorem Nontrivial.infsep_of_fintype [DecidableEq α] [Fintype s] (hs : s.Nontri
 #align set.nontrivial.infsep_of_fintype Set.Nontrivial.infsep_of_fintype
 -/
 
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 theorem Finite.infsep [Decidable s.Nontrivial] (hsf : s.Finite) :
     s.infsep =
       if hs : s.Nontrivial then hsf.offDiag.toFinset.inf' (by simpa) (uncurry dist) else 0 :=
@@ -903,12 +531,6 @@ theorem Finite.infsep_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
 #align set.finite.infsep_of_nontrivial Set.Finite.infsep_of_nontrivial
 -/
 
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-Case conversion may be inaccurate. Consider using '#align finset.coe_infsep Finset.coe_infsepₓ'. -/
 theorem Finset.coe_infsep [DecidableEq α] (s : Finset α) :
     (s : Set α).infsep = if hs : s.offDiag.Nonempty then s.offDiag.inf' hs (uncurry dist) else 0 :=
   by
@@ -926,12 +548,6 @@ theorem Finset.coe_infsep_of_offDiag_nonempty [DecidableEq α] {s : Finset α}
 #align finset.coe_infsep_of_off_diag_nonempty Finset.coe_infsep_of_offDiag_nonempty
 -/
 
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-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {s : Finset.{u1} α}, (Eq.{succ u1} (Finset.{u1} (Prod.{u1, u1} α α)) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} (Prod.{u1, u1} α α)) (Finset.instEmptyCollectionFinset.{u1} (Prod.{u1, u1} α α)))) -> (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Finset.toSet.{u1} α s)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_emptyₓ'. -/
 theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs : s.offDiag = ∅) :
     (s : Set α).infsep = 0 := by rw [← Finset.not_nonempty_iff_eq_empty] at hs;
   rw [Finset.coe_infsep, dif_neg hs]
@@ -966,69 +582,33 @@ section MetricSpace
 
 variable [MetricSpace α] {s : Set α}
 
-/- warning: set.infsep_zero_iff_subsingleton_of_finite -> Set.infsep_zero_iff_subsingleton_of_finite is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)], Iff (Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) s) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Set.Subsingleton.{u1} α s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (Set.Elem.{u1} α s)], Iff (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1))) s) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Set.Subsingleton.{u1} α s)
-Case conversion may be inaccurate. Consider using '#align set.infsep_zero_iff_subsingleton_of_finite Set.infsep_zero_iff_subsingleton_of_finiteₓ'. -/
 theorem infsep_zero_iff_subsingleton_of_finite [Finite s] : s.infsep = 0 ↔ s.Subsingleton :=
   by
   rw [infsep_zero, einfsep_eq_top_iff, or_iff_right_iff_imp]
   exact fun H => (einfsep_pos_of_finite.ne' H).elim
 #align set.infsep_zero_iff_subsingleton_of_finite Set.infsep_zero_iff_subsingleton_of_finite
 
-/- warning: set.infsep_pos_iff_nontrivial_of_finite -> Set.infsep_pos_iff_nontrivial_of_finite is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)], Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) s)) (Set.Nontrivial.{u1} α s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (Set.Elem.{u1} α s)], Iff (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1))) s)) (Set.Nontrivial.{u1} α s)
-Case conversion may be inaccurate. Consider using '#align set.infsep_pos_iff_nontrivial_of_finite Set.infsep_pos_iff_nontrivial_of_finiteₓ'. -/
 theorem infsep_pos_iff_nontrivial_of_finite [Finite s] : 0 < s.infsep ↔ s.Nontrivial :=
   by
   rw [infsep_pos, einfsep_lt_top_iff, and_iff_right_iff_imp]
   exact fun _ => einfsep_pos_of_finite
 #align set.infsep_pos_iff_nontrivial_of_finite Set.infsep_pos_iff_nontrivial_of_finite
 
-/- warning: set.finite.infsep_zero_iff_subsingleton -> Set.Finite.infsep_zero_iff_subsingleton is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Iff (Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) s) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Set.Subsingleton.{u1} α s))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Iff (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1))) s) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Set.Subsingleton.{u1} α s))
-Case conversion may be inaccurate. Consider using '#align set.finite.infsep_zero_iff_subsingleton Set.Finite.infsep_zero_iff_subsingletonₓ'. -/
 theorem Finite.infsep_zero_iff_subsingleton (hs : s.Finite) : s.infsep = 0 ↔ s.Subsingleton :=
   letI := hs.fintype
   infsep_zero_iff_subsingleton_of_finite
 #align set.finite.infsep_zero_iff_subsingleton Set.Finite.infsep_zero_iff_subsingleton
 
-/- warning: set.finite.infsep_pos_iff_nontrivial -> Set.Finite.infsep_pos_iff_nontrivial is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) s)) (Set.Nontrivial.{u1} α s))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Iff (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1))) s)) (Set.Nontrivial.{u1} α s))
-Case conversion may be inaccurate. Consider using '#align set.finite.infsep_pos_iff_nontrivial Set.Finite.infsep_pos_iff_nontrivialₓ'. -/
 theorem Finite.infsep_pos_iff_nontrivial (hs : s.Finite) : 0 < s.infsep ↔ s.Nontrivial :=
   letI := hs.fintype
   infsep_pos_iff_nontrivial_of_finite
 #align set.finite.infsep_pos_iff_nontrivial Set.Finite.infsep_pos_iff_nontrivial
 
-/- warning: finset.infsep_zero_iff_subsingleton -> Finset.infsep_zero_iff_subsingleton is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] (s : Finset.{u1} α), Iff (Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Set.Subsingleton.{u1} α ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] (s : Finset.{u1} α), Iff (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1))) (Finset.toSet.{u1} α s)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Set.Subsingleton.{u1} α (Finset.toSet.{u1} α s))
-Case conversion may be inaccurate. Consider using '#align finset.infsep_zero_iff_subsingleton Finset.infsep_zero_iff_subsingletonₓ'. -/
 theorem Finset.infsep_zero_iff_subsingleton (s : Finset α) :
     (s : Set α).infsep = 0 ↔ (s : Set α).Subsingleton :=
   infsep_zero_iff_subsingleton_of_finite
 #align finset.infsep_zero_iff_subsingleton Finset.infsep_zero_iff_subsingleton
 
-/- warning: finset.infsep_pos_iff_nontrivial -> Finset.infsep_pos_iff_nontrivial is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] (s : Finset.{u1} α), Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s))) (Set.Nontrivial.{u1} α ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] (s : Finset.{u1} α), Iff (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1))) (Finset.toSet.{u1} α s))) (Set.Nontrivial.{u1} α (Finset.toSet.{u1} α s))
-Case conversion may be inaccurate. Consider using '#align finset.infsep_pos_iff_nontrivial Finset.infsep_pos_iff_nontrivialₓ'. -/
 theorem Finset.infsep_pos_iff_nontrivial (s : Finset α) :
     0 < (s : Set α).infsep ↔ (s : Set α).Nontrivial :=
   infsep_pos_iff_nontrivial_of_finite

f4758115

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -90,9 +90,7 @@ Case conversion may be inaccurate. Consider using '#align set.einfsep_pos Set.ei
 theorem einfsep_pos :
     0 < s.einfsep ↔
       ∃ (C : _)(hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
-  by
-  rw [pos_iff_ne_zero, Ne.def, einfsep_zero]
-  simp only [not_forall, not_exists, not_lt]
+  by rw [pos_iff_ne_zero, Ne.def, einfsep_zero]; simp only [not_forall, not_exists, not_lt]
 #align set.einfsep_pos Set.einfsep_pos
 
 /- warning: set.einfsep_top -> Set.einfsep_top is a dubious translation:
@@ -149,10 +147,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Set.Nontrivial.{u1} α s)
 Case conversion may be inaccurate. Consider using '#align set.nontrivial_of_einfsep_lt_top Set.nontrivial_of_einfsep_lt_topₓ'. -/
-theorem nontrivial_of_einfsep_lt_top (hs : s.einfsep < ∞) : s.Nontrivial :=
-  by
-  rcases einfsep_lt_top.1 hs with ⟨_, hx, _, hy, hxy, _⟩
-  exact ⟨_, hx, _, hy, hxy⟩
+theorem nontrivial_of_einfsep_lt_top (hs : s.einfsep < ∞) : s.Nontrivial := by
+  rcases einfsep_lt_top.1 hs with ⟨_, hx, _, hy, hxy, _⟩; exact ⟨_, hx, _, hy, hxy⟩
 #align set.nontrivial_of_einfsep_lt_top Set.nontrivial_of_einfsep_lt_top
 
 /- warning: set.nontrivial_of_einfsep_ne_top -> Set.nontrivial_of_einfsep_ne_top is a dubious translation:
@@ -171,9 +167,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (Set.Subsingleton.{u1} α s) -> (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))
 Case conversion may be inaccurate. Consider using '#align set.subsingleton.einfsep Set.Subsingleton.einfsepₓ'. -/
-theorem Subsingleton.einfsep (hs : s.Subsingleton) : s.einfsep = ∞ :=
-  by
-  rw [einfsep_top]
+theorem Subsingleton.einfsep (hs : s.Subsingleton) : s.einfsep = ∞ := by rw [einfsep_top];
   exact fun _ hx _ hy hxy => (hxy <| hs hx hy).elim
 #align set.subsingleton.einfsep Set.Subsingleton.einfsep
 
@@ -432,8 +426,7 @@ theorem einfsep_insert : einfsep (insert x s) = (⨅ (y ∈ s) (hxy : x ≠ y),
   rintro y (rfl | hy) z (rfl | hz) hyz
   · exact False.elim (hyz rfl)
   · exact Or.inl (iInf_le_of_le _ (iInf₂_le hz hyz))
-  · rw [edist_comm]
-    exact Or.inl (iInf_le_of_le _ (iInf₂_le hy hyz.symm))
+  · rw [edist_comm]; exact Or.inl (iInf_le_of_le _ (iInf₂_le hy hyz.symm))
   · exact Or.inr (einfsep_le_edist_of_mem hy hz hyz)
 #align set.einfsep_insert Set.einfsep_insert
 
@@ -499,11 +492,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (Ne.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))
 Case conversion may be inaccurate. Consider using '#align set.nontrivial.einfsep_ne_top Set.Nontrivial.einfsep_ne_topₓ'. -/
-theorem Nontrivial.einfsep_ne_top (hs : s.Nontrivial) : s.einfsep ≠ ∞ :=
-  by
-  contrapose! hs
-  rw [not_nontrivial_iff]
-  exact subsingleton_of_einfsep_eq_top hs
+theorem Nontrivial.einfsep_ne_top (hs : s.Nontrivial) : s.einfsep ≠ ∞ := by contrapose! hs;
+  rw [not_nontrivial_iff]; exact subsingleton_of_einfsep_eq_top hs
 #align set.nontrivial.einfsep_ne_top Set.Nontrivial.einfsep_ne_top
 
 /- warning: set.nontrivial.einfsep_lt_top -> Set.Nontrivial.einfsep_lt_top is a dubious translation:
@@ -512,9 +502,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))
 Case conversion may be inaccurate. Consider using '#align set.nontrivial.einfsep_lt_top Set.Nontrivial.einfsep_lt_topₓ'. -/
-theorem Nontrivial.einfsep_lt_top (hs : s.Nontrivial) : s.einfsep < ∞ :=
-  by
-  rw [lt_top_iff_ne_top]
+theorem Nontrivial.einfsep_lt_top (hs : s.Nontrivial) : s.einfsep < ∞ := by rw [lt_top_iff_ne_top];
   exact hs.einfsep_ne_top
 #align set.nontrivial.einfsep_lt_top Set.Nontrivial.einfsep_lt_top
 
@@ -581,10 +569,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align set.relatively_discrete_of_finite Set.relatively_discrete_of_finiteₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem relatively_discrete_of_finite [Finite s] :
-    ∃ (C : _)(hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
-  by
-  rw [← einfsep_pos]
-  exact einfsep_pos_of_finite
+    ∃ (C : _)(hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y := by
+  rw [← einfsep_pos]; exact einfsep_pos_of_finite
 #align set.relatively_discrete_of_finite Set.relatively_discrete_of_finite
 
 /- warning: set.finite.einfsep_pos -> Set.Finite.einfsep_pos is a dubious translation:
@@ -668,11 +654,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (Set.Subsingleton.{u1} α s) -> (Eq.{1} Real (Set.infsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align set.subsingleton.infsep_zero Set.Subsingleton.infsep_zeroₓ'. -/
-theorem Subsingleton.infsep_zero (hs : s.Subsingleton) : s.infsep = 0 :=
-  by
-  rw [infsep_zero, hs.einfsep]
-  right
-  rfl
+theorem Subsingleton.infsep_zero (hs : s.Subsingleton) : s.infsep = 0 := by
+  rw [infsep_zero, hs.einfsep]; right; rfl
 #align set.subsingleton.infsep_zero Set.Subsingleton.infsep_zero
 
 /- warning: set.nontrivial_of_infsep_pos -> Set.nontrivial_of_infsep_pos is a dubious translation:
@@ -681,11 +664,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.infsep.{u1} α _inst_1 s)) -> (Set.Nontrivial.{u1} α s)
 Case conversion may be inaccurate. Consider using '#align set.nontrivial_of_infsep_pos Set.nontrivial_of_infsep_posₓ'. -/
-theorem nontrivial_of_infsep_pos (hs : 0 < s.infsep) : s.Nontrivial :=
-  by
-  contrapose hs
-  rw [not_nontrivial_iff] at hs
-  exact hs.infsep_zero ▸ lt_irrefl _
+theorem nontrivial_of_infsep_pos (hs : 0 < s.infsep) : s.Nontrivial := by contrapose hs;
+  rw [not_nontrivial_iff] at hs; exact hs.infsep_zero ▸ lt_irrefl _
 #align set.nontrivial_of_infsep_pos Set.nontrivial_of_infsep_pos
 
 /- warning: set.infsep_empty -> Set.infsep_empty is a dubious translation:
@@ -729,8 +709,7 @@ variable [PseudoEMetricSpace α] {x y : α} {s : Set α}
 theorem infsep_pair_eq_toReal : ({x, y} : Set α).infsep = (edist x y).toReal :=
   by
   by_cases hxy : x = y
-  · rw [hxy]
-    simp only [infsep_singleton, pair_eq_singleton, edist_self, ENNReal.zero_toReal]
+  · rw [hxy]; simp only [infsep_singleton, pair_eq_singleton, edist_self, ENNReal.zero_toReal]
   · rw [infsep, einfsep_pair hxy]
 #align set.infsep_pair_eq_to_real Set.infsep_pair_eq_toReal
 -/
@@ -762,11 +741,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align set.nontrivial.infsep_lt_iff Set.Nontrivial.infsep_lt_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
-    s.infsep < d ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), dist x y < d :=
-  by
-  rw [← not_iff_not]
-  push_neg
-  exact hs.le_infsep_iff
+    s.infsep < d ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), dist x y < d := by
+  rw [← not_iff_not]; push_neg; exact hs.le_infsep_iff
 #align set.nontrivial.infsep_lt_iff Set.Nontrivial.infsep_lt_iff
 
 /- warning: set.nontrivial.le_infsep -> Set.Nontrivial.le_infsep is a dubious translation:
@@ -819,10 +795,8 @@ theorem infsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hx
 #align set.infsep_le_of_mem_of_edist_le Set.infsep_le_of_mem_of_edist_le
 
 #print Set.infsep_pair /-
-theorem infsep_pair : ({x, y} : Set α).infsep = dist x y :=
-  by
-  rw [infsep_pair_eq_to_real, edist_dist]
-  exact ENNReal.toReal_ofReal dist_nonneg
+theorem infsep_pair : ({x, y} : Set α).infsep = dist x y := by
+  rw [infsep_pair_eq_to_real, edist_dist]; exact ENNReal.toReal_ofReal dist_nonneg
 #align set.infsep_pair Set.infsep_pair
 -/
 
@@ -895,8 +869,7 @@ theorem infsep_of_fintype [Decidable s.Nontrivial] [DecidableEq α] [Fintype s]
   · refine' eq_of_forall_le_iff fun _ => _
     simp_rw [hs.le_infsep_iff, imp_forall_iff, Finset.le_inf'_iff, mem_to_finset, mem_off_diag,
       Prod.forall, uncurry_apply_pair, and_imp]
-  · rw [not_nontrivial_iff] at hs
-    exact hs.infsep_zero
+  · rw [not_nontrivial_iff] at hs; exact hs.infsep_zero
 #align set.infsep_of_fintype Set.infsep_of_fintype
 
 #print Set.Nontrivial.infsep_of_fintype /-
@@ -920,8 +893,7 @@ theorem Finite.infsep [Decidable s.Nontrivial] (hsf : s.Finite) :
   · refine' eq_of_forall_le_iff fun _ => _
     simp_rw [hs.le_infsep_iff, imp_forall_iff, Finset.le_inf'_iff, finite.mem_to_finset,
       mem_off_diag, Prod.forall, uncurry_apply_pair, and_imp]
-  · rw [not_nontrivial_iff] at hs
-    exact hs.infsep_zero
+  · rw [not_nontrivial_iff] at hs; exact hs.infsep_zero
 #align set.finite.infsep Set.Finite.infsep
 
 #print Set.Finite.infsep_of_nontrivial /-
@@ -961,9 +933,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {s : Finset.{u1} α}, (Eq.{succ u1} (Finset.{u1} (Prod.{u1, u1} α α)) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} (Prod.{u1, u1} α α)) (Finset.instEmptyCollectionFinset.{u1} (Prod.{u1, u1} α α)))) -> (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Finset.toSet.{u1} α s)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_emptyₓ'. -/
 theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs : s.offDiag = ∅) :
-    (s : Set α).infsep = 0 :=
-  by
-  rw [← Finset.not_nonempty_iff_eq_empty] at hs
+    (s : Set α).infsep = 0 := by rw [← Finset.not_nonempty_iff_eq_empty] at hs;
   rw [Finset.coe_infsep, dif_neg hs]
 #align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_empty

f4758115

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -57,7 +57,7 @@ variable [EDist α] {x y : α} {s t : Set α}
 
 /- warning: set.le_einfsep_iff -> Set.le_einfsep_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (Set.einfsep.{u1} α _inst_1 s)) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (EDist.edist.{u1} α _inst_1 x y))))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (Set.einfsep.{u1} α _inst_1 s)) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (EDist.edist.{u1} α _inst_1 x y))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (Set.einfsep.{u1} α _inst_1 s)) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (EDist.edist.{u1} α _inst_1 x y))))
 Case conversion may be inaccurate. Consider using '#align set.le_einfsep_iff Set.le_einfsep_iffₓ'. -/
@@ -69,7 +69,7 @@ theorem le_einfsep_iff {d} :
 
 /- warning: set.einfsep_zero -> Set.einfsep_zero is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (forall (C : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) C)))))))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (forall (C : ENNReal), (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) C)))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall (C : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α _inst_1 x y) C)))))))
 Case conversion may be inaccurate. Consider using '#align set.einfsep_zero Set.einfsep_zeroₓ'. -/
@@ -82,7 +82,7 @@ theorem einfsep_zero :
 
 /- warning: set.einfsep_pos -> Set.einfsep_pos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (Set.einfsep.{u1} α _inst_1 s)) (Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) => forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) C (EDist.edist.{u1} α _inst_1 x y))))))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (Set.einfsep.{u1} α _inst_1 s)) (Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) => forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) C (EDist.edist.{u1} α _inst_1 x y))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (Set.einfsep.{u1} α _inst_1 s)) (Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) => forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) C (EDist.edist.{u1} α _inst_1 x y))))))
 Case conversion may be inaccurate. Consider using '#align set.einfsep_pos Set.einfsep_posₓ'. -/
@@ -109,7 +109,7 @@ theorem einfsep_top :
 
 /- warning: set.einfsep_lt_top -> Set.einfsep_lt_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))))))))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α _inst_1 x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))))))))
 Case conversion may be inaccurate. Consider using '#align set.einfsep_lt_top Set.einfsep_lt_topₓ'. -/
@@ -133,7 +133,7 @@ theorem einfsep_ne_top :
 
 /- warning: set.einfsep_lt_iff -> Set.einfsep_lt_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) d) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (h : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) d))))))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) d) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (h : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) d))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 s) d) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (h : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α _inst_1 x y) d))))))
 Case conversion may be inaccurate. Consider using '#align set.einfsep_lt_iff Set.einfsep_lt_iffₓ'. -/
@@ -145,7 +145,7 @@ theorem einfsep_lt_iff {d} :
 
 /- warning: set.nontrivial_of_einfsep_lt_top -> Set.nontrivial_of_einfsep_lt_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Set.Nontrivial.{u1} α s)
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Set.Nontrivial.{u1} α s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Set.Nontrivial.{u1} α s)
 Case conversion may be inaccurate. Consider using '#align set.nontrivial_of_einfsep_lt_top Set.nontrivial_of_einfsep_lt_topₓ'. -/
@@ -179,7 +179,7 @@ theorem Subsingleton.einfsep (hs : s.Subsingleton) : s.einfsep = ∞ :=
 
 /- warning: set.le_einfsep_image_iff -> Set.le_einfsep_image_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : EDist.{u1} α] {d : ENNReal} {f : β -> α} {s : Set.{u2} β}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (Set.einfsep.{u1} α _inst_1 (Set.image.{u2, u1} β α f s))) (forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) -> (forall (y : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y s) -> (Ne.{succ u1} α (f x) (f y)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (EDist.edist.{u1} α _inst_1 (f x) (f y)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : EDist.{u1} α] {d : ENNReal} {f : β -> α} {s : Set.{u2} β}, Iff (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (Set.einfsep.{u1} α _inst_1 (Set.image.{u2, u1} β α f s))) (forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) -> (forall (y : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y s) -> (Ne.{succ u1} α (f x) (f y)) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (EDist.edist.{u1} α _inst_1 (f x) (f y)))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : EDist.{u1} α] {d : ENNReal} {f : β -> α} {s : Set.{u2} β}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (Set.einfsep.{u1} α _inst_1 (Set.image.{u2, u1} β α f s))) (forall (x : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) -> (forall (y : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) y s) -> (Ne.{succ u1} α (f x) (f y)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (EDist.edist.{u1} α _inst_1 (f x) (f y)))))
 Case conversion may be inaccurate. Consider using '#align set.le_einfsep_image_iff Set.le_einfsep_image_iffₓ'. -/
@@ -191,7 +191,7 @@ theorem le_einfsep_image_iff {d} {f : β → α} {s : Set β} :
 
 /- warning: set.le_edist_of_le_einfsep -> Set.le_edist_of_le_einfsep is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal} {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall {y : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (Set.einfsep.{u1} α _inst_1 s)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (EDist.edist.{u1} α _inst_1 x y)))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal} {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall {y : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (Set.einfsep.{u1} α _inst_1 s)) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (EDist.edist.{u1} α _inst_1 x y)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal} {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall {y : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (Set.einfsep.{u1} α _inst_1 s)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (EDist.edist.{u1} α _inst_1 x y)))
 Case conversion may be inaccurate. Consider using '#align set.le_edist_of_le_einfsep Set.le_edist_of_le_einfsepₓ'. -/
@@ -202,7 +202,7 @@ theorem le_edist_of_le_einfsep {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x
 
 /- warning: set.einfsep_le_edist_of_mem -> Set.einfsep_le_edist_of_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall {y : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) (EDist.edist.{u1} α _inst_1 x y)))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall {y : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) (EDist.edist.{u1} α _inst_1 x y)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall {y : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 s) (EDist.edist.{u1} α _inst_1 x y)))
 Case conversion may be inaccurate. Consider using '#align set.einfsep_le_edist_of_mem Set.einfsep_le_edist_of_memₓ'. -/
@@ -213,7 +213,7 @@ theorem einfsep_le_edist_of_mem {x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x 
 
 /- warning: set.einfsep_le_of_mem_of_edist_le -> Set.einfsep_le_of_mem_of_edist_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal} {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall {y : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) d) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) d))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal} {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall {y : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) d) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) d))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal} {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall {y : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α _inst_1 x y) d) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 s) d))
 Case conversion may be inaccurate. Consider using '#align set.einfsep_le_of_mem_of_edist_le Set.einfsep_le_of_mem_of_edist_leₓ'. -/
@@ -224,7 +224,7 @@ theorem einfsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (h
 
 /- warning: set.le_einfsep -> Set.le_einfsep is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (EDist.edist.{u1} α _inst_1 x y)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (Set.einfsep.{u1} α _inst_1 s))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (EDist.edist.{u1} α _inst_1 x y)))) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (Set.einfsep.{u1} α _inst_1 s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (EDist.edist.{u1} α _inst_1 x y)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (Set.einfsep.{u1} α _inst_1 s))
 Case conversion may be inaccurate. Consider using '#align set.le_einfsep Set.le_einfsepₓ'. -/
@@ -268,7 +268,7 @@ theorem einfsep_iUnion_mem_option {ι : Type _} (o : Option ι) (s : ι → Set
 
 /- warning: set.einfsep_anti -> Set.einfsep_anti is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 t) (Set.einfsep.{u1} α _inst_1 s))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 t) (Set.einfsep.{u1} α _inst_1 s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 t) (Set.einfsep.{u1} α _inst_1 s))
 Case conversion may be inaccurate. Consider using '#align set.einfsep_anti Set.einfsep_antiₓ'. -/
@@ -278,7 +278,7 @@ theorem einfsep_anti (hst : s ⊆ t) : t.einfsep ≤ s.einfsep :=
 
 /- warning: set.einfsep_insert_le -> Set.einfsep_insert_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {s : Set.{u1} α}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x s)) (iInf.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) α (fun (y : α) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α _inst_1 x y))))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {s : Set.{u1} α}, LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x s)) (iInf.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) α (fun (y : α) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α _inst_1 x y))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {s : Set.{u1} α}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x s)) (iInf.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) α (fun (y : α) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α _inst_1 x y))))
 Case conversion may be inaccurate. Consider using '#align set.einfsep_insert_le Set.einfsep_insert_leₓ'. -/
@@ -290,7 +290,7 @@ theorem einfsep_insert_le : (insert x s).einfsep ≤ ⨅ (y ∈ s) (hxy : x ≠
 
 /- warning: set.le_einfsep_pair -> Set.le_einfsep_pair is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Inf.inf.{0} ENNReal (SemilatticeInf.toHasInf.{0} ENNReal (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) (EDist.edist.{u1} α _inst_1 y x)) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) y)))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Inf.inf.{0} ENNReal (SemilatticeInf.toHasInf.{0} ENNReal (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) (EDist.edist.{u1} α _inst_1 y x)) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) y)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Inf.inf.{0} ENNReal (Lattice.toInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α _inst_1 x y) (EDist.edist.{u1} α _inst_1 y x)) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) y)))
 Case conversion may be inaccurate. Consider using '#align set.le_einfsep_pair Set.le_einfsep_pairₓ'. -/
@@ -302,7 +302,7 @@ theorem le_einfsep_pair : edist x y ⊓ edist y x ≤ ({x, y} : Set α).einfsep
 
 /- warning: set.einfsep_pair_le_left -> Set.einfsep_pair_le_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) y))) (EDist.edist.{u1} α _inst_1 x y))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) y))) (EDist.edist.{u1} α _inst_1 x y))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) y))) (EDist.edist.{u1} α _inst_1 x y))
 Case conversion may be inaccurate. Consider using '#align set.einfsep_pair_le_left Set.einfsep_pair_le_leftₓ'. -/
@@ -312,7 +312,7 @@ theorem einfsep_pair_le_left (hxy : x ≠ y) : ({x, y} : Set α).einfsep ≤ edi
 
 /- warning: set.einfsep_pair_le_right -> Set.einfsep_pair_le_right is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) y))) (EDist.edist.{u1} α _inst_1 y x))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) y))) (EDist.edist.{u1} α _inst_1 y x))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) y))) (EDist.edist.{u1} α _inst_1 y x))
 Case conversion may be inaccurate. Consider using '#align set.einfsep_pair_le_right Set.einfsep_pair_le_rightₓ'. -/
@@ -451,7 +451,7 @@ theorem einfsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
 
 /- warning: set.le_einfsep_pi_of_le -> Set.le_einfsep_pi_of_le is a dubious translation:
 lean 3 declaration is
-  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] {s : forall (b : β), Set.{u2} (π b)} {c : ENNReal}, (forall (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) c (Set.einfsep.{u2} (π b) (PseudoEMetricSpace.toHasEdist.{u2} (π b) (_inst_3 b)) (s b))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) c (Set.einfsep.{max u1 u2} (forall (i : β), π i) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (forall (i : β), π i) (pseudoEMetricSpacePi.{u1, u2} β (fun (i : β) => π i) _inst_2 (fun (b : β) => _inst_3 b))) (Set.pi.{u1, u2} β (fun (b : β) => π b) (Set.univ.{u1} β) s)))
+  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] {s : forall (b : β), Set.{u2} (π b)} {c : ENNReal}, (forall (b : β), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) c (Set.einfsep.{u2} (π b) (PseudoEMetricSpace.toHasEdist.{u2} (π b) (_inst_3 b)) (s b))) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) c (Set.einfsep.{max u1 u2} (forall (i : β), π i) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (forall (i : β), π i) (pseudoEMetricSpacePi.{u1, u2} β (fun (i : β) => π i) _inst_2 (fun (b : β) => _inst_3 b))) (Set.pi.{u1, u2} β (fun (b : β) => π b) (Set.univ.{u1} β) s)))
 but is expected to have type
   forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] {s : forall (b : β), Set.{u2} (π b)} {c : ENNReal}, (forall (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) c (Set.einfsep.{u2} (π b) (PseudoEMetricSpace.toEDist.{u2} (π b) (_inst_3 b)) (s b))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) c (Set.einfsep.{max u2 u1} (forall (i : β), π i) (instEDistForAll.{u1, u2} β (fun (i : β) => π i) _inst_2 (fun (b : β) => PseudoEMetricSpace.toEDist.{u2} (π b) (_inst_3 b))) (Set.pi.{u1, u2} β (fun (b : β) => π b) (Set.univ.{u1} β) s)))
 Case conversion may be inaccurate. Consider using '#align set.le_einfsep_pi_of_le Set.le_einfsep_pi_of_leₓ'. -/
@@ -508,7 +508,7 @@ theorem Nontrivial.einfsep_ne_top (hs : s.Nontrivial) : s.einfsep ≠ ∞ :=
 
 /- warning: set.nontrivial.einfsep_lt_top -> Set.Nontrivial.einfsep_lt_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))
 Case conversion may be inaccurate. Consider using '#align set.nontrivial.einfsep_lt_top Set.Nontrivial.einfsep_lt_topₓ'. -/
@@ -520,7 +520,7 @@ theorem Nontrivial.einfsep_lt_top (hs : s.Nontrivial) : s.einfsep < ∞ :=
 
 /- warning: set.einfsep_lt_top_iff -> Set.einfsep_lt_top_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (Set.Nontrivial.{u1} α s)
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (Set.Nontrivial.{u1} α s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Set.Nontrivial.{u1} α s)
 Case conversion may be inaccurate. Consider using '#align set.einfsep_lt_top_iff Set.einfsep_lt_top_iffₓ'. -/
@@ -540,7 +540,7 @@ theorem einfsep_ne_top_iff : s.einfsep ≠ ∞ ↔ s.Nontrivial :=
 
 /- warning: set.le_einfsep_of_forall_dist_le -> Set.le_einfsep_of_forall_dist_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.hasLe d (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) x y)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (ENNReal.ofReal d) (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.hasLe d (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) x y)))) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (ENNReal.ofReal d) (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real}, (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.instLEReal d (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) x y)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (ENNReal.ofReal d) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s))
 Case conversion may be inaccurate. Consider using '#align set.le_einfsep_of_forall_dist_le Set.le_einfsep_of_forall_dist_leₓ'. -/
@@ -559,7 +559,7 @@ variable [EMetricSpace α] {x y z : α} {s t : Set α} {C : ℝ≥0∞} {sC : Se
 
 /- warning: set.einfsep_pos_of_finite -> Set.einfsep_pos_of_finite is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)], LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s)
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)], LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (Set.Elem.{u1} α s)], LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s)
 Case conversion may be inaccurate. Consider using '#align set.einfsep_pos_of_finite Set.einfsep_pos_of_finiteₓ'. -/
@@ -575,7 +575,7 @@ theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
 
 /- warning: set.relatively_discrete_of_finite -> Set.relatively_discrete_of_finite is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)], Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) => forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) C (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y)))))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)], Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) => forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) C (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (Set.Elem.{u1} α s)], Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) => forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) C (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y)))))
 Case conversion may be inaccurate. Consider using '#align set.relatively_discrete_of_finite Set.relatively_discrete_of_finiteₓ'. -/
@@ -589,7 +589,7 @@ theorem relatively_discrete_of_finite [Finite s] :
 
 /- warning: set.finite.einfsep_pos -> Set.Finite.einfsep_pos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s))
 Case conversion may be inaccurate. Consider using '#align set.finite.einfsep_pos Set.Finite.einfsep_posₓ'. -/
@@ -600,7 +600,7 @@ theorem Finite.einfsep_pos (hs : s.Finite) : 0 < s.einfsep :=
 
 /- warning: set.finite.relatively_discrete -> Set.Finite.relatively_discrete is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) => forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) C (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y))))))
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) => forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) C (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) => forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) C (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y))))))
 Case conversion may be inaccurate. Consider using '#align set.finite.relatively_discrete Set.Finite.relatively_discreteₓ'. -/
@@ -654,7 +654,7 @@ theorem infsep_nonneg : 0 ≤ s.infsep :=
 
 /- warning: set.infsep_pos -> Set.infsep_pos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.infsep.{u1} α _inst_1 s)) (And (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (Set.einfsep.{u1} α _inst_1 s)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.infsep.{u1} α _inst_1 s)) (And (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (Set.einfsep.{u1} α _inst_1 s)) (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.infsep.{u1} α _inst_1 s)) (And (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (Set.einfsep.{u1} α _inst_1 s)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))))
 Case conversion may be inaccurate. Consider using '#align set.infsep_pos Set.infsep_posₓ'. -/

f4758115

bump to nightly-2023-05-14-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

d31da313

Diff

@@ -64,7 +64,7 @@ Case conversion may be inaccurate. Consider using '#align set.le_einfsep_iff Set
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_iff {d} :
     d ≤ s.einfsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y := by
-  simp_rw [einfsep, le_infᵢ_iff]
+  simp_rw [einfsep, le_iInf_iff]
 #align set.le_einfsep_iff Set.le_einfsep_iff
 
 /- warning: set.einfsep_zero -> Set.einfsep_zero is a dubious translation:
@@ -77,7 +77,7 @@ Case conversion may be inaccurate. Consider using '#align set.einfsep_zero Set.e
 theorem einfsep_zero :
     s.einfsep = 0 ↔
       ∀ (C) (hC : 0 < C), ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), edist x y < C :=
-  by simp_rw [einfsep, ← bot_eq_zero, infᵢ_eq_bot, infᵢ_lt_iff]
+  by simp_rw [einfsep, ← bot_eq_zero, iInf_eq_bot, iInf_lt_iff]
 #align set.einfsep_zero Set.einfsep_zero
 
 /- warning: set.einfsep_pos -> Set.einfsep_pos is a dubious translation:
@@ -104,7 +104,7 @@ Case conversion may be inaccurate. Consider using '#align set.einfsep_top Set.ei
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_top :
     s.einfsep = ∞ ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), edist x y = ∞ := by
-  simp_rw [einfsep, infᵢ_eq_top]
+  simp_rw [einfsep, iInf_eq_top]
 #align set.einfsep_top Set.einfsep_top
 
 /- warning: set.einfsep_lt_top -> Set.einfsep_lt_top is a dubious translation:
@@ -116,7 +116,7 @@ Case conversion may be inaccurate. Consider using '#align set.einfsep_lt_top Set
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_lt_top :
     s.einfsep < ∞ ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), edist x y < ∞ := by
-  simp_rw [einfsep, infᵢ_lt_iff]
+  simp_rw [einfsep, iInf_lt_iff]
 #align set.einfsep_lt_top Set.einfsep_lt_top
 
 /- warning: set.einfsep_ne_top -> Set.einfsep_ne_top is a dubious translation:
@@ -140,7 +140,7 @@ Case conversion may be inaccurate. Consider using '#align set.einfsep_lt_iff Set
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_lt_iff {d} :
     s.einfsep < d ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(h : x ≠ y), edist x y < d := by
-  simp_rw [einfsep, infᵢ_lt_iff]
+  simp_rw [einfsep, iInf_lt_iff]
 #align set.einfsep_lt_iff Set.einfsep_lt_iff
 
 /- warning: set.nontrivial_of_einfsep_lt_top -> Set.nontrivial_of_einfsep_lt_top is a dubious translation:
@@ -256,15 +256,15 @@ theorem einfsep_singleton : ({x} : Set α).einfsep = ∞ :=
   subsingleton_singleton.einfsep
 #align set.einfsep_singleton Set.einfsep_singleton
 
-/- warning: set.einfsep_Union_mem_option -> Set.einfsep_unionᵢ_mem_option is a dubious translation:
+/- warning: set.einfsep_Union_mem_option -> Set.einfsep_iUnion_mem_option is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {ι : Type.{u2}} (o : Option.{u2} ι) (s : ι -> (Set.{u1} α)), Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) (fun (H : Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) => s i)))) (infᵢ.{0, succ u2} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) ι (fun (i : ι) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) (fun (H : Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) => Set.einfsep.{u1} α _inst_1 (s i))))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {ι : Type.{u2}} (o : Option.{u2} ι) (s : ι -> (Set.{u1} α)), Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) (fun (H : Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) => s i)))) (iInf.{0, succ u2} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) ι (fun (i : ι) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) (fun (H : Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) => Set.einfsep.{u1} α _inst_1 (s i))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {ι : Type.{u2}} (o : Option.{u2} ι) (s : ι -> (Set.{u1} α)), Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u2, u2} ι (Option.{u2} ι) (Option.instMembershipOption.{u2} ι) i o) (fun (H : Membership.mem.{u2, u2} ι (Option.{u2} ι) (Option.instMembershipOption.{u2} ι) i o) => s i)))) (infᵢ.{0, succ u2} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) ι (fun (i : ι) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u2, u2} ι (Option.{u2} ι) (Option.instMembershipOption.{u2} ι) i o) (fun (H : Membership.mem.{u2, u2} ι (Option.{u2} ι) (Option.instMembershipOption.{u2} ι) i o) => Set.einfsep.{u1} α _inst_1 (s i))))
-Case conversion may be inaccurate. Consider using '#align set.einfsep_Union_mem_option Set.einfsep_unionᵢ_mem_optionₓ'. -/
-theorem einfsep_unionᵢ_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {ι : Type.{u2}} (o : Option.{u2} ι) (s : ι -> (Set.{u1} α)), Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.mem.{u2, u2} ι (Option.{u2} ι) (Option.instMembershipOption.{u2} ι) i o) (fun (H : Membership.mem.{u2, u2} ι (Option.{u2} ι) (Option.instMembershipOption.{u2} ι) i o) => s i)))) (iInf.{0, succ u2} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) ι (fun (i : ι) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u2, u2} ι (Option.{u2} ι) (Option.instMembershipOption.{u2} ι) i o) (fun (H : Membership.mem.{u2, u2} ι (Option.{u2} ι) (Option.instMembershipOption.{u2} ι) i o) => Set.einfsep.{u1} α _inst_1 (s i))))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_Union_mem_option Set.einfsep_iUnion_mem_optionₓ'. -/
+theorem einfsep_iUnion_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
     (⋃ i ∈ o, s i).einfsep = ⨅ i ∈ o, (s i).einfsep := by cases o <;> simp
-#align set.einfsep_Union_mem_option Set.einfsep_unionᵢ_mem_option
+#align set.einfsep_Union_mem_option Set.einfsep_iUnion_mem_option
 
 /- warning: set.einfsep_anti -> Set.einfsep_anti is a dubious translation:
 lean 3 declaration is
@@ -278,13 +278,13 @@ theorem einfsep_anti (hst : s ⊆ t) : t.einfsep ≤ s.einfsep :=
 
 /- warning: set.einfsep_insert_le -> Set.einfsep_insert_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {s : Set.{u1} α}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x s)) (infᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) α (fun (y : α) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α _inst_1 x y))))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {s : Set.{u1} α}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x s)) (iInf.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) α (fun (y : α) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α _inst_1 x y))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {s : Set.{u1} α}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x s)) (infᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) α (fun (y : α) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α _inst_1 x y))))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {s : Set.{u1} α}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x s)) (iInf.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) α (fun (y : α) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α _inst_1 x y))))
 Case conversion may be inaccurate. Consider using '#align set.einfsep_insert_le Set.einfsep_insert_leₓ'. -/
 theorem einfsep_insert_le : (insert x s).einfsep ≤ ⨅ (y ∈ s) (hxy : x ≠ y), edist x y :=
   by
-  simp_rw [le_infᵢ_iff]
+  simp_rw [le_iInf_iff]
   refine' fun _ hy hxy => einfsep_le_edist_of_mem (mem_insert _ _) (mem_insert_of_mem _ hy) hxy
 #align set.einfsep_insert_le Set.einfsep_insert_le
 
@@ -330,18 +330,18 @@ theorem einfsep_pair_eq_inf (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist
   le_antisymm (le_inf (einfsep_pair_le_left hxy) (einfsep_pair_le_right hxy)) le_einfsep_pair
 #align set.einfsep_pair_eq_inf Set.einfsep_pair_eq_inf
 
-/- warning: set.einfsep_eq_infi -> Set.einfsep_eq_infᵢ is a dubious translation:
+/- warning: set.einfsep_eq_infi -> Set.einfsep_eq_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (infᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (fun (d : coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α ENNReal (EDist.edist.{u1} α _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeSubtype.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)))))) d)))
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (iInf.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (fun (d : coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α ENNReal (EDist.edist.{u1} α _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeSubtype.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)))))) d)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (infᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (fun (d : Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α ENNReal (EDist.edist.{u1} α _inst_1) (Subtype.val.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)) d)))
-Case conversion may be inaccurate. Consider using '#align set.einfsep_eq_infi Set.einfsep_eq_infᵢₓ'. -/
-theorem einfsep_eq_infᵢ : s.einfsep = ⨅ d : s.offDiag, (uncurry edist) (d : α × α) :=
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (iInf.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (fun (d : Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α ENNReal (EDist.edist.{u1} α _inst_1) (Subtype.val.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)) d)))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_eq_infi Set.einfsep_eq_iInfₓ'. -/
+theorem einfsep_eq_iInf : s.einfsep = ⨅ d : s.offDiag, (uncurry edist) (d : α × α) :=
   by
   refine' eq_of_forall_le_iff fun _ => _
-  simp_rw [le_einfsep_iff, le_infᵢ_iff, imp_forall_iff, SetCoe.forall, Subtype.coe_mk, mem_off_diag,
+  simp_rw [le_einfsep_iff, le_iInf_iff, imp_forall_iff, SetCoe.forall, Subtype.coe_mk, mem_off_diag,
     Prod.forall, uncurry_apply_pair, and_imp]
-#align set.einfsep_eq_infi Set.einfsep_eq_infᵢ
+#align set.einfsep_eq_infi Set.einfsep_eq_iInf
 
 /- warning: set.einfsep_of_fintype -> Set.einfsep_of_fintype is a dubious translation:
 lean 3 declaration is
@@ -421,9 +421,9 @@ theorem einfsep_pair (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist x y :=
 
 /- warning: set.einfsep_insert -> Set.einfsep_insert is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x s)) (Inf.inf.{0} ENNReal (SemilatticeInf.toHasInf.{0} ENNReal (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (infᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) α (fun (y : α) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y)))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x s)) (Inf.inf.{0} ENNReal (SemilatticeInf.toHasInf.{0} ENNReal (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (iInf.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) α (fun (y : α) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y)))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x s)) (Inf.inf.{0} ENNReal (Lattice.toInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (infᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) α (fun (y : α) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y)))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x s)) (Inf.inf.{0} ENNReal (Lattice.toInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (iInf.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) α (fun (y : α) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => iInf.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y)))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align set.einfsep_insert Set.einfsep_insertₓ'. -/
 theorem einfsep_insert : einfsep (insert x s) = (⨅ (y ∈ s) (hxy : x ≠ y), edist x y) ⊓ s.einfsep :=
   by
@@ -431,9 +431,9 @@ theorem einfsep_insert : einfsep (insert x s) = (⨅ (y ∈ s) (hxy : x ≠ y),
   simp_rw [le_einfsep_iff, inf_le_iff, mem_insert_iff]
   rintro y (rfl | hy) z (rfl | hz) hyz
   · exact False.elim (hyz rfl)
-  · exact Or.inl (infᵢ_le_of_le _ (infᵢ₂_le hz hyz))
+  · exact Or.inl (iInf_le_of_le _ (iInf₂_le hz hyz))
   · rw [edist_comm]
-    exact Or.inl (infᵢ_le_of_le _ (infᵢ₂_le hy hyz.symm))
+    exact Or.inl (iInf_le_of_le _ (iInf₂_le hy hyz.symm))
   · exact Or.inr (einfsep_le_edist_of_mem hy hz hyz)
 #align set.einfsep_insert Set.einfsep_insert
 
@@ -445,8 +445,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align set.einfsep_triple Set.einfsep_tripleₓ'. -/
 theorem einfsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
     einfsep ({x, y, z} : Set α) = edist x y ⊓ edist x z ⊓ edist y z := by
-  simp_rw [einfsep_insert, infᵢ_insert, infᵢ_singleton, einfsep_singleton, inf_top_eq,
-    cinfᵢ_pos hxy, cinfᵢ_pos hyz, cinfᵢ_pos hxz]
+  simp_rw [einfsep_insert, iInf_insert, iInf_singleton, einfsep_singleton, inf_top_eq,
+    ciInf_pos hxy, ciInf_pos hyz, ciInf_pos hxz]
 #align set.einfsep_triple Set.einfsep_triple
 
 /- warning: set.le_einfsep_pi_of_le -> Set.le_einfsep_pi_of_le is a dubious translation:
@@ -849,13 +849,13 @@ theorem Nontrivial.infsep_anti (hs : s.Nontrivial) (hst : s ⊆ t) : t.infsep 
   ENNReal.toReal_mono hs.einfsep_ne_top (einfsep_anti hst)
 #align set.nontrivial.infsep_anti Set.Nontrivial.infsep_anti
 
-/- warning: set.infsep_eq_infi -> Set.infsep_eq_infᵢ is a dubious translation:
+/- warning: set.infsep_eq_infi -> Set.infsep_eq_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)], Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (ite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (infᵢ.{0, succ u1} Real Real.hasInf (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (fun (d : coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeSubtype.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)))))) d))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)], Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (ite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (iInf.{0, succ u1} Real Real.hasInf (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (fun (d : coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeSubtype.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)))))) d))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)], Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (ite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (infᵢ.{0, succ u1} Real Real.instInfSetReal (Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (fun (d : Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)) (Subtype.val.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)) d))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align set.infsep_eq_infi Set.infsep_eq_infᵢₓ'. -/
-theorem infsep_eq_infᵢ [Decidable s.Nontrivial] :
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)], Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (ite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (iInf.{0, succ u1} Real Real.instInfSetReal (Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (fun (d : Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)) (Subtype.val.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)) d))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align set.infsep_eq_infi Set.infsep_eq_iInfₓ'. -/
+theorem infsep_eq_iInf [Decidable s.Nontrivial] :
     s.infsep = if s.Nontrivial then ⨅ d : s.offDiag, (uncurry dist) (d : α × α) else 0 :=
   by
   split_ifs with hs
@@ -866,21 +866,21 @@ theorem infsep_eq_infᵢ [Decidable s.Nontrivial] :
       rcases h with ⟨_, _, _, rfl⟩
       exact dist_nonneg
     refine' eq_of_forall_le_iff fun _ => _
-    simp_rw [hs.le_infsep_iff, le_cinfᵢ_set_iff (off_diag_nonempty.mpr hs) hb, imp_forall_iff,
+    simp_rw [hs.le_infsep_iff, le_ciInf_set_iff (off_diag_nonempty.mpr hs) hb, imp_forall_iff,
       mem_off_diag, Prod.forall, uncurry_apply_pair, and_imp]
   · exact (not_nontrivial_iff.mp hs).infsep_zero
-#align set.infsep_eq_infi Set.infsep_eq_infᵢ
+#align set.infsep_eq_infi Set.infsep_eq_iInf
 
-/- warning: set.nontrivial.infsep_eq_infi -> Set.Nontrivial.infsep_eq_infᵢ is a dubious translation:
+/- warning: set.nontrivial.infsep_eq_infi -> Set.Nontrivial.infsep_eq_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (infᵢ.{0, succ u1} Real Real.hasInf (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (fun (d : coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeSubtype.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)))))) d))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (iInf.{0, succ u1} Real Real.hasInf (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (fun (d : coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeSubtype.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)))))) d))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (infᵢ.{0, succ u1} Real Real.instInfSetReal (Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (fun (d : Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)) (Subtype.val.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)) d))))
-Case conversion may be inaccurate. Consider using '#align set.nontrivial.infsep_eq_infi Set.Nontrivial.infsep_eq_infᵢₓ'. -/
-theorem Nontrivial.infsep_eq_infᵢ (hs : s.Nontrivial) :
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (iInf.{0, succ u1} Real Real.instInfSetReal (Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (fun (d : Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)) (Subtype.val.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)) d))))
+Case conversion may be inaccurate. Consider using '#align set.nontrivial.infsep_eq_infi Set.Nontrivial.infsep_eq_iInfₓ'. -/
+theorem Nontrivial.infsep_eq_iInf (hs : s.Nontrivial) :
     s.infsep = ⨅ d : s.offDiag, (uncurry dist) (d : α × α) := by
   classical rw [infsep_eq_infi, if_pos hs]
-#align set.nontrivial.infsep_eq_infi Set.Nontrivial.infsep_eq_infᵢ
+#align set.nontrivial.infsep_eq_infi Set.Nontrivial.infsep_eq_iInf
 
 /- warning: set.infsep_of_fintype -> Set.infsep_of_fintype is a dubious translation:
 lean 3 declaration is

f4758115

bump to nightly-2023-05-03-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

aa7b8e08

Diff

@@ -886,7 +886,7 @@ theorem Nontrivial.infsep_eq_infᵢ (hs : s.Nontrivial) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)] [_inst_3 : DecidableEq.{succ u1} α] [_inst_4 : Fintype.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)], Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (dite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (fun (hs : Set.Nontrivial.{u1} α s) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.semilatticeInf (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4)) (Eq.mpr.{0} (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nontrivial.{u1} α s) (id_tag Tactic.IdTag.simp (Eq.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nontrivial.{u1} α s)) (Eq.trans.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (propext (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.toFinset_nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (propext (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (Set.offDiag_nonempty.{u1} α s)))) hs) (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1)))) (fun (hs : Not (Set.Nontrivial.{u1} α s)) => OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)] [_inst_3 : DecidableEq.{succ u1} α] [_inst_4 : Fintype.{u1} (Set.Elem.{u1} α s)], Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (dite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (fun (hs : Set.Nontrivial.{u1} α s) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.instSemilatticeInfReal (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4)) (Eq.mpr.{0} (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nontrivial.{u1} α s) (id.{0} (Eq.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nontrivial.{u1} α s)) (Eq.trans.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (Mathlib.Data.Fintype.Basic._auxLemma.20.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4)) (Mathlib.Data.Set.Prod._auxLemma.34.{u1} α s))) hs) (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)))) (fun (hs : Not (Set.Nontrivial.{u1} α s)) => OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)] [_inst_3 : DecidableEq.{succ u1} α] [_inst_4 : Fintype.{u1} (Set.Elem.{u1} α s)], Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (dite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (fun (hs : Set.Nontrivial.{u1} α s) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.instSemilatticeInfReal (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4)) (Eq.mpr.{0} (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nontrivial.{u1} α s) (id.{0} (Eq.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nontrivial.{u1} α s)) (Eq.trans.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (Mathlib.Data.Fintype.Basic._auxLemma.20.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4)) (Mathlib.Data.Set.Prod._auxLemma.33.{u1} α s))) hs) (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)))) (fun (hs : Not (Set.Nontrivial.{u1} α s)) => OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align set.infsep_of_fintype Set.infsep_of_fintypeₓ'. -/
 theorem infsep_of_fintype [Decidable s.Nontrivial] [DecidableEq α] [Fintype s] :
     s.infsep = if hs : s.Nontrivial then s.offDiag.toFinset.inf' (by simpa) (uncurry dist) else 0 :=
@@ -910,7 +910,7 @@ theorem Nontrivial.infsep_of_fintype [DecidableEq α] [Fintype s] (hs : s.Nontri
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)] (hsf : Set.Finite.{u1} α s), Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (dite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (fun (hs : Set.Nontrivial.{u1} α s) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.semilatticeInf (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf)) (Eq.mpr.{0} (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s) (id_tag Tactic.IdTag.simp (Eq.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s)) (Eq.trans.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (propext (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Finite.toFinset_nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (propext (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (Set.offDiag_nonempty.{u1} α s)))) hs) (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1)))) (fun (hs : Not (Set.Nontrivial.{u1} α s)) => OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)] (hsf : Set.Finite.{u1} α s), Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (dite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (fun (hs : Set.Nontrivial.{u1} α s) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.instSemilatticeInfReal (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf)) (Eq.mpr.{0} (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s) (id.{0} (Eq.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s)) (Eq.trans.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (Mathlib.Data.Set.Finite._auxLemma.4.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf)) (Mathlib.Data.Set.Prod._auxLemma.34.{u1} α s))) hs) (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)))) (fun (hs : Not (Set.Nontrivial.{u1} α s)) => OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)] (hsf : Set.Finite.{u1} α s), Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (dite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (fun (hs : Set.Nontrivial.{u1} α s) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.instSemilatticeInfReal (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf)) (Eq.mpr.{0} (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s) (id.{0} (Eq.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s)) (Eq.trans.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (Mathlib.Data.Set.Finite._auxLemma.4.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf)) (Mathlib.Data.Set.Prod._auxLemma.33.{u1} α s))) hs) (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)))) (fun (hs : Not (Set.Nontrivial.{u1} α s)) => OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align set.finite.infsep Set.Finite.infsepₓ'. -/
 theorem Finite.infsep [Decidable s.Nontrivial] (hsf : s.Finite) :
     s.infsep =

f4758115

bump to nightly-2023-04-25-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c

ed327085

Diff

@@ -931,13 +931,13 @@ theorem Finite.infsep_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
 #align set.finite.infsep_of_nontrivial Set.Finite.infsep_of_nontrivial
 -/
 
-/- warning: finset.coe_infsep -> Set.Finset.coe_infsep is a dubious translation:
+/- warning: finset.coe_infsep -> Finset.coe_infsep is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (s : Finset.{u1} α), Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s)) (dite.{1} Real (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s)) (Finset.decidableNonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s)) (fun (hs : Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s)) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.semilatticeInf (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s) hs (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1)))) (fun (hs : Not (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s))) => OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (s : Finset.{u1} α), Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Finset.toSet.{u1} α s)) (dite.{1} Real (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s)) (Finset.decidableNonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s)) (fun (hs : Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s)) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.instSemilatticeInfReal (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s) hs (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)))) (fun (hs : Not (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s))) => OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align finset.coe_infsep Set.Finset.coe_infsepₓ'. -/
-theorem Set.Finset.coe_infsep [DecidableEq α] (s : Finset α) :
+Case conversion may be inaccurate. Consider using '#align finset.coe_infsep Finset.coe_infsepₓ'. -/
+theorem Finset.coe_infsep [DecidableEq α] (s : Finset α) :
     (s : Set α).infsep = if hs : s.offDiag.Nonempty then s.offDiag.inf' hs (uncurry dist) else 0 :=
   by
   have H : (s : Set α).Nontrivial ↔ s.off_diag.nonempty := by
@@ -945,27 +945,27 @@ theorem Set.Finset.coe_infsep [DecidableEq α] (s : Finset α) :
   split_ifs with hs
   · simp_rw [(H.mpr hs).infsep_of_fintype, ← Finset.coe_offDiag, Finset.toFinset_coe]
   · exact (not_nontrivial_iff.mp (H.mp.mt hs)).infsep_zero
-#align finset.coe_infsep Set.Finset.coe_infsep
+#align finset.coe_infsep Finset.coe_infsep
 
-#print Set.Finset.coe_infsep_of_offDiag_nonempty /-
-theorem Set.Finset.coe_infsep_of_offDiag_nonempty [DecidableEq α] {s : Finset α}
+#print Finset.coe_infsep_of_offDiag_nonempty /-
+theorem Finset.coe_infsep_of_offDiag_nonempty [DecidableEq α] {s : Finset α}
     (hs : s.offDiag.Nonempty) : (s : Set α).infsep = s.offDiag.inf' hs (uncurry dist) := by
-  rw [Set.Finset.coe_infsep, dif_pos hs]
-#align finset.coe_infsep_of_off_diag_nonempty Set.Finset.coe_infsep_of_offDiag_nonempty
+  rw [Finset.coe_infsep, dif_pos hs]
+#align finset.coe_infsep_of_off_diag_nonempty Finset.coe_infsep_of_offDiag_nonempty
 -/
 
-/- warning: finset.coe_infsep_of_off_diag_empty -> Set.Finset.coe_infsep_of_offDiag_empty is a dubious translation:
+/- warning: finset.coe_infsep_of_off_diag_empty -> Finset.coe_infsep_of_offDiag_empty is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {s : Finset.{u1} α}, (Eq.{succ u1} (Finset.{u1} (Prod.{u1, u1} α α)) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} (Prod.{u1, u1} α α)) (Finset.hasEmptyc.{u1} (Prod.{u1, u1} α α)))) -> (Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {s : Finset.{u1} α}, (Eq.{succ u1} (Finset.{u1} (Prod.{u1, u1} α α)) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} (Prod.{u1, u1} α α)) (Finset.instEmptyCollectionFinset.{u1} (Prod.{u1, u1} α α)))) -> (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Finset.toSet.{u1} α s)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align finset.coe_infsep_of_off_diag_empty Set.Finset.coe_infsep_of_offDiag_emptyₓ'. -/
-theorem Set.Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs : s.offDiag = ∅) :
+Case conversion may be inaccurate. Consider using '#align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_emptyₓ'. -/
+theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs : s.offDiag = ∅) :
     (s : Set α).infsep = 0 :=
   by
   rw [← Finset.not_nonempty_iff_eq_empty] at hs
-  rw [Set.Finset.coe_infsep, dif_neg hs]
-#align finset.coe_infsep_of_off_diag_empty Set.Finset.coe_infsep_of_offDiag_empty
+  rw [Finset.coe_infsep, dif_neg hs]
+#align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_empty
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 #print Set.Nontrivial.infsep_exists_of_finite /-
@@ -1042,27 +1042,27 @@ theorem Finite.infsep_pos_iff_nontrivial (hs : s.Finite) : 0 < s.infsep ↔ s.No
   infsep_pos_iff_nontrivial_of_finite
 #align set.finite.infsep_pos_iff_nontrivial Set.Finite.infsep_pos_iff_nontrivial
 
-/- warning: finset.infsep_zero_iff_subsingleton -> Set.Finset.infsep_zero_iff_subsingleton is a dubious translation:
+/- warning: finset.infsep_zero_iff_subsingleton -> Finset.infsep_zero_iff_subsingleton is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] (s : Finset.{u1} α), Iff (Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Set.Subsingleton.{u1} α ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] (s : Finset.{u1} α), Iff (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1))) (Finset.toSet.{u1} α s)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Set.Subsingleton.{u1} α (Finset.toSet.{u1} α s))
-Case conversion may be inaccurate. Consider using '#align finset.infsep_zero_iff_subsingleton Set.Finset.infsep_zero_iff_subsingletonₓ'. -/
-theorem Set.Finset.infsep_zero_iff_subsingleton (s : Finset α) :
+Case conversion may be inaccurate. Consider using '#align finset.infsep_zero_iff_subsingleton Finset.infsep_zero_iff_subsingletonₓ'. -/
+theorem Finset.infsep_zero_iff_subsingleton (s : Finset α) :
     (s : Set α).infsep = 0 ↔ (s : Set α).Subsingleton :=
   infsep_zero_iff_subsingleton_of_finite
-#align finset.infsep_zero_iff_subsingleton Set.Finset.infsep_zero_iff_subsingleton
+#align finset.infsep_zero_iff_subsingleton Finset.infsep_zero_iff_subsingleton
 
-/- warning: finset.infsep_pos_iff_nontrivial -> Set.Finset.infsep_pos_iff_nontrivial is a dubious translation:
+/- warning: finset.infsep_pos_iff_nontrivial -> Finset.infsep_pos_iff_nontrivial is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] (s : Finset.{u1} α), Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s))) (Set.Nontrivial.{u1} α ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] (s : Finset.{u1} α), Iff (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1))) (Finset.toSet.{u1} α s))) (Set.Nontrivial.{u1} α (Finset.toSet.{u1} α s))
-Case conversion may be inaccurate. Consider using '#align finset.infsep_pos_iff_nontrivial Set.Finset.infsep_pos_iff_nontrivialₓ'. -/
-theorem Set.Finset.infsep_pos_iff_nontrivial (s : Finset α) :
+Case conversion may be inaccurate. Consider using '#align finset.infsep_pos_iff_nontrivial Finset.infsep_pos_iff_nontrivialₓ'. -/
+theorem Finset.infsep_pos_iff_nontrivial (s : Finset α) :
     0 < (s : Set α).infsep ↔ (s : Set α).Nontrivial :=
   infsep_pos_iff_nontrivial_of_finite
-#align finset.infsep_pos_iff_nontrivial Set.Finset.infsep_pos_iff_nontrivial
+#align finset.infsep_pos_iff_nontrivial Finset.infsep_pos_iff_nontrivial
 
 end MetricSpace

f4758115

bump to nightly-2023-04-01-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/172bf2812857f5e56938cc148b7a539f52f84ca9

b22e1dc9

Diff

@@ -910,7 +910,7 @@ theorem Nontrivial.infsep_of_fintype [DecidableEq α] [Fintype s] (hs : s.Nontri
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)] (hsf : Set.Finite.{u1} α s), Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (dite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (fun (hs : Set.Nontrivial.{u1} α s) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.semilatticeInf (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf)) (Eq.mpr.{0} (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s) (id_tag Tactic.IdTag.simp (Eq.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s)) (Eq.trans.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (propext (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Finite.toFinset_nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (propext (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (Set.offDiag_nonempty.{u1} α s)))) hs) (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1)))) (fun (hs : Not (Set.Nontrivial.{u1} α s)) => OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)] (hsf : Set.Finite.{u1} α s), Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (dite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (fun (hs : Set.Nontrivial.{u1} α s) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.instSemilatticeInfReal (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf)) (Eq.mpr.{0} (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s) (id.{0} (Eq.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s)) (Eq.trans.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (Mathlib.Data.Set.Finite._auxLemma.3.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf)) (Mathlib.Data.Set.Prod._auxLemma.34.{u1} α s))) hs) (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)))) (fun (hs : Not (Set.Nontrivial.{u1} α s)) => OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)] (hsf : Set.Finite.{u1} α s), Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (dite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (fun (hs : Set.Nontrivial.{u1} α s) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.instSemilatticeInfReal (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf)) (Eq.mpr.{0} (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s) (id.{0} (Eq.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s)) (Eq.trans.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (Mathlib.Data.Set.Finite._auxLemma.4.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf)) (Mathlib.Data.Set.Prod._auxLemma.34.{u1} α s))) hs) (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)))) (fun (hs : Not (Set.Nontrivial.{u1} α s)) => OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align set.finite.infsep Set.Finite.infsepₓ'. -/
 theorem Finite.infsep [Decidable s.Nontrivial] (hsf : s.Finite) :
     s.infsep =

f4758115

bump to nightly-2023-03-09-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

061741a1

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Wrenna Robson
 
 ! This file was ported from Lean 3 source module topology.metric_space.infsep
-! leanprover-community/mathlib commit 5316314b553dcf8c6716541851517c1a9715e22b
+! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Topology.MetricSpace.Basic
 /-!
 # Infimum separation
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines the extended infimum separation of a set. This is approximately dual to the
 diameter of a set, but where the extended diameter of a set is the supremum of the extended distance
 between elements of the set, the extended infimum separation is the infimum of the (extended)

5316314b

bump to nightly-2023-03-04-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

726b2da6

Diff

@@ -41,21 +41,35 @@ open ENNReal
 
 open Function
 
+#print Set.einfsep /-
 /-- The "extended infimum separation" of a set with an edist function. -/
 noncomputable def einfsep [EDist α] (s : Set α) : ℝ≥0∞ :=
   ⨅ (x ∈ s) (y ∈ s) (hxy : x ≠ y), edist x y
 #align set.einfsep Set.einfsep
+-/
 
 section EDist
 
 variable [EDist α] {x y : α} {s t : Set α}
 
+/- warning: set.le_einfsep_iff -> Set.le_einfsep_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (Set.einfsep.{u1} α _inst_1 s)) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (EDist.edist.{u1} α _inst_1 x y))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (Set.einfsep.{u1} α _inst_1 s)) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (EDist.edist.{u1} α _inst_1 x y))))
+Case conversion may be inaccurate. Consider using '#align set.le_einfsep_iff Set.le_einfsep_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_iff {d} :
     d ≤ s.einfsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y := by
   simp_rw [einfsep, le_infᵢ_iff]
 #align set.le_einfsep_iff Set.le_einfsep_iff
 
+/- warning: set.einfsep_zero -> Set.einfsep_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (forall (C : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) C)))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall (C : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α _inst_1 x y) C)))))))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_zero Set.einfsep_zeroₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_zero :
     s.einfsep = 0 ↔
@@ -63,6 +77,12 @@ theorem einfsep_zero :
   by simp_rw [einfsep, ← bot_eq_zero, infᵢ_eq_bot, infᵢ_lt_iff]
 #align set.einfsep_zero Set.einfsep_zero
 
+/- warning: set.einfsep_pos -> Set.einfsep_pos is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (Set.einfsep.{u1} α _inst_1 s)) (Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) => forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) C (EDist.edist.{u1} α _inst_1 x y))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (Set.einfsep.{u1} α _inst_1 s)) (Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) => forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) C (EDist.edist.{u1} α _inst_1 x y))))))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_pos Set.einfsep_posₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_pos :
     0 < s.einfsep ↔
@@ -72,115 +92,247 @@ theorem einfsep_pos :
   simp only [not_forall, not_exists, not_lt]
 #align set.einfsep_pos Set.einfsep_pos
 
+/- warning: set.einfsep_top -> Set.einfsep_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (Eq.{1} ENNReal (EDist.edist.{u1} α _inst_1 x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (Eq.{1} ENNReal (EDist.edist.{u1} α _inst_1 x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_top Set.einfsep_topₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_top :
     s.einfsep = ∞ ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), edist x y = ∞ := by
   simp_rw [einfsep, infᵢ_eq_top]
 #align set.einfsep_top Set.einfsep_top
 
+/- warning: set.einfsep_lt_top -> Set.einfsep_lt_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α _inst_1 x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))))))))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_lt_top Set.einfsep_lt_topₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_lt_top :
     s.einfsep < ∞ ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), edist x y < ∞ := by
   simp_rw [einfsep, infᵢ_lt_iff]
 #align set.einfsep_lt_top Set.einfsep_lt_top
 
+/- warning: set.einfsep_ne_top -> Set.einfsep_ne_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Ne.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => Ne.{1} ENNReal (EDist.edist.{u1} α _inst_1 x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Ne.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => Ne.{1} ENNReal (EDist.edist.{u1} α _inst_1 x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))))))))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_ne_top Set.einfsep_ne_topₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_ne_top :
     s.einfsep ≠ ∞ ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), edist x y ≠ ∞ := by
   simp_rw [← lt_top_iff_ne_top, einfsep_lt_top]
 #align set.einfsep_ne_top Set.einfsep_ne_top
 
+/- warning: set.einfsep_lt_iff -> Set.einfsep_lt_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) d) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (h : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) d))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 s) d) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (h : Ne.{succ u1} α x y) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α _inst_1 x y) d))))))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_lt_iff Set.einfsep_lt_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_lt_iff {d} :
     s.einfsep < d ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(h : x ≠ y), edist x y < d := by
   simp_rw [einfsep, infᵢ_lt_iff]
 #align set.einfsep_lt_iff Set.einfsep_lt_iff
 
+/- warning: set.nontrivial_of_einfsep_lt_top -> Set.nontrivial_of_einfsep_lt_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Set.Nontrivial.{u1} α s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Set.Nontrivial.{u1} α s)
+Case conversion may be inaccurate. Consider using '#align set.nontrivial_of_einfsep_lt_top Set.nontrivial_of_einfsep_lt_topₓ'. -/
 theorem nontrivial_of_einfsep_lt_top (hs : s.einfsep < ∞) : s.Nontrivial :=
   by
   rcases einfsep_lt_top.1 hs with ⟨_, hx, _, hy, hxy, _⟩
   exact ⟨_, hx, _, hy, hxy⟩
 #align set.nontrivial_of_einfsep_lt_top Set.nontrivial_of_einfsep_lt_top
 
+/- warning: set.nontrivial_of_einfsep_ne_top -> Set.nontrivial_of_einfsep_ne_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (Ne.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Set.Nontrivial.{u1} α s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (Ne.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Set.Nontrivial.{u1} α s)
+Case conversion may be inaccurate. Consider using '#align set.nontrivial_of_einfsep_ne_top Set.nontrivial_of_einfsep_ne_topₓ'. -/
 theorem nontrivial_of_einfsep_ne_top (hs : s.einfsep ≠ ∞) : s.Nontrivial :=
   nontrivial_of_einfsep_lt_top (lt_top_iff_ne_top.mpr hs)
 #align set.nontrivial_of_einfsep_ne_top Set.nontrivial_of_einfsep_ne_top
 
+/- warning: set.subsingleton.einfsep -> Set.Subsingleton.einfsep is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (Set.Subsingleton.{u1} α s) -> (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (Set.Subsingleton.{u1} α s) -> (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))
+Case conversion may be inaccurate. Consider using '#align set.subsingleton.einfsep Set.Subsingleton.einfsepₓ'. -/
 theorem Subsingleton.einfsep (hs : s.Subsingleton) : s.einfsep = ∞ :=
   by
   rw [einfsep_top]
   exact fun _ hx _ hy hxy => (hxy <| hs hx hy).elim
 #align set.subsingleton.einfsep Set.Subsingleton.einfsep
 
+/- warning: set.le_einfsep_image_iff -> Set.le_einfsep_image_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : EDist.{u1} α] {d : ENNReal} {f : β -> α} {s : Set.{u2} β}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (Set.einfsep.{u1} α _inst_1 (Set.image.{u2, u1} β α f s))) (forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) -> (forall (y : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y s) -> (Ne.{succ u1} α (f x) (f y)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (EDist.edist.{u1} α _inst_1 (f x) (f y)))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : EDist.{u1} α] {d : ENNReal} {f : β -> α} {s : Set.{u2} β}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (Set.einfsep.{u1} α _inst_1 (Set.image.{u2, u1} β α f s))) (forall (x : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) -> (forall (y : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) y s) -> (Ne.{succ u1} α (f x) (f y)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (EDist.edist.{u1} α _inst_1 (f x) (f y)))))
+Case conversion may be inaccurate. Consider using '#align set.le_einfsep_image_iff Set.le_einfsep_image_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_image_iff {d} {f : β → α} {s : Set β} :
     d ≤ einfsep (f '' s) ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s), f x ≠ f y → d ≤ edist (f x) (f y) :=
   by simp_rw [le_einfsep_iff, ball_image_iff]
 #align set.le_einfsep_image_iff Set.le_einfsep_image_iff
 
+/- warning: set.le_edist_of_le_einfsep -> Set.le_edist_of_le_einfsep is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal} {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall {y : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (Set.einfsep.{u1} α _inst_1 s)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (EDist.edist.{u1} α _inst_1 x y)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal} {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall {y : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (Set.einfsep.{u1} α _inst_1 s)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (EDist.edist.{u1} α _inst_1 x y)))
+Case conversion may be inaccurate. Consider using '#align set.le_edist_of_le_einfsep Set.le_edist_of_le_einfsepₓ'. -/
 theorem le_edist_of_le_einfsep {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y)
     (hd : d ≤ s.einfsep) : d ≤ edist x y :=
   le_einfsep_iff.1 hd x hx y hy hxy
 #align set.le_edist_of_le_einfsep Set.le_edist_of_le_einfsep
 
+/- warning: set.einfsep_le_edist_of_mem -> Set.einfsep_le_edist_of_mem is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall {y : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) (EDist.edist.{u1} α _inst_1 x y)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall {y : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 s) (EDist.edist.{u1} α _inst_1 x y)))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_le_edist_of_mem Set.einfsep_le_edist_of_memₓ'. -/
 theorem einfsep_le_edist_of_mem {x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y) :
     s.einfsep ≤ edist x y :=
   le_edist_of_le_einfsep hx hy hxy le_rfl
 #align set.einfsep_le_edist_of_mem Set.einfsep_le_edist_of_mem
 
+/- warning: set.einfsep_le_of_mem_of_edist_le -> Set.einfsep_le_of_mem_of_edist_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal} {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall {y : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) d) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) d))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal} {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall {y : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α _inst_1 x y) d) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 s) d))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_le_of_mem_of_edist_le Set.einfsep_le_of_mem_of_edist_leₓ'. -/
 theorem einfsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y)
     (hxy' : edist x y ≤ d) : s.einfsep ≤ d :=
   le_trans (einfsep_le_edist_of_mem hx hy hxy) hxy'
 #align set.einfsep_le_of_mem_of_edist_le Set.einfsep_le_of_mem_of_edist_le
 
+/- warning: set.le_einfsep -> Set.le_einfsep is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (EDist.edist.{u1} α _inst_1 x y)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) d (Set.einfsep.{u1} α _inst_1 s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {d : ENNReal}, (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (EDist.edist.{u1} α _inst_1 x y)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) d (Set.einfsep.{u1} α _inst_1 s))
+Case conversion may be inaccurate. Consider using '#align set.le_einfsep Set.le_einfsepₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep {d} (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y) :
     d ≤ s.einfsep :=
   le_einfsep_iff.2 h
 #align set.le_einfsep Set.le_einfsep
 
+/- warning: set.einfsep_empty -> Set.einfsep_empty is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α], Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α], Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_empty Set.einfsep_emptyₓ'. -/
 @[simp]
 theorem einfsep_empty : (∅ : Set α).einfsep = ∞ :=
   subsingleton_empty.einfsep
 #align set.einfsep_empty Set.einfsep_empty
 
+/- warning: set.einfsep_singleton -> Set.einfsep_singleton is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α}, Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) x)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α}, Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) x)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_singleton Set.einfsep_singletonₓ'. -/
 @[simp]
 theorem einfsep_singleton : ({x} : Set α).einfsep = ∞ :=
   subsingleton_singleton.einfsep
 #align set.einfsep_singleton Set.einfsep_singleton
 
+/- warning: set.einfsep_Union_mem_option -> Set.einfsep_unionᵢ_mem_option is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {ι : Type.{u2}} (o : Option.{u2} ι) (s : ι -> (Set.{u1} α)), Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) (fun (H : Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) => s i)))) (infᵢ.{0, succ u2} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) ι (fun (i : ι) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) (fun (H : Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) => Set.einfsep.{u1} α _inst_1 (s i))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {ι : Type.{u2}} (o : Option.{u2} ι) (s : ι -> (Set.{u1} α)), Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u2, u2} ι (Option.{u2} ι) (Option.instMembershipOption.{u2} ι) i o) (fun (H : Membership.mem.{u2, u2} ι (Option.{u2} ι) (Option.instMembershipOption.{u2} ι) i o) => s i)))) (infᵢ.{0, succ u2} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) ι (fun (i : ι) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u2, u2} ι (Option.{u2} ι) (Option.instMembershipOption.{u2} ι) i o) (fun (H : Membership.mem.{u2, u2} ι (Option.{u2} ι) (Option.instMembershipOption.{u2} ι) i o) => Set.einfsep.{u1} α _inst_1 (s i))))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_Union_mem_option Set.einfsep_unionᵢ_mem_optionₓ'. -/
 theorem einfsep_unionᵢ_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
     (⋃ i ∈ o, s i).einfsep = ⨅ i ∈ o, (s i).einfsep := by cases o <;> simp
 #align set.einfsep_Union_mem_option Set.einfsep_unionᵢ_mem_option
 
+/- warning: set.einfsep_anti -> Set.einfsep_anti is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 t) (Set.einfsep.{u1} α _inst_1 s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 t) (Set.einfsep.{u1} α _inst_1 s))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_anti Set.einfsep_antiₓ'. -/
 theorem einfsep_anti (hst : s ⊆ t) : t.einfsep ≤ s.einfsep :=
   le_einfsep fun x hx y hy => einfsep_le_edist_of_mem (hst hx) (hst hy)
 #align set.einfsep_anti Set.einfsep_anti
 
+/- warning: set.einfsep_insert_le -> Set.einfsep_insert_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {s : Set.{u1} α}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x s)) (infᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) α (fun (y : α) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α _inst_1 x y))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {s : Set.{u1} α}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x s)) (infᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) α (fun (y : α) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α _inst_1 x y))))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_insert_le Set.einfsep_insert_leₓ'. -/
 theorem einfsep_insert_le : (insert x s).einfsep ≤ ⨅ (y ∈ s) (hxy : x ≠ y), edist x y :=
   by
   simp_rw [le_infᵢ_iff]
   refine' fun _ hy hxy => einfsep_le_edist_of_mem (mem_insert _ _) (mem_insert_of_mem _ hy) hxy
 #align set.einfsep_insert_le Set.einfsep_insert_le
 
+/- warning: set.le_einfsep_pair -> Set.le_einfsep_pair is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Inf.inf.{0} ENNReal (SemilatticeInf.toHasInf.{0} ENNReal (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) (EDist.edist.{u1} α _inst_1 y x)) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) y)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Inf.inf.{0} ENNReal (Lattice.toInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α _inst_1 x y) (EDist.edist.{u1} α _inst_1 y x)) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) y)))
+Case conversion may be inaccurate. Consider using '#align set.le_einfsep_pair Set.le_einfsep_pairₓ'. -/
 theorem le_einfsep_pair : edist x y ⊓ edist y x ≤ ({x, y} : Set α).einfsep :=
   by
   simp_rw [le_einfsep_iff, inf_le_iff, mem_insert_iff, mem_singleton_iff]
   rintro a (rfl | rfl) b (rfl | rfl) hab <;> finish
 #align set.le_einfsep_pair Set.le_einfsep_pair
 
+/- warning: set.einfsep_pair_le_left -> Set.einfsep_pair_le_left is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) y))) (EDist.edist.{u1} α _inst_1 x y))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) y))) (EDist.edist.{u1} α _inst_1 x y))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_pair_le_left Set.einfsep_pair_le_leftₓ'. -/
 theorem einfsep_pair_le_left (hxy : x ≠ y) : ({x, y} : Set α).einfsep ≤ edist x y :=
   einfsep_le_edist_of_mem (mem_insert _ _) (mem_insert_of_mem _ (mem_singleton _)) hxy
 #align set.einfsep_pair_le_left Set.einfsep_pair_le_left
 
+/- warning: set.einfsep_pair_le_right -> Set.einfsep_pair_le_right is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) y))) (EDist.edist.{u1} α _inst_1 y x))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) y))) (EDist.edist.{u1} α _inst_1 y x))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_pair_le_right Set.einfsep_pair_le_rightₓ'. -/
 theorem einfsep_pair_le_right (hxy : x ≠ y) : ({x, y} : Set α).einfsep ≤ edist y x := by
   rw [pair_comm] <;> exact einfsep_pair_le_left hxy.symm
 #align set.einfsep_pair_le_right Set.einfsep_pair_le_right
 
+/- warning: set.einfsep_pair_eq_inf -> Set.einfsep_pair_eq_inf is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, (Ne.{succ u1} α x y) -> (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) y))) (Inf.inf.{0} ENNReal (SemilatticeInf.toHasInf.{0} ENNReal (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) (EDist.edist.{u1} α _inst_1 y x)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, (Ne.{succ u1} α x y) -> (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) y))) (Inf.inf.{0} ENNReal (Lattice.toInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α _inst_1 x y) (EDist.edist.{u1} α _inst_1 y x)))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_pair_eq_inf Set.einfsep_pair_eq_infₓ'. -/
 theorem einfsep_pair_eq_inf (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist x y ⊓ edist y x :=
   le_antisymm (le_inf (einfsep_pair_le_left hxy) (einfsep_pair_le_right hxy)) le_einfsep_pair
 #align set.einfsep_pair_eq_inf Set.einfsep_pair_eq_inf
 
+/- warning: set.einfsep_eq_infi -> Set.einfsep_eq_infᵢ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (infᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (fun (d : coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α ENNReal (EDist.edist.{u1} α _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeSubtype.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)))))) d)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (infᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (fun (d : Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α ENNReal (EDist.edist.{u1} α _inst_1) (Subtype.val.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)) d)))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_eq_infi Set.einfsep_eq_infᵢₓ'. -/
 theorem einfsep_eq_infᵢ : s.einfsep = ⨅ d : s.offDiag, (uncurry edist) (d : α × α) :=
   by
   refine' eq_of_forall_le_iff fun _ => _
@@ -188,6 +340,12 @@ theorem einfsep_eq_infᵢ : s.einfsep = ⨅ d : s.offDiag, (uncurry edist) (d :
     Prod.forall, uncurry_apply_pair, and_imp]
 #align set.einfsep_eq_infi Set.einfsep_eq_infᵢ
 
+/- warning: set.einfsep_of_fintype -> Set.einfsep_of_fintype is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} [_inst_2 : DecidableEq.{succ u1} α] [_inst_3 : Fintype.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)], Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Finset.inf.{0, u1} ENNReal (Prod.{u1, u1} α α) (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (LinearOrderedAddCommMonoidWithTop.toOrderTop.{0} ENNReal ENNReal.linearOrderedAddCommMonoidWithTop) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s _inst_3)) (Function.uncurry.{u1, u1, 0} α α ENNReal (EDist.edist.{u1} α _inst_1)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} [_inst_2 : DecidableEq.{succ u1} α] [_inst_3 : Fintype.{u1} (Set.Elem.{u1} α s)], Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Finset.inf.{0, u1} ENNReal (Prod.{u1, u1} α α) (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (BoundedOrder.toOrderTop.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (SemilatticeInf.toPartialOrder.{0} ENNReal (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))))))) ENNReal.instBoundedOrderENNRealToLEToPreorderToPartialOrderToSemilatticeInfToLatticeInstENNRealDistribLattice) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s _inst_3)) (Function.uncurry.{u1, u1, 0} α α ENNReal (EDist.edist.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_of_fintype Set.einfsep_of_fintypeₓ'. -/
 theorem einfsep_of_fintype [DecidableEq α] [Fintype s] :
     s.einfsep = s.offDiag.toFinset.inf (uncurry edist) :=
   by
@@ -196,6 +354,12 @@ theorem einfsep_of_fintype [DecidableEq α] [Fintype s] :
     Prod.forall, uncurry_apply_pair, and_imp]
 #align set.einfsep_of_fintype Set.einfsep_of_fintype
 
+/- warning: set.finite.einfsep -> Set.Finite.einfsep is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} (hs : Set.Finite.{u1} α s), Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Finset.inf.{0, u1} ENNReal (Prod.{u1, u1} α α) (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (LinearOrderedAddCommMonoidWithTop.toOrderTop.{0} ENNReal ENNReal.linearOrderedAddCommMonoidWithTop) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hs)) (Function.uncurry.{u1, u1, 0} α α ENNReal (EDist.edist.{u1} α _inst_1)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α} (hs : Set.Finite.{u1} α s), Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Finset.inf.{0, u1} ENNReal (Prod.{u1, u1} α α) (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (BoundedOrder.toOrderTop.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (SemilatticeInf.toPartialOrder.{0} ENNReal (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))))))) ENNReal.instBoundedOrderENNRealToLEToPreorderToPartialOrderToSemilatticeInfToLatticeInstENNRealDistribLattice) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hs)) (Function.uncurry.{u1, u1, 0} α α ENNReal (EDist.edist.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align set.finite.einfsep Set.Finite.einfsepₓ'. -/
 theorem Finite.einfsep (hs : s.Finite) : s.einfsep = hs.offDiag.toFinset.inf (uncurry edist) :=
   by
   refine' eq_of_forall_le_iff fun _ => _
@@ -203,12 +367,19 @@ theorem Finite.einfsep (hs : s.Finite) : s.einfsep = hs.offDiag.toFinset.inf (un
     Prod.forall, uncurry_apply_pair, and_imp]
 #align set.finite.einfsep Set.Finite.einfsep
 
+/- warning: set.finset.coe_einfsep -> Set.Finset.coe_einfsep is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {s : Finset.{u1} α}, Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s)) (Finset.inf.{0, u1} ENNReal (Prod.{u1, u1} α α) (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (LinearOrderedAddCommMonoidWithTop.toOrderTop.{0} ENNReal ENNReal.linearOrderedAddCommMonoidWithTop) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s) (Function.uncurry.{u1, u1, 0} α α ENNReal (EDist.edist.{u1} α _inst_1)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {s : Finset.{u1} α}, Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 (Finset.toSet.{u1} α s)) (Finset.inf.{0, u1} ENNReal (Prod.{u1, u1} α α) (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (BoundedOrder.toOrderTop.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (SemilatticeInf.toPartialOrder.{0} ENNReal (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))))))) ENNReal.instBoundedOrderENNRealToLEToPreorderToPartialOrderToSemilatticeInfToLatticeInstENNRealDistribLattice) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s) (Function.uncurry.{u1, u1, 0} α α ENNReal (EDist.edist.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align set.finset.coe_einfsep Set.Finset.coe_einfsepₓ'. -/
 theorem Finset.coe_einfsep [DecidableEq α] {s : Finset α} :
     (s : Set α).einfsep = s.offDiag.inf (uncurry edist) := by
   simp_rw [einfsep_of_fintype, ← Finset.coe_offDiag, Finset.toFinset_coe]
 #align set.finset.coe_einfsep Set.Finset.coe_einfsep
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.Nontrivial.einfsep_exists_of_finite /-
 theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), s.einfsep = edist x y := by
   classical
@@ -219,13 +390,16 @@ theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     simp_rw [mem_to_finset] at hxy
     refine' ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.einfsep_exists_of_finite Set.Nontrivial.einfsep_exists_of_finite
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.Finite.einfsep_exists_of_nontrivial /-
 theorem Finite.einfsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
     ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), s.einfsep = edist x y :=
   letI := hsf.fintype
   hs.einfsep_exists_of_finite
 #align set.finite.einfsep_exists_of_nontrivial Set.Finite.einfsep_exists_of_nontrivial
+-/
 
 end EDist
 
@@ -233,13 +407,21 @@ section PseudoEMetricSpace
 
 variable [PseudoEMetricSpace α] {x y z : α} {s t : Set α}
 
+#print Set.einfsep_pair /-
 theorem einfsep_pair (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist x y :=
   by
   nth_rw 1 [← min_self (edist x y)]
   convert einfsep_pair_eq_inf hxy using 2
   rw [edist_comm]
 #align set.einfsep_pair Set.einfsep_pair
+-/
 
+/- warning: set.einfsep_insert -> Set.einfsep_insert is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x s)) (Inf.inf.{0} ENNReal (SemilatticeInf.toHasInf.{0} ENNReal (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (infᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) α (fun (y : α) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasInf.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y)))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x s)) (Inf.inf.{0} ENNReal (Lattice.toInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (infᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) α (fun (y : α) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => infᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toInfSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y)))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_insert Set.einfsep_insertₓ'. -/
 theorem einfsep_insert : einfsep (insert x s) = (⨅ (y ∈ s) (hxy : x ≠ y), edist x y) ⊓ s.einfsep :=
   by
   refine' le_antisymm (le_min einfsep_insert_le (einfsep_anti (subset_insert _ _))) _
@@ -252,12 +434,24 @@ theorem einfsep_insert : einfsep (insert x s) = (⨅ (y ∈ s) (hxy : x ≠ y),
   · exact Or.inr (einfsep_le_edist_of_mem hy hz hyz)
 #align set.einfsep_insert Set.einfsep_insert
 
+/- warning: set.einfsep_triple -> Set.einfsep_triple is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {z : α}, (Ne.{succ u1} α x y) -> (Ne.{succ u1} α y z) -> (Ne.{succ u1} α x z) -> (Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) y (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) z)))) (Inf.inf.{0} ENNReal (SemilatticeInf.toHasInf.{0} ENNReal (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Inf.inf.{0} ENNReal (SemilatticeInf.toHasInf.{0} ENNReal (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x z)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y z)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {z : α}, (Ne.{succ u1} α x y) -> (Ne.{succ u1} α y z) -> (Ne.{succ u1} α x z) -> (Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) y (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) z)))) (Inf.inf.{0} ENNReal (Lattice.toInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Inf.inf.{0} ENNReal (Lattice.toInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x z)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) y z)))
+Case conversion may be inaccurate. Consider using '#align set.einfsep_triple Set.einfsep_tripleₓ'. -/
 theorem einfsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
     einfsep ({x, y, z} : Set α) = edist x y ⊓ edist x z ⊓ edist y z := by
   simp_rw [einfsep_insert, infᵢ_insert, infᵢ_singleton, einfsep_singleton, inf_top_eq,
     cinfᵢ_pos hxy, cinfᵢ_pos hyz, cinfᵢ_pos hxz]
 #align set.einfsep_triple Set.einfsep_triple
 
+/- warning: set.le_einfsep_pi_of_le -> Set.le_einfsep_pi_of_le is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] {s : forall (b : β), Set.{u2} (π b)} {c : ENNReal}, (forall (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) c (Set.einfsep.{u2} (π b) (PseudoEMetricSpace.toHasEdist.{u2} (π b) (_inst_3 b)) (s b))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) c (Set.einfsep.{max u1 u2} (forall (i : β), π i) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (forall (i : β), π i) (pseudoEMetricSpacePi.{u1, u2} β (fun (i : β) => π i) _inst_2 (fun (b : β) => _inst_3 b))) (Set.pi.{u1, u2} β (fun (b : β) => π b) (Set.univ.{u1} β) s)))
+but is expected to have type
+  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] {s : forall (b : β), Set.{u2} (π b)} {c : ENNReal}, (forall (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) c (Set.einfsep.{u2} (π b) (PseudoEMetricSpace.toEDist.{u2} (π b) (_inst_3 b)) (s b))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) c (Set.einfsep.{max u2 u1} (forall (i : β), π i) (instEDistForAll.{u1, u2} β (fun (i : β) => π i) _inst_2 (fun (b : β) => PseudoEMetricSpace.toEDist.{u2} (π b) (_inst_3 b))) (Set.pi.{u1, u2} β (fun (b : β) => π b) (Set.univ.{u1} β) s)))
+Case conversion may be inaccurate. Consider using '#align set.le_einfsep_pi_of_le Set.le_einfsep_pi_of_leₓ'. -/
 theorem le_einfsep_pi_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMetricSpace (π b)]
     {s : ∀ b : β, Set (π b)} {c : ℝ≥0∞} (h : ∀ b, c ≤ einfsep (s b)) :
     c ≤ einfsep (Set.pi univ s) :=
@@ -274,16 +468,34 @@ section PseudoMetricSpace
 
 variable [PseudoMetricSpace α] {s : Set α}
 
+/- warning: set.subsingleton_of_einfsep_eq_top -> Set.subsingleton_of_einfsep_eq_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (Set.Subsingleton.{u1} α s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (Set.Subsingleton.{u1} α s)
+Case conversion may be inaccurate. Consider using '#align set.subsingleton_of_einfsep_eq_top Set.subsingleton_of_einfsep_eq_topₓ'. -/
 theorem subsingleton_of_einfsep_eq_top (hs : s.einfsep = ∞) : s.Subsingleton :=
   by
   rw [einfsep_top] at hs
   exact fun _ hx _ hy => of_not_not fun hxy => edist_ne_top _ _ (hs _ hx _ hy hxy)
 #align set.subsingleton_of_einfsep_eq_top Set.subsingleton_of_einfsep_eq_top
 
+/- warning: set.einfsep_eq_top_iff -> Set.einfsep_eq_top_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (Set.Subsingleton.{u1} α s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Set.Subsingleton.{u1} α s)
+Case conversion may be inaccurate. Consider using '#align set.einfsep_eq_top_iff Set.einfsep_eq_top_iffₓ'. -/
 theorem einfsep_eq_top_iff : s.einfsep = ∞ ↔ s.Subsingleton :=
   ⟨subsingleton_of_einfsep_eq_top, Subsingleton.einfsep⟩
 #align set.einfsep_eq_top_iff Set.einfsep_eq_top_iff
 
+/- warning: set.nontrivial.einfsep_ne_top -> Set.Nontrivial.einfsep_ne_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (Ne.{1} ENNReal (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (Ne.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))
+Case conversion may be inaccurate. Consider using '#align set.nontrivial.einfsep_ne_top Set.Nontrivial.einfsep_ne_topₓ'. -/
 theorem Nontrivial.einfsep_ne_top (hs : s.Nontrivial) : s.einfsep ≠ ∞ :=
   by
   contrapose! hs
@@ -291,20 +503,44 @@ theorem Nontrivial.einfsep_ne_top (hs : s.Nontrivial) : s.einfsep ≠ ∞ :=
   exact subsingleton_of_einfsep_eq_top hs
 #align set.nontrivial.einfsep_ne_top Set.Nontrivial.einfsep_ne_top
 
+/- warning: set.nontrivial.einfsep_lt_top -> Set.Nontrivial.einfsep_lt_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))
+Case conversion may be inaccurate. Consider using '#align set.nontrivial.einfsep_lt_top Set.Nontrivial.einfsep_lt_topₓ'. -/
 theorem Nontrivial.einfsep_lt_top (hs : s.Nontrivial) : s.einfsep < ∞ :=
   by
   rw [lt_top_iff_ne_top]
   exact hs.einfsep_ne_top
 #align set.nontrivial.einfsep_lt_top Set.Nontrivial.einfsep_lt_top
 
+/- warning: set.einfsep_lt_top_iff -> Set.einfsep_lt_top_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (Set.Nontrivial.{u1} α s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Set.Nontrivial.{u1} α s)
+Case conversion may be inaccurate. Consider using '#align set.einfsep_lt_top_iff Set.einfsep_lt_top_iffₓ'. -/
 theorem einfsep_lt_top_iff : s.einfsep < ∞ ↔ s.Nontrivial :=
   ⟨nontrivial_of_einfsep_lt_top, Nontrivial.einfsep_lt_top⟩
 #align set.einfsep_lt_top_iff Set.einfsep_lt_top_iff
 
+/- warning: set.einfsep_ne_top_iff -> Set.einfsep_ne_top_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (Ne.{1} ENNReal (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (Set.Nontrivial.{u1} α s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (Ne.{1} ENNReal (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Set.Nontrivial.{u1} α s)
+Case conversion may be inaccurate. Consider using '#align set.einfsep_ne_top_iff Set.einfsep_ne_top_iffₓ'. -/
 theorem einfsep_ne_top_iff : s.einfsep ≠ ∞ ↔ s.Nontrivial :=
   ⟨nontrivial_of_einfsep_ne_top, Nontrivial.einfsep_ne_top⟩
 #align set.einfsep_ne_top_iff Set.einfsep_ne_top_iff
 
+/- warning: set.le_einfsep_of_forall_dist_le -> Set.le_einfsep_of_forall_dist_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.hasLe d (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) x y)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (ENNReal.ofReal d) (Set.einfsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real}, (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.instLEReal d (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) x y)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (ENNReal.ofReal d) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s))
+Case conversion may be inaccurate. Consider using '#align set.le_einfsep_of_forall_dist_le Set.le_einfsep_of_forall_dist_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_of_forall_dist_le {d}
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) :
@@ -318,6 +554,12 @@ section EMetricSpace
 
 variable [EMetricSpace α] {x y z : α} {s t : Set α} {C : ℝ≥0∞} {sC : Set ℝ≥0∞}
 
+/- warning: set.einfsep_pos_of_finite -> Set.einfsep_pos_of_finite is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)], LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (Set.Elem.{u1} α s)], LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s)
+Case conversion may be inaccurate. Consider using '#align set.einfsep_pos_of_finite Set.einfsep_pos_of_finiteₓ'. -/
 theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
   by
   cases nonempty_fintype s
@@ -328,6 +570,12 @@ theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
     exact hs.einfsep.symm ▸ WithTop.zero_lt_top
 #align set.einfsep_pos_of_finite Set.einfsep_pos_of_finite
 
+/- warning: set.relatively_discrete_of_finite -> Set.relatively_discrete_of_finite is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)], Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) => forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) C (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (Set.Elem.{u1} α s)], Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) => forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) C (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y)))))
+Case conversion may be inaccurate. Consider using '#align set.relatively_discrete_of_finite Set.relatively_discrete_of_finiteₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem relatively_discrete_of_finite [Finite s] :
     ∃ (C : _)(hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
@@ -336,11 +584,23 @@ theorem relatively_discrete_of_finite [Finite s] :
   exact einfsep_pos_of_finite
 #align set.relatively_discrete_of_finite Set.relatively_discrete_of_finite
 
+/- warning: set.finite.einfsep_pos -> Set.Finite.einfsep_pos is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (Set.einfsep.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (Set.einfsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s))
+Case conversion may be inaccurate. Consider using '#align set.finite.einfsep_pos Set.Finite.einfsep_posₓ'. -/
 theorem Finite.einfsep_pos (hs : s.Finite) : 0 < s.einfsep :=
   letI := hs.fintype
   einfsep_pos_of_finite
 #align set.finite.einfsep_pos Set.Finite.einfsep_pos
 
+/- warning: set.finite.relatively_discrete -> Set.Finite.relatively_discrete is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) C) => forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) C (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α (EMetricSpace.toPseudoEmetricSpace.{u1} α _inst_1)) x y))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Exists.{1} ENNReal (fun (C : ENNReal) => Exists.{0} (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) (fun (hC : LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) C) => forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) C (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) x y))))))
+Case conversion may be inaccurate. Consider using '#align set.finite.relatively_discrete Set.Finite.relatively_discreteₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Finite.relatively_discrete (hs : s.Finite) :
     ∃ (C : _)(hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
@@ -358,27 +618,53 @@ open ENNReal
 
 open Set Function
 
+#print Set.infsep /-
 /-- The "infimum separation" of a set with an edist function. -/
 noncomputable def infsep [EDist α] (s : Set α) : ℝ :=
   ENNReal.toReal s.einfsep
 #align set.infsep Set.infsep
+-/
 
 section EDist
 
 variable [EDist α] {x y : α} {s : Set α}
 
+/- warning: set.infsep_zero -> Set.infsep_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} Real (Set.infsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Or (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (Eq.{1} Real (Set.infsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Or (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (Eq.{1} ENNReal (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))))
+Case conversion may be inaccurate. Consider using '#align set.infsep_zero Set.infsep_zeroₓ'. -/
 theorem infsep_zero : s.infsep = 0 ↔ s.einfsep = 0 ∨ s.einfsep = ∞ := by
   rw [infsep, ENNReal.toReal_eq_zero_iff]
 #align set.infsep_zero Set.infsep_zero
 
+/- warning: set.infsep_nonneg -> Set.infsep_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.infsep.{u1} α _inst_1 s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.infsep.{u1} α _inst_1 s)
+Case conversion may be inaccurate. Consider using '#align set.infsep_nonneg Set.infsep_nonnegₓ'. -/
 theorem infsep_nonneg : 0 ≤ s.infsep :=
   ENNReal.toReal_nonneg
 #align set.infsep_nonneg Set.infsep_nonneg
 
+/- warning: set.infsep_pos -> Set.infsep_pos is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.infsep.{u1} α _inst_1 s)) (And (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (Set.einfsep.{u1} α _inst_1 s)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, Iff (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.infsep.{u1} α _inst_1 s)) (And (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (Set.einfsep.{u1} α _inst_1 s)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (Set.einfsep.{u1} α _inst_1 s) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))))
+Case conversion may be inaccurate. Consider using '#align set.infsep_pos Set.infsep_posₓ'. -/
 theorem infsep_pos : 0 < s.infsep ↔ 0 < s.einfsep ∧ s.einfsep < ∞ := by
   simp_rw [infsep, ENNReal.toReal_pos_iff]
 #align set.infsep_pos Set.infsep_pos
 
+/- warning: set.subsingleton.infsep_zero -> Set.Subsingleton.infsep_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (Set.Subsingleton.{u1} α s) -> (Eq.{1} Real (Set.infsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (Set.Subsingleton.{u1} α s) -> (Eq.{1} Real (Set.infsep.{u1} α _inst_1 s) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align set.subsingleton.infsep_zero Set.Subsingleton.infsep_zeroₓ'. -/
 theorem Subsingleton.infsep_zero (hs : s.Subsingleton) : s.infsep = 0 :=
   by
   rw [infsep_zero, hs.einfsep]
@@ -386,6 +672,12 @@ theorem Subsingleton.infsep_zero (hs : s.Subsingleton) : s.infsep = 0 :=
   rfl
 #align set.subsingleton.infsep_zero Set.Subsingleton.infsep_zero
 
+/- warning: set.nontrivial_of_infsep_pos -> Set.nontrivial_of_infsep_pos is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.infsep.{u1} α _inst_1 s)) -> (Set.Nontrivial.{u1} α s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {s : Set.{u1} α}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.infsep.{u1} α _inst_1 s)) -> (Set.Nontrivial.{u1} α s)
+Case conversion may be inaccurate. Consider using '#align set.nontrivial_of_infsep_pos Set.nontrivial_of_infsep_posₓ'. -/
 theorem nontrivial_of_infsep_pos (hs : 0 < s.infsep) : s.Nontrivial :=
   by
   contrapose hs
@@ -393,14 +685,32 @@ theorem nontrivial_of_infsep_pos (hs : 0 < s.infsep) : s.Nontrivial :=
   exact hs.infsep_zero ▸ lt_irrefl _
 #align set.nontrivial_of_infsep_pos Set.nontrivial_of_infsep_pos
 
+/- warning: set.infsep_empty -> Set.infsep_empty is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α], Eq.{1} Real (Set.infsep.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α], Eq.{1} Real (Set.infsep.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align set.infsep_empty Set.infsep_emptyₓ'. -/
 theorem infsep_empty : (∅ : Set α).infsep = 0 :=
   subsingleton_empty.infsep_zero
 #align set.infsep_empty Set.infsep_empty
 
+/- warning: set.infsep_singleton -> Set.infsep_singleton is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α}, Eq.{1} Real (Set.infsep.{u1} α _inst_1 (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) x)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α}, Eq.{1} Real (Set.infsep.{u1} α _inst_1 (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) x)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align set.infsep_singleton Set.infsep_singletonₓ'. -/
 theorem infsep_singleton : ({x} : Set α).infsep = 0 :=
   subsingleton_singleton.infsep_zero
 #align set.infsep_singleton Set.infsep_singleton
 
+/- warning: set.infsep_pair_le_to_real_inf -> Set.infsep_pair_le_toReal_inf is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.hasLe (Set.infsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) y))) (ENNReal.toReal (Inf.inf.{0} ENNReal (SemilatticeInf.toHasInf.{0} ENNReal (Lattice.toSemilatticeInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α _inst_1 x y) (EDist.edist.{u1} α _inst_1 y x))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : EDist.{u1} α] {x : α} {y : α}, (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.instLEReal (Set.infsep.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) y))) (ENNReal.toReal (Inf.inf.{0} ENNReal (Lattice.toInf.{0} ENNReal (ConditionallyCompleteLattice.toLattice.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α _inst_1 x y) (EDist.edist.{u1} α _inst_1 y x))))
+Case conversion may be inaccurate. Consider using '#align set.infsep_pair_le_to_real_inf Set.infsep_pair_le_toReal_infₓ'. -/
 theorem infsep_pair_le_toReal_inf (hxy : x ≠ y) :
     ({x, y} : Set α).infsep ≤ (edist x y ⊓ edist y x).toReal := by
   simp_rw [infsep, einfsep_pair_eq_inf hxy]
@@ -412,6 +722,7 @@ section PseudoEMetricSpace
 
 variable [PseudoEMetricSpace α] {x y : α} {s : Set α}
 
+#print Set.infsep_pair_eq_toReal /-
 theorem infsep_pair_eq_toReal : ({x, y} : Set α).infsep = (edist x y).toReal :=
   by
   by_cases hxy : x = y
@@ -419,6 +730,7 @@ theorem infsep_pair_eq_toReal : ({x, y} : Set α).infsep = (edist x y).toReal :=
     simp only [infsep_singleton, pair_eq_singleton, edist_self, ENNReal.zero_toReal]
   · rw [infsep, einfsep_pair hxy]
 #align set.infsep_pair_eq_to_real Set.infsep_pair_eq_toReal
+-/
 
 end PseudoEMetricSpace
 
@@ -426,6 +738,12 @@ section PseudoMetricSpace
 
 variable [PseudoMetricSpace α] {x y z : α} {s t : Set α}
 
+/- warning: set.nontrivial.le_infsep_iff -> Set.Nontrivial.le_infsep_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real}, (Set.Nontrivial.{u1} α s) -> (Iff (LE.le.{0} Real Real.hasLe d (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s)) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.hasLe d (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) x y)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real}, (Set.Nontrivial.{u1} α s) -> (Iff (LE.le.{0} Real Real.instLEReal d (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s)) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.instLEReal d (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) x y)))))
+Case conversion may be inaccurate. Consider using '#align set.nontrivial.le_infsep_iff Set.Nontrivial.le_infsep_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
     d ≤ s.infsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y := by
@@ -433,6 +751,12 @@ theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
     ENNReal.ofReal_le_ofReal_iff dist_nonneg]
 #align set.nontrivial.le_infsep_iff Set.Nontrivial.le_infsep_iff
 
+/- warning: set.nontrivial.infsep_lt_iff -> Set.Nontrivial.infsep_lt_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real}, (Set.Nontrivial.{u1} α s) -> (Iff (LT.lt.{0} Real Real.hasLt (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) d) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => LT.lt.{0} Real Real.hasLt (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) x y) d)))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real}, (Set.Nontrivial.{u1} α s) -> (Iff (LT.lt.{0} Real Real.instLTReal (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) d) (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) => Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => Exists.{0} (Ne.{succ u1} α x y) (fun (hxy : Ne.{succ u1} α x y) => LT.lt.{0} Real Real.instLTReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) x y) d)))))))
+Case conversion may be inaccurate. Consider using '#align set.nontrivial.infsep_lt_iff Set.Nontrivial.infsep_lt_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
     s.infsep < d ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), dist x y < d :=
@@ -442,12 +766,24 @@ theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
   exact hs.le_infsep_iff
 #align set.nontrivial.infsep_lt_iff Set.Nontrivial.infsep_lt_iff
 
+/- warning: set.nontrivial.le_infsep -> Set.Nontrivial.le_infsep is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real}, (Set.Nontrivial.{u1} α s) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.hasLe d (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) x y)))) -> (LE.le.{0} Real Real.hasLe d (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real}, (Set.Nontrivial.{u1} α s) -> (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.instLEReal d (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) x y)))) -> (LE.le.{0} Real Real.instLEReal d (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s))
+Case conversion may be inaccurate. Consider using '#align set.nontrivial.le_infsep Set.Nontrivial.le_infsepₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.le_infsep {d} (hs : s.Nontrivial)
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) : d ≤ s.infsep :=
   hs.le_infsep_iff.2 h
 #align set.nontrivial.le_infsep Set.Nontrivial.le_infsep
 
+/- warning: set.le_edist_of_le_infsep -> Set.le_edist_of_le_infsep is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real} {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall {y : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.hasLe d (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s)) -> (LE.le.{0} Real Real.hasLe d (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) x y)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real} {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall {y : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.instLEReal d (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s)) -> (LE.le.{0} Real Real.instLEReal d (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) x y)))
+Case conversion may be inaccurate. Consider using '#align set.le_edist_of_le_infsep Set.le_edist_of_le_infsepₓ'. -/
 theorem le_edist_of_le_infsep {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y)
     (hd : d ≤ s.infsep) : d ≤ dist x y :=
   by
@@ -458,21 +794,41 @@ theorem le_edist_of_le_infsep {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x 
     exact le_trans hd dist_nonneg
 #align set.le_edist_of_le_infsep Set.le_edist_of_le_infsep
 
+/- warning: set.infsep_le_dist_of_mem -> Set.infsep_le_dist_of_mem is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.hasLe (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) x y))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.instLEReal (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) x y))
+Case conversion may be inaccurate. Consider using '#align set.infsep_le_dist_of_mem Set.infsep_le_dist_of_memₓ'. -/
 theorem infsep_le_dist_of_mem (hx : x ∈ s) (hy : y ∈ s) (hxy : x ≠ y) : s.infsep ≤ dist x y :=
   le_edist_of_le_infsep hx hy hxy le_rfl
 #align set.infsep_le_dist_of_mem Set.infsep_le_dist_of_mem
 
+/- warning: set.infsep_le_of_mem_of_edist_le -> Set.infsep_le_of_mem_of_edist_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real} {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall {y : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.hasLe (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) x y) d) -> (LE.le.{0} Real Real.hasLe (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) d))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {d : Real} {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall {y : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (Ne.{succ u1} α x y) -> (LE.le.{0} Real Real.instLEReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) x y) d) -> (LE.le.{0} Real Real.instLEReal (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) d))
+Case conversion may be inaccurate. Consider using '#align set.infsep_le_of_mem_of_edist_le Set.infsep_le_of_mem_of_edist_leₓ'. -/
 theorem infsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y)
     (hxy' : dist x y ≤ d) : s.infsep ≤ d :=
   le_trans (infsep_le_dist_of_mem hx hy hxy) hxy'
 #align set.infsep_le_of_mem_of_edist_le Set.infsep_le_of_mem_of_edist_le
 
+#print Set.infsep_pair /-
 theorem infsep_pair : ({x, y} : Set α).infsep = dist x y :=
   by
   rw [infsep_pair_eq_to_real, edist_dist]
   exact ENNReal.toReal_ofReal dist_nonneg
 #align set.infsep_pair Set.infsep_pair
+-/
 
+/- warning: set.infsep_triple -> Set.infsep_triple is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {x : α} {y : α} {z : α}, (Ne.{succ u1} α x y) -> (Ne.{succ u1} α y z) -> (Ne.{succ u1} α x z) -> (Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) y (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) z)))) (Inf.inf.{0} Real Real.hasInf (Inf.inf.{0} Real Real.hasInf (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) x y) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) x z)) (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1) y z)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {x : α} {y : α} {z : α}, (Ne.{succ u1} α x y) -> (Ne.{succ u1} α y z) -> (Ne.{succ u1} α x z) -> (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) y (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) z)))) (Inf.inf.{0} Real Real.instInfReal (Inf.inf.{0} Real Real.instInfReal (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) x y) (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) x z)) (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1) y z)))
+Case conversion may be inaccurate. Consider using '#align set.infsep_triple Set.infsep_tripleₓ'. -/
 theorem infsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
     ({x, y, z} : Set α).infsep = dist x y ⊓ dist x z ⊓ dist y z := by
   simp only [infsep, einfsep_triple hxy hyz hxz, ENNReal.toReal_inf, edist_ne_top x y,
@@ -480,10 +836,22 @@ theorem infsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
     not_false_iff]
 #align set.infsep_triple Set.infsep_triple
 
+/- warning: set.nontrivial.infsep_anti -> Set.Nontrivial.infsep_anti is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{0} Real Real.hasLe (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) t) (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{0} Real Real.instLEReal (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) t) (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s))
+Case conversion may be inaccurate. Consider using '#align set.nontrivial.infsep_anti Set.Nontrivial.infsep_antiₓ'. -/
 theorem Nontrivial.infsep_anti (hs : s.Nontrivial) (hst : s ⊆ t) : t.infsep ≤ s.infsep :=
   ENNReal.toReal_mono hs.einfsep_ne_top (einfsep_anti hst)
 #align set.nontrivial.infsep_anti Set.Nontrivial.infsep_anti
 
+/- warning: set.infsep_eq_infi -> Set.infsep_eq_infᵢ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)], Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (ite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (infᵢ.{0, succ u1} Real Real.hasInf (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (fun (d : coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeSubtype.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)))))) d))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)], Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (ite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (infᵢ.{0, succ u1} Real Real.instInfSetReal (Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (fun (d : Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)) (Subtype.val.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)) d))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align set.infsep_eq_infi Set.infsep_eq_infᵢₓ'. -/
 theorem infsep_eq_infᵢ [Decidable s.Nontrivial] :
     s.infsep = if s.Nontrivial then ⨅ d : s.offDiag, (uncurry dist) (d : α × α) else 0 :=
   by
@@ -500,11 +868,23 @@ theorem infsep_eq_infᵢ [Decidable s.Nontrivial] :
   · exact (not_nontrivial_iff.mp hs).infsep_zero
 #align set.infsep_eq_infi Set.infsep_eq_infᵢ
 
+/- warning: set.nontrivial.infsep_eq_infi -> Set.Nontrivial.infsep_eq_infᵢ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (infᵢ.{0, succ u1} Real Real.hasInf (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (fun (d : coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Prod.{u1, u1} α α)) Type.{u1} (Set.hasCoeToSort.{u1} (Prod.{u1, u1} α α)) (Set.offDiag.{u1} α s)) (Prod.{u1, u1} α α) (coeSubtype.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)))))) d))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Nontrivial.{u1} α s) -> (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (infᵢ.{0, succ u1} Real Real.instInfSetReal (Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (fun (d : Set.Elem.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) => Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)) (Subtype.val.{succ u1} (Prod.{u1, u1} α α) (fun (x : Prod.{u1, u1} α α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) x (Set.offDiag.{u1} α s)) d))))
+Case conversion may be inaccurate. Consider using '#align set.nontrivial.infsep_eq_infi Set.Nontrivial.infsep_eq_infᵢₓ'. -/
 theorem Nontrivial.infsep_eq_infᵢ (hs : s.Nontrivial) :
     s.infsep = ⨅ d : s.offDiag, (uncurry dist) (d : α × α) := by
   classical rw [infsep_eq_infi, if_pos hs]
 #align set.nontrivial.infsep_eq_infi Set.Nontrivial.infsep_eq_infᵢ
 
+/- warning: set.infsep_of_fintype -> Set.infsep_of_fintype is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)] [_inst_3 : DecidableEq.{succ u1} α] [_inst_4 : Fintype.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)], Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (dite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (fun (hs : Set.Nontrivial.{u1} α s) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.semilatticeInf (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4)) (Eq.mpr.{0} (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nontrivial.{u1} α s) (id_tag Tactic.IdTag.simp (Eq.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nontrivial.{u1} α s)) (Eq.trans.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (propext (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.toFinset_nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (propext (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (Set.offDiag_nonempty.{u1} α s)))) hs) (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1)))) (fun (hs : Not (Set.Nontrivial.{u1} α s)) => OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)] [_inst_3 : DecidableEq.{succ u1} α] [_inst_4 : Fintype.{u1} (Set.Elem.{u1} α s)], Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (dite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (fun (hs : Set.Nontrivial.{u1} α s) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.instSemilatticeInfReal (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4)) (Eq.mpr.{0} (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nontrivial.{u1} α s) (id.{0} (Eq.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nontrivial.{u1} α s)) (Eq.trans.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (Mathlib.Data.Fintype.Basic._auxLemma.20.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.fintypeOffDiag.{u1} α (fun (a : α) (b : α) => _inst_3 a b) s _inst_4)) (Mathlib.Data.Set.Prod._auxLemma.34.{u1} α s))) hs) (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)))) (fun (hs : Not (Set.Nontrivial.{u1} α s)) => OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align set.infsep_of_fintype Set.infsep_of_fintypeₓ'. -/
 theorem infsep_of_fintype [Decidable s.Nontrivial] [DecidableEq α] [Fintype s] :
     s.infsep = if hs : s.Nontrivial then s.offDiag.toFinset.inf' (by simpa) (uncurry dist) else 0 :=
   by
@@ -516,11 +896,19 @@ theorem infsep_of_fintype [Decidable s.Nontrivial] [DecidableEq α] [Fintype s]
     exact hs.infsep_zero
 #align set.infsep_of_fintype Set.infsep_of_fintype
 
+#print Set.Nontrivial.infsep_of_fintype /-
 theorem Nontrivial.infsep_of_fintype [DecidableEq α] [Fintype s] (hs : s.Nontrivial) :
     s.infsep = s.offDiag.toFinset.inf' (by simpa) (uncurry dist) := by
   classical rw [infsep_of_fintype, dif_pos hs]
 #align set.nontrivial.infsep_of_fintype Set.Nontrivial.infsep_of_fintype
+-/
 
+/- warning: set.finite.infsep -> Set.Finite.infsep is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)] (hsf : Set.Finite.{u1} α s), Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) s) (dite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (fun (hs : Set.Nontrivial.{u1} α s) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.semilatticeInf (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf)) (Eq.mpr.{0} (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s) (id_tag Tactic.IdTag.simp (Eq.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s)) (Eq.trans.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (propext (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Finite.toFinset_nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (propext (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (Set.offDiag_nonempty.{u1} α s)))) hs) (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1)))) (fun (hs : Not (Set.Nontrivial.{u1} α s)) => OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Decidable (Set.Nontrivial.{u1} α s)] (hsf : Set.Finite.{u1} α s), Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) s) (dite.{1} Real (Set.Nontrivial.{u1} α s) _inst_2 (fun (hs : Set.Nontrivial.{u1} α s) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.instSemilatticeInfReal (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf)) (Eq.mpr.{0} (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s) (id.{0} (Eq.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nontrivial.{u1} α s)) (Eq.trans.{1} Prop (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.Finite.toFinset.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf))) (Set.Nonempty.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s)) (Set.Nontrivial.{u1} α s) (Mathlib.Data.Set.Finite._auxLemma.3.{u1} (Prod.{u1, u1} α α) (Set.offDiag.{u1} α s) (Set.Finite.offDiag.{u1} α s hsf)) (Mathlib.Data.Set.Prod._auxLemma.34.{u1} α s))) hs) (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)))) (fun (hs : Not (Set.Nontrivial.{u1} α s)) => OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align set.finite.infsep Set.Finite.infsepₓ'. -/
 theorem Finite.infsep [Decidable s.Nontrivial] (hsf : s.Finite) :
     s.infsep =
       if hs : s.Nontrivial then hsf.offDiag.toFinset.inf' (by simpa) (uncurry dist) else 0 :=
@@ -533,12 +921,20 @@ theorem Finite.infsep [Decidable s.Nontrivial] (hsf : s.Finite) :
     exact hs.infsep_zero
 #align set.finite.infsep Set.Finite.infsep
 
+#print Set.Finite.infsep_of_nontrivial /-
 theorem Finite.infsep_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
     s.infsep = hsf.offDiag.toFinset.inf' (by simpa) (uncurry dist) := by
   classical simp_rw [hsf.infsep, dif_pos hs]
 #align set.finite.infsep_of_nontrivial Set.Finite.infsep_of_nontrivial
+-/
 
-theorem Finset.coe_infsep [DecidableEq α] (s : Finset α) :
+/- warning: finset.coe_infsep -> Set.Finset.coe_infsep is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (s : Finset.{u1} α), Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s)) (dite.{1} Real (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s)) (Finset.decidableNonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s)) (fun (hs : Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s)) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.semilatticeInf (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s) hs (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toHasDist.{u1} α _inst_1)))) (fun (hs : Not (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s))) => OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] (s : Finset.{u1} α), Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Finset.toSet.{u1} α s)) (dite.{1} Real (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s)) (Finset.decidableNonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s)) (fun (hs : Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s)) => Finset.inf'.{0, u1} Real (Prod.{u1, u1} α α) Real.instSemilatticeInfReal (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s) hs (Function.uncurry.{u1, u1, 0} α α Real (Dist.dist.{u1} α (PseudoMetricSpace.toDist.{u1} α _inst_1)))) (fun (hs : Not (Finset.Nonempty.{u1} (Prod.{u1, u1} α α) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s))) => OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align finset.coe_infsep Set.Finset.coe_infsepₓ'. -/
+theorem Set.Finset.coe_infsep [DecidableEq α] (s : Finset α) :
     (s : Set α).infsep = if hs : s.offDiag.Nonempty then s.offDiag.inf' hs (uncurry dist) else 0 :=
   by
   have H : (s : Set α).Nontrivial ↔ s.off_diag.nonempty := by
@@ -546,21 +942,30 @@ theorem Finset.coe_infsep [DecidableEq α] (s : Finset α) :
   split_ifs with hs
   · simp_rw [(H.mpr hs).infsep_of_fintype, ← Finset.coe_offDiag, Finset.toFinset_coe]
   · exact (not_nontrivial_iff.mp (H.mp.mt hs)).infsep_zero
-#align finset.coe_infsep Finset.coe_infsep
+#align finset.coe_infsep Set.Finset.coe_infsep
 
-theorem Finset.coe_infsep_of_offDiag_nonempty [DecidableEq α] {s : Finset α}
+#print Set.Finset.coe_infsep_of_offDiag_nonempty /-
+theorem Set.Finset.coe_infsep_of_offDiag_nonempty [DecidableEq α] {s : Finset α}
     (hs : s.offDiag.Nonempty) : (s : Set α).infsep = s.offDiag.inf' hs (uncurry dist) := by
-  rw [Finset.coe_infsep, dif_pos hs]
-#align finset.coe_infsep_of_off_diag_nonempty Finset.coe_infsep_of_offDiag_nonempty
+  rw [Set.Finset.coe_infsep, dif_pos hs]
+#align finset.coe_infsep_of_off_diag_nonempty Set.Finset.coe_infsep_of_offDiag_nonempty
+-/
 
-theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs : s.offDiag = ∅) :
+/- warning: finset.coe_infsep_of_off_diag_empty -> Set.Finset.coe_infsep_of_offDiag_empty is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {s : Finset.{u1} α}, (Eq.{succ u1} (Finset.{u1} (Prod.{u1, u1} α α)) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} (Prod.{u1, u1} α α)) (Finset.hasEmptyc.{u1} (Prod.{u1, u1} α α)))) -> (Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} α] [_inst_2 : DecidableEq.{succ u1} α] {s : Finset.{u1} α}, (Eq.{succ u1} (Finset.{u1} (Prod.{u1, u1} α α)) (Finset.offDiag.{u1} α (fun (a : α) (b : α) => _inst_2 a b) s) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} (Prod.{u1, u1} α α)) (Finset.instEmptyCollectionFinset.{u1} (Prod.{u1, u1} α α)))) -> (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (PseudoMetricSpace.toPseudoEMetricSpace.{u1} α _inst_1)) (Finset.toSet.{u1} α s)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align finset.coe_infsep_of_off_diag_empty Set.Finset.coe_infsep_of_offDiag_emptyₓ'. -/
+theorem Set.Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs : s.offDiag = ∅) :
     (s : Set α).infsep = 0 :=
   by
   rw [← Finset.not_nonempty_iff_eq_empty] at hs
-  rw [Finset.coe_infsep, dif_neg hs]
-#align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_empty
+  rw [Set.Finset.coe_infsep, dif_neg hs]
+#align finset.coe_infsep_of_off_diag_empty Set.Finset.coe_infsep_of_offDiag_empty
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.Nontrivial.infsep_exists_of_finite /-
 theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), s.infsep = dist x y := by
   classical
@@ -571,13 +976,16 @@ theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     simp_rw [mem_to_finset] at hxy
     exact ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.infsep_exists_of_finite Set.Nontrivial.infsep_exists_of_finite
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+#print Set.Finite.infsep_exists_of_nontrivial /-
 theorem Finite.infsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
     ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), s.infsep = dist x y :=
   letI := hsf.fintype
   hs.infsep_exists_of_finite
 #align set.finite.infsep_exists_of_nontrivial Set.Finite.infsep_exists_of_nontrivial
+-/
 
 end PseudoMetricSpace
 
@@ -585,37 +993,73 @@ section MetricSpace
 
 variable [MetricSpace α] {s : Set α}
 
+/- warning: set.infsep_zero_iff_subsingleton_of_finite -> Set.infsep_zero_iff_subsingleton_of_finite is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)], Iff (Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) s) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Set.Subsingleton.{u1} α s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (Set.Elem.{u1} α s)], Iff (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1))) s) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Set.Subsingleton.{u1} α s)
+Case conversion may be inaccurate. Consider using '#align set.infsep_zero_iff_subsingleton_of_finite Set.infsep_zero_iff_subsingleton_of_finiteₓ'. -/
 theorem infsep_zero_iff_subsingleton_of_finite [Finite s] : s.infsep = 0 ↔ s.Subsingleton :=
   by
   rw [infsep_zero, einfsep_eq_top_iff, or_iff_right_iff_imp]
   exact fun H => (einfsep_pos_of_finite.ne' H).elim
 #align set.infsep_zero_iff_subsingleton_of_finite Set.infsep_zero_iff_subsingleton_of_finite
 
+/- warning: set.infsep_pos_iff_nontrivial_of_finite -> Set.infsep_pos_iff_nontrivial_of_finite is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)], Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) s)) (Set.Nontrivial.{u1} α s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : Finite.{succ u1} (Set.Elem.{u1} α s)], Iff (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1))) s)) (Set.Nontrivial.{u1} α s)
+Case conversion may be inaccurate. Consider using '#align set.infsep_pos_iff_nontrivial_of_finite Set.infsep_pos_iff_nontrivial_of_finiteₓ'. -/
 theorem infsep_pos_iff_nontrivial_of_finite [Finite s] : 0 < s.infsep ↔ s.Nontrivial :=
   by
   rw [infsep_pos, einfsep_lt_top_iff, and_iff_right_iff_imp]
   exact fun _ => einfsep_pos_of_finite
 #align set.infsep_pos_iff_nontrivial_of_finite Set.infsep_pos_iff_nontrivial_of_finite
 
+/- warning: set.finite.infsep_zero_iff_subsingleton -> Set.Finite.infsep_zero_iff_subsingleton is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Iff (Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) s) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Set.Subsingleton.{u1} α s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Iff (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1))) s) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Set.Subsingleton.{u1} α s))
+Case conversion may be inaccurate. Consider using '#align set.finite.infsep_zero_iff_subsingleton Set.Finite.infsep_zero_iff_subsingletonₓ'. -/
 theorem Finite.infsep_zero_iff_subsingleton (hs : s.Finite) : s.infsep = 0 ↔ s.Subsingleton :=
   letI := hs.fintype
   infsep_zero_iff_subsingleton_of_finite
 #align set.finite.infsep_zero_iff_subsingleton Set.Finite.infsep_zero_iff_subsingleton
 
+/- warning: set.finite.infsep_pos_iff_nontrivial -> Set.Finite.infsep_pos_iff_nontrivial is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) s)) (Set.Nontrivial.{u1} α s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Iff (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1))) s)) (Set.Nontrivial.{u1} α s))
+Case conversion may be inaccurate. Consider using '#align set.finite.infsep_pos_iff_nontrivial Set.Finite.infsep_pos_iff_nontrivialₓ'. -/
 theorem Finite.infsep_pos_iff_nontrivial (hs : s.Finite) : 0 < s.infsep ↔ s.Nontrivial :=
   letI := hs.fintype
   infsep_pos_iff_nontrivial_of_finite
 #align set.finite.infsep_pos_iff_nontrivial Set.Finite.infsep_pos_iff_nontrivial
 
-theorem Finset.infsep_zero_iff_subsingleton (s : Finset α) :
+/- warning: finset.infsep_zero_iff_subsingleton -> Set.Finset.infsep_zero_iff_subsingleton is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] (s : Finset.{u1} α), Iff (Eq.{1} Real (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Set.Subsingleton.{u1} α ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] (s : Finset.{u1} α), Iff (Eq.{1} Real (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1))) (Finset.toSet.{u1} α s)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Set.Subsingleton.{u1} α (Finset.toSet.{u1} α s))
+Case conversion may be inaccurate. Consider using '#align finset.infsep_zero_iff_subsingleton Set.Finset.infsep_zero_iff_subsingletonₓ'. -/
+theorem Set.Finset.infsep_zero_iff_subsingleton (s : Finset α) :
     (s : Set α).infsep = 0 ↔ (s : Set α).Subsingleton :=
   infsep_zero_iff_subsingleton_of_finite
-#align finset.infsep_zero_iff_subsingleton Finset.infsep_zero_iff_subsingleton
-
-theorem Finset.infsep_pos_iff_nontrivial (s : Finset α) :
+#align finset.infsep_zero_iff_subsingleton Set.Finset.infsep_zero_iff_subsingleton
+
+/- warning: finset.infsep_pos_iff_nontrivial -> Set.Finset.infsep_pos_iff_nontrivial is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] (s : Finset.{u1} α), Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.infsep.{u1} α (PseudoMetricSpace.toEDist.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s))) (Set.Nontrivial.{u1} α ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] (s : Finset.{u1} α), Iff (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.infsep.{u1} α (PseudoEMetricSpace.toEDist.{u1} α (EMetricSpace.toPseudoEMetricSpace.{u1} α (MetricSpace.toEMetricSpace.{u1} α _inst_1))) (Finset.toSet.{u1} α s))) (Set.Nontrivial.{u1} α (Finset.toSet.{u1} α s))
+Case conversion may be inaccurate. Consider using '#align finset.infsep_pos_iff_nontrivial Set.Finset.infsep_pos_iff_nontrivialₓ'. -/
+theorem Set.Finset.infsep_pos_iff_nontrivial (s : Finset α) :
     0 < (s : Set α).infsep ↔ (s : Set α).Nontrivial :=
   infsep_pos_iff_nontrivial_of_finite
-#align finset.infsep_pos_iff_nontrivial Finset.infsep_pos_iff_nontrivial
+#align finset.infsep_pos_iff_nontrivial Set.Finset.infsep_pos_iff_nontrivial
 
 end MetricSpace

5316314b

bump to nightly-2023-03-03-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

04b5c979

Diff

@@ -42,13 +42,13 @@ open ENNReal
 open Function
 
 /-- The "extended infimum separation" of a set with an edist function. -/
-noncomputable def einfsep [HasEdist α] (s : Set α) : ℝ≥0∞ :=
+noncomputable def einfsep [EDist α] (s : Set α) : ℝ≥0∞ :=
   ⨅ (x ∈ s) (y ∈ s) (hxy : x ≠ y), edist x y
 #align set.einfsep Set.einfsep
 
-section HasEdist
+section EDist
 
-variable [HasEdist α] {x y : α} {s t : Set α}
+variable [EDist α] {x y : α} {s t : Set α}
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_iff {d} :
@@ -227,11 +227,11 @@ theorem Finite.einfsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial)
   hs.einfsep_exists_of_finite
 #align set.finite.einfsep_exists_of_nontrivial Set.Finite.einfsep_exists_of_nontrivial
 
-end HasEdist
+end EDist
 
-section PseudoEmetricSpace
+section PseudoEMetricSpace
 
-variable [PseudoEmetricSpace α] {x y z : α} {s t : Set α}
+variable [PseudoEMetricSpace α] {x y z : α} {s t : Set α}
 
 theorem einfsep_pair (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist x y :=
   by
@@ -258,7 +258,7 @@ theorem einfsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
     cinfᵢ_pos hxy, cinfᵢ_pos hyz, cinfᵢ_pos hxz]
 #align set.einfsep_triple Set.einfsep_triple
 
-theorem le_einfsep_pi_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEmetricSpace (π b)]
+theorem le_einfsep_pi_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMetricSpace (π b)]
     {s : ∀ b : β, Set (π b)} {c : ℝ≥0∞} (h : ∀ b, c ≤ einfsep (s b)) :
     c ≤ einfsep (Set.pi univ s) :=
   by
@@ -268,7 +268,7 @@ theorem le_einfsep_pi_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEmet
   exact le_trans (le_einfsep_iff.1 (h i) _ (hx _) _ (hy _) hi) (edist_le_pi_edist _ _ i)
 #align set.le_einfsep_pi_of_le Set.le_einfsep_pi_of_le
 
-end PseudoEmetricSpace
+end PseudoEMetricSpace
 
 section PseudoMetricSpace
 
@@ -314,9 +314,9 @@ theorem le_einfsep_of_forall_dist_le {d}
 
 end PseudoMetricSpace
 
-section EmetricSpace
+section EMetricSpace
 
-variable [EmetricSpace α] {x y z : α} {s t : Set α} {C : ℝ≥0∞} {sC : Set ℝ≥0∞}
+variable [EMetricSpace α] {x y z : α} {s t : Set α} {C : ℝ≥0∞} {sC : Set ℝ≥0∞}
 
 theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
   by
@@ -348,7 +348,7 @@ theorem Finite.relatively_discrete (hs : s.Finite) :
   relatively_discrete_of_finite
 #align set.finite.relatively_discrete Set.Finite.relatively_discrete
 
-end EmetricSpace
+end EMetricSpace
 
 end Einfsep
 
@@ -359,13 +359,13 @@ open ENNReal
 open Set Function
 
 /-- The "infimum separation" of a set with an edist function. -/
-noncomputable def infsep [HasEdist α] (s : Set α) : ℝ :=
+noncomputable def infsep [EDist α] (s : Set α) : ℝ :=
   ENNReal.toReal s.einfsep
 #align set.infsep Set.infsep
 
-section HasEdist
+section EDist
 
-variable [HasEdist α] {x y : α} {s : Set α}
+variable [EDist α] {x y : α} {s : Set α}
 
 theorem infsep_zero : s.infsep = 0 ↔ s.einfsep = 0 ∨ s.einfsep = ∞ := by
   rw [infsep, ENNReal.toReal_eq_zero_iff]
@@ -406,11 +406,11 @@ theorem infsep_pair_le_toReal_inf (hxy : x ≠ y) :
   simp_rw [infsep, einfsep_pair_eq_inf hxy]
 #align set.infsep_pair_le_to_real_inf Set.infsep_pair_le_toReal_inf
 
-end HasEdist
+end EDist
 
-section PseudoEmetricSpace
+section PseudoEMetricSpace
 
-variable [PseudoEmetricSpace α] {x y : α} {s : Set α}
+variable [PseudoEMetricSpace α] {x y : α} {s : Set α}
 
 theorem infsep_pair_eq_toReal : ({x, y} : Set α).infsep = (edist x y).toReal :=
   by
@@ -420,7 +420,7 @@ theorem infsep_pair_eq_toReal : ({x, y} : Set α).infsep = (edist x y).toReal :=
   · rw [infsep, einfsep_pair hxy]
 #align set.infsep_pair_eq_to_real Set.infsep_pair_eq_toReal
 
-end PseudoEmetricSpace
+end PseudoEMetricSpace
 
 section PseudoMetricSpace

5316314b

bump to nightly-2023-03-01-20

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

20cadee0

Diff

@@ -50,20 +50,20 @@ section HasEdist
 
 variable [HasEdist α] {x y : α} {s t : Set α}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_iff {d} :
     d ≤ s.einfsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y := by
   simp_rw [einfsep, le_infᵢ_iff]
 #align set.le_einfsep_iff Set.le_einfsep_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_zero :
     s.einfsep = 0 ↔
       ∀ (C) (hC : 0 < C), ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), edist x y < C :=
   by simp_rw [einfsep, ← bot_eq_zero, infᵢ_eq_bot, infᵢ_lt_iff]
 #align set.einfsep_zero Set.einfsep_zero
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_pos :
     0 < s.einfsep ↔
       ∃ (C : _)(hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
@@ -72,25 +72,25 @@ theorem einfsep_pos :
   simp only [not_forall, not_exists, not_lt]
 #align set.einfsep_pos Set.einfsep_pos
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_top :
     s.einfsep = ∞ ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), edist x y = ∞ := by
   simp_rw [einfsep, infᵢ_eq_top]
 #align set.einfsep_top Set.einfsep_top
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_lt_top :
     s.einfsep < ∞ ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), edist x y < ∞ := by
   simp_rw [einfsep, infᵢ_lt_iff]
 #align set.einfsep_lt_top Set.einfsep_lt_top
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_ne_top :
     s.einfsep ≠ ∞ ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), edist x y ≠ ∞ := by
   simp_rw [← lt_top_iff_ne_top, einfsep_lt_top]
 #align set.einfsep_ne_top Set.einfsep_ne_top
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem einfsep_lt_iff {d} :
     s.einfsep < d ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(h : x ≠ y), edist x y < d := by
   simp_rw [einfsep, infᵢ_lt_iff]
@@ -112,7 +112,7 @@ theorem Subsingleton.einfsep (hs : s.Subsingleton) : s.einfsep = ∞ :=
   exact fun _ hx _ hy hxy => (hxy <| hs hx hy).elim
 #align set.subsingleton.einfsep Set.Subsingleton.einfsep
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_image_iff {d} {f : β → α} {s : Set β} :
     d ≤ einfsep (f '' s) ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s), f x ≠ f y → d ≤ edist (f x) (f y) :=
   by simp_rw [le_einfsep_iff, ball_image_iff]
@@ -133,7 +133,7 @@ theorem einfsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (h
   le_trans (einfsep_le_edist_of_mem hx hy hxy) hxy'
 #align set.einfsep_le_of_mem_of_edist_le Set.einfsep_le_of_mem_of_edist_le
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep {d} (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ edist x y) :
     d ≤ s.einfsep :=
   le_einfsep_iff.2 h
@@ -208,7 +208,7 @@ theorem Finset.coe_einfsep [DecidableEq α] {s : Finset α} :
   simp_rw [einfsep_of_fintype, ← Finset.coe_offDiag, Finset.toFinset_coe]
 #align set.finset.coe_einfsep Set.Finset.coe_einfsep
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), s.einfsep = edist x y := by
   classical
@@ -220,7 +220,7 @@ theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     refine' ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.einfsep_exists_of_finite Set.Nontrivial.einfsep_exists_of_finite
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Finite.einfsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
     ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), s.einfsep = edist x y :=
   letI := hsf.fintype
@@ -305,7 +305,7 @@ theorem einfsep_ne_top_iff : s.einfsep ≠ ∞ ↔ s.Nontrivial :=
   ⟨nontrivial_of_einfsep_ne_top, Nontrivial.einfsep_ne_top⟩
 #align set.einfsep_ne_top_iff Set.einfsep_ne_top_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_of_forall_dist_le {d}
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) :
     ENNReal.ofReal d ≤ s.einfsep :=
@@ -328,7 +328,7 @@ theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep :=
     exact hs.einfsep.symm ▸ WithTop.zero_lt_top
 #align set.einfsep_pos_of_finite Set.einfsep_pos_of_finite
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem relatively_discrete_of_finite [Finite s] :
     ∃ (C : _)(hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
   by
@@ -341,7 +341,7 @@ theorem Finite.einfsep_pos (hs : s.Finite) : 0 < s.einfsep :=
   einfsep_pos_of_finite
 #align set.finite.einfsep_pos Set.Finite.einfsep_pos
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Finite.relatively_discrete (hs : s.Finite) :
     ∃ (C : _)(hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), C ≤ edist x y :=
   letI := hs.fintype
@@ -426,14 +426,14 @@ section PseudoMetricSpace
 
 variable [PseudoMetricSpace α] {x y z : α} {s t : Set α}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
     d ≤ s.infsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y := by
   simp_rw [infsep, ← ENNReal.ofReal_le_iff_le_toReal hs.einfsep_ne_top, le_einfsep_iff, edist_dist,
     ENNReal.ofReal_le_ofReal_iff dist_nonneg]
 #align set.nontrivial.le_infsep_iff Set.Nontrivial.le_infsep_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
     s.infsep < d ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), dist x y < d :=
   by
@@ -442,7 +442,7 @@ theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
   exact hs.le_infsep_iff
 #align set.nontrivial.infsep_lt_iff Set.Nontrivial.infsep_lt_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.le_infsep {d} (hs : s.Nontrivial)
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) : d ≤ s.infsep :=
   hs.le_infsep_iff.2 h
@@ -560,7 +560,7 @@ theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs
   rw [Finset.coe_infsep, dif_neg hs]
 #align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_empty
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), s.infsep = dist x y := by
   classical
@@ -572,7 +572,7 @@ theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     exact ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.infsep_exists_of_finite Set.Nontrivial.infsep_exists_of_finite
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Finite.infsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
     ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(hxy : x ≠ y), s.infsep = dist x y :=
   letI := hsf.fintype

5316314b

bump to nightly-2023-02-27-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

49ff026a

Diff

@@ -37,7 +37,7 @@ namespace Set
 
 section Einfsep
 
-open Ennreal
+open ENNReal
 
 open Function
 
@@ -308,8 +308,8 @@ theorem einfsep_ne_top_iff : s.einfsep ≠ ∞ ↔ s.Nontrivial :=
 /- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem le_einfsep_of_forall_dist_le {d}
     (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y) :
-    Ennreal.ofReal d ≤ s.einfsep :=
-  le_einfsep fun x hx y hy hxy => (edist_dist x y).symm ▸ Ennreal.ofReal_le_ofReal (h x hx y hy hxy)
+    ENNReal.ofReal d ≤ s.einfsep :=
+  le_einfsep fun x hx y hy hxy => (edist_dist x y).symm ▸ ENNReal.ofReal_le_ofReal (h x hx y hy hxy)
 #align set.le_einfsep_of_forall_dist_le Set.le_einfsep_of_forall_dist_le
 
 end PseudoMetricSpace
@@ -354,13 +354,13 @@ end Einfsep
 
 section Infsep
 
-open Ennreal
+open ENNReal
 
 open Set Function
 
 /-- The "infimum separation" of a set with an edist function. -/
 noncomputable def infsep [HasEdist α] (s : Set α) : ℝ :=
-  Ennreal.toReal s.einfsep
+  ENNReal.toReal s.einfsep
 #align set.infsep Set.infsep
 
 section HasEdist
@@ -368,15 +368,15 @@ section HasEdist
 variable [HasEdist α] {x y : α} {s : Set α}
 
 theorem infsep_zero : s.infsep = 0 ↔ s.einfsep = 0 ∨ s.einfsep = ∞ := by
-  rw [infsep, Ennreal.toReal_eq_zero_iff]
+  rw [infsep, ENNReal.toReal_eq_zero_iff]
 #align set.infsep_zero Set.infsep_zero
 
 theorem infsep_nonneg : 0 ≤ s.infsep :=
-  Ennreal.toReal_nonneg
+  ENNReal.toReal_nonneg
 #align set.infsep_nonneg Set.infsep_nonneg
 
 theorem infsep_pos : 0 < s.infsep ↔ 0 < s.einfsep ∧ s.einfsep < ∞ := by
-  simp_rw [infsep, Ennreal.toReal_pos_iff]
+  simp_rw [infsep, ENNReal.toReal_pos_iff]
 #align set.infsep_pos Set.infsep_pos
 
 theorem Subsingleton.infsep_zero (hs : s.Subsingleton) : s.infsep = 0 :=
@@ -416,7 +416,7 @@ theorem infsep_pair_eq_toReal : ({x, y} : Set α).infsep = (edist x y).toReal :=
   by
   by_cases hxy : x = y
   · rw [hxy]
-    simp only [infsep_singleton, pair_eq_singleton, edist_self, Ennreal.zero_toReal]
+    simp only [infsep_singleton, pair_eq_singleton, edist_self, ENNReal.zero_toReal]
   · rw [infsep, einfsep_pair hxy]
 #align set.infsep_pair_eq_to_real Set.infsep_pair_eq_toReal
 
@@ -429,8 +429,8 @@ variable [PseudoMetricSpace α] {x y z : α} {s t : Set α}
 /- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
 theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
     d ≤ s.infsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (hxy : x ≠ y), d ≤ dist x y := by
-  simp_rw [infsep, ← Ennreal.ofReal_le_iff_le_toReal hs.einfsep_ne_top, le_einfsep_iff, edist_dist,
-    Ennreal.ofReal_le_ofReal_iff dist_nonneg]
+  simp_rw [infsep, ← ENNReal.ofReal_le_iff_le_toReal hs.einfsep_ne_top, le_einfsep_iff, edist_dist,
+    ENNReal.ofReal_le_ofReal_iff dist_nonneg]
 #align set.nontrivial.le_infsep_iff Set.Nontrivial.le_infsep_iff
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » s) -/
@@ -470,18 +470,18 @@ theorem infsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hx
 theorem infsep_pair : ({x, y} : Set α).infsep = dist x y :=
   by
   rw [infsep_pair_eq_to_real, edist_dist]
-  exact Ennreal.toReal_ofReal dist_nonneg
+  exact ENNReal.toReal_ofReal dist_nonneg
 #align set.infsep_pair Set.infsep_pair
 
 theorem infsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
     ({x, y, z} : Set α).infsep = dist x y ⊓ dist x z ⊓ dist y z := by
-  simp only [infsep, einfsep_triple hxy hyz hxz, Ennreal.toReal_inf, edist_ne_top x y,
+  simp only [infsep, einfsep_triple hxy hyz hxz, ENNReal.toReal_inf, edist_ne_top x y,
     edist_ne_top x z, edist_ne_top y z, dist_edist, Ne.def, inf_eq_top_iff, and_self_iff,
     not_false_iff]
 #align set.infsep_triple Set.infsep_triple
 
 theorem Nontrivial.infsep_anti (hs : s.Nontrivial) (hst : s ⊆ t) : t.infsep ≤ s.infsep :=
-  Ennreal.toReal_mono hs.einfsep_ne_top (einfsep_anti hst)
+  ENNReal.toReal_mono hs.einfsep_ne_top (einfsep_anti hst)
 #align set.nontrivial.infsep_anti Set.Nontrivial.infsep_anti
 
 theorem infsep_eq_infᵢ [Decidable s.Nontrivial] :

5316314b

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

5316314b

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11813)

08686b25

Diff

@@ -57,7 +57,7 @@ theorem einfsep_zero : s.einfsep = 0 ↔ ∀ C > 0, ∃ x ∈ s, ∃ y ∈ s, x
 #align set.einfsep_zero Set.einfsep_zero
 
 theorem einfsep_pos : 0 < s.einfsep ↔ ∃ C > 0, ∀ x ∈ s, ∀ y ∈ s, x ≠ y → C ≤ edist x y := by
-  rw [pos_iff_ne_zero, Ne.def, einfsep_zero]
+  rw [pos_iff_ne_zero, Ne, einfsep_zero]
   simp only [not_forall, not_exists, not_lt, exists_prop, not_and]
 #align set.einfsep_pos Set.einfsep_pos
 
@@ -428,7 +428,7 @@ theorem infsep_pair : ({x, y} : Set α).infsep = dist x y := by
 theorem infsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
     ({x, y, z} : Set α).infsep = dist x y ⊓ dist x z ⊓ dist y z := by
   simp only [infsep, einfsep_triple hxy hyz hxz, ENNReal.toReal_inf, edist_ne_top x y,
-    edist_ne_top x z, edist_ne_top y z, dist_edist, Ne.def, inf_eq_top_iff, and_self_iff,
+    edist_ne_top x z, edist_ne_top y z, dist_edist, Ne, inf_eq_top_iff, and_self_iff,
     not_false_iff]
 #align set.infsep_triple Set.infsep_triple

5316314b

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

@@ -97,7 +97,7 @@ theorem Subsingleton.einfsep (hs : s.Subsingleton) : s.einfsep = ∞ := by
 
 theorem le_einfsep_image_iff {d} {f : β → α} {s : Set β} : d ≤ einfsep (f '' s)
     ↔ ∀ x ∈ s, ∀ y ∈ s, f x ≠ f y → d ≤ edist (f x) (f y) := by
-  simp_rw [le_einfsep_iff, ball_image_iff]
+  simp_rw [le_einfsep_iff, forall_mem_image]
 #align set.le_einfsep_image_iff Set.le_einfsep_image_iff
 
 theorem le_edist_of_le_einfsep {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y)

5316314b

chore: remove terminal, terminal refines (#10762)

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

ea36aa7d

Diff

@@ -139,7 +139,7 @@ theorem einfsep_anti (hst : s ⊆ t) : t.einfsep ≤ s.einfsep :=
 
 theorem einfsep_insert_le : (insert x s).einfsep ≤ ⨅ (y ∈ s) (_ : x ≠ y), edist x y := by
   simp_rw [le_iInf_iff]
-  refine' fun _ hy hxy => einfsep_le_edist_of_mem (mem_insert _ _) (mem_insert_of_mem _ hy) hxy
+  exact fun _ hy hxy => einfsep_le_edist_of_mem (mem_insert _ _) (mem_insert_of_mem _ hy) hxy
 #align set.einfsep_insert_le Set.einfsep_insert_le
 
 theorem le_einfsep_pair : edist x y ⊓ edist y x ≤ ({x, y} : Set α).einfsep := by
@@ -191,7 +191,7 @@ theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     simp_rw [einfsep_of_fintype]
     rcases Finset.exists_mem_eq_inf s.offDiag.toFinset (by simpa) (uncurry edist) with ⟨w, hxy, hed⟩
     simp_rw [mem_toFinset] at hxy
-    refine' ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
+    exact ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.einfsep_exists_of_finite Set.Nontrivial.einfsep_exists_of_finite
 
 theorem Finite.einfsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :

5316314b

chore: tidy various files (#8880)

d510164f

Diff

@@ -48,40 +48,37 @@ section EDist
 variable [EDist α] {x y : α} {s t : Set α}
 
 theorem le_einfsep_iff {d} :
-    d ≤ s.einfsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), d ≤ edist x y := by
+    d ≤ s.einfsep ↔ ∀ x ∈ s, ∀ y ∈ s, x ≠ y → d ≤ edist x y := by
   simp_rw [einfsep, le_iInf_iff]
 #align set.le_einfsep_iff Set.le_einfsep_iff
 
-theorem einfsep_zero : s.einfsep = 0 ↔ ∀ (C) (_hC : 0 < C),
-    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), edist x y < C := by
-  simp_rw [einfsep, ← _root_.bot_eq_zero, iInf_eq_bot, iInf_lt_iff]
+theorem einfsep_zero : s.einfsep = 0 ↔ ∀ C > 0, ∃ x ∈ s, ∃ y ∈ s, x ≠ y ∧ edist x y < C := by
+  simp_rw [einfsep, ← _root_.bot_eq_zero, iInf_eq_bot, iInf_lt_iff, exists_prop]
 #align set.einfsep_zero Set.einfsep_zero
 
-theorem einfsep_pos :
-    0 < s.einfsep ↔
-      ∃ (C : _) (_hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), C ≤ edist x y := by
+theorem einfsep_pos : 0 < s.einfsep ↔ ∃ C > 0, ∀ x ∈ s, ∀ y ∈ s, x ≠ y → C ≤ edist x y := by
   rw [pos_iff_ne_zero, Ne.def, einfsep_zero]
-  simp only [not_forall, not_exists, not_lt]
+  simp only [not_forall, not_exists, not_lt, exists_prop, not_and]
 #align set.einfsep_pos Set.einfsep_pos
 
 theorem einfsep_top :
-    s.einfsep = ∞ ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), edist x y = ∞ := by
+    s.einfsep = ∞ ↔ ∀ x ∈ s, ∀ y ∈ s, x ≠ y → edist x y = ∞ := by
   simp_rw [einfsep, iInf_eq_top]
 #align set.einfsep_top Set.einfsep_top
 
 theorem einfsep_lt_top :
-    s.einfsep < ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), edist x y < ∞ := by
-  simp_rw [einfsep, iInf_lt_iff]
+    s.einfsep < ∞ ↔ ∃ x ∈ s, ∃ y ∈ s, x ≠ y ∧ edist x y < ∞ := by
+  simp_rw [einfsep, iInf_lt_iff, exists_prop]
 #align set.einfsep_lt_top Set.einfsep_lt_top
 
 theorem einfsep_ne_top :
-    s.einfsep ≠ ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), edist x y ≠ ∞ := by
+    s.einfsep ≠ ∞ ↔ ∃ x ∈ s, ∃ y ∈ s, x ≠ y ∧ edist x y ≠ ∞ := by
   simp_rw [← lt_top_iff_ne_top, einfsep_lt_top]
 #align set.einfsep_ne_top Set.einfsep_ne_top
 
 theorem einfsep_lt_iff {d} :
-    s.einfsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_h : x ≠ y), edist x y < d := by
-  simp_rw [einfsep, iInf_lt_iff]
+    s.einfsep < d ↔ ∃ x ∈ s, ∃ y ∈ s, x ≠ y ∧ edist x y < d := by
+  simp_rw [einfsep, iInf_lt_iff, exists_prop]
 #align set.einfsep_lt_iff Set.einfsep_lt_iff
 
 theorem nontrivial_of_einfsep_lt_top (hs : s.einfsep < ∞) : s.Nontrivial := by
@@ -118,8 +115,7 @@ theorem einfsep_le_of_mem_of_edist_le {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (h
   le_trans (einfsep_le_edist_of_mem hx hy hxy) hxy'
 #align set.einfsep_le_of_mem_of_edist_le Set.einfsep_le_of_mem_of_edist_le
 
-theorem le_einfsep {d} (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), d ≤ edist x y) :
-    d ≤ s.einfsep :=
+theorem le_einfsep {d} (h : ∀ x ∈ s, ∀ y ∈ s, x ≠ y → d ≤ edist x y) : d ≤ s.einfsep :=
   le_einfsep_iff.2 h
 #align set.le_einfsep Set.le_einfsep
 
@@ -189,18 +185,17 @@ theorem Finset.coe_einfsep [DecidableEq α] {s : Finset α} :
 #align set.finset.coe_einfsep Set.Finset.coe_einfsep
 
 theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
-    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), s.einfsep = edist x y := by
+    ∃ x ∈ s, ∃ y ∈ s, x ≠ y ∧ s.einfsep = edist x y := by
   classical
     cases nonempty_fintype s
     simp_rw [einfsep_of_fintype]
-    rcases@Finset.exists_mem_eq_inf _ _ _ _ s.offDiag.toFinset (by simpa) (uncurry edist) with
-      ⟨w, hxy, hed⟩
+    rcases Finset.exists_mem_eq_inf s.offDiag.toFinset (by simpa) (uncurry edist) with ⟨w, hxy, hed⟩
     simp_rw [mem_toFinset] at hxy
     refine' ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.einfsep_exists_of_finite Set.Nontrivial.einfsep_exists_of_finite
 
 theorem Finite.einfsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
-    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), s.einfsep = edist x y :=
+    ∃ x ∈ s, ∃ y ∈ s, x ≠ y ∧ s.einfsep = edist x y :=
   letI := hsf.fintype
   hs.einfsep_exists_of_finite
 #align set.finite.einfsep_exists_of_nontrivial Set.Finite.einfsep_exists_of_nontrivial
@@ -278,8 +273,7 @@ theorem einfsep_ne_top_iff : s.einfsep ≠ ∞ ↔ s.Nontrivial :=
   ⟨nontrivial_of_einfsep_ne_top, Nontrivial.einfsep_ne_top⟩
 #align set.einfsep_ne_top_iff Set.einfsep_ne_top_iff
 
-theorem le_einfsep_of_forall_dist_le {d}
-    (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), d ≤ dist x y) :
+theorem le_einfsep_of_forall_dist_le {d} (h : ∀ x ∈ s, ∀ y ∈ s, x ≠ y → d ≤ dist x y) :
     ENNReal.ofReal d ≤ s.einfsep :=
   le_einfsep fun x hx y hy hxy => (edist_dist x y).symm ▸ ENNReal.ofReal_le_ofReal (h x hx y hy hxy)
 #align set.le_einfsep_of_forall_dist_le Set.le_einfsep_of_forall_dist_le
@@ -300,7 +294,7 @@ theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep := by
 #align set.einfsep_pos_of_finite Set.einfsep_pos_of_finite
 
 theorem relatively_discrete_of_finite [Finite s] :
-    ∃ (C : _) (_hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), C ≤ edist x y := by
+    ∃ C > 0, ∀ x ∈ s, ∀ y ∈ s, x ≠ y → C ≤ edist x y := by
   rw [← einfsep_pos]
   exact einfsep_pos_of_finite
 #align set.relatively_discrete_of_finite Set.relatively_discrete_of_finite
@@ -311,7 +305,7 @@ theorem Finite.einfsep_pos (hs : s.Finite) : 0 < s.einfsep :=
 #align set.finite.einfsep_pos Set.Finite.einfsep_pos
 
 theorem Finite.relatively_discrete (hs : s.Finite) :
-    ∃ (C : _) (_hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), C ≤ edist x y :=
+    ∃ C > 0, ∀ x ∈ s, ∀ y ∈ s, x ≠ y → C ≤ edist x y :=
   letI := hs.fintype
   relatively_discrete_of_finite
 #align set.finite.relatively_discrete Set.Finite.relatively_discrete
@@ -347,10 +341,8 @@ theorem infsep_pos : 0 < s.infsep ↔ 0 < s.einfsep ∧ s.einfsep < ∞ := by
   simp_rw [infsep, ENNReal.toReal_pos_iff]
 #align set.infsep_pos Set.infsep_pos
 
-theorem Subsingleton.infsep_zero (hs : s.Subsingleton) : s.infsep = 0 := by
-  rw [infsep_zero.mpr]
-  right
-  exact hs.einfsep
+theorem Subsingleton.infsep_zero (hs : s.Subsingleton) : s.infsep = 0 :=
+  Set.infsep_zero.mpr <| Or.inr hs.einfsep
 #align set.subsingleton.infsep_zero Set.Subsingleton.infsep_zero
 
 theorem nontrivial_of_infsep_pos (hs : 0 < s.infsep) : s.Nontrivial := by
@@ -393,20 +385,20 @@ section PseudoMetricSpace
 variable [PseudoMetricSpace α] {x y z : α} {s t : Set α}
 
 theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
-    d ≤ s.infsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), d ≤ dist x y := by
+    d ≤ s.infsep ↔ ∀ x ∈ s, ∀ y ∈ s, x ≠ y → d ≤ dist x y := by
   simp_rw [infsep, ← ENNReal.ofReal_le_iff_le_toReal hs.einfsep_ne_top, le_einfsep_iff, edist_dist,
     ENNReal.ofReal_le_ofReal_iff dist_nonneg]
 #align set.nontrivial.le_infsep_iff Set.Nontrivial.le_infsep_iff
 
 theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
-    s.infsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), dist x y < d := by
+    s.infsep < d ↔ ∃ x ∈ s, ∃ y ∈ s, x ≠ y ∧ dist x y < d := by
   rw [← not_iff_not]
   push_neg
   exact hs.le_infsep_iff
 #align set.nontrivial.infsep_lt_iff Set.Nontrivial.infsep_lt_iff
 
 theorem Nontrivial.le_infsep {d} (hs : s.Nontrivial)
-    (h : ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), d ≤ dist x y) : d ≤ s.infsep :=
+    (h : ∀ x ∈ s, ∀ y ∈ s, x ≠ y → d ≤ dist x y) : d ≤ s.infsep :=
   hs.le_infsep_iff.2 h
 #align set.nontrivial.le_infsep Set.Nontrivial.le_infsep
 
@@ -515,18 +507,18 @@ theorem _root_.Finset.coe_infsep_of_offDiag_empty
 #align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_empty
 
 theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
-    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), s.infsep = dist x y := by
+    ∃ x ∈ s, ∃ y ∈ s, x ≠ y ∧ s.infsep = dist x y := by
   classical
     cases nonempty_fintype s
     simp_rw [hs.infsep_of_fintype]
-    rcases@Finset.exists_mem_eq_inf' _ _ _ s.offDiag.toFinset (by simpa) (uncurry dist) with
+    rcases Finset.exists_mem_eq_inf' (s := s.offDiag.toFinset) (by simpa) (uncurry dist) with
       ⟨w, hxy, hed⟩
     simp_rw [mem_toFinset] at hxy
     exact ⟨w.fst, hxy.1, w.snd, hxy.2.1, hxy.2.2, hed⟩
 #align set.nontrivial.infsep_exists_of_finite Set.Nontrivial.infsep_exists_of_finite
 
 theorem Finite.infsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
-    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), s.infsep = dist x y :=
+    ∃ x ∈ s, ∃ y ∈ s, x ≠ y ∧ s.infsep = dist x y :=
   letI := hsf.fintype
   hs.infsep_exists_of_finite
 #align set.finite.infsep_exists_of_nontrivial Set.Finite.infsep_exists_of_nontrivial

5316314b

chore: tidy various files (#8818)

397ec08b

Diff

@@ -99,7 +99,7 @@ theorem Subsingleton.einfsep (hs : s.Subsingleton) : s.einfsep = ∞ := by
 #align set.subsingleton.einfsep Set.Subsingleton.einfsep
 
 theorem le_einfsep_image_iff {d} {f : β → α} {s : Set β} : d ≤ einfsep (f '' s)
-    ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s), f x ≠ f y → d ≤ edist (f x) (f y) := by
+    ↔ ∀ x ∈ s, ∀ y ∈ s, f x ≠ f y → d ≤ edist (f x) (f y) := by
   simp_rw [le_einfsep_iff, ball_image_iff]
 #align set.le_einfsep_image_iff Set.le_einfsep_image_iff

5316314b

style: cleanup by putting by on the same line as := (#8407)

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

5e9b46ed

Diff

@@ -52,9 +52,9 @@ theorem le_einfsep_iff {d} :
   simp_rw [einfsep, le_iInf_iff]
 #align set.le_einfsep_iff Set.le_einfsep_iff
 
-theorem einfsep_zero : s.einfsep = 0 ↔
-    ∀ (C) (_hC : 0 < C), ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), edist x y < C :=
-  by simp_rw [einfsep, ← _root_.bot_eq_zero, iInf_eq_bot, iInf_lt_iff]
+theorem einfsep_zero : s.einfsep = 0 ↔ ∀ (C) (_hC : 0 < C),
+    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), edist x y < C := by
+  simp_rw [einfsep, ← _root_.bot_eq_zero, iInf_eq_bot, iInf_lt_iff]
 #align set.einfsep_zero Set.einfsep_zero
 
 theorem einfsep_pos :
@@ -98,9 +98,9 @@ theorem Subsingleton.einfsep (hs : s.Subsingleton) : s.einfsep = ∞ := by
   exact fun _ hx _ hy hxy => (hxy <| hs hx hy).elim
 #align set.subsingleton.einfsep Set.Subsingleton.einfsep
 
-theorem le_einfsep_image_iff {d} {f : β → α} {s : Set β} :
-    d ≤ einfsep (f '' s) ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s), f x ≠ f y → d ≤ edist (f x) (f y) :=
-  by simp_rw [le_einfsep_iff, ball_image_iff]
+theorem le_einfsep_image_iff {d} {f : β → α} {s : Set β} : d ≤ einfsep (f '' s)
+    ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s), f x ≠ f y → d ≤ edist (f x) (f y) := by
+  simp_rw [le_einfsep_iff, ball_image_iff]
 #align set.le_einfsep_image_iff Set.le_einfsep_image_iff
 
 theorem le_edist_of_le_einfsep {d x} (hx : x ∈ s) {y} (hy : y ∈ s) (hxy : x ≠ y)

5316314b

chore: bump to nightly-2023-08-17 (#6019)

The major change here is adapting to simp failing if it makes no progress. The vast majority of the redundant simps found due to this change were extracted to #6632.

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

8c53b718

Diff

@@ -148,7 +148,8 @@ theorem einfsep_insert_le : (insert x s).einfsep ≤ ⨅ (y ∈ s) (_ : x ≠ y)
 
 theorem le_einfsep_pair : edist x y ⊓ edist y x ≤ ({x, y} : Set α).einfsep := by
   simp_rw [le_einfsep_iff, inf_le_iff, mem_insert_iff, mem_singleton_iff]
-  rintro a (rfl | rfl) b (rfl | rfl) hab <;> simp only [le_refl, true_or, or_true] <;> contradiction
+  rintro a (rfl | rfl) b (rfl | rfl) hab <;> (try simp only [le_refl, true_or, or_true]) <;>
+    contradiction
 #align set.le_einfsep_pair Set.le_einfsep_pair
 
 theorem einfsep_pair_le_left (hxy : x ≠ y) : ({x, y} : Set α).einfsep ≤ edist x y :=

5316314b

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

@@ -28,7 +28,7 @@ All lemmas and definitions are in the `Set` namespace to give access to dot nota
 !-/
 
 
-variable {α β : Type _}
+variable {α β : Type*}
 
 namespace Set
 
@@ -133,7 +133,7 @@ theorem einfsep_singleton : ({x} : Set α).einfsep = ∞ :=
   subsingleton_singleton.einfsep
 #align set.einfsep_singleton Set.einfsep_singleton
 
-theorem einfsep_iUnion_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
+theorem einfsep_iUnion_mem_option {ι : Type*} (o : Option ι) (s : ι → Set α) :
     (⋃ i ∈ o, s i).einfsep = ⨅ i ∈ o, (s i).einfsep := by cases o <;> simp
 #align set.einfsep_Union_mem_option Set.einfsep_iUnion_mem_option
 
@@ -234,7 +234,7 @@ theorem einfsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
     ciInf_pos hxy, ciInf_pos hyz, ciInf_pos hxz]
 #align set.einfsep_triple Set.einfsep_triple
 
-theorem le_einfsep_pi_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMetricSpace (π b)]
+theorem le_einfsep_pi_of_le {π : β → Type*} [Fintype β] [∀ b, PseudoEMetricSpace (π b)]
     {s : ∀ b : β, Set (π b)} {c : ℝ≥0∞} (h : ∀ b, c ≤ einfsep (s b)) :
     c ≤ einfsep (Set.pi univ s) := by
   refine' le_einfsep fun x hx y hy hxy => _

5316314b

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

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Wrenna Robson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Wrenna Robson
-
-! This file was ported from Lean 3 source module topology.metric_space.infsep
-! leanprover-community/mathlib commit 5316314b553dcf8c6716541851517c1a9715e22b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.MetricSpace.Basic
 
+#align_import topology.metric_space.infsep from "leanprover-community/mathlib"@"5316314b553dcf8c6716541851517c1a9715e22b"
+
 /-!
 # Infimum separation

5316314b

chore: remove occurrences of semicolon after space (#5713)

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

c795bd35

Diff

@@ -159,7 +159,7 @@ theorem einfsep_pair_le_left (hxy : x ≠ y) : ({x, y} : Set α).einfsep ≤ edi
 #align set.einfsep_pair_le_left Set.einfsep_pair_le_left
 
 theorem einfsep_pair_le_right (hxy : x ≠ y) : ({x, y} : Set α).einfsep ≤ edist y x := by
-  rw [pair_comm] ; exact einfsep_pair_le_left hxy.symm
+  rw [pair_comm]; exact einfsep_pair_le_left hxy.symm
 #align set.einfsep_pair_le_right Set.einfsep_pair_le_right
 
 theorem einfsep_pair_eq_inf (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist x y ⊓ edist y x :=

5316314b

chore: formatting issues (#4947)

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

5068808d

Diff

@@ -55,15 +55,14 @@ theorem le_einfsep_iff {d} :
   simp_rw [einfsep, le_iInf_iff]
 #align set.le_einfsep_iff Set.le_einfsep_iff
 
-theorem einfsep_zero :
-    s.einfsep = 0 ↔
-      ∀ (C) (_hC : 0 < C), ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(_hxy : x ≠ y), edist x y < C :=
+theorem einfsep_zero : s.einfsep = 0 ↔
+    ∀ (C) (_hC : 0 < C), ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), edist x y < C :=
   by simp_rw [einfsep, ← _root_.bot_eq_zero, iInf_eq_bot, iInf_lt_iff]
 #align set.einfsep_zero Set.einfsep_zero
 
 theorem einfsep_pos :
     0 < s.einfsep ↔
-      ∃ (C : _)(_hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), C ≤ edist x y := by
+      ∃ (C : _) (_hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), C ≤ edist x y := by
   rw [pos_iff_ne_zero, Ne.def, einfsep_zero]
   simp only [not_forall, not_exists, not_lt]
 #align set.einfsep_pos Set.einfsep_pos
@@ -74,17 +73,17 @@ theorem einfsep_top :
 #align set.einfsep_top Set.einfsep_top
 
 theorem einfsep_lt_top :
-    s.einfsep < ∞ ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(_hxy : x ≠ y), edist x y < ∞ := by
+    s.einfsep < ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), edist x y < ∞ := by
   simp_rw [einfsep, iInf_lt_iff]
 #align set.einfsep_lt_top Set.einfsep_lt_top
 
 theorem einfsep_ne_top :
-    s.einfsep ≠ ∞ ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(_hxy : x ≠ y), edist x y ≠ ∞ := by
+    s.einfsep ≠ ∞ ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), edist x y ≠ ∞ := by
   simp_rw [← lt_top_iff_ne_top, einfsep_lt_top]
 #align set.einfsep_ne_top Set.einfsep_ne_top
 
 theorem einfsep_lt_iff {d} :
-    s.einfsep < d ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(_h : x ≠ y), edist x y < d := by
+    s.einfsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_h : x ≠ y), edist x y < d := by
   simp_rw [einfsep, iInf_lt_iff]
 #align set.einfsep_lt_iff Set.einfsep_lt_iff
 
@@ -192,7 +191,7 @@ theorem Finset.coe_einfsep [DecidableEq α] {s : Finset α} :
 #align set.finset.coe_einfsep Set.Finset.coe_einfsep
 
 theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
-    ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(_hxy : x ≠ y), s.einfsep = edist x y := by
+    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), s.einfsep = edist x y := by
   classical
     cases nonempty_fintype s
     simp_rw [einfsep_of_fintype]
@@ -203,7 +202,7 @@ theorem Nontrivial.einfsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
 #align set.nontrivial.einfsep_exists_of_finite Set.Nontrivial.einfsep_exists_of_finite
 
 theorem Finite.einfsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
-    ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(_hxy : x ≠ y), s.einfsep = edist x y :=
+    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), s.einfsep = edist x y :=
   letI := hsf.fintype
   hs.einfsep_exists_of_finite
 #align set.finite.einfsep_exists_of_nontrivial Set.Finite.einfsep_exists_of_nontrivial
@@ -303,7 +302,7 @@ theorem einfsep_pos_of_finite [Finite s] : 0 < s.einfsep := by
 #align set.einfsep_pos_of_finite Set.einfsep_pos_of_finite
 
 theorem relatively_discrete_of_finite [Finite s] :
-    ∃ (C : _)(_hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), C ≤ edist x y := by
+    ∃ (C : _) (_hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), C ≤ edist x y := by
   rw [← einfsep_pos]
   exact einfsep_pos_of_finite
 #align set.relatively_discrete_of_finite Set.relatively_discrete_of_finite
@@ -314,7 +313,7 @@ theorem Finite.einfsep_pos (hs : s.Finite) : 0 < s.einfsep :=
 #align set.finite.einfsep_pos Set.Finite.einfsep_pos
 
 theorem Finite.relatively_discrete (hs : s.Finite) :
-    ∃ (C : _)(_hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), C ≤ edist x y :=
+    ∃ (C : _) (_hC : 0 < C), ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), C ≤ edist x y :=
   letI := hs.fintype
   relatively_discrete_of_finite
 #align set.finite.relatively_discrete Set.Finite.relatively_discrete
@@ -402,7 +401,7 @@ theorem Nontrivial.le_infsep_iff {d} (hs : s.Nontrivial) :
 #align set.nontrivial.le_infsep_iff Set.Nontrivial.le_infsep_iff
 
 theorem Nontrivial.infsep_lt_iff {d} (hs : s.Nontrivial) :
-    s.infsep < d ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(_hxy : x ≠ y), dist x y < d := by
+    s.infsep < d ↔ ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), dist x y < d := by
   rw [← not_iff_not]
   push_neg
   exact hs.le_infsep_iff
@@ -518,7 +517,7 @@ theorem _root_.Finset.coe_infsep_of_offDiag_empty
 #align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_empty
 
 theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
-    ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(_hxy : x ≠ y), s.infsep = dist x y := by
+    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), s.infsep = dist x y := by
   classical
     cases nonempty_fintype s
     simp_rw [hs.infsep_of_fintype]
@@ -529,7 +528,7 @@ theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
 #align set.nontrivial.infsep_exists_of_finite Set.Nontrivial.infsep_exists_of_finite
 
 theorem Finite.infsep_exists_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
-    ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(_hxy : x ≠ y), s.infsep = dist x y :=
+    ∃ (x : _) (_ : x ∈ s) (y : _) (_ : y ∈ s) (_hxy : x ≠ y), s.infsep = dist x y :=
   letI := hsf.fintype
   hs.infsep_exists_of_finite
 #align set.finite.infsep_exists_of_nontrivial Set.Finite.infsep_exists_of_nontrivial

5316314b

style: allow _ for an argument in notation3 & replace _foo with _ in notation3 (#4652)

e2b5ca37

Diff

@@ -43,7 +43,7 @@ open Function
 
 /-- The "extended infimum separation" of a set with an edist function. -/
 noncomputable def einfsep [EDist α] (s : Set α) : ℝ≥0∞ :=
-  ⨅ (x ∈ s) (y ∈ s) (_hxy : x ≠ y), edist x y
+  ⨅ (x ∈ s) (y ∈ s) (_ : x ≠ y), edist x y
 #align set.einfsep Set.einfsep
 
 section EDist
@@ -145,7 +145,7 @@ theorem einfsep_anti (hst : s ⊆ t) : t.einfsep ≤ s.einfsep :=
   le_einfsep fun _x hx _y hy => einfsep_le_edist_of_mem (hst hx) (hst hy)
 #align set.einfsep_anti Set.einfsep_anti
 
-theorem einfsep_insert_le : (insert x s).einfsep ≤ ⨅ (y ∈ s) (_hxy : x ≠ y), edist x y := by
+theorem einfsep_insert_le : (insert x s).einfsep ≤ ⨅ (y ∈ s) (_ : x ≠ y), edist x y := by
   simp_rw [le_iInf_iff]
   refine' fun _ hy hxy => einfsep_le_edist_of_mem (mem_insert _ _) (mem_insert_of_mem _ hy) hxy
 #align set.einfsep_insert_le Set.einfsep_insert_le
@@ -221,7 +221,7 @@ theorem einfsep_pair (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist x y :=
 #align set.einfsep_pair Set.einfsep_pair
 
 theorem einfsep_insert : einfsep (insert x s) =
-    (⨅ (y ∈ s) (_hxy : x ≠ y), edist x y) ⊓ s.einfsep := by
+    (⨅ (y ∈ s) (_ : x ≠ y), edist x y) ⊓ s.einfsep := by
   refine' le_antisymm (le_min einfsep_insert_le (einfsep_anti (subset_insert _ _))) _
   simp_rw [le_einfsep_iff, inf_le_iff, mem_insert_iff]
   rintro y (rfl | hy) z (rfl | hz) hyz

5316314b

chore: Rename to sSup/iSup (#3938)

As discussed on Zulip

Renames

supₛ → sSup
infₛ → sInf
supᵢ → iSup
infᵢ → iInf
bsupₛ → bsSup
binfₛ → bsInf
bsupᵢ → biSup
binfᵢ → biInf
csupₛ → csSup
cinfₛ → csInf
csupᵢ → ciSup
cinfᵢ → ciInf
unionₛ → sUnion
interₛ → sInter
unionᵢ → iUnion
interᵢ → iInter
bunionₛ → bsUnion
binterₛ → bsInter
bunionᵢ → biUnion
binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

d1eb6264

Diff

@@ -52,13 +52,13 @@ variable [EDist α] {x y : α} {s t : Set α}
 
 theorem le_einfsep_iff {d} :
     d ≤ s.einfsep ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), d ≤ edist x y := by
-  simp_rw [einfsep, le_infᵢ_iff]
+  simp_rw [einfsep, le_iInf_iff]
 #align set.le_einfsep_iff Set.le_einfsep_iff
 
 theorem einfsep_zero :
     s.einfsep = 0 ↔
       ∀ (C) (_hC : 0 < C), ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(_hxy : x ≠ y), edist x y < C :=
-  by simp_rw [einfsep, ← _root_.bot_eq_zero, infᵢ_eq_bot, infᵢ_lt_iff]
+  by simp_rw [einfsep, ← _root_.bot_eq_zero, iInf_eq_bot, iInf_lt_iff]
 #align set.einfsep_zero Set.einfsep_zero
 
 theorem einfsep_pos :
@@ -70,12 +70,12 @@ theorem einfsep_pos :
 
 theorem einfsep_top :
     s.einfsep = ∞ ↔ ∀ (x) (_ : x ∈ s) (y) (_ : y ∈ s) (_hxy : x ≠ y), edist x y = ∞ := by
-  simp_rw [einfsep, infᵢ_eq_top]
+  simp_rw [einfsep, iInf_eq_top]
 #align set.einfsep_top Set.einfsep_top
 
 theorem einfsep_lt_top :
     s.einfsep < ∞ ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(_hxy : x ≠ y), edist x y < ∞ := by
-  simp_rw [einfsep, infᵢ_lt_iff]
+  simp_rw [einfsep, iInf_lt_iff]
 #align set.einfsep_lt_top Set.einfsep_lt_top
 
 theorem einfsep_ne_top :
@@ -85,7 +85,7 @@ theorem einfsep_ne_top :
 
 theorem einfsep_lt_iff {d} :
     s.einfsep < d ↔ ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(_h : x ≠ y), edist x y < d := by
-  simp_rw [einfsep, infᵢ_lt_iff]
+  simp_rw [einfsep, iInf_lt_iff]
 #align set.einfsep_lt_iff Set.einfsep_lt_iff
 
 theorem nontrivial_of_einfsep_lt_top (hs : s.einfsep < ∞) : s.Nontrivial := by
@@ -137,16 +137,16 @@ theorem einfsep_singleton : ({x} : Set α).einfsep = ∞ :=
   subsingleton_singleton.einfsep
 #align set.einfsep_singleton Set.einfsep_singleton
 
-theorem einfsep_unionᵢ_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
+theorem einfsep_iUnion_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
     (⋃ i ∈ o, s i).einfsep = ⨅ i ∈ o, (s i).einfsep := by cases o <;> simp
-#align set.einfsep_Union_mem_option Set.einfsep_unionᵢ_mem_option
+#align set.einfsep_Union_mem_option Set.einfsep_iUnion_mem_option
 
 theorem einfsep_anti (hst : s ⊆ t) : t.einfsep ≤ s.einfsep :=
   le_einfsep fun _x hx _y hy => einfsep_le_edist_of_mem (hst hx) (hst hy)
 #align set.einfsep_anti Set.einfsep_anti
 
 theorem einfsep_insert_le : (insert x s).einfsep ≤ ⨅ (y ∈ s) (_hxy : x ≠ y), edist x y := by
-  simp_rw [le_infᵢ_iff]
+  simp_rw [le_iInf_iff]
   refine' fun _ hy hxy => einfsep_le_edist_of_mem (mem_insert _ _) (mem_insert_of_mem _ hy) hxy
 #align set.einfsep_insert_le Set.einfsep_insert_le
 
@@ -167,11 +167,11 @@ theorem einfsep_pair_eq_inf (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist
   le_antisymm (le_inf (einfsep_pair_le_left hxy) (einfsep_pair_le_right hxy)) le_einfsep_pair
 #align set.einfsep_pair_eq_inf Set.einfsep_pair_eq_inf
 
-theorem einfsep_eq_infᵢ : s.einfsep = ⨅ d : s.offDiag, (uncurry edist) (d : α × α) := by
+theorem einfsep_eq_iInf : s.einfsep = ⨅ d : s.offDiag, (uncurry edist) (d : α × α) := by
   refine' eq_of_forall_le_iff fun _ => _
-  simp_rw [le_einfsep_iff, le_infᵢ_iff, imp_forall_iff, SetCoe.forall, mem_offDiag,
+  simp_rw [le_einfsep_iff, le_iInf_iff, imp_forall_iff, SetCoe.forall, mem_offDiag,
     Prod.forall, uncurry_apply_pair, and_imp]
-#align set.einfsep_eq_infi Set.einfsep_eq_infᵢ
+#align set.einfsep_eq_infi Set.einfsep_eq_iInf
 
 theorem einfsep_of_fintype [DecidableEq α] [Fintype s] :
     s.einfsep = s.offDiag.toFinset.inf (uncurry edist) := by
@@ -226,16 +226,16 @@ theorem einfsep_insert : einfsep (insert x s) =
   simp_rw [le_einfsep_iff, inf_le_iff, mem_insert_iff]
   rintro y (rfl | hy) z (rfl | hz) hyz
   · exact False.elim (hyz rfl)
-  · exact Or.inl (infᵢ_le_of_le _ (infᵢ₂_le hz hyz))
+  · exact Or.inl (iInf_le_of_le _ (iInf₂_le hz hyz))
   · rw [edist_comm]
-    exact Or.inl (infᵢ_le_of_le _ (infᵢ₂_le hy hyz.symm))
+    exact Or.inl (iInf_le_of_le _ (iInf₂_le hy hyz.symm))
   · exact Or.inr (einfsep_le_edist_of_mem hy hz hyz)
 #align set.einfsep_insert Set.einfsep_insert
 
 theorem einfsep_triple (hxy : x ≠ y) (hyz : y ≠ z) (hxz : x ≠ z) :
     einfsep ({x, y, z} : Set α) = edist x y ⊓ edist x z ⊓ edist y z := by
-  simp_rw [einfsep_insert, infᵢ_insert, infᵢ_singleton, einfsep_singleton, inf_top_eq,
-    cinfᵢ_pos hxy, cinfᵢ_pos hyz, cinfᵢ_pos hxz]
+  simp_rw [einfsep_insert, iInf_insert, iInf_singleton, einfsep_singleton, inf_top_eq,
+    ciInf_pos hxy, ciInf_pos hyz, ciInf_pos hxz]
 #align set.einfsep_triple Set.einfsep_triple
 
 theorem le_einfsep_pi_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMetricSpace (π b)]
@@ -447,7 +447,7 @@ theorem Nontrivial.infsep_anti (hs : s.Nontrivial) (hst : s ⊆ t) : t.infsep 
   ENNReal.toReal_mono hs.einfsep_ne_top (einfsep_anti hst)
 #align set.nontrivial.infsep_anti Set.Nontrivial.infsep_anti
 
-theorem infsep_eq_infᵢ [Decidable s.Nontrivial] :
+theorem infsep_eq_iInf [Decidable s.Nontrivial] :
     s.infsep = if s.Nontrivial then ⨅ d : s.offDiag, (uncurry dist) (d : α × α) else 0 := by
   split_ifs with hs
   · have hb : BddBelow (uncurry dist '' s.offDiag) := by
@@ -456,15 +456,15 @@ theorem infsep_eq_infᵢ [Decidable s.Nontrivial] :
       rcases h with ⟨_, _, _, rfl⟩
       exact dist_nonneg
     refine' eq_of_forall_le_iff fun _ => _
-    simp_rw [hs.le_infsep_iff, le_cinfᵢ_set_iff (offDiag_nonempty.mpr hs) hb, imp_forall_iff,
+    simp_rw [hs.le_infsep_iff, le_ciInf_set_iff (offDiag_nonempty.mpr hs) hb, imp_forall_iff,
       mem_offDiag, Prod.forall, uncurry_apply_pair, and_imp]
   · exact (not_nontrivial_iff.mp hs).infsep_zero
-#align set.infsep_eq_infi Set.infsep_eq_infᵢ
+#align set.infsep_eq_infi Set.infsep_eq_iInf
 
-theorem Nontrivial.infsep_eq_infᵢ (hs : s.Nontrivial) :
+theorem Nontrivial.infsep_eq_iInf (hs : s.Nontrivial) :
     s.infsep = ⨅ d : s.offDiag, (uncurry dist) (d : α × α) := by
-  classical rw [Set.infsep_eq_infᵢ, if_pos hs]
-#align set.nontrivial.infsep_eq_infi Set.Nontrivial.infsep_eq_infᵢ
+  classical rw [Set.infsep_eq_iInf, if_pos hs]
+#align set.nontrivial.infsep_eq_infi Set.Nontrivial.infsep_eq_iInf
 
 theorem infsep_of_fintype [Decidable s.Nontrivial] [DecidableEq α] [Fintype s] : s.infsep =
     if hs : s.Nontrivial then s.offDiag.toFinset.inf' (by simpa) (uncurry dist) else 0 := by

5316314b

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -220,8 +220,8 @@ theorem einfsep_pair (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist x y :=
   rw [edist_comm]
 #align set.einfsep_pair Set.einfsep_pair
 
-theorem einfsep_insert : einfsep (insert x s) = (⨅ (y ∈ s) (_hxy : x ≠ y), edist x y) ⊓ s.einfsep :=
-  by
+theorem einfsep_insert : einfsep (insert x s) =
+    (⨅ (y ∈ s) (_hxy : x ≠ y), edist x y) ⊓ s.einfsep := by
   refine' le_antisymm (le_min einfsep_insert_le (einfsep_anti (subset_insert _ _))) _
   simp_rw [le_einfsep_iff, inf_le_iff, mem_insert_iff]
   rintro y (rfl | hy) z (rfl | hz) hyz
@@ -466,9 +466,8 @@ theorem Nontrivial.infsep_eq_infᵢ (hs : s.Nontrivial) :
   classical rw [Set.infsep_eq_infᵢ, if_pos hs]
 #align set.nontrivial.infsep_eq_infi Set.Nontrivial.infsep_eq_infᵢ
 
-theorem infsep_of_fintype [Decidable s.Nontrivial] [DecidableEq α] [Fintype s] :
-    s.infsep = if hs : s.Nontrivial then s.offDiag.toFinset.inf' (by simpa) (uncurry dist) else 0 :=
-  by
+theorem infsep_of_fintype [Decidable s.Nontrivial] [DecidableEq α] [Fintype s] : s.infsep =
+    if hs : s.Nontrivial then s.offDiag.toFinset.inf' (by simpa) (uncurry dist) else 0 := by
   split_ifs with hs
   · refine' eq_of_forall_le_iff fun _ => _
     simp_rw [hs.le_infsep_iff, imp_forall_iff, Finset.le_inf'_iff, mem_toFinset, mem_offDiag,
@@ -498,9 +497,8 @@ theorem Finite.infsep_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
   classical simp_rw [hsf.infsep, dif_pos hs]
 #align set.finite.infsep_of_nontrivial Set.Finite.infsep_of_nontrivial
 
-theorem _root_.Finset.coe_infsep [DecidableEq α] (s : Finset α) :
-    (s : Set α).infsep = if hs : s.offDiag.Nonempty then s.offDiag.inf' hs (uncurry dist) else 0 :=
-  by
+theorem _root_.Finset.coe_infsep [DecidableEq α] (s : Finset α) : (s : Set α).infsep =
+    if hs : s.offDiag.Nonempty then s.offDiag.inf' hs (uncurry dist) else 0 := by
   have H : (s : Set α).Nontrivial ↔ s.offDiag.Nonempty := by
     rw [← Set.offDiag_nonempty, ← Finset.coe_offDiag, Finset.coe_nonempty]
   split_ifs with hs

5316314b

feat: implement intermediate state for simp_rw (#3738)

closes #3680, see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Stepping.20through.20simp_rw/near/326712986

ff334843

Diff

@@ -169,7 +169,7 @@ theorem einfsep_pair_eq_inf (hxy : x ≠ y) : ({x, y} : Set α).einfsep = edist
 
 theorem einfsep_eq_infᵢ : s.einfsep = ⨅ d : s.offDiag, (uncurry edist) (d : α × α) := by
   refine' eq_of_forall_le_iff fun _ => _
-  simp_rw [le_einfsep_iff, le_infᵢ_iff, imp_forall_iff, SetCoe.forall, Subtype.coe_mk, mem_offDiag,
+  simp_rw [le_einfsep_iff, le_infᵢ_iff, imp_forall_iff, SetCoe.forall, mem_offDiag,
     Prod.forall, uncurry_apply_pair, and_imp]
 #align set.einfsep_eq_infi Set.einfsep_eq_infᵢ

5316314b

fix: add missing _root_ (#3630)

Mathport doesn't understand this, and apparently nor do many of the humans fixing the errors it creates.

If your #align statement complains the def doesn't exist, don't change the #align; work out why it doesn't exist instead.

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

b7f71b0a

Diff

@@ -498,7 +498,7 @@ theorem Finite.infsep_of_nontrivial (hsf : s.Finite) (hs : s.Nontrivial) :
   classical simp_rw [hsf.infsep, dif_pos hs]
 #align set.finite.infsep_of_nontrivial Set.Finite.infsep_of_nontrivial
 
-theorem Finset.coe_infsep [DecidableEq α] (s : Finset α) :
+theorem _root_.Finset.coe_infsep [DecidableEq α] (s : Finset α) :
     (s : Set α).infsep = if hs : s.offDiag.Nonempty then s.offDiag.inf' hs (uncurry dist) else 0 :=
   by
   have H : (s : Set α).Nontrivial ↔ s.offDiag.Nonempty := by
@@ -506,18 +506,18 @@ theorem Finset.coe_infsep [DecidableEq α] (s : Finset α) :
   split_ifs with hs
   · simp_rw [(H.mpr hs).infsep_of_fintype, ← Finset.coe_offDiag, Finset.toFinset_coe]
   · exact (not_nontrivial_iff.mp (H.mp.mt hs)).infsep_zero
-#align finset.coe_infsep Set.Finset.coe_infsep
+#align finset.coe_infsep Finset.coe_infsep
 
-theorem Finset.coe_infsep_of_offDiag_nonempty [DecidableEq α] {s : Finset α}
+theorem _root_.Finset.coe_infsep_of_offDiag_nonempty [DecidableEq α] {s : Finset α}
     (hs : s.offDiag.Nonempty) : (s : Set α).infsep = s.offDiag.inf' hs (uncurry dist) := by
   rw [Finset.coe_infsep, dif_pos hs]
-#align finset.coe_infsep_of_off_diag_nonempty Set.Finset.coe_infsep_of_offDiag_nonempty
+#align finset.coe_infsep_of_off_diag_nonempty Finset.coe_infsep_of_offDiag_nonempty
 
-theorem Finset.coe_infsep_of_offDiag_empty [DecidableEq α] {s : Finset α} (hs : s.offDiag = ∅) :
-    (s : Set α).infsep = 0 := by
+theorem _root_.Finset.coe_infsep_of_offDiag_empty
+    [DecidableEq α] {s : Finset α} (hs : s.offDiag = ∅) : (s : Set α).infsep = 0 := by
   rw [← Finset.not_nonempty_iff_eq_empty] at hs
   rw [Finset.coe_infsep, dif_neg hs]
-#align finset.coe_infsep_of_off_diag_empty Set.Finset.coe_infsep_of_offDiag_empty
+#align finset.coe_infsep_of_off_diag_empty Finset.coe_infsep_of_offDiag_empty
 
 theorem Nontrivial.infsep_exists_of_finite [Finite s] (hs : s.Nontrivial) :
     ∃ (x : _)(_ : x ∈ s)(y : _)(_ : y ∈ s)(_hxy : x ≠ y), s.infsep = dist x y := by
@@ -562,15 +562,15 @@ theorem Finite.infsep_pos_iff_nontrivial (hs : s.Finite) : 0 < s.infsep ↔ s.No
   infsep_pos_iff_nontrivial_of_finite
 #align set.finite.infsep_pos_iff_nontrivial Set.Finite.infsep_pos_iff_nontrivial
 
-theorem Finset.infsep_zero_iff_subsingleton (s : Finset α) :
+theorem _root_.Finset.infsep_zero_iff_subsingleton (s : Finset α) :
     (s : Set α).infsep = 0 ↔ (s : Set α).Subsingleton :=
   infsep_zero_iff_subsingleton_of_finite
-#align finset.infsep_zero_iff_subsingleton Set.Finset.infsep_zero_iff_subsingleton
+#align finset.infsep_zero_iff_subsingleton Finset.infsep_zero_iff_subsingleton
 
-theorem Finset.infsep_pos_iff_nontrivial (s : Finset α) :
+theorem _root_.Finset.infsep_pos_iff_nontrivial (s : Finset α) :
     0 < (s : Set α).infsep ↔ (s : Set α).Nontrivial :=
   infsep_pos_iff_nontrivial_of_finite
-#align finset.infsep_pos_iff_nontrivial Set.Finset.infsep_pos_iff_nontrivial
+#align finset.infsep_pos_iff_nontrivial Finset.infsep_pos_iff_nontrivial
 
 end MetricSpace

5316314b

chore: tidy various files (#3124)

55209140

Diff

@@ -22,7 +22,7 @@ We also define the infimum separation as the cast of the extended infimum separa
 This is the infimum of the distance between distinct elements of the set when in a pseudometric
 space.
 
-All lemmas and definitions are in the `set` namespace to give access to dot notation.
+All lemmas and definitions are in the `Set` namespace to give access to dot notation.
 
 ## Main definitions
 * `Set.einfsep`: Extended infimum separation of a set.
@@ -577,4 +577,3 @@ end MetricSpace
 end Infsep
 
 end Set
-

5316314b

feat: Port Topology.MetricSpace.Infsep (#2613)

70daecbe

`topology.metric_space.infsep` ⟷ `Mathlib.Topology.MetricSpace.Infsep`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 10 + 443

topology.metric_space.infsep ⟷ Mathlib.Topology.MetricSpace.Infsep

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 10 + 443

`topology.metric_space.infsep` ⟷ `Mathlib.Topology.MetricSpace.Infsep`