order.zorn_atomsMathlib.Order.ZornAtoms

This file has been ported!

Changes since the initial port

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

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -22,7 +22,7 @@ statement.
 
 open Set
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x «expr ≠ » «expr⊤»()) -/
 #print IsCoatomic.of_isChain_bounded /-
 /-- **Zorn's lemma**: A partial order is coatomic if every nonempty chain `c`, `⊤ ∉ c`, has an upper
 bound not equal to `⊤`. -/
@@ -41,7 +41,7 @@ theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop
 #align is_coatomic.of_is_chain_bounded IsCoatomic.of_isChain_bounded
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x «expr ≠ » «expr⊥»()) -/
 #print IsAtomic.of_isChain_bounded /-
 /-- **Zorn's lemma**: A partial order is atomic if every nonempty chain `c`, `⊥ ∉ c`, has an lower
 bound not equal to `⊥`. -/
Diff
@@ -3,8 +3,8 @@ Copyright (c) 2022 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.Order.Zorn
-import Mathbin.Order.Atoms
+import Order.Zorn
+import Order.Atoms
 
 #align_import order.zorn_atoms from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
 
@@ -22,7 +22,7 @@ statement.
 
 open Set
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ≠ » «expr⊤»()) -/
 #print IsCoatomic.of_isChain_bounded /-
 /-- **Zorn's lemma**: A partial order is coatomic if every nonempty chain `c`, `⊤ ∉ c`, has an upper
 bound not equal to `⊤`. -/
@@ -41,7 +41,7 @@ theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop
 #align is_coatomic.of_is_chain_bounded IsCoatomic.of_isChain_bounded
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ≠ » «expr⊥»()) -/
 #print IsAtomic.of_isChain_bounded /-
 /-- **Zorn's lemma**: A partial order is atomic if every nonempty chain `c`, `⊥ ∉ c`, has an lower
 bound not equal to `⊥`. -/
Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2022 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module order.zorn_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.Zorn
 import Mathbin.Order.Atoms
 
+#align_import order.zorn_atoms from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
 /-!
 # Zorn lemma for (co)atoms
 
@@ -25,7 +22,7 @@ statement.
 
 open Set
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » «expr⊤»()) -/
 #print IsCoatomic.of_isChain_bounded /-
 /-- **Zorn's lemma**: A partial order is coatomic if every nonempty chain `c`, `⊤ ∉ c`, has an upper
 bound not equal to `⊤`. -/
@@ -44,7 +41,7 @@ theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop
 #align is_coatomic.of_is_chain_bounded IsCoatomic.of_isChain_bounded
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » «expr⊥»()) -/
 #print IsAtomic.of_isChain_bounded /-
 /-- **Zorn's lemma**: A partial order is atomic if every nonempty chain `c`, `⊥ ∉ c`, has an lower
 bound not equal to `⊥`. -/
Diff
@@ -26,6 +26,7 @@ statement.
 open Set
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » «expr⊤»()) -/
+#print IsCoatomic.of_isChain_bounded /-
 /-- **Zorn's lemma**: A partial order is coatomic if every nonempty chain `c`, `⊤ ∉ c`, has an upper
 bound not equal to `⊤`. -/
 theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop α]
@@ -41,8 +42,10 @@ theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop
   · rcases h c hc ⟨y, hy⟩ fun h => (hxc h).2.Ne rfl with ⟨z, hz, hcz⟩
     exact ⟨z, ⟨le_trans (hxc hy).1 (hcz hy), hz.lt_top⟩, hcz⟩
 #align is_coatomic.of_is_chain_bounded IsCoatomic.of_isChain_bounded
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » «expr⊥»()) -/
+#print IsAtomic.of_isChain_bounded /-
 /-- **Zorn's lemma**: A partial order is atomic if every nonempty chain `c`, `⊥ ∉ c`, has an lower
 bound not equal to `⊥`. -/
 theorem IsAtomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderBot α]
@@ -52,4 +55,5 @@ theorem IsAtomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderBot α
     IsAtomic α :=
   isCoatomic_dual_iff_isAtomic.mp <| IsCoatomic.of_isChain_bounded fun c hc => h c hc.symm
 #align is_atomic.of_is_chain_bounded IsAtomic.of_isChain_bounded
+-/
 
Diff
@@ -25,7 +25,7 @@ statement.
 
 open Set
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » «expr⊤»()) -/
 /-- **Zorn's lemma**: A partial order is coatomic if every nonempty chain `c`, `⊤ ∉ c`, has an upper
 bound not equal to `⊤`. -/
 theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop α]
@@ -42,7 +42,7 @@ theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop
     exact ⟨z, ⟨le_trans (hxc hy).1 (hcz hy), hz.lt_top⟩, hcz⟩
 #align is_coatomic.of_is_chain_bounded IsCoatomic.of_isChain_bounded
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » «expr⊥»()) -/
 /-- **Zorn's lemma**: A partial order is atomic if every nonempty chain `c`, `⊥ ∉ c`, has an lower
 bound not equal to `⊥`. -/
 theorem IsAtomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderBot α]
Diff
@@ -31,7 +31,7 @@ bound not equal to `⊤`. -/
 theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop α]
     (h :
       ∀ c : Set α,
-        IsChain (· ≤ ·) c → c.Nonempty → ⊤ ∉ c → ∃ (x : _)(_ : x ≠ ⊤), x ∈ upperBounds c) :
+        IsChain (· ≤ ·) c → c.Nonempty → ⊤ ∉ c → ∃ (x : _) (_ : x ≠ ⊤), x ∈ upperBounds c) :
     IsCoatomic α := by
   refine' ⟨fun x => le_top.eq_or_lt.imp_right fun hx => _⟩
   rcases zorn_nonempty_partialOrder₀ (Ico x ⊤) (fun c hxc hc y hy => _) x (left_mem_Ico.2 hx) with
@@ -48,7 +48,7 @@ bound not equal to `⊥`. -/
 theorem IsAtomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderBot α]
     (h :
       ∀ c : Set α,
-        IsChain (· ≤ ·) c → c.Nonempty → ⊥ ∉ c → ∃ (x : _)(_ : x ≠ ⊥), x ∈ lowerBounds c) :
+        IsChain (· ≤ ·) c → c.Nonempty → ⊥ ∉ c → ∃ (x : _) (_ : x ≠ ⊥), x ∈ lowerBounds c) :
     IsAtomic α :=
   isCoatomic_dual_iff_isAtomic.mp <| IsCoatomic.of_isChain_bounded fun c hc => h c hc.symm
 #align is_atomic.of_is_chain_bounded IsAtomic.of_isChain_bounded
Diff
@@ -25,12 +25,6 @@ statement.
 
 open Set
 
-/- warning: is_coatomic.of_is_chain_bounded -> IsCoatomic.of_isChain_bounded 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))], (forall (c : Set.{u1} α), (IsChain.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) c) -> (Set.Nonempty.{u1} α c) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) c)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Ne.{succ u1} α x (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (fun (H : Ne.{succ u1} α x (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) c))))) -> (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))], (forall (c : Set.{u1} α), (IsChain.{u1} α (fun (x._@.Mathlib.Order.ZornAtoms._hyg.26 : α) (x._@.Mathlib.Order.ZornAtoms._hyg.28 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x._@.Mathlib.Order.ZornAtoms._hyg.26 x._@.Mathlib.Order.ZornAtoms._hyg.28) c) -> (Set.Nonempty.{u1} α c) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) c)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Ne.{succ u1} α x (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (fun (H : Ne.{succ u1} α x (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) c))))) -> (IsCoatomic.{u1} α _inst_1 _inst_2)
-Case conversion may be inaccurate. Consider using '#align is_coatomic.of_is_chain_bounded IsCoatomic.of_isChain_boundedₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » «expr⊤»()) -/
 /-- **Zorn's lemma**: A partial order is coatomic if every nonempty chain `c`, `⊤ ∉ c`, has an upper
 bound not equal to `⊤`. -/
@@ -48,12 +42,6 @@ theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop
     exact ⟨z, ⟨le_trans (hxc hy).1 (hcz hy), hz.lt_top⟩, hcz⟩
 #align is_coatomic.of_is_chain_bounded IsCoatomic.of_isChain_bounded
 
-/- warning: is_atomic.of_is_chain_bounded -> IsAtomic.of_isChain_bounded 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))], (forall (c : Set.{u1} α), (IsChain.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) c) -> (Set.Nonempty.{u1} α c) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) c)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Ne.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (fun (H : Ne.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) c))))) -> (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))], (forall (c : Set.{u1} α), (IsChain.{u1} α (fun (x._@.Mathlib.Order.ZornAtoms._hyg.303 : α) (x._@.Mathlib.Order.ZornAtoms._hyg.305 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x._@.Mathlib.Order.ZornAtoms._hyg.303 x._@.Mathlib.Order.ZornAtoms._hyg.305) c) -> (Set.Nonempty.{u1} α c) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) c)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Ne.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (fun (H : Ne.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) c))))) -> (IsAtomic.{u1} α _inst_1 _inst_2)
-Case conversion may be inaccurate. Consider using '#align is_atomic.of_is_chain_bounded IsAtomic.of_isChain_boundedₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » «expr⊥»()) -/
 /-- **Zorn's lemma**: A partial order is atomic if every nonempty chain `c`, `⊥ ∉ c`, has an lower
 bound not equal to `⊥`. -/
Diff
@@ -27,7 +27,7 @@ open Set
 
 /- warning: is_coatomic.of_is_chain_bounded -> IsCoatomic.of_isChain_bounded 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))], (forall (c : Set.{u1} α), (IsChain.{u1} α (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) c) -> (Set.Nonempty.{u1} α c) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) c)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Ne.{succ u1} α x (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (fun (H : Ne.{succ u1} α x (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) c))))) -> (IsCoatomic.{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))], (forall (c : Set.{u1} α), (IsChain.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) c) -> (Set.Nonempty.{u1} α c) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) c)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Ne.{succ u1} α x (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (fun (H : Ne.{succ u1} α x (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) c))))) -> (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))], (forall (c : Set.{u1} α), (IsChain.{u1} α (fun (x._@.Mathlib.Order.ZornAtoms._hyg.26 : α) (x._@.Mathlib.Order.ZornAtoms._hyg.28 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x._@.Mathlib.Order.ZornAtoms._hyg.26 x._@.Mathlib.Order.ZornAtoms._hyg.28) c) -> (Set.Nonempty.{u1} α c) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) c)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Ne.{succ u1} α x (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (fun (H : Ne.{succ u1} α x (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) c))))) -> (IsCoatomic.{u1} α _inst_1 _inst_2)
 Case conversion may be inaccurate. Consider using '#align is_coatomic.of_is_chain_bounded IsCoatomic.of_isChain_boundedₓ'. -/
@@ -50,7 +50,7 @@ theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop
 
 /- warning: is_atomic.of_is_chain_bounded -> IsAtomic.of_isChain_bounded 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))], (forall (c : Set.{u1} α), (IsChain.{u1} α (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) c) -> (Set.Nonempty.{u1} α c) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) c)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Ne.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (fun (H : Ne.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) c))))) -> (IsAtomic.{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))], (forall (c : Set.{u1} α), (IsChain.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1))) c) -> (Set.Nonempty.{u1} α c) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) c)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Ne.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (fun (H : Ne.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) c))))) -> (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))], (forall (c : Set.{u1} α), (IsChain.{u1} α (fun (x._@.Mathlib.Order.ZornAtoms._hyg.303 : α) (x._@.Mathlib.Order.ZornAtoms._hyg.305 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x._@.Mathlib.Order.ZornAtoms._hyg.303 x._@.Mathlib.Order.ZornAtoms._hyg.305) c) -> (Set.Nonempty.{u1} α c) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) c)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Ne.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (fun (H : Ne.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) c))))) -> (IsAtomic.{u1} α _inst_1 _inst_2)
 Case conversion may be inaccurate. Consider using '#align is_atomic.of_is_chain_bounded IsAtomic.of_isChain_boundedₓ'. -/
Diff
@@ -31,7 +31,7 @@ lean 3 declaration is
 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))], (forall (c : Set.{u1} α), (IsChain.{u1} α (fun (x._@.Mathlib.Order.ZornAtoms._hyg.26 : α) (x._@.Mathlib.Order.ZornAtoms._hyg.28 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x._@.Mathlib.Order.ZornAtoms._hyg.26 x._@.Mathlib.Order.ZornAtoms._hyg.28) c) -> (Set.Nonempty.{u1} α c) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) c)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Ne.{succ u1} α x (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (fun (H : Ne.{succ u1} α x (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) c))))) -> (IsCoatomic.{u1} α _inst_1 _inst_2)
 Case conversion may be inaccurate. Consider using '#align is_coatomic.of_is_chain_bounded IsCoatomic.of_isChain_boundedₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » «expr⊤»()) -/
 /-- **Zorn's lemma**: A partial order is coatomic if every nonempty chain `c`, `⊤ ∉ c`, has an upper
 bound not equal to `⊤`. -/
 theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop α]
@@ -54,7 +54,7 @@ lean 3 declaration is
 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))], (forall (c : Set.{u1} α), (IsChain.{u1} α (fun (x._@.Mathlib.Order.ZornAtoms._hyg.303 : α) (x._@.Mathlib.Order.ZornAtoms._hyg.305 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) x._@.Mathlib.Order.ZornAtoms._hyg.303 x._@.Mathlib.Order.ZornAtoms._hyg.305) c) -> (Set.Nonempty.{u1} α c) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2)) c)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Ne.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) (fun (H : Ne.{succ u1} α x (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) _inst_2))) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) c))))) -> (IsAtomic.{u1} α _inst_1 _inst_2)
 Case conversion may be inaccurate. Consider using '#align is_atomic.of_is_chain_bounded IsAtomic.of_isChain_boundedₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » «expr⊥»()) -/
 /-- **Zorn's lemma**: A partial order is atomic if every nonempty chain `c`, `⊥ ∉ c`, has an lower
 bound not equal to `⊥`. -/
 theorem IsAtomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderBot α]

Changes in mathlib4

mathlib3
mathlib4
chore: tidy various files (#11490)
Diff
@@ -24,7 +24,7 @@ bound not equal to `⊤`. -/
 theorem IsCoatomic.of_isChain_bounded {α : Type*} [PartialOrder α] [OrderTop α]
     (h :
       ∀ c : Set α,
-        IsChain (· ≤ ·) c → c.Nonempty → ⊤ ∉ c → ∃ (x : _) (_ : x ≠ ⊤), x ∈ upperBounds c) :
+        IsChain (· ≤ ·) c → c.Nonempty → ⊤ ∉ c → ∃ x ≠ ⊤, x ∈ upperBounds c) :
     IsCoatomic α := by
   refine ⟨fun x => le_top.eq_or_lt.imp_right fun hx => ?_⟩
   have : ∃ y ∈ Ico x ⊤, x ≤ y ∧ ∀ z ∈ Ico x ⊤, y ≤ z → z = y := by
@@ -41,7 +41,7 @@ bound not equal to `⊥`. -/
 theorem IsAtomic.of_isChain_bounded {α : Type*} [PartialOrder α] [OrderBot α]
     (h :
       ∀ c : Set α,
-        IsChain (· ≤ ·) c → c.Nonempty → ⊥ ∉ c → ∃ (x : _) (_ : x ≠ ⊥), x ∈ lowerBounds c) :
+        IsChain (· ≤ ·) c → c.Nonempty → ⊥ ∉ c → ∃ x ≠ ⊥, x ∈ lowerBounds c) :
     IsAtomic α :=
   isCoatomic_dual_iff_isAtomic.mp <| IsCoatomic.of_isChain_bounded fun c hc => h c hc.symm
 #align is_atomic.of_is_chain_bounded IsAtomic.of_isChain_bounded
chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

Diff
@@ -21,7 +21,7 @@ open Set
 
 /-- **Zorn's lemma**: A partial order is coatomic if every nonempty chain `c`, `⊤ ∉ c`, has an upper
 bound not equal to `⊤`. -/
-theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop α]
+theorem IsCoatomic.of_isChain_bounded {α : Type*} [PartialOrder α] [OrderTop α]
     (h :
       ∀ c : Set α,
         IsChain (· ≤ ·) c → c.Nonempty → ⊤ ∉ c → ∃ (x : _) (_ : x ≠ ⊤), x ∈ upperBounds c) :
@@ -38,7 +38,7 @@ theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop
 
 /-- **Zorn's lemma**: A partial order is atomic if every nonempty chain `c`, `⊥ ∉ c`, has a lower
 bound not equal to `⊥`. -/
-theorem IsAtomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderBot α]
+theorem IsAtomic.of_isChain_bounded {α : Type*} [PartialOrder α] [OrderBot α]
     (h :
       ∀ c : Set α,
         IsChain (· ≤ ·) c → c.Nonempty → ⊥ ∉ c → ∃ (x : _) (_ : x ≠ ⊥), x ∈ lowerBounds c) :
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

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

Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2022 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module order.zorn_atoms
-! leanprover-community/mathlib commit 9aba7801eeecebb61f58a5763c2b6dd1b47dc6ef
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Order.Zorn
 import Mathlib.Order.Atoms
 
+#align_import order.zorn_atoms from "leanprover-community/mathlib"@"9aba7801eeecebb61f58a5763c2b6dd1b47dc6ef"
+
 /-!
 # Zorn lemma for (co)atoms
 
chore: fix grammar 3/3 (#5003)

Part 3 of #5001

Diff
@@ -39,7 +39,7 @@ theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop
   exact hyz.ne' (hy' z ⟨hxy.trans hyz.le, hz⟩ hyz.le)
 #align is_coatomic.of_is_chain_bounded IsCoatomic.of_isChain_bounded
 
-/-- **Zorn's lemma**: A partial order is atomic if every nonempty chain `c`, `⊥ ∉ c`, has an lower
+/-- **Zorn's lemma**: A partial order is atomic if every nonempty chain `c`, `⊥ ∉ c`, has a lower
 bound not equal to `⊥`. -/
 theorem IsAtomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderBot α]
     (h :
chore: formatting issues (#4947)

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

Diff
@@ -27,7 +27,7 @@ bound not equal to `⊤`. -/
 theorem IsCoatomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderTop α]
     (h :
       ∀ c : Set α,
-        IsChain (· ≤ ·) c → c.Nonempty → ⊤ ∉ c → ∃ (x : _)(_ : x ≠ ⊤), x ∈ upperBounds c) :
+        IsChain (· ≤ ·) c → c.Nonempty → ⊤ ∉ c → ∃ (x : _) (_ : x ≠ ⊤), x ∈ upperBounds c) :
     IsCoatomic α := by
   refine ⟨fun x => le_top.eq_or_lt.imp_right fun hx => ?_⟩
   have : ∃ y ∈ Ico x ⊤, x ≤ y ∧ ∀ z ∈ Ico x ⊤, y ≤ z → z = y := by
@@ -44,7 +44,7 @@ bound not equal to `⊥`. -/
 theorem IsAtomic.of_isChain_bounded {α : Type _} [PartialOrder α] [OrderBot α]
     (h :
       ∀ c : Set α,
-        IsChain (· ≤ ·) c → c.Nonempty → ⊥ ∉ c → ∃ (x : _)(_ : x ≠ ⊥), x ∈ lowerBounds c) :
+        IsChain (· ≤ ·) c → c.Nonempty → ⊥ ∉ c → ∃ (x : _) (_ : x ≠ ⊥), x ∈ lowerBounds c) :
     IsAtomic α :=
   isCoatomic_dual_iff_isAtomic.mp <| IsCoatomic.of_isChain_bounded fun c hc => h c hc.symm
 #align is_atomic.of_is_chain_bounded IsAtomic.of_isChain_bounded
feat: port Order.ZornAtoms (#1293)

Dependencies 73

74 files ported (100.0%)
37655 lines ported (100.0%)

All dependencies are ported!