order.fixed_points | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

ba2245ed

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

c3291da4

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -365,7 +365,7 @@ instance : CompleteSemilatticeSup (fixedPoints f) :=
         (f.le_map_sSup_subset_fixedPoints (coe '' s) fun z ⟨x, hx⟩ => hx.2 ▸ x.2)
     le_sup := fun s x hx =>
       Subtype.coe_le_coe.1 <| le_trans (le_sSup <| Set.mem_image_of_mem _ hx) (f.le_nextFixed _)
-    sup_le := fun s x hx => f.nextFixed_le _ <| sSup_le <| Set.ball_image_iff.2 hx }
+    sup_le := fun s x hx => f.nextFixed_le _ <| sSup_le <| Set.forall_mem_image.2 hx }
 
 instance : CompleteSemilatticeInf (fixedPoints f) :=
   {
@@ -374,7 +374,7 @@ instance : CompleteSemilatticeInf (fixedPoints f) :=
     sInf := fun s =>
       f.prevFixed (sInf (coe '' s))
         (f.map_sInf_subset_fixedPoints_le (coe '' s) fun z ⟨x, hx⟩ => hx.2 ▸ x.2)
-    le_inf := fun s x hx => f.le_prevFixed _ <| le_sInf <| Set.ball_image_iff.2 hx
+    le_inf := fun s x hx => f.le_prevFixed _ <| le_sInf <| Set.forall_mem_image.2 hx
     inf_le := fun s x hx =>
       Subtype.coe_le_coe.1 <| le_trans (f.prevFixed_le _) (sInf_le <| Set.mem_image_of_mem _ hx) }

c3291da4

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau, Yury Kudryashov
 -/
-import Mathbin.Dynamics.FixedPoints.Basic
-import Mathbin.Order.Hom.Order
+import Dynamics.FixedPoints.Basic
+import Order.Hom.Order
 
 #align_import order.fixed_points from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"

c3291da4

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau, Yury Kudryashov
-
-! This file was ported from Lean 3 source module order.fixed_points
-! 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.Dynamics.FixedPoints.Basic
 import Mathbin.Order.Hom.Order
 
+#align_import order.fixed_points from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
 /-!
 # Fixed point construction on complete lattices

c3291da4

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -118,10 +118,13 @@ theorem isLeast_lfp_le : IsLeast {a | f a ≤ a} (lfp f) :=
 
 /- warning: order_hom.is_least_lfp clashes with order_hom.is_least_lfp_le -> OrderHom.isLeast_lfp_le
 Case conversion may be inaccurate. Consider using '#align order_hom.is_least_lfp OrderHom.isLeast_lfp_leₓ'. -/
+#print OrderHom.isLeast_lfp_le /-
 theorem isLeast_lfp_le : IsLeast (fixedPoints f) (lfp f) :=
   ⟨f.isFixedPt_lfp, fun a => f.lfp_le_fixed⟩
 #align order_hom.is_least_lfp OrderHom.isLeast_lfp_le
+-/
 
+#print OrderHom.lfp_induction /-
 theorem lfp_induction {p : α → Prop} (step : ∀ a, p a → a ≤ lfp f → p (f a))
     (hSup : ∀ s, (∀ a ∈ s, p a) → p (sSup s)) : p (lfp f) :=
   by
@@ -132,6 +135,7 @@ theorem lfp_induction {p : α → Prop} (step : ∀ a, p a → a ≤ lfp f → p
   have hmem : f (Sup s) ∈ s := ⟨f.map_le_lfp h, step _ hSup h⟩
   exact h.antisymm (f.lfp_le <| le_sSup hmem)
 #align order_hom.lfp_induction OrderHom.lfp_induction
+-/
 
 #print OrderHom.le_gfp /-
 theorem le_gfp {a : α} (h : a ≤ f a) : a ≤ gfp f :=
@@ -182,10 +186,12 @@ theorem isGreatest_gfp : IsGreatest (fixedPoints f) (gfp f) :=
 #align order_hom.is_greatest_gfp OrderHom.isGreatest_gfp
 -/
 
+#print OrderHom.gfp_induction /-
 theorem gfp_induction {p : α → Prop} (step : ∀ a, p a → gfp f ≤ a → p (f a))
     (hInf : ∀ s, (∀ a ∈ s, p a) → p (sInf s)) : p (gfp f) :=
   f.dual.lfp_induction step hInf
 #align order_hom.gfp_induction OrderHom.gfp_induction
+-/
 
 end Basic
 
@@ -234,9 +240,11 @@ section PrevNext
 
 variable [CompleteLattice α] (f : α →o α)
 
+#print OrderHom.gfp_const_inf_le /-
 theorem gfp_const_inf_le (x : α) : gfp (const α x ⊓ f) ≤ x :=
   gfp_le _ fun b hb => hb.trans inf_le_left
 #align order_hom.gfp_const_inf_le OrderHom.gfp_const_inf_le
+-/
 
 #print OrderHom.prevFixed /-
 /-- Previous fixed point of a monotone map. If `f` is a monotone self-map of a complete lattice and
@@ -302,23 +310,31 @@ theorem le_prevFixed {x : α} (hx : f x ≤ x) {y : fixedPoints f} (h : ↑y ≤
 #align order_hom.le_prev_fixed OrderHom.le_prevFixed
 -/
 
+#print OrderHom.le_map_sup_fixedPoints /-
 theorem le_map_sup_fixedPoints (x y : fixedPoints f) : (x ⊔ y : α) ≤ f (x ⊔ y) :=
   calc
     (x ⊔ y : α) = f x ⊔ f y := congr_arg₂ (· ⊔ ·) x.2.symm y.2.symm
     _ ≤ f (x ⊔ y) := f.mono.le_map_sup x y
 #align order_hom.le_map_sup_fixed_points OrderHom.le_map_sup_fixedPoints
+-/
 
+#print OrderHom.map_inf_fixedPoints_le /-
 theorem map_inf_fixedPoints_le (x y : fixedPoints f) : f (x ⊓ y) ≤ x ⊓ y :=
   f.dual.le_map_sup_fixedPoints x y
 #align order_hom.map_inf_fixed_points_le OrderHom.map_inf_fixedPoints_le
+-/
 
+#print OrderHom.le_map_sSup_subset_fixedPoints /-
 theorem le_map_sSup_subset_fixedPoints (A : Set α) (hA : A ⊆ fixedPoints f) : sSup A ≤ f (sSup A) :=
   sSup_le fun x hx => hA hx ▸ (f.mono <| le_sSup hx)
 #align order_hom.le_map_Sup_subset_fixed_points OrderHom.le_map_sSup_subset_fixedPoints
+-/
 
+#print OrderHom.map_sInf_subset_fixedPoints_le /-
 theorem map_sInf_subset_fixedPoints_le (A : Set α) (hA : A ⊆ fixedPoints f) : f (sInf A) ≤ sInf A :=
   le_sInf fun x hx => hA hx ▸ (f.mono <| sInf_le hx)
 #align order_hom.map_Inf_subset_fixed_points_le OrderHom.map_sInf_subset_fixedPoints_le
+-/
 
 end PrevNext

c3291da4

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -107,7 +107,6 @@ theorem lfp_le_map {a : α} (ha : lfp f ≤ a) : lfp f ≤ f a :=
   calc
     lfp f = f (lfp f) := f.map_lfp.symm
     _ ≤ f a := f.mono ha
-    
 #align order_hom.lfp_le_map OrderHom.lfp_le_map
 -/
 
@@ -220,7 +219,6 @@ theorem lfp_lfp (h : α →o α →o α) : lfp (lfp.comp h) = lfp h.onDiag :=
     h a a = h a (lfp (h a)) := congr_arg (h a) ha.symm
     _ = lfp (h a) := (h a).map_lfp
     _ = a := ha
-    
 #align order_hom.lfp_lfp OrderHom.lfp_lfp
 -/
 
@@ -249,8 +247,7 @@ def prevFixed (x : α) (hx : f x ≤ x) : fixedPoints f :=
     calc
       f (gfp (const α x ⊓ f)) = x ⊓ f (gfp (const α x ⊓ f)) :=
         Eq.symm <| inf_of_le_right <| (f.mono <| f.gfp_const_inf_le x).trans hx
-      _ = gfp (const α x ⊓ f) := (const α x ⊓ f).map_gfp
-      ⟩
+      _ = gfp (const α x ⊓ f) := (const α x ⊓ f).map_gfp⟩
 #align order_hom.prev_fixed OrderHom.prevFixed
 -/
 
@@ -309,7 +306,6 @@ theorem le_map_sup_fixedPoints (x y : fixedPoints f) : (x ⊔ y : α) ≤ f (x 
   calc
     (x ⊔ y : α) = f x ⊔ f y := congr_arg₂ (· ⊔ ·) x.2.symm y.2.symm
     _ ≤ f (x ⊔ y) := f.mono.le_map_sup x y
-    
 #align order_hom.le_map_sup_fixed_points OrderHom.le_map_sup_fixedPoints
 
 theorem map_inf_fixedPoints_le (x y : fixedPoints f) : f (x ⊓ y) ≤ x ⊓ y :=

c3291da4

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -51,7 +51,7 @@ variable [CompleteLattice α] (f : α →o α)
 #print OrderHom.lfp /-
 /-- Least fixed point of a monotone function -/
 def lfp : (α →o α) →o α where
-  toFun f := sInf { a | f a ≤ a }
+  toFun f := sInf {a | f a ≤ a}
   monotone' f g hle := sInf_le_sInf fun a ha => (hle a).trans ha
 #align order_hom.lfp OrderHom.lfp
 -/
@@ -59,7 +59,7 @@ def lfp : (α →o α) →o α where
 #print OrderHom.gfp /-
 /-- Greatest fixed point of a monotone function -/
 def gfp : (α →o α) →o α where
-  toFun f := sSup { a | a ≤ f a }
+  toFun f := sSup {a | a ≤ f a}
   monotone' f g hle := sSup_le_sSup fun a ha => le_trans ha (hle a)
 #align order_hom.gfp OrderHom.gfp
 -/
@@ -112,7 +112,7 @@ theorem lfp_le_map {a : α} (ha : lfp f ≤ a) : lfp f ≤ f a :=
 -/
 
 #print OrderHom.isLeast_lfp_le /-
-theorem isLeast_lfp_le : IsLeast { a | f a ≤ a } (lfp f) :=
+theorem isLeast_lfp_le : IsLeast {a | f a ≤ a} (lfp f) :=
   ⟨f.map_lfp.le, fun a => f.lfp_le⟩
 #align order_hom.is_least_lfp_le OrderHom.isLeast_lfp_le
 -/
@@ -126,7 +126,7 @@ theorem isLeast_lfp_le : IsLeast (fixedPoints f) (lfp f) :=
 theorem lfp_induction {p : α → Prop} (step : ∀ a, p a → a ≤ lfp f → p (f a))
     (hSup : ∀ s, (∀ a ∈ s, p a) → p (sSup s)) : p (lfp f) :=
   by
-  set s := { a | a ≤ lfp f ∧ p a }
+  set s := {a | a ≤ lfp f ∧ p a}
   specialize hSup s fun a => And.right
   suffices : Sup s = lfp f; exact this ▸ hSup
   have h : Sup s ≤ lfp f := sSup_le fun b => And.left
@@ -172,7 +172,7 @@ theorem gfp_le_map {a : α} (ha : gfp f ≤ a) : gfp f ≤ f a :=
 -/
 
 #print OrderHom.isGreatest_gfp_le /-
-theorem isGreatest_gfp_le : IsGreatest { a | a ≤ f a } (gfp f) :=
+theorem isGreatest_gfp_le : IsGreatest {a | a ≤ f a} (gfp f) :=
   f.dual.isLeast_lfp_le
 #align order_hom.is_greatest_gfp_le OrderHom.isGreatest_gfp_le
 -/

c3291da4

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -64,21 +64,29 @@ def gfp : (α →o α) →o α where
 #align order_hom.gfp OrderHom.gfp
 -/
 
+#print OrderHom.lfp_le /-
 theorem lfp_le {a : α} (h : f a ≤ a) : lfp f ≤ a :=
   sInf_le h
 #align order_hom.lfp_le OrderHom.lfp_le
+-/
 
+#print OrderHom.lfp_le_fixed /-
 theorem lfp_le_fixed {a : α} (h : f a = a) : lfp f ≤ a :=
   f.lfp_le h.le
 #align order_hom.lfp_le_fixed OrderHom.lfp_le_fixed
+-/
 
+#print OrderHom.le_lfp /-
 theorem le_lfp {a : α} (h : ∀ b, f b ≤ b → a ≤ b) : a ≤ lfp f :=
   le_sInf h
 #align order_hom.le_lfp OrderHom.le_lfp
+-/
 
+#print OrderHom.map_le_lfp /-
 theorem map_le_lfp {a : α} (ha : a ≤ f.lfp) : f a ≤ f.lfp :=
   f.le_lfp fun b hb => (f.mono <| le_sInf_iff.1 ha _ hb).trans hb
 #align order_hom.map_le_lfp OrderHom.map_le_lfp
+-/
 
 #print OrderHom.map_lfp /-
 @[simp]
@@ -94,16 +102,20 @@ theorem isFixedPt_lfp : IsFixedPt f f.lfp :=
 #align order_hom.is_fixed_pt_lfp OrderHom.isFixedPt_lfp
 -/
 
+#print OrderHom.lfp_le_map /-
 theorem lfp_le_map {a : α} (ha : lfp f ≤ a) : lfp f ≤ f a :=
   calc
     lfp f = f (lfp f) := f.map_lfp.symm
     _ ≤ f a := f.mono ha
     
 #align order_hom.lfp_le_map OrderHom.lfp_le_map
+-/
 
+#print OrderHom.isLeast_lfp_le /-
 theorem isLeast_lfp_le : IsLeast { a | f a ≤ a } (lfp f) :=
   ⟨f.map_lfp.le, fun a => f.lfp_le⟩
 #align order_hom.is_least_lfp_le OrderHom.isLeast_lfp_le
+-/
 
 /- warning: order_hom.is_least_lfp clashes with order_hom.is_least_lfp_le -> OrderHom.isLeast_lfp_le
 Case conversion may be inaccurate. Consider using '#align order_hom.is_least_lfp OrderHom.isLeast_lfp_leₓ'. -/
@@ -122,13 +134,17 @@ theorem lfp_induction {p : α → Prop} (step : ∀ a, p a → a ≤ lfp f → p
   exact h.antisymm (f.lfp_le <| le_sSup hmem)
 #align order_hom.lfp_induction OrderHom.lfp_induction
 
+#print OrderHom.le_gfp /-
 theorem le_gfp {a : α} (h : a ≤ f a) : a ≤ gfp f :=
   le_sSup h
 #align order_hom.le_gfp OrderHom.le_gfp
+-/
 
+#print OrderHom.gfp_le /-
 theorem gfp_le {a : α} (h : ∀ b, b ≤ f b → b ≤ a) : gfp f ≤ a :=
   sSup_le h
 #align order_hom.gfp_le OrderHom.gfp_le
+-/
 
 #print OrderHom.isFixedPt_gfp /-
 theorem isFixedPt_gfp : IsFixedPt f (gfp f) :=
@@ -143,17 +159,23 @@ theorem map_gfp : f (gfp f) = gfp f :=
 #align order_hom.map_gfp OrderHom.map_gfp
 -/
 
+#print OrderHom.map_le_gfp /-
 theorem map_le_gfp {a : α} (ha : a ≤ gfp f) : f a ≤ gfp f :=
   f.dual.lfp_le_map ha
 #align order_hom.map_le_gfp OrderHom.map_le_gfp
+-/
 
+#print OrderHom.gfp_le_map /-
 theorem gfp_le_map {a : α} (ha : gfp f ≤ a) : gfp f ≤ f a :=
   f.dual.map_le_lfp ha
 #align order_hom.gfp_le_map OrderHom.gfp_le_map
+-/
 
+#print OrderHom.isGreatest_gfp_le /-
 theorem isGreatest_gfp_le : IsGreatest { a | a ≤ f a } (gfp f) :=
   f.dual.isLeast_lfp_le
 #align order_hom.is_greatest_gfp_le OrderHom.isGreatest_gfp_le
+-/
 
 #print OrderHom.isGreatest_gfp /-
 theorem isGreatest_gfp : IsGreatest (fixedPoints f) (gfp f) :=
@@ -218,6 +240,7 @@ theorem gfp_const_inf_le (x : α) : gfp (const α x ⊓ f) ≤ x :=
   gfp_le _ fun b hb => hb.trans inf_le_left
 #align order_hom.gfp_const_inf_le OrderHom.gfp_const_inf_le
 
+#print OrderHom.prevFixed /-
 /-- Previous fixed point of a monotone map. If `f` is a monotone self-map of a complete lattice and
 `x` is a point such that `f x ≤ x`, then `f.prev_fixed x hx` is the greatest fixed point of `f`
 that is less than or equal to `x`. -/
@@ -229,43 +252,58 @@ def prevFixed (x : α) (hx : f x ≤ x) : fixedPoints f :=
       _ = gfp (const α x ⊓ f) := (const α x ⊓ f).map_gfp
       ⟩
 #align order_hom.prev_fixed OrderHom.prevFixed
+-/
 
+#print OrderHom.nextFixed /-
 /-- Next fixed point of a monotone map. If `f` is a monotone self-map of a complete lattice and
 `x` is a point such that `x ≤ f x`, then `f.next_fixed x hx` is the least fixed point of `f`
 that is greater than or equal to `x`. -/
 def nextFixed (x : α) (hx : x ≤ f x) : fixedPoints f :=
   { f.dual.prevFixed x hx with val := (const α x ⊔ f).lfp }
 #align order_hom.next_fixed OrderHom.nextFixed
+-/
 
+#print OrderHom.prevFixed_le /-
 theorem prevFixed_le {x : α} (hx : f x ≤ x) : ↑(f.prevFixed x hx) ≤ x :=
   f.gfp_const_inf_le x
 #align order_hom.prev_fixed_le OrderHom.prevFixed_le
+-/
 
+#print OrderHom.le_nextFixed /-
 theorem le_nextFixed {x : α} (hx : x ≤ f x) : x ≤ f.nextFixed x hx :=
   f.dual.prevFixed_le hx
 #align order_hom.le_next_fixed OrderHom.le_nextFixed
+-/
 
+#print OrderHom.nextFixed_le /-
 theorem nextFixed_le {x : α} (hx : x ≤ f x) {y : fixedPoints f} (h : x ≤ y) :
     f.nextFixed x hx ≤ y :=
   Subtype.coe_le_coe.1 <| lfp_le _ <| sup_le h y.2.le
 #align order_hom.next_fixed_le OrderHom.nextFixed_le
+-/
 
+#print OrderHom.nextFixed_le_iff /-
 @[simp]
 theorem nextFixed_le_iff {x : α} (hx : x ≤ f x) {y : fixedPoints f} :
     f.nextFixed x hx ≤ y ↔ x ≤ y :=
   ⟨fun h => (f.le_nextFixed hx).trans h, f.nextFixed_le hx⟩
 #align order_hom.next_fixed_le_iff OrderHom.nextFixed_le_iff
+-/
 
+#print OrderHom.le_prevFixed_iff /-
 @[simp]
 theorem le_prevFixed_iff {x : α} (hx : f x ≤ x) {y : fixedPoints f} :
     y ≤ f.prevFixed x hx ↔ ↑y ≤ x :=
   f.dual.nextFixed_le_iff hx
 #align order_hom.le_prev_fixed_iff OrderHom.le_prevFixed_iff
+-/
 
+#print OrderHom.le_prevFixed /-
 theorem le_prevFixed {x : α} (hx : f x ≤ x) {y : fixedPoints f} (h : ↑y ≤ x) :
     y ≤ f.prevFixed x hx :=
   (f.le_prevFixed_iff hx).2 h
 #align order_hom.le_prev_fixed OrderHom.le_prevFixed
+-/
 
 theorem le_map_sup_fixedPoints (x y : fixedPoints f) : (x ⊔ y : α) ≤ f (x ⊔ y) :=
   calc

c3291da4

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -64,42 +64,18 @@ def gfp : (α →o α) →o α where
 #align order_hom.gfp OrderHom.gfp
 -/
 
-/- warning: order_hom.lfp_le -> OrderHom.lfp_le is a dubious translation:
-lean 3 declaration is
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 theorem lfp_le {a : α} (h : f a ≤ a) : lfp f ≤ a :=
   sInf_le h
 #align order_hom.lfp_le OrderHom.lfp_le
 
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 theorem lfp_le_fixed {a : α} (h : f a = a) : lfp f ≤ a :=
   f.lfp_le h.le
 #align order_hom.lfp_le_fixed OrderHom.lfp_le_fixed
 
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 theorem le_lfp {a : α} (h : ∀ b, f b ≤ b → a ≤ b) : a ≤ lfp f :=
   le_sInf h
 #align order_hom.le_lfp OrderHom.le_lfp
 
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-Case conversion may be inaccurate. Consider using '#align order_hom.map_le_lfp OrderHom.map_le_lfpₓ'. -/
 theorem map_le_lfp {a : α} (ha : a ≤ f.lfp) : f a ≤ f.lfp :=
   f.le_lfp fun b hb => (f.mono <| le_sInf_iff.1 ha _ hb).trans hb
 #align order_hom.map_le_lfp OrderHom.map_le_lfp
@@ -118,12 +94,6 @@ theorem isFixedPt_lfp : IsFixedPt f f.lfp :=
 #align order_hom.is_fixed_pt_lfp OrderHom.isFixedPt_lfp
 -/
 
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-Case conversion may be inaccurate. Consider using '#align order_hom.lfp_le_map OrderHom.lfp_le_mapₓ'. -/
 theorem lfp_le_map {a : α} (ha : lfp f ≤ a) : lfp f ≤ f a :=
   calc
     lfp f = f (lfp f) := f.map_lfp.symm
@@ -131,30 +101,16 @@ theorem lfp_le_map {a : α} (ha : lfp f ≤ a) : lfp f ≤ f a :=
     
 #align order_hom.lfp_le_map OrderHom.lfp_le_map
 
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-Case conversion may be inaccurate. Consider using '#align order_hom.is_least_lfp_le OrderHom.isLeast_lfp_leₓ'. -/
 theorem isLeast_lfp_le : IsLeast { a | f a ≤ a } (lfp f) :=
   ⟨f.map_lfp.le, fun a => f.lfp_le⟩
 #align order_hom.is_least_lfp_le OrderHom.isLeast_lfp_le
 
 /- warning: order_hom.is_least_lfp clashes with order_hom.is_least_lfp_le -> OrderHom.isLeast_lfp_le
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 Case conversion may be inaccurate. Consider using '#align order_hom.is_least_lfp OrderHom.isLeast_lfp_leₓ'. -/
 theorem isLeast_lfp_le : IsLeast (fixedPoints f) (lfp f) :=
   ⟨f.isFixedPt_lfp, fun a => f.lfp_le_fixed⟩
 #align order_hom.is_least_lfp OrderHom.isLeast_lfp_le
 
-/- warning: order_hom.lfp_induction -> OrderHom.lfp_induction is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align order_hom.lfp_induction OrderHom.lfp_inductionₓ'. -/
 theorem lfp_induction {p : α → Prop} (step : ∀ a, p a → a ≤ lfp f → p (f a))
     (hSup : ∀ s, (∀ a ∈ s, p a) → p (sSup s)) : p (lfp f) :=
   by
@@ -166,22 +122,10 @@ theorem lfp_induction {p : α → Prop} (step : ∀ a, p a → a ≤ lfp f → p
   exact h.antisymm (f.lfp_le <| le_sSup hmem)
 #align order_hom.lfp_induction OrderHom.lfp_induction
 
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-Case conversion may be inaccurate. Consider using '#align order_hom.le_gfp OrderHom.le_gfpₓ'. -/
 theorem le_gfp {a : α} (h : a ≤ f a) : a ≤ gfp f :=
   le_sSup h
 #align order_hom.le_gfp OrderHom.le_gfp
 
-/- warning: order_hom.gfp_le -> OrderHom.gfp_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align order_hom.gfp_le OrderHom.gfp_leₓ'. -/
 theorem gfp_le {a : α} (h : ∀ b, b ≤ f b → b ≤ a) : gfp f ≤ a :=
   sSup_le h
 #align order_hom.gfp_le OrderHom.gfp_le
@@ -199,32 +143,14 @@ theorem map_gfp : f (gfp f) = gfp f :=
 #align order_hom.map_gfp OrderHom.map_gfp
 -/
 
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-Case conversion may be inaccurate. Consider using '#align order_hom.map_le_gfp OrderHom.map_le_gfpₓ'. -/
 theorem map_le_gfp {a : α} (ha : a ≤ gfp f) : f a ≤ gfp f :=
   f.dual.lfp_le_map ha
 #align order_hom.map_le_gfp OrderHom.map_le_gfp
 
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-Case conversion may be inaccurate. Consider using '#align order_hom.gfp_le_map OrderHom.gfp_le_mapₓ'. -/
 theorem gfp_le_map {a : α} (ha : gfp f ≤ a) : gfp f ≤ f a :=
   f.dual.map_le_lfp ha
 #align order_hom.gfp_le_map OrderHom.gfp_le_map
 
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-Case conversion may be inaccurate. Consider using '#align order_hom.is_greatest_gfp_le OrderHom.isGreatest_gfp_leₓ'. -/
 theorem isGreatest_gfp_le : IsGreatest { a | a ≤ f a } (gfp f) :=
   f.dual.isLeast_lfp_le
 #align order_hom.is_greatest_gfp_le OrderHom.isGreatest_gfp_le
@@ -235,9 +161,6 @@ theorem isGreatest_gfp : IsGreatest (fixedPoints f) (gfp f) :=
 #align order_hom.is_greatest_gfp OrderHom.isGreatest_gfp
 -/
 
-/- warning: order_hom.gfp_induction -> OrderHom.gfp_induction is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align order_hom.gfp_induction OrderHom.gfp_inductionₓ'. -/
 theorem gfp_induction {p : α → Prop} (step : ∀ a, p a → gfp f ≤ a → p (f a))
     (hInf : ∀ s, (∀ a ∈ s, p a) → p (sInf s)) : p (gfp f) :=
   f.dual.lfp_induction step hInf
@@ -291,22 +214,10 @@ section PrevNext
 
 variable [CompleteLattice α] (f : α →o α)
 
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 theorem gfp_const_inf_le (x : α) : gfp (const α x ⊓ f) ≤ x :=
   gfp_le _ fun b hb => hb.trans inf_le_left
 #align order_hom.gfp_const_inf_le OrderHom.gfp_const_inf_le
 
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 /-- Previous fixed point of a monotone map. If `f` is a monotone self-map of a complete lattice and
 `x` is a point such that `f x ≤ x`, then `f.prev_fixed x hx` is the greatest fixed point of `f`
 that is less than or equal to `x`. -/
@@ -319,12 +230,6 @@ def prevFixed (x : α) (hx : f x ≤ x) : fixedPoints f :=
       ⟩
 #align order_hom.prev_fixed OrderHom.prevFixed
 
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 /-- Next fixed point of a monotone map. If `f` is a monotone self-map of a complete lattice and
 `x` is a point such that `x ≤ f x`, then `f.next_fixed x hx` is the least fixed point of `f`
 that is greater than or equal to `x`. -/
@@ -332,63 +237,36 @@ def nextFixed (x : α) (hx : x ≤ f x) : fixedPoints f :=
   { f.dual.prevFixed x hx with val := (const α x ⊔ f).lfp }
 #align order_hom.next_fixed OrderHom.nextFixed
 
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 theorem prevFixed_le {x : α} (hx : f x ≤ x) : ↑(f.prevFixed x hx) ≤ x :=
   f.gfp_const_inf_le x
 #align order_hom.prev_fixed_le OrderHom.prevFixed_le
 
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 theorem le_nextFixed {x : α} (hx : x ≤ f x) : x ≤ f.nextFixed x hx :=
   f.dual.prevFixed_le hx
 #align order_hom.le_next_fixed OrderHom.le_nextFixed
 
-/- warning: order_hom.next_fixed_le -> OrderHom.nextFixed_le is a dubious translation:
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 theorem nextFixed_le {x : α} (hx : x ≤ f x) {y : fixedPoints f} (h : x ≤ y) :
     f.nextFixed x hx ≤ y :=
   Subtype.coe_le_coe.1 <| lfp_le _ <| sup_le h y.2.le
 #align order_hom.next_fixed_le OrderHom.nextFixed_le
 
-/- warning: order_hom.next_fixed_le_iff -> OrderHom.nextFixed_le_iff is a dubious translation:
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 @[simp]
 theorem nextFixed_le_iff {x : α} (hx : x ≤ f x) {y : fixedPoints f} :
     f.nextFixed x hx ≤ y ↔ x ≤ y :=
   ⟨fun h => (f.le_nextFixed hx).trans h, f.nextFixed_le hx⟩
 #align order_hom.next_fixed_le_iff OrderHom.nextFixed_le_iff
 
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 @[simp]
 theorem le_prevFixed_iff {x : α} (hx : f x ≤ x) {y : fixedPoints f} :
     y ≤ f.prevFixed x hx ↔ ↑y ≤ x :=
   f.dual.nextFixed_le_iff hx
 #align order_hom.le_prev_fixed_iff OrderHom.le_prevFixed_iff
 
-/- warning: order_hom.le_prev_fixed -> OrderHom.le_prevFixed is a dubious translation:
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 theorem le_prevFixed {x : α} (hx : f x ≤ x) {y : fixedPoints f} (h : ↑y ≤ x) :
     y ≤ f.prevFixed x hx :=
   (f.le_prevFixed_iff hx).2 h
 #align order_hom.le_prev_fixed OrderHom.le_prevFixed
 
-/- warning: order_hom.le_map_sup_fixed_points -> OrderHom.le_map_sup_fixedPoints is a dubious translation:
-<too large>
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 theorem le_map_sup_fixedPoints (x y : fixedPoints f) : (x ⊔ y : α) ≤ f (x ⊔ y) :=
   calc
     (x ⊔ y : α) = f x ⊔ f y := congr_arg₂ (· ⊔ ·) x.2.symm y.2.symm
@@ -396,29 +274,14 @@ theorem le_map_sup_fixedPoints (x y : fixedPoints f) : (x ⊔ y : α) ≤ f (x 
     
 #align order_hom.le_map_sup_fixed_points OrderHom.le_map_sup_fixedPoints
 
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 theorem map_inf_fixedPoints_le (x y : fixedPoints f) : f (x ⊓ y) ≤ x ⊓ y :=
   f.dual.le_map_sup_fixedPoints x y
 #align order_hom.map_inf_fixed_points_le OrderHom.map_inf_fixedPoints_le
 
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-Case conversion may be inaccurate. Consider using '#align order_hom.le_map_Sup_subset_fixed_points OrderHom.le_map_sSup_subset_fixedPointsₓ'. -/
 theorem le_map_sSup_subset_fixedPoints (A : Set α) (hA : A ⊆ fixedPoints f) : sSup A ≤ f (sSup A) :=
   sSup_le fun x hx => hA hx ▸ (f.mono <| le_sSup hx)
 #align order_hom.le_map_Sup_subset_fixed_points OrderHom.le_map_sSup_subset_fixedPoints
 
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-Case conversion may be inaccurate. Consider using '#align order_hom.map_Inf_subset_fixed_points_le OrderHom.map_sInf_subset_fixedPoints_leₓ'. -/
 theorem map_sInf_subset_fixedPoints_le (A : Set α) (hA : A ⊆ fixedPoints f) : f (sInf A) ≤ sInf A :=
   le_sInf fun x hx => hA hx ▸ (f.mono <| sInf_le hx)
 #align order_hom.map_Inf_subset_fixed_points_le OrderHom.map_sInf_subset_fixedPoints_le

c3291da4

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -160,8 +160,7 @@ theorem lfp_induction {p : α → Prop} (step : ∀ a, p a → a ≤ lfp f → p
   by
   set s := { a | a ≤ lfp f ∧ p a }
   specialize hSup s fun a => And.right
-  suffices : Sup s = lfp f
-  exact this ▸ hSup
+  suffices : Sup s = lfp f; exact this ▸ hSup
   have h : Sup s ≤ lfp f := sSup_le fun b => And.left
   have hmem : f (Sup s) ∈ s := ⟨f.map_le_lfp h, step _ hSup h⟩
   exact h.antisymm (f.lfp_le <| le_sSup hmem)

c3291da4

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -153,10 +153,7 @@ theorem isLeast_lfp_le : IsLeast (fixedPoints f) (lfp f) :=
 #align order_hom.is_least_lfp OrderHom.isLeast_lfp_le
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align order_hom.lfp_induction OrderHom.lfp_inductionₓ'. -/
 theorem lfp_induction {p : α → Prop} (step : ∀ a, p a → a ≤ lfp f → p (f a))
     (hSup : ∀ s, (∀ a ∈ s, p a) → p (sSup s)) : p (lfp f) :=
@@ -240,10 +237,7 @@ theorem isGreatest_gfp : IsGreatest (fixedPoints f) (gfp f) :=
 -/
 
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 Case conversion may be inaccurate. Consider using '#align order_hom.gfp_induction OrderHom.gfp_inductionₓ'. -/
 theorem gfp_induction {p : α → Prop} (step : ∀ a, p a → gfp f ≤ a → p (f a))
     (hInf : ∀ s, (∀ a ∈ s, p a) → p (sInf s)) : p (gfp f) :=
@@ -360,10 +354,7 @@ theorem le_nextFixed {x : α} (hx : x ≤ f x) : x ≤ f.nextFixed x hx :=
 #align order_hom.le_next_fixed OrderHom.le_nextFixed
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align order_hom.next_fixed_le OrderHom.nextFixed_leₓ'. -/
 theorem nextFixed_le {x : α} (hx : x ≤ f x) {y : fixedPoints f} (h : x ≤ y) :
     f.nextFixed x hx ≤ y :=
@@ -371,10 +362,7 @@ theorem nextFixed_le {x : α} (hx : x ≤ f x) {y : fixedPoints f} (h : x ≤ y)
 #align order_hom.next_fixed_le OrderHom.nextFixed_le
 
 /- warning: order_hom.next_fixed_le_iff -> OrderHom.nextFixed_le_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align order_hom.next_fixed_le_iff OrderHom.nextFixed_le_iffₓ'. -/
 @[simp]
 theorem nextFixed_le_iff {x : α} (hx : x ≤ f x) {y : fixedPoints f} :
@@ -383,10 +371,7 @@ theorem nextFixed_le_iff {x : α} (hx : x ≤ f x) {y : fixedPoints f} :
 #align order_hom.next_fixed_le_iff OrderHom.nextFixed_le_iff
 
 /- warning: order_hom.le_prev_fixed_iff -> OrderHom.le_prevFixed_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align order_hom.le_prev_fixed_iff OrderHom.le_prevFixed_iffₓ'. -/
 @[simp]
 theorem le_prevFixed_iff {x : α} (hx : f x ≤ x) {y : fixedPoints f} :
@@ -395,10 +380,7 @@ theorem le_prevFixed_iff {x : α} (hx : f x ≤ x) {y : fixedPoints f} :
 #align order_hom.le_prev_fixed_iff OrderHom.le_prevFixed_iff
 
 /- warning: order_hom.le_prev_fixed -> OrderHom.le_prevFixed is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align order_hom.le_prev_fixed OrderHom.le_prevFixedₓ'. -/
 theorem le_prevFixed {x : α} (hx : f x ≤ x) {y : fixedPoints f} (h : ↑y ≤ x) :
     y ≤ f.prevFixed x hx :=
@@ -406,10 +388,7 @@ theorem le_prevFixed {x : α} (hx : f x ≤ x) {y : fixedPoints f} (h : ↑y ≤
 #align order_hom.le_prev_fixed OrderHom.le_prevFixed
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align order_hom.le_map_sup_fixed_points OrderHom.le_map_sup_fixedPointsₓ'. -/
 theorem le_map_sup_fixedPoints (x y : fixedPoints f) : (x ⊔ y : α) ≤ f (x ⊔ y) :=
   calc
@@ -419,10 +398,7 @@ theorem le_map_sup_fixedPoints (x y : fixedPoints f) : (x ⊔ y : α) ≤ f (x 
 #align order_hom.le_map_sup_fixed_points OrderHom.le_map_sup_fixedPoints
 
 /- warning: order_hom.map_inf_fixed_points_le -> OrderHom.map_inf_fixedPoints_le is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (x : Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) (y : Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{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 (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) x) (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) y))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{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 (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) x) (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align order_hom.map_inf_fixed_points_le OrderHom.map_inf_fixedPoints_leₓ'. -/
 theorem map_inf_fixedPoints_le (x y : fixedPoints f) : f (x ⊓ y) ≤ x ⊓ y :=
   f.dual.le_map_sup_fixedPoints x y

c3291da4

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -64,29 +64,45 @@ def gfp : (α →o α) →o α where
 #align order_hom.gfp OrderHom.gfp
 -/
 
-#print OrderHom.lfp_le /-
+/- warning: order_hom.lfp_le -> OrderHom.lfp_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f a) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.lfp.{u1} α _inst_1) f) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.lfp.{u1} α _inst_1) f) a)
+Case conversion may be inaccurate. Consider using '#align order_hom.lfp_le OrderHom.lfp_leₓ'. -/
 theorem lfp_le {a : α} (h : f a ≤ a) : lfp f ≤ a :=
   sInf_le h
 #align order_hom.lfp_le OrderHom.lfp_le
--/
 
-#print OrderHom.lfp_le_fixed /-
+/- warning: order_hom.lfp_le_fixed -> OrderHom.lfp_le_fixed is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (Eq.{succ u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f a) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.lfp.{u1} α _inst_1) f) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (Eq.{succ u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.lfp.{u1} α _inst_1) f) a)
+Case conversion may be inaccurate. Consider using '#align order_hom.lfp_le_fixed OrderHom.lfp_le_fixedₓ'. -/
 theorem lfp_le_fixed {a : α} (h : f a = a) : lfp f ≤ a :=
   f.lfp_le h.le
 #align order_hom.lfp_le_fixed OrderHom.lfp_le_fixed
--/
 
-#print OrderHom.le_lfp /-
+/- warning: order_hom.le_lfp -> OrderHom.le_lfp is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (forall (b : α), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f b) b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.lfp.{u1} α _inst_1) f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (forall (b : α), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f b) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.lfp.{u1} α _inst_1) f))
+Case conversion may be inaccurate. Consider using '#align order_hom.le_lfp OrderHom.le_lfpₓ'. -/
 theorem le_lfp {a : α} (h : ∀ b, f b ≤ b → a ≤ b) : a ≤ lfp f :=
   le_sInf h
 #align order_hom.le_lfp OrderHom.le_lfp
--/
 
-#print OrderHom.map_le_lfp /-
+/- warning: order_hom.map_le_lfp -> OrderHom.map_le_lfp is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.lfp.{u1} α _inst_1) f)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f a) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.lfp.{u1} α _inst_1) f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.lfp.{u1} α _inst_1) f)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.lfp.{u1} α _inst_1) f))
+Case conversion may be inaccurate. Consider using '#align order_hom.map_le_lfp OrderHom.map_le_lfpₓ'. -/
 theorem map_le_lfp {a : α} (ha : a ≤ f.lfp) : f a ≤ f.lfp :=
   f.le_lfp fun b hb => (f.mono <| le_sInf_iff.1 ha _ hb).trans hb
 #align order_hom.map_le_lfp OrderHom.map_le_lfp
--/
 
 #print OrderHom.map_lfp /-
 @[simp]
@@ -102,20 +118,28 @@ theorem isFixedPt_lfp : IsFixedPt f f.lfp :=
 #align order_hom.is_fixed_pt_lfp OrderHom.isFixedPt_lfp
 -/
 
-#print OrderHom.lfp_le_map /-
+/- warning: order_hom.lfp_le_map -> OrderHom.lfp_le_map is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.lfp.{u1} α _inst_1) f) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.lfp.{u1} α _inst_1) f) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.lfp.{u1} α _inst_1) f) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.lfp.{u1} α _inst_1) f) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a))
+Case conversion may be inaccurate. Consider using '#align order_hom.lfp_le_map OrderHom.lfp_le_mapₓ'. -/
 theorem lfp_le_map {a : α} (ha : lfp f ≤ a) : lfp f ≤ f a :=
   calc
     lfp f = f (lfp f) := f.map_lfp.symm
     _ ≤ f a := f.mono ha
     
 #align order_hom.lfp_le_map OrderHom.lfp_le_map
--/
 
-#print OrderHom.isLeast_lfp_le /-
+/- warning: order_hom.is_least_lfp_le -> OrderHom.isLeast_lfp_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))), IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (setOf.{u1} α (fun (a : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f a) a)) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.lfp.{u1} α _inst_1) f)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))), IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (setOf.{u1} α (fun (a : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a) a)) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.lfp.{u1} α _inst_1) f)
+Case conversion may be inaccurate. Consider using '#align order_hom.is_least_lfp_le OrderHom.isLeast_lfp_leₓ'. -/
 theorem isLeast_lfp_le : IsLeast { a | f a ≤ a } (lfp f) :=
   ⟨f.map_lfp.le, fun a => f.lfp_le⟩
 #align order_hom.is_least_lfp_le OrderHom.isLeast_lfp_le
--/
 
 /- warning: order_hom.is_least_lfp clashes with order_hom.is_least_lfp_le -> OrderHom.isLeast_lfp_le
 warning: order_hom.is_least_lfp -> OrderHom.isLeast_lfp_le is a dubious translation:
@@ -130,7 +154,7 @@ theorem isLeast_lfp_le : IsLeast (fixedPoints f) (lfp f) :=
 
 /- warning: order_hom.lfp_induction -> OrderHom.lfp_induction is a dubious translation:
 lean 3 declaration is
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(CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.lfp.{u1} α _inst_1) f)) -> (p (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f a))) -> (forall (s : Set.{u1} α), (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (p a)) -> (p (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))) -> (p (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.lfp.{u1} α _inst_1) f))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {p : α -> Prop}, (forall (a : α), (p a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.lfp.{u1} α _inst_1) f)) -> (p (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f a))) -> (forall (s : Set.{u1} α), (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (p a)) -> (p (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))) -> (p (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.lfp.{u1} α _inst_1) f))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {p : α -> Prop}, (forall (a : α), (p a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.lfp.{u1} α _inst_1) f)) -> (p (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a))) -> (forall (s : Set.{u1} α), (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (p a)) -> (p (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))) -> (p (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.lfp.{u1} α _inst_1) f))
 Case conversion may be inaccurate. Consider using '#align order_hom.lfp_induction OrderHom.lfp_inductionₓ'. -/
@@ -146,17 +170,25 @@ theorem lfp_induction {p : α → Prop} (step : ∀ a, p a → a ≤ lfp f → p
   exact h.antisymm (f.lfp_le <| le_sSup hmem)
 #align order_hom.lfp_induction OrderHom.lfp_induction
 
-#print OrderHom.le_gfp /-
+/- warning: order_hom.le_gfp -> OrderHom.le_gfp is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f a)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.gfp.{u1} α _inst_1) f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) f))
+Case conversion may be inaccurate. Consider using '#align order_hom.le_gfp OrderHom.le_gfpₓ'. -/
 theorem le_gfp {a : α} (h : a ≤ f a) : a ≤ gfp f :=
   le_sSup h
 #align order_hom.le_gfp OrderHom.le_gfp
--/
 
-#print OrderHom.gfp_le /-
+/- warning: order_hom.gfp_le -> OrderHom.gfp_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (forall (b : α), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f b)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b a)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.gfp.{u1} α _inst_1) f) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (forall (b : α), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) f) a)
+Case conversion may be inaccurate. Consider using '#align order_hom.gfp_le OrderHom.gfp_leₓ'. -/
 theorem gfp_le {a : α} (h : ∀ b, b ≤ f b → b ≤ a) : gfp f ≤ a :=
   sSup_le h
 #align order_hom.gfp_le OrderHom.gfp_le
--/
 
 #print OrderHom.isFixedPt_gfp /-
 theorem isFixedPt_gfp : IsFixedPt f (gfp f) :=
@@ -171,23 +203,35 @@ theorem map_gfp : f (gfp f) = gfp f :=
 #align order_hom.map_gfp OrderHom.map_gfp
 -/
 
-#print OrderHom.map_le_gfp /-
+/- warning: order_hom.map_le_gfp -> OrderHom.map_le_gfp is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α 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(PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f a) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.gfp.{u1} α _inst_1) f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) f)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) f))
+Case conversion may be inaccurate. Consider using '#align order_hom.map_le_gfp OrderHom.map_le_gfpₓ'. -/
 theorem map_le_gfp {a : α} (ha : a ≤ gfp f) : f a ≤ gfp f :=
   f.dual.lfp_le_map ha
 #align order_hom.map_le_gfp OrderHom.map_le_gfp
--/
 
-#print OrderHom.gfp_le_map /-
+/- warning: order_hom.gfp_le_map -> OrderHom.gfp_le_map is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.gfp.{u1} α _inst_1) f) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.gfp.{u1} α _inst_1) f) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {a : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) f) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) f) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a))
+Case conversion may be inaccurate. Consider using '#align order_hom.gfp_le_map OrderHom.gfp_le_mapₓ'. -/
 theorem gfp_le_map {a : α} (ha : gfp f ≤ a) : gfp f ≤ f a :=
   f.dual.map_le_lfp ha
 #align order_hom.gfp_le_map OrderHom.gfp_le_map
--/
 
-#print OrderHom.isGreatest_gfp_le /-
+/- warning: order_hom.is_greatest_gfp_le -> OrderHom.isGreatest_gfp_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))), IsGreatest.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (setOf.{u1} α (fun (a : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f a))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.gfp.{u1} α _inst_1) f)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))), IsGreatest.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (setOf.{u1} α (fun (a : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a))) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) f)
+Case conversion may be inaccurate. Consider using '#align order_hom.is_greatest_gfp_le OrderHom.isGreatest_gfp_leₓ'. -/
 theorem isGreatest_gfp_le : IsGreatest { a | a ≤ f a } (gfp f) :=
   f.dual.isLeast_lfp_le
 #align order_hom.is_greatest_gfp_le OrderHom.isGreatest_gfp_le
--/
 
 #print OrderHom.isGreatest_gfp /-
 theorem isGreatest_gfp : IsGreatest (fixedPoints f) (gfp f) :=
@@ -197,7 +241,7 @@ theorem isGreatest_gfp : IsGreatest (fixedPoints f) (gfp f) :=
 
 /- warning: order_hom.gfp_induction -> OrderHom.gfp_induction is a dubious translation:
 lean 3 declaration is
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(OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f a))) -> (forall (s : Set.{u1} α), (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (p a)) -> (p (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s))) -> (p (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.gfp.{u1} α _inst_1) f))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {p : α -> Prop}, (forall (a : α), (p a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) f) a) -> (p (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a))) -> (forall (s : Set.{u1} α), (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (p a)) -> (p (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s))) -> (p (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) f))
 Case conversion may be inaccurate. Consider using '#align order_hom.gfp_induction OrderHom.gfp_inductionₓ'. -/
@@ -256,7 +300,7 @@ variable [CompleteLattice α] (f : α →o α)
 
 /- warning: order_hom.gfp_const_inf_le -> OrderHom.gfp_const_inf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (x : α), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.gfp.{u1} α _inst_1) (Inf.inf.{u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.hasInf.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (fun (_x : OrderHom.{u1, u1} α (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) => α -> (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (OrderHom.hasCoeToFun.{u1, u1} α (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (OrderHom.const.{u1, u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) x) f)) x
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (x : α), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.gfp.{u1} α _inst_1) (Inf.inf.{u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.hasInf.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (fun (_x : OrderHom.{u1, u1} α (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) => α -> (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (OrderHom.hasCoeToFun.{u1, u1} α (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (OrderHom.const.{u1, u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) x) f)) x
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (x : α), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) (Inf.inf.{u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.instInfOrderHomToPreorderToPartialOrder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (OrderHom.toFun.{u1, u1} α (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.const.{u1, u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) x) f)) x
 Case conversion may be inaccurate. Consider using '#align order_hom.gfp_const_inf_le OrderHom.gfp_const_inf_leₓ'. -/
@@ -264,7 +308,12 @@ theorem gfp_const_inf_le (x : α) : gfp (const α x ⊓ f) ≤ x :=
   gfp_le _ fun b hb => hb.trans inf_le_left
 #align order_hom.gfp_const_inf_le OrderHom.gfp_const_inf_le
 
-#print OrderHom.prevFixed /-
+/- warning: order_hom.prev_fixed -> OrderHom.prevFixed is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (x : α), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f x) x) -> (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (x : α), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f x) x) -> (Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f)))
+Case conversion may be inaccurate. Consider using '#align order_hom.prev_fixed OrderHom.prevFixedₓ'. -/
 /-- Previous fixed point of a monotone map. If `f` is a monotone self-map of a complete lattice and
 `x` is a point such that `f x ≤ x`, then `f.prev_fixed x hx` is the greatest fixed point of `f`
 that is less than or equal to `x`. -/
@@ -276,62 +325,89 @@ def prevFixed (x : α) (hx : f x ≤ x) : fixedPoints f :=
       _ = gfp (const α x ⊓ f) := (const α x ⊓ f).map_gfp
       ⟩
 #align order_hom.prev_fixed OrderHom.prevFixed
--/
 
-#print OrderHom.nextFixed /-
+/- warning: order_hom.next_fixed -> OrderHom.nextFixed is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (x : α), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) x (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f x)) -> (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (x : α), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) x (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f x)) -> (Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f)))
+Case conversion may be inaccurate. Consider using '#align order_hom.next_fixed OrderHom.nextFixedₓ'. -/
 /-- Next fixed point of a monotone map. If `f` is a monotone self-map of a complete lattice and
 `x` is a point such that `x ≤ f x`, then `f.next_fixed x hx` is the least fixed point of `f`
 that is greater than or equal to `x`. -/
 def nextFixed (x : α) (hx : x ≤ f x) : fixedPoints f :=
   { f.dual.prevFixed x hx with val := (const α x ⊔ f).lfp }
 #align order_hom.next_fixed OrderHom.nextFixed
--/
 
-#print OrderHom.prevFixed_le /-
+/- warning: order_hom.prev_fixed_le -> OrderHom.prevFixed_le is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {x : α} (hx : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f x) x), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) (OrderHom.prevFixed.{u1} α _inst_1 f x hx)) x
+Case conversion may be inaccurate. Consider using '#align order_hom.prev_fixed_le OrderHom.prevFixed_leₓ'. -/
 theorem prevFixed_le {x : α} (hx : f x ≤ x) : ↑(f.prevFixed x hx) ≤ x :=
   f.gfp_const_inf_le x
 #align order_hom.prev_fixed_le OrderHom.prevFixed_le
--/
 
-#print OrderHom.le_nextFixed /-
+/- warning: order_hom.le_next_fixed -> OrderHom.le_nextFixed is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align order_hom.le_next_fixed OrderHom.le_nextFixedₓ'. -/
 theorem le_nextFixed {x : α} (hx : x ≤ f x) : x ≤ f.nextFixed x hx :=
   f.dual.prevFixed_le hx
 #align order_hom.le_next_fixed OrderHom.le_nextFixed
--/
 
-#print OrderHom.nextFixed_le /-
+/- warning: order_hom.next_fixed_le -> OrderHom.nextFixed_le is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {x : α} (hx : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) x (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f x)) {y : Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) x (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) y)) -> (LE.le.{u1} (Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) (Subtype.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f)))) (OrderHom.nextFixed.{u1} α _inst_1 f x hx) y)
+Case conversion may be inaccurate. Consider using '#align order_hom.next_fixed_le OrderHom.nextFixed_leₓ'. -/
 theorem nextFixed_le {x : α} (hx : x ≤ f x) {y : fixedPoints f} (h : x ≤ y) :
     f.nextFixed x hx ≤ y :=
   Subtype.coe_le_coe.1 <| lfp_le _ <| sup_le h y.2.le
 #align order_hom.next_fixed_le OrderHom.nextFixed_le
--/
 
-#print OrderHom.nextFixed_le_iff /-
+/- warning: order_hom.next_fixed_le_iff -> OrderHom.nextFixed_le_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {x : α} (hx : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) x (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f x)) {y : Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))}, Iff (LE.le.{u1} (Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) (Subtype.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f)))) (OrderHom.nextFixed.{u1} α _inst_1 f x hx) y) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) x (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) y))
+Case conversion may be inaccurate. Consider using '#align order_hom.next_fixed_le_iff OrderHom.nextFixed_le_iffₓ'. -/
 @[simp]
 theorem nextFixed_le_iff {x : α} (hx : x ≤ f x) {y : fixedPoints f} :
     f.nextFixed x hx ≤ y ↔ x ≤ y :=
   ⟨fun h => (f.le_nextFixed hx).trans h, f.nextFixed_le hx⟩
 #align order_hom.next_fixed_le_iff OrderHom.nextFixed_le_iff
--/
 
-#print OrderHom.le_prevFixed_iff /-
+/- warning: order_hom.le_prev_fixed_iff -> OrderHom.le_prevFixed_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {x : α} (hx : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f x) x) {y : Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))}, Iff (LE.le.{u1} (Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) (Subtype.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f)))) y (OrderHom.prevFixed.{u1} α _inst_1 f x hx)) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) y) x)
+Case conversion may be inaccurate. Consider using '#align order_hom.le_prev_fixed_iff OrderHom.le_prevFixed_iffₓ'. -/
 @[simp]
 theorem le_prevFixed_iff {x : α} (hx : f x ≤ x) {y : fixedPoints f} :
     y ≤ f.prevFixed x hx ↔ ↑y ≤ x :=
   f.dual.nextFixed_le_iff hx
 #align order_hom.le_prev_fixed_iff OrderHom.le_prevFixed_iff
--/
 
-#print OrderHom.le_prevFixed /-
+/- warning: order_hom.le_prev_fixed -> OrderHom.le_prevFixed is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align order_hom.le_prev_fixed OrderHom.le_prevFixedₓ'. -/
 theorem le_prevFixed {x : α} (hx : f x ≤ x) {y : fixedPoints f} (h : ↑y ≤ x) :
     y ≤ f.prevFixed x hx :=
   (f.le_prevFixed_iff hx).2 h
 #align order_hom.le_prev_fixed OrderHom.le_prevFixed
--/
 
 /- warning: order_hom.le_map_sup_fixed_points -> OrderHom.le_map_sup_fixedPoints is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (x : Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) (y : Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{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 (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) x) (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) y)) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{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 (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) x) (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) y)))
 Case conversion may be inaccurate. Consider using '#align order_hom.le_map_sup_fixed_points OrderHom.le_map_sup_fixedPointsₓ'. -/
@@ -344,7 +420,7 @@ theorem le_map_sup_fixedPoints (x y : fixedPoints f) : (x ⊔ y : α) ≤ f (x 
 
 /- warning: order_hom.map_inf_fixed_points_le -> OrderHom.map_inf_fixedPoints_le is a dubious translation:
 lean 3 declaration is
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(CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))))))) y))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (x : Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) (y : Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{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 (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) x) (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) y))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{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 (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) x) (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) y))
 Case conversion may be inaccurate. Consider using '#align order_hom.map_inf_fixed_points_le OrderHom.map_inf_fixedPoints_leₓ'. -/
@@ -354,7 +430,7 @@ theorem map_inf_fixedPoints_le (x y : fixedPoints f) : f (x ⊓ y) ≤ x ⊓ y :
 
 /- warning: order_hom.le_map_Sup_subset_fixed_points -> OrderHom.le_map_sSup_subset_fixedPoints is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (A : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) A (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) A) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) A)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (A : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) A (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) A) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) A)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (A : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) A (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) A) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) A)))
 Case conversion may be inaccurate. Consider using '#align order_hom.le_map_Sup_subset_fixed_points OrderHom.le_map_sSup_subset_fixedPointsₓ'. -/
@@ -364,7 +440,7 @@ theorem le_map_sSup_subset_fixedPoints (A : Set α) (hA : A ⊆ fixedPoints f) :
 
 /- warning: order_hom.map_Inf_subset_fixed_points_le -> OrderHom.map_sInf_subset_fixedPoints_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (A : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) A (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) A)) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) A))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (A : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) A (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) A)) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) A))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (A : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) A (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) A)) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) A))
 Case conversion may be inaccurate. Consider using '#align order_hom.map_Inf_subset_fixed_points_le OrderHom.map_sInf_subset_fixedPoints_leₓ'. -/

c3291da4

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -51,22 +51,22 @@ variable [CompleteLattice α] (f : α →o α)
 #print OrderHom.lfp /-
 /-- Least fixed point of a monotone function -/
 def lfp : (α →o α) →o α where
-  toFun f := infₛ { a | f a ≤ a }
-  monotone' f g hle := infₛ_le_infₛ fun a ha => (hle a).trans ha
+  toFun f := sInf { a | f a ≤ a }
+  monotone' f g hle := sInf_le_sInf fun a ha => (hle a).trans ha
 #align order_hom.lfp OrderHom.lfp
 -/
 
 #print OrderHom.gfp /-
 /-- Greatest fixed point of a monotone function -/
 def gfp : (α →o α) →o α where
-  toFun f := supₛ { a | a ≤ f a }
-  monotone' f g hle := supₛ_le_supₛ fun a ha => le_trans ha (hle a)
+  toFun f := sSup { a | a ≤ f a }
+  monotone' f g hle := sSup_le_sSup fun a ha => le_trans ha (hle a)
 #align order_hom.gfp OrderHom.gfp
 -/
 
 #print OrderHom.lfp_le /-
 theorem lfp_le {a : α} (h : f a ≤ a) : lfp f ≤ a :=
-  infₛ_le h
+  sInf_le h
 #align order_hom.lfp_le OrderHom.lfp_le
 -/
 
@@ -78,13 +78,13 @@ theorem lfp_le_fixed {a : α} (h : f a = a) : lfp f ≤ a :=
 
 #print OrderHom.le_lfp /-
 theorem le_lfp {a : α} (h : ∀ b, f b ≤ b → a ≤ b) : a ≤ lfp f :=
-  le_infₛ h
+  le_sInf h
 #align order_hom.le_lfp OrderHom.le_lfp
 -/
 
 #print OrderHom.map_le_lfp /-
 theorem map_le_lfp {a : α} (ha : a ≤ f.lfp) : f a ≤ f.lfp :=
-  f.le_lfp fun b hb => (f.mono <| le_infₛ_iff.1 ha _ hb).trans hb
+  f.le_lfp fun b hb => (f.mono <| le_sInf_iff.1 ha _ hb).trans hb
 #align order_hom.map_le_lfp OrderHom.map_le_lfp
 -/
 
@@ -130,31 +130,31 @@ theorem isLeast_lfp_le : IsLeast (fixedPoints f) (lfp f) :=
 
 /- warning: order_hom.lfp_induction -> OrderHom.lfp_induction is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {p : α -> Prop}, (forall (a : α), (p a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.lfp.{u1} α _inst_1) f)) -> (p (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a))) -> (forall (s : Set.{u1} α), (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (p a)) -> (p (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))) -> (p (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.lfp.{u1} α _inst_1) f))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {p : α -> Prop}, (forall (a : α), (p a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.lfp.{u1} α _inst_1) f)) -> (p (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a))) -> (forall (s : Set.{u1} α), (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (p a)) -> (p (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))) -> (p (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.lfp.{u1} α _inst_1) f))
 Case conversion may be inaccurate. Consider using '#align order_hom.lfp_induction OrderHom.lfp_inductionₓ'. -/
 theorem lfp_induction {p : α → Prop} (step : ∀ a, p a → a ≤ lfp f → p (f a))
-    (hSup : ∀ s, (∀ a ∈ s, p a) → p (supₛ s)) : p (lfp f) :=
+    (hSup : ∀ s, (∀ a ∈ s, p a) → p (sSup s)) : p (lfp f) :=
   by
   set s := { a | a ≤ lfp f ∧ p a }
   specialize hSup s fun a => And.right
   suffices : Sup s = lfp f
   exact this ▸ hSup
-  have h : Sup s ≤ lfp f := supₛ_le fun b => And.left
+  have h : Sup s ≤ lfp f := sSup_le fun b => And.left
   have hmem : f (Sup s) ∈ s := ⟨f.map_le_lfp h, step _ hSup h⟩
-  exact h.antisymm (f.lfp_le <| le_supₛ hmem)
+  exact h.antisymm (f.lfp_le <| le_sSup hmem)
 #align order_hom.lfp_induction OrderHom.lfp_induction
 
 #print OrderHom.le_gfp /-
 theorem le_gfp {a : α} (h : a ≤ f a) : a ≤ gfp f :=
-  le_supₛ h
+  le_sSup h
 #align order_hom.le_gfp OrderHom.le_gfp
 -/
 
 #print OrderHom.gfp_le /-
 theorem gfp_le {a : α} (h : ∀ b, b ≤ f b → b ≤ a) : gfp f ≤ a :=
-  supₛ_le h
+  sSup_le h
 #align order_hom.gfp_le OrderHom.gfp_le
 -/
 
@@ -197,12 +197,12 @@ theorem isGreatest_gfp : IsGreatest (fixedPoints f) (gfp f) :=
 
 /- warning: order_hom.gfp_induction -> OrderHom.gfp_induction is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {p : α -> Prop}, (forall (a : α), (p a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α 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(OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f a))) -> (forall (s : Set.{u1} α), (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (p a)) -> (p (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s))) -> (p (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.gfp.{u1} α _inst_1) f))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {p : α -> Prop}, (forall (a : α), (p a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) f) a) -> (p (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a))) -> (forall (s : Set.{u1} α), (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (p a)) -> (p (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s))) -> (p (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) f))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) {p : α -> Prop}, (forall (a : α), (p a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) f) a) -> (p (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f a))) -> (forall (s : Set.{u1} α), (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (p a)) -> (p (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s))) -> (p (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) f))
 Case conversion may be inaccurate. Consider using '#align order_hom.gfp_induction OrderHom.gfp_inductionₓ'. -/
 theorem gfp_induction {p : α → Prop} (step : ∀ a, p a → gfp f ≤ a → p (f a))
-    (hInf : ∀ s, (∀ a ∈ s, p a) → p (infₛ s)) : p (gfp f) :=
+    (hInf : ∀ s, (∀ a ∈ s, p a) → p (sInf s)) : p (gfp f) :=
   f.dual.lfp_induction step hInf
 #align order_hom.gfp_induction OrderHom.gfp_induction
 
@@ -352,25 +352,25 @@ theorem map_inf_fixedPoints_le (x y : fixedPoints f) : f (x ⊓ y) ≤ x ⊓ y :
   f.dual.le_map_sup_fixedPoints x y
 #align order_hom.map_inf_fixed_points_le OrderHom.map_inf_fixedPoints_le
 
-/- warning: order_hom.le_map_Sup_subset_fixed_points -> OrderHom.le_map_supₛ_subset_fixedPoints is a dubious translation:
+/- warning: order_hom.le_map_Sup_subset_fixed_points -> OrderHom.le_map_sSup_subset_fixedPoints is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (A : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) A (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) A) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) A)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (A : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) A (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) A) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) A)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (A : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) A (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) A) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) A)))
-Case conversion may be inaccurate. Consider using '#align order_hom.le_map_Sup_subset_fixed_points OrderHom.le_map_supₛ_subset_fixedPointsₓ'. -/
-theorem le_map_supₛ_subset_fixedPoints (A : Set α) (hA : A ⊆ fixedPoints f) : supₛ A ≤ f (supₛ A) :=
-  supₛ_le fun x hx => hA hx ▸ (f.mono <| le_supₛ hx)
-#align order_hom.le_map_Sup_subset_fixed_points OrderHom.le_map_supₛ_subset_fixedPoints
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (A : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) A (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) A) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) A)))
+Case conversion may be inaccurate. Consider using '#align order_hom.le_map_Sup_subset_fixed_points OrderHom.le_map_sSup_subset_fixedPointsₓ'. -/
+theorem le_map_sSup_subset_fixedPoints (A : Set α) (hA : A ⊆ fixedPoints f) : sSup A ≤ f (sSup A) :=
+  sSup_le fun x hx => hA hx ▸ (f.mono <| le_sSup hx)
+#align order_hom.le_map_Sup_subset_fixed_points OrderHom.le_map_sSup_subset_fixedPoints
 
-/- warning: order_hom.map_Inf_subset_fixed_points_le -> OrderHom.map_infₛ_subset_fixedPoints_le is a dubious translation:
+/- warning: order_hom.map_Inf_subset_fixed_points_le -> OrderHom.map_sInf_subset_fixedPoints_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (A : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) A (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) A)) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) A))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (A : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) A (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) A)) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) A))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (A : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) A (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) A)) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) A))
-Case conversion may be inaccurate. Consider using '#align order_hom.map_Inf_subset_fixed_points_le OrderHom.map_infₛ_subset_fixedPoints_leₓ'. -/
-theorem map_infₛ_subset_fixedPoints_le (A : Set α) (hA : A ⊆ fixedPoints f) : f (infₛ A) ≤ infₛ A :=
-  le_infₛ fun x hx => hA hx ▸ (f.mono <| infₛ_le hx)
-#align order_hom.map_Inf_subset_fixed_points_le OrderHom.map_infₛ_subset_fixedPoints_le
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (A : Set.{u1} α), (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) A (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) A)) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) A))
+Case conversion may be inaccurate. Consider using '#align order_hom.map_Inf_subset_fixed_points_le OrderHom.map_sInf_subset_fixedPoints_leₓ'. -/
+theorem map_sInf_subset_fixedPoints_le (A : Set α) (hA : A ⊆ fixedPoints f) : f (sInf A) ≤ sInf A :=
+  le_sInf fun x hx => hA hx ▸ (f.mono <| sInf_le hx)
+#align order_hom.map_Inf_subset_fixed_points_le OrderHom.map_sInf_subset_fixedPoints_le
 
 end PrevNext
 
@@ -399,23 +399,23 @@ instance : CompleteSemilatticeSup (fixedPoints f) :=
   {
     Subtype.partialOrder
       _ with
-    supₛ := fun s =>
-      f.nextFixed (supₛ (coe '' s))
-        (f.le_map_supₛ_subset_fixedPoints (coe '' s) fun z ⟨x, hx⟩ => hx.2 ▸ x.2)
+    sSup := fun s =>
+      f.nextFixed (sSup (coe '' s))
+        (f.le_map_sSup_subset_fixedPoints (coe '' s) fun z ⟨x, hx⟩ => hx.2 ▸ x.2)
     le_sup := fun s x hx =>
-      Subtype.coe_le_coe.1 <| le_trans (le_supₛ <| Set.mem_image_of_mem _ hx) (f.le_nextFixed _)
-    sup_le := fun s x hx => f.nextFixed_le _ <| supₛ_le <| Set.ball_image_iff.2 hx }
+      Subtype.coe_le_coe.1 <| le_trans (le_sSup <| Set.mem_image_of_mem _ hx) (f.le_nextFixed _)
+    sup_le := fun s x hx => f.nextFixed_le _ <| sSup_le <| Set.ball_image_iff.2 hx }
 
 instance : CompleteSemilatticeInf (fixedPoints f) :=
   {
     Subtype.partialOrder
       _ with
-    infₛ := fun s =>
-      f.prevFixed (infₛ (coe '' s))
-        (f.map_infₛ_subset_fixedPoints_le (coe '' s) fun z ⟨x, hx⟩ => hx.2 ▸ x.2)
-    le_inf := fun s x hx => f.le_prevFixed _ <| le_infₛ <| Set.ball_image_iff.2 hx
+    sInf := fun s =>
+      f.prevFixed (sInf (coe '' s))
+        (f.map_sInf_subset_fixedPoints_le (coe '' s) fun z ⟨x, hx⟩ => hx.2 ▸ x.2)
+    le_inf := fun s x hx => f.le_prevFixed _ <| le_sInf <| Set.ball_image_iff.2 hx
     inf_le := fun s x hx =>
-      Subtype.coe_le_coe.1 <| le_trans (f.prevFixed_le _) (infₛ_le <| Set.mem_image_of_mem _ hx) }
+      Subtype.coe_le_coe.1 <| le_trans (f.prevFixed_le _) (sInf_le <| Set.mem_image_of_mem _ hx) }
 
 /-- **Knaster-Tarski Theorem**: The fixed points of `f` form a complete lattice. -/
 instance : CompleteLattice (fixedPoints f) :=

c3291da4

bump to nightly-2023-02-28-04

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

2097f8af

Diff

@@ -254,11 +254,15 @@ section PrevNext
 
 variable [CompleteLattice α] (f : α →o α)
 
-#print OrderHom.gfp_const_inf_le /-
+/- warning: order_hom.gfp_const_inf_le -> OrderHom.gfp_const_inf_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (x : α), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) -> α) (OrderHom.hasCoeToFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.gfp.{u1} α _inst_1) (Inf.inf.{u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.hasInf.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (fun (_x : OrderHom.{u1, u1} α (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) => α -> (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (OrderHom.hasCoeToFun.{u1, u1} α (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.preorder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (OrderHom.const.{u1, u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) x) f)) x
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (x : α), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) α (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.gfp.{u1} α _inst_1) (Inf.inf.{u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.instInfOrderHomToPreorderToPartialOrder.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (OrderHom.toFun.{u1, u1} α (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (OrderHom.instPreorderOrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.const.{u1, u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) x) f)) x
+Case conversion may be inaccurate. Consider using '#align order_hom.gfp_const_inf_le OrderHom.gfp_const_inf_leₓ'. -/
 theorem gfp_const_inf_le (x : α) : gfp (const α x ⊓ f) ≤ x :=
   gfp_le _ fun b hb => hb.trans inf_le_left
 #align order_hom.gfp_const_inf_le OrderHom.gfp_const_inf_le
--/
 
 #print OrderHom.prevFixed /-
 /-- Previous fixed point of a monotone map. If `f` is a monotone self-map of a complete lattice and
@@ -325,20 +329,28 @@ theorem le_prevFixed {x : α} (hx : f x ≤ x) {y : fixedPoints f} (h : ↑y ≤
 #align order_hom.le_prev_fixed OrderHom.le_prevFixed
 -/
 
-#print OrderHom.le_map_sup_fixedPoints /-
+/- warning: order_hom.le_map_sup_fixed_points -> OrderHom.le_map_sup_fixedPoints is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align order_hom.le_map_sup_fixed_points OrderHom.le_map_sup_fixedPointsₓ'. -/
 theorem le_map_sup_fixedPoints (x y : fixedPoints f) : (x ⊔ y : α) ≤ f (x ⊔ y) :=
   calc
     (x ⊔ y : α) = f x ⊔ f y := congr_arg₂ (· ⊔ ·) x.2.symm y.2.symm
     _ ≤ f (x ⊔ y) := f.mono.le_map_sup x y
     
 #align order_hom.le_map_sup_fixed_points OrderHom.le_map_sup_fixedPoints
--/
 
-#print OrderHom.map_inf_fixedPoints_le /-
+/- warning: order_hom.map_inf_fixed_points_le -> OrderHom.map_inf_fixedPoints_le is a dubious translation:
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(CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))))))) x) ((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) (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Function.fixedPoints.{u1} α (coeFn.{succ u1, succ u1} (OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (fun (_x : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) => α -> α) (OrderHom.hasCoeToFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) f))))))) y))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : OrderHom.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (x : Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) (y : Set.Elem.{u1} α (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{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 (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) x) (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) y))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{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 (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) x) (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Function.fixedPoints.{u1} α (OrderHom.toFun.{u1, u1} α α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f))) y))
+Case conversion may be inaccurate. Consider using '#align order_hom.map_inf_fixed_points_le OrderHom.map_inf_fixedPoints_leₓ'. -/
 theorem map_inf_fixedPoints_le (x y : fixedPoints f) : f (x ⊓ y) ≤ x ⊓ y :=
   f.dual.le_map_sup_fixedPoints x y
 #align order_hom.map_inf_fixed_points_le OrderHom.map_inf_fixedPoints_le
--/
 
 /- warning: order_hom.le_map_Sup_subset_fixed_points -> OrderHom.le_map_supₛ_subset_fixedPoints is a dubious translation:
 lean 3 declaration is

c3291da4

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

ba2245ed

chore(Order): add missing inst prefix to instance names (#11238)

This is not exhaustive; it largely does not rename instances that relate to algebra, and only focuses on the "core" order files.

4d23d2cb

Diff

@@ -279,7 +279,7 @@ instance : SemilatticeSup (fixedPoints f) :=
 /- porting note: removed `Subtype.partialOrder _` from mathlib3port version,
   threw `typeclass instance` error and was seemingly unnecessary?-/
 instance : SemilatticeInf (fixedPoints f) :=
-  { OrderDual.semilatticeInf (fixedPoints (OrderHom.dual f)) with
+  { OrderDual.instSemilatticeInf (fixedPoints (OrderHom.dual f)) with
     inf := fun x y => f.prevFixed (x ⊓ y) (f.map_inf_fixedPoints_le x y) }
 
 -- Porting note: `coe` replaced with `Subtype.val`

ba2245ed

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

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

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

c697e040

Diff

@@ -291,14 +291,14 @@ instance : CompleteSemilatticeSup (fixedPoints f) :=
           fun _ ⟨x, hx⟩ => hx.2 ▸ x.2)
     le_sSup := fun _ _ hx =>
       Subtype.coe_le_coe.1 <| le_trans (le_sSup <| Set.mem_image_of_mem _ hx) (f.le_nextFixed _)
-    sSup_le := fun _ _ hx => f.nextFixed_le _ <| sSup_le <| Set.ball_image_iff.2 hx }
+    sSup_le := fun _ _ hx => f.nextFixed_le _ <| sSup_le <| Set.forall_mem_image.2 hx }
 
 instance : CompleteSemilatticeInf (fixedPoints f) :=
   { Subtype.partialOrder _ with
     sInf := fun s =>
       f.prevFixed (sInf (Subtype.val '' s))
         (f.map_sInf_subset_fixedPoints_le (Subtype.val '' s) fun _ ⟨x, hx⟩ => hx.2 ▸ x.2)
-    le_sInf := fun _ _ hx => f.le_prevFixed _ <| le_sInf <| Set.ball_image_iff.2 hx
+    le_sInf := fun _ _ hx => f.le_prevFixed _ <| le_sInf <| Set.forall_mem_image.2 hx
     sInf_le := fun _ _ hx =>
       Subtype.coe_le_coe.1 <| le_trans (f.prevFixed_le _) (sInf_le <| Set.mem_image_of_mem _ hx) }

ba2245ed

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

8be0b69c

Diff

@@ -66,7 +66,7 @@ theorem le_lfp {a : α} (h : ∀ b, f b ≤ b → a ≤ b) : a ≤ lfp f :=
   le_sInf h
 #align order_hom.le_lfp OrderHom.le_lfp
 
--- porting note: for the rest of the file, replace the dot notation `_.lfp` with `lfp _`
+-- Porting note: for the rest of the file, replace the dot notation `_.lfp` with `lfp _`
 -- same for `_.gfp`, `_.dual`
 -- Probably related to https://github.com/leanprover/lean4/issues/1910
 theorem map_le_lfp {a : α} (ha : a ≤ lfp f) : f a ≤ lfp f :=
@@ -243,7 +243,7 @@ theorem le_map_sup_fixedPoints (x y : fixedPoints f) : (x ⊔ y : α) ≤ f (x 
     _ ≤ f (x ⊔ y) := f.mono.le_map_sup x y
 #align order_hom.le_map_sup_fixed_points OrderHom.le_map_sup_fixedPoints
 
--- porting note: `x ⊓ y` without the `.val`sw fails to synthesize `Inf` instance
+-- Porting note: `x ⊓ y` without the `.val`sw fails to synthesize `Inf` instance
 theorem map_inf_fixedPoints_le (x y : fixedPoints f) : f (x ⊓ y) ≤ x.val ⊓ y.val :=
   f.dual.le_map_sup_fixedPoints x y
 #align order_hom.map_inf_fixed_points_le OrderHom.map_inf_fixedPoints_le
@@ -282,7 +282,7 @@ instance : SemilatticeInf (fixedPoints f) :=
   { OrderDual.semilatticeInf (fixedPoints (OrderHom.dual f)) with
     inf := fun x y => f.prevFixed (x ⊓ y) (f.map_inf_fixedPoints_le x y) }
 
--- porting note: `coe` replaced with `Subtype.val`
+-- Porting note: `coe` replaced with `Subtype.val`
 instance : CompleteSemilatticeSup (fixedPoints f) :=
   { Subtype.partialOrder _ with
     sSup := fun s =>

ba2245ed

chore: avoid lean3 style have/suffices (#6964)

Many proofs use the "stream of consciousness" style from Lean 3, rather than have ... := or suffices ... from/by.

This PR updates a fraction of these to the preferred Lean 4 style.

I think a good goal would be to delete the "deferred" versions of have, suffices, and let at the bottom of Mathlib.Tactic.Have

(Anyone who would like to contribute more cleanup is welcome to push directly to this branch.)

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

bdc47f68

Diff

@@ -101,8 +101,7 @@ theorem lfp_induction {p : α → Prop} (step : ∀ a, p a → a ≤ lfp f → p
     (hSup : ∀ s, (∀ a ∈ s, p a) → p (sSup s)) : p (lfp f) := by
   set s := { a | a ≤ lfp f ∧ p a }
   specialize hSup s fun a => And.right
-  suffices : sSup s = lfp f
-  exact this ▸ hSup
+  suffices sSup s = lfp f from this ▸ hSup
   have h : sSup s ≤ lfp f := sSup_le fun b => And.left
   have hmem : f (sSup s) ∈ s := ⟨f.map_le_lfp h, step _ hSup h⟩
   exact h.antisymm (f.lfp_le <| le_sSup hmem)

ba2245ed

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Kenny Lau, Yury Kudryashov
-
-! This file was ported from Lean 3 source module order.fixed_points
-! leanprover-community/mathlib commit ba2245edf0c8bb155f1569fd9b9492a9b384cde6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Dynamics.FixedPoints.Basic
 import Mathlib.Order.Hom.Order
 
+#align_import order.fixed_points from "leanprover-community/mathlib"@"ba2245edf0c8bb155f1569fd9b9492a9b384cde6"
+
 /-!
 # Fixed point construction on complete lattices

ba2245ed

feat: add Mathlib.Tactic.Common, and import (#4056)

This makes a mathlib4 version of mathlib3's tactic.basic, now called Mathlib.Tactic.Common, which imports all tactics which do not have significant theory requirements, and then is imported all across the base of the hierarchy.

This ensures that all common tactics are available nearly everywhere in the library, rather than having to be imported one-by-one as you need them.

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

a4eaf1c4

Diff

@@ -10,7 +10,6 @@ Authors: Johannes Hölzl, Kenny Lau, Yury Kudryashov
 -/
 import Mathlib.Dynamics.FixedPoints.Basic
 import Mathlib.Order.Hom.Order
-import Mathlib.Tactic.Set
 
 /-!
 # Fixed point construction on complete lattices

ba2245ed

chore: Rename to sSup/iSup (#3938)

As discussed on Zulip

Renames

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

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

d1eb6264

Diff

@@ -48,18 +48,18 @@ variable [CompleteLattice α] (f : α →o α)
 
 /-- Least fixed point of a monotone function -/
 def lfp : (α →o α) →o α where
-  toFun f := infₛ { a | f a ≤ a }
-  monotone' _ _ hle := infₛ_le_infₛ fun a ha => (hle a).trans ha
+  toFun f := sInf { a | f a ≤ a }
+  monotone' _ _ hle := sInf_le_sInf fun a ha => (hle a).trans ha
 #align order_hom.lfp OrderHom.lfp
 
 /-- Greatest fixed point of a monotone function -/
 def gfp : (α →o α) →o α where
-  toFun f := supₛ { a | a ≤ f a }
-  monotone' _ _ hle := supₛ_le_supₛ fun a ha => le_trans ha (hle a)
+  toFun f := sSup { a | a ≤ f a }
+  monotone' _ _ hle := sSup_le_sSup fun a ha => le_trans ha (hle a)
 #align order_hom.gfp OrderHom.gfp
 
 theorem lfp_le {a : α} (h : f a ≤ a) : lfp f ≤ a :=
-  infₛ_le h
+  sInf_le h
 #align order_hom.lfp_le OrderHom.lfp_le
 
 theorem lfp_le_fixed {a : α} (h : f a = a) : lfp f ≤ a :=
@@ -67,14 +67,14 @@ theorem lfp_le_fixed {a : α} (h : f a = a) : lfp f ≤ a :=
 #align order_hom.lfp_le_fixed OrderHom.lfp_le_fixed
 
 theorem le_lfp {a : α} (h : ∀ b, f b ≤ b → a ≤ b) : a ≤ lfp f :=
-  le_infₛ h
+  le_sInf h
 #align order_hom.le_lfp OrderHom.le_lfp
 
 -- porting note: for the rest of the file, replace the dot notation `_.lfp` with `lfp _`
 -- same for `_.gfp`, `_.dual`
 -- Probably related to https://github.com/leanprover/lean4/issues/1910
 theorem map_le_lfp {a : α} (ha : a ≤ lfp f) : f a ≤ lfp f :=
-  f.le_lfp fun _ hb => (f.mono <| le_infₛ_iff.1 ha _ hb).trans hb
+  f.le_lfp fun _ hb => (f.mono <| le_sInf_iff.1 ha _ hb).trans hb
 #align order_hom.map_le_lfp OrderHom.map_le_lfp
 
 @[simp]
@@ -102,22 +102,22 @@ theorem isLeast_lfp : IsLeast (fixedPoints f) (lfp f) :=
 #align order_hom.is_least_lfp OrderHom.isLeast_lfp_le
 
 theorem lfp_induction {p : α → Prop} (step : ∀ a, p a → a ≤ lfp f → p (f a))
-    (hSup : ∀ s, (∀ a ∈ s, p a) → p (supₛ s)) : p (lfp f) := by
+    (hSup : ∀ s, (∀ a ∈ s, p a) → p (sSup s)) : p (lfp f) := by
   set s := { a | a ≤ lfp f ∧ p a }
   specialize hSup s fun a => And.right
-  suffices : supₛ s = lfp f
+  suffices : sSup s = lfp f
   exact this ▸ hSup
-  have h : supₛ s ≤ lfp f := supₛ_le fun b => And.left
-  have hmem : f (supₛ s) ∈ s := ⟨f.map_le_lfp h, step _ hSup h⟩
-  exact h.antisymm (f.lfp_le <| le_supₛ hmem)
+  have h : sSup s ≤ lfp f := sSup_le fun b => And.left
+  have hmem : f (sSup s) ∈ s := ⟨f.map_le_lfp h, step _ hSup h⟩
+  exact h.antisymm (f.lfp_le <| le_sSup hmem)
 #align order_hom.lfp_induction OrderHom.lfp_induction
 
 theorem le_gfp {a : α} (h : a ≤ f a) : a ≤ gfp f :=
-  le_supₛ h
+  le_sSup h
 #align order_hom.le_gfp OrderHom.le_gfp
 
 theorem gfp_le {a : α} (h : ∀ b, b ≤ f b → b ≤ a) : gfp f ≤ a :=
-  supₛ_le h
+  sSup_le h
 #align order_hom.gfp_le OrderHom.gfp_le
 
 theorem isFixedPt_gfp : IsFixedPt f (gfp f) :=
@@ -146,7 +146,7 @@ theorem isGreatest_gfp : IsGreatest (fixedPoints f) (gfp f) :=
 #align order_hom.is_greatest_gfp OrderHom.isGreatest_gfp
 
 theorem gfp_induction {p : α → Prop} (step : ∀ a, p a → gfp f ≤ a → p (f a))
-    (hInf : ∀ s, (∀ a ∈ s, p a) → p (infₛ s)) : p (gfp f) :=
+    (hInf : ∀ s, (∀ a ∈ s, p a) → p (sInf s)) : p (gfp f) :=
   f.dual.lfp_induction step hInf
 #align order_hom.gfp_induction OrderHom.gfp_induction
 
@@ -253,15 +253,15 @@ theorem map_inf_fixedPoints_le (x y : fixedPoints f) : f (x ⊓ y) ≤ x.val ⊓
   f.dual.le_map_sup_fixedPoints x y
 #align order_hom.map_inf_fixed_points_le OrderHom.map_inf_fixedPoints_le
 
-theorem le_map_supₛ_subset_fixedPoints (A : Set α) (hA : A ⊆ fixedPoints f) :
-    supₛ A ≤ f (supₛ A) :=
-  supₛ_le fun _ hx => hA hx ▸ (f.mono <| le_supₛ hx)
-#align order_hom.le_map_Sup_subset_fixed_points OrderHom.le_map_supₛ_subset_fixedPoints
+theorem le_map_sSup_subset_fixedPoints (A : Set α) (hA : A ⊆ fixedPoints f) :
+    sSup A ≤ f (sSup A) :=
+  sSup_le fun _ hx => hA hx ▸ (f.mono <| le_sSup hx)
+#align order_hom.le_map_Sup_subset_fixed_points OrderHom.le_map_sSup_subset_fixedPoints
 
-theorem map_infₛ_subset_fixedPoints_le (A : Set α) (hA : A ⊆ fixedPoints f) :
-    f (infₛ A) ≤ infₛ A :=
-  le_infₛ fun _ hx => hA hx ▸ (f.mono <| infₛ_le hx)
-#align order_hom.map_Inf_subset_fixed_points_le OrderHom.map_infₛ_subset_fixedPoints_le
+theorem map_sInf_subset_fixedPoints_le (A : Set α) (hA : A ⊆ fixedPoints f) :
+    f (sInf A) ≤ sInf A :=
+  le_sInf fun _ hx => hA hx ▸ (f.mono <| sInf_le hx)
+#align order_hom.map_Inf_subset_fixed_points_le OrderHom.map_sInf_subset_fixedPoints_le
 
 end PrevNext
 
@@ -290,22 +290,22 @@ instance : SemilatticeInf (fixedPoints f) :=
 -- porting note: `coe` replaced with `Subtype.val`
 instance : CompleteSemilatticeSup (fixedPoints f) :=
   { Subtype.partialOrder _ with
-    supₛ := fun s =>
-      f.nextFixed (supₛ (Subtype.val '' s))
-        (f.le_map_supₛ_subset_fixedPoints (Subtype.val '' s)
+    sSup := fun s =>
+      f.nextFixed (sSup (Subtype.val '' s))
+        (f.le_map_sSup_subset_fixedPoints (Subtype.val '' s)
           fun _ ⟨x, hx⟩ => hx.2 ▸ x.2)
-    le_supₛ := fun _ _ hx =>
-      Subtype.coe_le_coe.1 <| le_trans (le_supₛ <| Set.mem_image_of_mem _ hx) (f.le_nextFixed _)
-    supₛ_le := fun _ _ hx => f.nextFixed_le _ <| supₛ_le <| Set.ball_image_iff.2 hx }
+    le_sSup := fun _ _ hx =>
+      Subtype.coe_le_coe.1 <| le_trans (le_sSup <| Set.mem_image_of_mem _ hx) (f.le_nextFixed _)
+    sSup_le := fun _ _ hx => f.nextFixed_le _ <| sSup_le <| Set.ball_image_iff.2 hx }
 
 instance : CompleteSemilatticeInf (fixedPoints f) :=
   { Subtype.partialOrder _ with
-    infₛ := fun s =>
-      f.prevFixed (infₛ (Subtype.val '' s))
-        (f.map_infₛ_subset_fixedPoints_le (Subtype.val '' s) fun _ ⟨x, hx⟩ => hx.2 ▸ x.2)
-    le_infₛ := fun _ _ hx => f.le_prevFixed _ <| le_infₛ <| Set.ball_image_iff.2 hx
-    infₛ_le := fun _ _ hx =>
-      Subtype.coe_le_coe.1 <| le_trans (f.prevFixed_le _) (infₛ_le <| Set.mem_image_of_mem _ hx) }
+    sInf := fun s =>
+      f.prevFixed (sInf (Subtype.val '' s))
+        (f.map_sInf_subset_fixedPoints_le (Subtype.val '' s) fun _ ⟨x, hx⟩ => hx.2 ▸ x.2)
+    le_sInf := fun _ _ hx => f.le_prevFixed _ <| le_sInf <| Set.ball_image_iff.2 hx
+    sInf_le := fun _ _ hx =>
+      Subtype.coe_le_coe.1 <| le_trans (f.prevFixed_le _) (sInf_le <| Set.mem_image_of_mem _ hx) }
 
 /- porting note: mathlib3port version contained the instances as a list,
    giving various "expected structure" errors -/

ba2245ed

chore: fix #align lines (#3640)

This PR fixes two things:

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

2b42dc7c

Diff

@@ -91,7 +91,6 @@ theorem lfp_le_map {a : α} (ha : lfp f ≤ a) : lfp f ≤ f a :=
   calc
     lfp f = f (lfp f) := f.map_lfp.symm
     _ ≤ f a := f.mono ha
-
 #align order_hom.lfp_le_map OrderHom.lfp_le_map
 
 theorem isLeast_lfp_le : IsLeast { a | f a ≤ a } (lfp f) :=

ba2245ed

refactor: rename HasSup/HasInf to Sup/Inf (#2475)

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

294082ef

Diff

@@ -249,7 +249,7 @@ theorem le_map_sup_fixedPoints (x y : fixedPoints f) : (x ⊔ y : α) ≤ f (x 
     _ ≤ f (x ⊔ y) := f.mono.le_map_sup x y
 #align order_hom.le_map_sup_fixed_points OrderHom.le_map_sup_fixedPoints
 
--- porting note: `x ⊓ y` without the `.val`sw fails to synthesize `HasInf` instance
+-- porting note: `x ⊓ y` without the `.val`sw fails to synthesize `Inf` instance
 theorem map_inf_fixedPoints_le (x y : fixedPoints f) : f (x ⊓ y) ≤ x.val ⊓ y.val :=
   f.dual.le_map_sup_fixedPoints x y
 #align order_hom.map_inf_fixed_points_le OrderHom.map_inf_fixedPoints_le

ba2245ed

chore: tidy various files (#1247)

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>

0690e5fb

Diff

@@ -10,6 +10,7 @@ Authors: Johannes Hölzl, Kenny Lau, Yury Kudryashov
 -/
 import Mathlib.Dynamics.FixedPoints.Basic
 import Mathlib.Order.Hom.Order
+import Mathlib.Tactic.Set
 
 /-!
 # Fixed point construction on complete lattices
@@ -101,10 +102,9 @@ theorem isLeast_lfp : IsLeast (fixedPoints f) (lfp f) :=
   ⟨f.isFixedPt_lfp, fun _ => f.lfp_le_fixed⟩
 #align order_hom.is_least_lfp OrderHom.isLeast_lfp_le
 
--- porting note: replaced `set` with `let` below, unknown tactic
 theorem lfp_induction {p : α → Prop} (step : ∀ a, p a → a ≤ lfp f → p (f a))
     (hSup : ∀ s, (∀ a ∈ s, p a) → p (supₛ s)) : p (lfp f) := by
-  let s := { a | a ≤ lfp f ∧ p a }
+  set s := { a | a ≤ lfp f ∧ p a }
   specialize hSup s fun a => And.right
   suffices : supₛ s = lfp f
   exact this ▸ hSup
@@ -195,7 +195,7 @@ theorem gfp_const_inf_le (x : α) : gfp (const α x ⊓ f) ≤ x :=
 #align order_hom.gfp_const_inf_le OrderHom.gfp_const_inf_le
 
 /-- Previous fixed point of a monotone map. If `f` is a monotone self-map of a complete lattice and
-`x` is a point such that `f x ≤ x`, then `f.prev_fixed x hx` is the greatest fixed point of `f`
+`x` is a point such that `f x ≤ x`, then `f.prevFixed x hx` is the greatest fixed point of `f`
 that is less than or equal to `x`. -/
 def prevFixed (x : α) (hx : f x ≤ x) : fixedPoints f :=
   ⟨gfp (const α x ⊓ f),
@@ -207,7 +207,7 @@ def prevFixed (x : α) (hx : f x ≤ x) : fixedPoints f :=
 #align order_hom.prev_fixed OrderHom.prevFixed
 
 /-- Next fixed point of a monotone map. If `f` is a monotone self-map of a complete lattice and
-`x` is a point such that `x ≤ f x`, then `f.next_fixed x hx` is the least fixed point of `f`
+`x` is a point such that `x ≤ f x`, then `f.nextFixed x hx` is the least fixed point of `f`
 that is greater than or equal to `x`. -/
 def nextFixed (x : α) (hx : x ≤ f x) : fixedPoints f :=
   { f.dual.prevFixed x hx with val := lfp (const α x ⊔ f) }
@@ -311,12 +311,12 @@ instance : CompleteSemilatticeInf (fixedPoints f) :=
 /- porting note: mathlib3port version contained the instances as a list,
    giving various "expected structure" errors -/
 /-- **Knaster-Tarski Theorem**: The fixed points of `f` form a complete lattice. -/
-instance completeLattice: CompleteLattice (fixedPoints f) where
+instance completeLattice : CompleteLattice (fixedPoints f) where
   __ := inferInstanceAs (SemilatticeInf (fixedPoints f))
   __ := inferInstanceAs (SemilatticeSup (fixedPoints f))
   __ := inferInstanceAs (CompleteSemilatticeInf (fixedPoints f))
   __ := inferInstanceAs (CompleteSemilatticeSup (fixedPoints f))
   top := ⟨gfp f, f.isFixedPt_gfp⟩
   bot := ⟨lfp f, f.isFixedPt_lfp⟩
-  le_top := fun x => f.le_gfp x.2.ge
-  bot_le := fun x => f.lfp_le x.2.le
+  le_top x := f.le_gfp x.2.ge
+  bot_le x := f.lfp_le x.2.le

ba2245ed

feat: port Order.FixedPoints (#1174)

49c9c7c0

`order.fixed_points` ⟷ `Mathlib.Order.FixedPoints`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 3 + 146

order.fixed_points ⟷ Mathlib.Order.FixedPoints

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 3 + 146

`order.fixed_points` ⟷ `Mathlib.Order.FixedPoints`