order.atoms ⟷ Mathlib.Order.Atoms

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

@@ -82,7 +82,7 @@ theorem IsAtom.of_isAtom_coe_Iic {a : Set.Iic x} (ha : IsAtom a) : IsAtom (a : 
 #align is_atom.of_is_atom_coe_Iic IsAtom.of_isAtom_coe_Iic
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (b «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (b «expr ≠ » «expr⊥»()) -/
 #print isAtom_iff_le_of_ge /-
 theorem isAtom_iff_le_of_ge {a : α} : IsAtom a ↔ a ≠ ⊥ ∧ ∀ (b) (_ : b ≠ ⊥), b ≤ a → a ≤ b :=
   and_congr Iff.rfl <|
@@ -172,7 +172,7 @@ theorem IsCoatom.of_isCoatom_coe_Ici {a : Set.Ici x} (ha : IsCoatom a) : IsCoato
 #align is_coatom.of_is_coatom_coe_Ici IsCoatom.of_isCoatom_coe_Ici
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (b «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (b «expr ≠ » «expr⊤»()) -/
 #print isCoatom_iff_ge_of_le /-
 theorem isCoatom_iff_ge_of_le {a : α} : IsCoatom a ↔ a ≠ ⊤ ∧ ∀ (b) (_ : b ≠ ⊤), a ≤ b → b ≤ a :=
   @isAtom_iff_le_of_ge αᵒᵈ _ _ _
@@ -776,7 +776,7 @@ namespace IsSimpleOrder
 
 variable [CompleteLattice α] [IsSimpleOrder α]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:339:40: warning: unsupported option default_priority -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:340:40: warning: unsupported option default_priority -/
 set_option default_priority 100
 
 instance : IsAtomistic α :=

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

@@ -111,16 +111,16 @@ theorem IsAtom.Iic_eq (h : IsAtom a) : Set.Iic a = {⊥, a} :=
 #align is_atom.Iic_eq IsAtom.Iic_eq
 -/
 
-#print bot_covby_iff /-
+#print bot_covBy_iff /-
 @[simp]
-theorem bot_covby_iff : ⊥ ⋖ a ↔ IsAtom a := by
-  simp only [Covby, bot_lt_iff_ne_bot, IsAtom, not_imp_not]
-#align bot_covby_iff bot_covby_iff
+theorem bot_covBy_iff : ⊥ ⋖ a ↔ IsAtom a := by
+  simp only [CovBy, bot_lt_iff_ne_bot, IsAtom, not_imp_not]
+#align bot_covby_iff bot_covBy_iff
 -/
 
-alias ⟨Covby.is_atom, IsAtom.bot_covby⟩ := bot_covby_iff
-#align covby.is_atom Covby.is_atom
-#align is_atom.bot_covby IsAtom.bot_covby
+alias ⟨CovBy.is_atom, IsAtom.bot_covBy⟩ := bot_covBy_iff
+#align covby.is_atom CovBy.is_atom
+#align is_atom.bot_covby IsAtom.bot_covBy
 
 end IsAtom
 
@@ -201,16 +201,16 @@ theorem IsCoatom.Ici_eq (h : IsCoatom a) : Set.Ici a = {⊤, a} :=
 #align is_coatom.Ici_eq IsCoatom.Ici_eq
 -/
 
-#print covby_top_iff /-
+#print covBy_top_iff /-
 @[simp]
-theorem covby_top_iff : a ⋖ ⊤ ↔ IsCoatom a :=
-  toDual_covby_toDual_iff.symm.trans bot_covby_iff
-#align covby_top_iff covby_top_iff
+theorem covBy_top_iff : a ⋖ ⊤ ↔ IsCoatom a :=
+  toDual_covBy_toDual_iff.symm.trans bot_covBy_iff
+#align covby_top_iff covBy_top_iff
 -/
 
-alias ⟨Covby.is_coatom, IsCoatom.covby_top⟩ := covby_top_iff
-#align covby.is_coatom Covby.is_coatom
-#align is_coatom.covby_top IsCoatom.covby_top
+alias ⟨CovBy.isCoatom, IsCoatom.covBy_top⟩ := covBy_top_iff
+#align covby.is_coatom CovBy.isCoatom
+#align is_coatom.covby_top IsCoatom.covBy_top
 
 end IsCoatom
 
@@ -222,8 +222,8 @@ variable [PartialOrder α] {a b : α}
 @[simp]
 theorem Set.Ici.isAtom_iff {b : Set.Ici a} : IsAtom b ↔ a ⋖ b :=
   by
-  rw [← bot_covby_iff]
-  refine' (Set.OrdConnected.apply_covby_apply_iff (OrderEmbedding.subtype fun c => a ≤ c) _).symm
+  rw [← bot_covBy_iff]
+  refine' (Set.OrdConnected.apply_covBy_apply_iff (OrderEmbedding.subtype fun c => a ≤ c) _).symm
   simpa only [OrderEmbedding.subtype_apply, Subtype.range_coe_subtype] using Set.ordConnected_Ici
 #align set.Ici.is_atom_iff Set.Ici.isAtom_iff
 -/
@@ -232,20 +232,20 @@ theorem Set.Ici.isAtom_iff {b : Set.Ici a} : IsAtom b ↔ a ⋖ b :=
 @[simp]
 theorem Set.Iic.isCoatom_iff {a : Set.Iic b} : IsCoatom a ↔ ↑a ⋖ b :=
   by
-  rw [← covby_top_iff]
-  refine' (Set.OrdConnected.apply_covby_apply_iff (OrderEmbedding.subtype fun c => c ≤ b) _).symm
+  rw [← covBy_top_iff]
+  refine' (Set.OrdConnected.apply_covBy_apply_iff (OrderEmbedding.subtype fun c => c ≤ b) _).symm
   simpa only [OrderEmbedding.subtype_apply, Subtype.range_coe_subtype] using Set.ordConnected_Iic
 #align set.Iic.is_coatom_iff Set.Iic.isCoatom_iff
 -/
 
-#print covby_iff_atom_Ici /-
-theorem covby_iff_atom_Ici (h : a ≤ b) : a ⋖ b ↔ IsAtom (⟨b, h⟩ : Set.Ici a) := by simp
-#align covby_iff_atom_Ici covby_iff_atom_Ici
+#print covBy_iff_atom_Ici /-
+theorem covBy_iff_atom_Ici (h : a ≤ b) : a ⋖ b ↔ IsAtom (⟨b, h⟩ : Set.Ici a) := by simp
+#align covby_iff_atom_Ici covBy_iff_atom_Ici
 -/
 
-#print covby_iff_coatom_Iic /-
-theorem covby_iff_coatom_Iic (h : a ≤ b) : a ⋖ b ↔ IsCoatom (⟨a, h⟩ : Set.Iic b) := by simp
-#align covby_iff_coatom_Iic covby_iff_coatom_Iic
+#print covBy_iff_coatom_Iic /-
+theorem covBy_iff_coatom_Iic (h : a ≤ b) : a ⋖ b ↔ IsCoatom (⟨a, h⟩ : Set.Iic b) := by simp
+#align covby_iff_coatom_Iic covBy_iff_coatom_Iic
 -/
 
 end PartialOrder
@@ -598,10 +598,10 @@ theorem isCoatom_bot : IsCoatom (⊥ : α) :=
 #align is_coatom_bot isCoatom_bot
 -/
 
-#print bot_covby_top /-
-theorem bot_covby_top : (⊥ : α) ⋖ ⊤ :=
-  isAtom_top.bot_covby
-#align bot_covby_top bot_covby_top
+#print bot_covBy_top /-
+theorem bot_covBy_top : (⊥ : α) ⋖ ⊤ :=
+  isAtom_top.bot_covBy
+#align bot_covby_top bot_covBy_top
 -/
 
 end IsSimpleOrder
@@ -838,8 +838,8 @@ variable [PartialOrder α] [PartialOrder β]
 
 #print OrderEmbedding.isAtom_of_map_bot_of_image /-
 theorem isAtom_of_map_bot_of_image [OrderBot α] [OrderBot β] (f : β ↪o α) (hbot : f ⊥ = ⊥) {b : β}
-    (hb : IsAtom (f b)) : IsAtom b := by simp only [← bot_covby_iff] at hb ⊢;
-  exact Covby.of_image f (hbot.symm ▸ hb)
+    (hb : IsAtom (f b)) : IsAtom b := by simp only [← bot_covBy_iff] at hb ⊢;
+  exact CovBy.of_image f (hbot.symm ▸ hb)
 #align order_embedding.is_atom_of_map_bot_of_image OrderEmbedding.isAtom_of_map_bot_of_image
 -/
 

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

@@ -996,7 +996,7 @@ theorem isSimpleOrder [BoundedOrder α] [BoundedOrder β] [h : IsSimpleOrder β]
 #print OrderIso.isAtomic_iff /-
 protected theorem isAtomic_iff [OrderBot α] [OrderBot β] (f : α ≃o β) : IsAtomic α ↔ IsAtomic β :=
   by
-  simp only [IsAtomic_iff, f.surjective.forall, f.surjective.exists, ← map_bot f, f.eq_iff_eq,
+  simp only [isAtomic_iff, f.surjective.forall, f.surjective.exists, ← map_bot f, f.eq_iff_eq,
     f.le_iff_le, f.is_atom_iff]
 #align order_iso.is_atomic_iff OrderIso.isAtomic_iff
 -/

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

@@ -83,11 +83,11 @@ theorem IsAtom.of_isAtom_coe_Iic {a : Set.Iic x} (ha : IsAtom a) : IsAtom (a : 
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (b «expr ≠ » «expr⊥»()) -/
-#print isAtom_iff /-
-theorem isAtom_iff {a : α} : IsAtom a ↔ a ≠ ⊥ ∧ ∀ (b) (_ : b ≠ ⊥), b ≤ a → a ≤ b :=
+#print isAtom_iff_le_of_ge /-
+theorem isAtom_iff_le_of_ge {a : α} : IsAtom a ↔ a ≠ ⊥ ∧ ∀ (b) (_ : b ≠ ⊥), b ≤ a → a ≤ b :=
   and_congr Iff.rfl <|
     forall_congr' fun b => by simp only [Ne.def, @not_imp_comm (b = ⊥), not_imp, lt_iff_le_not_le]
-#align is_atom_iff isAtom_iff
+#align is_atom_iff isAtom_iff_le_of_ge
 -/
 
 end Preorder
@@ -173,10 +173,10 @@ theorem IsCoatom.of_isCoatom_coe_Ici {a : Set.Ici x} (ha : IsCoatom a) : IsCoato
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (b «expr ≠ » «expr⊤»()) -/
-#print isCoatom_iff /-
-theorem isCoatom_iff {a : α} : IsCoatom a ↔ a ≠ ⊤ ∧ ∀ (b) (_ : b ≠ ⊤), a ≤ b → b ≤ a :=
-  @isAtom_iff αᵒᵈ _ _ _
-#align is_coatom_iff isCoatom_iff
+#print isCoatom_iff_ge_of_le /-
+theorem isCoatom_iff_ge_of_le {a : α} : IsCoatom a ↔ a ≠ ⊤ ∧ ∀ (b) (_ : b ≠ ⊤), a ≤ b → b ≤ a :=
+  @isAtom_iff_le_of_ge αᵒᵈ _ _ _
+#align is_coatom_iff isCoatom_iff_ge_of_le
 -/
 
 end Preorder
@@ -931,7 +931,7 @@ theorem isCoatom_of_l_top [OrderTop α] [OrderTop β] {l : α → β} {u : β 
 theorem isCoatom_iff [OrderTop α] [OrderTop β] [IsCoatomic β] {l : α → β} {u : β → α}
     (gi : GaloisCoinsertion l u) (htop : l ⊤ = ⊤) (h_coatom : ∀ b, IsCoatom b → l (u b) = b)
     (b : β) : IsCoatom (u b) ↔ IsCoatom b :=
-  gi.dual.isAtom_iff htop h_coatom b
+  gi.dual.isAtom_iff_le_of_ge htop h_coatom b
 #align galois_coinsertion.is_coatom_iff GaloisCoinsertion.isCoatom_iff
 -/
 
@@ -954,7 +954,7 @@ theorem isAtom_of_image [OrderBot α] [OrderBot β] {l : α → β} {u : β →
 theorem isAtom_iff [OrderBot α] [OrderBot β] [IsAtomic β] {l : α → β} {u : β → α}
     (gi : GaloisCoinsertion l u) (h_atom : ∀ b, IsAtom b → l (u b) = b) (a : α) :
     IsAtom (l a) ↔ IsAtom a :=
-  gi.dual.isCoatom_iff h_atom a
+  gi.dual.isCoatom_iff_ge_of_le h_atom a
 #align galois_coinsertion.is_atom_iff GaloisCoinsertion.isAtom_iff
 -/
 
@@ -975,7 +975,7 @@ theorem isAtom_iff [OrderBot α] [OrderBot β] (f : α ≃o β) (a : α) : IsAto
 #print OrderIso.isCoatom_iff /-
 @[simp]
 theorem isCoatom_iff [OrderTop α] [OrderTop β] (f : α ≃o β) (a : α) : IsCoatom (f a) ↔ IsCoatom a :=
-  f.dual.isAtom_iff a
+  f.dual.isAtom_iff_le_of_ge a
 #align order_iso.is_coatom_iff OrderIso.isCoatom_iff
 -/
 
@@ -1077,7 +1077,7 @@ theorem isAtom_singleton (x : α) : IsAtom ({x} : Set α) :=
 theorem isAtom_iff (s : Set α) : IsAtom s ↔ ∃ x, s = {x} :=
   by
   refine' ⟨_, by rintro ⟨x, rfl⟩; exact is_atom_singleton x⟩
-  rw [isAtom_iff, bot_eq_empty, ← nonempty_iff_ne_empty]
+  rw [isAtom_iff_le_of_ge, bot_eq_empty, ← nonempty_iff_ne_empty]
   rintro ⟨⟨x, hx⟩, hs⟩
   exact
     ⟨x,
@@ -1088,7 +1088,7 @@ theorem isAtom_iff (s : Set α) : IsAtom s ↔ ∃ x, s = {x} :=
 
 #print Set.isCoatom_iff /-
 theorem isCoatom_iff (s : Set α) : IsCoatom s ↔ ∃ x, s = {x}ᶜ := by
-  simp_rw [is_compl_compl.is_coatom_iff_is_atom, isAtom_iff, @eq_comm _ s, compl_eq_comm]
+  simp_rw [is_compl_compl.is_coatom_iff_is_atom, isAtom_iff_le_of_ge, @eq_comm _ s, compl_eq_comm]
 #align set.is_coatom_iff Set.isCoatom_iff
 -/
 

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

@@ -378,7 +378,7 @@ section WellFounded
 theorem isAtomic_of_orderBot_wellFounded_lt [OrderBot α]
     (h : WellFounded ((· < ·) : α → α → Prop)) : IsAtomic α :=
   ⟨fun a =>
-    or_iff_not_imp_left.2 fun ha =>
+    Classical.or_iff_not_imp_left.2 fun ha =>
       let ⟨b, hb, hm⟩ := h.has_min {b | b ≠ ⊥ ∧ b ≤ a} ⟨a, ha, le_rfl⟩
       ⟨b, ⟨hb.1, fun c => not_imp_not.1 fun hc hl => hm c ⟨hc, hl.le.trans hb.2⟩ hl⟩, hb.2⟩⟩
 #align is_atomic_of_order_bot_well_founded_lt isAtomic_of_orderBot_wellFounded_lt

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
 -/
-import Mathbin.Order.ModularLattice
-import Mathbin.Order.WellFounded
+import Order.ModularLattice
+import Order.WellFounded
 
 #align_import order.atoms from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
 
@@ -82,7 +82,7 @@ theorem IsAtom.of_isAtom_coe_Iic {a : Set.Iic x} (ha : IsAtom a) : IsAtom (a : 
 #align is_atom.of_is_atom_coe_Iic IsAtom.of_isAtom_coe_Iic
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (b «expr ≠ » «expr⊥»()) -/
 #print isAtom_iff /-
 theorem isAtom_iff {a : α} : IsAtom a ↔ a ≠ ⊥ ∧ ∀ (b) (_ : b ≠ ⊥), b ≤ a → a ≤ b :=
   and_congr Iff.rfl <|
@@ -172,7 +172,7 @@ theorem IsCoatom.of_isCoatom_coe_Ici {a : Set.Ici x} (ha : IsCoatom a) : IsCoato
 #align is_coatom.of_is_coatom_coe_Ici IsCoatom.of_isCoatom_coe_Ici
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (b «expr ≠ » «expr⊤»()) -/
 #print isCoatom_iff /-
 theorem isCoatom_iff {a : α} : IsCoatom a ↔ a ≠ ⊤ ∧ ∀ (b) (_ : b ≠ ⊤), a ≤ b → b ≤ a :=
   @isAtom_iff αᵒᵈ _ _ _
@@ -776,7 +776,7 @@ namespace IsSimpleOrder
 
 variable [CompleteLattice α] [IsSimpleOrder α]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:334:40: warning: unsupported option default_priority -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:339:40: warning: unsupported option default_priority -/
 set_option default_priority 100
 
 instance : IsAtomistic α :=

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

@@ -118,7 +118,7 @@ theorem bot_covby_iff : ⊥ ⋖ a ↔ IsAtom a := by
 #align bot_covby_iff bot_covby_iff
 -/
 
-alias bot_covby_iff ↔ Covby.is_atom IsAtom.bot_covby
+alias ⟨Covby.is_atom, IsAtom.bot_covby⟩ := bot_covby_iff
 #align covby.is_atom Covby.is_atom
 #align is_atom.bot_covby IsAtom.bot_covby
 
@@ -152,10 +152,10 @@ theorem isAtom_dual_iff_isCoatom [OrderTop α] {a : α} : IsAtom (OrderDual.toDu
 #align is_atom_dual_iff_is_coatom isAtom_dual_iff_isCoatom
 -/
 
-alias isCoatom_dual_iff_isAtom ↔ _ IsAtom.dual
+alias ⟨_, IsAtom.dual⟩ := isCoatom_dual_iff_isAtom
 #align is_atom.dual IsAtom.dual
 
-alias isAtom_dual_iff_isCoatom ↔ _ IsCoatom.dual
+alias ⟨_, IsCoatom.dual⟩ := isAtom_dual_iff_isCoatom
 #align is_coatom.dual IsCoatom.dual
 
 variable [OrderTop α] {a x : α}
@@ -208,7 +208,7 @@ theorem covby_top_iff : a ⋖ ⊤ ↔ IsCoatom a :=
 #align covby_top_iff covby_top_iff
 -/
 
-alias covby_top_iff ↔ Covby.is_coatom IsCoatom.covby_top
+alias ⟨Covby.is_coatom, IsCoatom.covby_top⟩ := covby_top_iff
 #align covby.is_coatom Covby.is_coatom
 #align is_coatom.covby_top IsCoatom.covby_top
 
@@ -624,10 +624,10 @@ theorem eq_top_of_lt : b = ⊤ :=
 #align is_simple_order.eq_top_of_lt IsSimpleOrder.eq_top_of_lt
 -/
 
-alias eq_bot_of_lt ← has_lt.lt.eq_bot
+alias has_lt.lt.eq_bot := eq_bot_of_lt
 #align is_simple_order.has_lt.lt.eq_bot IsSimpleOrder.HasLt.Lt.eq_bot
 
-alias eq_top_of_lt ← has_lt.lt.eq_top
+alias has_lt.lt.eq_top := eq_top_of_lt
 #align is_simple_order.has_lt.lt.eq_top IsSimpleOrder.HasLt.Lt.eq_top
 
 end Preorder

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module order.atoms
-! leanprover-community/mathlib commit c3291da49cfa65f0d43b094750541c0731edc932
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Order.ModularLattice
 import Mathbin.Order.WellFounded
 
+#align_import order.atoms from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
 /-!
 # Atoms, Coatoms, and Simple Lattices
 
@@ -85,7 +82,7 @@ theorem IsAtom.of_isAtom_coe_Iic {a : Set.Iic x} (ha : IsAtom a) : IsAtom (a : 
 #align is_atom.of_is_atom_coe_Iic IsAtom.of_isAtom_coe_Iic
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (b «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ≠ » «expr⊥»()) -/
 #print isAtom_iff /-
 theorem isAtom_iff {a : α} : IsAtom a ↔ a ≠ ⊥ ∧ ∀ (b) (_ : b ≠ ⊥), b ≤ a → a ≤ b :=
   and_congr Iff.rfl <|
@@ -175,7 +172,7 @@ theorem IsCoatom.of_isCoatom_coe_Ici {a : Set.Ici x} (ha : IsCoatom a) : IsCoato
 #align is_coatom.of_is_coatom_coe_Ici IsCoatom.of_isCoatom_coe_Ici
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (b «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ≠ » «expr⊤»()) -/
 #print isCoatom_iff /-
 theorem isCoatom_iff {a : α} : IsCoatom a ↔ a ≠ ⊤ ∧ ∀ (b) (_ : b ≠ ⊤), a ≤ b → b ≤ a :=
   @isAtom_iff αᵒᵈ _ _ _

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

@@ -86,30 +86,40 @@ theorem IsAtom.of_isAtom_coe_Iic {a : Set.Iic x} (ha : IsAtom a) : IsAtom (a : 
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (b «expr ≠ » «expr⊥»()) -/
+#print isAtom_iff /-
 theorem isAtom_iff {a : α} : IsAtom a ↔ a ≠ ⊥ ∧ ∀ (b) (_ : b ≠ ⊥), b ≤ a → a ≤ b :=
   and_congr Iff.rfl <|
     forall_congr' fun b => by simp only [Ne.def, @not_imp_comm (b = ⊥), not_imp, lt_iff_le_not_le]
 #align is_atom_iff isAtom_iff
+-/
 
 end Preorder
 
 variable [PartialOrder α] [OrderBot α] {a b x : α}
 
+#print IsAtom.lt_iff /-
 theorem IsAtom.lt_iff (h : IsAtom a) : x < a ↔ x = ⊥ :=
   ⟨h.2 x, fun hx => hx.symm ▸ h.1.bot_lt⟩
 #align is_atom.lt_iff IsAtom.lt_iff
+-/
 
+#print IsAtom.le_iff /-
 theorem IsAtom.le_iff (h : IsAtom a) : x ≤ a ↔ x = ⊥ ∨ x = a := by rw [le_iff_lt_or_eq, h.lt_iff]
 #align is_atom.le_iff IsAtom.le_iff
+-/
 
+#print IsAtom.Iic_eq /-
 theorem IsAtom.Iic_eq (h : IsAtom a) : Set.Iic a = {⊥, a} :=
   Set.ext fun x => h.le_iff
 #align is_atom.Iic_eq IsAtom.Iic_eq
+-/
 
+#print bot_covby_iff /-
 @[simp]
 theorem bot_covby_iff : ⊥ ⋖ a ↔ IsAtom a := by
   simp only [Covby, bot_lt_iff_ne_bot, IsAtom, not_imp_not]
 #align bot_covby_iff bot_covby_iff
+-/
 
 alias bot_covby_iff ↔ Covby.is_atom IsAtom.bot_covby
 #align covby.is_atom Covby.is_atom
@@ -166,30 +176,40 @@ theorem IsCoatom.of_isCoatom_coe_Ici {a : Set.Ici x} (ha : IsCoatom a) : IsCoato
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (b «expr ≠ » «expr⊤»()) -/
+#print isCoatom_iff /-
 theorem isCoatom_iff {a : α} : IsCoatom a ↔ a ≠ ⊤ ∧ ∀ (b) (_ : b ≠ ⊤), a ≤ b → b ≤ a :=
   @isAtom_iff αᵒᵈ _ _ _
 #align is_coatom_iff isCoatom_iff
+-/
 
 end Preorder
 
 variable [PartialOrder α] [OrderTop α] {a b x : α}
 
+#print IsCoatom.lt_iff /-
 theorem IsCoatom.lt_iff (h : IsCoatom a) : a < x ↔ x = ⊤ :=
   h.dual.lt_iff
 #align is_coatom.lt_iff IsCoatom.lt_iff
+-/
 
+#print IsCoatom.le_iff /-
 theorem IsCoatom.le_iff (h : IsCoatom a) : a ≤ x ↔ x = ⊤ ∨ x = a :=
   h.dual.le_iff
 #align is_coatom.le_iff IsCoatom.le_iff
+-/
 
+#print IsCoatom.Ici_eq /-
 theorem IsCoatom.Ici_eq (h : IsCoatom a) : Set.Ici a = {⊤, a} :=
   h.dual.Iic_eq
 #align is_coatom.Ici_eq IsCoatom.Ici_eq
+-/
 
+#print covby_top_iff /-
 @[simp]
 theorem covby_top_iff : a ⋖ ⊤ ↔ IsCoatom a :=
   toDual_covby_toDual_iff.symm.trans bot_covby_iff
 #align covby_top_iff covby_top_iff
+-/
 
 alias covby_top_iff ↔ Covby.is_coatom IsCoatom.covby_top
 #align covby.is_coatom Covby.is_coatom
@@ -235,10 +255,12 @@ end PartialOrder
 
 section Pairwise
 
+#print IsAtom.inf_eq_bot_of_ne /-
 theorem IsAtom.inf_eq_bot_of_ne [SemilatticeInf α] [OrderBot α] {a b : α} (ha : IsAtom a)
     (hb : IsAtom b) (hab : a ≠ b) : a ⊓ b = ⊥ :=
   hab.not_le_or_not_le.elim (ha.lt_iff.1 ∘ inf_lt_left.2) (hb.lt_iff.1 ∘ inf_lt_right.2)
 #align is_atom.inf_eq_bot_of_ne IsAtom.inf_eq_bot_of_ne
+-/
 
 #print IsAtom.disjoint_of_ne /-
 theorem IsAtom.disjoint_of_ne [SemilatticeInf α] [OrderBot α] {a b : α} (ha : IsAtom a)
@@ -247,10 +269,12 @@ theorem IsAtom.disjoint_of_ne [SemilatticeInf α] [OrderBot α] {a b : α} (ha :
 #align is_atom.disjoint_of_ne IsAtom.disjoint_of_ne
 -/
 
+#print IsCoatom.sup_eq_top_of_ne /-
 theorem IsCoatom.sup_eq_top_of_ne [SemilatticeSup α] [OrderTop α] {a b : α} (ha : IsCoatom a)
     (hb : IsCoatom b) (hab : a ≠ b) : a ⊔ b = ⊤ :=
   ha.dual.inf_eq_bot_of_ne hb.dual hab
 #align is_coatom.sup_eq_top_of_ne IsCoatom.sup_eq_top_of_ne
+-/
 
 end Pairwise
 
@@ -435,19 +459,23 @@ section IsAtomistic
 
 variable [IsAtomistic α]
 
+#print sSup_atoms_le_eq /-
 @[simp]
 theorem sSup_atoms_le_eq (b : α) : sSup {a : α | IsAtom a ∧ a ≤ b} = b :=
   by
   rcases eq_Sup_atoms b with ⟨s, rfl, hs⟩
   exact le_antisymm (sSup_le fun _ => And.right) (sSup_le_sSup fun a ha => ⟨hs a ha, le_sSup ha⟩)
 #align Sup_atoms_le_eq sSup_atoms_le_eq
+-/
 
+#print sSup_atoms_eq_top /-
 @[simp]
 theorem sSup_atoms_eq_top : sSup {a : α | IsAtom a} = ⊤ :=
   by
   refine' Eq.trans (congr rfl (Set.ext fun x => _)) (sSup_atoms_le_eq ⊤)
   exact (and_iff_left le_top).symm
 #align Sup_atoms_eq_top sSup_atoms_eq_top
+-/
 
 #print le_iff_atom_le_imp /-
 theorem le_iff_atom_le_imp {a b : α} : a ≤ b ↔ ∀ c : α, IsAtom c → c ≤ a → c ≤ b :=
@@ -506,6 +534,7 @@ theorem isSimpleOrder_iff_isSimpleOrder_orderDual [LE α] [BoundedOrder α] :
 #align is_simple_order_iff_is_simple_order_order_dual isSimpleOrder_iff_isSimpleOrder_orderDual
 -/
 
+#print IsSimpleOrder.bot_ne_top /-
 theorem IsSimpleOrder.bot_ne_top [LE α] [BoundedOrder α] [IsSimpleOrder α] : (⊥ : α) ≠ (⊤ : α) :=
   by
   obtain ⟨a, b, h⟩ := exists_pair_ne α
@@ -514,6 +543,7 @@ theorem IsSimpleOrder.bot_ne_top [LE α] [BoundedOrder α] [IsSimpleOrder α] :
     | simpa
     | simpa using h.symm
 #align is_simple_order.bot_ne_top IsSimpleOrder.bot_ne_top
+-/
 
 section IsSimpleOrder
 
@@ -557,19 +587,25 @@ protected def IsSimpleOrder.linearOrder [DecidableEq α] : LinearOrder α :=
 #align is_simple_order.linear_order IsSimpleOrder.linearOrder
 -/
 
+#print isAtom_top /-
 @[simp]
 theorem isAtom_top : IsAtom (⊤ : α) :=
   ⟨top_ne_bot, fun a ha => Or.resolve_right (eq_bot_or_eq_top a) (ne_of_lt ha)⟩
 #align is_atom_top isAtom_top
+-/
 
+#print isCoatom_bot /-
 @[simp]
 theorem isCoatom_bot : IsCoatom (⊥ : α) :=
   isAtom_dual_iff_isCoatom.1 isAtom_top
 #align is_coatom_bot isCoatom_bot
+-/
 
+#print bot_covby_top /-
 theorem bot_covby_top : (⊥ : α) ⋖ ⊤ :=
   isAtom_top.bot_covby
 #align bot_covby_top bot_covby_top
+-/
 
 end IsSimpleOrder
 
@@ -579,13 +615,17 @@ section Preorder
 
 variable [Preorder α] [BoundedOrder α] [IsSimpleOrder α] {a b : α} (h : a < b)
 
+#print IsSimpleOrder.eq_bot_of_lt /-
 theorem eq_bot_of_lt : a = ⊥ :=
   (IsSimpleOrder.eq_bot_or_eq_top _).resolve_right h.ne_top
 #align is_simple_order.eq_bot_of_lt IsSimpleOrder.eq_bot_of_lt
+-/
 
+#print IsSimpleOrder.eq_top_of_lt /-
 theorem eq_top_of_lt : b = ⊤ :=
   (IsSimpleOrder.eq_bot_or_eq_top _).resolve_left h.ne_bot
 #align is_simple_order.eq_top_of_lt IsSimpleOrder.eq_top_of_lt
+-/
 
 alias eq_bot_of_lt ← has_lt.lt.eq_bot
 #align is_simple_order.has_lt.lt.eq_bot IsSimpleOrder.HasLt.Lt.eq_bot
@@ -644,6 +684,7 @@ def equivBool {α} [DecidableEq α] [LE α] [BoundedOrder α] [IsSimpleOrder α]
 #align is_simple_order.equiv_bool IsSimpleOrder.equivBool
 -/
 
+#print IsSimpleOrder.orderIsoBool /-
 /-- Every simple lattice over a partial order is order-isomorphic to `bool`. -/
 def orderIsoBool : α ≃o Bool :=
   { equivBool with
@@ -655,6 +696,7 @@ def orderIsoBool : α ≃o Bool :=
         · simp [bot_ne_top.symm, bot_ne_top, Bool.false_lt_true]
         · simp [bot_ne_top] }
 #align is_simple_order.order_iso_bool IsSimpleOrder.orderIsoBool
+-/
 
 #print IsSimpleOrder.booleanAlgebra /-
 /-- A simple `bounded_order` is also a `boolean_algebra`. -/
@@ -753,20 +795,25 @@ instance : IsCoatomistic α :=
 
 end IsSimpleOrder
 
+#print isSimpleOrder_iff_isAtom_top /-
 theorem isSimpleOrder_iff_isAtom_top [PartialOrder α] [BoundedOrder α] :
     IsSimpleOrder α ↔ IsAtom (⊤ : α) :=
   ⟨fun h => @isAtom_top _ _ _ h, fun h =>
     { exists_pair_ne := ⟨⊤, ⊥, h.1⟩
       eq_bot_or_eq_top := fun a => ((eq_or_lt_of_le le_top).imp_right (h.2 a)).symm }⟩
 #align is_simple_order_iff_is_atom_top isSimpleOrder_iff_isAtom_top
+-/
 
+#print isSimpleOrder_iff_isCoatom_bot /-
 theorem isSimpleOrder_iff_isCoatom_bot [PartialOrder α] [BoundedOrder α] :
     IsSimpleOrder α ↔ IsCoatom (⊥ : α) :=
   isSimpleOrder_iff_isSimpleOrder_orderDual.trans isSimpleOrder_iff_isAtom_top
 #align is_simple_order_iff_is_coatom_bot isSimpleOrder_iff_isCoatom_bot
+-/
 
 namespace Set
 
+#print Set.isSimpleOrder_Iic_iff_isAtom /-
 theorem isSimpleOrder_Iic_iff_isAtom [PartialOrder α] [OrderBot α] {a : α} :
     IsSimpleOrder (Iic a) ↔ IsAtom a :=
   isSimpleOrder_iff_isAtom_top.trans <|
@@ -774,6 +821,7 @@ theorem isSimpleOrder_Iic_iff_isAtom [PartialOrder α] [OrderBot α] {a : α} :
       ⟨fun h b ab => Subtype.mk_eq_mk.1 (h ⟨b, le_of_lt ab⟩ ab), fun h ⟨b, hab⟩ hbotb =>
         Subtype.mk_eq_mk.2 (h b (Subtype.mk_lt_mk.1 hbotb))⟩
 #align set.is_simple_order_Iic_iff_is_atom Set.isSimpleOrder_Iic_iff_isAtom
+-/
 
 #print Set.isSimpleOrder_Ici_iff_isCoatom /-
 theorem isSimpleOrder_Ici_iff_isCoatom [PartialOrder α] [OrderTop α] {a : α} :
@@ -791,15 +839,19 @@ namespace OrderEmbedding
 
 variable [PartialOrder α] [PartialOrder β]
 
+#print OrderEmbedding.isAtom_of_map_bot_of_image /-
 theorem isAtom_of_map_bot_of_image [OrderBot α] [OrderBot β] (f : β ↪o α) (hbot : f ⊥ = ⊥) {b : β}
     (hb : IsAtom (f b)) : IsAtom b := by simp only [← bot_covby_iff] at hb ⊢;
   exact Covby.of_image f (hbot.symm ▸ hb)
 #align order_embedding.is_atom_of_map_bot_of_image OrderEmbedding.isAtom_of_map_bot_of_image
+-/
 
+#print OrderEmbedding.isCoatom_of_map_top_of_image /-
 theorem isCoatom_of_map_top_of_image [OrderTop α] [OrderTop β] (f : β ↪o α) (htop : f ⊤ = ⊤) {b : β}
     (hb : IsCoatom (f b)) : IsCoatom b :=
   f.dual.isAtom_of_map_bot_of_image htop hb
 #align order_embedding.is_coatom_of_map_top_of_image OrderEmbedding.isCoatom_of_map_top_of_image
+-/
 
 end OrderEmbedding
 
@@ -807,12 +859,15 @@ namespace GaloisInsertion
 
 variable [PartialOrder α] [PartialOrder β]
 
+#print GaloisInsertion.isAtom_of_u_bot /-
 theorem isAtom_of_u_bot [OrderBot α] [OrderBot β] {l : α → β} {u : β → α} (gi : GaloisInsertion l u)
     (hbot : u ⊥ = ⊥) {b : β} (hb : IsAtom (u b)) : IsAtom b :=
   OrderEmbedding.isAtom_of_map_bot_of_image
     ⟨⟨u, gi.u_injective⟩, @GaloisInsertion.u_le_u_iff _ _ _ _ _ _ gi⟩ hbot hb
 #align galois_insertion.is_atom_of_u_bot GaloisInsertion.isAtom_of_u_bot
+-/
 
+#print GaloisInsertion.isAtom_iff /-
 theorem isAtom_iff [OrderBot α] [IsAtomic α] [OrderBot β] {l : α → β} {u : β → α}
     (gi : GaloisInsertion l u) (hbot : u ⊥ = ⊥) (h_atom : ∀ a, IsAtom a → u (l a) = a) (a : α) :
     IsAtom (l a) ↔ IsAtom a :=
@@ -829,18 +884,24 @@ theorem isAtom_iff [OrderBot α] [IsAtomic α] [OrderBot β] {l : α → β} {u
       (mt (congr_arg l) (gi.gc.l_bot.symm ▸ hla.1))
   exact haa'.symm ▸ ha'
 #align galois_insertion.is_atom_iff GaloisInsertion.isAtom_iff
+-/
 
+#print GaloisInsertion.isAtom_iff' /-
 theorem isAtom_iff' [OrderBot α] [IsAtomic α] [OrderBot β] {l : α → β} {u : β → α}
     (gi : GaloisInsertion l u) (hbot : u ⊥ = ⊥) (h_atom : ∀ a, IsAtom a → u (l a) = a) (b : β) :
     IsAtom (u b) ↔ IsAtom b := by rw [← gi.is_atom_iff hbot h_atom, gi.l_u_eq]
 #align galois_insertion.is_atom_iff' GaloisInsertion.isAtom_iff'
+-/
 
+#print GaloisInsertion.isCoatom_of_image /-
 theorem isCoatom_of_image [OrderTop α] [OrderTop β] {l : α → β} {u : β → α}
     (gi : GaloisInsertion l u) {b : β} (hb : IsCoatom (u b)) : IsCoatom b :=
   OrderEmbedding.isCoatom_of_map_top_of_image
     ⟨⟨u, gi.u_injective⟩, @GaloisInsertion.u_le_u_iff _ _ _ _ _ _ gi⟩ gi.gc.u_top hb
 #align galois_insertion.is_coatom_of_image GaloisInsertion.isCoatom_of_image
+-/
 
+#print GaloisInsertion.isCoatom_iff /-
 theorem isCoatom_iff [OrderTop α] [IsCoatomic α] [OrderTop β] {l : α → β} {u : β → α}
     (gi : GaloisInsertion l u) (h_coatom : ∀ a : α, IsCoatom a → u (l a) = a) (b : β) :
     IsCoatom (u b) ↔ IsCoatom b :=
@@ -854,6 +915,7 @@ theorem isCoatom_iff [OrderTop α] [IsCoatomic α] [OrderTop β] {l : α → β}
       ha.1 (gi.gc.u_top ▸ h_coatom a ha ▸ congr_arg u hla)
   exact this ▸ (h_coatom a ha).symm ▸ ha
 #align galois_insertion.is_coatom_iff GaloisInsertion.isCoatom_iff
+-/
 
 end GaloisInsertion
 
@@ -861,33 +923,43 @@ namespace GaloisCoinsertion
 
 variable [PartialOrder α] [PartialOrder β]
 
+#print GaloisCoinsertion.isCoatom_of_l_top /-
 theorem isCoatom_of_l_top [OrderTop α] [OrderTop β] {l : α → β} {u : β → α}
     (gi : GaloisCoinsertion l u) (hbot : l ⊤ = ⊤) {a : α} (hb : IsCoatom (l a)) : IsCoatom a :=
   gi.dual.isAtom_of_u_bot hbot hb.dual
 #align galois_coinsertion.is_coatom_of_l_top GaloisCoinsertion.isCoatom_of_l_top
+-/
 
+#print GaloisCoinsertion.isCoatom_iff /-
 theorem isCoatom_iff [OrderTop α] [OrderTop β] [IsCoatomic β] {l : α → β} {u : β → α}
     (gi : GaloisCoinsertion l u) (htop : l ⊤ = ⊤) (h_coatom : ∀ b, IsCoatom b → l (u b) = b)
     (b : β) : IsCoatom (u b) ↔ IsCoatom b :=
   gi.dual.isAtom_iff htop h_coatom b
 #align galois_coinsertion.is_coatom_iff GaloisCoinsertion.isCoatom_iff
+-/
 
+#print GaloisCoinsertion.isCoatom_iff' /-
 theorem isCoatom_iff' [OrderTop α] [OrderTop β] [IsCoatomic β] {l : α → β} {u : β → α}
     (gi : GaloisCoinsertion l u) (htop : l ⊤ = ⊤) (h_coatom : ∀ b, IsCoatom b → l (u b) = b)
     (a : α) : IsCoatom (l a) ↔ IsCoatom a :=
   gi.dual.isAtom_iff' htop h_coatom a
 #align galois_coinsertion.is_coatom_iff' GaloisCoinsertion.isCoatom_iff'
+-/
 
+#print GaloisCoinsertion.isAtom_of_image /-
 theorem isAtom_of_image [OrderBot α] [OrderBot β] {l : α → β} {u : β → α}
     (gi : GaloisCoinsertion l u) {a : α} (hb : IsAtom (l a)) : IsAtom a :=
   gi.dual.isCoatom_of_image hb.dual
 #align galois_coinsertion.is_atom_of_image GaloisCoinsertion.isAtom_of_image
+-/
 
+#print GaloisCoinsertion.isAtom_iff /-
 theorem isAtom_iff [OrderBot α] [OrderBot β] [IsAtomic β] {l : α → β} {u : β → α}
     (gi : GaloisCoinsertion l u) (h_atom : ∀ b, IsAtom b → l (u b) = b) (a : α) :
     IsAtom (l a) ↔ IsAtom a :=
   gi.dual.isCoatom_iff h_atom a
 #align galois_coinsertion.is_atom_iff GaloisCoinsertion.isAtom_iff
+-/
 
 end GaloisCoinsertion
 
@@ -895,37 +967,49 @@ namespace OrderIso
 
 variable [PartialOrder α] [PartialOrder β]
 
+#print OrderIso.isAtom_iff /-
 @[simp]
 theorem isAtom_iff [OrderBot α] [OrderBot β] (f : α ≃o β) (a : α) : IsAtom (f a) ↔ IsAtom a :=
   ⟨f.toGaloisCoinsertion.isAtom_of_image, fun ha =>
     f.toGaloisInsertion.isAtom_of_u_bot (map_bot f.symm) <| (f.symm_apply_apply a).symm ▸ ha⟩
 #align order_iso.is_atom_iff OrderIso.isAtom_iff
+-/
 
+#print OrderIso.isCoatom_iff /-
 @[simp]
 theorem isCoatom_iff [OrderTop α] [OrderTop β] (f : α ≃o β) (a : α) : IsCoatom (f a) ↔ IsCoatom a :=
   f.dual.isAtom_iff a
 #align order_iso.is_coatom_iff OrderIso.isCoatom_iff
+-/
 
+#print OrderIso.isSimpleOrder_iff /-
 theorem isSimpleOrder_iff [BoundedOrder α] [BoundedOrder β] (f : α ≃o β) :
     IsSimpleOrder α ↔ IsSimpleOrder β := by
   rw [isSimpleOrder_iff_isAtom_top, isSimpleOrder_iff_isAtom_top, ← f.is_atom_iff ⊤, f.map_top]
 #align order_iso.is_simple_order_iff OrderIso.isSimpleOrder_iff
+-/
 
+#print OrderIso.isSimpleOrder /-
 theorem isSimpleOrder [BoundedOrder α] [BoundedOrder β] [h : IsSimpleOrder β] (f : α ≃o β) :
     IsSimpleOrder α :=
   f.isSimpleOrder_iff.mpr h
 #align order_iso.is_simple_order OrderIso.isSimpleOrder
+-/
 
+#print OrderIso.isAtomic_iff /-
 protected theorem isAtomic_iff [OrderBot α] [OrderBot β] (f : α ≃o β) : IsAtomic α ↔ IsAtomic β :=
   by
   simp only [IsAtomic_iff, f.surjective.forall, f.surjective.exists, ← map_bot f, f.eq_iff_eq,
     f.le_iff_le, f.is_atom_iff]
 #align order_iso.is_atomic_iff OrderIso.isAtomic_iff
+-/
 
+#print OrderIso.isCoatomic_iff /-
 protected theorem isCoatomic_iff [OrderTop α] [OrderTop β] (f : α ≃o β) :
     IsCoatomic α ↔ IsCoatomic β := by
   simp only [← isAtomic_dual_iff_isCoatomic, f.dual.is_atomic_iff]
 #align order_iso.is_coatomic_iff OrderIso.isCoatomic_iff
+-/
 
 end OrderIso
 
@@ -937,8 +1021,6 @@ namespace IsCompl
 
 variable {a b : α} (hc : IsCompl a b)
 
-include hc
-
 #print IsCompl.isAtom_iff_isCoatom /-
 theorem isAtom_iff_isCoatom : IsAtom a ↔ IsCoatom b :=
   Set.isSimpleOrder_Iic_iff_isAtom.symm.trans <|
@@ -988,10 +1070,13 @@ end IsModularLattice
 
 namespace Set
 
+#print Set.isAtom_singleton /-
 theorem isAtom_singleton (x : α) : IsAtom ({x} : Set α) :=
   ⟨singleton_ne_empty _, fun s hs => ssubset_singleton_iff.mp hs⟩
 #align set.is_atom_singleton Set.isAtom_singleton
+-/
 
+#print Set.isAtom_iff /-
 theorem isAtom_iff (s : Set α) : IsAtom s ↔ ∃ x, s = {x} :=
   by
   refine' ⟨_, by rintro ⟨x, rfl⟩; exact is_atom_singleton x⟩
@@ -1002,14 +1087,19 @@ theorem isAtom_iff (s : Set α) : IsAtom s ↔ ∃ x, s = {x} :=
       eq_singleton_iff_unique_mem.2
         ⟨hx, fun y hy => (hs {y} (singleton_ne_empty _) (singleton_subset_iff.2 hy) hx).symm⟩⟩
 #align set.is_atom_iff Set.isAtom_iff
+-/
 
+#print Set.isCoatom_iff /-
 theorem isCoatom_iff (s : Set α) : IsCoatom s ↔ ∃ x, s = {x}ᶜ := by
   simp_rw [is_compl_compl.is_coatom_iff_is_atom, isAtom_iff, @eq_comm _ s, compl_eq_comm]
 #align set.is_coatom_iff Set.isCoatom_iff
+-/
 
+#print Set.isCoatom_singleton_compl /-
 theorem isCoatom_singleton_compl (x : α) : IsCoatom ({x}ᶜ : Set α) :=
   (isCoatom_iff ({x}ᶜ)).mpr ⟨x, rfl⟩
 #align set.is_coatom_singleton_compl Set.isCoatom_singleton_compl
+-/
 
 instance : IsAtomistic (Set α)
     where eq_sSup_atoms s :=

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

@@ -85,7 +85,7 @@ theorem IsAtom.of_isAtom_coe_Iic {a : Set.Iic x} (ha : IsAtom a) : IsAtom (a : 
 #align is_atom.of_is_atom_coe_Iic IsAtom.of_isAtom_coe_Iic
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (b «expr ≠ » «expr⊥»()) -/
 theorem isAtom_iff {a : α} : IsAtom a ↔ a ≠ ⊥ ∧ ∀ (b) (_ : b ≠ ⊥), b ≤ a → a ≤ b :=
   and_congr Iff.rfl <|
     forall_congr' fun b => by simp only [Ne.def, @not_imp_comm (b = ⊥), not_imp, lt_iff_le_not_le]
@@ -165,7 +165,7 @@ theorem IsCoatom.of_isCoatom_coe_Ici {a : Set.Ici x} (ha : IsCoatom a) : IsCoato
 #align is_coatom.of_is_coatom_coe_Ici IsCoatom.of_isCoatom_coe_Ici
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (b «expr ≠ » «expr⊤»()) -/
 theorem isCoatom_iff {a : α} : IsCoatom a ↔ a ≠ ⊤ ∧ ∀ (b) (_ : b ≠ ⊤), a ≤ b → b ≤ a :=
   @isAtom_iff αᵒᵈ _ _ _
 #align is_coatom_iff isCoatom_iff

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

@@ -358,7 +358,7 @@ theorem isAtomic_of_orderBot_wellFounded_lt [OrderBot α]
     (h : WellFounded ((· < ·) : α → α → Prop)) : IsAtomic α :=
   ⟨fun a =>
     or_iff_not_imp_left.2 fun ha =>
-      let ⟨b, hb, hm⟩ := h.has_min { b | b ≠ ⊥ ∧ b ≤ a } ⟨a, ha, le_rfl⟩
+      let ⟨b, hb, hm⟩ := h.has_min {b | b ≠ ⊥ ∧ b ≤ a} ⟨a, ha, le_rfl⟩
       ⟨b, ⟨hb.1, fun c => not_imp_not.1 fun hc hl => hm c ⟨hc, hl.le.trans hb.2⟩ hl⟩, hb.2⟩⟩
 #align is_atomic_of_order_bot_well_founded_lt isAtomic_of_orderBot_wellFounded_lt
 -/
@@ -436,14 +436,14 @@ section IsAtomistic
 variable [IsAtomistic α]
 
 @[simp]
-theorem sSup_atoms_le_eq (b : α) : sSup { a : α | IsAtom a ∧ a ≤ b } = b :=
+theorem sSup_atoms_le_eq (b : α) : sSup {a : α | IsAtom a ∧ a ≤ b} = b :=
   by
   rcases eq_Sup_atoms b with ⟨s, rfl, hs⟩
   exact le_antisymm (sSup_le fun _ => And.right) (sSup_le_sSup fun a ha => ⟨hs a ha, le_sSup ha⟩)
 #align Sup_atoms_le_eq sSup_atoms_le_eq
 
 @[simp]
-theorem sSup_atoms_eq_top : sSup { a : α | IsAtom a } = ⊤ :=
+theorem sSup_atoms_eq_top : sSup {a : α | IsAtom a} = ⊤ :=
   by
   refine' Eq.trans (congr rfl (Set.ext fun x => _)) (sSup_atoms_le_eq ⊤)
   exact (and_iff_left le_top).symm

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

@@ -510,7 +510,9 @@ theorem IsSimpleOrder.bot_ne_top [LE α] [BoundedOrder α] [IsSimpleOrder α] :
   by
   obtain ⟨a, b, h⟩ := exists_pair_ne α
   rcases eq_bot_or_eq_top a with (rfl | rfl) <;> rcases eq_bot_or_eq_top b with (rfl | rfl) <;>
-    first |simpa|simpa using h.symm
+    first
+    | simpa
+    | simpa using h.symm
 #align is_simple_order.bot_ne_top IsSimpleOrder.bot_ne_top
 
 section IsSimpleOrder
@@ -790,7 +792,7 @@ namespace OrderEmbedding
 variable [PartialOrder α] [PartialOrder β]
 
 theorem isAtom_of_map_bot_of_image [OrderBot α] [OrderBot β] (f : β ↪o α) (hbot : f ⊥ = ⊥) {b : β}
-    (hb : IsAtom (f b)) : IsAtom b := by simp only [← bot_covby_iff] at hb⊢;
+    (hb : IsAtom (f b)) : IsAtom b := by simp only [← bot_covby_iff] at hb ⊢;
   exact Covby.of_image f (hbot.symm ▸ hb)
 #align order_embedding.is_atom_of_map_bot_of_image OrderEmbedding.isAtom_of_map_bot_of_image
 

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

@@ -64,20 +64,26 @@ section Preorder
 
 variable [Preorder α] [OrderBot α] {a b x : α}
 
+#print IsAtom /-
 /-- An atom of an `order_bot` is an element with no other element between it and `⊥`,
   which is not `⊥`. -/
 def IsAtom (a : α) : Prop :=
   a ≠ ⊥ ∧ ∀ b, b < a → b = ⊥
 #align is_atom IsAtom
+-/
 
+#print IsAtom.Iic /-
 theorem IsAtom.Iic (ha : IsAtom a) (hax : a ≤ x) : IsAtom (⟨a, hax⟩ : Set.Iic x) :=
   ⟨fun con => ha.1 (Subtype.mk_eq_mk.1 Con), fun ⟨b, hb⟩ hba => Subtype.mk_eq_mk.2 (ha.2 b hba)⟩
 #align is_atom.Iic IsAtom.Iic
+-/
 
+#print IsAtom.of_isAtom_coe_Iic /-
 theorem IsAtom.of_isAtom_coe_Iic {a : Set.Iic x} (ha : IsAtom a) : IsAtom (a : α) :=
   ⟨fun con => ha.1 (Subtype.ext Con), fun b hba =>
     Subtype.mk_eq_mk.1 (ha.2 ⟨b, hba.le.trans a.Prop⟩ hba)⟩
 #align is_atom.of_is_atom_coe_Iic IsAtom.of_isAtom_coe_Iic
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ≠ » «expr⊥»()) -/
 theorem isAtom_iff {a : α} : IsAtom a ↔ a ≠ ⊥ ∧ ∀ (b) (_ : b ≠ ⊥), b ≤ a → a ≤ b :=
@@ -117,21 +123,27 @@ section Preorder
 
 variable [Preorder α]
 
+#print IsCoatom /-
 /-- A coatom of an `order_top` is an element with no other element between it and `⊤`,
   which is not `⊤`. -/
 def IsCoatom [OrderTop α] (a : α) : Prop :=
   a ≠ ⊤ ∧ ∀ b, a < b → b = ⊤
 #align is_coatom IsCoatom
+-/
 
+#print isCoatom_dual_iff_isAtom /-
 @[simp]
 theorem isCoatom_dual_iff_isAtom [OrderBot α] {a : α} : IsCoatom (OrderDual.toDual a) ↔ IsAtom a :=
   Iff.rfl
 #align is_coatom_dual_iff_is_atom isCoatom_dual_iff_isAtom
+-/
 
+#print isAtom_dual_iff_isCoatom /-
 @[simp]
 theorem isAtom_dual_iff_isCoatom [OrderTop α] {a : α} : IsAtom (OrderDual.toDual a) ↔ IsCoatom a :=
   Iff.rfl
 #align is_atom_dual_iff_is_coatom isAtom_dual_iff_isCoatom
+-/
 
 alias isCoatom_dual_iff_isAtom ↔ _ IsAtom.dual
 #align is_atom.dual IsAtom.dual
@@ -141,13 +153,17 @@ alias isAtom_dual_iff_isCoatom ↔ _ IsCoatom.dual
 
 variable [OrderTop α] {a x : α}
 
+#print IsCoatom.Ici /-
 theorem IsCoatom.Ici (ha : IsCoatom a) (hax : x ≤ a) : IsCoatom (⟨a, hax⟩ : Set.Ici x) :=
   ha.dual.Iic hax
 #align is_coatom.Ici IsCoatom.Ici
+-/
 
+#print IsCoatom.of_isCoatom_coe_Ici /-
 theorem IsCoatom.of_isCoatom_coe_Ici {a : Set.Ici x} (ha : IsCoatom a) : IsCoatom (a : α) :=
   @IsAtom.of_isAtom_coe_Iic αᵒᵈ _ _ x a ha
 #align is_coatom.of_is_coatom_coe_Ici IsCoatom.of_isCoatom_coe_Ici
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ≠ » «expr⊤»()) -/
 theorem isCoatom_iff {a : α} : IsCoatom a ↔ a ≠ ⊤ ∧ ∀ (b) (_ : b ≠ ⊤), a ≤ b → b ≤ a :=
@@ -185,6 +201,7 @@ section PartialOrder
 
 variable [PartialOrder α] {a b : α}
 
+#print Set.Ici.isAtom_iff /-
 @[simp]
 theorem Set.Ici.isAtom_iff {b : Set.Ici a} : IsAtom b ↔ a ⋖ b :=
   by
@@ -192,7 +209,9 @@ theorem Set.Ici.isAtom_iff {b : Set.Ici a} : IsAtom b ↔ a ⋖ b :=
   refine' (Set.OrdConnected.apply_covby_apply_iff (OrderEmbedding.subtype fun c => a ≤ c) _).symm
   simpa only [OrderEmbedding.subtype_apply, Subtype.range_coe_subtype] using Set.ordConnected_Ici
 #align set.Ici.is_atom_iff Set.Ici.isAtom_iff
+-/
 
+#print Set.Iic.isCoatom_iff /-
 @[simp]
 theorem Set.Iic.isCoatom_iff {a : Set.Iic b} : IsCoatom a ↔ ↑a ⋖ b :=
   by
@@ -200,12 +219,17 @@ theorem Set.Iic.isCoatom_iff {a : Set.Iic b} : IsCoatom a ↔ ↑a ⋖ b :=
   refine' (Set.OrdConnected.apply_covby_apply_iff (OrderEmbedding.subtype fun c => c ≤ b) _).symm
   simpa only [OrderEmbedding.subtype_apply, Subtype.range_coe_subtype] using Set.ordConnected_Iic
 #align set.Iic.is_coatom_iff Set.Iic.isCoatom_iff
+-/
 
+#print covby_iff_atom_Ici /-
 theorem covby_iff_atom_Ici (h : a ≤ b) : a ⋖ b ↔ IsAtom (⟨b, h⟩ : Set.Ici a) := by simp
 #align covby_iff_atom_Ici covby_iff_atom_Ici
+-/
 
+#print covby_iff_coatom_Iic /-
 theorem covby_iff_coatom_Iic (h : a ≤ b) : a ⋖ b ↔ IsCoatom (⟨a, h⟩ : Set.Iic b) := by simp
 #align covby_iff_coatom_Iic covby_iff_coatom_Iic
+-/
 
 end PartialOrder
 
@@ -216,10 +240,12 @@ theorem IsAtom.inf_eq_bot_of_ne [SemilatticeInf α] [OrderBot α] {a b : α} (ha
   hab.not_le_or_not_le.elim (ha.lt_iff.1 ∘ inf_lt_left.2) (hb.lt_iff.1 ∘ inf_lt_right.2)
 #align is_atom.inf_eq_bot_of_ne IsAtom.inf_eq_bot_of_ne
 
+#print IsAtom.disjoint_of_ne /-
 theorem IsAtom.disjoint_of_ne [SemilatticeInf α] [OrderBot α] {a b : α} (ha : IsAtom a)
     (hb : IsAtom b) (hab : a ≠ b) : Disjoint a b :=
   disjoint_iff.mpr (IsAtom.inf_eq_bot_of_ne ha hb hab)
 #align is_atom.disjoint_of_ne IsAtom.disjoint_of_ne
+-/
 
 theorem IsCoatom.sup_eq_top_of_ne [SemilatticeSup α] [OrderTop α] {a b : α} (ha : IsCoatom a)
     (hb : IsCoatom b) (hab : a ≠ b) : a ⊔ b = ⊤ :=
@@ -234,17 +260,21 @@ section Atomic
 
 variable [PartialOrder α] (α)
 
+#print IsAtomic /-
 /-- A lattice is atomic iff every element other than `⊥` has an atom below it. -/
 @[mk_iff]
 class IsAtomic [OrderBot α] : Prop where
   eq_bot_or_exists_atom_le : ∀ b : α, b = ⊥ ∨ ∃ a : α, IsAtom a ∧ a ≤ b
 #align is_atomic IsAtomic
+-/
 
+#print IsCoatomic /-
 /-- A lattice is coatomic iff every element other than `⊤` has a coatom above it. -/
 @[mk_iff]
 class IsCoatomic [OrderTop α] : Prop where
   eq_top_or_exists_le_coatom : ∀ b : α, b = ⊤ ∨ ∃ a : α, IsCoatom a ∧ b ≤ a
 #align is_coatomic IsCoatomic
+-/
 
 export IsAtomic (eq_bot_or_exists_atom_le)
 
@@ -252,25 +282,31 @@ export IsCoatomic (eq_top_or_exists_le_coatom)
 
 variable {α}
 
+#print isCoatomic_dual_iff_isAtomic /-
 @[simp]
 theorem isCoatomic_dual_iff_isAtomic [OrderBot α] : IsCoatomic αᵒᵈ ↔ IsAtomic α :=
   ⟨fun h => ⟨fun b => by apply h.eq_top_or_exists_le_coatom⟩, fun h =>
     ⟨fun b => by apply h.eq_bot_or_exists_atom_le⟩⟩
 #align is_coatomic_dual_iff_is_atomic isCoatomic_dual_iff_isAtomic
+-/
 
+#print isAtomic_dual_iff_isCoatomic /-
 @[simp]
 theorem isAtomic_dual_iff_isCoatomic [OrderTop α] : IsAtomic αᵒᵈ ↔ IsCoatomic α :=
   ⟨fun h => ⟨fun b => by apply h.eq_bot_or_exists_atom_le⟩, fun h =>
     ⟨fun b => by apply h.eq_top_or_exists_le_coatom⟩⟩
 #align is_atomic_dual_iff_is_coatomic isAtomic_dual_iff_isCoatomic
+-/
 
 namespace IsAtomic
 
 variable [OrderBot α] [IsAtomic α]
 
+#print IsAtomic.isCoatomic_dual /-
 instance isCoatomic_dual : IsCoatomic αᵒᵈ :=
   isCoatomic_dual_iff_isAtomic.2 ‹IsAtomic α›
 #align is_atomic.is_coatomic_dual IsAtomic.isCoatomic_dual
+-/
 
 instance {x : α} : IsAtomic (Set.Iic x) :=
   ⟨fun ⟨y, hy⟩ =>
@@ -283,9 +319,11 @@ namespace IsCoatomic
 
 variable [OrderTop α] [IsCoatomic α]
 
+#print IsCoatomic.isCoatomic /-
 instance isCoatomic : IsAtomic αᵒᵈ :=
   isAtomic_dual_iff_isCoatomic.2 ‹IsCoatomic α›
 #align is_coatomic.is_coatomic IsCoatomic.isCoatomic
+-/
 
 instance {x : α} : IsCoatomic (Set.Ici x) :=
   ⟨fun ⟨y, hy⟩ =>
@@ -294,6 +332,7 @@ instance {x : α} : IsCoatomic (Set.Ici x) :=
 
 end IsCoatomic
 
+#print isAtomic_iff_forall_isAtomic_Iic /-
 theorem isAtomic_iff_forall_isAtomic_Iic [OrderBot α] :
     IsAtomic α ↔ ∀ x : α, IsAtomic (Set.Iic x) :=
   ⟨@IsAtomic.Set.Iic.isAtomic _ _ _, fun h =>
@@ -301,16 +340,20 @@ theorem isAtomic_iff_forall_isAtomic_Iic [OrderBot α] :
       ((@eq_bot_or_exists_atom_le _ _ _ (h x)) (⊤ : Set.Iic x)).imp Subtype.mk_eq_mk.1
         (Exists.imp' coe fun ⟨a, ha⟩ => And.imp_left IsAtom.of_isAtom_coe_Iic)⟩⟩
 #align is_atomic_iff_forall_is_atomic_Iic isAtomic_iff_forall_isAtomic_Iic
+-/
 
+#print isCoatomic_iff_forall_isCoatomic_Ici /-
 theorem isCoatomic_iff_forall_isCoatomic_Ici [OrderTop α] :
     IsCoatomic α ↔ ∀ x : α, IsCoatomic (Set.Ici x) :=
   isAtomic_dual_iff_isCoatomic.symm.trans <|
     isAtomic_iff_forall_isAtomic_Iic.trans <|
       forall_congr' fun x => isCoatomic_dual_iff_isAtomic.symm.trans Iff.rfl
 #align is_coatomic_iff_forall_is_coatomic_Ici isCoatomic_iff_forall_isCoatomic_Ici
+-/
 
 section WellFounded
 
+#print isAtomic_of_orderBot_wellFounded_lt /-
 theorem isAtomic_of_orderBot_wellFounded_lt [OrderBot α]
     (h : WellFounded ((· < ·) : α → α → Prop)) : IsAtomic α :=
   ⟨fun a =>
@@ -318,11 +361,14 @@ theorem isAtomic_of_orderBot_wellFounded_lt [OrderBot α]
       let ⟨b, hb, hm⟩ := h.has_min { b | b ≠ ⊥ ∧ b ≤ a } ⟨a, ha, le_rfl⟩
       ⟨b, ⟨hb.1, fun c => not_imp_not.1 fun hc hl => hm c ⟨hc, hl.le.trans hb.2⟩ hl⟩, hb.2⟩⟩
 #align is_atomic_of_order_bot_well_founded_lt isAtomic_of_orderBot_wellFounded_lt
+-/
 
+#print isCoatomic_of_orderTop_gt_wellFounded /-
 theorem isCoatomic_of_orderTop_gt_wellFounded [OrderTop α]
     (h : WellFounded ((· > ·) : α → α → Prop)) : IsCoatomic α :=
   isAtomic_dual_iff_isCoatomic.1 (@isAtomic_of_orderBot_wellFounded_lt αᵒᵈ _ _ h)
 #align is_coatomic_of_order_top_gt_well_founded isCoatomic_of_orderTop_gt_wellFounded
+-/
 
 end WellFounded
 
@@ -403,12 +449,14 @@ theorem sSup_atoms_eq_top : sSup { a : α | IsAtom a } = ⊤ :=
   exact (and_iff_left le_top).symm
 #align Sup_atoms_eq_top sSup_atoms_eq_top
 
+#print le_iff_atom_le_imp /-
 theorem le_iff_atom_le_imp {a b : α} : a ≤ b ↔ ∀ c : α, IsAtom c → c ≤ a → c ≤ b :=
   ⟨fun ab c hc ca => le_trans ca ab, fun h =>
     by
     rw [← sSup_atoms_le_eq a, ← sSup_atoms_le_eq b]
     exact sSup_le_sSup fun c hc => ⟨hc.1, h c hc.1 hc.2⟩⟩
 #align le_iff_atom_le_imp le_iff_atom_le_imp
+-/
 
 end IsAtomistic
 
@@ -487,6 +535,7 @@ protected def IsSimpleOrder.preorder {α} [LE α] [BoundedOrder α] [IsSimpleOrd
 #align is_simple_order.preorder IsSimpleOrder.preorder
 -/
 
+#print IsSimpleOrder.linearOrder /-
 /-- A simple partial ordered `bounded_order` induces a linear order.
 This is not an instance to prevent loops. -/
 protected def IsSimpleOrder.linearOrder [DecidableEq α] : LinearOrder α :=
@@ -504,6 +553,7 @@ protected def IsSimpleOrder.linearOrder [DecidableEq α] : LinearOrder α :=
             hb (top_unique (le_trans (top_le_iff.mpr (Or.resolve_left (eq_bot_or_eq_top a) ha)) H))
     DecidableEq := by assumption }
 #align is_simple_order.linear_order IsSimpleOrder.linearOrder
+-/
 
 @[simp]
 theorem isAtom_top : IsAtom (⊤ : α) :=
@@ -547,19 +597,23 @@ section BoundedOrder
 
 variable [Lattice α] [BoundedOrder α] [IsSimpleOrder α]
 
+#print IsSimpleOrder.lattice /-
 /-- A simple partial ordered `bounded_order` induces a lattice.
 This is not an instance to prevent loops -/
 protected def lattice {α} [DecidableEq α] [PartialOrder α] [BoundedOrder α] [IsSimpleOrder α] :
     Lattice α :=
   @LinearOrder.toLattice α IsSimpleOrder.linearOrder
 #align is_simple_order.lattice IsSimpleOrder.lattice
+-/
 
+#print IsSimpleOrder.distribLattice /-
 /-- A lattice that is a `bounded_order` is a distributive lattice.
 This is not an instance to prevent loops -/
 protected def distribLattice : DistribLattice α :=
   { (inferInstance : Lattice α) with
     le_sup_inf := fun x y z => by rcases eq_bot_or_eq_top x with (rfl | rfl) <;> simp }
 #align is_simple_order.distrib_lattice IsSimpleOrder.distribLattice
+-/
 
 -- see Note [lower instance priority]
 instance (priority := 100) : IsAtomic α :=
@@ -600,6 +654,7 @@ def orderIsoBool : α ≃o Bool :=
         · simp [bot_ne_top] }
 #align is_simple_order.order_iso_bool IsSimpleOrder.orderIsoBool
 
+#print IsSimpleOrder.booleanAlgebra /-
 /-- A simple `bounded_order` is also a `boolean_algebra`. -/
 protected def booleanAlgebra {α} [DecidableEq α] [Lattice α] [BoundedOrder α] [IsSimpleOrder α] :
     BooleanAlgebra α :=
@@ -617,13 +672,15 @@ protected def booleanAlgebra {α} [DecidableEq α] [Lattice α] [BoundedOrder α
         split_ifs with h h <;> simp [h]
     top_le_sup_compl := fun x => by rcases eq_bot_or_eq_top x with (rfl | rfl) <;> simp }
 #align is_simple_order.boolean_algebra IsSimpleOrder.booleanAlgebra
+-/
 
 end DecidableEq
 
 variable [Lattice α] [BoundedOrder α] [IsSimpleOrder α]
 
-open Classical
+open scoped Classical
 
+#print IsSimpleOrder.completeLattice /-
 /-- A simple `bounded_order` is also complete. -/
 protected noncomputable def completeLattice : CompleteLattice α :=
   { (inferInstance : Lattice α),
@@ -652,7 +709,9 @@ protected noncomputable def completeLattice : CompleteLattice α :=
         intro con
         exact top_ne_bot (eq_bot_iff.2 (h ⊥ Con)) }
 #align is_simple_order.complete_lattice IsSimpleOrder.completeLattice
+-/
 
+#print IsSimpleOrder.completeBooleanAlgebra /-
 /-- A simple `bounded_order` is also a `complete_boolean_algebra`. -/
 protected noncomputable def completeBooleanAlgebra : CompleteBooleanAlgebra α :=
   { IsSimpleOrder.completeLattice,
@@ -668,6 +727,7 @@ protected noncomputable def completeBooleanAlgebra : CompleteBooleanAlgebra α :
       · simp only [bot_inf_eq, bot_le]
       · simp only [top_inf_eq, ← sSup_eq_iSup]; exact le_rfl }
 #align is_simple_order.complete_boolean_algebra IsSimpleOrder.completeBooleanAlgebra
+-/
 
 end IsSimpleOrder
 
@@ -713,6 +773,7 @@ theorem isSimpleOrder_Iic_iff_isAtom [PartialOrder α] [OrderBot α] {a : α} :
         Subtype.mk_eq_mk.2 (h b (Subtype.mk_lt_mk.1 hbotb))⟩
 #align set.is_simple_order_Iic_iff_is_atom Set.isSimpleOrder_Iic_iff_isAtom
 
+#print Set.isSimpleOrder_Ici_iff_isCoatom /-
 theorem isSimpleOrder_Ici_iff_isCoatom [PartialOrder α] [OrderTop α] {a : α} :
     IsSimpleOrder (Ici a) ↔ IsCoatom a :=
   isSimpleOrder_iff_isCoatom_bot.trans <|
@@ -720,6 +781,7 @@ theorem isSimpleOrder_Ici_iff_isCoatom [PartialOrder α] [OrderTop α] {a : α}
       ⟨fun h b ab => Subtype.mk_eq_mk.1 (h ⟨b, le_of_lt ab⟩ ab), fun h ⟨b, hab⟩ hbotb =>
         Subtype.mk_eq_mk.2 (h b (Subtype.mk_lt_mk.1 hbotb))⟩
 #align set.is_simple_order_Ici_iff_is_coatom Set.isSimpleOrder_Ici_iff_isCoatom
+-/
 
 end Set
 
@@ -875,19 +937,24 @@ variable {a b : α} (hc : IsCompl a b)
 
 include hc
 
+#print IsCompl.isAtom_iff_isCoatom /-
 theorem isAtom_iff_isCoatom : IsAtom a ↔ IsCoatom b :=
   Set.isSimpleOrder_Iic_iff_isAtom.symm.trans <|
     hc.IicOrderIsoIci.isSimpleOrder_iff.trans Set.isSimpleOrder_Ici_iff_isCoatom
 #align is_compl.is_atom_iff_is_coatom IsCompl.isAtom_iff_isCoatom
+-/
 
+#print IsCompl.isCoatom_iff_isAtom /-
 theorem isCoatom_iff_isAtom : IsCoatom a ↔ IsAtom b :=
   hc.symm.isAtom_iff_isCoatom.symm
 #align is_compl.is_coatom_iff_is_atom IsCompl.isCoatom_iff_isAtom
+-/
 
 end IsCompl
 
 variable [ComplementedLattice α]
 
+#print isCoatomic_of_isAtomic_of_complementedLattice_of_isModular /-
 theorem isCoatomic_of_isAtomic_of_complementedLattice_of_isModular [IsAtomic α] : IsCoatomic α :=
   ⟨fun x => by
     rcases exists_is_compl x with ⟨y, xy⟩
@@ -900,15 +967,20 @@ theorem isCoatomic_of_isAtomic_of_complementedLattice_of_isModular [IsAtomic α]
       rw [← hb.is_atom_iff_is_coatom, OrderIso.isAtom_iff]
       apply ha.Iic⟩
 #align is_coatomic_of_is_atomic_of_complemented_lattice_of_is_modular isCoatomic_of_isAtomic_of_complementedLattice_of_isModular
+-/
 
+#print isAtomic_of_isCoatomic_of_complementedLattice_of_isModular /-
 theorem isAtomic_of_isCoatomic_of_complementedLattice_of_isModular [IsCoatomic α] : IsAtomic α :=
   isCoatomic_dual_iff_isAtomic.1 isCoatomic_of_isAtomic_of_complementedLattice_of_isModular
 #align is_atomic_of_is_coatomic_of_complemented_lattice_of_is_modular isAtomic_of_isCoatomic_of_complementedLattice_of_isModular
+-/
 
+#print isAtomic_iff_isCoatomic /-
 theorem isAtomic_iff_isCoatomic : IsAtomic α ↔ IsCoatomic α :=
   ⟨fun h => @isCoatomic_of_isAtomic_of_complementedLattice_of_isModular _ _ _ _ _ h, fun h =>
     @isAtomic_of_isCoatomic_of_complementedLattice_of_isModular _ _ _ _ _ h⟩
 #align is_atomic_iff_is_coatomic isAtomic_iff_isCoatomic
+-/
 
 end IsModularLattice
 

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

@@ -64,45 +64,21 @@ section Preorder
 
 variable [Preorder α] [OrderBot α] {a b x : α}
 
-/- warning: is_atom -> IsAtom is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], α -> Prop
-but is expected to have type
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 /-- An atom of an `order_bot` is an element with no other element between it and `⊥`,
   which is not `⊥`. -/
 def IsAtom (a : α) : Prop :=
   a ≠ ⊥ ∧ ∀ b, b < a → b = ⊥
 #align is_atom IsAtom
 
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 theorem IsAtom.Iic (ha : IsAtom a) (hax : a ≤ x) : IsAtom (⟨a, hax⟩ : Set.Iic x) :=
   ⟨fun con => ha.1 (Subtype.mk_eq_mk.1 Con), fun ⟨b, hb⟩ hba => Subtype.mk_eq_mk.2 (ha.2 b hba)⟩
 #align is_atom.Iic IsAtom.Iic
 
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 theorem IsAtom.of_isAtom_coe_Iic {a : Set.Iic x} (ha : IsAtom a) : IsAtom (a : α) :=
   ⟨fun con => ha.1 (Subtype.ext Con), fun b hba =>
     Subtype.mk_eq_mk.1 (ha.2 ⟨b, hba.le.trans a.Prop⟩ hba)⟩
 #align is_atom.of_is_atom_coe_Iic IsAtom.of_isAtom_coe_Iic
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ≠ » «expr⊥»()) -/
 theorem isAtom_iff {a : α} : IsAtom a ↔ a ≠ ⊥ ∧ ∀ (b) (_ : b ≠ ⊥), b ≤ a → a ≤ b :=
   and_congr Iff.rfl <|
@@ -113,58 +89,22 @@ end Preorder
 
 variable [PartialOrder α] [OrderBot α] {a b x : α}
 
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 theorem IsAtom.lt_iff (h : IsAtom a) : x < a ↔ x = ⊥ :=
   ⟨h.2 x, fun hx => hx.symm ▸ h.1.bot_lt⟩
 #align is_atom.lt_iff IsAtom.lt_iff
 
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 theorem IsAtom.le_iff (h : IsAtom a) : x ≤ a ↔ x = ⊥ ∨ x = a := by rw [le_iff_lt_or_eq, h.lt_iff]
 #align is_atom.le_iff IsAtom.le_iff
 
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 theorem IsAtom.Iic_eq (h : IsAtom a) : Set.Iic a = {⊥, a} :=
   Set.ext fun x => h.le_iff
 #align is_atom.Iic_eq IsAtom.Iic_eq
 
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 @[simp]
 theorem bot_covby_iff : ⊥ ⋖ a ↔ IsAtom a := by
   simp only [Covby, bot_lt_iff_ne_bot, IsAtom, not_imp_not]
 #align bot_covby_iff bot_covby_iff
 
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 alias bot_covby_iff ↔ Covby.is_atom IsAtom.bot_covby
 #align covby.is_atom Covby.is_atom
 #align is_atom.bot_covby IsAtom.bot_covby
@@ -177,86 +117,38 @@ section Preorder
 
 variable [Preorder α]
 
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 /-- A coatom of an `order_top` is an element with no other element between it and `⊤`,
   which is not `⊤`. -/
 def IsCoatom [OrderTop α] (a : α) : Prop :=
   a ≠ ⊤ ∧ ∀ b, a < b → b = ⊤
 #align is_coatom IsCoatom
 
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 @[simp]
 theorem isCoatom_dual_iff_isAtom [OrderBot α] {a : α} : IsCoatom (OrderDual.toDual a) ↔ IsAtom a :=
   Iff.rfl
 #align is_coatom_dual_iff_is_atom isCoatom_dual_iff_isAtom
 
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 @[simp]
 theorem isAtom_dual_iff_isCoatom [OrderTop α] {a : α} : IsAtom (OrderDual.toDual a) ↔ IsCoatom a :=
   Iff.rfl
 #align is_atom_dual_iff_is_coatom isAtom_dual_iff_isCoatom
 
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 alias isCoatom_dual_iff_isAtom ↔ _ IsAtom.dual
 #align is_atom.dual IsAtom.dual
 
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 alias isAtom_dual_iff_isCoatom ↔ _ IsCoatom.dual
 #align is_coatom.dual IsCoatom.dual
 
 variable [OrderTop α] {a x : α}
 
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 theorem IsCoatom.Ici (ha : IsCoatom a) (hax : x ≤ a) : IsCoatom (⟨a, hax⟩ : Set.Ici x) :=
   ha.dual.Iic hax
 #align is_coatom.Ici IsCoatom.Ici
 
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 theorem IsCoatom.of_isCoatom_coe_Ici {a : Set.Ici x} (ha : IsCoatom a) : IsCoatom (a : α) :=
   @IsAtom.of_isAtom_coe_Iic αᵒᵈ _ _ x a ha
 #align is_coatom.of_is_coatom_coe_Ici IsCoatom.of_isCoatom_coe_Ici
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ≠ » «expr⊤»()) -/
 theorem isCoatom_iff {a : α} : IsCoatom a ↔ a ≠ ⊤ ∧ ∀ (b) (_ : b ≠ ⊤), a ≤ b → b ≤ a :=
   @isAtom_iff αᵒᵈ _ _ _
@@ -266,59 +158,23 @@ end Preorder
 
 variable [PartialOrder α] [OrderTop α] {a b x : α}
 
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 theorem IsCoatom.lt_iff (h : IsCoatom a) : a < x ↔ x = ⊤ :=
   h.dual.lt_iff
 #align is_coatom.lt_iff IsCoatom.lt_iff
 
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 theorem IsCoatom.le_iff (h : IsCoatom a) : a ≤ x ↔ x = ⊤ ∨ x = a :=
   h.dual.le_iff
 #align is_coatom.le_iff IsCoatom.le_iff
 
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 theorem IsCoatom.Ici_eq (h : IsCoatom a) : Set.Ici a = {⊤, a} :=
   h.dual.Iic_eq
 #align is_coatom.Ici_eq IsCoatom.Ici_eq
 
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 @[simp]
 theorem covby_top_iff : a ⋖ ⊤ ↔ IsCoatom a :=
   toDual_covby_toDual_iff.symm.trans bot_covby_iff
 #align covby_top_iff covby_top_iff
 
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 alias covby_top_iff ↔ Covby.is_coatom IsCoatom.covby_top
 #align covby.is_coatom Covby.is_coatom
 #align is_coatom.covby_top IsCoatom.covby_top
@@ -329,12 +185,6 @@ section PartialOrder
 
 variable [PartialOrder α] {a b : α}
 
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 @[simp]
 theorem Set.Ici.isAtom_iff {b : Set.Ici a} : IsAtom b ↔ a ⋖ b :=
   by
@@ -343,12 +193,6 @@ theorem Set.Ici.isAtom_iff {b : Set.Ici a} : IsAtom b ↔ a ⋖ b :=
   simpa only [OrderEmbedding.subtype_apply, Subtype.range_coe_subtype] using Set.ordConnected_Ici
 #align set.Ici.is_atom_iff Set.Ici.isAtom_iff
 
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 @[simp]
 theorem Set.Iic.isCoatom_iff {a : Set.Iic b} : IsCoatom a ↔ ↑a ⋖ b :=
   by
@@ -357,21 +201,9 @@ theorem Set.Iic.isCoatom_iff {a : Set.Iic b} : IsCoatom a ↔ ↑a ⋖ b :=
   simpa only [OrderEmbedding.subtype_apply, Subtype.range_coe_subtype] using Set.ordConnected_Iic
 #align set.Iic.is_coatom_iff Set.Iic.isCoatom_iff
 
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 theorem covby_iff_atom_Ici (h : a ≤ b) : a ⋖ b ↔ IsAtom (⟨b, h⟩ : Set.Ici a) := by simp
 #align covby_iff_atom_Ici covby_iff_atom_Ici
 
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 theorem covby_iff_coatom_Iic (h : a ≤ b) : a ⋖ b ↔ IsCoatom (⟨a, h⟩ : Set.Iic b) := by simp
 #align covby_iff_coatom_Iic covby_iff_coatom_Iic
 
@@ -379,34 +211,16 @@ end PartialOrder
 
 section Pairwise
 
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 theorem IsAtom.inf_eq_bot_of_ne [SemilatticeInf α] [OrderBot α] {a b : α} (ha : IsAtom a)
     (hb : IsAtom b) (hab : a ≠ b) : a ⊓ b = ⊥ :=
   hab.not_le_or_not_le.elim (ha.lt_iff.1 ∘ inf_lt_left.2) (hb.lt_iff.1 ∘ inf_lt_right.2)
 #align is_atom.inf_eq_bot_of_ne IsAtom.inf_eq_bot_of_ne
 
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 theorem IsAtom.disjoint_of_ne [SemilatticeInf α] [OrderBot α] {a b : α} (ha : IsAtom a)
     (hb : IsAtom b) (hab : a ≠ b) : Disjoint a b :=
   disjoint_iff.mpr (IsAtom.inf_eq_bot_of_ne ha hb hab)
 #align is_atom.disjoint_of_ne IsAtom.disjoint_of_ne
 
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 theorem IsCoatom.sup_eq_top_of_ne [SemilatticeSup α] [OrderTop α] {a b : α} (ha : IsCoatom a)
     (hb : IsCoatom b) (hab : a ≠ b) : a ⊔ b = ⊤ :=
   ha.dual.inf_eq_bot_of_ne hb.dual hab
@@ -420,24 +234,12 @@ section Atomic
 
 variable [PartialOrder α] (α)
 
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-Case conversion may be inaccurate. Consider using '#align is_atomic IsAtomicₓ'. -/
 /-- A lattice is atomic iff every element other than `⊥` has an atom below it. -/
 @[mk_iff]
 class IsAtomic [OrderBot α] : Prop where
   eq_bot_or_exists_atom_le : ∀ b : α, b = ⊥ ∨ ∃ a : α, IsAtom a ∧ a ≤ b
 #align is_atomic IsAtomic
 
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 /-- A lattice is coatomic iff every element other than `⊤` has a coatom above it. -/
 @[mk_iff]
 class IsCoatomic [OrderTop α] : Prop where
@@ -450,24 +252,12 @@ export IsCoatomic (eq_top_or_exists_le_coatom)
 
 variable {α}
 
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 @[simp]
 theorem isCoatomic_dual_iff_isAtomic [OrderBot α] : IsCoatomic αᵒᵈ ↔ IsAtomic α :=
   ⟨fun h => ⟨fun b => by apply h.eq_top_or_exists_le_coatom⟩, fun h =>
     ⟨fun b => by apply h.eq_bot_or_exists_atom_le⟩⟩
 #align is_coatomic_dual_iff_is_atomic isCoatomic_dual_iff_isAtomic
 
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 @[simp]
 theorem isAtomic_dual_iff_isCoatomic [OrderTop α] : IsAtomic αᵒᵈ ↔ IsCoatomic α :=
   ⟨fun h => ⟨fun b => by apply h.eq_bot_or_exists_atom_le⟩, fun h =>
@@ -478,12 +268,6 @@ namespace IsAtomic
 
 variable [OrderBot α] [IsAtomic α]
 
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 instance isCoatomic_dual : IsCoatomic αᵒᵈ :=
   isCoatomic_dual_iff_isAtomic.2 ‹IsAtomic α›
 #align is_atomic.is_coatomic_dual IsAtomic.isCoatomic_dual
@@ -499,12 +283,6 @@ namespace IsCoatomic
 
 variable [OrderTop α] [IsCoatomic α]
 
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 instance isCoatomic : IsAtomic αᵒᵈ :=
   isAtomic_dual_iff_isCoatomic.2 ‹IsCoatomic α›
 #align is_coatomic.is_coatomic IsCoatomic.isCoatomic
@@ -516,12 +294,6 @@ instance {x : α} : IsCoatomic (Set.Ici x) :=
 
 end IsCoatomic
 
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 theorem isAtomic_iff_forall_isAtomic_Iic [OrderBot α] :
     IsAtomic α ↔ ∀ x : α, IsAtomic (Set.Iic x) :=
   ⟨@IsAtomic.Set.Iic.isAtomic _ _ _, fun h =>
@@ -530,12 +302,6 @@ theorem isAtomic_iff_forall_isAtomic_Iic [OrderBot α] :
         (Exists.imp' coe fun ⟨a, ha⟩ => And.imp_left IsAtom.of_isAtom_coe_Iic)⟩⟩
 #align is_atomic_iff_forall_is_atomic_Iic isAtomic_iff_forall_isAtomic_Iic
 
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 theorem isCoatomic_iff_forall_isCoatomic_Ici [OrderTop α] :
     IsCoatomic α ↔ ∀ x : α, IsCoatomic (Set.Ici x) :=
   isAtomic_dual_iff_isCoatomic.symm.trans <|
@@ -545,12 +311,6 @@ theorem isCoatomic_iff_forall_isCoatomic_Ici [OrderTop α] :
 
 section WellFounded
 
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 theorem isAtomic_of_orderBot_wellFounded_lt [OrderBot α]
     (h : WellFounded ((· < ·) : α → α → Prop)) : IsAtomic α :=
   ⟨fun a =>
@@ -559,12 +319,6 @@ theorem isAtomic_of_orderBot_wellFounded_lt [OrderBot α]
       ⟨b, ⟨hb.1, fun c => not_imp_not.1 fun hc hl => hm c ⟨hc, hl.le.trans hb.2⟩ hl⟩, hb.2⟩⟩
 #align is_atomic_of_order_bot_well_founded_lt isAtomic_of_orderBot_wellFounded_lt
 
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 theorem isCoatomic_of_orderTop_gt_wellFounded [OrderTop α]
     (h : WellFounded ((· > ·) : α → α → Prop)) : IsCoatomic α :=
   isAtomic_dual_iff_isCoatomic.1 (@isAtomic_of_orderBot_wellFounded_lt αᵒᵈ _ _ h)
@@ -635,12 +389,6 @@ section IsAtomistic
 
 variable [IsAtomistic α]
 
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 @[simp]
 theorem sSup_atoms_le_eq (b : α) : sSup { a : α | IsAtom a ∧ a ≤ b } = b :=
   by
@@ -648,12 +396,6 @@ theorem sSup_atoms_le_eq (b : α) : sSup { a : α | IsAtom a ∧ a ≤ b } = b :
   exact le_antisymm (sSup_le fun _ => And.right) (sSup_le_sSup fun a ha => ⟨hs a ha, le_sSup ha⟩)
 #align Sup_atoms_le_eq sSup_atoms_le_eq
 
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 @[simp]
 theorem sSup_atoms_eq_top : sSup { a : α | IsAtom a } = ⊤ :=
   by
@@ -661,12 +403,6 @@ theorem sSup_atoms_eq_top : sSup { a : α | IsAtom a } = ⊤ :=
   exact (and_iff_left le_top).symm
 #align Sup_atoms_eq_top sSup_atoms_eq_top
 
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 theorem le_iff_atom_le_imp {a b : α} : a ≤ b ↔ ∀ c : α, IsAtom c → c ≤ a → c ≤ b :=
   ⟨fun ab c hc ca => le_trans ca ab, fun h =>
     by
@@ -722,12 +458,6 @@ theorem isSimpleOrder_iff_isSimpleOrder_orderDual [LE α] [BoundedOrder α] :
 #align is_simple_order_iff_is_simple_order_order_dual isSimpleOrder_iff_isSimpleOrder_orderDual
 -/
 
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 theorem IsSimpleOrder.bot_ne_top [LE α] [BoundedOrder α] [IsSimpleOrder α] : (⊥ : α) ≠ (⊤ : α) :=
   by
   obtain ⟨a, b, h⟩ := exists_pair_ne α
@@ -757,12 +487,6 @@ protected def IsSimpleOrder.preorder {α} [LE α] [BoundedOrder α] [IsSimpleOrd
 #align is_simple_order.preorder IsSimpleOrder.preorder
 -/
 
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 /-- A simple partial ordered `bounded_order` induces a linear order.
 This is not an instance to prevent loops. -/
 protected def IsSimpleOrder.linearOrder [DecidableEq α] : LinearOrder α :=
@@ -781,34 +505,16 @@ protected def IsSimpleOrder.linearOrder [DecidableEq α] : LinearOrder α :=
     DecidableEq := by assumption }
 #align is_simple_order.linear_order IsSimpleOrder.linearOrder
 
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 @[simp]
 theorem isAtom_top : IsAtom (⊤ : α) :=
   ⟨top_ne_bot, fun a ha => Or.resolve_right (eq_bot_or_eq_top a) (ne_of_lt ha)⟩
 #align is_atom_top isAtom_top
 
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 @[simp]
 theorem isCoatom_bot : IsCoatom (⊥ : α) :=
   isAtom_dual_iff_isCoatom.1 isAtom_top
 #align is_coatom_bot isCoatom_bot
 
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 theorem bot_covby_top : (⊥ : α) ⋖ ⊤ :=
   isAtom_top.bot_covby
 #align bot_covby_top bot_covby_top
@@ -821,22 +527,10 @@ section Preorder
 
 variable [Preorder α] [BoundedOrder α] [IsSimpleOrder α] {a b : α} (h : a < b)
 
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 theorem eq_bot_of_lt : a = ⊥ :=
   (IsSimpleOrder.eq_bot_or_eq_top _).resolve_right h.ne_top
 #align is_simple_order.eq_bot_of_lt IsSimpleOrder.eq_bot_of_lt
 
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 theorem eq_top_of_lt : b = ⊤ :=
   (IsSimpleOrder.eq_bot_or_eq_top _).resolve_left h.ne_bot
 #align is_simple_order.eq_top_of_lt IsSimpleOrder.eq_top_of_lt
@@ -853,12 +547,6 @@ section BoundedOrder
 
 variable [Lattice α] [BoundedOrder α] [IsSimpleOrder α]
 
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 /-- A simple partial ordered `bounded_order` induces a lattice.
 This is not an instance to prevent loops -/
 protected def lattice {α} [DecidableEq α] [PartialOrder α] [BoundedOrder α] [IsSimpleOrder α] :
@@ -866,12 +554,6 @@ protected def lattice {α} [DecidableEq α] [PartialOrder α] [BoundedOrder α]
   @LinearOrder.toLattice α IsSimpleOrder.linearOrder
 #align is_simple_order.lattice IsSimpleOrder.lattice
 
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 /-- A lattice that is a `bounded_order` is a distributive lattice.
 This is not an instance to prevent loops -/
 protected def distribLattice : DistribLattice α :=
@@ -906,12 +588,6 @@ def equivBool {α} [DecidableEq α] [LE α] [BoundedOrder α] [IsSimpleOrder α]
 #align is_simple_order.equiv_bool IsSimpleOrder.equivBool
 -/
 
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 /-- Every simple lattice over a partial order is order-isomorphic to `bool`. -/
 def orderIsoBool : α ≃o Bool :=
   { equivBool with
@@ -924,12 +600,6 @@ def orderIsoBool : α ≃o Bool :=
         · simp [bot_ne_top] }
 #align is_simple_order.order_iso_bool IsSimpleOrder.orderIsoBool
 
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 /-- A simple `bounded_order` is also a `boolean_algebra`. -/
 protected def booleanAlgebra {α} [DecidableEq α] [Lattice α] [BoundedOrder α] [IsSimpleOrder α] :
     BooleanAlgebra α :=
@@ -954,12 +624,6 @@ variable [Lattice α] [BoundedOrder α] [IsSimpleOrder α]
 
 open Classical
 
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 /-- A simple `bounded_order` is also complete. -/
 protected noncomputable def completeLattice : CompleteLattice α :=
   { (inferInstance : Lattice α),
@@ -989,12 +653,6 @@ protected noncomputable def completeLattice : CompleteLattice α :=
         exact top_ne_bot (eq_bot_iff.2 (h ⊥ Con)) }
 #align is_simple_order.complete_lattice IsSimpleOrder.completeLattice
 
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 /-- A simple `bounded_order` is also a `complete_boolean_algebra`. -/
 protected noncomputable def completeBooleanAlgebra : CompleteBooleanAlgebra α :=
   { IsSimpleOrder.completeLattice,
@@ -1033,12 +691,6 @@ instance : IsCoatomistic α :=
 
 end IsSimpleOrder
 
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 theorem isSimpleOrder_iff_isAtom_top [PartialOrder α] [BoundedOrder α] :
     IsSimpleOrder α ↔ IsAtom (⊤ : α) :=
   ⟨fun h => @isAtom_top _ _ _ h, fun h =>
@@ -1046,12 +698,6 @@ theorem isSimpleOrder_iff_isAtom_top [PartialOrder α] [BoundedOrder α] :
       eq_bot_or_eq_top := fun a => ((eq_or_lt_of_le le_top).imp_right (h.2 a)).symm }⟩
 #align is_simple_order_iff_is_atom_top isSimpleOrder_iff_isAtom_top
 
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 theorem isSimpleOrder_iff_isCoatom_bot [PartialOrder α] [BoundedOrder α] :
     IsSimpleOrder α ↔ IsCoatom (⊥ : α) :=
   isSimpleOrder_iff_isSimpleOrder_orderDual.trans isSimpleOrder_iff_isAtom_top
@@ -1059,12 +705,6 @@ theorem isSimpleOrder_iff_isCoatom_bot [PartialOrder α] [BoundedOrder α] :
 
 namespace Set
 
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 theorem isSimpleOrder_Iic_iff_isAtom [PartialOrder α] [OrderBot α] {a : α} :
     IsSimpleOrder (Iic a) ↔ IsAtom a :=
   isSimpleOrder_iff_isAtom_top.trans <|
@@ -1073,12 +713,6 @@ theorem isSimpleOrder_Iic_iff_isAtom [PartialOrder α] [OrderBot α] {a : α} :
         Subtype.mk_eq_mk.2 (h b (Subtype.mk_lt_mk.1 hbotb))⟩
 #align set.is_simple_order_Iic_iff_is_atom Set.isSimpleOrder_Iic_iff_isAtom
 
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 theorem isSimpleOrder_Ici_iff_isCoatom [PartialOrder α] [OrderTop α] {a : α} :
     IsSimpleOrder (Ici a) ↔ IsCoatom a :=
   isSimpleOrder_iff_isCoatom_bot.trans <|
@@ -1093,23 +727,11 @@ namespace OrderEmbedding
 
 variable [PartialOrder α] [PartialOrder β]
 
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 theorem isAtom_of_map_bot_of_image [OrderBot α] [OrderBot β] (f : β ↪o α) (hbot : f ⊥ = ⊥) {b : β}
     (hb : IsAtom (f b)) : IsAtom b := by simp only [← bot_covby_iff] at hb⊢;
   exact Covby.of_image f (hbot.symm ▸ hb)
 #align order_embedding.is_atom_of_map_bot_of_image OrderEmbedding.isAtom_of_map_bot_of_image
 
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 theorem isCoatom_of_map_top_of_image [OrderTop α] [OrderTop β] (f : β ↪o α) (htop : f ⊤ = ⊤) {b : β}
     (hb : IsCoatom (f b)) : IsCoatom b :=
   f.dual.isAtom_of_map_bot_of_image htop hb
@@ -1121,24 +743,12 @@ namespace GaloisInsertion
 
 variable [PartialOrder α] [PartialOrder β]
 
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 theorem isAtom_of_u_bot [OrderBot α] [OrderBot β] {l : α → β} {u : β → α} (gi : GaloisInsertion l u)
     (hbot : u ⊥ = ⊥) {b : β} (hb : IsAtom (u b)) : IsAtom b :=
   OrderEmbedding.isAtom_of_map_bot_of_image
     ⟨⟨u, gi.u_injective⟩, @GaloisInsertion.u_le_u_iff _ _ _ _ _ _ gi⟩ hbot hb
 #align galois_insertion.is_atom_of_u_bot GaloisInsertion.isAtom_of_u_bot
 
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 theorem isAtom_iff [OrderBot α] [IsAtomic α] [OrderBot β] {l : α → β} {u : β → α}
     (gi : GaloisInsertion l u) (hbot : u ⊥ = ⊥) (h_atom : ∀ a, IsAtom a → u (l a) = a) (a : α) :
     IsAtom (l a) ↔ IsAtom a :=
@@ -1156,35 +766,17 @@ theorem isAtom_iff [OrderBot α] [IsAtomic α] [OrderBot β] {l : α → β} {u
   exact haa'.symm ▸ ha'
 #align galois_insertion.is_atom_iff GaloisInsertion.isAtom_iff
 
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 theorem isAtom_iff' [OrderBot α] [IsAtomic α] [OrderBot β] {l : α → β} {u : β → α}
     (gi : GaloisInsertion l u) (hbot : u ⊥ = ⊥) (h_atom : ∀ a, IsAtom a → u (l a) = a) (b : β) :
     IsAtom (u b) ↔ IsAtom b := by rw [← gi.is_atom_iff hbot h_atom, gi.l_u_eq]
 #align galois_insertion.is_atom_iff' GaloisInsertion.isAtom_iff'
 
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 theorem isCoatom_of_image [OrderTop α] [OrderTop β] {l : α → β} {u : β → α}
     (gi : GaloisInsertion l u) {b : β} (hb : IsCoatom (u b)) : IsCoatom b :=
   OrderEmbedding.isCoatom_of_map_top_of_image
     ⟨⟨u, gi.u_injective⟩, @GaloisInsertion.u_le_u_iff _ _ _ _ _ _ gi⟩ gi.gc.u_top hb
 #align galois_insertion.is_coatom_of_image GaloisInsertion.isCoatom_of_image
 
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 theorem isCoatom_iff [OrderTop α] [IsCoatomic α] [OrderTop β] {l : α → β} {u : β → α}
     (gi : GaloisInsertion l u) (h_coatom : ∀ a : α, IsCoatom a → u (l a) = a) (b : β) :
     IsCoatom (u b) ↔ IsCoatom b :=
@@ -1205,58 +797,28 @@ namespace GaloisCoinsertion
 
 variable [PartialOrder α] [PartialOrder β]
 
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 theorem isCoatom_of_l_top [OrderTop α] [OrderTop β] {l : α → β} {u : β → α}
     (gi : GaloisCoinsertion l u) (hbot : l ⊤ = ⊤) {a : α} (hb : IsCoatom (l a)) : IsCoatom a :=
   gi.dual.isAtom_of_u_bot hbot hb.dual
 #align galois_coinsertion.is_coatom_of_l_top GaloisCoinsertion.isCoatom_of_l_top
 
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 theorem isCoatom_iff [OrderTop α] [OrderTop β] [IsCoatomic β] {l : α → β} {u : β → α}
     (gi : GaloisCoinsertion l u) (htop : l ⊤ = ⊤) (h_coatom : ∀ b, IsCoatom b → l (u b) = b)
     (b : β) : IsCoatom (u b) ↔ IsCoatom b :=
   gi.dual.isAtom_iff htop h_coatom b
 #align galois_coinsertion.is_coatom_iff GaloisCoinsertion.isCoatom_iff
 
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 theorem isCoatom_iff' [OrderTop α] [OrderTop β] [IsCoatomic β] {l : α → β} {u : β → α}
     (gi : GaloisCoinsertion l u) (htop : l ⊤ = ⊤) (h_coatom : ∀ b, IsCoatom b → l (u b) = b)
     (a : α) : IsCoatom (l a) ↔ IsCoatom a :=
   gi.dual.isAtom_iff' htop h_coatom a
 #align galois_coinsertion.is_coatom_iff' GaloisCoinsertion.isCoatom_iff'
 
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 theorem isAtom_of_image [OrderBot α] [OrderBot β] {l : α → β} {u : β → α}
     (gi : GaloisCoinsertion l u) {a : α} (hb : IsAtom (l a)) : IsAtom a :=
   gi.dual.isCoatom_of_image hb.dual
 #align galois_coinsertion.is_atom_of_image GaloisCoinsertion.isAtom_of_image
 
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 theorem isAtom_iff [OrderBot α] [OrderBot β] [IsAtomic β] {l : α → β} {u : β → α}
     (gi : GaloisCoinsertion l u) (h_atom : ∀ b, IsAtom b → l (u b) = b) (a : α) :
     IsAtom (l a) ↔ IsAtom a :=
@@ -1269,69 +831,33 @@ namespace OrderIso
 
 variable [PartialOrder α] [PartialOrder β]
 
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 @[simp]
 theorem isAtom_iff [OrderBot α] [OrderBot β] (f : α ≃o β) (a : α) : IsAtom (f a) ↔ IsAtom a :=
   ⟨f.toGaloisCoinsertion.isAtom_of_image, fun ha =>
     f.toGaloisInsertion.isAtom_of_u_bot (map_bot f.symm) <| (f.symm_apply_apply a).symm ▸ ha⟩
 #align order_iso.is_atom_iff OrderIso.isAtom_iff
 
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 @[simp]
 theorem isCoatom_iff [OrderTop α] [OrderTop β] (f : α ≃o β) (a : α) : IsCoatom (f a) ↔ IsCoatom a :=
   f.dual.isAtom_iff a
 #align order_iso.is_coatom_iff OrderIso.isCoatom_iff
 
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 theorem isSimpleOrder_iff [BoundedOrder α] [BoundedOrder β] (f : α ≃o β) :
     IsSimpleOrder α ↔ IsSimpleOrder β := by
   rw [isSimpleOrder_iff_isAtom_top, isSimpleOrder_iff_isAtom_top, ← f.is_atom_iff ⊤, f.map_top]
 #align order_iso.is_simple_order_iff OrderIso.isSimpleOrder_iff
 
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-Case conversion may be inaccurate. Consider using '#align order_iso.is_simple_order OrderIso.isSimpleOrderₓ'. -/
 theorem isSimpleOrder [BoundedOrder α] [BoundedOrder β] [h : IsSimpleOrder β] (f : α ≃o β) :
     IsSimpleOrder α :=
   f.isSimpleOrder_iff.mpr h
 #align order_iso.is_simple_order OrderIso.isSimpleOrder
 
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-Case conversion may be inaccurate. Consider using '#align order_iso.is_atomic_iff OrderIso.isAtomic_iffₓ'. -/
 protected theorem isAtomic_iff [OrderBot α] [OrderBot β] (f : α ≃o β) : IsAtomic α ↔ IsAtomic β :=
   by
   simp only [IsAtomic_iff, f.surjective.forall, f.surjective.exists, ← map_bot f, f.eq_iff_eq,
     f.le_iff_le, f.is_atom_iff]
 #align order_iso.is_atomic_iff OrderIso.isAtomic_iff
 
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-Case conversion may be inaccurate. Consider using '#align order_iso.is_coatomic_iff OrderIso.isCoatomic_iffₓ'. -/
 protected theorem isCoatomic_iff [OrderTop α] [OrderTop β] (f : α ≃o β) :
     IsCoatomic α ↔ IsCoatomic β := by
   simp only [← isAtomic_dual_iff_isCoatomic, f.dual.is_atomic_iff]
@@ -1349,23 +875,11 @@ variable {a b : α} (hc : IsCompl a b)
 
 include hc
 
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-Case conversion may be inaccurate. Consider using '#align is_compl.is_atom_iff_is_coatom IsCompl.isAtom_iff_isCoatomₓ'. -/
 theorem isAtom_iff_isCoatom : IsAtom a ↔ IsCoatom b :=
   Set.isSimpleOrder_Iic_iff_isAtom.symm.trans <|
     hc.IicOrderIsoIci.isSimpleOrder_iff.trans Set.isSimpleOrder_Ici_iff_isCoatom
 #align is_compl.is_atom_iff_is_coatom IsCompl.isAtom_iff_isCoatom
 
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 theorem isCoatom_iff_isAtom : IsCoatom a ↔ IsAtom b :=
   hc.symm.isAtom_iff_isCoatom.symm
 #align is_compl.is_coatom_iff_is_atom IsCompl.isCoatom_iff_isAtom
@@ -1374,12 +888,6 @@ end IsCompl
 
 variable [ComplementedLattice α]
 
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-Case conversion may be inaccurate. Consider using '#align is_coatomic_of_is_atomic_of_complemented_lattice_of_is_modular isCoatomic_of_isAtomic_of_complementedLattice_of_isModularₓ'. -/
 theorem isCoatomic_of_isAtomic_of_complementedLattice_of_isModular [IsAtomic α] : IsCoatomic α :=
   ⟨fun x => by
     rcases exists_is_compl x with ⟨y, xy⟩
@@ -1393,22 +901,10 @@ theorem isCoatomic_of_isAtomic_of_complementedLattice_of_isModular [IsAtomic α]
       apply ha.Iic⟩
 #align is_coatomic_of_is_atomic_of_complemented_lattice_of_is_modular isCoatomic_of_isAtomic_of_complementedLattice_of_isModular
 
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-Case conversion may be inaccurate. Consider using '#align is_atomic_of_is_coatomic_of_complemented_lattice_of_is_modular isAtomic_of_isCoatomic_of_complementedLattice_of_isModularₓ'. -/
 theorem isAtomic_of_isCoatomic_of_complementedLattice_of_isModular [IsCoatomic α] : IsAtomic α :=
   isCoatomic_dual_iff_isAtomic.1 isCoatomic_of_isAtomic_of_complementedLattice_of_isModular
 #align is_atomic_of_is_coatomic_of_complemented_lattice_of_is_modular isAtomic_of_isCoatomic_of_complementedLattice_of_isModular
 
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-Case conversion may be inaccurate. Consider using '#align is_atomic_iff_is_coatomic isAtomic_iff_isCoatomicₓ'. -/
 theorem isAtomic_iff_isCoatomic : IsAtomic α ↔ IsCoatomic α :=
   ⟨fun h => @isCoatomic_of_isAtomic_of_complementedLattice_of_isModular _ _ _ _ _ h, fun h =>
     @isAtomic_of_isCoatomic_of_complementedLattice_of_isModular _ _ _ _ _ h⟩
@@ -1418,22 +914,10 @@ end IsModularLattice
 
 namespace Set
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align set.is_atom_singleton Set.isAtom_singletonₓ'. -/
 theorem isAtom_singleton (x : α) : IsAtom ({x} : Set α) :=
   ⟨singleton_ne_empty _, fun s hs => ssubset_singleton_iff.mp hs⟩
 #align set.is_atom_singleton Set.isAtom_singleton
 
-/- warning: set.is_atom_iff -> Set.isAtom_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (s : Set.{u1} α), Iff (IsAtom.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α))))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s) (Exists.{succ u1} α (fun (x : α) => Eq.{succ u1} (Set.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) x)))
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-  forall {α : Type.{u1}} (s : Set.{u1} α), Iff (IsAtom.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) s) (Exists.{succ u1} α (fun (x : α) => Eq.{succ u1} (Set.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) x)))
-Case conversion may be inaccurate. Consider using '#align set.is_atom_iff Set.isAtom_iffₓ'. -/
 theorem isAtom_iff (s : Set α) : IsAtom s ↔ ∃ x, s = {x} :=
   by
   refine' ⟨_, by rintro ⟨x, rfl⟩; exact is_atom_singleton x⟩
@@ -1445,22 +929,10 @@ theorem isAtom_iff (s : Set α) : IsAtom s ↔ ∃ x, s = {x} :=
         ⟨hx, fun y hy => (hs {y} (singleton_ne_empty _) (singleton_subset_iff.2 hy) hx).symm⟩⟩
 #align set.is_atom_iff Set.isAtom_iff
 
-/- warning: set.is_coatom_iff -> Set.isCoatom_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (s : Set.{u1} α), Iff (IsCoatom.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α))))))) (Set.orderTop.{u1} α) s) (Exists.{succ u1} α (fun (x : α) => Eq.{succ u1} (Set.{u1} α) s (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) x))))
-but is expected to have type
-  forall {α : Type.{u1}} (s : Set.{u1} α), Iff (IsCoatom.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (Set.instOrderTopSetInstLESet.{u1} α) s) (Exists.{succ u1} α (fun (x : α) => Eq.{succ u1} (Set.{u1} α) s (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) x))))
-Case conversion may be inaccurate. Consider using '#align set.is_coatom_iff Set.isCoatom_iffₓ'. -/
 theorem isCoatom_iff (s : Set α) : IsCoatom s ↔ ∃ x, s = {x}ᶜ := by
   simp_rw [is_compl_compl.is_coatom_iff_is_atom, isAtom_iff, @eq_comm _ s, compl_eq_comm]
 #align set.is_coatom_iff Set.isCoatom_iff
 
-/- warning: set.is_coatom_singleton_compl -> Set.isCoatom_singleton_compl is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (x : α), IsCoatom.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α))))))) (Set.orderTop.{u1} α) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) x))
-but is expected to have type
-  forall {α : Type.{u1}} (x : α), IsCoatom.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (Set.instOrderTopSetInstLESet.{u1} α) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) x))
-Case conversion may be inaccurate. Consider using '#align set.is_coatom_singleton_compl Set.isCoatom_singleton_complₓ'. -/
 theorem isCoatom_singleton_compl (x : α) : IsCoatom ({x}ᶜ : Set α) :=
   (isCoatom_iff ({x}ᶜ)).mpr ⟨x, rfl⟩
 #align set.is_coatom_singleton_compl Set.isCoatom_singleton_compl

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

@@ -1002,15 +1002,13 @@ protected noncomputable def completeBooleanAlgebra : CompleteBooleanAlgebra α :
     iInf_sup_le_sup_inf := fun x s =>
       by
       rcases eq_bot_or_eq_top x with (rfl | rfl)
-      · simp only [bot_sup_eq, ← sInf_eq_iInf]
-        exact le_rfl
+      · simp only [bot_sup_eq, ← sInf_eq_iInf]; exact le_rfl
       · simp only [top_sup_eq, le_top]
     inf_sup_le_iSup_inf := fun x s =>
       by
       rcases eq_bot_or_eq_top x with (rfl | rfl)
       · simp only [bot_inf_eq, bot_le]
-      · simp only [top_inf_eq, ← sSup_eq_iSup]
-        exact le_rfl }
+      · simp only [top_inf_eq, ← sSup_eq_iSup]; exact le_rfl }
 #align is_simple_order.complete_boolean_algebra IsSimpleOrder.completeBooleanAlgebra
 
 end IsSimpleOrder
@@ -1102,9 +1100,7 @@ but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))), (Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) f (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Bot.bot.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (OrderBot.toBot.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) _inst_1)) _inst_3))) -> (forall {b : β}, (IsAtom.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) b) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) b) _inst_1) _inst_3 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) f b)) -> (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b))
 Case conversion may be inaccurate. Consider using '#align order_embedding.is_atom_of_map_bot_of_image OrderEmbedding.isAtom_of_map_bot_of_imageₓ'. -/
 theorem isAtom_of_map_bot_of_image [OrderBot α] [OrderBot β] (f : β ↪o α) (hbot : f ⊥ = ⊥) {b : β}
-    (hb : IsAtom (f b)) : IsAtom b :=
-  by
-  simp only [← bot_covby_iff] at hb⊢
+    (hb : IsAtom (f b)) : IsAtom b := by simp only [← bot_covby_iff] at hb⊢;
   exact Covby.of_image f (hbot.symm ▸ hb)
 #align order_embedding.is_atom_of_map_bot_of_image OrderEmbedding.isAtom_of_map_bot_of_image
 
@@ -1440,10 +1436,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align set.is_atom_iff Set.isAtom_iffₓ'. -/
 theorem isAtom_iff (s : Set α) : IsAtom s ↔ ∃ x, s = {x} :=
   by
-  refine'
-    ⟨_, by
-      rintro ⟨x, rfl⟩
-      exact is_atom_singleton x⟩
+  refine' ⟨_, by rintro ⟨x, rfl⟩; exact is_atom_singleton x⟩
   rw [isAtom_iff, bot_eq_empty, ← nonempty_iff_ne_empty]
   rintro ⟨⟨x, hx⟩, hs⟩
   exact
@@ -1474,18 +1467,14 @@ theorem isCoatom_singleton_compl (x : α) : IsCoatom ({x}ᶜ : Set α) :=
 
 instance : IsAtomistic (Set α)
     where eq_sSup_atoms s :=
-    ⟨(fun x => {x}) '' s, by rw [Sup_eq_sUnion, sUnion_image, bUnion_of_singleton],
-      by
-      rintro - ⟨x, hx, rfl⟩
-      exact is_atom_singleton x⟩
+    ⟨(fun x => {x}) '' s, by rw [Sup_eq_sUnion, sUnion_image, bUnion_of_singleton], by
+      rintro - ⟨x, hx, rfl⟩; exact is_atom_singleton x⟩
 
 instance : IsCoatomistic (Set α)
     where eq_sInf_coatoms s :=
     ⟨(fun x => {x}ᶜ) '' sᶜ, by
-      rw [Inf_eq_sInter, sInter_image, ← compl_Union₂, bUnion_of_singleton, compl_compl],
-      by
-      rintro - ⟨x, hx, rfl⟩
-      exact is_coatom_singleton_compl x⟩
+      rw [Inf_eq_sInter, sInter_image, ← compl_Union₂, bUnion_of_singleton, compl_compl], by
+      rintro - ⟨x, hx, rfl⟩; exact is_coatom_singleton_compl x⟩
 
 end Set
 

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

@@ -193,7 +193,7 @@ def IsCoatom [OrderTop α] (a : α) : Prop :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {a : α}, Iff (IsCoatom.{u1} (OrderDual.{u1} α) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a)) (IsAtom.{u1} α _inst_1 _inst_2 a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, Iff (IsCoatom.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) a) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a)) (IsAtom.{u1} α _inst_1 _inst_2 a)
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, Iff (IsCoatom.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u1} α) a) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u1} α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a)) (IsAtom.{u1} α _inst_1 _inst_2 a)
 Case conversion may be inaccurate. Consider using '#align is_coatom_dual_iff_is_atom isCoatom_dual_iff_isAtomₓ'. -/
 @[simp]
 theorem isCoatom_dual_iff_isAtom [OrderBot α] {a : α} : IsCoatom (OrderDual.toDual a) ↔ IsAtom a :=
@@ -204,7 +204,7 @@ theorem isCoatom_dual_iff_isAtom [OrderBot α] {a : α} : IsCoatom (OrderDual.to
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {a : α}, Iff (IsAtom.{u1} (OrderDual.{u1} α) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a)) (IsCoatom.{u1} α _inst_1 _inst_2 a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, Iff (IsAtom.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) a) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a)) (IsCoatom.{u1} α _inst_1 _inst_2 a)
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, Iff (IsAtom.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u1} α) a) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u1} α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a)) (IsCoatom.{u1} α _inst_1 _inst_2 a)
 Case conversion may be inaccurate. Consider using '#align is_atom_dual_iff_is_coatom isAtom_dual_iff_isCoatomₓ'. -/
 @[simp]
 theorem isAtom_dual_iff_isCoatom [OrderTop α] {a : α} : IsAtom (OrderDual.toDual a) ↔ IsCoatom a :=
@@ -215,7 +215,7 @@ theorem isAtom_dual_iff_isCoatom [OrderTop α] {a : α} : IsAtom (OrderDual.toDu
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {a : α}, (IsAtom.{u1} α _inst_1 _inst_2 a) -> (IsCoatom.{u1} (OrderDual.{u1} α) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, (IsAtom.{u1} α _inst_1 _inst_2 a) -> (IsCoatom.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) a) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, (IsAtom.{u1} α _inst_1 _inst_2 a) -> (IsCoatom.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u1} α) a) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u1} α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a))
 Case conversion may be inaccurate. Consider using '#align is_atom.dual IsAtom.dualₓ'. -/
 alias isCoatom_dual_iff_isAtom ↔ _ IsAtom.dual
 #align is_atom.dual IsAtom.dual
@@ -224,7 +224,7 @@ alias isCoatom_dual_iff_isAtom ↔ _ IsAtom.dual
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {a : α}, (IsCoatom.{u1} α _inst_1 _inst_2 a) -> (IsAtom.{u1} (OrderDual.{u1} α) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, (IsCoatom.{u1} α _inst_1 _inst_2 a) -> (IsAtom.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) a) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, (IsCoatom.{u1} α _inst_1 _inst_2 a) -> (IsAtom.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u1} α) a) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u1} α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a))
 Case conversion may be inaccurate. Consider using '#align is_coatom.dual IsCoatom.dualₓ'. -/
 alias isAtom_dual_iff_isCoatom ↔ _ IsCoatom.dual
 #align is_coatom.dual IsCoatom.dual
@@ -1099,7 +1099,7 @@ variable [PartialOrder α] [PartialOrder β]
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderEmbedding.{u2, u1} β α (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))), (Eq.{succ u1} α (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) -> (forall {b : β}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f b)) -> (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))), (Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Bot.bot.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (OrderBot.toBot.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) _inst_1)) _inst_3))) -> (forall {b : β}, (IsAtom.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) b) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) b) _inst_1) _inst_3 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f b)) -> (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))), (Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) f (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Bot.bot.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (OrderBot.toBot.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) _inst_1)) _inst_3))) -> (forall {b : β}, (IsAtom.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) b) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) b) _inst_1) _inst_3 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) f b)) -> (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b))
 Case conversion may be inaccurate. Consider using '#align order_embedding.is_atom_of_map_bot_of_image OrderEmbedding.isAtom_of_map_bot_of_imageₓ'. -/
 theorem isAtom_of_map_bot_of_image [OrderBot α] [OrderBot β] (f : β ↪o α) (hbot : f ⊥ = ⊥) {b : β}
     (hb : IsAtom (f b)) : IsAtom b :=
@@ -1112,7 +1112,7 @@ theorem isAtom_of_map_bot_of_image [OrderBot α] [OrderBot β] (f : β ↪o α)
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderEmbedding.{u2, u1} β α (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))), (Eq.{succ u1} α (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) -> (forall {b : β}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f b)) -> (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))), (Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Top.top.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (OrderTop.toTop.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) _inst_1)) _inst_3))) -> (forall {b : β}, (IsCoatom.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) b) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) b) _inst_1) _inst_3 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f b)) -> (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))), (Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) f (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Top.top.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (OrderTop.toTop.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) _inst_1)) _inst_3))) -> (forall {b : β}, (IsCoatom.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) b) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) b) _inst_1) _inst_3 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) f b)) -> (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b))
 Case conversion may be inaccurate. Consider using '#align order_embedding.is_coatom_of_map_top_of_image OrderEmbedding.isCoatom_of_map_top_of_imageₓ'. -/
 theorem isCoatom_of_map_top_of_image [OrderTop α] [OrderTop β] (f : β ↪o α) (htop : f ⊤ = ⊤) {b : β}
     (hb : IsCoatom (f b)) : IsCoatom b :=
@@ -1277,7 +1277,7 @@ variable [PartialOrder α] [PartialOrder β]
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (a : α), Iff (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) f a)) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))) (a : α), Iff (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a)) (IsAtom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a)
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))) (a : α), Iff (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f a)) (IsAtom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a)
 Case conversion may be inaccurate. Consider using '#align order_iso.is_atom_iff OrderIso.isAtom_iffₓ'. -/
 @[simp]
 theorem isAtom_iff [OrderBot α] [OrderBot β] (f : α ≃o β) (a : α) : IsAtom (f a) ↔ IsAtom a :=
@@ -1289,7 +1289,7 @@ theorem isAtom_iff [OrderBot α] [OrderBot β] (f : α ≃o β) (a : α) : IsAto
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (a : α), Iff (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) f a)) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))) (a : α), Iff (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a)) (IsCoatom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a)
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))) (a : α), Iff (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f a)) (IsCoatom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a)
 Case conversion may be inaccurate. Consider using '#align order_iso.is_coatom_iff OrderIso.isCoatom_iffₓ'. -/
 @[simp]
 theorem isCoatom_iff [OrderTop α] [OrderTop β] (f : α ≃o β) (a : α) : IsCoatom (f a) ↔ IsCoatom a :=

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

@@ -64,30 +64,42 @@ section Preorder
 
 variable [Preorder α] [OrderBot α] {a b x : α}
 
-#print IsAtom /-
+/- warning: is_atom -> IsAtom is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], α -> Prop
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)], α -> Prop
+Case conversion may be inaccurate. Consider using '#align is_atom IsAtomₓ'. -/
 /-- An atom of an `order_bot` is an element with no other element between it and `⊥`,
   which is not `⊥`. -/
 def IsAtom (a : α) : Prop :=
   a ≠ ⊥ ∧ ∀ b, b < a → b = ⊥
 #align is_atom IsAtom
--/
 
-#print IsAtom.Iic /-
+/- warning: is_atom.Iic -> IsAtom.Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {a : α} {x : α}, (IsAtom.{u1} α _inst_1 _inst_2 a) -> (forall (hax : LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) a x), IsAtom.{u1} (Subtype.{succ u1} α (fun (x_1 : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x_1 (Set.Iic.{u1} α _inst_1 x))) (Subtype.preorder.{u1} α _inst_1 (fun (x_1 : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x_1 (Set.Iic.{u1} α _inst_1 x))) (Set.Iic.orderBot.{u1} α _inst_1 _inst_2 x) (Subtype.mk.{succ u1} α (fun (x_1 : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x_1 (Set.Iic.{u1} α _inst_1 x)) a hax))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α} {x : α}, (IsAtom.{u1} α _inst_1 _inst_2 a) -> (forall (hax : LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) a x), IsAtom.{u1} (Subtype.{succ u1} α (fun (x_1 : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x_1 (Set.Iic.{u1} α _inst_1 x))) (Subtype.preorder.{u1} α _inst_1 (fun (x_1 : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x_1 (Set.Iic.{u1} α _inst_1 x))) (Set.Iic.orderBot.{u1} α _inst_1 _inst_2 x) (Subtype.mk.{succ u1} α (fun (x_1 : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x_1 (Set.Iic.{u1} α _inst_1 x)) a hax))
+Case conversion may be inaccurate. Consider using '#align is_atom.Iic IsAtom.Iicₓ'. -/
 theorem IsAtom.Iic (ha : IsAtom a) (hax : a ≤ x) : IsAtom (⟨a, hax⟩ : Set.Iic x) :=
   ⟨fun con => ha.1 (Subtype.mk_eq_mk.1 Con), fun ⟨b, hb⟩ hba => Subtype.mk_eq_mk.2 (ha.2 b hba)⟩
 #align is_atom.Iic IsAtom.Iic
--/
 
-#print IsAtom.of_isAtom_coe_Iic /-
+/- warning: is_atom.of_is_atom_coe_Iic -> IsAtom.of_isAtom_coe_Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {x : α} {a : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α _inst_1 x)}, (IsAtom.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α _inst_1 x)) (Subtype.preorder.{u1} α _inst_1 (fun (x_1 : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x_1 (Set.Iic.{u1} α _inst_1 x))) (Set.Iic.orderBot.{u1} α _inst_1 _inst_2 x) a) -> (IsAtom.{u1} α _inst_1 _inst_2 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α _inst_1 x)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α _inst_1 x)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α _inst_1 x)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α _inst_1 x)) α (coeSubtype.{succ u1} α (fun (x_1 : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x_1 (Set.Iic.{u1} α _inst_1 x)))))) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {x : α} {a : Set.Elem.{u1} α (Set.Iic.{u1} α _inst_1 x)}, (IsAtom.{u1} (Set.Elem.{u1} α (Set.Iic.{u1} α _inst_1 x)) (Subtype.preorder.{u1} α _inst_1 (fun (x_1 : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x_1 (Set.Iic.{u1} α _inst_1 x))) (Set.Iic.orderBot.{u1} α _inst_1 _inst_2 x) a) -> (IsAtom.{u1} α _inst_1 _inst_2 (Subtype.val.{succ u1} α (fun (x_1 : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x_1 (Set.Iic.{u1} α _inst_1 x)) a))
+Case conversion may be inaccurate. Consider using '#align is_atom.of_is_atom_coe_Iic IsAtom.of_isAtom_coe_Iicₓ'. -/
 theorem IsAtom.of_isAtom_coe_Iic {a : Set.Iic x} (ha : IsAtom a) : IsAtom (a : α) :=
   ⟨fun con => ha.1 (Subtype.ext Con), fun b hba =>
     Subtype.mk_eq_mk.1 (ha.2 ⟨b, hba.le.trans a.Prop⟩ hba)⟩
 #align is_atom.of_is_atom_coe_Iic IsAtom.of_isAtom_coe_Iic
--/
 
 /- warning: is_atom_iff -> isAtom_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, Iff (IsAtom.{u1} α _inst_1 _inst_2 a) (And (Ne.{succ u1} α a (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))) (forall (b : α), (Ne.{succ u1} α b (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) a b)))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {a : α}, Iff (IsAtom.{u1} α _inst_1 _inst_2 a) (And (Ne.{succ u1} α a (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2))) (forall (b : α), (Ne.{succ u1} α b (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) b a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) a b)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, Iff (IsAtom.{u1} α _inst_1 _inst_2 a) (And (Ne.{succ u1} α a (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))) (forall (b : α), (Ne.{succ u1} α b (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) a b)))
 Case conversion may be inaccurate. Consider using '#align is_atom_iff isAtom_iffₓ'. -/
@@ -103,7 +115,7 @@ variable [PartialOrder α] [OrderBot α] {a b x : α}
 
 /- warning: is_atom.lt_iff -> IsAtom.lt_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α} {x : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x a) (Eq.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))))
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α} {x : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Iff (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x a) (Eq.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α} {x : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x a) (Eq.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))))
 Case conversion may be inaccurate. Consider using '#align is_atom.lt_iff IsAtom.lt_iffₓ'. -/
@@ -113,7 +125,7 @@ theorem IsAtom.lt_iff (h : IsAtom a) : x < a ↔ x = ⊥ :=
 
 /- warning: is_atom.le_iff -> IsAtom.le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α} {x : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x a) (Or (Eq.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (Eq.{succ u1} α x a)))
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α} {x : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x a) (Or (Eq.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (Eq.{succ u1} α x a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α} {x : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x a) (Or (Eq.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (Eq.{succ u1} α x a)))
 Case conversion may be inaccurate. Consider using '#align is_atom.le_iff IsAtom.le_iffₓ'. -/
@@ -122,7 +134,7 @@ theorem IsAtom.le_iff (h : IsAtom a) : x ≤ a ↔ x = ⊥ ∨ x = a := by rw [l
 
 /- warning: is_atom.Iic_eq -> IsAtom.Iic_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Eq.{succ u1} (Set.{u1} α) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)))
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Eq.{succ u1} (Set.{u1} α) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Eq.{succ u1} (Set.{u1} α) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)))
 Case conversion may be inaccurate. Consider using '#align is_atom.Iic_eq IsAtom.Iic_eqₓ'. -/
@@ -132,7 +144,7 @@ theorem IsAtom.Iic_eq (h : IsAtom a) : Set.Iic a = {⊥, a} :=
 
 /- warning: bot_covby_iff -> bot_covby_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, Iff (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) a) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, Iff (Covby.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) a) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, Iff (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) a) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
 Case conversion may be inaccurate. Consider using '#align bot_covby_iff bot_covby_iffₓ'. -/
@@ -143,13 +155,13 @@ theorem bot_covby_iff : ⊥ ⋖ a ↔ IsAtom a := by
 
 /- warning: covby.is_atom -> Covby.is_atom is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) a) -> (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (Covby.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) a) -> (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) a) -> (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
 Case conversion may be inaccurate. Consider using '#align covby.is_atom Covby.is_atomₓ'. -/
 /- warning: is_atom.bot_covby -> IsAtom.bot_covby is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) a)
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Covby.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) a)
 Case conversion may be inaccurate. Consider using '#align is_atom.bot_covby IsAtom.bot_covbyₓ'. -/
@@ -165,51 +177,83 @@ section Preorder
 
 variable [Preorder α]
 
-#print IsCoatom /-
+/- warning: is_coatom -> IsCoatom is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], α -> Prop
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)], α -> Prop
+Case conversion may be inaccurate. Consider using '#align is_coatom IsCoatomₓ'. -/
 /-- A coatom of an `order_top` is an element with no other element between it and `⊤`,
   which is not `⊤`. -/
 def IsCoatom [OrderTop α] (a : α) : Prop :=
   a ≠ ⊤ ∧ ∀ b, a < b → b = ⊤
 #align is_coatom IsCoatom
--/
 
-#print isCoatom_dual_iff_isAtom /-
+/- warning: is_coatom_dual_iff_is_atom -> isCoatom_dual_iff_isAtom is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {a : α}, Iff (IsCoatom.{u1} (OrderDual.{u1} α) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a)) (IsAtom.{u1} α _inst_1 _inst_2 a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, Iff (IsCoatom.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) a) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a)) (IsAtom.{u1} α _inst_1 _inst_2 a)
+Case conversion may be inaccurate. Consider using '#align is_coatom_dual_iff_is_atom isCoatom_dual_iff_isAtomₓ'. -/
 @[simp]
 theorem isCoatom_dual_iff_isAtom [OrderBot α] {a : α} : IsCoatom (OrderDual.toDual a) ↔ IsAtom a :=
   Iff.rfl
 #align is_coatom_dual_iff_is_atom isCoatom_dual_iff_isAtom
--/
 
-#print isAtom_dual_iff_isCoatom /-
+/- warning: is_atom_dual_iff_is_coatom -> isAtom_dual_iff_isCoatom is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {a : α}, Iff (IsAtom.{u1} (OrderDual.{u1} α) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a)) (IsCoatom.{u1} α _inst_1 _inst_2 a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, Iff (IsAtom.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) a) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a)) (IsCoatom.{u1} α _inst_1 _inst_2 a)
+Case conversion may be inaccurate. Consider using '#align is_atom_dual_iff_is_coatom isAtom_dual_iff_isCoatomₓ'. -/
 @[simp]
 theorem isAtom_dual_iff_isCoatom [OrderTop α] {a : α} : IsAtom (OrderDual.toDual a) ↔ IsCoatom a :=
   Iff.rfl
 #align is_atom_dual_iff_is_coatom isAtom_dual_iff_isCoatom
--/
 
+/- warning: is_atom.dual -> IsAtom.dual is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {a : α}, (IsAtom.{u1} α _inst_1 _inst_2 a) -> (IsCoatom.{u1} (OrderDual.{u1} α) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, (IsAtom.{u1} α _inst_1 _inst_2 a) -> (IsCoatom.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) a) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a))
+Case conversion may be inaccurate. Consider using '#align is_atom.dual IsAtom.dualₓ'. -/
 alias isCoatom_dual_iff_isAtom ↔ _ IsAtom.dual
 #align is_atom.dual IsAtom.dual
 
+/- warning: is_coatom.dual -> IsCoatom.dual is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {a : α}, (IsCoatom.{u1} α _inst_1 _inst_2 a) -> (IsAtom.{u1} (OrderDual.{u1} α) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, (IsCoatom.{u1} α _inst_1 _inst_2 a) -> (IsAtom.{u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) a) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.orderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u1} α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) a))
+Case conversion may be inaccurate. Consider using '#align is_coatom.dual IsCoatom.dualₓ'. -/
 alias isAtom_dual_iff_isCoatom ↔ _ IsCoatom.dual
 #align is_coatom.dual IsCoatom.dual
 
 variable [OrderTop α] {a x : α}
 
-#print IsCoatom.Ici /-
+/- warning: is_coatom.Ici -> IsCoatom.Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {a : α} {x : α}, (IsCoatom.{u1} α _inst_1 _inst_2 a) -> (forall (hax : LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) x a), IsCoatom.{u1} (Subtype.{succ u1} α (fun (x_1 : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x_1 (Set.Ici.{u1} α _inst_1 x))) (Subtype.preorder.{u1} α _inst_1 (fun (x_1 : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x_1 (Set.Ici.{u1} α _inst_1 x))) (Set.Ici.orderTop.{u1} α _inst_1 _inst_2 x) (Subtype.mk.{succ u1} α (fun (x_1 : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x_1 (Set.Ici.{u1} α _inst_1 x)) a hax))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α} {x : α}, (IsCoatom.{u1} α _inst_1 _inst_2 a) -> (forall (hax : LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x a), IsCoatom.{u1} (Subtype.{succ u1} α (fun (x_1 : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x_1 (Set.Ici.{u1} α _inst_1 x))) (Subtype.preorder.{u1} α _inst_1 (fun (x_1 : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x_1 (Set.Ici.{u1} α _inst_1 x))) (Set.Ici.orderTop.{u1} α _inst_1 _inst_2 x) (Subtype.mk.{succ u1} α (fun (x_1 : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x_1 (Set.Ici.{u1} α _inst_1 x)) a hax))
+Case conversion may be inaccurate. Consider using '#align is_coatom.Ici IsCoatom.Iciₓ'. -/
 theorem IsCoatom.Ici (ha : IsCoatom a) (hax : x ≤ a) : IsCoatom (⟨a, hax⟩ : Set.Ici x) :=
   ha.dual.Iic hax
 #align is_coatom.Ici IsCoatom.Ici
--/
 
-#print IsCoatom.of_isCoatom_coe_Ici /-
+/- warning: is_coatom.of_is_coatom_coe_Ici -> IsCoatom.of_isCoatom_coe_Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {x : α} {a : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 x)}, (IsCoatom.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 x)) (Subtype.preorder.{u1} α _inst_1 (fun (x_1 : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x_1 (Set.Ici.{u1} α _inst_1 x))) (Set.Ici.orderTop.{u1} α _inst_1 _inst_2 x) a) -> (IsCoatom.{u1} α _inst_1 _inst_2 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 x)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 x)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 x)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 x)) α (coeSubtype.{succ u1} α (fun (x_1 : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x_1 (Set.Ici.{u1} α _inst_1 x)))))) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {x : α} {a : Set.Elem.{u1} α (Set.Ici.{u1} α _inst_1 x)}, (IsCoatom.{u1} (Set.Elem.{u1} α (Set.Ici.{u1} α _inst_1 x)) (Subtype.preorder.{u1} α _inst_1 (fun (x_1 : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x_1 (Set.Ici.{u1} α _inst_1 x))) (Set.Ici.orderTop.{u1} α _inst_1 _inst_2 x) a) -> (IsCoatom.{u1} α _inst_1 _inst_2 (Subtype.val.{succ u1} α (fun (x_1 : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x_1 (Set.Ici.{u1} α _inst_1 x)) a))
+Case conversion may be inaccurate. Consider using '#align is_coatom.of_is_coatom_coe_Ici IsCoatom.of_isCoatom_coe_Iciₓ'. -/
 theorem IsCoatom.of_isCoatom_coe_Ici {a : Set.Ici x} (ha : IsCoatom a) : IsCoatom (a : α) :=
   @IsAtom.of_isAtom_coe_Iic αᵒᵈ _ _ x a ha
 #align is_coatom.of_is_coatom_coe_Ici IsCoatom.of_isCoatom_coe_Ici
--/
 
 /- warning: is_coatom_iff -> isCoatom_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, Iff (IsCoatom.{u1} α _inst_1 _inst_2 a) (And (Ne.{succ u1} α a (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))) (forall (b : α), (Ne.{succ u1} α b (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) b a)))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {a : α}, Iff (IsCoatom.{u1} α _inst_1 _inst_2 a) (And (Ne.{succ u1} α a (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2))) (forall (b : α), (Ne.{succ u1} α b (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) a b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) b a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, Iff (IsCoatom.{u1} α _inst_1 _inst_2 a) (And (Ne.{succ u1} α a (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))) (forall (b : α), (Ne.{succ u1} α b (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) b a)))
 Case conversion may be inaccurate. Consider using '#align is_coatom_iff isCoatom_iffₓ'. -/
@@ -224,7 +268,7 @@ variable [PartialOrder α] [OrderTop α] {a b x : α}
 
 /- warning: is_coatom.lt_iff -> IsCoatom.lt_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α} {x : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a x) (Eq.{succ u1} α x (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))))
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α} {x : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Iff (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a x) (Eq.{succ u1} α x (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α} {x : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a x) (Eq.{succ u1} α x (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))))
 Case conversion may be inaccurate. Consider using '#align is_coatom.lt_iff IsCoatom.lt_iffₓ'. -/
@@ -234,7 +278,7 @@ theorem IsCoatom.lt_iff (h : IsCoatom a) : a < x ↔ x = ⊤ :=
 
 /- warning: is_coatom.le_iff -> IsCoatom.le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α} {x : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a x) (Or (Eq.{succ u1} α x (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (Eq.{succ u1} α x a)))
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α} {x : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a x) (Or (Eq.{succ u1} α x (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (Eq.{succ u1} α x a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α} {x : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a x) (Or (Eq.{succ u1} α x (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (Eq.{succ u1} α x a)))
 Case conversion may be inaccurate. Consider using '#align is_coatom.le_iff IsCoatom.le_iffₓ'. -/
@@ -244,7 +288,7 @@ theorem IsCoatom.le_iff (h : IsCoatom a) : a ≤ x ↔ x = ⊤ ∨ x = a :=
 
 /- warning: is_coatom.Ici_eq -> IsCoatom.Ici_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Eq.{succ u1} (Set.{u1} α) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)))
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Eq.{succ u1} (Set.{u1} α) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Eq.{succ u1} (Set.{u1} α) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)))
 Case conversion may be inaccurate. Consider using '#align is_coatom.Ici_eq IsCoatom.Ici_eqₓ'. -/
@@ -254,7 +298,7 @@ theorem IsCoatom.Ici_eq (h : IsCoatom a) : Set.Ici a = {⊤, a} :=
 
 /- warning: covby_top_iff -> covby_top_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, Iff (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, Iff (Covby.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, Iff (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
 Case conversion may be inaccurate. Consider using '#align covby_top_iff covby_top_iffₓ'. -/
@@ -265,13 +309,13 @@ theorem covby_top_iff : a ⋖ ⊤ ↔ IsCoatom a :=
 
 /- warning: covby.is_coatom -> Covby.is_coatom is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) -> (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (Covby.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) -> (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) -> (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
 Case conversion may be inaccurate. Consider using '#align covby.is_coatom Covby.is_coatomₓ'. -/
 /- warning: is_coatom.covby_top -> IsCoatom.covby_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)))
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Covby.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a) -> (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)))
 Case conversion may be inaccurate. Consider using '#align is_coatom.covby_top IsCoatom.covby_topₓ'. -/
@@ -285,7 +329,12 @@ section PartialOrder
 
 variable [PartialOrder α] {a b : α}
 
-#print Set.Ici.isAtom_iff /-
+/- warning: set.Ici.is_atom_iff -> Set.Ici.isAtom_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {a : α} {b : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)}, Iff (IsAtom.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a))) (Set.Ici.orderBot.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) b) (Covby.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)))))) b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {a : α} {b : Set.Elem.{u1} α (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)}, Iff (IsAtom.{u1} (Set.Elem.{u1} α (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a))) (Set.Ici.orderBot.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) b) (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)) b))
+Case conversion may be inaccurate. Consider using '#align set.Ici.is_atom_iff Set.Ici.isAtom_iffₓ'. -/
 @[simp]
 theorem Set.Ici.isAtom_iff {b : Set.Ici a} : IsAtom b ↔ a ⋖ b :=
   by
@@ -293,9 +342,13 @@ theorem Set.Ici.isAtom_iff {b : Set.Ici a} : IsAtom b ↔ a ⋖ b :=
   refine' (Set.OrdConnected.apply_covby_apply_iff (OrderEmbedding.subtype fun c => a ≤ c) _).symm
   simpa only [OrderEmbedding.subtype_apply, Subtype.range_coe_subtype] using Set.ordConnected_Ici
 #align set.Ici.is_atom_iff Set.Ici.isAtom_iff
--/
 
-#print Set.Iic.isCoatom_iff /-
+/- warning: set.Iic.is_coatom_iff -> Set.Iic.isCoatom_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {b : α} {a : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b)}, Iff (IsCoatom.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b))) (Set.Iic.orderTop.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b) a) (Covby.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{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} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b)))))) a) b)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {b : α} {a : Set.Elem.{u1} α (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b)}, Iff (IsCoatom.{u1} (Set.Elem.{u1} α (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b))) (Set.Iic.orderTop.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b) a) (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b)) a) b)
+Case conversion may be inaccurate. Consider using '#align set.Iic.is_coatom_iff Set.Iic.isCoatom_iffₓ'. -/
 @[simp]
 theorem Set.Iic.isCoatom_iff {a : Set.Iic b} : IsCoatom a ↔ ↑a ⋖ b :=
   by
@@ -303,17 +356,24 @@ theorem Set.Iic.isCoatom_iff {a : Set.Iic b} : IsCoatom a ↔ ↑a ⋖ b :=
   refine' (Set.OrdConnected.apply_covby_apply_iff (OrderEmbedding.subtype fun c => c ≤ b) _).symm
   simpa only [OrderEmbedding.subtype_apply, Subtype.range_coe_subtype] using Set.ordConnected_Iic
 #align set.Iic.is_coatom_iff Set.Iic.isCoatom_iff
--/
 
-#print covby_iff_atom_Ici /-
+/- warning: covby_iff_atom_Ici -> covby_iff_atom_Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a b), Iff (Covby.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a b) (IsAtom.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a))) (Set.Ici.orderBot.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)) b h))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a b), Iff (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a b) (IsAtom.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a))) (Set.Ici.orderBot.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)) b h))
+Case conversion may be inaccurate. Consider using '#align covby_iff_atom_Ici covby_iff_atom_Iciₓ'. -/
 theorem covby_iff_atom_Ici (h : a ≤ b) : a ⋖ b ↔ IsAtom (⟨b, h⟩ : Set.Ici a) := by simp
 #align covby_iff_atom_Ici covby_iff_atom_Ici
--/
 
-#print covby_iff_coatom_Iic /-
+/- warning: covby_iff_coatom_Iic -> covby_iff_coatom_Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a b), Iff (Covby.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a b) (IsCoatom.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b))) (Set.Iic.orderTop.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b)) a h))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {a : α} {b : α} (h : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a b), Iff (Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a b) (IsCoatom.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b))) (Set.Iic.orderTop.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b) (Subtype.mk.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) b)) a h))
+Case conversion may be inaccurate. Consider using '#align covby_iff_coatom_Iic covby_iff_coatom_Iicₓ'. -/
 theorem covby_iff_coatom_Iic (h : a ≤ b) : a ⋖ b ↔ IsCoatom (⟨a, h⟩ : Set.Iic b) := by simp
 #align covby_iff_coatom_Iic covby_iff_coatom_Iic
--/
 
 end PartialOrder
 
@@ -321,7 +381,7 @@ section Pairwise
 
 /- warning: is_atom.inf_eq_bot_of_ne -> IsAtom.inf_eq_bot_of_ne is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) a b) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))) _inst_2)))
+  forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) a b) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))) _inst_2)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toInf.{u1} α _inst_1) a b) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))) _inst_2)))
 Case conversion may be inaccurate. Consider using '#align is_atom.inf_eq_bot_of_ne IsAtom.inf_eq_bot_of_neₓ'. -/
@@ -330,16 +390,20 @@ theorem IsAtom.inf_eq_bot_of_ne [SemilatticeInf α] [OrderBot α] {a b : α} (ha
   hab.not_le_or_not_le.elim (ha.lt_iff.1 ∘ inf_lt_left.2) (hb.lt_iff.1 ∘ inf_lt_right.2)
 #align is_atom.inf_eq_bot_of_ne IsAtom.inf_eq_bot_of_ne
 
-#print IsAtom.disjoint_of_ne /-
+/- warning: is_atom.disjoint_of_ne -> IsAtom.disjoint_of_ne is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Disjoint.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1) _inst_2 a b)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Disjoint.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1) _inst_2 a b)
+Case conversion may be inaccurate. Consider using '#align is_atom.disjoint_of_ne IsAtom.disjoint_of_neₓ'. -/
 theorem IsAtom.disjoint_of_ne [SemilatticeInf α] [OrderBot α] {a b : α} (ha : IsAtom a)
     (hb : IsAtom b) (hab : a ≠ b) : Disjoint a b :=
   disjoint_iff.mpr (IsAtom.inf_eq_bot_of_ne ha hb hab)
 #align is_atom.disjoint_of_ne IsAtom.disjoint_of_ne
--/
 
 /- warning: is_coatom.sup_eq_top_of_ne -> IsCoatom.sup_eq_top_of_ne is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) a b) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))) _inst_2)))
+  forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) a b) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))) _inst_2)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α _inst_1) a b) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))) _inst_2)))
 Case conversion may be inaccurate. Consider using '#align is_coatom.sup_eq_top_of_ne IsCoatom.sup_eq_top_of_neₓ'. -/
@@ -356,21 +420,29 @@ section Atomic
 
 variable [PartialOrder α] (α)
 
-#print IsAtomic /-
+/- warning: is_atomic -> IsAtomic is a dubious translation:
+lean 3 declaration is
+  forall (α : Type.{u1}) [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Prop
+but is expected to have type
+  forall (α : Type.{u1}) [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Prop
+Case conversion may be inaccurate. Consider using '#align is_atomic IsAtomicₓ'. -/
 /-- A lattice is atomic iff every element other than `⊥` has an atom below it. -/
 @[mk_iff]
 class IsAtomic [OrderBot α] : Prop where
   eq_bot_or_exists_atom_le : ∀ b : α, b = ⊥ ∨ ∃ a : α, IsAtom a ∧ a ≤ b
 #align is_atomic IsAtomic
--/
 
-#print IsCoatomic /-
+/- warning: is_coatomic -> IsCoatomic is a dubious translation:
+lean 3 declaration is
+  forall (α : Type.{u1}) [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Prop
+but is expected to have type
+  forall (α : Type.{u1}) [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Prop
+Case conversion may be inaccurate. Consider using '#align is_coatomic IsCoatomicₓ'. -/
 /-- A lattice is coatomic iff every element other than `⊤` has a coatom above it. -/
 @[mk_iff]
 class IsCoatomic [OrderTop α] : Prop where
   eq_top_or_exists_le_coatom : ∀ b : α, b = ⊤ ∨ ∃ a : α, IsCoatom a ∧ b ≤ a
 #align is_coatomic IsCoatomic
--/
 
 export IsAtomic (eq_bot_or_exists_atom_le)
 
@@ -378,31 +450,43 @@ export IsCoatomic (eq_top_or_exists_le_coatom)
 
 variable {α}
 
-#print isCoatomic_dual_iff_isAtomic /-
+/- warning: is_coatomic_dual_iff_is_atomic -> isCoatomic_dual_iff_isAtomic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Iff (IsCoatomic.{u1} (OrderDual.{u1} α) (OrderDual.partialOrder.{u1} α _inst_1) (OrderDual.orderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) (IsAtomic.{u1} α _inst_1 _inst_2)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Iff (IsCoatomic.{u1} (OrderDual.{u1} α) (OrderDual.partialOrder.{u1} α _inst_1) (OrderDual.orderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) (IsAtomic.{u1} α _inst_1 _inst_2)
+Case conversion may be inaccurate. Consider using '#align is_coatomic_dual_iff_is_atomic isCoatomic_dual_iff_isAtomicₓ'. -/
 @[simp]
 theorem isCoatomic_dual_iff_isAtomic [OrderBot α] : IsCoatomic αᵒᵈ ↔ IsAtomic α :=
   ⟨fun h => ⟨fun b => by apply h.eq_top_or_exists_le_coatom⟩, fun h =>
     ⟨fun b => by apply h.eq_bot_or_exists_atom_le⟩⟩
 #align is_coatomic_dual_iff_is_atomic isCoatomic_dual_iff_isAtomic
--/
 
-#print isAtomic_dual_iff_isCoatomic /-
+/- warning: is_atomic_dual_iff_is_coatomic -> isAtomic_dual_iff_isCoatomic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Iff (IsAtomic.{u1} (OrderDual.{u1} α) (OrderDual.partialOrder.{u1} α _inst_1) (OrderDual.orderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) (IsCoatomic.{u1} α _inst_1 _inst_2)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Iff (IsAtomic.{u1} (OrderDual.{u1} α) (OrderDual.partialOrder.{u1} α _inst_1) (OrderDual.orderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) (IsCoatomic.{u1} α _inst_1 _inst_2)
+Case conversion may be inaccurate. Consider using '#align is_atomic_dual_iff_is_coatomic isAtomic_dual_iff_isCoatomicₓ'. -/
 @[simp]
 theorem isAtomic_dual_iff_isCoatomic [OrderTop α] : IsAtomic αᵒᵈ ↔ IsCoatomic α :=
   ⟨fun h => ⟨fun b => by apply h.eq_bot_or_exists_atom_le⟩, fun h =>
     ⟨fun b => by apply h.eq_top_or_exists_le_coatom⟩⟩
 #align is_atomic_dual_iff_is_coatomic isAtomic_dual_iff_isCoatomic
--/
 
 namespace IsAtomic
 
 variable [OrderBot α] [IsAtomic α]
 
-#print IsAtomic.isCoatomic_dual /-
+/- warning: is_atomic.is_coatomic_dual -> IsAtomic.isCoatomic_dual is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsAtomic.{u1} α _inst_1 _inst_2], IsCoatomic.{u1} (OrderDual.{u1} α) (OrderDual.partialOrder.{u1} α _inst_1) (OrderDual.orderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsAtomic.{u1} α _inst_1 _inst_2], IsCoatomic.{u1} (OrderDual.{u1} α) (OrderDual.partialOrder.{u1} α _inst_1) (OrderDual.orderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)
+Case conversion may be inaccurate. Consider using '#align is_atomic.is_coatomic_dual IsAtomic.isCoatomic_dualₓ'. -/
 instance isCoatomic_dual : IsCoatomic αᵒᵈ :=
   isCoatomic_dual_iff_isAtomic.2 ‹IsAtomic α›
 #align is_atomic.is_coatomic_dual IsAtomic.isCoatomic_dual
--/
 
 instance {x : α} : IsAtomic (Set.Iic x) :=
   ⟨fun ⟨y, hy⟩ =>
@@ -415,11 +499,15 @@ namespace IsCoatomic
 
 variable [OrderTop α] [IsCoatomic α]
 
-#print IsCoatomic.isCoatomic /-
+/- warning: is_coatomic.is_coatomic -> IsCoatomic.isCoatomic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsCoatomic.{u1} α _inst_1 _inst_2], IsAtomic.{u1} (OrderDual.{u1} α) (OrderDual.partialOrder.{u1} α _inst_1) (OrderDual.orderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsCoatomic.{u1} α _inst_1 _inst_2], IsAtomic.{u1} (OrderDual.{u1} α) (OrderDual.partialOrder.{u1} α _inst_1) (OrderDual.orderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)
+Case conversion may be inaccurate. Consider using '#align is_coatomic.is_coatomic IsCoatomic.isCoatomicₓ'. -/
 instance isCoatomic : IsAtomic αᵒᵈ :=
   isAtomic_dual_iff_isCoatomic.2 ‹IsCoatomic α›
 #align is_coatomic.is_coatomic IsCoatomic.isCoatomic
--/
 
 instance {x : α} : IsCoatomic (Set.Ici x) :=
   ⟨fun ⟨y, hy⟩ =>
@@ -428,7 +516,12 @@ instance {x : α} : IsCoatomic (Set.Ici x) :=
 
 end IsCoatomic
 
-#print isAtomic_iff_forall_isAtomic_Iic /-
+/- warning: is_atomic_iff_forall_is_atomic_Iic -> isAtomic_iff_forall_isAtomic_Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Iff (IsAtomic.{u1} α _inst_1 _inst_2) (forall (x : α), IsAtomic.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) x)) (Subtype.partialOrder.{u1} α _inst_1 (fun (x_1 : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x_1 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) x))) (Set.Iic.orderBot.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 x))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Iff (IsAtomic.{u1} α _inst_1 _inst_2) (forall (x : α), IsAtomic.{u1} (Set.Elem.{u1} α (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) x)) (Subtype.partialOrder.{u1} α _inst_1 (fun (x_1 : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x_1 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) x))) (Set.Iic.orderBot.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 x))
+Case conversion may be inaccurate. Consider using '#align is_atomic_iff_forall_is_atomic_Iic isAtomic_iff_forall_isAtomic_Iicₓ'. -/
 theorem isAtomic_iff_forall_isAtomic_Iic [OrderBot α] :
     IsAtomic α ↔ ∀ x : α, IsAtomic (Set.Iic x) :=
   ⟨@IsAtomic.Set.Iic.isAtomic _ _ _, fun h =>
@@ -436,20 +529,28 @@ theorem isAtomic_iff_forall_isAtomic_Iic [OrderBot α] :
       ((@eq_bot_or_exists_atom_le _ _ _ (h x)) (⊤ : Set.Iic x)).imp Subtype.mk_eq_mk.1
         (Exists.imp' coe fun ⟨a, ha⟩ => And.imp_left IsAtom.of_isAtom_coe_Iic)⟩⟩
 #align is_atomic_iff_forall_is_atomic_Iic isAtomic_iff_forall_isAtomic_Iic
--/
 
-#print isCoatomic_iff_forall_isCoatomic_Ici /-
+/- warning: is_coatomic_iff_forall_is_coatomic_Ici -> isCoatomic_iff_forall_isCoatomic_Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Iff (IsCoatomic.{u1} α _inst_1 _inst_2) (forall (x : α), IsCoatomic.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) x)) (Subtype.partialOrder.{u1} α _inst_1 (fun (x_1 : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x_1 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) x))) (Set.Ici.orderTop.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 x))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Iff (IsCoatomic.{u1} α _inst_1 _inst_2) (forall (x : α), IsCoatomic.{u1} (Set.Elem.{u1} α (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) x)) (Subtype.partialOrder.{u1} α _inst_1 (fun (x_1 : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x_1 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) x))) (Set.Ici.orderTop.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 x))
+Case conversion may be inaccurate. Consider using '#align is_coatomic_iff_forall_is_coatomic_Ici isCoatomic_iff_forall_isCoatomic_Iciₓ'. -/
 theorem isCoatomic_iff_forall_isCoatomic_Ici [OrderTop α] :
     IsCoatomic α ↔ ∀ x : α, IsCoatomic (Set.Ici x) :=
   isAtomic_dual_iff_isCoatomic.symm.trans <|
     isAtomic_iff_forall_isAtomic_Iic.trans <|
       forall_congr' fun x => isCoatomic_dual_iff_isAtomic.symm.trans Iff.rfl
 #align is_coatomic_iff_forall_is_coatomic_Ici isCoatomic_iff_forall_isCoatomic_Ici
--/
 
 section WellFounded
 
-#print isAtomic_of_orderBot_wellFounded_lt /-
+/- warning: is_atomic_of_order_bot_well_founded_lt -> isAtomic_of_orderBot_wellFounded_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], (WellFounded.{succ u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) -> (IsAtomic.{u1} α _inst_1 _inst_2)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], (WellFounded.{succ u1} α (fun (x._@.Mathlib.Order.Atoms._hyg.1887 : α) (x._@.Mathlib.Order.Atoms._hyg.1889 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x._@.Mathlib.Order.Atoms._hyg.1887 x._@.Mathlib.Order.Atoms._hyg.1889)) -> (IsAtomic.{u1} α _inst_1 _inst_2)
+Case conversion may be inaccurate. Consider using '#align is_atomic_of_order_bot_well_founded_lt isAtomic_of_orderBot_wellFounded_ltₓ'. -/
 theorem isAtomic_of_orderBot_wellFounded_lt [OrderBot α]
     (h : WellFounded ((· < ·) : α → α → Prop)) : IsAtomic α :=
   ⟨fun a =>
@@ -457,14 +558,17 @@ theorem isAtomic_of_orderBot_wellFounded_lt [OrderBot α]
       let ⟨b, hb, hm⟩ := h.has_min { b | b ≠ ⊥ ∧ b ≤ a } ⟨a, ha, le_rfl⟩
       ⟨b, ⟨hb.1, fun c => not_imp_not.1 fun hc hl => hm c ⟨hc, hl.le.trans hb.2⟩ hl⟩, hb.2⟩⟩
 #align is_atomic_of_order_bot_well_founded_lt isAtomic_of_orderBot_wellFounded_lt
--/
 
-#print isCoatomic_of_orderTop_gt_wellFounded /-
+/- warning: is_coatomic_of_order_top_gt_well_founded -> isCoatomic_of_orderTop_gt_wellFounded is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], (WellFounded.{succ u1} α (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) -> (IsCoatomic.{u1} α _inst_1 _inst_2)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], (WellFounded.{succ u1} α (fun (x._@.Mathlib.Order.Atoms._hyg.2010 : α) (x._@.Mathlib.Order.Atoms._hyg.2012 : α) => GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x._@.Mathlib.Order.Atoms._hyg.2010 x._@.Mathlib.Order.Atoms._hyg.2012)) -> (IsCoatomic.{u1} α _inst_1 _inst_2)
+Case conversion may be inaccurate. Consider using '#align is_coatomic_of_order_top_gt_well_founded isCoatomic_of_orderTop_gt_wellFoundedₓ'. -/
 theorem isCoatomic_of_orderTop_gt_wellFounded [OrderTop α]
     (h : WellFounded ((· > ·) : α → α → Prop)) : IsCoatomic α :=
   isAtomic_dual_iff_isCoatomic.1 (@isAtomic_of_orderBot_wellFounded_lt αᵒᵈ _ _ h)
 #align is_coatomic_of_order_top_gt_well_founded isCoatomic_of_orderTop_gt_wellFounded
--/
 
 end WellFounded
 
@@ -533,7 +637,7 @@ variable [IsAtomistic α]
 
 /- warning: Sup_atoms_le_eq -> sSup_atoms_le_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1] (b : α), Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (setOf.{u1} α (fun (a : α) => And (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) a) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)))) b
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1] (b : α), Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (setOf.{u1} α (fun (a : α) => And (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) a) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)))) b
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1] (b : α), Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => And (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) a) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)))) b
 Case conversion may be inaccurate. Consider using '#align Sup_atoms_le_eq sSup_atoms_le_eqₓ'. -/
@@ -546,7 +650,7 @@ theorem sSup_atoms_le_eq (b : α) : sSup { a : α | IsAtom a ∧ a ≤ b } = b :
 
 /- warning: Sup_atoms_eq_top -> sSup_atoms_eq_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1], Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (setOf.{u1} α (fun (a : α) => IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) a))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1], Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (setOf.{u1} α (fun (a : α) => IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) a))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1], Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) a))) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
 Case conversion may be inaccurate. Consider using '#align Sup_atoms_eq_top sSup_atoms_eq_topₓ'. -/
@@ -557,14 +661,18 @@ theorem sSup_atoms_eq_top : sSup { a : α | IsAtom a } = ⊤ :=
   exact (and_iff_left le_top).symm
 #align Sup_atoms_eq_top sSup_atoms_eq_top
 
-#print le_iff_atom_le_imp /-
+/- warning: le_iff_atom_le_imp -> le_iff_atom_le_imp is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1] {a : α} {b : α}, Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b) (forall (c : α), (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) c a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) c b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1] {a : α} {b : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b) (forall (c : α), (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) c a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) c b))
+Case conversion may be inaccurate. Consider using '#align le_iff_atom_le_imp le_iff_atom_le_impₓ'. -/
 theorem le_iff_atom_le_imp {a b : α} : a ≤ b ↔ ∀ c : α, IsAtom c → c ≤ a → c ≤ b :=
   ⟨fun ab c hc ca => le_trans ca ab, fun h =>
     by
     rw [← sSup_atoms_le_eq a, ← sSup_atoms_le_eq b]
     exact sSup_le_sSup fun c hc => ⟨hc.1, h c hc.1 hc.2⟩⟩
 #align le_iff_atom_le_imp le_iff_atom_le_imp
--/
 
 end IsAtomistic
 
@@ -649,7 +757,12 @@ protected def IsSimpleOrder.preorder {α} [LE α] [BoundedOrder α] [IsSimpleOrd
 #align is_simple_order.preorder IsSimpleOrder.preorder
 -/
 
-#print IsSimpleOrder.linearOrder /-
+/- warning: is_simple_order.linear_order -> IsSimpleOrder.linearOrder is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2] [_inst_4 : DecidableEq.{succ u1} α], LinearOrder.{u1} α
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2] [_inst_4 : DecidableEq.{succ u1} α], LinearOrder.{u1} α
+Case conversion may be inaccurate. Consider using '#align is_simple_order.linear_order IsSimpleOrder.linearOrderₓ'. -/
 /-- A simple partial ordered `bounded_order` induces a linear order.
 This is not an instance to prevent loops. -/
 protected def IsSimpleOrder.linearOrder [DecidableEq α] : LinearOrder α :=
@@ -667,11 +780,10 @@ protected def IsSimpleOrder.linearOrder [DecidableEq α] : LinearOrder α :=
             hb (top_unique (le_trans (top_le_iff.mpr (Or.resolve_left (eq_bot_or_eq_top a) ha)) H))
     DecidableEq := by assumption }
 #align is_simple_order.linear_order IsSimpleOrder.linearOrder
--/
 
 /- warning: is_atom_top -> isAtom_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2], IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)))
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2], IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2], IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)))
 Case conversion may be inaccurate. Consider using '#align is_atom_top isAtom_topₓ'. -/
@@ -682,7 +794,7 @@ theorem isAtom_top : IsAtom (⊤ : α) :=
 
 /- warning: is_coatom_bot -> isCoatom_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2], IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)))
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2], IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2], IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)))
 Case conversion may be inaccurate. Consider using '#align is_coatom_bot isCoatom_botₓ'. -/
@@ -693,7 +805,7 @@ theorem isCoatom_bot : IsCoatom (⊥ : α) :=
 
 /- warning: bot_covby_top -> bot_covby_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2], Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)))
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2], Covby.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2], Covby.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)))
 Case conversion may be inaccurate. Consider using '#align bot_covby_top bot_covby_topₓ'. -/
@@ -711,7 +823,7 @@ variable [Preorder α] [BoundedOrder α] [IsSimpleOrder α] {a b : α} (h : a <
 
 /- warning: is_simple_order.eq_bot_of_lt -> IsSimpleOrder.eq_bot_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) a b) -> (Eq.{succ u1} α a (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) a b) -> (Eq.{succ u1} α a (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) a b) -> (Eq.{succ u1} α a (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))))
 Case conversion may be inaccurate. Consider using '#align is_simple_order.eq_bot_of_lt IsSimpleOrder.eq_bot_of_ltₓ'. -/
@@ -721,7 +833,7 @@ theorem eq_bot_of_lt : a = ⊥ :=
 
 /- warning: is_simple_order.eq_top_of_lt -> IsSimpleOrder.eq_top_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) a b) -> (Eq.{succ u1} α b (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) a b) -> (Eq.{succ u1} α b (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) a b) -> (Eq.{succ u1} α b (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))))
 Case conversion may be inaccurate. Consider using '#align is_simple_order.eq_top_of_lt IsSimpleOrder.eq_top_of_ltₓ'. -/
@@ -741,23 +853,31 @@ section BoundedOrder
 
 variable [Lattice α] [BoundedOrder α] [IsSimpleOrder α]
 
-#print IsSimpleOrder.lattice /-
+/- warning: is_simple_order.lattice -> IsSimpleOrder.lattice is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_4 : DecidableEq.{succ u1} α] [_inst_5 : PartialOrder.{u1} α] [_inst_6 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_5))] [_inst_7 : IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_5)) _inst_6], Lattice.{u1} α
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_4 : DecidableEq.{succ u1} α] [_inst_5 : PartialOrder.{u1} α] [_inst_6 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_5))] [_inst_7 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_5)) _inst_6], Lattice.{u1} α
+Case conversion may be inaccurate. Consider using '#align is_simple_order.lattice IsSimpleOrder.latticeₓ'. -/
 /-- A simple partial ordered `bounded_order` induces a lattice.
 This is not an instance to prevent loops -/
 protected def lattice {α} [DecidableEq α] [PartialOrder α] [BoundedOrder α] [IsSimpleOrder α] :
     Lattice α :=
   @LinearOrder.toLattice α IsSimpleOrder.linearOrder
 #align is_simple_order.lattice IsSimpleOrder.lattice
--/
 
-#print IsSimpleOrder.distribLattice /-
+/- warning: is_simple_order.distrib_lattice -> IsSimpleOrder.distribLattice is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2], DistribLattice.{u1} α
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2], DistribLattice.{u1} α
+Case conversion may be inaccurate. Consider using '#align is_simple_order.distrib_lattice IsSimpleOrder.distribLatticeₓ'. -/
 /-- A lattice that is a `bounded_order` is a distributive lattice.
 This is not an instance to prevent loops -/
 protected def distribLattice : DistribLattice α :=
   { (inferInstance : Lattice α) with
     le_sup_inf := fun x y z => by rcases eq_bot_or_eq_top x with (rfl | rfl) <;> simp }
 #align is_simple_order.distrib_lattice IsSimpleOrder.distribLattice
--/
 
 -- see Note [lower instance priority]
 instance (priority := 100) : IsAtomic α :=
@@ -788,7 +908,7 @@ def equivBool {α} [DecidableEq α] [LE α] [BoundedOrder α] [IsSimpleOrder α]
 
 /- warning: is_simple_order.order_iso_bool -> IsSimpleOrder.orderIsoBool is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2))] [_inst_4 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) _inst_3], OrderIso.{u1, 0} α Bool (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (Preorder.toLE.{0} Bool (PartialOrder.toPreorder.{0} Bool (SemilatticeInf.toPartialOrder.{0} Bool (Lattice.toSemilatticeInf.{0} Bool (GeneralizedCoheytingAlgebra.toLattice.{0} Bool (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{0} Bool (BooleanAlgebra.toGeneralizedBooleanAlgebra.{0} Bool Bool.booleanAlgebra)))))))
+  forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2))] [_inst_4 : IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) _inst_3], OrderIso.{u1, 0} α Bool (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (Preorder.toHasLe.{0} Bool (PartialOrder.toPreorder.{0} Bool (SemilatticeInf.toPartialOrder.{0} Bool (Lattice.toSemilatticeInf.{0} Bool (GeneralizedCoheytingAlgebra.toLattice.{0} Bool (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{0} Bool (BooleanAlgebra.toGeneralizedBooleanAlgebra.{0} Bool Bool.booleanAlgebra)))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2))] [_inst_4 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) _inst_3], OrderIso.{u1, 0} α Bool (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (Preorder.toLE.{0} Bool (PartialOrder.toPreorder.{0} Bool (SemilatticeInf.toPartialOrder.{0} Bool (Lattice.toSemilatticeInf.{0} Bool (GeneralizedCoheytingAlgebra.toLattice.{0} Bool (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{0} Bool (BiheytingAlgebra.toCoheytingAlgebra.{0} Bool (BooleanAlgebra.toBiheytingAlgebra.{0} Bool instBooleanAlgebraBool))))))))
 Case conversion may be inaccurate. Consider using '#align is_simple_order.order_iso_bool IsSimpleOrder.orderIsoBoolₓ'. -/
@@ -804,7 +924,12 @@ def orderIsoBool : α ≃o Bool :=
         · simp [bot_ne_top] }
 #align is_simple_order.order_iso_bool IsSimpleOrder.orderIsoBool
 
-#print IsSimpleOrder.booleanAlgebra /-
+/- warning: is_simple_order.boolean_algebra -> IsSimpleOrder.booleanAlgebra is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_5 : DecidableEq.{succ u1} α] [_inst_6 : Lattice.{u1} α] [_inst_7 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_6))))] [_inst_8 : IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_6)))) _inst_7], BooleanAlgebra.{u1} α
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_5 : DecidableEq.{succ u1} α] [_inst_6 : Lattice.{u1} α] [_inst_7 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_6))))] [_inst_8 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_6)))) _inst_7], BooleanAlgebra.{u1} α
+Case conversion may be inaccurate. Consider using '#align is_simple_order.boolean_algebra IsSimpleOrder.booleanAlgebraₓ'. -/
 /-- A simple `bounded_order` is also a `boolean_algebra`. -/
 protected def booleanAlgebra {α} [DecidableEq α] [Lattice α] [BoundedOrder α] [IsSimpleOrder α] :
     BooleanAlgebra α :=
@@ -822,7 +947,6 @@ protected def booleanAlgebra {α} [DecidableEq α] [Lattice α] [BoundedOrder α
         split_ifs with h h <;> simp [h]
     top_le_sup_compl := fun x => by rcases eq_bot_or_eq_top x with (rfl | rfl) <;> simp }
 #align is_simple_order.boolean_algebra IsSimpleOrder.booleanAlgebra
--/
 
 end DecidableEq
 
@@ -830,7 +954,12 @@ variable [Lattice α] [BoundedOrder α] [IsSimpleOrder α]
 
 open Classical
 
-#print IsSimpleOrder.completeLattice /-
+/- warning: is_simple_order.complete_lattice -> IsSimpleOrder.completeLattice is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2], CompleteLattice.{u1} α
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2], CompleteLattice.{u1} α
+Case conversion may be inaccurate. Consider using '#align is_simple_order.complete_lattice IsSimpleOrder.completeLatticeₓ'. -/
 /-- A simple `bounded_order` is also complete. -/
 protected noncomputable def completeLattice : CompleteLattice α :=
   { (inferInstance : Lattice α),
@@ -859,9 +988,13 @@ protected noncomputable def completeLattice : CompleteLattice α :=
         intro con
         exact top_ne_bot (eq_bot_iff.2 (h ⊥ Con)) }
 #align is_simple_order.complete_lattice IsSimpleOrder.completeLattice
--/
 
-#print IsSimpleOrder.completeBooleanAlgebra /-
+/- warning: is_simple_order.complete_boolean_algebra -> IsSimpleOrder.completeBooleanAlgebra is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2], CompleteBooleanAlgebra.{u1} α
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2], CompleteBooleanAlgebra.{u1} α
+Case conversion may be inaccurate. Consider using '#align is_simple_order.complete_boolean_algebra IsSimpleOrder.completeBooleanAlgebraₓ'. -/
 /-- A simple `bounded_order` is also a `complete_boolean_algebra`. -/
 protected noncomputable def completeBooleanAlgebra : CompleteBooleanAlgebra α :=
   { IsSimpleOrder.completeLattice,
@@ -879,7 +1012,6 @@ protected noncomputable def completeBooleanAlgebra : CompleteBooleanAlgebra α :
       · simp only [top_inf_eq, ← sSup_eq_iSup]
         exact le_rfl }
 #align is_simple_order.complete_boolean_algebra IsSimpleOrder.completeBooleanAlgebra
--/
 
 end IsSimpleOrder
 
@@ -905,7 +1037,7 @@ end IsSimpleOrder
 
 /- warning: is_simple_order_iff_is_atom_top -> isSimpleOrder_iff_isAtom_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Iff (IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))))
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Iff (IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Iff (IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))))
 Case conversion may be inaccurate. Consider using '#align is_simple_order_iff_is_atom_top isSimpleOrder_iff_isAtom_topₓ'. -/
@@ -918,7 +1050,7 @@ theorem isSimpleOrder_iff_isAtom_top [PartialOrder α] [BoundedOrder α] :
 
 /- warning: is_simple_order_iff_is_coatom_bot -> isSimpleOrder_iff_isCoatom_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Iff (IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))))
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Iff (IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))], Iff (IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))))
 Case conversion may be inaccurate. Consider using '#align is_simple_order_iff_is_coatom_bot isSimpleOrder_iff_isCoatom_botₓ'. -/
@@ -931,7 +1063,7 @@ namespace Set
 
 /- warning: set.is_simple_order_Iic_iff_is_atom -> Set.isSimpleOrder_Iic_iff_isAtom is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, Iff (IsSimpleOrder.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)) (Subtype.hasLe.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a))) (Set.Iic.boundedOrder.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, Iff (IsSimpleOrder.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)) (Subtype.hasLe.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a))) (Set.Iic.boundedOrder.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, Iff (IsSimpleOrder.{u1} (Set.Elem.{u1} α (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)) (Subtype.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a))) (Set.Iic.instBoundedOrderElemIicLeToLEMemSetInstMembershipSet.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
 Case conversion may be inaccurate. Consider using '#align set.is_simple_order_Iic_iff_is_atom Set.isSimpleOrder_Iic_iff_isAtomₓ'. -/
@@ -943,7 +1075,12 @@ theorem isSimpleOrder_Iic_iff_isAtom [PartialOrder α] [OrderBot α] {a : α} :
         Subtype.mk_eq_mk.2 (h b (Subtype.mk_lt_mk.1 hbotb))⟩
 #align set.is_simple_order_Iic_iff_is_atom Set.isSimpleOrder_Iic_iff_isAtom
 
-#print Set.isSimpleOrder_Ici_iff_isCoatom /-
+/- warning: set.is_simple_order_Ici_iff_is_coatom -> Set.isSimpleOrder_Ici_iff_isCoatom is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, Iff (IsSimpleOrder.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)) (Subtype.hasLe.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a))) (Set.Ici.boundedOrder.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] {a : α}, Iff (IsSimpleOrder.{u1} (Set.Elem.{u1} α (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a)) (Subtype.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a))) (Set.Ici.boundedOrder.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_2 a)
+Case conversion may be inaccurate. Consider using '#align set.is_simple_order_Ici_iff_is_coatom Set.isSimpleOrder_Ici_iff_isCoatomₓ'. -/
 theorem isSimpleOrder_Ici_iff_isCoatom [PartialOrder α] [OrderTop α] {a : α} :
     IsSimpleOrder (Ici a) ↔ IsCoatom a :=
   isSimpleOrder_iff_isCoatom_bot.trans <|
@@ -951,7 +1088,6 @@ theorem isSimpleOrder_Ici_iff_isCoatom [PartialOrder α] [OrderTop α] {a : α}
       ⟨fun h b ab => Subtype.mk_eq_mk.1 (h ⟨b, le_of_lt ab⟩ ab), fun h ⟨b, hab⟩ hbotb =>
         Subtype.mk_eq_mk.2 (h b (Subtype.mk_lt_mk.1 hbotb))⟩
 #align set.is_simple_order_Ici_iff_is_coatom Set.isSimpleOrder_Ici_iff_isCoatom
--/
 
 end Set
 
@@ -961,7 +1097,7 @@ variable [PartialOrder α] [PartialOrder β]
 
 /- warning: order_embedding.is_atom_of_map_bot_of_image -> OrderEmbedding.isAtom_of_map_bot_of_image is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderEmbedding.{u2, u1} β α (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))), (Eq.{succ u1} α (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) -> (forall {b : β}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f b)) -> (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderEmbedding.{u2, u1} β α (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))), (Eq.{succ u1} α (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) -> (forall {b : β}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f b)) -> (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))), (Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Bot.bot.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (OrderBot.toBot.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) _inst_1)) _inst_3))) -> (forall {b : β}, (IsAtom.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) b) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) b) _inst_1) _inst_3 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f b)) -> (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b))
 Case conversion may be inaccurate. Consider using '#align order_embedding.is_atom_of_map_bot_of_image OrderEmbedding.isAtom_of_map_bot_of_imageₓ'. -/
@@ -974,7 +1110,7 @@ theorem isAtom_of_map_bot_of_image [OrderBot α] [OrderBot β] (f : β ↪o α)
 
 /- warning: order_embedding.is_coatom_of_map_top_of_image -> OrderEmbedding.isCoatom_of_map_top_of_image is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderEmbedding.{u2, u1} β α (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))), (Eq.{succ u1} α (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) -> (forall {b : β}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f b)) -> (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderEmbedding.{u2, u1} β α (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))), (Eq.{succ u1} α (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) -> (forall {b : β}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f b)) -> (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))), (Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Top.top.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (OrderTop.toTop.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) _inst_1)) _inst_3))) -> (forall {b : β}, (IsCoatom.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) b) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) b) _inst_1) _inst_3 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f b)) -> (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b))
 Case conversion may be inaccurate. Consider using '#align order_embedding.is_coatom_of_map_top_of_image OrderEmbedding.isCoatom_of_map_top_of_imageₓ'. -/
@@ -991,7 +1127,7 @@ variable [PartialOrder α] [PartialOrder β]
 
 /- warning: galois_insertion.is_atom_of_u_bot -> GaloisInsertion.isAtom_of_u_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (Eq.{succ u1} α (u (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) -> (forall {b : β}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (u b)) -> (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (Eq.{succ u1} α (u (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) -> (forall {b : β}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (u b)) -> (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u2, u1} α β (PartialOrder.toPreorder.{u2} α _inst_1) (PartialOrder.toPreorder.{u1} β _inst_2) l u) -> (Eq.{succ u2} α (u (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Bot.bot.{u2} α (OrderBot.toBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) _inst_3))) -> (forall {b : β}, (IsAtom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 (u b)) -> (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b))
 Case conversion may be inaccurate. Consider using '#align galois_insertion.is_atom_of_u_bot GaloisInsertion.isAtom_of_u_botₓ'. -/
@@ -1003,7 +1139,7 @@ theorem isAtom_of_u_bot [OrderBot α] [OrderBot β] {l : α → β} {u : β →
 
 /- warning: galois_insertion.is_atom_iff -> GaloisInsertion.isAtom_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : IsAtomic.{u1} α _inst_1 _inst_3] [_inst_5 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (Eq.{succ u1} α (u (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_5))) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) -> (forall (a : α), (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a) -> (Eq.{succ u1} α (u (l a)) a)) -> (forall (a : α), Iff (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_5 (l a)) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : IsAtomic.{u1} α _inst_1 _inst_3] [_inst_5 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (Eq.{succ u1} α (u (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_5))) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) -> (forall (a : α), (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a) -> (Eq.{succ u1} α (u (l a)) a)) -> (forall (a : α), Iff (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_5 (l a)) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : IsAtomic.{u2} α _inst_1 _inst_3] [_inst_5 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u2, u1} α β (PartialOrder.toPreorder.{u2} α _inst_1) (PartialOrder.toPreorder.{u1} β _inst_2) l u) -> (Eq.{succ u2} α (u (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_5))) (Bot.bot.{u2} α (OrderBot.toBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) _inst_3))) -> (forall (a : α), (IsAtom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a) -> (Eq.{succ u2} α (u (l a)) a)) -> (forall (a : α), Iff (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_5 (l a)) (IsAtom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a))
 Case conversion may be inaccurate. Consider using '#align galois_insertion.is_atom_iff GaloisInsertion.isAtom_iffₓ'. -/
@@ -1026,7 +1162,7 @@ theorem isAtom_iff [OrderBot α] [IsAtomic α] [OrderBot β] {l : α → β} {u
 
 /- warning: galois_insertion.is_atom_iff' -> GaloisInsertion.isAtom_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : IsAtomic.{u1} α _inst_1 _inst_3] [_inst_5 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (Eq.{succ u1} α (u (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_5))) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) -> (forall (a : α), (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a) -> (Eq.{succ u1} α (u (l a)) a)) -> (forall (b : β), Iff (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (u b)) (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_5 b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : IsAtomic.{u1} α _inst_1 _inst_3] [_inst_5 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (Eq.{succ u1} α (u (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_5))) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) -> (forall (a : α), (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a) -> (Eq.{succ u1} α (u (l a)) a)) -> (forall (b : β), Iff (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (u b)) (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_5 b))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : IsAtomic.{u2} α _inst_1 _inst_3] [_inst_5 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u2, u1} α β (PartialOrder.toPreorder.{u2} α _inst_1) (PartialOrder.toPreorder.{u1} β _inst_2) l u) -> (Eq.{succ u2} α (u (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_5))) (Bot.bot.{u2} α (OrderBot.toBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) _inst_3))) -> (forall (a : α), (IsAtom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a) -> (Eq.{succ u2} α (u (l a)) a)) -> (forall (b : β), Iff (IsAtom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 (u b)) (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_5 b))
 Case conversion may be inaccurate. Consider using '#align galois_insertion.is_atom_iff' GaloisInsertion.isAtom_iff'ₓ'. -/
@@ -1037,7 +1173,7 @@ theorem isAtom_iff' [OrderBot α] [IsAtomic α] [OrderBot β] {l : α → β} {u
 
 /- warning: galois_insertion.is_coatom_of_image -> GaloisInsertion.isCoatom_of_image is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (forall {b : β}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (u b)) -> (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (forall {b : β}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (u b)) -> (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u2, u1} α β (PartialOrder.toPreorder.{u2} α _inst_1) (PartialOrder.toPreorder.{u1} β _inst_2) l u) -> (forall {b : β}, (IsCoatom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 (u b)) -> (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b))
 Case conversion may be inaccurate. Consider using '#align galois_insertion.is_coatom_of_image GaloisInsertion.isCoatom_of_imageₓ'. -/
@@ -1049,7 +1185,7 @@ theorem isCoatom_of_image [OrderTop α] [OrderTop β] {l : α → β} {u : β 
 
 /- warning: galois_insertion.is_coatom_iff -> GaloisInsertion.isCoatom_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : IsCoatomic.{u1} α _inst_1 _inst_3] [_inst_5 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (forall (a : α), (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a) -> (Eq.{succ u1} α (u (l a)) a)) -> (forall (b : β), Iff (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (u b)) (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_5 b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : IsCoatomic.{u1} α _inst_1 _inst_3] [_inst_5 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (forall (a : α), (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a) -> (Eq.{succ u1} α (u (l a)) a)) -> (forall (b : β), Iff (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (u b)) (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_5 b))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : IsCoatomic.{u2} α _inst_1 _inst_3] [_inst_5 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisInsertion.{u2, u1} α β (PartialOrder.toPreorder.{u2} α _inst_1) (PartialOrder.toPreorder.{u1} β _inst_2) l u) -> (forall (a : α), (IsCoatom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a) -> (Eq.{succ u2} α (u (l a)) a)) -> (forall (b : β), Iff (IsCoatom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 (u b)) (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_5 b))
 Case conversion may be inaccurate. Consider using '#align galois_insertion.is_coatom_iff GaloisInsertion.isCoatom_iffₓ'. -/
@@ -1075,7 +1211,7 @@ variable [PartialOrder α] [PartialOrder β]
 
 /- warning: galois_coinsertion.is_coatom_of_l_top -> GaloisCoinsertion.isCoatom_of_l_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (Eq.{succ u2} β (l (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) -> (forall {a : α}, (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (l a)) -> (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (Eq.{succ u2} β (l (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) -> (forall {a : α}, (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (l a)) -> (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u2, u1} α β (PartialOrder.toPreorder.{u2} α _inst_1) (PartialOrder.toPreorder.{u1} β _inst_2) l u) -> (Eq.{succ u1} β (l (Top.top.{u2} α (OrderTop.toTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) _inst_3))) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) -> (forall {a : α}, (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 (l a)) -> (IsCoatom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a))
 Case conversion may be inaccurate. Consider using '#align galois_coinsertion.is_coatom_of_l_top GaloisCoinsertion.isCoatom_of_l_topₓ'. -/
@@ -1086,7 +1222,7 @@ theorem isCoatom_of_l_top [OrderTop α] [OrderTop β] {l : α → β} {u : β 
 
 /- warning: galois_coinsertion.is_coatom_iff -> GaloisCoinsertion.isCoatom_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] [_inst_5 : IsCoatomic.{u2} β _inst_2 _inst_4] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (Eq.{succ u2} β (l (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) -> (forall (b : β), (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b) -> (Eq.{succ u2} β (l (u b)) b)) -> (forall (b : β), Iff (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (u b)) (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] [_inst_5 : IsCoatomic.{u2} β _inst_2 _inst_4] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (Eq.{succ u2} β (l (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) -> (forall (b : β), (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b) -> (Eq.{succ u2} β (l (u b)) b)) -> (forall (b : β), Iff (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (u b)) (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] [_inst_5 : IsCoatomic.{u1} β _inst_2 _inst_4] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u2, u1} α β (PartialOrder.toPreorder.{u2} α _inst_1) (PartialOrder.toPreorder.{u1} β _inst_2) l u) -> (Eq.{succ u1} β (l (Top.top.{u2} α (OrderTop.toTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) _inst_3))) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) -> (forall (b : β), (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b) -> (Eq.{succ u1} β (l (u b)) b)) -> (forall (b : β), Iff (IsCoatom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 (u b)) (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b))
 Case conversion may be inaccurate. Consider using '#align galois_coinsertion.is_coatom_iff GaloisCoinsertion.isCoatom_iffₓ'. -/
@@ -1098,7 +1234,7 @@ theorem isCoatom_iff [OrderTop α] [OrderTop β] [IsCoatomic β] {l : α → β}
 
 /- warning: galois_coinsertion.is_coatom_iff' -> GaloisCoinsertion.isCoatom_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] [_inst_5 : IsCoatomic.{u2} β _inst_2 _inst_4] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (Eq.{succ u2} β (l (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) -> (forall (b : β), (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b) -> (Eq.{succ u2} β (l (u b)) b)) -> (forall (a : α), Iff (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (l a)) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] [_inst_5 : IsCoatomic.{u2} β _inst_2 _inst_4] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (Eq.{succ u2} β (l (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) -> (forall (b : β), (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b) -> (Eq.{succ u2} β (l (u b)) b)) -> (forall (a : α), Iff (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (l a)) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] [_inst_5 : IsCoatomic.{u1} β _inst_2 _inst_4] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u2, u1} α β (PartialOrder.toPreorder.{u2} α _inst_1) (PartialOrder.toPreorder.{u1} β _inst_2) l u) -> (Eq.{succ u1} β (l (Top.top.{u2} α (OrderTop.toTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) _inst_3))) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) -> (forall (b : β), (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b) -> (Eq.{succ u1} β (l (u b)) b)) -> (forall (a : α), Iff (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 (l a)) (IsCoatom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a))
 Case conversion may be inaccurate. Consider using '#align galois_coinsertion.is_coatom_iff' GaloisCoinsertion.isCoatom_iff'ₓ'. -/
@@ -1110,7 +1246,7 @@ theorem isCoatom_iff' [OrderTop α] [OrderTop β] [IsCoatomic β] {l : α → β
 
 /- warning: galois_coinsertion.is_atom_of_image -> GaloisCoinsertion.isAtom_of_image is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (forall {a : α}, (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (l a)) -> (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (forall {a : α}, (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (l a)) -> (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u2, u1} α β (PartialOrder.toPreorder.{u2} α _inst_1) (PartialOrder.toPreorder.{u1} β _inst_2) l u) -> (forall {a : α}, (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 (l a)) -> (IsAtom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a))
 Case conversion may be inaccurate. Consider using '#align galois_coinsertion.is_atom_of_image GaloisCoinsertion.isAtom_of_imageₓ'. -/
@@ -1121,7 +1257,7 @@ theorem isAtom_of_image [OrderBot α] [OrderBot β] {l : α → β} {u : β →
 
 /- warning: galois_coinsertion.is_atom_iff -> GaloisCoinsertion.isAtom_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] [_inst_5 : IsAtomic.{u2} β _inst_2 _inst_4] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (forall (b : β), (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b) -> (Eq.{succ u2} β (l (u b)) b)) -> (forall (a : α), Iff (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (l a)) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] [_inst_5 : IsAtomic.{u2} β _inst_2 _inst_4] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u1, u2} α β (PartialOrder.toPreorder.{u1} α _inst_1) (PartialOrder.toPreorder.{u2} β _inst_2) l u) -> (forall (b : β), (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b) -> (Eq.{succ u2} β (l (u b)) b)) -> (forall (a : α), Iff (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (l a)) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] [_inst_5 : IsAtomic.{u1} β _inst_2 _inst_4] {l : α -> β} {u : β -> α}, (GaloisCoinsertion.{u2, u1} α β (PartialOrder.toPreorder.{u2} α _inst_1) (PartialOrder.toPreorder.{u1} β _inst_2) l u) -> (forall (b : β), (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b) -> (Eq.{succ u1} β (l (u b)) b)) -> (forall (a : α), Iff (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 (l a)) (IsAtom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a))
 Case conversion may be inaccurate. Consider using '#align galois_coinsertion.is_atom_iff GaloisCoinsertion.isAtom_iffₓ'. -/
@@ -1139,7 +1275,7 @@ variable [PartialOrder α] [PartialOrder β]
 
 /- warning: order_iso.is_atom_iff -> OrderIso.isAtom_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (a : α), Iff (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) f a)) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (a : α), Iff (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) f a)) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a)
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))) (a : α), Iff (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a)) (IsAtom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a)
 Case conversion may be inaccurate. Consider using '#align order_iso.is_atom_iff OrderIso.isAtom_iffₓ'. -/
@@ -1151,7 +1287,7 @@ theorem isAtom_iff [OrderBot α] [OrderBot β] (f : α ≃o β) (a : α) : IsAto
 
 /- warning: order_iso.is_coatom_iff -> OrderIso.isCoatom_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (a : α), Iff (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) f a)) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (a : α), Iff (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) f a)) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a)
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))) (a : α), Iff (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a)) (IsCoatom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a)
 Case conversion may be inaccurate. Consider using '#align order_iso.is_coatom_iff OrderIso.isCoatom_iffₓ'. -/
@@ -1162,7 +1298,7 @@ theorem isCoatom_iff [OrderTop α] [OrderTop β] (f : α ≃o β) (a : α) : IsC
 
 /- warning: order_iso.is_simple_order_iff -> OrderIso.isSimpleOrder_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))], (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) -> (Iff (IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3) (IsSimpleOrder.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))], (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) -> (Iff (IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3) (IsSimpleOrder.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : BoundedOrder.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : BoundedOrder.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))], (OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))) -> (Iff (IsSimpleOrder.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) _inst_3) (IsSimpleOrder.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))
 Case conversion may be inaccurate. Consider using '#align order_iso.is_simple_order_iff OrderIso.isSimpleOrder_iffₓ'. -/
@@ -1173,7 +1309,7 @@ theorem isSimpleOrder_iff [BoundedOrder α] [BoundedOrder β] (f : α ≃o β) :
 
 /- warning: order_iso.is_simple_order -> OrderIso.isSimpleOrder is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] [h : IsSimpleOrder.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4], (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) -> (IsSimpleOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] [h : IsSimpleOrder.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4], (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) -> (IsSimpleOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3)
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : BoundedOrder.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : BoundedOrder.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] [h : IsSimpleOrder.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4], (OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))) -> (IsSimpleOrder.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) _inst_3)
 Case conversion may be inaccurate. Consider using '#align order_iso.is_simple_order OrderIso.isSimpleOrderₓ'. -/
@@ -1184,7 +1320,7 @@ theorem isSimpleOrder [BoundedOrder α] [BoundedOrder β] [h : IsSimpleOrder β]
 
 /- warning: order_iso.is_atomic_iff -> OrderIso.isAtomic_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))], (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) -> (Iff (IsAtomic.{u1} α _inst_1 _inst_3) (IsAtomic.{u2} β _inst_2 _inst_4))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))], (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) -> (Iff (IsAtomic.{u1} α _inst_1 _inst_3) (IsAtomic.{u2} β _inst_2 _inst_4))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))], (OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))) -> (Iff (IsAtomic.{u2} α _inst_1 _inst_3) (IsAtomic.{u1} β _inst_2 _inst_4))
 Case conversion may be inaccurate. Consider using '#align order_iso.is_atomic_iff OrderIso.isAtomic_iffₓ'. -/
@@ -1196,7 +1332,7 @@ protected theorem isAtomic_iff [OrderBot α] [OrderBot β] (f : α ≃o β) : Is
 
 /- warning: order_iso.is_coatomic_iff -> OrderIso.isCoatomic_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))], (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) -> (Iff (IsCoatomic.{u1} α _inst_1 _inst_3) (IsCoatomic.{u2} β _inst_2 _inst_4))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))], (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) -> (Iff (IsCoatomic.{u1} α _inst_1 _inst_3) (IsCoatomic.{u2} β _inst_2 _inst_4))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))], (OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))) -> (Iff (IsCoatomic.{u2} α _inst_1 _inst_3) (IsCoatomic.{u1} β _inst_2 _inst_4))
 Case conversion may be inaccurate. Consider using '#align order_iso.is_coatomic_iff OrderIso.isCoatomic_iffₓ'. -/
@@ -1217,24 +1353,37 @@ variable {a b : α} (hc : IsCompl a b)
 
 include hc
 
-#print IsCompl.isAtom_iff_isCoatom /-
+/- warning: is_compl.is_atom_iff_is_coatom -> IsCompl.isAtom_iff_isCoatom is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsModularLattice.{u1} α _inst_1] {a : α} {b : α}, (IsCompl.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) _inst_2 a b) -> (Iff (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2) a) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2) b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsModularLattice.{u1} α _inst_1] {a : α} {b : α}, (IsCompl.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) _inst_2 a b) -> (Iff (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2) a) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2) b))
+Case conversion may be inaccurate. Consider using '#align is_compl.is_atom_iff_is_coatom IsCompl.isAtom_iff_isCoatomₓ'. -/
 theorem isAtom_iff_isCoatom : IsAtom a ↔ IsCoatom b :=
   Set.isSimpleOrder_Iic_iff_isAtom.symm.trans <|
     hc.IicOrderIsoIci.isSimpleOrder_iff.trans Set.isSimpleOrder_Ici_iff_isCoatom
 #align is_compl.is_atom_iff_is_coatom IsCompl.isAtom_iff_isCoatom
--/
 
-#print IsCompl.isCoatom_iff_isAtom /-
+/- warning: is_compl.is_coatom_iff_is_atom -> IsCompl.isCoatom_iff_isAtom is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsModularLattice.{u1} α _inst_1] {a : α} {b : α}, (IsCompl.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) _inst_2 a b) -> (Iff (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2) a) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2) b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsModularLattice.{u1} α _inst_1] {a : α} {b : α}, (IsCompl.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) _inst_2 a b) -> (Iff (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2) a) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2) b))
+Case conversion may be inaccurate. Consider using '#align is_compl.is_coatom_iff_is_atom IsCompl.isCoatom_iff_isAtomₓ'. -/
 theorem isCoatom_iff_isAtom : IsCoatom a ↔ IsAtom b :=
   hc.symm.isAtom_iff_isCoatom.symm
 #align is_compl.is_coatom_iff_is_atom IsCompl.isCoatom_iff_isAtom
--/
 
 end IsCompl
 
 variable [ComplementedLattice α]
 
-#print isCoatomic_of_isAtomic_of_complementedLattice_of_isModular /-
+/- warning: is_coatomic_of_is_atomic_of_complemented_lattice_of_is_modular -> isCoatomic_of_isAtomic_of_complementedLattice_of_isModular is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsModularLattice.{u1} α _inst_1] [_inst_4 : ComplementedLattice.{u1} α _inst_1 _inst_2] [_inst_5 : IsAtomic.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2)], IsCoatomic.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsModularLattice.{u1} α _inst_1] [_inst_4 : ComplementedLattice.{u1} α _inst_1 _inst_2] [_inst_5 : IsAtomic.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2)], IsCoatomic.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2)
+Case conversion may be inaccurate. Consider using '#align is_coatomic_of_is_atomic_of_complemented_lattice_of_is_modular isCoatomic_of_isAtomic_of_complementedLattice_of_isModularₓ'. -/
 theorem isCoatomic_of_isAtomic_of_complementedLattice_of_isModular [IsAtomic α] : IsCoatomic α :=
   ⟨fun x => by
     rcases exists_is_compl x with ⟨y, xy⟩
@@ -1247,20 +1396,27 @@ theorem isCoatomic_of_isAtomic_of_complementedLattice_of_isModular [IsAtomic α]
       rw [← hb.is_atom_iff_is_coatom, OrderIso.isAtom_iff]
       apply ha.Iic⟩
 #align is_coatomic_of_is_atomic_of_complemented_lattice_of_is_modular isCoatomic_of_isAtomic_of_complementedLattice_of_isModular
--/
 
-#print isAtomic_of_isCoatomic_of_complementedLattice_of_isModular /-
+/- warning: is_atomic_of_is_coatomic_of_complemented_lattice_of_is_modular -> isAtomic_of_isCoatomic_of_complementedLattice_of_isModular is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsModularLattice.{u1} α _inst_1] [_inst_4 : ComplementedLattice.{u1} α _inst_1 _inst_2] [_inst_5 : IsCoatomic.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2)], IsAtomic.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsModularLattice.{u1} α _inst_1] [_inst_4 : ComplementedLattice.{u1} α _inst_1 _inst_2] [_inst_5 : IsCoatomic.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2)], IsAtomic.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2)
+Case conversion may be inaccurate. Consider using '#align is_atomic_of_is_coatomic_of_complemented_lattice_of_is_modular isAtomic_of_isCoatomic_of_complementedLattice_of_isModularₓ'. -/
 theorem isAtomic_of_isCoatomic_of_complementedLattice_of_isModular [IsCoatomic α] : IsAtomic α :=
   isCoatomic_dual_iff_isAtomic.1 isCoatomic_of_isAtomic_of_complementedLattice_of_isModular
 #align is_atomic_of_is_coatomic_of_complemented_lattice_of_is_modular isAtomic_of_isCoatomic_of_complementedLattice_of_isModular
--/
 
-#print isAtomic_iff_isCoatomic /-
+/- warning: is_atomic_iff_is_coatomic -> isAtomic_iff_isCoatomic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsModularLattice.{u1} α _inst_1] [_inst_4 : ComplementedLattice.{u1} α _inst_1 _inst_2], Iff (IsAtomic.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2)) (IsCoatomic.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Lattice.{u1} α] [_inst_2 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1))))] [_inst_3 : IsModularLattice.{u1} α _inst_1] [_inst_4 : ComplementedLattice.{u1} α _inst_1 _inst_2], Iff (IsAtomic.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2)) (IsCoatomic.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α _inst_1)))) _inst_2))
+Case conversion may be inaccurate. Consider using '#align is_atomic_iff_is_coatomic isAtomic_iff_isCoatomicₓ'. -/
 theorem isAtomic_iff_isCoatomic : IsAtomic α ↔ IsCoatomic α :=
   ⟨fun h => @isCoatomic_of_isAtomic_of_complementedLattice_of_isModular _ _ _ _ _ h, fun h =>
     @isAtomic_of_isCoatomic_of_complementedLattice_of_isModular _ _ _ _ _ h⟩
 #align is_atomic_iff_is_coatomic isAtomic_iff_isCoatomic
--/
 
 end IsModularLattice
 

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

@@ -477,20 +477,20 @@ variable (α) [CompleteLattice α]
 #print IsAtomistic /-
 /-- A lattice is atomistic iff every element is a `Sup` of a set of atoms. -/
 class IsAtomistic : Prop where
-  eq_supₛ_atoms : ∀ b : α, ∃ s : Set α, b = supₛ s ∧ ∀ a, a ∈ s → IsAtom a
+  eq_sSup_atoms : ∀ b : α, ∃ s : Set α, b = sSup s ∧ ∀ a, a ∈ s → IsAtom a
 #align is_atomistic IsAtomistic
 -/
 
 #print IsCoatomistic /-
 /-- A lattice is coatomistic iff every element is an `Inf` of a set of coatoms. -/
 class IsCoatomistic : Prop where
-  eq_infₛ_coatoms : ∀ b : α, ∃ s : Set α, b = infₛ s ∧ ∀ a, a ∈ s → IsCoatom a
+  eq_sInf_coatoms : ∀ b : α, ∃ s : Set α, b = sInf s ∧ ∀ a, a ∈ s → IsCoatom a
 #align is_coatomistic IsCoatomistic
 -/
 
-export IsAtomistic (eq_supₛ_atoms)
+export IsAtomistic (eq_sSup_atoms)
 
-export IsCoatomistic (eq_infₛ_coatoms)
+export IsCoatomistic (eq_sInf_coatoms)
 
 variable {α}
 
@@ -523,7 +523,7 @@ instance (priority := 100) : IsAtomic α :=
     rcases eq_Sup_atoms b with ⟨s, rfl, hs⟩
     cases' s.eq_empty_or_nonempty with h h
     · simp [h]
-    · exact Or.intro_right _ ⟨h.some, hs _ h.some_spec, le_supₛ h.some_spec⟩⟩
+    · exact Or.intro_right _ ⟨h.some, hs _ h.some_spec, le_sSup h.some_spec⟩⟩
 
 end IsAtomistic
 
@@ -531,38 +531,38 @@ section IsAtomistic
 
 variable [IsAtomistic α]
 
-/- warning: Sup_atoms_le_eq -> supₛ_atoms_le_eq is a dubious translation:
+/- warning: Sup_atoms_le_eq -> sSup_atoms_le_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1] (b : α), Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (setOf.{u1} α (fun (a : α) => And (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) a) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)))) b
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1] (b : α), Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (setOf.{u1} α (fun (a : α) => And (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) a) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)))) b
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1] (b : α), Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => And (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) a) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)))) b
-Case conversion may be inaccurate. Consider using '#align Sup_atoms_le_eq supₛ_atoms_le_eqₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1] (b : α), Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => And (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) a) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)))) b
+Case conversion may be inaccurate. Consider using '#align Sup_atoms_le_eq sSup_atoms_le_eqₓ'. -/
 @[simp]
-theorem supₛ_atoms_le_eq (b : α) : supₛ { a : α | IsAtom a ∧ a ≤ b } = b :=
+theorem sSup_atoms_le_eq (b : α) : sSup { a : α | IsAtom a ∧ a ≤ b } = b :=
   by
   rcases eq_Sup_atoms b with ⟨s, rfl, hs⟩
-  exact le_antisymm (supₛ_le fun _ => And.right) (supₛ_le_supₛ fun a ha => ⟨hs a ha, le_supₛ ha⟩)
-#align Sup_atoms_le_eq supₛ_atoms_le_eq
+  exact le_antisymm (sSup_le fun _ => And.right) (sSup_le_sSup fun a ha => ⟨hs a ha, le_sSup ha⟩)
+#align Sup_atoms_le_eq sSup_atoms_le_eq
 
-/- warning: Sup_atoms_eq_top -> supₛ_atoms_eq_top is a dubious translation:
+/- warning: Sup_atoms_eq_top -> sSup_atoms_eq_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1], Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (setOf.{u1} α (fun (a : α) => IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) a))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1], Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (setOf.{u1} α (fun (a : α) => IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) a))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1], Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) a))) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align Sup_atoms_eq_top supₛ_atoms_eq_topₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsAtomistic.{u1} α _inst_1], Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) a))) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align Sup_atoms_eq_top sSup_atoms_eq_topₓ'. -/
 @[simp]
-theorem supₛ_atoms_eq_top : supₛ { a : α | IsAtom a } = ⊤ :=
+theorem sSup_atoms_eq_top : sSup { a : α | IsAtom a } = ⊤ :=
   by
-  refine' Eq.trans (congr rfl (Set.ext fun x => _)) (supₛ_atoms_le_eq ⊤)
+  refine' Eq.trans (congr rfl (Set.ext fun x => _)) (sSup_atoms_le_eq ⊤)
   exact (and_iff_left le_top).symm
-#align Sup_atoms_eq_top supₛ_atoms_eq_top
+#align Sup_atoms_eq_top sSup_atoms_eq_top
 
 #print le_iff_atom_le_imp /-
 theorem le_iff_atom_le_imp {a b : α} : a ≤ b ↔ ∀ c : α, IsAtom c → c ≤ a → c ≤ b :=
   ⟨fun ab c hc ca => le_trans ca ab, fun h =>
     by
-    rw [← supₛ_atoms_le_eq a, ← supₛ_atoms_le_eq b]
-    exact supₛ_le_supₛ fun c hc => ⟨hc.1, h c hc.1 hc.2⟩⟩
+    rw [← sSup_atoms_le_eq a, ← sSup_atoms_le_eq b]
+    exact sSup_le_sSup fun c hc => ⟨hc.1, h c hc.1 hc.2⟩⟩
 #align le_iff_atom_le_imp le_iff_atom_le_imp
 -/
 
@@ -583,7 +583,7 @@ instance (priority := 100) : IsCoatomic α :=
     rcases eq_Inf_coatoms b with ⟨s, rfl, hs⟩
     cases' s.eq_empty_or_nonempty with h h
     · simp [h]
-    · exact Or.intro_right _ ⟨h.some, hs _ h.some_spec, infₛ_le h.some_spec⟩⟩
+    · exact Or.intro_right _ ⟨h.some, hs _ h.some_spec, sInf_le h.some_spec⟩⟩
 
 end IsCoatomistic
 
@@ -836,8 +836,8 @@ protected noncomputable def completeLattice : CompleteLattice α :=
   { (inferInstance : Lattice α),
     (inferInstance :
       BoundedOrder α) with
-    supₛ := fun s => if ⊤ ∈ s then ⊤ else ⊥
-    infₛ := fun s => if ⊥ ∈ s then ⊥ else ⊤
+    sSup := fun s => if ⊤ ∈ s then ⊤ else ⊥
+    sInf := fun s => if ⊥ ∈ s then ⊥ else ⊤
     le_sup := fun s x h => by
       rcases eq_bot_or_eq_top x with (rfl | rfl)
       · exact bot_le
@@ -866,17 +866,17 @@ protected noncomputable def completeLattice : CompleteLattice α :=
 protected noncomputable def completeBooleanAlgebra : CompleteBooleanAlgebra α :=
   { IsSimpleOrder.completeLattice,
     IsSimpleOrder.booleanAlgebra with
-    infᵢ_sup_le_sup_inf := fun x s =>
+    iInf_sup_le_sup_inf := fun x s =>
       by
       rcases eq_bot_or_eq_top x with (rfl | rfl)
-      · simp only [bot_sup_eq, ← infₛ_eq_infᵢ]
+      · simp only [bot_sup_eq, ← sInf_eq_iInf]
         exact le_rfl
       · simp only [top_sup_eq, le_top]
-    inf_sup_le_supᵢ_inf := fun x s =>
+    inf_sup_le_iSup_inf := fun x s =>
       by
       rcases eq_bot_or_eq_top x with (rfl | rfl)
       · simp only [bot_inf_eq, bot_le]
-      · simp only [top_inf_eq, ← supₛ_eq_supᵢ]
+      · simp only [top_inf_eq, ← sSup_eq_iSup]
         exact le_rfl }
 #align is_simple_order.complete_boolean_algebra IsSimpleOrder.completeBooleanAlgebra
 -/
@@ -893,9 +893,9 @@ set_option default_priority 100
 instance : IsAtomistic α :=
   ⟨fun b =>
     (eq_bot_or_eq_top b).elim
-      (fun h => ⟨∅, ⟨h.trans supₛ_empty.symm, fun a ha => False.elim (Set.not_mem_empty _ ha)⟩⟩)
+      (fun h => ⟨∅, ⟨h.trans sSup_empty.symm, fun a ha => False.elim (Set.not_mem_empty _ ha)⟩⟩)
       fun h =>
-      ⟨{⊤}, h.trans supₛ_singleton.symm, fun a ha =>
+      ⟨{⊤}, h.trans sSup_singleton.symm, fun a ha =>
         (Set.mem_singleton_iff.1 ha).symm ▸ isAtom_top⟩⟩
 
 instance : IsCoatomistic α :=
@@ -1317,14 +1317,14 @@ theorem isCoatom_singleton_compl (x : α) : IsCoatom ({x}ᶜ : Set α) :=
 #align set.is_coatom_singleton_compl Set.isCoatom_singleton_compl
 
 instance : IsAtomistic (Set α)
-    where eq_supₛ_atoms s :=
+    where eq_sSup_atoms s :=
     ⟨(fun x => {x}) '' s, by rw [Sup_eq_sUnion, sUnion_image, bUnion_of_singleton],
       by
       rintro - ⟨x, hx, rfl⟩
       exact is_atom_singleton x⟩
 
 instance : IsCoatomistic (Set α)
-    where eq_infₛ_coatoms s :=
+    where eq_sInf_coatoms s :=
     ⟨(fun x => {x}ᶜ) '' sᶜ, by
       rw [Inf_eq_sInter, sInter_image, ← compl_Union₂, bUnion_of_singleton, compl_compl],
       by

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

@@ -963,7 +963,7 @@ variable [PartialOrder α] [PartialOrder β]
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderEmbedding.{u2, u1} β α (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))), (Eq.{succ u1} α (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) -> (forall {b : β}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f b)) -> (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))), (Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} β α) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} β α) β α (Function.instEmbeddingLikeEmbedding.{succ u1, succ u2} β α)) (RelEmbedding.toEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) f) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Bot.bot.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (OrderBot.toBot.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) _inst_1)) _inst_3))) -> (forall {b : β}, (IsAtom.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) b) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) b) _inst_1) _inst_3 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} β α) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} β α) β α (Function.instEmbeddingLikeEmbedding.{succ u1, succ u2} β α)) (RelEmbedding.toEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) f) b)) -> (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))), (Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Bot.bot.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (OrderBot.toBot.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Bot.bot.{u1} β (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) _inst_1)) _inst_3))) -> (forall {b : β}, (IsAtom.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) b) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) b) _inst_1) _inst_3 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f b)) -> (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b))
 Case conversion may be inaccurate. Consider using '#align order_embedding.is_atom_of_map_bot_of_image OrderEmbedding.isAtom_of_map_bot_of_imageₓ'. -/
 theorem isAtom_of_map_bot_of_image [OrderBot α] [OrderBot β] (f : β ↪o α) (hbot : f ⊥ = ⊥) {b : β}
     (hb : IsAtom (f b)) : IsAtom b :=
@@ -976,7 +976,7 @@ theorem isAtom_of_map_bot_of_image [OrderBot α] [OrderBot β] (f : β ↪o α)
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderEmbedding.{u2, u1} β α (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))), (Eq.{succ u1} α (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) _inst_4))) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_3))) -> (forall {b : β}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderEmbedding.{u2, u1} β α (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (fun (_x : RelEmbedding.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) => β -> α) (RelEmbedding.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)))) f b)) -> (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 b))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))), (Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} β α) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} β α) β α (Function.instEmbeddingLikeEmbedding.{succ u1, succ u2} β α)) (RelEmbedding.toEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) f) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Top.top.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (OrderTop.toTop.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) _inst_1)) _inst_3))) -> (forall {b : β}, (IsCoatom.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) b) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) b) _inst_1) _inst_3 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} β α) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} β α) β α (Function.instEmbeddingLikeEmbedding.{succ u1, succ u2} β α)) (RelEmbedding.toEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) f) b)) -> (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))), (Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Top.top.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (OrderTop.toTop.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Top.top.{u1} β (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) _inst_4))) _inst_1)) _inst_3))) -> (forall {b : β}, (IsCoatom.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) b) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) b) _inst_1) _inst_3 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{max u2 u1, u1, u2} (OrderEmbedding.{u1, u2} β α (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) f b)) -> (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 b))
 Case conversion may be inaccurate. Consider using '#align order_embedding.is_coatom_of_map_top_of_image OrderEmbedding.isCoatom_of_map_top_of_imageₓ'. -/
 theorem isCoatom_of_map_top_of_image [OrderTop α] [OrderTop β] (f : β ↪o α) (htop : f ⊤ = ⊤) {b : β}
     (hb : IsCoatom (f b)) : IsCoatom b :=
@@ -1141,7 +1141,7 @@ variable [PartialOrder α] [PartialOrder β]
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (a : α), Iff (IsAtom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) f a)) (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))) (a : α), Iff (IsAtom.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) _inst_2) _inst_4 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) (RelEmbedding.toEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f)) a)) (IsAtom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a)
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderBot.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))) (a : α), Iff (IsAtom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a)) (IsAtom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a)
 Case conversion may be inaccurate. Consider using '#align order_iso.is_atom_iff OrderIso.isAtom_iffₓ'. -/
 @[simp]
 theorem isAtom_iff [OrderBot α] [OrderBot β] (f : α ≃o β) (a : α) : IsAtom (f a) ↔ IsAtom a :=
@@ -1153,7 +1153,7 @@ theorem isAtom_iff [OrderBot α] [OrderBot β] (f : α ≃o β) (a : α) : IsAto
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))] [_inst_4 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (a : α), Iff (IsCoatom.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2) _inst_4 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)))) f a)) (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) _inst_3 a)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))) (a : α), Iff (IsCoatom.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) _inst_2) _inst_4 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) (RelEmbedding.toEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f)) a)) (IsCoatom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a)
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : PartialOrder.{u2} α] [_inst_2 : PartialOrder.{u1} β] [_inst_3 : OrderTop.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1))] [_inst_4 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2))) (a : α), Iff (IsCoatom.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2) _inst_4 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1)) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β _inst_2)) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a)) (IsCoatom.{u2} α (PartialOrder.toPreorder.{u2} α _inst_1) _inst_3 a)
 Case conversion may be inaccurate. Consider using '#align order_iso.is_coatom_iff OrderIso.isCoatom_iffₓ'. -/
 @[simp]
 theorem isCoatom_iff [OrderTop α] [OrderTop β] (f : α ≃o β) (a : α) : IsCoatom (f a) ↔ IsCoatom a :=

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

@@ -91,7 +91,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, Iff (IsAtom.{u1} α _inst_1 _inst_2 a) (And (Ne.{succ u1} α a (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))) (forall (b : α), (Ne.{succ u1} α b (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) a b)))
 Case conversion may be inaccurate. Consider using '#align is_atom_iff isAtom_iffₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (b «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ≠ » «expr⊥»()) -/
 theorem isAtom_iff {a : α} : IsAtom a ↔ a ≠ ⊥ ∧ ∀ (b) (_ : b ≠ ⊥), b ≤ a → a ≤ b :=
   and_congr Iff.rfl <|
     forall_congr' fun b => by simp only [Ne.def, @not_imp_comm (b = ⊥), not_imp, lt_iff_le_not_le]
@@ -213,7 +213,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, Iff (IsCoatom.{u1} α _inst_1 _inst_2 a) (And (Ne.{succ u1} α a (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))) (forall (b : α), (Ne.{succ u1} α b (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) b a)))
 Case conversion may be inaccurate. Consider using '#align is_coatom_iff isCoatom_iffₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (b «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (b «expr ≠ » «expr⊤»()) -/
 theorem isCoatom_iff {a : α} : IsCoatom a ↔ a ≠ ⊤ ∧ ∀ (b) (_ : b ≠ ⊤), a ≤ b → b ≤ a :=
   @isAtom_iff αᵒᵈ _ _ _
 #align is_coatom_iff isCoatom_iff

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -321,9 +321,9 @@ section Pairwise
 
 /- warning: is_atom.inf_eq_bot_of_ne -> IsAtom.inf_eq_bot_of_ne is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Eq.{succ u1} α (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) a b) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))) _inst_2)))
+  forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) a b) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))) _inst_2)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Eq.{succ u1} α (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) a b) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))) _inst_2)))
+  forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsAtom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toInf.{u1} α _inst_1) a b) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))) _inst_2)))
 Case conversion may be inaccurate. Consider using '#align is_atom.inf_eq_bot_of_ne IsAtom.inf_eq_bot_of_neₓ'. -/
 theorem IsAtom.inf_eq_bot_of_ne [SemilatticeInf α] [OrderBot α] {a b : α} (ha : IsAtom a)
     (hb : IsAtom b) (hab : a ≠ b) : a ⊓ b = ⊥ :=
@@ -339,9 +339,9 @@ theorem IsAtom.disjoint_of_ne [SemilatticeInf α] [OrderBot α] {a b : α} (ha :
 
 /- warning: is_coatom.sup_eq_top_of_ne -> IsCoatom.sup_eq_top_of_ne is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) a b) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))) _inst_2)))
+  forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) a b) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))) _inst_2)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) a b) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))) _inst_2)))
+  forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))] {a : α} {b : α}, (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) _inst_2 a) -> (IsCoatom.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) _inst_2 b) -> (Ne.{succ u1} α a b) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α _inst_1) a b) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))) _inst_2)))
 Case conversion may be inaccurate. Consider using '#align is_coatom.sup_eq_top_of_ne IsCoatom.sup_eq_top_of_neₓ'. -/
 theorem IsCoatom.sup_eq_top_of_ne [SemilatticeSup α] [OrderTop α] {a b : α} (ha : IsCoatom a)
     (hb : IsCoatom b) (hab : a ≠ b) : a ⊔ b = ⊤ :=

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

These are changes from #11997, the latest adaptation PR for nightly-2024-04-07, which can be made directly on master.

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

@@ -79,7 +79,7 @@ theorem IsAtom.of_isAtom_coe_Iic {a : Set.Iic x} (ha : IsAtom a) : IsAtom (a : 
 
 theorem isAtom_iff_le_of_ge : IsAtom a ↔ a ≠ ⊥ ∧ ∀ b ≠ ⊥, b ≤ a → a ≤ b :=
   and_congr Iff.rfl <|
-    forall_congr' fun b => by simp only [Ne.def, @not_imp_comm (b = ⊥), not_imp, lt_iff_le_not_le]
+    forall_congr' fun b => by simp only [Ne, @not_imp_comm (b = ⊥), not_imp, lt_iff_le_not_le]
 #align is_atom_iff isAtom_iff_le_of_ge
 
 end Preorder

Also do the same for "/-A". This is a purely aesthetic change (and exhaustive).

@@ -263,7 +263,7 @@ variable [PartialOrder α] (α)
 /-- A lattice is atomic iff every element other than `⊥` has an atom below it. -/
 @[mk_iff]
 class IsAtomic [OrderBot α] : Prop where
-  /--Every element other than `⊥` has an atom below it. -/
+  /-- Every element other than `⊥` has an atom below it. -/
   eq_bot_or_exists_atom_le : ∀ b : α, b = ⊥ ∨ ∃ a : α, IsAtom a ∧ a ≤ b
 #align is_atomic IsAtomic
 #align is_atomic_iff isAtomic_iff
@@ -271,7 +271,7 @@ class IsAtomic [OrderBot α] : Prop where
 /-- A lattice is coatomic iff every element other than `⊤` has a coatom above it. -/
 @[mk_iff]
 class IsCoatomic [OrderTop α] : Prop where
-  /--Every element other than `⊤` has an atom above it. -/
+  /-- Every element other than `⊤` has an atom above it. -/
   eq_top_or_exists_le_coatom : ∀ b : α, b = ⊤ ∨ ∃ a : α, IsCoatom a ∧ b ≤ a
 #align is_coatomic IsCoatomic
 #align is_coatomic_iff isCoatomic_iff
@@ -399,14 +399,14 @@ variable (α) [CompleteLattice α]
 
 /-- A lattice is atomistic iff every element is a `sSup` of a set of atoms. -/
 class IsAtomistic : Prop where
-  /--Every element is a `sSup` of a set of atoms. -/
+  /-- Every element is a `sSup` of a set of atoms. -/
   eq_sSup_atoms : ∀ b : α, ∃ s : Set α, b = sSup s ∧ ∀ a, a ∈ s → IsAtom a
 #align is_atomistic IsAtomistic
 #align is_atomistic.eq_Sup_atoms IsAtomistic.eq_sSup_atoms
 
 /-- A lattice is coatomistic iff every element is an `sInf` of a set of coatoms. -/
 class IsCoatomistic : Prop where
-  /--Every element is a `sInf` of a set of coatoms. -/
+  /-- Every element is a `sInf` of a set of coatoms. -/
   eq_sInf_coatoms : ∀ b : α, ∃ s : Set α, b = sInf s ∧ ∀ a, a ∈ s → IsCoatom a
 #align is_coatomistic IsCoatomistic
 #align is_coatomistic.eq_Inf_coatoms IsCoatomistic.eq_sInf_coatoms

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -685,7 +685,7 @@ end DecidableEq
 
 variable [Lattice α] [BoundedOrder α] [IsSimpleOrder α]
 
-open Classical
+open scoped Classical
 
 /-- A simple `BoundedOrder` is also complete. -/
 protected noncomputable def completeLattice : CompleteLattice α :=
@@ -1048,7 +1048,7 @@ instance isAtomic [∀ i, PartialOrder (π i)] [∀ i, OrderBot (π i)] [∀ i,
   eq_bot_or_exists_atom_le b := or_iff_not_imp_left.2 fun h =>
     have ⟨i, hi⟩ : ∃ i, b i ≠ ⊥ := not_forall.1 (h.imp Pi.eq_bot_iff.2)
     have ⟨a, ha, hab⟩ := (eq_bot_or_exists_atom_le (b i)).resolve_left hi
-    have : DecidableEq ι := open Classical in inferInstance
+    have : DecidableEq ι := open scoped Classical in inferInstance
     ⟨Function.update ⊥ i a, isAtom_single ha, update_le_iff.2 ⟨hab, by simp⟩⟩
 
 instance isCoatomic [∀ i, PartialOrder (π i)] [∀ i, OrderTop (π i)] [∀ i, IsCoatomic (π i)] :

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -717,9 +717,8 @@ protected noncomputable def completeLattice : CompleteLattice α :=
 
 /-- A simple `BoundedOrder` is also a `CompleteBooleanAlgebra`. -/
 protected noncomputable def completeBooleanAlgebra : CompleteBooleanAlgebra α :=
-  let src := IsSimpleOrder.completeLattice
-  let src₁ := IsSimpleOrder.booleanAlgebra
-  { src, src₁ with
+  { __ := IsSimpleOrder.completeLattice
+    __ := IsSimpleOrder.booleanAlgebra
     iInf_sup_le_sup_sInf := fun x s => by
       rcases eq_bot_or_eq_top x with (rfl | rfl)
       · simp [bot_sup_eq, ← sInf_eq_iInf]
@@ -728,7 +727,7 @@ protected noncomputable def completeBooleanAlgebra : CompleteBooleanAlgebra α :
       rcases eq_bot_or_eq_top x with (rfl | rfl)
       · simp only [le_bot_iff, sSup_eq_bot, bot_inf_eq, iSup_bot, le_refl]
       · simp only [top_inf_eq, ← sSup_eq_iSup]
-        exact le_rfl } -- v4.7.0-rc1 issues
+        exact le_rfl }
 #align is_simple_order.complete_boolean_algebra IsSimpleOrder.completeBooleanAlgebra
 
 instance : ComplementedLattice α :=

• Prove isSemisimple_of_mem_adjoin: if two commuting endomorphisms of a finite-dimensional vector space over a perfect field are both semisimple, then every endomorphism in the algebra generated by them (in particular their product and sum) is semisimple.

• In the same file LinearAlgebra/Semisimple.lean, eq_zero_of_isNilpotent_isSemisimple and isSemisimple_of_squarefree_aeval_eq_zero are golfed, and IsSemisimple.minpoly_squarefree is proved

RingTheory/SimpleModule.lean:

• Define IsSemisimpleRing R to mean that R is a semisimple R-module. add properties of simple modules and a characterization (they are exactly the quotients of the ring by maximal left ideals).

• The annihilator of a semisimple module is a radical ideal.

• Any module over a semisimple ring is semisimple.

• A finite product of semisimple rings is semisimple.

• Any quotient of a semisimple ring is semisimple.

• Add Artin--Wedderburn as a TODO (proof_wanted).

• Order/Atoms.lean: add the instance from IsSimpleOrder to ComplementedLattice, so that IsSimpleModule → IsSemisimpleModule is automatically inferred.

Prerequisites for showing a product of semisimple rings is semisimple:

• Algebra/Module/Submodule/Map.lean: generalize orderIsoMapComap so that it only requires RingHomSurjective rather than RingHomInvPair

• Algebra/Ring/CompTypeclasses.lean, Mathlib/Algebra/Ring/Pi.lean, Algebra/Ring/Prod.lean: add RingHomSurjective instances

RingTheory/Artinian.lean:

• quotNilradicalEquivPi: the quotient of a commutative Artinian ring R by its nilradical is isomorphic to the (finite) product of its quotients by maximal ideals (therefore a product of fields). equivPi: if the ring is moreover reduced, then the ring itself is a product of fields. Deduce that R is a semisimple ring and both R and R[X] are decomposition monoids. Requires RingEquiv.quotientBot in RingTheory/Ideal/QuotientOperations.lean.

• Data/Polynomial/Eval.lean: the polynomial ring over a finite product of rings is isomorphic to the product of polynomial rings over individual rings. (Used to show R[X] is a decomposition monoid.)

Other necessary results:

• FieldTheory/Minpoly/Field.lean: the minimal polynomial of an element in a reduced algebra over a field is radical.

• RingTheory/PowerBasis.lean: generalize PowerBasis.finiteDimensional and rename it to .finite.

Annihilator stuff, some of which do not end up being used:

• RingTheory/Ideal/Operations.lean: define Module.annihilator and redefine Submodule.annihilator in terms of it; add lemmas, including one that says an arbitrary intersection of radical ideals is radical. The new lemma Ideal.isRadical_iff_pow_one_lt depends on pow_imp_self_of_one_lt in Mathlib/Data/Nat/Interval.lean, which is also used to golf the proof of isRadical_iff_pow_one_lt.

• Algebra/Module/Torsion.lean: add a lemma and an instance (unused)

• Data/Polynomial/Module/Basic.lean: add a def (unused) and a lemma

• LinearAlgebra/AnnihilatingPolynomial.lean: add lemma span_minpoly_eq_annihilator

Some results about idempotent linear maps (projections) and idempotent elements, used to show that any (left) ideal in a semisimple ring is spanned by an idempotent element (unused):

• LinearAlgebra/Projection.lean: add def isIdempotentElemEquiv

• LinearAlgebra/Span.lean: add two lemmas

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -731,6 +731,9 @@ protected noncomputable def completeBooleanAlgebra : CompleteBooleanAlgebra α :
         exact le_rfl } -- v4.7.0-rc1 issues
 #align is_simple_order.complete_boolean_algebra IsSimpleOrder.completeBooleanAlgebra
 
+instance : ComplementedLattice α :=
+  letI := IsSimpleOrder.completeBooleanAlgebra (α := α); inferInstance
+
 end IsSimpleOrder
 
 namespace IsSimpleOrder

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -737,7 +737,8 @@ namespace IsSimpleOrder
 
 variable [CompleteLattice α] [IsSimpleOrder α]
 
---set_option default_priority 100 --Porting note: not supported, done for each instance individually
+--set_option default_priority 100
+-- Porting note: not supported, done for each instance individually
 
 instance (priority := 100) : IsAtomistic α :=
   ⟨fun b =>

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -717,18 +717,18 @@ protected noncomputable def completeLattice : CompleteLattice α :=
 
 /-- A simple `BoundedOrder` is also a `CompleteBooleanAlgebra`. -/
 protected noncomputable def completeBooleanAlgebra : CompleteBooleanAlgebra α :=
-  { IsSimpleOrder.completeLattice,
-    IsSimpleOrder.booleanAlgebra with
+  let src := IsSimpleOrder.completeLattice
+  let src₁ := IsSimpleOrder.booleanAlgebra
+  { src, src₁ with
     iInf_sup_le_sup_sInf := fun x s => by
       rcases eq_bot_or_eq_top x with (rfl | rfl)
-      · simp only [bot_sup_eq, ← sInf_eq_iInf]
-        exact le_rfl
+      · simp [bot_sup_eq, ← sInf_eq_iInf]
       · simp only [top_le_iff, top_sup_eq, iInf_top, le_sInf_iff, le_refl]
     inf_sSup_le_iSup_inf := fun x s => by
       rcases eq_bot_or_eq_top x with (rfl | rfl)
       · simp only [le_bot_iff, sSup_eq_bot, bot_inf_eq, iSup_bot, le_refl]
       · simp only [top_inf_eq, ← sSup_eq_iSup]
-        exact le_rfl }
+        exact le_rfl } -- v4.7.0-rc1 issues
 #align is_simple_order.complete_boolean_algebra IsSimpleOrder.completeBooleanAlgebra
 
 end IsSimpleOrder

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.

@@ -1004,7 +1004,7 @@ theorem isAtom_iff {f : ∀ i, π i} [∀ i, PartialOrder (π i)] [∀ i, OrderB
     have ⟨hgf, k, hgfk⟩ := Pi.lt_def.1 hgf
     obtain rfl : i = k := of_not_not fun hki => by rw [hbot _ (Ne.symm hki)] at hgfk; simp at hgfk
     if hij : j = i then subst hij; refine hlt _ hgfk else
-    refine eq_bot_iff.2 <| le_trans (hgf _) (eq_bot_iff.1 (hbot _ hij))
+    exact eq_bot_iff.2 <| le_trans (hgf _) (eq_bot_iff.1 (hbot _ hij))
   case mp =>
     rintro ⟨hbot, h⟩
     have ⟨i, hbot⟩ : ∃ i, f i ≠ ⊥ := by rw [ne_eq, Pi.eq_bot_iff, not_forall] at hbot; exact hbot

@@ -3,7 +3,7 @@ Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
 -/
-import Mathlib.Data.Set.Image
+import Mathlib.Data.Set.Lattice
 import Mathlib.Order.ModularLattice
 import Mathlib.Order.WellFounded
 import Mathlib.Tactic.Nontriviality

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -3,6 +3,7 @@ Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
 -/
+import Mathlib.Data.Set.Image
 import Mathlib.Order.ModularLattice
 import Mathlib.Order.WellFounded
 import Mathlib.Tactic.Nontriviality

Rename

• Covby → CovBy, Wcovby → WCovBy
• *covby* → *covBy*
• wcovby.finset_val → WCovBy.finset_val, wcovby.finset_coe → WCovBy.finset_coe
• Covby.is_coatom → CovBy.isCoatom

@@ -102,13 +102,13 @@ theorem IsAtom.Iic_eq (h : IsAtom a) : Set.Iic a = {⊥, a} :=
 #align is_atom.Iic_eq IsAtom.Iic_eq
 
 @[simp]
-theorem bot_covby_iff : ⊥ ⋖ a ↔ IsAtom a := by
-  simp only [Covby, bot_lt_iff_ne_bot, IsAtom, not_imp_not]
-#align bot_covby_iff bot_covby_iff
+theorem bot_covBy_iff : ⊥ ⋖ a ↔ IsAtom a := by
+  simp only [CovBy, bot_lt_iff_ne_bot, IsAtom, not_imp_not]
+#align bot_covby_iff bot_covBy_iff
 
-alias ⟨Covby.is_atom, IsAtom.bot_covby⟩ := bot_covby_iff
-#align covby.is_atom Covby.is_atom
-#align is_atom.bot_covby IsAtom.bot_covby
+alias ⟨CovBy.is_atom, IsAtom.bot_covBy⟩ := bot_covBy_iff
+#align covby.is_atom CovBy.is_atom
+#align is_atom.bot_covby IsAtom.bot_covBy
 
 end PartialOrder
 
@@ -192,13 +192,13 @@ theorem IsCoatom.Ici_eq (h : IsCoatom a) : Set.Ici a = {⊤, a} :=
 #align is_coatom.Ici_eq IsCoatom.Ici_eq
 
 @[simp]
-theorem covby_top_iff : a ⋖ ⊤ ↔ IsCoatom a :=
-  toDual_covby_toDual_iff.symm.trans bot_covby_iff
-#align covby_top_iff covby_top_iff
+theorem covBy_top_iff : a ⋖ ⊤ ↔ IsCoatom a :=
+  toDual_covBy_toDual_iff.symm.trans bot_covBy_iff
+#align covby_top_iff covBy_top_iff
 
-alias ⟨Covby.is_coatom, IsCoatom.covby_top⟩ := covby_top_iff
-#align covby.is_coatom Covby.is_coatom
-#align is_coatom.covby_top IsCoatom.covby_top
+alias ⟨CovBy.isCoatom, IsCoatom.covBy_top⟩ := covBy_top_iff
+#align covby.is_coatom CovBy.isCoatom
+#align is_coatom.covby_top IsCoatom.covBy_top
 
 end PartialOrder
 
@@ -214,23 +214,23 @@ variable [PartialOrder α] {a b : α}
 
 @[simp]
 theorem Set.Ici.isAtom_iff {b : Set.Ici a} : IsAtom b ↔ a ⋖ b := by
-  rw [← bot_covby_iff]
-  refine' (Set.OrdConnected.apply_covby_apply_iff (OrderEmbedding.subtype fun c => a ≤ c) _).symm
+  rw [← bot_covBy_iff]
+  refine' (Set.OrdConnected.apply_covBy_apply_iff (OrderEmbedding.subtype fun c => a ≤ c) _).symm
   simpa only [OrderEmbedding.subtype_apply, Subtype.range_coe_subtype] using Set.ordConnected_Ici
 #align set.Ici.is_atom_iff Set.Ici.isAtom_iff
 
 @[simp]
 theorem Set.Iic.isCoatom_iff {a : Set.Iic b} : IsCoatom a ↔ ↑a ⋖ b := by
-  rw [← covby_top_iff]
-  refine' (Set.OrdConnected.apply_covby_apply_iff (OrderEmbedding.subtype fun c => c ≤ b) _).symm
+  rw [← covBy_top_iff]
+  refine' (Set.OrdConnected.apply_covBy_apply_iff (OrderEmbedding.subtype fun c => c ≤ b) _).symm
   simpa only [OrderEmbedding.subtype_apply, Subtype.range_coe_subtype] using Set.ordConnected_Iic
 #align set.Iic.is_coatom_iff Set.Iic.isCoatom_iff
 
-theorem covby_iff_atom_Ici (h : a ≤ b) : a ⋖ b ↔ IsAtom (⟨b, h⟩ : Set.Ici a) := by simp
-#align covby_iff_atom_Ici covby_iff_atom_Ici
+theorem covBy_iff_atom_Ici (h : a ≤ b) : a ⋖ b ↔ IsAtom (⟨b, h⟩ : Set.Ici a) := by simp
+#align covby_iff_atom_Ici covBy_iff_atom_Ici
 
-theorem covby_iff_coatom_Iic (h : a ≤ b) : a ⋖ b ↔ IsCoatom (⟨a, h⟩ : Set.Iic b) := by simp
-#align covby_iff_coatom_Iic covby_iff_coatom_Iic
+theorem covBy_iff_coatom_Iic (h : a ≤ b) : a ⋖ b ↔ IsCoatom (⟨a, h⟩ : Set.Iic b) := by simp
+#align covby_iff_coatom_Iic covBy_iff_coatom_Iic
 
 end PartialOrder
 
@@ -583,9 +583,9 @@ theorem isCoatom_bot : IsCoatom (⊥ : α) :=
   isAtom_dual_iff_isCoatom.1 isAtom_top
 #align is_coatom_bot isCoatom_bot
 
-theorem bot_covby_top : (⊥ : α) ⋖ ⊤ :=
-  isAtom_top.bot_covby
-#align bot_covby_top bot_covby_top
+theorem bot_covBy_top : (⊥ : α) ⋖ ⊤ :=
+  isAtom_top.bot_covBy
+#align bot_covby_top bot_covBy_top
 
 end IsSimpleOrder
 
@@ -789,8 +789,8 @@ variable [PartialOrder α] [PartialOrder β]
 
 theorem isAtom_of_map_bot_of_image [OrderBot α] [OrderBot β] (f : β ↪o α) (hbot : f ⊥ = ⊥) {b : β}
     (hb : IsAtom (f b)) : IsAtom b := by
-  simp only [← bot_covby_iff] at hb ⊢
-  exact Covby.of_image f (hbot.symm ▸ hb)
+  simp only [← bot_covBy_iff] at hb ⊢
+  exact CovBy.of_image f (hbot.symm ▸ hb)
 #align order_embedding.is_atom_of_map_bot_of_image OrderEmbedding.isAtom_of_map_bot_of_image
 
 theorem isCoatom_of_map_top_of_image [OrderTop α] [OrderTop β] (f : β ↪o α) (htop : f ⊤ = ⊤)

See Zulip thread for the discussion.

@@ -95,7 +95,7 @@ theorem IsAtom.le_iff (h : IsAtom a) : x ≤ a ↔ x = ⊥ ∨ x = a := by rw [l
 #align is_atom.le_iff IsAtom.le_iff
 
 lemma IsAtom.le_iff_eq (ha : IsAtom a) (hb : b ≠ ⊥) : b ≤ a ↔ b = a :=
-  ha.le_iff.trans $ or_iff_right hb
+  ha.le_iff.trans <| or_iff_right hb
 
 theorem IsAtom.Iic_eq (h : IsAtom a) : Set.Iic a = {⊥, a} :=
   Set.ext fun _ => h.le_iff

• @[mk_iff] class MyPred now generates myPred_iff, not MyPred_iff
• add Lean.Name.decapitalize
• fix indentation and a few typos in the docs/comments.

Partially addresses issue #9129

@@ -265,7 +265,7 @@ class IsAtomic [OrderBot α] : Prop where
   /--Every element other than `⊥` has an atom below it. -/
   eq_bot_or_exists_atom_le : ∀ b : α, b = ⊥ ∨ ∃ a : α, IsAtom a ∧ a ≤ b
 #align is_atomic IsAtomic
-#align is_atomic_iff IsAtomic_iff
+#align is_atomic_iff isAtomic_iff
 
 /-- A lattice is coatomic iff every element other than `⊤` has a coatom above it. -/
 @[mk_iff]
@@ -273,7 +273,7 @@ class IsCoatomic [OrderTop α] : Prop where
   /--Every element other than `⊤` has an atom above it. -/
   eq_top_or_exists_le_coatom : ∀ b : α, b = ⊤ ∨ ∃ a : α, IsCoatom a ∧ b ≤ a
 #align is_coatomic IsCoatomic
-#align is_coatomic_iff IsCoatomic_iff
+#align is_coatomic_iff isCoatomic_iff
 
 export IsAtomic (eq_bot_or_exists_atom_le)
 
@@ -915,7 +915,7 @@ theorem isSimpleOrder [BoundedOrder α] [BoundedOrder β] [h : IsSimpleOrder β]
 
 protected theorem isAtomic_iff [OrderBot α] [OrderBot β] (f : α ≃o β) :
     IsAtomic α ↔ IsAtomic β := by
-  simp only [IsAtomic_iff, f.surjective.forall, f.surjective.exists, ← map_bot f, f.eq_iff_eq,
+  simp only [isAtomic_iff, f.surjective.forall, f.surjective.exists, ← map_bot f, f.eq_iff_eq,
     f.le_iff_le, f.isAtom_iff]
 #align order_iso.is_atomic_iff OrderIso.isAtomic_iff
 

This converts usages of the pattern

cases h
case inl h' => ...
case inr h' => ...

which derive from mathported code, to the "structured cases" syntax:

cases h with
| inl h' => ...
| inr h' => ...

The case where the subgoals are handled with · instead of case is more contentious (and much more numerous) so I left those alone. This pattern also appears with cases', induction, induction', and rcases. Furthermore, there is a similar transformation for by_cases:

by_cases h : cond
case pos => ...
case neg => ...

is replaced by:

if h : cond then
  ...
else
  ...

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -499,7 +499,7 @@ instance {α} [CompleteAtomicBooleanAlgebra α] : IsAtomistic α where
     have : (⨅ c : α, ⨆ x, b ⊓ cond x c (cᶜ)) = b := by simp [iSup_bool_eq, iInf_const]
     rw [← this]; clear this
     simp_rw [iInf_iSup_eq, iSup_le_iff]; intro g
-    by_cases h : (⨅ a, b ⊓ cond (g a) a (aᶜ)) = ⊥; case pos => simp [h]
+    if h : (⨅ a, b ⊓ cond (g a) a (aᶜ)) = ⊥ then simp [h] else
     refine le_sSup ⟨⟨h, fun c hc => ?_⟩, le_trans (by rfl) (le_iSup _ g)⟩; clear h
     have := lt_of_lt_of_le hc (le_trans (iInf_le _ c) inf_le_right)
     revert this
@@ -1002,7 +1002,7 @@ theorem isAtom_iff {f : ∀ i, π i} [∀ i, PartialOrder (π i)] [∀ i, OrderB
     refine ⟨fun h => hfi ((Pi.eq_bot_iff.1 h) _), fun g hgf => Pi.eq_bot_iff.2 fun j => ?_⟩
     have ⟨hgf, k, hgfk⟩ := Pi.lt_def.1 hgf
     obtain rfl : i = k := of_not_not fun hki => by rw [hbot _ (Ne.symm hki)] at hgfk; simp at hgfk
-    by_cases hij : j = i; case pos => subst hij; refine hlt _ hgfk
+    if hij : j = i then subst hij; refine hlt _ hgfk else
     refine eq_bot_iff.2 <| le_trans (hgf _) (eq_bot_iff.1 (hbot _ hij))
   case mp =>
     rintro ⟨hbot, h⟩
@@ -1063,14 +1063,12 @@ instance isAtomistic [∀ i, CompleteLattice (π i)] [∀ i, IsAtomistic (π i)]
     refine le_antisymm ?le ?ge
     case le =>
       refine sSup_le fun a ⟨ha, hle⟩ => ?_
-      refine le_sSup ⟨⟨_, ⟨_, _, ha, rfl⟩, ?_⟩, by simp⟩
-      intro j; by_cases hij : j = i
-      case pos => subst hij; simpa
-      case neg => simp [hij]
+      refine le_sSup ⟨⟨_, ⟨_, _, ha, rfl⟩, fun j => ?_⟩, by simp⟩
+      if hij : j = i then subst hij; simpa else simp [hij]
     case ge =>
       refine sSup_le ?_
       rintro _ ⟨⟨_, ⟨j, a, ha, rfl⟩, hle⟩, rfl⟩
-      by_cases hij : i = j; case neg => simp [Function.update_noteq hij]
+      if hij : i = j then ?_ else simp [Function.update_noteq hij]
       subst hij; simp only [Function.update_same]
       exact le_sSup ⟨ha, by simpa using hle i⟩
 

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -437,7 +437,7 @@ variable [IsAtomistic α]
 instance (priority := 100) : IsAtomic α :=
   ⟨fun b => by
     rcases eq_sSup_atoms b with ⟨s, rfl, hs⟩
-    cases' s.eq_empty_or_nonempty with h h
+    rcases s.eq_empty_or_nonempty with h | h
     · simp [h]
     · exact Or.intro_right _ ⟨h.some, hs _ h.choose_spec, le_sSup h.choose_spec⟩⟩
 
@@ -483,7 +483,7 @@ variable [IsCoatomistic α]
 instance (priority := 100) : IsCoatomic α :=
   ⟨fun b => by
     rcases eq_sInf_coatoms b with ⟨s, rfl, hs⟩
-    cases' s.eq_empty_or_nonempty with h h
+    rcases s.eq_empty_or_nonempty with h | h
     · simp [h]
     · exact Or.intro_right _ ⟨h.some, hs _ h.choose_spec, sInf_le h.choose_spec⟩⟩
 

Characterise IsAtom, IsCoatom, Covby in Set α, Multiset α, Finset α and deduce that Multiset α, Finset α are graded orders.

Note I am moving some existing characterisations to here because it makes sense thematically, but I could be convinced otherwise.

@@ -76,10 +76,10 @@ theorem IsAtom.of_isAtom_coe_Iic {a : Set.Iic x} (ha : IsAtom a) : IsAtom (a : 
     Subtype.mk_eq_mk.1 (ha.2 ⟨b, hba.le.trans a.prop⟩ hba)⟩
 #align is_atom.of_is_atom_coe_Iic IsAtom.of_isAtom_coe_Iic
 
-theorem isAtom_iff {a : α} : IsAtom a ↔ a ≠ ⊥ ∧ ∀ (b) (_ : b ≠ ⊥), b ≤ a → a ≤ b :=
+theorem isAtom_iff_le_of_ge : IsAtom a ↔ a ≠ ⊥ ∧ ∀ b ≠ ⊥, b ≤ a → a ≤ b :=
   and_congr Iff.rfl <|
     forall_congr' fun b => by simp only [Ne.def, @not_imp_comm (b = ⊥), not_imp, lt_iff_le_not_le]
-#align is_atom_iff isAtom_iff
+#align is_atom_iff isAtom_iff_le_of_ge
 
 end Preorder
 
@@ -94,6 +94,9 @@ theorem IsAtom.lt_iff (h : IsAtom a) : x < a ↔ x = ⊥ :=
 theorem IsAtom.le_iff (h : IsAtom a) : x ≤ a ↔ x = ⊥ ∨ x = a := by rw [le_iff_lt_or_eq, h.lt_iff]
 #align is_atom.le_iff IsAtom.le_iff
 
+lemma IsAtom.le_iff_eq (ha : IsAtom a) (hb : b ≠ ⊥) : b ≤ a ↔ b = a :=
+  ha.le_iff.trans $ or_iff_right hb
+
 theorem IsAtom.Iic_eq (h : IsAtom a) : Set.Iic a = {⊥, a} :=
   Set.ext fun _ => h.le_iff
 #align is_atom.Iic_eq IsAtom.Iic_eq
@@ -164,9 +167,9 @@ theorem IsCoatom.of_isCoatom_coe_Ici {a : Set.Ici x} (ha : IsCoatom a) : IsCoato
   @IsAtom.of_isAtom_coe_Iic αᵒᵈ _ _ x a ha
 #align is_coatom.of_is_coatom_coe_Ici IsCoatom.of_isCoatom_coe_Ici
 
-theorem isCoatom_iff {a : α} : IsCoatom a ↔ a ≠ ⊤ ∧ ∀ (b) (_ : b ≠ ⊤), a ≤ b → b ≤ a :=
-  @isAtom_iff αᵒᵈ _ _ _
-#align is_coatom_iff isCoatom_iff
+theorem isCoatom_iff_ge_of_le : IsCoatom a ↔ a ≠ ⊤ ∧ ∀ b ≠ ⊤, a ≤ b → b ≤ a :=
+  isAtom_iff_le_of_ge (α := αᵒᵈ)
+#align is_coatom_iff isCoatom_iff_ge_of_le
 
 end Preorder
 
@@ -182,6 +185,8 @@ theorem IsCoatom.le_iff (h : IsCoatom a) : a ≤ x ↔ x = ⊤ ∨ x = a :=
   h.dual.le_iff
 #align is_coatom.le_iff IsCoatom.le_iff
 
+lemma IsCoatom.le_iff_eq (ha : IsCoatom a) (hb : b ≠ ⊤) : a ≤ b ↔ b = a := ha.dual.le_iff_eq hb
+
 theorem IsCoatom.Ici_eq (h : IsCoatom a) : Set.Ici a = {⊤, a} :=
   h.dual.Iic_eq
 #align is_coatom.Ici_eq IsCoatom.Ici_eq
@@ -1076,18 +1081,29 @@ instance isCoatomistic [∀ i, CompleteLattice (π i)] [∀ i, IsCoatomistic (π
 
 end Pi
 
+section BooleanAlgebra
+variable [BooleanAlgebra α] {a b : α}
+
+@[simp] lemma isAtom_compl : IsAtom aᶜ ↔ IsCoatom a := isCompl_compl.symm.isAtom_iff_isCoatom
+@[simp] lemma isCoatom_compl : IsCoatom aᶜ ↔ IsAtom a := isCompl_compl.symm.isCoatom_iff_isAtom
+
+protected alias ⟨IsAtom.of_compl, IsCoatom.compl⟩ := isAtom_compl
+protected alias ⟨IsCoatom.of_compl, IsAtom.compl⟩ := isCoatom_compl
+
+end BooleanAlgebra
+
 namespace Set
 
 theorem isAtom_singleton (x : α) : IsAtom ({x} : Set α) :=
   ⟨singleton_ne_empty _, fun _ hs => ssubset_singleton_iff.mp hs⟩
 #align set.is_atom_singleton Set.isAtom_singleton
 
-theorem isAtom_iff (s : Set α) : IsAtom s ↔ ∃ x, s = {x} := by
+theorem isAtom_iff {s : Set α} : IsAtom s ↔ ∃ x, s = {x} := by
   refine'
     ⟨_, by
       rintro ⟨x, rfl⟩
       exact isAtom_singleton x⟩
-  rw [_root_.isAtom_iff, bot_eq_empty, ← nonempty_iff_ne_empty]
+  rw [isAtom_iff_le_of_ge, bot_eq_empty, ← nonempty_iff_ne_empty]
   rintro ⟨⟨x, hx⟩, hs⟩
   exact
     ⟨x, eq_singleton_iff_unique_mem.2

I've also got a change to make this required, but I'd like to land this first.

@@ -494,7 +494,7 @@ instance {α} [CompleteAtomicBooleanAlgebra α] : IsAtomistic α where
     have : (⨅ c : α, ⨆ x, b ⊓ cond x c (cᶜ)) = b := by simp [iSup_bool_eq, iInf_const]
     rw [← this]; clear this
     simp_rw [iInf_iSup_eq, iSup_le_iff]; intro g
-    by_cases (⨅ a, b ⊓ cond (g a) a (aᶜ)) = ⊥; case pos => simp [h]
+    by_cases h : (⨅ a, b ⊓ cond (g a) a (aᶜ)) = ⊥; case pos => simp [h]
     refine le_sSup ⟨⟨h, fun c hc => ?_⟩, le_trans (by rfl) (le_iSup _ g)⟩; clear h
     have := lt_of_lt_of_le hc (le_trans (iInf_le _ c) inf_le_right)
     revert this
@@ -977,7 +977,7 @@ namespace «Prop»
   simp [IsCoatom, show ⊤ = True from rfl, fun q r : Prop => show q < r ↔ _ ∧ _ from .rfl]; tauto
 
 instance : IsSimpleOrder Prop where
-  eq_bot_or_eq_top p := by by_cases p <;> simp [h] <;> tauto
+  eq_bot_or_eq_top p := by by_cases h : p <;> simp [h] <;> tauto
 
 end «Prop»
 
@@ -1014,7 +1014,7 @@ theorem isAtom_iff {f : ∀ i, π i} [∀ i, PartialOrder (π i)] [∀ i, OrderB
       intro j hj
       have := h (Function.update ⊥ j (f j))
       simp only [lt_def, le_def, ge_iff_le, Pi.eq_bot_iff, and_imp, forall_exists_index] at this
-      simpa using this (fun k => by by_cases k = j; { subst h; simp }; simp [h]) i
+      simpa using this (fun k => by by_cases h : k = j; { subst h; simp }; simp [h]) i
         (by rwa [Function.update_noteq (Ne.symm hj), bot_apply, bot_lt_iff_ne_bot]) j
 
 theorem isAtom_single [DecidableEq ι] [∀ i, PartialOrder (π i)] [∀ i, OrderBot (π i)] {a : π i}

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